From a9dfb6767fe59bec3ffcbff62c2637b2751c2afb Mon Sep 17 00:00:00 2001
From: fromor <francesco.romor@gmail.com>
Date: Fri, 21 Oct 2022 00:22:06 +0200
Subject: [PATCH 01/59] init hyper-reduction class

---
 src/ITHACA_HR/Make/files       |   3 +
 src/ITHACA_HR/Make/options     |  34 +++
 src/ITHACA_HR/hyperReduction.C | 531 +++++++++++++++++++++++++++++++++
 src/ITHACA_HR/hyperReduction.H | 211 +++++++++++++
 4 files changed, 779 insertions(+)
 create mode 100644 src/ITHACA_HR/Make/files
 create mode 100644 src/ITHACA_HR/Make/options
 create mode 100644 src/ITHACA_HR/hyperReduction.C
 create mode 100644 src/ITHACA_HR/hyperReduction.H

diff --git a/src/ITHACA_HR/Make/files b/src/ITHACA_HR/Make/files
new file mode 100644
index 000000000..a30075081
--- /dev/null
+++ b/src/ITHACA_HR/Make/files
@@ -0,0 +1,3 @@
+hyperReduction.C
+
+LIB = $(FOAM_USER_LIBBIN)/libITHACA_HR
diff --git a/src/ITHACA_HR/Make/options b/src/ITHACA_HR/Make/options
new file mode 100644
index 000000000..d51b789a2
--- /dev/null
+++ b/src/ITHACA_HR/Make/options
@@ -0,0 +1,34 @@
+sinclude $(GENERAL_RULES)/module-path-user
+
+/* Failsafe - user location */
+ifeq (,$(strip $(FOAM_MODULE_APPBIN)))
+    FOAM_MODULE_APPBIN = $(FOAM_USER_APPBIN)
+endif
+ifeq (,$(strip $(FOAM_MODULE_LIBBIN)))
+    FOAM_MODULE_LIBBIN = $(FOAM_USER_LIBBIN)
+endif
+
+EXE_INC = \
+    -I$(LIB_SRC)/finiteVolume/lnInclude \
+    -I$(LIB_SRC)/meshTools/lnInclude \
+    -I$(LIB_SRC)/dynamicMesh/lnInclude \
+    -I$(LIB_SRC)/dynamicFvMesh/lnInclude \
+    -I$(LIB_ITHACA_SRC)/ITHACA_DEIM/DEIM \
+    -I$(LIB_ITHACA_SRC)/thirdparty/Eigen \
+    -I$(LIB_ITHACA_SRC)/thirdparty/spectra/include \
+    -I$(LIB_ITHACA_SRC)/ITHACA_CORE/ITHACAutilities \
+    -I$(LIB_ITHACA_SRC)/ITHACA_CORE/ITHACAstream \
+    -I$(LIB_ITHACA_SRC)/ITHACA_CORE/ITHACAPOD \
+    -I$(LIB_ITHACA_SRC)/ITHACA_CORE/Foam2Eigen \
+    -I$(LIB_ITHACA_SRC)/ITHACA_CORE/EigenFunctions \
+    -I$(LIB_ITHACA_SRC)/ITHACA_CORE/Containers \
+    -Wno-comment \
+    -DOFVER=$${WM_PROJECT_VERSION%.*} \
+    -std=c++17
+
+EXE_LIBS = \
+    -lITHACA-CORE \
+    -lmeshTools \
+    -lsampling \
+    -lfileFormats \
+    -lfiniteVolume
diff --git a/src/ITHACA_HR/hyperReduction.C b/src/ITHACA_HR/hyperReduction.C
new file mode 100644
index 000000000..0805c9a5d
--- /dev/null
+++ b/src/ITHACA_HR/hyperReduction.C
@@ -0,0 +1,531 @@
+/*---------------------------------------------------------------------------*\
+     ██╗████████╗██╗  ██╗ █████╗  ██████╗ █████╗       ███████╗██╗   ██╗
+     ██║╚══██╔══╝██║  ██║██╔══██╗██╔════╝██╔══██╗      ██╔════╝██║   ██║
+     ██║   ██║   ███████║███████║██║     ███████║█████╗█████╗  ██║   ██║
+     ██║   ██║   ██╔══██║██╔══██║██║     ██╔══██║╚════╝██╔══╝  ╚██╗ ██╔╝
+     ██║   ██║   ██║  ██║██║  ██║╚██████╗██║  ██║      ██║      ╚████╔╝
+     ╚═╝   ╚═╝   ╚═╝  ╚═╝╚═╝  ╚═╝ ╚═════╝╚═╝  ╚═╝      ╚═╝       ╚═══╝
+
+ * In real Time Highly Advanced Computational Applications for Finite Volumes
+ * Copyright (C) 2017 by the ITHACA-FV authors
+-------------------------------------------------------------------------------
+
+License
+    This file is part of ITHACA-FV
+
+    ITHACA-FV is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    ITHACA-FV is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU Lesser General Public License for more details.
+
+    You should have received a copy of the GNU Lesser General Public License
+    along with ITHACA-FV. If not, see <http://www.gnu.org/licenses/>.
+
+\*---------------------------------------------------------------------------*/
+
+#include "hyperReduction.H"
+
+// Using the Eigen library, using the SVD decomposition method to solve the
+// matrix pseudo-inverse, the default error er is 0
+Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0) {
+  // perform svd decomposition
+  Eigen::JacobiSVD<Eigen::MatrixXd> svd_holder(origin, Eigen::ComputeThinU |
+                                                           Eigen::ComputeThinV);
+  // Build SVD decomposition results
+  Eigen::MatrixXd U = svd_holder.matrixU();
+  Eigen::MatrixXd V = svd_holder.matrixV();
+  Eigen::MatrixXd D = svd_holder.singularValues();
+
+  // Build the S matrix
+  Eigen::MatrixXd S(V.cols(), U.cols());
+  S.setZero();
+
+  for (unsigned int i = 0; i < D.size(); ++i) {
+
+    if (D(i, 0) > er) {
+      S(i, i) = 1 / D(i, 0);
+    } else {
+      S(i, i) = 0;
+    }
+  }
+
+  std::cout << "Condition number of inverse: " <<  D(D.size()-1, 0)/D(0, 0) << std::endl;
+  // pinv_matrix = V * S * U^T
+  return V * S * U.transpose();
+}
+
+// Template function constructor
+template <typename... SnapshotsLists>
+HyperReduction<SnapshotsLists...>::HyperReduction(HyperReductionMethod hrMethod,
+                                                  label maxModes,
+                                                  label maxNodes,
+                                                  Eigen::VectorXi initialSeeds,
+                                                  word functionName,
+                                                  SnapshotsLists &&...snapshotsLists)
+    :  methodName{methodNames[int(hrMethod)]},
+      vectorial_dim{compute_vectorial_dim(snapshotsLists...)},
+      maxModes{maxModes},
+      maxNodes{maxNodes},
+      initialSeeds{initialSeeds},
+      functionName{functionName},
+      snapshotsTuple{std::forward_as_tuple(snapshotsLists...)}
+{
+    // check snapshotsLists is not empty
+    // check that the first snapshotsList is not empty (includes above)
+
+    // TODO initialize vectorial_dim only from SnapshotsLists type
+    // vectorial_dim = std::apply(compute_vectorial_dim<SnapshotsLists&&...>, snapshotsTuple);
+
+    ITHACAparameters *para(ITHACAparameters::getInstance());
+    Folder = "ITHACAoutput/" + methodName + "/" + functionName;
+
+    nodePoints = autoPtr<IOList<label>>(new IOList<label>(
+        IOobject("nodePoints", para->runTime.time().constant(), "../" + Folder,
+                 para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
+
+    nodePointsFields = autoPtr<IOList<label>>(new IOList<label>(IOobject(
+        "nodePointsFields", para->runTime.time().constant(), "../" + Folder,
+        para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
+
+    n_snapshots = std::get<0>(snapshotsTuple).size();
+    Info << "The number of snapshots is: " << n_snapshots << endl;
+    n_cells = std::get<0>(snapshotsTuple)[0].size();
+    Info << "The number of cells is: " << n_cells << endl;
+    
+    std::apply([this](auto& ...x){(..., compute_matrix_modes(x));}, snapshotsTuple);
+
+    if (!nodePoints().headerOk())
+    {
+
+        assert(maxModes > 0);
+        assert(maxNodes >= maxModes);
+
+        Eigen::VectorXd mp_not_mask = Eigen::VectorXd::Constant(n_cells * vectorial_dim, 1);
+
+        // set initialSeeds
+        if (initialSeeds.rows() > 0)
+        {
+
+            P.resize(n_cells * vectorial_dim, initialSeeds.rows() * vectorial_dim);
+            P.reserve(Eigen::VectorXi::Constant(initialSeeds.rows() * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
+
+            int col_index{0};
+            for (int i = 0; i < initialSeeds.rows(); i++)
+            {
+                for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+                {
+                    P.insert(initialSeeds(i)+ith_field*n_cells, col_index++) = 1;
+                    mp_not_mask(initialSeeds(i) + ith_field * n_cells) = 0;
+                }
+                
+                nodePointsSet.insert(initialSeeds(i));
+            }
+
+            P.makeCompressed();
+        }
+
+        // std::cout << "Initial seeds: " << P << std::endl;
+
+        for (int k = 0; k < initialSeeds.outerSize(); ++k) {
+          for (Eigen::SparseMatrix<double>::InnerIterator it(P, k); it; ++it) {
+            assert(it.value() == 1);
+            nodePointsSet.insert(it.row() % n_cells);
+          }
+        }
+
+        int na = maxNodes - initialSeeds.rows();
+        if (na > 0)
+        {
+            int nb = 0;
+            int nit = std::min(maxModes, na);
+            int ncimin = std::floor(maxModes / nit);
+            int naimin = std::floor(na / maxModes);
+
+            Eigen::MatrixXd A;
+            Eigen::VectorXd b;
+            Eigen::VectorXd c;
+            Eigen::VectorXd r;
+            label ind_max, c1;
+
+            double max;
+
+            Info << "######## Begin HR training ########" << endl;
+            Info << "######## Modes=" <<  maxModes
+                 << ", nodePoints=" << maxNodes << " ########"
+                 << endl;
+
+            for (int i = 1; i <= nit; i++)
+            {
+                int nci = ncimin;
+                // add the remaining modes in the quotien maxModes / nite
+                if (i <= maxModes % nit)
+                {
+                    nci = ncimin + 1;
+                }
+                int nai = naimin;
+                // add the remaining nodePoints_xyz in the quotien na / maxModes
+                if (i <= na % maxModes)
+                {
+                    nai = naimin + 1;
+                }
+
+                Eigen::MatrixXd V;
+
+                // select basis
+                if (i == 1)
+                {
+                    V = matrixModes.leftCols(nci);
+                }
+                else
+                {
+                    for (int q = 1; q <= nci; q++)
+                    {
+                        A = P.transpose() * U;
+
+                        b = P.transpose() * matrixModes.col(nb + q - 1);
+
+                        c = A.fullPivLu().solve(b);
+
+                        r = matrixModes.col(nb + q - 1) - U * c;
+
+                        V.conservativeResize(matrixModes.rows(), q);
+                        V.col(q - 1) = r;
+                    }
+                }
+
+                // select nodePoints_xyz
+                for (int j = 1; j <= nai; j++)
+                {
+                    // TODO: implement as in Carlberg paper taking into account degrees
+                    // of freedom associated to each node
+                    // auto Id = Eigen::MatrixXd::Identity(P.rows(), P.rows());
+
+                    if (P.cols() > 0)
+                    {
+                        // std::cout << mp_not_mask.asDiagonal().rows() << " " << V.rows() << V.cols() << std::endl;
+                        max = (mp_not_mask.asDiagonal() * V)
+                                  .rowwise()
+                                  .lpNorm<2>()
+                                  .maxCoeff(&ind_max, &c1);
+                    }
+                    else
+                    {
+                        // max = V.topRows(2*n_cells).rowwise().lpNorm<2>().maxCoeff(&ind_max, &c1);
+                        max = V.rowwise().lpNorm<2>().maxCoeff(&ind_max, &c1);
+                    }
+
+                    // std::cout << "Maximum found: " << max << " at " << ind_max
+                    //           << std::endl;
+
+                    int idxes = P.cols();
+                    int maxFirstMesh = ind_max % n_cells;
+                    P.conservativeResize(matrixModes.rows(), idxes + vectorial_dim);
+                    
+                    for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+                    {
+                        P.insert(maxFirstMesh + ith_field * n_cells, idxes + ith_field) = 1;
+                        mp_not_mask(maxFirstMesh + ith_field * n_cells) = 0;
+                    }
+
+                    nodePointsSet.insert(maxFirstMesh);
+                }
+
+                nb += nci;
+                U = matrixModes.leftCols(nb);
+            }
+        }
+        else
+        {
+            U = matrixModes;
+        }
+
+        // convert nodePointsSet to nodePoints i.e. list
+        for (const int &x : nodePointsSet)
+        {
+            nodePoints().append(x);
+        }
+
+        // int i{0};
+        // nodePoints->resize(nodePoints().size());
+        // for (int &x : nodePoints())
+        // {
+        //     std::cout << x << " ";
+        //     nodePoints()(i) = x;
+        //     i++;
+        // }
+        // cnpy::save(nodePoints(), "./numpy_datasets/mp.npy");
+        // Info << "\n # DEBUG GNAT.C, line 740 # " << endl;
+        // std::cout << std::endl;
+
+        // evaluatePinv(P, U);
+        // std::cout << "pinv_PU: " << pinv_PU.rows() << std::endl;
+
+        mkDir(Folder);
+        cnpy::save(pinv_PU, Folder + "/MatrixOnline.npy");
+        // cnpy::save(pinv_PUV, Folder + "/MatrixOnlineV.npy");
+        // cnpy::save(pinv_PUS, Folder + "/MatrixOnlineS.npy");
+        cnpy::save(maskAux, Folder + "/MaskAux.npy");
+
+        // std::cout << "nodePoints size: " << nodePoints().size() << "\n" << std::endl;
+        // nodePoints.resize(nodePoints().size(), 1);
+        // for (int i = 0; i < nodePoints().size(); i++)
+        // {
+        //   nodePoints.coeffRef(i, 0) = nodePoints()[i];
+        // }
+        // cnpy::save(nodePoints, "./nummpy_datasets/mp.npy");
+        nodePoints().write();
+    }
+    else
+    {
+        cnpy::load(pinv_PU, Folder + "/MatrixOnline.npy");
+        // cnpy::load(pinv_PUV, Folder + "/MatrixOnlineV.np
+        // cnpy::load(pinv_PUS, Folder + "/MatrixOnlineS.npy");y");
+        // cnpy::load(pinv_PUS, Folder + "/MatrixOnlineS.npy");
+        cnpy::load(maskAux, Folder + "/MaskAux.npy");
+        Info << "Loaded mask and UpinvPU with size: "
+                  << pinv_PU.rows() << "x" << pinv_PU.cols() << endl;
+    }
+}
+
+template <typename... SnapshotsLists>
+template <typename SnapshotsList>
+void HyperReduction<SnapshotsLists...>::compute_matrix_modes(SnapshotsList sList)
+{
+    // TODO normalization
+    // Eigen::MatrixXf::Index maxIndex;
+    // double maxVal = modes.col(0).cwiseAbs().maxCoeff(&maxIndex);
+    // std::cout << "MaxValues: " << maxVal << std::endl;
+
+    // modes = modes / maxVal;
+
+    // maxVal = modes.col(0).cwiseAbs().maxCoeff(&maxIndex);
+    // std::cout << "MaxValues: " << maxVal << std::endl;
+
+    word fieldName = sList[0].name();
+    unsigned int field_dim = get_field_dim<typename SnapshotsList::value_type>();
+
+    auto tmp_modes = ITHACAPOD::DEIMmodes(sList, maxModes, "GNAT/" + functionName + "V", fieldName);
+
+    matrixModes.conservativeResize(n_cells * field_dim, n_snapshots);
+    matrixModes.bottomRows(n_cells * field_dim) = Foam2Eigen::PtrList2Eigen(tmp_modes);
+}
+
+template<typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::evaluatePinv(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes) {
+  assert(Projector.cols() > 0);
+  Eigen::MatrixXd restricted = Projector.transpose() * Modes;
+
+//   Info << "Restricted modes matrix: " << restricted.rows() << " x "
+//             << restricted.cols() << endl;
+
+  int ssize = restricted.rows()/3;
+  int vsize = 2*ssize;
+  
+  pinv_PU = pinv_eigen_based(restricted);
+//   Eigen::MatrixXd PUV = restricted.topRows(vsize);
+//   Eigen::MatrixXd PUS = restricted.bottomRows(ssize);
+//   cnpy::save(restricted, "./numpy_datasets/restricted.npy");
+//   pinv_PUV = pinv_eigen_based(PUV, 1e-10);
+//   pinv_PUS = pinv_eigen_based(PUS, 1e-10);
+//   Info << "PUV: " << PUV.rows() << " " << PUV.cols() << endl;
+//   Info << "PUS: " << PUS.rows() << " " << PUS.cols() << endl;
+
+//   pinv_PU.resize(restricted.cols(), ssize*3);
+//   pinv_PU.leftCols(vsize) = pinv_PUV;
+//   pinv_PU.rightCols(ssize) = pinv_PUS;
+  // Info << "pinv_PU: " << pinv_PU << endl;
+
+//   Info << "Pseudo inverse of restricted modes: " << pinv_PU.rows() << " x "
+//             << pinv_PU.cols() << endl;
+
+  Eigen::MatrixXd Upinv_PU_ = restricted * pinv_PU;
+  Info << "Pseudo inverse of restricted modes: " << Upinv_PU_.rows()
+            << " x " << Upinv_PU_.cols() << endl;
+
+  maskingAux = Modes * pinv_PU;
+//   Info << "Masking auxiliary matrix: " << maskingAux.rows() << " x "
+//             << maskingAux.cols() << endl;
+
+  // auto ret = std::make_pair<Eigen::MatrixXd, Eigen::MatrixXd>(Upinv_PU, maskingAux);
+}
+
+template<typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::generateSubmeshes(label layers, fvMesh &mesh, label secondTime) {
+
+  ITHACAparameters *para(ITHACAparameters::getInstance());
+
+  totalMagicPoints = autoPtr<IOList<labelList>>(new IOList<labelList>(IOobject(
+      "totalMagicPoints", para->runTime.time().constant(),  Folder,
+      para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
+
+  uniqueMagicPoints = autoPtr<IOList<label>>(new IOList<label>(IOobject(
+      "uniqueMagicPoints", para->runTime.time().constant(),  Folder,
+      para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
+
+  volScalarField Indici(
+      IOobject(FunctionName + "_indices", mesh.time().timeName(), mesh,
+               IOobject::NO_READ, IOobject::NO_WRITE),
+      mesh,
+      dimensionedScalar(FunctionName + "_indices",
+                        dimensionSet(0, 0, 0, 0, 0, 0, 0), 0.0));
+
+  submesh = autoPtr<fvMeshSubset>(new fvMeshSubset(mesh));
+
+  if (!totalMagicPoints().headerOk()) {
+    List<label> indices;
+
+    for (label i = 0; i < magicPoints().size(); i++) {
+      indices = ITHACAutilities::getIndices(mesh, magicPoints()[i], layers);
+      totalMagicPoints().append(indices);
+    }
+
+    labelList a = ListListOps::combine<labelList>(totalMagicPoints(),
+                                                  accessOp<labelList>());
+
+    inplaceUniqueSort(a);
+    uniqueMagicPoints() = a;
+
+    scalar zerodot25 = 0.25;
+    ITHACAutilities::assignIF(Indici, zerodot25,
+                              uniqueMagicPoints().List<label>::clone()());
+    ITHACAutilities::assignONE(Indici, magicPoints());
+
+    totalMagicPoints().write();
+    uniqueMagicPoints().write();
+  }
+
+  submesh->setCellSubset(uniqueMagicPoints());
+  submesh->subMesh().fvSchemes::readOpt() = mesh.fvSchemes::readOpt();
+  submesh->subMesh().fvSolution::readOpt() = mesh.fvSolution::readOpt();
+  submesh->subMesh().fvSchemes::read();
+  submesh->subMesh().fvSolution::read();
+  std::cout.clear();
+
+  if (!secondTime) {
+      localMagicPoints = global2local(magicPoints(), submesh());
+      ITHACAstream::exportSolution(Indici, "1",
+                                 "./ITHACAoutput/" + methodName + "/");
+  }
+
+  NcellsSubfields = submesh().cellMap().size();
+  createMasks();
+}
+
+template<typename... SnapshotsLists>
+List<label> HyperReduction<SnapshotsLists...>::global2local(List<label> &points, fvMeshSubset &submesh) {
+  List<label> localPoints;
+
+  for (label i = 0; i < points.size(); i++) {
+    for (label j = 0; j < submesh.cellMap().size(); j++) {
+      if (submesh.cellMap()[j] == points[i]) {
+        localPoints.append(j);
+        break;
+      }
+    }
+  }
+
+  return localPoints;
+}
+
+template<typename... SnapshotsLists>
+template<typename FieldType>
+void HyperReduction<SnapshotsLists...>::interpolateField(FieldType& field) {
+    return autoPtr<FieldType>(new FieldType(submesh->interpolate(field)));
+}
+
+template<typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::createMasks() {
+  assert(uniqueMagicPoints().size() > 0);
+
+  // initialize nonRepeatedSubmeshes
+  nonRepeatedSubmeshes.resize(uniqueMagicPoints().size());
+  int vector_idx{0};
+  for (int &x : uniqueMagicPoints()) {
+    nonRepeatedSubmeshes(vector_idx) = x;
+    vector_idx++;
+  }
+
+  // initialize nonRepeatedSubmeshes_xy
+  nonRepeatedSubmeshes_xy.resize(uniqueMagicPoints().size() * 3);
+  nonRepeatedSubmeshes_xy.head(uniqueMagicPoints().size()) =
+      nonRepeatedSubmeshes;
+  nonRepeatedSubmeshes_xy.segment(uniqueMagicPoints().size(), uniqueMagicPoints().size()) = (Ncells + nonRepeatedSubmeshes.array()).matrix();
+  nonRepeatedSubmeshes_xy.tail(uniqueMagicPoints().size()) =
+      (2 * Ncells + nonRepeatedSubmeshes.array()).matrix();
+
+
+  // initialize P_xymp_mp
+  // due to the fact that x, y coordinates of the residual in a single cell are
+  // computed at the same time in OF, if two magicPoints_xy refer to the same
+  // cell, the residual can be evaluated just once. In case only one coordinate
+  // is a magicPoint the following mask will be used to distinguish the two
+  // cases
+  cnpy::load(magicpoints, "./numpy_datasets/mp.npy");
+  // std::cout << magicpoints << std::endl;
+
+  P_xymp_submesh.resize(2 * magicpoints.rows(), 2 * NcellsSubfields);
+  P_xymp_submesh_scalar.resize(magicpoints.rows(), NcellsSubfields);
+
+
+  // ITHACAparameters *para(ITHACAparameters::getInstance());
+  // magicPoints.clear();
+  // magicPoints = autoPtr<IOList<label>>(new IOList<label>(
+  //     IOobject("magicPoints", para->runTime.time().constant(), "../ITHACAoutput/GNAT/" + FunctionName,
+  //              para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
+
+  // for (int i{0}; i< magicPoints().size(); i++){
+  //   std::cout << magicPoints()[i] << " ";
+  // }
+
+  int index_row = 0;
+  int index_col = 0;
+  for (const int &cell : submesh().cellMap()) {
+    for (int mpxy{0}; mpxy < magicpoints.rows(); mpxy++) {
+      // std::cout << "cell: "<< cell << " mp: " << magicpoints(mpxy) << std::endl;
+      if (cell == int(magicpoints(mpxy))) {
+        P_xymp_submesh.insert(index_row, index_col) = 1;
+        P_xymp_submesh.insert(index_row + magicpoints.rows(), index_col + NcellsSubfields) = 1;
+
+        P_xymp_submesh_scalar.insert(index_row, index_col) = 1;
+      }
+
+      index_row++;volVectorField fieldV, volScalarField fieldS
+    }
+    index_row = 0;
+    index_col++;
+  }
+//   Info << " # DEBUG GNAT.C, line 429 # " << P_xymp_submesh.rows() << " " << P_xymp_submesh.cols() << endl;
+// //   Info << " # DEBUG GNAT.C, line 430 # " << P_xymp_submesh_scalar.rows() << " " << P_xymp_submesh_scalar.cols() << endl;
+
+  Eigen::MatrixXd P_xymp_submesh_ = P_xymp_submesh;
+  Eigen::MatrixXd P_xymp_submesh_scalar_ = P_xymp_submesh_scalar;
+  cnpy::save(P_xymp_submesh_, "./numpy_datasets/submesh_vector.npy");
+  cnpy::save(P_xymp_submesh_scalar_, "./numpy_datasets/submesh_scalar.npy");
+}
+
+template HyperReduction<PtrList<volScalarField>&>::HyperReduction(HyperReductionMethod hrMethod,
+                                                        label maxModes,
+                                                        label maxNodes,
+                                                        Eigen::VectorXi initialSeeds,
+                                                        word functionName,
+                                                        PtrList<volScalarField>& snapshotsLists1);
+
+// template HyperReduction<PtrList<volVectorField>&>::HyperReduction(HyperReductionMethod hrMethod,
+//                                                         label maxModes,
+//                                                         label maxNodes,
+//                                                         Eigen::VectorXi initialSeeds,
+//                                                         word functionName,
+//                                                         PtrList<volVectorField>& snapshotsLists1);
+
+// template HyperReduction<PtrList<volVectorField>&, PtrList<volScalarField>&>::HyperReduction(HyperReductionMethod hrMethod,
+//                                                         label maxModes,
+//                                                         label maxNodes,
+//                                                         Eigen::VectorXi initialSeeds,
+//                                                         word functionName,
+//                                                         PtrList<volVectorField>& snapshotsLists1,
+//                                                         PtrList<volScalarField>&snapshotsLists2);
\ No newline at end of file
diff --git a/src/ITHACA_HR/hyperReduction.H b/src/ITHACA_HR/hyperReduction.H
new file mode 100644
index 000000000..23f784ac5
--- /dev/null
+++ b/src/ITHACA_HR/hyperReduction.H
@@ -0,0 +1,211 @@
+/*---------------------------------------------------------------------------*\
+     ██╗████████╗██╗  ██╗ █████╗  ██████╗ █████╗       ███████╗██╗   ██╗
+     ██║╚══██╔══╝██║  ██║██╔══██╗██╔════╝██╔══██╗      ██╔════╝██║   ██║
+     ██║   ██║   ███████║███████║██║     ███████║█████╗█████╗  ██║   ██║
+     ██║   ██║   ██╔══██║██╔══██║██║     ██╔══██║╚════╝██╔══╝  ╚██╗ ██╔╝
+     ██║   ██║   ██║  ██║██║  ██║╚██████╗██║  ██║      ██║      ╚████╔╝
+     ╚═╝   ╚═╝   ╚═╝  ╚═╝╚═╝  ╚═╝ ╚═════╝╚═╝  ╚═╝      ╚═╝       ╚═══╝
+
+ * In real Time Highly Advanced Computational Applications for Finite Volumes
+ * Copyright (C) 2017 by the ITHACA-FV authors
+-------------------------------------------------------------------------------
+License
+    This file is part of ITHACA-FV
+    ITHACA-FV is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+    ITHACA-FV is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU Lesser General Public License for more details.
+    You should have received a copy of the GNU Lesser General Public License
+    along with ITHACA-FV. If not, see <http://www.gnu.org/licenses/>.
+Class
+    HyperReduction
+Description
+    Implementation of the hyper-reduction methods.
+SourceFiles
+    hyperReduction.C
+\*---------------------------------------------------------------------------*/
+#include "fvCFD.H"
+#include "ITHACAPOD.H"
+#include "Foam2Eigen.H"
+#include "EigenFunctions.H"
+#include "ITHACAutilities.H"
+#include "fvMeshSubset.H"
+#include <set>
+
+template <typename... SnapshotsLists>
+class HyperReduction
+{
+public:
+
+    enum class HyperReductionMethod { GNAT };
+    const word methodNames[1] = {"GNAT"};
+    const word methodName;
+
+    using SnapshotsTuple = std::tuple<std::decay_t<SnapshotsLists>...>;
+    using FieldsTuple = std::tuple<std::decay_t<SnapshotsLists>...>;
+    static constexpr auto n_fields = sizeof...(SnapshotsLists);
+    unsigned int vectorial_dim;
+
+    template <std::size_t N>
+    using NthFieldListType = typename std::tuple_element<N, SnapshotsTuple>::type;
+
+    template <std::size_t N>
+    using NthFieldType = typename NthFieldListType<N>::value_type;
+
+    //----------------------------------------------------------------------
+    /// @brief      Construct HyperReduction.
+    ///
+    /// @param[in]  snapshotsLists  The snapshots matrix
+    /// @param[in]  maxModes         The maximum number of modes
+    ///
+    HyperReduction(HyperReductionMethod hrMethod,
+                   label maxModes,
+                   label maxNodes,
+                   Eigen::VectorXi initialSeeds,
+                   word functionName,
+                   SnapshotsLists&&... snapshotsLists);
+
+    /// The maximum number of modes to be considered
+    label maxModes;
+
+    /// The maximum number of modes to be considered
+    label maxNodes;
+
+    label n_snapshots;
+    
+    // Initial nodes
+    Eigen::VectorXi initialSeeds;
+
+    /// The name of the non-linear function e.g. HR_method/residual
+    word functionName;
+
+    /// The snapshots matrix containing the nonlinear function or operator
+    SnapshotsTuple snapshotsTuple;
+
+    /// The POD modes of the HyperReduction procedure that can be
+    SnapshotsTuple modes;
+
+    /// Matrix Modes
+    Eigen::MatrixXd matrixModes;
+
+    // TODO
+    Eigen::MatrixXd pinv_PU;
+
+    /// TODO
+    Eigen::MatrixXd maskAux;
+
+    /// TODO
+    std::set<label> nodePointsSet;
+
+    /// Int Number of Cells;
+    label n_cells;
+
+    /// Int Number of Cells in submeshes;
+    label n_cellsSubfields;
+
+    /// Submeshes
+    autoPtr<volVectorField> submesh_field;
+
+    /// Online Matrices
+    ///@{
+    Eigen::MatrixXd MatrixOnline;
+
+    /// The U matrix of the HyperReduction method
+    Eigen::MatrixXd U;
+
+    /// Magic points in the case of the a nonlinear function
+    autoPtr<IOList<label>> nodePoints;
+    /// Magic points in the case of the a nonlinear function
+    autoPtr<IOList<label>> nodePointsFields;
+    /// Magic points in the case of the a matrix function (rows indices)
+    autoPtr<IOList<label>> nodePointsArow;
+    /// Magic points in the case of the a matrix function (cols indices)
+    autoPtr<IOList<label>> nodePointsAcol;
+    /// Magic points in the case of the a matrix function, right hand side
+    autoPtr<IOList<label>> nodePointsB;
+
+    /// Magic points and indices of the surrounding layers
+    ///@{
+    autoPtr<IOList<labelList>> totalnodePoints;
+    autoPtr<IOList<labelList>> totalnodePointsA;
+    autoPtr<IOList<labelList>> totalnodePointsB;
+    ///@}
+
+    /// List of unique indices that define the submesh
+    ///@{
+    autoPtr<IOList<label>> uniquenodePoints;
+    autoPtr<IOList<label>> uniquenodePointsA;
+    autoPtr<IOList<label>> uniquenodePointsB;
+    ///@}
+
+    /// Folder for nonlinear functions
+    word Folder;
+    /// Folder in the matrix case
+    word FolderM;
+
+    /// Definition of the x, y, z coordinate of the identified element in the matrix or source term
+    /// 0 for x, 1 for y, 2 for z
+    ///@{
+    autoPtr<IOList<label>> xyz;
+    autoPtr<IOList<label>> xyz_Arow;
+    autoPtr<IOList<label>> xyz_Acol;
+    autoPtr<IOList<label>> xyz_B;
+    ///@}
+
+    /// Indices of the local magic points in the subMesh
+    ///@{
+    List<label> localnodePoints;
+    List<label> localnodePointsArow;
+    List<label> localnodePointsAcol;
+    List<label> localnodePointsB;
+    ///@}
+
+    /// The P matrix of the HyperReduction method
+    ///@{
+    Eigen::SparseMatrix<double> P;
+    List<Eigen::SparseMatrix<double>> PA;
+    Eigen::SparseMatrix<double> PB;
+    ///@}
+
+    /// Submesh of the HyperReduction method
+    ///@{
+    autoPtr<fvMeshSubset> submesh;
+    autoPtr<fvMeshSubset> submeshA;
+    autoPtr<fvMeshSubset> submeshB;
+
+    /// Non-repeated submeshes cells (only x coordinates)
+    Eigen::VectorXi nonRepeatedSubmeshes;
+
+    /// Non-repeated submeshes cells (only x, y coordinates)
+    Eigen::VectorXi nonRepeatedSubmeshes_xy;
+
+    void compute_basis();
+                                      
+    void evaluatePinv(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes);
+    
+    voidgenerateSubmeshes(label layers, fvMesh &mesh, label secondTime);
+
+    List<label> global2local(List<label> &points, fvMeshSubset &submesh);
+
+    template<typename... SnapshotsLists>
+    void createMasks()
+
+    template<typename FieldType>
+    void interpolateField(FieldType& field)
+
+    template<typename SnapshotsList>
+    void compute_matrix_modes(SnapshotsList sList);
+    template<typename Field>
+    inline constexpr unsigned int get_field_dim(){return std::is_same<typename Field::DimensionedField::FieldType, Foam::scalar>::value? 1: 3;}
+
+    template <typename LastList>
+    inline constexpr unsigned int compute_vectorial_dim(LastList x) {return get_field_dim<typename std::decay_t<LastList>::value_type>();}
+
+    template<typename List, typename... RemainingLists>
+    inline constexpr unsigned int compute_vectorial_dim(List&& head, RemainingLists&&... tail)  {
+        return get_field_dim<typename std::decay_t<List>::value_type>() + compute_vectorial_dim<RemainingLists...>(tail...);}
+};

From f21ec1b2cb141689793ebc219570c4332695f632 Mon Sep 17 00:00:00 2001
From: fromor <francesco.romor@gmail.com>
Date: Sun, 23 Oct 2022 18:23:32 +0200
Subject: [PATCH 02/59] add working gappy DEIM normalized with arbitrary fields

---
 src/ITHACA_HR/Make/options                    |      2 +-
 src/ITHACA_HR/hyperReduction.C                |    423 +-
 src/ITHACA_HR/hyperReduction.H                |    260 +-
 src/ITHACA_HR/hyperReduction.templates.H      |    488 +
 tutorials/CFD/24HyperReduction/.gitignore     |      2 +
 .../24HyperReduction/0/ITHACAOutput/DEIM/S    |  25053 ++++
 tutorials/CFD/24HyperReduction/0/T            |     48 +
 tutorials/CFD/24HyperReduction/0/U            |     48 +
 .../CFD/24HyperReduction/24HyperReduction.C   |    451 +
 tutorials/CFD/24HyperReduction/Allclean       |     11 +
 tutorials/CFD/24HyperReduction/Allrun         |      7 +
 .../CFD/24HyperReduction/Make/.gitignore      |      1 +
 tutorials/CFD/24HyperReduction/Make/files     |      3 +
 tutorials/CFD/24HyperReduction/Make/options   |     47 +
 .../constant/polyMesh/blockMeshDict           |     91 +
 .../constant/polyMesh/boundary                |     54 +
 .../24HyperReduction/constant/polyMesh/faces  | 100374 ++++++++++++++
 .../constant/polyMesh/neighbour               |  49675 +++++++
 .../24HyperReduction/constant/polyMesh/owner  | 100375 +++++++++++++++
 .../24HyperReduction/constant/polyMesh/points |  50726 ++++++++
 .../constant/transportProperties              |     19 +
 tutorials/CFD/24HyperReduction/createFields.H |     61 +
 .../CFD/24HyperReduction/system/ITHACAdict    |     29 +
 .../CFD/24HyperReduction/system/PODsolverDict |     50 +
 .../CFD/24HyperReduction/system/controlDict   |     53 +
 .../CFD/24HyperReduction/system/fvSchemes     |     56 +
 .../CFD/24HyperReduction/system/fvSolution    |     47 +
 27 files changed, 328131 insertions(+), 323 deletions(-)
 create mode 100644 src/ITHACA_HR/hyperReduction.templates.H
 create mode 100755 tutorials/CFD/24HyperReduction/.gitignore
 create mode 100755 tutorials/CFD/24HyperReduction/0/ITHACAOutput/DEIM/S
 create mode 100755 tutorials/CFD/24HyperReduction/0/T
 create mode 100755 tutorials/CFD/24HyperReduction/0/U
 create mode 100644 tutorials/CFD/24HyperReduction/24HyperReduction.C
 create mode 100755 tutorials/CFD/24HyperReduction/Allclean
 create mode 100755 tutorials/CFD/24HyperReduction/Allrun
 create mode 100755 tutorials/CFD/24HyperReduction/Make/.gitignore
 create mode 100644 tutorials/CFD/24HyperReduction/Make/files
 create mode 100644 tutorials/CFD/24HyperReduction/Make/options
 create mode 100755 tutorials/CFD/24HyperReduction/constant/polyMesh/blockMeshDict
 create mode 100755 tutorials/CFD/24HyperReduction/constant/polyMesh/boundary
 create mode 100755 tutorials/CFD/24HyperReduction/constant/polyMesh/faces
 create mode 100755 tutorials/CFD/24HyperReduction/constant/polyMesh/neighbour
 create mode 100755 tutorials/CFD/24HyperReduction/constant/polyMesh/owner
 create mode 100755 tutorials/CFD/24HyperReduction/constant/polyMesh/points
 create mode 100755 tutorials/CFD/24HyperReduction/constant/transportProperties
 create mode 100755 tutorials/CFD/24HyperReduction/createFields.H
 create mode 100755 tutorials/CFD/24HyperReduction/system/ITHACAdict
 create mode 100755 tutorials/CFD/24HyperReduction/system/PODsolverDict
 create mode 100755 tutorials/CFD/24HyperReduction/system/controlDict
 create mode 100755 tutorials/CFD/24HyperReduction/system/fvSchemes
 create mode 100755 tutorials/CFD/24HyperReduction/system/fvSolution

diff --git a/src/ITHACA_HR/Make/options b/src/ITHACA_HR/Make/options
index d51b789a2..2c343961d 100644
--- a/src/ITHACA_HR/Make/options
+++ b/src/ITHACA_HR/Make/options
@@ -24,7 +24,7 @@ EXE_INC = \
     -I$(LIB_ITHACA_SRC)/ITHACA_CORE/Containers \
     -Wno-comment \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++17
+    -std=c++17 
 
 EXE_LIBS = \
     -lITHACA-CORE \
diff --git a/src/ITHACA_HR/hyperReduction.C b/src/ITHACA_HR/hyperReduction.C
index 0805c9a5d..dfc1049ba 100644
--- a/src/ITHACA_HR/hyperReduction.C
+++ b/src/ITHACA_HR/hyperReduction.C
@@ -55,6 +55,7 @@ Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0) {
   }
 
   std::cout << "Condition number of inverse: " <<  D(D.size()-1, 0)/D(0, 0) << std::endl;
+
   // pinv_matrix = V * S * U^T
   return V * S * U.transpose();
 }
@@ -62,19 +63,20 @@ Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0) {
 // Template function constructor
 template <typename... SnapshotsLists>
 HyperReduction<SnapshotsLists...>::HyperReduction(HyperReductionMethod hrMethod,
-                                                  label maxModes,
-                                                  label maxNodes,
+                                                  label n_modes,
+                                                  label n_nodes,
                                                   Eigen::VectorXi initialSeeds,
                                                   word functionName,
                                                   SnapshotsLists &&...snapshotsLists)
     :  methodName{methodNames[int(hrMethod)]},
       vectorial_dim{compute_vectorial_dim(snapshotsLists...)},
-      maxModes{maxModes},
-      maxNodes{maxNodes},
+      n_modes{n_modes},
+      n_nodes{n_nodes},
       initialSeeds{initialSeeds},
       functionName{functionName},
       snapshotsTuple{std::forward_as_tuple(snapshotsLists...)}
 {
+    Info << "Init HyperReduction class with vectorial dim: " << vectorial_dim << endl;
     // check snapshotsLists is not empty
     // check that the first snapshotsList is not empty (includes above)
 
@@ -83,68 +85,70 @@ HyperReduction<SnapshotsLists...>::HyperReduction(HyperReductionMethod hrMethod,
 
     ITHACAparameters *para(ITHACAparameters::getInstance());
     Folder = "ITHACAoutput/" + methodName + "/" + functionName;
+    mkDir(Folder);
 
     nodePoints = autoPtr<IOList<label>>(new IOList<label>(
         IOobject("nodePoints", para->runTime.time().constant(), "../" + Folder,
                  para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
 
-    nodePointsFields = autoPtr<IOList<label>>(new IOList<label>(IOobject(
-        "nodePointsFields", para->runTime.time().constant(), "../" + Folder,
-        para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
-
     n_snapshots = std::get<0>(snapshotsTuple).size();
     Info << "The number of snapshots is: " << n_snapshots << endl;
     n_cells = std::get<0>(snapshotsTuple)[0].size();
     Info << "The number of cells is: " << n_cells << endl;
+    Info << "Initial seeds length: " << initialSeeds.rows() << endl;
     
     std::apply([this](auto& ...x){(..., compute_matrix_modes(x));}, snapshotsTuple);
 
     if (!nodePoints().headerOk())
     {
-
-        assert(maxModes > 0);
-        assert(maxNodes >= maxModes);
+        assert(n_modes > 0);
+        assert(n_nodes >= n_modes);
 
         Eigen::VectorXd mp_not_mask = Eigen::VectorXd::Constant(n_cells * vectorial_dim, 1);
+        std::set<label> nodePointsSet;
+        std::deque<label> nodePointsDeque;
 
         // set initialSeeds
         if (initialSeeds.rows() > 0)
         {
-
-            P.resize(n_cells * vectorial_dim, initialSeeds.rows() * vectorial_dim);
-            P.reserve(Eigen::VectorXi::Constant(initialSeeds.rows() * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
-
-            int col_index{0};
-            for (int i = 0; i < initialSeeds.rows(); i++)
-            {
-                for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-                {
-                    P.insert(initialSeeds(i)+ith_field*n_cells, col_index++) = 1;
-                    mp_not_mask(initialSeeds(i) + ith_field * n_cells) = 0;
-                }
-                
+          Info << "Add initialSeeds\n";
+          P.resize(n_cells * vectorial_dim, initialSeeds.rows() * vectorial_dim);
+          P.reserve(Eigen::VectorXi::Constant(initialSeeds.rows() * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
+
+          for (int i = 0; i < initialSeeds.rows(); i++)
+          {
+              for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+              {
+                P.insert(initialSeeds(i)+ith_field*n_cells, vectorial_dim*i+ith_field) = 1;
+                mp_not_mask(initialSeeds(i) + ith_field * n_cells) = 0;
+              }
+              
+              if (nodePointsSet.find(initialSeeds(i)) == nodePointsSet.end()){
                 nodePointsSet.insert(initialSeeds(i));
-            }
-
-            P.makeCompressed();
-        }
+                nodePointsDeque.push_back(initialSeeds(i));
+              }
+          }
 
-        // std::cout << "Initial seeds: " << P << std::endl;
+          P.makeCompressed();
 
-        for (int k = 0; k < initialSeeds.outerSize(); ++k) {
-          for (Eigen::SparseMatrix<double>::InnerIterator it(P, k); it; ++it) {
-            assert(it.value() == 1);
-            nodePointsSet.insert(it.row() % n_cells);
+          for (int k = 0; k < initialSeeds.outerSize(); ++k) {
+            for (Eigen::SparseMatrix<double>::InnerIterator it(P, k); it; ++it) {
+              assert(it.value() == 1);
+              if (nodePointsSet.find(it.row() % n_cells) == nodePointsSet.end()){
+                nodePointsSet.insert(it.row() % n_cells);
+                nodePointsDeque.push_back(it.row() % n_cells);
+              }
+            }
           }
         }
 
-        int na = maxNodes - initialSeeds.rows();
+        int na = n_nodes - initialSeeds.rows();
         if (na > 0)
         {
             int nb = 0;
-            int nit = std::min(maxModes, na);
-            int ncimin = std::floor(maxModes / nit);
-            int naimin = std::floor(na / maxModes);
+            int nit = std::min(n_modes, na);
+            int ncimin = std::floor(n_modes / nit);
+            int naimin = std::floor(na / n_modes);
 
             Eigen::MatrixXd A;
             Eigen::VectorXd b;
@@ -154,22 +158,22 @@ HyperReduction<SnapshotsLists...>::HyperReduction(HyperReductionMethod hrMethod,
 
             double max;
 
-            Info << "######## Begin HR training ########" << endl;
-            Info << "######## Modes=" <<  maxModes
-                 << ", nodePoints=" << maxNodes << " ########"
+            Info << "######## Begin Greedy GNAT ########" << endl;
+            Info << "######## Modes=" <<  n_modes
+                 << ", nodePoints=" << n_nodes << " ########"
                  << endl;
 
             for (int i = 1; i <= nit; i++)
             {
                 int nci = ncimin;
-                // add the remaining modes in the quotien maxModes / nite
-                if (i <= maxModes % nit)
+                // add the remaining modes in the quotien n_modes / nite
+                if (i <= n_modes % nit)
                 {
                     nci = ncimin + 1;
                 }
                 int nai = naimin;
-                // add the remaining nodePoints_xyz in the quotien na / maxModes
-                if (i <= na % maxModes)
+                // add the remaining nodePoints_xyz in the quotien na / n_modes
+                if (i <= na % n_modes)
                 {
                     nai = naimin + 1;
                 }
@@ -183,19 +187,15 @@ HyperReduction<SnapshotsLists...>::HyperReduction(HyperReductionMethod hrMethod,
                 }
                 else
                 {
-                    for (int q = 1; q <= nci; q++)
-                    {
-                        A = P.transpose() * U;
-
-                        b = P.transpose() * matrixModes.col(nb + q - 1);
-
-                        c = A.fullPivLu().solve(b);
-
-                        r = matrixModes.col(nb + q - 1) - U * c;
-
-                        V.conservativeResize(matrixModes.rows(), q);
-                        V.col(q - 1) = r;
-                    }
+                  for (int q = 1; q <= nci; q++)
+                  {
+                      A = P.transpose() * basisMatrix;
+                      b = P.transpose() * matrixModes.col(nb + q - 1);
+                      c = A.fullPivLu().solve(b);
+                      r = matrixModes.col(nb + q - 1) - basisMatrix * c;
+                      V.conservativeResize(matrixModes.rows(), q);
+                      V.col(q - 1) = r;
+                  }
                 }
 
                 // select nodePoints_xyz
@@ -204,7 +204,7 @@ HyperReduction<SnapshotsLists...>::HyperReduction(HyperReductionMethod hrMethod,
                     // TODO: implement as in Carlberg paper taking into account degrees
                     // of freedom associated to each node
                     // auto Id = Eigen::MatrixXd::Identity(P.rows(), P.rows());
-
+                    
                     if (P.cols() > 0)
                     {
                         // std::cout << mp_not_mask.asDiagonal().rows() << " " << V.rows() << V.cols() << std::endl;
@@ -232,63 +232,56 @@ HyperReduction<SnapshotsLists...>::HyperReduction(HyperReductionMethod hrMethod,
                         mp_not_mask(maxFirstMesh + ith_field * n_cells) = 0;
                     }
 
-                    nodePointsSet.insert(maxFirstMesh);
+                    if (nodePointsSet.find(maxFirstMesh) == nodePointsSet.end()){
+                      nodePointsSet.insert(maxFirstMesh);
+                      nodePointsDeque.push_back(maxFirstMesh);
+                    }
+
                 }
 
                 nb += nci;
-                U = matrixModes.leftCols(nb);
+                basisMatrix = matrixModes.leftCols(nb);
             }
         }
         else
         {
-            U = matrixModes;
+            basisMatrix = matrixModes;
         }
 
+        Info << "######## End of greedy GNAT ########\n";
+        cnpy::save(basisMatrix, Folder +"/basisMatrix.npy");
+        cnpy::save(P, Folder +"/projectionMatrix.npy");
+        std::cout << "P: " << P.rows() << " " << P.cols() << std::endl;
+        std::cout << "basisMatrix: " << basisMatrix.rows() << " " << basisMatrix.cols() << std::endl;
+
         // convert nodePointsSet to nodePoints i.e. list
-        for (const int &x : nodePointsSet)
+        for (auto &x : nodePointsDeque)
+        {
+          nodePoints().append(x);
+        }
+
+        int i{0};
+        Eigen::VectorXi nodes(nodePoints().size());
+        for (int &x : nodePoints())
         {
-            nodePoints().append(x);
+            nodes(i) = x;
+            i++;
         }
+        cnpy::save(nodes, Folder + "/mp.npy");
+
+        evaluatePinv(P, basisMatrix);
+
+        // std::cout << "Reconstruction : " << (basisMatrix*((P.transpose() * basisMatrix).fullPivLu().inverse())*P.transpose()-Eigen::MatrixXd::Identity(basisMatrix.rows(), basisMatrix.rows())).norm() << std::endl;
 
-        // int i{0};
-        // nodePoints->resize(nodePoints().size());
-        // for (int &x : nodePoints())
-        // {
-        //     std::cout << x << " ";
-        //     nodePoints()(i) = x;
-        //     i++;
-        // }
-        // cnpy::save(nodePoints(), "./numpy_datasets/mp.npy");
-        // Info << "\n # DEBUG GNAT.C, line 740 # " << endl;
-        // std::cout << std::endl;
-
-        // evaluatePinv(P, U);
-        // std::cout << "pinv_PU: " << pinv_PU.rows() << std::endl;
-
-        mkDir(Folder);
-        cnpy::save(pinv_PU, Folder + "/MatrixOnline.npy");
-        // cnpy::save(pinv_PUV, Folder + "/MatrixOnlineV.npy");
-        // cnpy::save(pinv_PUS, Folder + "/MatrixOnlineS.npy");
-        cnpy::save(maskAux, Folder + "/MaskAux.npy");
-
-        // std::cout << "nodePoints size: " << nodePoints().size() << "\n" << std::endl;
-        // nodePoints.resize(nodePoints().size(), 1);
-        // for (int i = 0; i < nodePoints().size(); i++)
-        // {
-        //   nodePoints.coeffRef(i, 0) = nodePoints()[i];
-        // }
-        // cnpy::save(nodePoints, "./nummpy_datasets/mp.npy");
+        // pinvPU =((P.transpose() * basisMatrix).fullPivLu().inverse());
+        std::cout << "pinvPU: " << pinvPU.rows() << " " << pinvPU.cols() << std::endl;
+
+        cnpy::save(pinvPU, Folder + "/pinvPU.npy");
         nodePoints().write();
     }
     else
     {
-        cnpy::load(pinv_PU, Folder + "/MatrixOnline.npy");
-        // cnpy::load(pinv_PUV, Folder + "/MatrixOnlineV.np
-        // cnpy::load(pinv_PUS, Folder + "/MatrixOnlineS.npy");y");
-        // cnpy::load(pinv_PUS, Folder + "/MatrixOnlineS.npy");
-        cnpy::load(maskAux, Folder + "/MaskAux.npy");
-        Info << "Loaded mask and UpinvPU with size: "
-                  << pinv_PU.rows() << "x" << pinv_PU.cols() << endl;
+        cnpy::load(pinvPU, Folder + "/basisMatrix.npy");
     }
 }
 
@@ -296,6 +289,7 @@ template <typename... SnapshotsLists>
 template <typename SnapshotsList>
 void HyperReduction<SnapshotsLists...>::compute_matrix_modes(SnapshotsList sList)
 {
+    Info << "####### Compute hyper-reduction basis #######\n";
     // TODO normalization
     // Eigen::MatrixXf::Index maxIndex;
     // double maxVal = modes.col(0).cwiseAbs().maxCoeff(&maxIndex);
@@ -309,10 +303,12 @@ void HyperReduction<SnapshotsLists...>::compute_matrix_modes(SnapshotsList sList
     word fieldName = sList[0].name();
     unsigned int field_dim = get_field_dim<typename SnapshotsList::value_type>();
 
-    auto tmp_modes = ITHACAPOD::DEIMmodes(sList, maxModes, "GNAT/" + functionName + "V", fieldName);
+    auto tmp_modes = ITHACAPOD::DEIMmodes(sList, n_modes, "GNAT/" + functionName + "V", fieldName);
 
-    matrixModes.conservativeResize(n_cells * field_dim, n_snapshots);
+    matrixModes.conservativeResize(n_cells * field_dim, n_modes);
     matrixModes.bottomRows(n_cells * field_dim) = Foam2Eigen::PtrList2Eigen(tmp_modes);
+
+    Info << "####### End of computing hyper-reduction basis #######\n";
 }
 
 template<typename... SnapshotsLists>
@@ -323,97 +319,96 @@ void HyperReduction<SnapshotsLists...>::evaluatePinv(Eigen::SparseMatrix<double>
 //   Info << "Restricted modes matrix: " << restricted.rows() << " x "
 //             << restricted.cols() << endl;
 
-  int ssize = restricted.rows()/3;
-  int vsize = 2*ssize;
+  // int ssize = restricted.rows()/3;
+  // int vsize = 2*ssize;
   
-  pinv_PU = pinv_eigen_based(restricted);
+  pinvPU = pinv_eigen_based(restricted);
 //   Eigen::MatrixXd PUV = restricted.topRows(vsize);
 //   Eigen::MatrixXd PUS = restricted.bottomRows(ssize);
 //   cnpy::save(restricted, "./numpy_datasets/restricted.npy");
-//   pinv_PUV = pinv_eigen_based(PUV, 1e-10);
-//   pinv_PUS = pinv_eigen_based(PUS, 1e-10);
+//   pinvPUV = pinv_eigen_based(PUV, 1e-10);
+//   pinvPUS = pinv_eigen_based(PUS, 1e-10);
 //   Info << "PUV: " << PUV.rows() << " " << PUV.cols() << endl;
 //   Info << "PUS: " << PUS.rows() << " " << PUS.cols() << endl;
 
-//   pinv_PU.resize(restricted.cols(), ssize*3);
-//   pinv_PU.leftCols(vsize) = pinv_PUV;
-//   pinv_PU.rightCols(ssize) = pinv_PUS;
-  // Info << "pinv_PU: " << pinv_PU << endl;
+//   pinvPU.resize(restricted.cols(), ssize*3);
+//   pinvPU.leftCols(vsize) = pinvPUV;
+//   pinvPU.rightCols(ssize) = pinvPUS;
+  // Info << "pinvPU: " << pinvPU << endl;
 
-//   Info << "Pseudo inverse of restricted modes: " << pinv_PU.rows() << " x "
-//             << pinv_PU.cols() << endl;
+//   Info << "Pseudo inverse of restricted modes: " << pinvPU.rows() << " x "
+//             << pinvPU.cols() << endl;
 
-  Eigen::MatrixXd Upinv_PU_ = restricted * pinv_PU;
-  Info << "Pseudo inverse of restricted modes: " << Upinv_PU_.rows()
-            << " x " << Upinv_PU_.cols() << endl;
+  // Eigen::MatrixXd UpinvPU_ = restricted * pinvPU;
+  // Info << "Pseudo inverse of restricted modes: " << UpinvPU_.rows()
+  //           << " x " << UpinvPU_.cols() << endl;
 
-  maskingAux = Modes * pinv_PU;
+  // maskingAux = Modes * pinvPU;
 //   Info << "Masking auxiliary matrix: " << maskingAux.rows() << " x "
 //             << maskingAux.cols() << endl;
 
-  // auto ret = std::make_pair<Eigen::MatrixXd, Eigen::MatrixXd>(Upinv_PU, maskingAux);
+  // auto ret = std::make_pair<Eigen::MatrixXd, Eigen::MatrixXd>(UpinvPU, maskingAux);
 }
 
 template<typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::generateSubmeshes(label layers, fvMesh &mesh, label secondTime) {
+void HyperReduction<SnapshotsLists...>::generateSubmesh(label layers, fvMesh &mesh) {
 
+  Info << "####### Extract submesh #######\n";
   ITHACAparameters *para(ITHACAparameters::getInstance());
 
-  totalMagicPoints = autoPtr<IOList<labelList>>(new IOList<labelList>(IOobject(
-      "totalMagicPoints", para->runTime.time().constant(),  Folder,
+  totalNodePoints = autoPtr<IOList<labelList>>(new IOList<labelList>(IOobject(
+      "totalNodePoints", para->runTime.time().constant(),  "../" + Folder,
       para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
 
-  uniqueMagicPoints = autoPtr<IOList<label>>(new IOList<label>(IOobject(
-      "uniqueMagicPoints", para->runTime.time().constant(),  Folder,
+  uniqueNodePoints = autoPtr<IOList<label>>(new IOList<label>(IOobject(
+      "uniqueNodePoints", para->runTime.time().constant(),  "../" + Folder,
       para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
 
   volScalarField Indici(
-      IOobject(FunctionName + "_indices", mesh.time().timeName(), mesh,
+      IOobject(functionName + "_indices", mesh.time().timeName(), mesh,
                IOobject::NO_READ, IOobject::NO_WRITE),
       mesh,
-      dimensionedScalar(FunctionName + "_indices",
+      dimensionedScalar(functionName + "_indices",
                         dimensionSet(0, 0, 0, 0, 0, 0, 0), 0.0));
 
   submesh = autoPtr<fvMeshSubset>(new fvMeshSubset(mesh));
 
-  if (!totalMagicPoints().headerOk()) {
+  if (!totalNodePoints().headerOk()) {
     List<label> indices;
 
-    for (label i = 0; i < magicPoints().size(); i++) {
-      indices = ITHACAutilities::getIndices(mesh, magicPoints()[i], layers);
-      totalMagicPoints().append(indices);
+    for (label i = 0; i < nodePoints().size(); i++) {
+      indices = ITHACAutilities::getIndices(mesh, nodePoints()[i], layers);
+      totalNodePoints().append(indices);
     }
 
-    labelList a = ListListOps::combine<labelList>(totalMagicPoints(),
+    labelList a = ListListOps::combine<labelList>(totalNodePoints(),
                                                   accessOp<labelList>());
 
     inplaceUniqueSort(a);
-    uniqueMagicPoints() = a;
+    uniqueNodePoints() = a;
 
     scalar zerodot25 = 0.25;
     ITHACAutilities::assignIF(Indici, zerodot25,
-                              uniqueMagicPoints().List<label>::clone()());
-    ITHACAutilities::assignONE(Indici, magicPoints());
+                              uniqueNodePoints().List<label>::clone()());
+    ITHACAutilities::assignONE(Indici, nodePoints());
 
-    totalMagicPoints().write();
-    uniqueMagicPoints().write();
+    totalNodePoints().write();
+    uniqueNodePoints().write();
   }
 
-  submesh->setCellSubset(uniqueMagicPoints());
+  submesh->setCellSubset(uniqueNodePoints());
   submesh->subMesh().fvSchemes::readOpt() = mesh.fvSchemes::readOpt();
   submesh->subMesh().fvSolution::readOpt() = mesh.fvSolution::readOpt();
   submesh->subMesh().fvSchemes::read();
   submesh->subMesh().fvSolution::read();
   std::cout.clear();
 
-  if (!secondTime) {
-      localMagicPoints = global2local(magicPoints(), submesh());
-      ITHACAstream::exportSolution(Indici, "1",
-                                 "./ITHACAoutput/" + methodName + "/");
-  }
+  localNodePoints = global2local(nodePoints(), submesh());
+  ITHACAstream::exportSolution(Indici, "1", "./ITHACAoutput/" + methodName + "/");
 
-  NcellsSubfields = submesh().cellMap().size();
+  n_cellsSubfields = submesh().cellMap().size();
   createMasks();
+  Info << "####### End extract submesh #######\n";
 }
 
 template<typename... SnapshotsLists>
@@ -434,80 +429,80 @@ List<label> HyperReduction<SnapshotsLists...>::global2local(List<label> &points,
 
 template<typename... SnapshotsLists>
 template<typename FieldType>
-void HyperReduction<SnapshotsLists...>::interpolateField(FieldType& field) {
+autoPtr<FieldType> HyperReduction<SnapshotsLists...>::interpolateField(FieldType& field) {
     return autoPtr<FieldType>(new FieldType(submesh->interpolate(field)));
 }
 
 template<typename... SnapshotsLists>
 void HyperReduction<SnapshotsLists...>::createMasks() {
-  assert(uniqueMagicPoints().size() > 0);
+  assert(uniqueNodePoints().size() > 0);
 
-  // initialize nonRepeatedSubmeshes
-  nonRepeatedSubmeshes.resize(uniqueMagicPoints().size());
+  // initialize uniqueNodePointsVector
+  uniqueNodePointsVector.resize(uniqueNodePoints().size());
   int vector_idx{0};
-  for (int &x : uniqueMagicPoints()) {
-    nonRepeatedSubmeshes(vector_idx) = x;
+  for (int &x : uniqueNodePoints()) {
+    uniqueNodePointsVector(vector_idx) = x;
     vector_idx++;
   }
 
-  // initialize nonRepeatedSubmeshes_xy
-  nonRepeatedSubmeshes_xy.resize(uniqueMagicPoints().size() * 3);
-  nonRepeatedSubmeshes_xy.head(uniqueMagicPoints().size()) =
-      nonRepeatedSubmeshes;
-  nonRepeatedSubmeshes_xy.segment(uniqueMagicPoints().size(), uniqueMagicPoints().size()) = (Ncells + nonRepeatedSubmeshes.array()).matrix();
-  nonRepeatedSubmeshes_xy.tail(uniqueMagicPoints().size()) =
-      (2 * Ncells + nonRepeatedSubmeshes.array()).matrix();
-
-
-  // initialize P_xymp_mp
-  // due to the fact that x, y coordinates of the residual in a single cell are
-  // computed at the same time in OF, if two magicPoints_xy refer to the same
-  // cell, the residual can be evaluated just once. In case only one coordinate
-  // is a magicPoint the following mask will be used to distinguish the two
-  // cases
-  cnpy::load(magicpoints, "./numpy_datasets/mp.npy");
-  // std::cout << magicpoints << std::endl;
-
-  P_xymp_submesh.resize(2 * magicpoints.rows(), 2 * NcellsSubfields);
-  P_xymp_submesh_scalar.resize(magicpoints.rows(), NcellsSubfields);
-
-
-  // ITHACAparameters *para(ITHACAparameters::getInstance());
-  // magicPoints.clear();
-  // magicPoints = autoPtr<IOList<label>>(new IOList<label>(
-  //     IOobject("magicPoints", para->runTime.time().constant(), "../ITHACAoutput/GNAT/" + FunctionName,
-  //              para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
-
-  // for (int i{0}; i< magicPoints().size(); i++){
-  //   std::cout << magicPoints()[i] << " ";
-  // }
-
-  int index_row = 0;
-  int index_col = 0;
-  for (const int &cell : submesh().cellMap()) {
-    for (int mpxy{0}; mpxy < magicpoints.rows(); mpxy++) {
-      // std::cout << "cell: "<< cell << " mp: " << magicpoints(mpxy) << std::endl;
-      if (cell == int(magicpoints(mpxy))) {
-        P_xymp_submesh.insert(index_row, index_col) = 1;
-        P_xymp_submesh.insert(index_row + magicpoints.rows(), index_col + NcellsSubfields) = 1;
-
-        P_xymp_submesh_scalar.insert(index_row, index_col) = 1;
-      }
-
-      index_row++;volVectorField fieldV, volScalarField fieldS
-    }
-    index_row = 0;
-    index_col++;
+  // initialize uniqueNodePointsVector_xy
+  uniqueNodePointsVector_xy.resize(uniqueNodePoints().size() * vectorial_dim);
+  for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+  {
+    uniqueNodePointsVector_xy.segment(ith_field * uniqueNodePoints().size(), uniqueNodePoints().size()*(ith_field + 1)) =
+      (ith_field  * n_cells + uniqueNodePointsVector.array()).matrix();
   }
-//   Info << " # DEBUG GNAT.C, line 429 # " << P_xymp_submesh.rows() << " " << P_xymp_submesh.cols() << endl;
-// //   Info << " # DEBUG GNAT.C, line 430 # " << P_xymp_submesh_scalar.rows() << " " << P_xymp_submesh_scalar.cols() << endl;
 
-  Eigen::MatrixXd P_xymp_submesh_ = P_xymp_submesh;
-  Eigen::MatrixXd P_xymp_submesh_scalar_ = P_xymp_submesh_scalar;
-  cnpy::save(P_xymp_submesh_, "./numpy_datasets/submesh_vector.npy");
-  cnpy::save(P_xymp_submesh_scalar_, "./numpy_datasets/submesh_scalar.npy");
+//   // initialize P_xymp_mp
+//   // due to the fact that x, y coordinates of the residual in a single cell are
+//   // computed at the same time in OF, if two nodePoints_xy refer to the same
+//   // cell, the residual can be evaluated just once. In case only one coordinate
+//   // is a magicPoint the following mask will be used to distinguish the two
+//   // cases
+//   cnpy::load(nodePoints, "./numpy_datasets/mp.npy");
+//   // std::cout << nodePoints << std::endl;
+
+//   P_xymp_submesh.resize(2 * nodePoints.rows(), 2 * NcellsSubfields);
+//   P_xymp_submesh_scalar.resize(nodePoints.rows(), NcellsSubfields);
+
+
+//   // ITHACAparameters *para(ITHACAparameters::getInstance());
+//   // nodePoints.clear();
+//   // nodePoints = autoPtr<IOList<label>>(new IOList<label>(
+//   //     IOobject("nodePoints", para->runTime.time().constant(), "../ITHACAoutput/GNAT/" + FunctionName,
+//   //              para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
+
+//   // for (int i{0}; i< nodePoints().size(); i++){
+//   //   std::cout << nodePoints()[i] << " ";
+//   // }
+
+//   int index_row = 0;
+//   int index_col = 0;
+//   for (const int &cell : submesh().cellMap()) {
+//     for (int mpxy{0}; mpxy < nodePoints.rows(); mpxy++) {
+//       // std::cout << "cell: "<< cell << " mp: " << nodePoints(mpxy) << std::endl;
+//       if (cell == int(nodePoints(mpxy))) {
+//         P_xymp_submesh.insert(index_row, index_col) = 1;
+//         P_xymp_submesh.insert(index_row + nodePoints.rows(), index_col + NcellsSubfields) = 1;
+
+//         P_xymp_submesh_scalar.insert(index_row, index_col) = 1;
+//       }
+
+//       index_row++;volVectorField fieldV, volScalarField fieldS
+//     }
+//     index_row = 0;
+//     index_col++;
+//   }
+// //   Info << " # DEBUG GNAT.C, line 429 # " << P_xymp_submesh.rows() << " " << P_xymp_submesh.cols() << endl;
+// // //   Info << " # DEBUG GNAT.C, line 430 # " << P_xymp_submesh_scalar.rows() << " " << P_xymp_submesh_scalar.cols() << endl;
+
+//   Eigen::MatrixXd P_xymp_submesh_ = P_xymp_submesh;
+//   Eigen::MatrixXd P_xymp_submesh_scalar_ = P_xymp_submesh_scalar;
+//   cnpy::save(P_xymp_submesh_, "./numpy_datasets/submesh_vector.npy");
+//   cnpy::save(P_xymp_submesh_scalar_, "./numpy_datasets/submesh_scalar.npy");
 }
 
+
 template HyperReduction<PtrList<volScalarField>&>::HyperReduction(HyperReductionMethod hrMethod,
                                                         label maxModes,
                                                         label maxNodes,
@@ -515,17 +510,17 @@ template HyperReduction<PtrList<volScalarField>&>::HyperReduction(HyperReduction
                                                         word functionName,
                                                         PtrList<volScalarField>& snapshotsLists1);
 
-// template HyperReduction<PtrList<volVectorField>&>::HyperReduction(HyperReductionMethod hrMethod,
-//                                                         label maxModes,
-//                                                         label maxNodes,
-//                                                         Eigen::VectorXi initialSeeds,
-//                                                         word functionName,
-//                                                         PtrList<volVectorField>& snapshotsLists1);
-
-// template HyperReduction<PtrList<volVectorField>&, PtrList<volScalarField>&>::HyperReduction(HyperReductionMethod hrMethod,
-//                                                         label maxModes,
-//                                                         label maxNodes,
-//                                                         Eigen::VectorXi initialSeeds,
-//                                                         word functionName,
-//                                                         PtrList<volVectorField>& snapshotsLists1,
-//                                                         PtrList<volScalarField>&snapshotsLists2);
\ No newline at end of file
+template HyperReduction<PtrList<volVectorField>&>::HyperReduction(HyperReductionMethod hrMethod,
+                                                        label maxModes,
+                                                        label maxNodes,
+                                                        Eigen::VectorXi initialSeeds,
+                                                        word functionName,
+                                                        PtrList<volVectorField>& snapshotsLists1);
+
+template HyperReduction<PtrList<volVectorField>&, PtrList<volScalarField>&>::HyperReduction(HyperReductionMethod hrMethod,
+                                                        label maxModes,
+                                                        label maxNodes,
+                                                        Eigen::VectorXi initialSeeds,
+                                                        word functionName,
+                                                        PtrList<volVectorField>& snapshotsLists1,
+                                                        PtrList<volScalarField>&snapshotsLists2);
\ No newline at end of file
diff --git a/src/ITHACA_HR/hyperReduction.H b/src/ITHACA_HR/hyperReduction.H
index 23f784ac5..b13432729 100644
--- a/src/ITHACA_HR/hyperReduction.H
+++ b/src/ITHACA_HR/hyperReduction.H
@@ -28,6 +28,9 @@ Description
 SourceFiles
     hyperReduction.C
 \*---------------------------------------------------------------------------*/
+#ifndef hyperReduction_H
+#define hyperReduction_H
+
 #include "fvCFD.H"
 #include "ITHACAPOD.H"
 #include "Foam2Eigen.H"
@@ -36,18 +39,23 @@ SourceFiles
 #include "fvMeshSubset.H"
 #include <set>
 
+enum class HyperReductionMethod
+{
+    GappyDEIM
+};
+
 template <typename... SnapshotsLists>
 class HyperReduction
 {
 public:
-
-    enum class HyperReductionMethod { GNAT };
-    const word methodNames[1] = {"GNAT"};
+    const word methodNames[1] = {"GappyDEIM"};
     const word methodName;
 
     using SnapshotsTuple = std::tuple<std::decay_t<SnapshotsLists>...>;
     using FieldsTuple = std::tuple<std::decay_t<SnapshotsLists>...>;
     static constexpr auto n_fields = sizeof...(SnapshotsLists);
+
+    // TODO get vectorial dim from class template parameters
     unsigned int vectorial_dim;
 
     template <std::size_t N>
@@ -57,49 +65,44 @@ public:
     using NthFieldType = typename NthFieldListType<N>::value_type;
 
     //----------------------------------------------------------------------
-    /// @brief      Construct HyperReduction.
+    /// @brief      Construct HyperReduction class, interpolation-based.`SnapshotsLists` is a variadic argument of PtrLists of fields e.g. for incompressible Navier-Stokes PtrList<volVectorField>, PtrList<volScalarField> for velocity and pressure.
     ///
-    /// @param[in]  snapshotsLists  The snapshots matrix
-    /// @param[in]  maxModes         The maximum number of modes
+    /// @param[in]  hrMethod          the chosen HR method
+    /// @param[in]  n_modes           dimension of the HR basis
+    /// @param[in]  n_nodes           number of nodes
+    /// @param[in]  initialSeeds      initial nodes
+    /// @param[in]  problemName       name of the function to be hyper-reduced
+    /// @param[in]  snapshotsLists    lists of fields
     ///
-    HyperReduction(HyperReductionMethod hrMethod,
-                   label maxModes,
-                   label maxNodes,
+    HyperReduction(label n_modes,
+                   label n_nodes,
                    Eigen::VectorXi initialSeeds,
-                   word functionName,
-                   SnapshotsLists&&... snapshotsLists);
+                   word problemName,
+                   SnapshotsLists &&...snapshotsLists);
 
     /// The maximum number of modes to be considered
-    label maxModes;
+    label n_modes;
 
     /// The maximum number of modes to be considered
-    label maxNodes;
+    label n_nodes;
 
+    /// The length of the snapshots lists
     label n_snapshots;
-    
+
     // Initial nodes
     Eigen::VectorXi initialSeeds;
 
     /// The name of the non-linear function e.g. HR_method/residual
-    word functionName;
+    word problemName;
 
     /// The snapshots matrix containing the nonlinear function or operator
     SnapshotsTuple snapshotsTuple;
 
-    /// The POD modes of the HyperReduction procedure that can be
-    SnapshotsTuple modes;
+    /// Names of the fields
+    List<word> fieldNames;
 
-    /// Matrix Modes
-    Eigen::MatrixXd matrixModes;
-
-    // TODO
-    Eigen::MatrixXd pinv_PU;
-
-    /// TODO
-    Eigen::MatrixXd maskAux;
-
-    /// TODO
-    std::set<label> nodePointsSet;
+    /// Dimensions of the fields
+    List<unsigned int> fieldDims;
 
     /// Int Number of Cells;
     label n_cells;
@@ -107,105 +110,146 @@ public:
     /// Int Number of Cells in submeshes;
     label n_cellsSubfields;
 
-    /// Submeshes
-    autoPtr<volVectorField> submesh_field;
-
-    /// Online Matrices
-    ///@{
-    Eigen::MatrixXd MatrixOnline;
+    /// Nodes in the case of the a nonlinear function
+    autoPtr<IOList<label>> nodePoints;
 
-    /// The U matrix of the HyperReduction method
-    Eigen::MatrixXd U;
+    /// List of label lists of the nodes and corresponding surrounding nodes
+    autoPtr<IOList<labelList>> totalNodePoints;
 
-    /// Magic points in the case of the a nonlinear function
-    autoPtr<IOList<label>> nodePoints;
-    /// Magic points in the case of the a nonlinear function
-    autoPtr<IOList<label>> nodePointsFields;
-    /// Magic points in the case of the a matrix function (rows indices)
-    autoPtr<IOList<label>> nodePointsArow;
-    /// Magic points in the case of the a matrix function (cols indices)
-    autoPtr<IOList<label>> nodePointsAcol;
-    /// Magic points in the case of the a matrix function, right hand side
-    autoPtr<IOList<label>> nodePointsB;
-
-    /// Magic points and indices of the surrounding layers
-    ///@{
-    autoPtr<IOList<labelList>> totalnodePoints;
-    autoPtr<IOList<labelList>> totalnodePointsA;
-    autoPtr<IOList<labelList>> totalnodePointsB;
-    ///@}
-
-    /// List of unique indices that define the submesh
-    ///@{
-    autoPtr<IOList<label>> uniquenodePoints;
-    autoPtr<IOList<label>> uniquenodePointsA;
-    autoPtr<IOList<label>> uniquenodePointsB;
-    ///@}
+    /// List of the unique indices of the nodes that define the submesh
+    autoPtr<IOList<label>> uniqueNodePoints;
 
     /// Folder for nonlinear functions
     word Folder;
-    /// Folder in the matrix case
-    word FolderM;
-
-    /// Definition of the x, y, z coordinate of the identified element in the matrix or source term
-    /// 0 for x, 1 for y, 2 for z
-    ///@{
-    autoPtr<IOList<label>> xyz;
-    autoPtr<IOList<label>> xyz_Arow;
-    autoPtr<IOList<label>> xyz_Acol;
-    autoPtr<IOList<label>> xyz_B;
-    ///@}
-
-    /// Indices of the local magic points in the subMesh
-    ///@{
-    List<label> localnodePoints;
-    List<label> localnodePointsArow;
-    List<label> localnodePointsAcol;
-    List<label> localnodePointsB;
-    ///@}
+
+    /// Indices of the local node points in the subMesh
+    List<label> localNodePoints;
+    
+    // Outputs
+    /// Orthonormal basis of HR
+    Eigen::MatrixXd basisMatrix;
+
+    /// Renormalized basis of HR
+    Eigen::MatrixXd renormalizedBasisMatrix;
+
+    // TODO
+    Eigen::MatrixXd pinvPU;
 
     /// The P matrix of the HyperReduction method
-    ///@{
     Eigen::SparseMatrix<double> P;
-    List<Eigen::SparseMatrix<double>> PA;
-    Eigen::SparseMatrix<double> PB;
-    ///@}
+
+    /// Normalizing weights of the offline snapshots
+    Eigen::VectorXd normalizingWeights;
 
     /// Submesh of the HyperReduction method
-    ///@{
     autoPtr<fvMeshSubset> submesh;
-    autoPtr<fvMeshSubset> submeshA;
-    autoPtr<fvMeshSubset> submeshB;
+    
+    /// Submeshes
+    autoPtr<volVectorField> submesh_field;
+    //----------------------------------------------------------------------
+    /// @brief      TODO
+    ///
+    void offlineStage();
 
-    /// Non-repeated submeshes cells (only x coordinates)
-    Eigen::VectorXi nonRepeatedSubmeshes;
+    //----------------------------------------------------------------------
+    /// @brief      TODO
+    ///
+    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+    /// @param[in]  sList  The list of snapshots
+    ///
+    void getModesSVD(SnapshotsTuple &snapshotsTuple, Eigen::MatrixXd &modesSVD, Eigen::VectorXd &fieldWeights);
 
-    /// Non-repeated submeshes cells (only x, y coordinates)
-    Eigen::VectorXi nonRepeatedSubmeshes_xy;
+    //----------------------------------------------------------------------
+    /// @brief      TODO
+    ///
+    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+    /// @param[in]  sList  The list of snapshots
+    ///
+    template <typename SnapshotsList>
+    void stackSnapshots(SnapshotsList sList, Eigen::MatrixXd &snapshotsMatrix, Eigen::VectorXd &fieldWeights);
 
-    void compute_basis();
-                                      
-    void evaluatePinv(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes);
-    
-    voidgenerateSubmeshes(label layers, fvMesh &mesh, label secondTime);
+    //----------------------------------------------------------------------
+    /// @brief      TODO
+    ///
+    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+    /// @param[in]  sList  The list of snapshots
+    ///
+    template <typename SnapshotsList>
+    void stackNames(SnapshotsList sList);
 
-    List<label> global2local(List<label> &points, fvMeshSubset &submesh);
+    //----------------------------------------------------------------------
+    /// @brief      TODO
+    ///
+    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+    /// @param[in]  sList  The list of snapshots
+    ///
+    template <typename SnapshotsList>
+    void stackDimensions(SnapshotsList sList);
 
-    template<typename... SnapshotsLists>
-    void createMasks()
+    //----------------------------------------------------------------------
+    /// @brief      Compute the pseudo-inverse of the matrix M restricted with the projector P
+    ///
+    /// @param[in]  Projector  projector into interpolation nodes
+    /// @param[in]  Modes      matrix to restrict and invert
+    ///
+    void evaluatePinv(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd& fieldWeights);
 
-    template<typename FieldType>
-    void interpolateField(FieldType& field)
+    //----------------------------------------------------------------------
+    /// @brief      Compute the submesh common to all fields in SnapshotsLists
+    ///
+    /// @param[in]  layers          projector into interpolation nodes
+    /// @param[in]  mesh            matrix to restrict and invert
+    ///
+    void generateSubmesh(label layers, fvMesh &mesh);
 
-    template<typename SnapshotsList>
-    void compute_matrix_modes(SnapshotsList sList);
-    template<typename Field>
-    inline constexpr unsigned int get_field_dim(){return std::is_same<typename Field::DimensionedField::FieldType, Foam::scalar>::value? 1: 3;}
+    //----------------------------------------------------------------------
+    /// @brief      Get local indices in the submesh from indices in the global ones
+    ///
+    /// @param      points       The points
+    /// @param      submesh      The submesh
+    ///
+    /// @return     The local indices
+    ///
+    List<label> global2local(List<label> &points, fvMeshSubset &submesh);
+
+    /// @brief      TODO
+    ///
+    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+    /// @param[in]  sList  The list of snapshots
+    ///
+    template <typename FieldType>
+    autoPtr<FieldType> interpolateField(FieldType &field);
 
+    /// @brief      TODO
+    ///
+    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+    /// @param[in]  sList  The list of snapshots
+    ///
+    // TODO expand with sphericalTensor, symmTensor, tensor
+    template <typename Field>
+    inline constexpr unsigned int get_field_dim()
+    {
+        return std::is_same<Field, volScalarField>::value ? 1 : 3;
+    }
+
+    /// @brief      TODO
+    ///
+    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+    /// @param[in]  sList  The list of snapshots
+    ///
     template <typename LastList>
-    inline constexpr unsigned int compute_vectorial_dim(LastList x) {return get_field_dim<typename std::decay_t<LastList>::value_type>();}
+    inline constexpr unsigned int compute_vectorial_dim(LastList x) { return get_field_dim<typename std::decay_t<LastList>::value_type>(); }
 
-    template<typename List, typename... RemainingLists>
-    inline constexpr unsigned int compute_vectorial_dim(List&& head, RemainingLists&&... tail)  {
-        return get_field_dim<typename std::decay_t<List>::value_type>() + compute_vectorial_dim<RemainingLists...>(tail...);}
+    /// @brief      TODO
+    ///
+    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+    /// @param[in]  sList  The list of snapshots
+    ///
+    template <typename List, typename... RemainingLists>
+    inline constexpr unsigned int compute_vectorial_dim(List &&head, RemainingLists &&...tail)
+    {
+        return get_field_dim<typename std::decay_t<List>::value_type>() + compute_vectorial_dim<RemainingLists...>(tail...);
+    }
 };
+
+#endif
diff --git a/src/ITHACA_HR/hyperReduction.templates.H b/src/ITHACA_HR/hyperReduction.templates.H
new file mode 100644
index 000000000..4440caea3
--- /dev/null
+++ b/src/ITHACA_HR/hyperReduction.templates.H
@@ -0,0 +1,488 @@
+/*---------------------------------------------------------------------------*\
+     ██╗████████╗██╗  ██╗ █████╗  ██████╗ █████╗       ███████╗██╗   ██╗
+     ██║╚══██╔══╝██║  ██║██╔══██╗██╔════╝██╔══██╗      ██╔════╝██║   ██║
+     ██║   ██║   ███████║███████║██║     ███████║█████╗█████╗  ██║   ██║
+     ██║   ██║   ██╔══██║██╔══██║██║     ██╔══██║╚════╝██╔══╝  ╚██╗ ██╔╝
+     ██║   ██║   ██║  ██║██║  ██║╚██████╗██║  ██║      ██║      ╚████╔╝
+     ╚═╝   ╚═╝   ╚═╝  ╚═╝╚═╝  ╚═╝ ╚═════╝╚═╝  ╚═╝      ╚═╝       ╚═══╝
+
+ * In real Time Highly Advanced Computational Applications for Finite Volumes
+ * Copyright (C) 2017 by the ITHACA-FV authors
+-------------------------------------------------------------------------------
+
+License
+    This file is part of ITHACA-FV
+
+    ITHACA-FV is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    ITHACA-FV is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU Lesser General Public License for more details.
+
+    You should have received a copy of the GNU Lesser General Public License
+    along with ITHACA-FV. If not, see <http://www.gnu.org/licenses/>.
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef hyperReduction_templates_H
+#define hyperReduction_templates_H
+
+#include "hyperReduction.H"
+
+// Using the Eigen library, using the SVD decomposition method to solve the
+// matrix pseudo-inverse, the default error er is 0
+Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0) {
+  // perform svd decomposition
+  Eigen::JacobiSVD<Eigen::MatrixXd> svd_holder(origin, Eigen::ComputeThinU | Eigen::ComputeThinV);
+  // Build SVD decomposition results
+  Eigen::MatrixXd U = svd_holder.matrixU();
+  Eigen::MatrixXd V = svd_holder.matrixV();
+  Eigen::MatrixXd D = svd_holder.singularValues();
+
+  // Build the S matrix
+  Eigen::MatrixXd S(V.cols(), U.cols());
+  S.setZero();
+
+  for (unsigned int i = 0; i < D.size(); ++i) {
+
+    if (D(i, 0) > er) {
+      S(i, i) = 1 / D(i, 0);
+    } else {
+      S(i, i) = 0;
+    }
+  }
+  return V * S * U.transpose();
+}
+
+template <typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::getModesSVD(
+    SnapshotsTuple& snapshotsTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights)
+{
+  ITHACAparameters* para(ITHACAparameters::getInstance());
+  if (!ITHACAutilities::check_folder(Folder + "/Modes/"))
+  {
+    // Initialize stacked snapshotsMatrix and normalizing weights
+    Eigen::MatrixXd snapMatrix;
+    std::apply([this, &snapMatrix, &fieldWeights](auto& ...snapList){(..., stackSnapshots(snapList, snapMatrix, fieldWeights));}, snapshotsTuple);
+
+    Info << "####### Performing SVD for " << problemName << " #######" << endl;
+
+    Eigen::JacobiSVD<Eigen::MatrixXd> svd(fieldWeights.array().cwiseInverse().matrix().asDiagonal()*snapMatrix,
+                                          Eigen::ComputeThinU | Eigen::ComputeThinV);
+
+    Info << "####### End of SVD for " << problemName << " #######" <<
+          endl;
+
+    Eigen::VectorXd eigenValueseig;
+    Eigen::MatrixXd eigenVectoreig;
+    eigenValueseig = svd.singularValues().real();
+    eigenVectoreig = svd.matrixU().real();
+
+    modesSVD = eigenVectoreig;
+
+    // TODO correct boundary conditions
+
+    eigenValueseig = eigenValueseig / eigenValueseig.sum();
+    Eigen::VectorXd cumEigenValues(eigenValueseig);
+
+    for (label j = 1; j < cumEigenValues.size(); ++j)
+    {
+        cumEigenValues(j) += cumEigenValues(j - 1);
+    }
+
+    mkDir(Folder + "/Modes/");
+    Eigen::saveMarketVector(eigenValueseig,
+                            Folder+"/Modes/Eigenvalues_" + problemName, para->precision,
+                            para->outytpe);
+    Eigen::saveMarketVector(cumEigenValues,
+                            Folder+"/Modes/CumEigenvalues_" + problemName, para->precision,
+                            para->outytpe);
+    cnpy::save(modesSVD, Folder + "/Modes/modes.npy");
+    cnpy::save(fieldWeights, Folder + "/Modes/normalizingWeights.npy");
+  }
+  else
+  {
+    Info << "Reading the existing modes" << endl;
+    cnpy::load(modesSVD, Folder + "/Modes/modes.npy");
+    cnpy::load(fieldWeights, Folder + "/Modes/normalizingWeights.npy");
+  }
+}
+
+// Template function constructor
+template <typename... SnapshotsLists>
+HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
+                                                  label n_nodes,
+                                                  Eigen::VectorXi initialSeeds,
+                                                  word problemName,
+                                                  SnapshotsLists &&...snapshotsLists)
+    : vectorial_dim{compute_vectorial_dim(snapshotsLists...)},
+      n_modes{n_modes},
+      n_nodes{n_nodes},
+      initialSeeds{initialSeeds},
+      problemName{problemName},
+      snapshotsTuple{std::forward_as_tuple(snapshotsLists...)}
+{
+  Info << "Init HyperReduction class with vectorial dim: " << vectorial_dim << endl;
+
+  // TODO check snapshotsLists is not empty
+  // TODO check that the first snapshotsList is not empty (includes above)
+
+  // TODO initialize vectorial_dim only from SnapshotsLists type
+  // vectorial_dim = std::apply(compute_vectorial_dim<SnapshotsLists&&...>, snapshotsTuple);
+
+  // Get fields' names
+  std::apply([this](auto& ...snapList){(..., stackNames(snapList));}, snapshotsTuple);
+
+  // Get fields' dimensions
+  std::apply([this](auto& ...snapList){(..., stackDimensions(snapList));}, snapshotsTuple);
+
+  Info << "Fields names: ";
+  for (unsigned int ith_field = 0; ith_field < fieldNames.size(); ith_field++)
+  {
+    Info << fieldNames[ith_field] << " (dim=" << fieldDims[ith_field] << "); ";
+  }
+  Info << endl;
+  
+  n_snapshots = std::get<0>(snapshotsTuple).size();
+  Info << "The number of snapshots is: " << n_snapshots << endl;
+  n_cells = std::get<0>(snapshotsTuple)[0].size();
+  Info << "The number of cells is: " << n_cells << endl;
+  Info << "Initial seeds length: " << initialSeeds.rows() << endl;
+}
+
+template <typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::offlineStage()
+{
+  ITHACAparameters *para(ITHACAparameters::getInstance());
+  word methodName = para->ITHACAdict->lookupOrDefault<word>("HyperReduction", "GappyDEIM");
+  
+  if (methodName=="GappyDEIM")
+  {
+    Folder = "ITHACAoutput/" + problemName + "/" + methodName;
+    mkDir(Folder);
+
+    nodePoints = autoPtr<IOList<label>>(new IOList<label>(
+        IOobject("nodePoints", para->runTime.time().constant(), "../" + Folder,
+                  para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
+
+    Eigen::MatrixXd snapshotsModes;
+    getModesSVD(snapshotsTuple, snapshotsModes, normalizingWeights);  
+
+    if (!nodePoints().headerOk())
+    {
+        assert(n_modes > 0);
+        assert(n_nodes >= n_modes);
+
+        Eigen::VectorXd mp_not_mask = Eigen::VectorXd::Constant(n_cells * vectorial_dim, 1);
+        std::set<label> nodePointsSet;
+        std::deque<label> nodePointsDeque;
+
+        // set initialSeeds
+        if (initialSeeds.rows() > 0)
+        {
+          Info << "Add initialSeeds\n";
+          P.resize(n_cells * vectorial_dim, initialSeeds.rows() * vectorial_dim);
+          P.reserve(Eigen::VectorXi::Constant(initialSeeds.rows() * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
+
+          for (int i = 0; i < initialSeeds.rows(); i++)
+          {
+            unsigned int index = initialSeeds(i) % n_cells;
+            for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+            {
+              P.insert(index+ith_field*n_cells, vectorial_dim*i+ith_field) = 1;
+              mp_not_mask(index + ith_field * n_cells) = 0;
+            }
+            
+            // check that are not repeated nodes in initialSeeds
+            if (nodePointsSet.find(index) == nodePointsSet.end()){
+              nodePointsSet.insert(index);
+              nodePointsDeque.push_back(index);
+            }
+          }
+
+          P.makeCompressed();
+        }
+
+        int na = n_nodes - initialSeeds.rows();
+        if (na > 0)
+        {
+            int nb = 0;
+            int nit = std::min(n_modes, na);
+            int ncimin = std::floor(n_modes / nit);
+            int naimin = std::floor(na / n_modes);
+
+            Eigen::MatrixXd A;
+            Eigen::VectorXd b;
+            Eigen::VectorXd c;
+            Eigen::VectorXd r;
+            label ind_max, c1;
+
+            double max;
+
+            Info << "####### Begin Greedy GappyDEIM #######" << endl;
+            Info << "####### Modes=" <<  n_modes
+                  << ", nodePoints=" << n_nodes << " #######"
+                  << endl;
+            
+
+
+            Eigen::SparseMatrix<double> reshapeMat;
+            reshapeMat.resize(n_cells, n_cells*vectorial_dim);
+            reshapeMat.reserve(Eigen::VectorXi::Constant(n_cells * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
+
+            for (unsigned int i = 0; i < n_cells; i++)
+            {
+              for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+              {
+                reshapeMat.insert(i, i+n_cells*ith_field) = 1;
+              }
+            }
+              
+            reshapeMat.makeCompressed();
+
+            for (int i = 1; i <= nit; i++)
+            {
+                int nci = ncimin;
+                // add the remaining modes in the quotient n_modes / nite
+                if (i <= n_modes % nit)
+                {
+                    nci = ncimin + 1;
+                }
+                int nai = naimin;
+                // add the remaining nodePoints_xyz in the quotient na / n_modes
+                if (i <= na % n_modes)
+                {
+                    nai = naimin + 1;
+                }
+
+                Eigen::MatrixXd V;
+
+                // select basis
+                if (i == 1)
+                {
+                    V = snapshotsModes.leftCols(nci);
+                }
+                else
+                {
+                  for (int q = 1; q <= nci; q++)
+                  {
+                      A = P.transpose() * basisMatrix;
+                      b = P.transpose() * snapshotsModes.col(nb + q - 1);
+                      c = A.fullPivLu().solve(b);
+                      r = snapshotsModes.col(nb + q - 1) - basisMatrix * c;
+                      V.conservativeResize(snapshotsModes.rows(), q);
+                      V.col(q - 1) = r;
+                  }
+                }
+
+                for (int j = 1; j <= nai; j++)
+                {
+                  
+                  if (P.cols() > 0)
+                  {
+                    max = (reshapeMat*(mp_not_mask.asDiagonal() * V)
+                              .rowwise()
+                              .lpNorm<2>())
+                              .maxCoeff(&ind_max, &c1);
+                  }
+                  else
+                  {
+                    max = V.rowwise().lpNorm<2>().maxCoeff(&ind_max, &c1);
+                  }
+                  int idxes = P.cols();
+                  int maxFirstMesh = ind_max % n_cells;
+                  P.conservativeResize(snapshotsModes.rows(), idxes + vectorial_dim);
+                  
+                  for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+                  {
+                    P.insert(maxFirstMesh + ith_field * n_cells, idxes + ith_field) = 1;
+                    mp_not_mask(maxFirstMesh + ith_field * n_cells) = 0;
+                  }
+
+                  nodePointsDeque.push_back(maxFirstMesh);
+                }
+
+                nb += nci;
+                basisMatrix = snapshotsModes.leftCols(nb);
+            }
+        }
+        else
+        {
+            basisMatrix = snapshotsModes;
+        }
+
+        Info << "####### End of greedy GappyDEIM #######\n";
+        cnpy::save(basisMatrix, Folder +"/basisMatrix.npy");
+        cnpy::save(P, Folder +"/projectionMatrix.npy");
+        Info << "Projection Matrix shape: " << P.rows() << " " << P.cols() << endl;
+        Info << "Basis Matrix shape: " << basisMatrix.rows() << " " << basisMatrix.cols() << endl;
+
+        evaluatePinv(P, basisMatrix, normalizingWeights);
+        renormalizedBasisMatrix = normalizingWeights.asDiagonal()*basisMatrix;
+        Info << "Pseudo Inverse Matrix shape: " << pinvPU.rows() << " " << pinvPU.cols() << endl;
+
+        // convert nodePointsSet to nodePoints i.e. list
+        Eigen::VectorXi nodes(nodePointsDeque.size());
+        unsigned int i{0};
+        for (auto &x : nodePointsDeque)
+        {
+          nodePoints().append(x);
+          nodes(i) = x;
+          i++;
+        }
+        cnpy::save(nodes, Folder + "/mp.npy");
+        cnpy::save(pinvPU, Folder + "/pinvPU.npy");
+        nodePoints().write();
+    }
+    else
+    {
+        cnpy::load(pinvPU, Folder + "/pinvPU.npy");
+        cnpy::load(basisMatrix, Folder +"/basisMatrix.npy");
+    }
+  }
+  else
+  {
+    Info << "Offline stage not performed. Invalid HR method.\n";
+  }
+}
+
+template <typename... SnapshotsLists>
+template <typename SnapshotsList>
+void HyperReduction<SnapshotsLists...>::stackSnapshots(SnapshotsList sList, Eigen::MatrixXd& snapshotsMatrix, Eigen::VectorXd& fieldWeights)
+{
+  Info << "####### Compute hyper-reduction basis #######\n";
+
+  unsigned int field_dim = get_field_dim<typename SnapshotsList::value_type>();
+
+  Eigen::MatrixXd tmpSnapshots = Foam2Eigen::PtrList2Eigen(sList);
+  auto fieldName = sList[0].name();
+
+  double maxVal = std::sqrt(tmpSnapshots.colwise().lpNorm<2>().maxCoeff());
+
+  // get volumes
+  Eigen::VectorXd V = ITHACAutilities::getMassMatrixFV(sList[0]);
+
+  fieldWeights.conservativeResize(fieldWeights.rows()+field_dim*n_cells);
+  fieldWeights.tail(n_cells * field_dim) = V.array().sqrt().cwiseInverse()*maxVal;
+
+  snapshotsMatrix.conservativeResize(snapshotsMatrix.rows() + n_cells * field_dim, n_snapshots);
+  snapshotsMatrix.bottomRows(n_cells * field_dim) = tmpSnapshots;
+
+  Info << "####### End of computing hyper-reduction basis #######\n";
+}
+
+template <typename... SnapshotsLists>
+template<typename SnapshotsList>
+void HyperReduction<SnapshotsLists...>::stackNames(SnapshotsList sList)
+{
+  fieldNames.append(sList[0].name());
+}
+
+template <typename... SnapshotsLists>
+template<typename SnapshotsList>
+void HyperReduction<SnapshotsLists...>::stackDimensions(SnapshotsList sList)
+{
+  fieldDims.append(get_field_dim<typename SnapshotsList::value_type>());
+}
+
+template<typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::evaluatePinv(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd &fieldWeights) {
+  assert(Projector.cols() > 0);
+  Eigen::MatrixXd restricted = Projector.transpose() * Modes;
+  pinvPU = pinv_eigen_based(restricted);
+  pinvPU = pinvPU*(Projector.transpose() * fieldWeights.array().cwiseInverse().matrix()).asDiagonal();
+}
+
+template<typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::generateSubmesh(label layers, fvMesh &mesh) {
+
+  Info << "####### Extract submesh #######\n";
+  ITHACAparameters *para(ITHACAparameters::getInstance());
+
+  totalNodePoints = autoPtr<IOList<labelList>>(new IOList<labelList>(IOobject(
+      "totalNodePoints", para->runTime.time().constant(),  "../" + Folder,
+      para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
+
+  uniqueNodePoints = autoPtr<IOList<label>>(new IOList<label>(IOobject(
+      "uniqueNodePoints", para->runTime.time().constant(),  "../" + Folder,
+      para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
+
+  volScalarField Indici
+  (
+      IOobject
+      (
+        problemName + "_indices",
+        mesh.time().timeName(),
+        mesh,
+        IOobject::NO_READ,
+        IOobject::NO_WRITE
+      ),
+      mesh,
+      dimensionedScalar(problemName + "_indices",
+                        dimensionSet(0, 0, 0, 0, 0, 0, 0), 0.0));
+
+  submesh = autoPtr<fvMeshSubset>(new fvMeshSubset(mesh));
+
+  if (!totalNodePoints().headerOk()) {
+    List<label> indices;
+    for (label i = 0; i < nodePoints().size(); i++) {
+      indices = ITHACAutilities::getIndices(mesh, nodePoints()[i], layers);
+      totalNodePoints().append(indices);
+    }
+
+    labelList a = ListListOps::combine<labelList>(totalNodePoints(),
+                                                  accessOp<labelList>());
+
+    inplaceUniqueSort(a);
+    uniqueNodePoints() = a;
+
+    scalar zerodot25 = 0.25;
+    ITHACAutilities::assignIF(Indici, zerodot25,
+                              uniqueNodePoints().List<label>::clone()());
+    ITHACAutilities::assignONE(Indici, nodePoints());
+
+    totalNodePoints().write();
+    uniqueNodePoints().write();
+  }
+
+  submesh->setCellSubset(uniqueNodePoints());
+  submesh->subMesh().fvSchemes::readOpt() = mesh.fvSchemes::readOpt();
+  submesh->subMesh().fvSolution::readOpt() = mesh.fvSolution::readOpt();
+  submesh->subMesh().fvSchemes::read();
+  submesh->subMesh().fvSolution::read();
+  std::cout.clear();
+
+  localNodePoints = global2local(nodePoints(), submesh());
+  ITHACAstream::exportSolution(Indici, "1", Folder);
+
+  n_cellsSubfields = submesh().cellMap().size();
+  Info << "####### End extract submesh #######\n";
+}
+
+template<typename... SnapshotsLists>
+List<label> HyperReduction<SnapshotsLists...>::global2local(List<label> &points, fvMeshSubset &submesh) {
+  List<label> localPoints;
+
+  for (label i = 0; i < points.size(); i++) {
+    for (label j = 0; j < submesh.cellMap().size(); j++) {
+      if (submesh.cellMap()[j] == points[i]) {
+        localPoints.append(j);
+        break;
+      }
+    }
+  }
+
+  return localPoints;
+}
+
+template<typename... SnapshotsLists>
+template<typename FieldType>
+autoPtr<FieldType> HyperReduction<SnapshotsLists...>::interpolateField(FieldType& field) {
+    return autoPtr<FieldType>(new FieldType(submesh->interpolate(field)));
+}
+
+#endif
diff --git a/tutorials/CFD/24HyperReduction/.gitignore b/tutorials/CFD/24HyperReduction/.gitignore
new file mode 100755
index 000000000..458c052a5
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/.gitignore
@@ -0,0 +1,2 @@
+ITHACAoutput
+*.dep
diff --git a/tutorials/CFD/24HyperReduction/0/ITHACAOutput/DEIM/S b/tutorials/CFD/24HyperReduction/0/ITHACAOutput/DEIM/S
new file mode 100755
index 000000000..744a5791c
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/0/ITHACAOutput/DEIM/S
@@ -0,0 +1,25053 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  5.0                                   |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       volScalarField;
+    location    "0";
+    object      S;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dimensions      [0 0 -1 1 0 0 0];
+
+internalField   nonuniform List<scalar> 
+25000
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+0.6361
+0.618477
+0.601153
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+0.377885
+0.365435
+0.353283
+0.341425
+0.32986
+2.19571
+2.18824
+2.1801
+2.1713
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+2.15173
+2.14099
+2.12962
+2.11764
+2.10505
+2.09187
+2.07812
+2.0638
+2.04893
+2.03352
+2.01759
+2.00114
+1.98421
+1.96679
+1.94891
+1.93058
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+1.85311
+1.83278
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+1.72627
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+1.61321
+1.59
+1.56663
+1.54312
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+1.49575
+1.47192
+1.44801
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+1.40003
+1.376
+1.35195
+1.3279
+1.30388
+1.27989
+1.25594
+1.23206
+1.20825
+1.18453
+1.16091
+1.1374
+1.11402
+1.09078
+1.06769
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+1.022
+0.999424
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+0.93288
+0.911125
+0.889598
+0.868306
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+0.785635
+0.765625
+0.745888
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+0.669784
+0.651489
+0.633493
+0.615799
+0.59841
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+0.564555
+0.548091
+0.531939
+0.516098
+0.500571
+0.485356
+0.470453
+0.455863
+0.441585
+0.427618
+0.41396
+0.40061
+0.387567
+0.374829
+0.362393
+0.350257
+0.33842
+)
+;
+
+boundaryField
+{
+    inlet
+    {
+        type            calculated;
+        value           uniform 0;
+    }
+    outlet
+    {
+        type            calculated;
+        value           uniform 0;
+    }
+    frontAndBack
+    {
+        type            empty;
+    }
+    inlet2
+    {
+        type            calculated;
+        value           uniform 0;
+    }
+    walls
+    {
+        type            calculated;
+        value           uniform 0;
+    }
+}
+
diff --git a/tutorials/CFD/24HyperReduction/0/T b/tutorials/CFD/24HyperReduction/0/T
new file mode 100755
index 000000000..a22633412
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/0/T
@@ -0,0 +1,48 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  5.0                                   |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       volScalarField;
+    location    "0";
+    object      T;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dimensions      [0 0 0 1 0 0 0];
+
+internalField   uniform 0;
+
+boundaryField
+{
+    inlet
+    {
+        type            fixedValue;
+        value           uniform 0;
+    }
+    inlet2
+    {
+        type            fixedValue;
+        value           uniform 50;
+    }
+
+    outlet
+    {
+        type            zeroGradient;
+    }
+    frontAndBack
+    {
+        type            empty;
+    }
+    walls
+    {
+        type            zeroGradient;
+    }
+}
+
diff --git a/tutorials/CFD/24HyperReduction/0/U b/tutorials/CFD/24HyperReduction/0/U
new file mode 100755
index 000000000..933054195
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/0/U
@@ -0,0 +1,48 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  5.0                                   |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       volVectorField;
+    location    "0";
+    object      T;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dimensions      [0 0 0 1 0 0 0];
+
+internalField   uniform (0 0 0);
+
+boundaryField
+{
+    inlet
+    {
+        type            fixedValue;
+        value           uniform (10 1 0);
+    }
+    inlet2
+    {
+        type            fixedValue;
+        value           uniform (5 0.5 0);
+    }
+
+    outlet
+    {
+        type            zeroGradient;
+    }
+    frontAndBack
+    {
+        type            empty;
+    }
+    walls
+    {
+        type            zeroGradient;
+    }
+}
+
diff --git a/tutorials/CFD/24HyperReduction/24HyperReduction.C b/tutorials/CFD/24HyperReduction/24HyperReduction.C
new file mode 100644
index 000000000..d7266ea65
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/24HyperReduction.C
@@ -0,0 +1,451 @@
+/*---------------------------------------------------------------------------*\
+     ██╗████████╗██╗  ██╗ █████╗  ██████╗ █████╗       ███████╗██╗   ██╗
+     ██║╚══██╔══╝██║  ██║██╔══██╗██╔════╝██╔══██╗      ██╔════╝██║   ██║
+     ██║   ██║   ███████║███████║██║     ███████║█████╗█████╗  ██║   ██║
+     ██║   ██║   ██╔══██║██╔══██║██║     ██╔══██║╚════╝██╔══╝  ╚██╗ ██╔╝
+     ██║   ██║   ██║  ██║██║  ██║╚██████╗██║  ██║      ██║      ╚████╔╝
+     ╚═╝   ╚═╝   ╚═╝  ╚═╝╚═╝  ╚═╝ ╚═════╝╚═╝  ╚═╝      ╚═╝       ╚═══╝
+
+ * In real Time Highly Advanced Computational Applications for Finite Volumes
+ * Copyright (C) 2017 by the ITHACA-FV authors
+-------------------------------------------------------------------------------
+License
+    This file is part of ITHACA-FV
+    ITHACA-FV is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+    ITHACA-FV is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU Lesser General Public License for more details.
+    You should have received a copy of the GNU Lesser General Public License
+    along with ITHACA-FV. If not, see <http://www.gnu.org/licenses/>.
+Description
+    Example of the reconstruction of a non-linear function using the HyperReduction
+SourceFiles
+    24HyperReduction.C
+\*---------------------------------------------------------------------------*/
+
+#include "fvCFD.H"
+#include "fvOptions.H"
+#include "simpleControl.H"
+#include "simpleControl.H"
+#include "fvMeshSubset.H"
+#include "ITHACAutilities.H"
+#include "Foam2Eigen.H"
+#include "ITHACAstream.H"
+#include "ITHACAPOD.H"
+#include "hyperReduction.templates.H"
+#include <chrono>
+
+class HyperReduction_function : public HyperReduction<PtrList<volScalarField>&>
+{
+    public:
+    using HyperReduction::HyperReduction;
+        static volScalarField evaluate_expression(volScalarField& S, Eigen::MatrixXd mu)
+        {
+            volScalarField yPos = S.mesh().C().component(vector::Y).ref();
+            volScalarField xPos = S.mesh().C().component(vector::X).ref();
+
+            for (auto i = 0; i < S.size(); i++)
+            {
+                S[i] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1,
+                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
+            }
+
+            return S;
+        }
+
+        static Eigen::VectorXd evaluate_expression(volScalarField& S, Eigen::MatrixXd mu, List<label> nodesList)
+        {
+            Eigen::VectorXd ret(nodesList.size());
+            volScalarField yPos = S.mesh().C().component(vector::Y).ref();
+            volScalarField xPos = S.mesh().C().component(vector::X).ref();
+
+            for (auto i = 0; i < nodesList.size(); i++)
+            {
+                ret[i] = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
+                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
+            }
+
+            return ret;
+        }
+        
+        Eigen::VectorXd onlineCoeffs(volScalarField& S, Eigen::MatrixXd mu, volScalarField& SS)
+        {
+            Eigen::VectorXd f = evaluate_expression(S, mu, localNodePoints);
+            return pinvPU*f;
+        }
+
+};
+
+class HyperReduction_vectorFunction : public HyperReduction<PtrList<volVectorField>&>
+{
+    public:
+    using HyperReduction::HyperReduction;
+        static volVectorField evaluate_expression(volVectorField& S, Eigen::MatrixXd mu)
+        {
+            volScalarField yPos = S.mesh().C().component(vector::Y).ref();
+            volScalarField xPos = S.mesh().C().component(vector::X).ref();
+
+            for (auto i = 0; i < S.size(); i++)
+            {
+                S[i][0] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1,
+                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
+                S[i][1] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 0.5,
+                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
+                S[i][2] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1.5,
+                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0., 2));
+            }
+
+            return S;
+        }
+
+        static Eigen::VectorXd evaluate_expression(volVectorField& S, Eigen::MatrixXd mu, List<label> nodesList)
+        {
+            Eigen::VectorXd ret(nodesList.size()*3);
+            volScalarField yPos = S.mesh().C().component(vector::Y).ref();
+            volScalarField xPos = S.mesh().C().component(vector::X).ref();
+
+            for (auto i = 0; i < nodesList.size(); i++)
+            {
+                ret(i*3) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
+                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
+                ret(i*3 + 1) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 0.5,
+                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
+                ret(i*3 + 2) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1.5,
+                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0., 2));
+            }
+
+            return ret;
+        }
+        
+        Eigen::VectorXd onlineCoeffs(volVectorField& S, Eigen::MatrixXd mu)
+        {
+            Eigen::VectorXd f = evaluate_expression(S, mu, localNodePoints);
+            return pinvPU*f;
+        }
+
+};
+
+class HyperReduction_vectorScalarFunction : public HyperReduction<PtrList<volVectorField>&, PtrList<volScalarField>&>
+{
+    public:
+    using HyperReduction::HyperReduction;
+        static std::pair<volVectorField, volScalarField> evaluate_expression(volVectorField& V, volScalarField& S, Eigen::MatrixXd mu)
+        {
+            volScalarField yPos = S.mesh().C().component(vector::Y).ref();
+            volScalarField xPos = S.mesh().C().component(vector::X).ref();
+
+            for (auto i = 0; i < S.size(); i++)
+            {
+                V[i][0] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1,
+                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
+                V[i][1] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 0.5,
+                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
+                V[i][2] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1.5,
+                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0., 2));
+                S[i] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1,
+                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
+            }
+
+            return std::make_pair(V, S);
+        }
+
+        static Eigen::VectorXd evaluate_expression(volScalarField& S, Eigen::MatrixXd mu, List<label> nodesList)
+        {
+            Eigen::VectorXd ret(nodesList.size()*4);
+            volScalarField yPos = S.mesh().C().component(vector::Y).ref();
+            volScalarField xPos = S.mesh().C().component(vector::X).ref();
+
+            for (auto i = 0; i < nodesList.size(); i++)
+            {
+                ret(i*4) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
+                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
+                ret(i*4 + 1) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 0.5,
+                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
+                ret(i*4 + 2) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1.5,
+                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0., 2));
+                ret(i*4 + 3) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
+                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
+            }
+
+            return ret;
+        }
+        
+        Eigen::VectorXd onlineCoeffs(volScalarField& S, Eigen::MatrixXd mu)
+        {
+            Eigen::VectorXd f = evaluate_expression(S, mu, localNodePoints);
+            return pinvPU*f;
+        }
+
+};
+
+void test_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime){
+    int n_modes = para->ITHACAdict->lookupOrDefault<int>("Modes", 15);
+    int n_nodes = para->ITHACAdict->lookupOrDefault<int>("Nodes", 15);
+    simpleControl simple(mesh);
+
+#include "createFields.H"
+    // List of volScalarField where the snapshots are stored
+    PtrList<volScalarField> Sp;
+    // Non linear function
+    volScalarField S
+    (
+        IOobject
+        (
+            "S",
+            runTime.timeName(),
+            mesh,
+            IOobject::NO_READ,
+            IOobject::AUTO_WRITE
+        ),
+        T.mesh(),
+        dimensionedScalar("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), 0)
+    );
+    // Parameters used to train the non-linear function
+    Eigen::MatrixXd pars = ITHACAutilities::rand(100, 2, -0.5, 0.5);
+
+    // Perform the offline phase
+    for (int i = 0; i < 100; i++)
+    {
+        HyperReduction_function::evaluate_expression(S, pars.row(i));
+        Sp.append((S).clone());
+        ITHACAstream::exportSolution(S, name(i + 1), "./ITHACAoutput/Offline/");
+    }
+
+    // Create HyperReduction object with given number of basis functions
+    Eigen::VectorXi initSeeds(0);
+
+    HyperReduction_function c(n_modes, n_nodes, initSeeds, "Gaussian_function", Sp);
+    c.offlineStage();
+
+    // Generate the submeshes with the depth of the layer
+    c.generateSubmesh(2, mesh);
+    auto sfield = c.interpolateField<volScalarField>(Sp[0]);
+    // Define a new online parameter
+    Eigen::MatrixXd par_new(2, 1);
+    par_new(0, 0) = 0;
+    par_new(1, 0) = 0;
+    // Online evaluation of the non linear function
+    Eigen::VectorXd aprfield = c.renormalizedBasisMatrix*c.onlineCoeffs(sfield(), par_new, Sp[0]);
+    // Transform to an OpenFOAM field and export
+    volScalarField S2("S_online", Foam2Eigen::Eigen2field(S, aprfield));
+    ITHACAstream::exportSolution(S2, name(1), "./ITHACAoutput/Online/");
+    // Evaluate the full order function and export it
+    HyperReduction_function::evaluate_expression(S, par_new);
+    ITHACAstream::exportSolution(S, name(1), "./ITHACAoutput/Online/");
+    // Compute the L2 error and print it
+    Info << ITHACAutilities::errorL2Rel(S2, S) << endl;
+}
+
+void test_vector(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime){
+    int n_modes = para->ITHACAdict->lookupOrDefault<int>("Modes", 15);
+    int n_nodes = para->ITHACAdict->lookupOrDefault<int>("Nodes", 15);
+    simpleControl simple(mesh);
+
+#include "createFields.H"
+    // List of volVectorField where the snapshots are stored
+    PtrList<volVectorField> Sp;
+    // Non linear function
+    volVectorField S
+    (
+        IOobject
+        (
+            "S",
+            runTime.timeName(),
+            mesh,
+            IOobject::NO_READ,
+            IOobject::AUTO_WRITE
+        ),
+        T.mesh(),
+        dimensionedVector("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), vector(0, 0, 0))
+    );
+    // Parameters used to train the non-linear function
+    Eigen::MatrixXd pars = ITHACAutilities::rand(100, 2, -0.5, 0.5);
+
+    // Perform the offline phase
+    for (int i = 0; i < 100; i++)
+    {
+        HyperReduction_vectorFunction::evaluate_expression(S, pars.row(i));
+        Sp.append((S).clone());
+        ITHACAstream::exportSolution(S, name(i + 1), "./ITHACAoutput/Offline/");
+    }
+
+    // Create HyperReduction object with given number of basis functions
+    Eigen::VectorXi initSeeds(0);
+
+    HyperReduction_vectorFunction c(n_modes, n_nodes, initSeeds, "Gaussian_function", Sp);
+    c.offlineStage();
+
+    // Generate the submeshes with the depth of the layer
+    c.generateSubmesh(2, mesh);
+    auto sfield = c.interpolateField<volVectorField>(Sp[0]);
+    // Define a new online parameter
+    Eigen::MatrixXd par_new(2, 1);
+    par_new(0, 0) = 0;
+    par_new(1, 0) = 0;
+    // Online evaluation of the non linear function
+    Eigen::VectorXd aprfield = c.renormalizedBasisMatrix*c.onlineCoeffs(sfield(), par_new);
+    // Transform to an OpenFOAM field and export
+    volVectorField S2("S_online", Foam2Eigen::Eigen2field(S, aprfield));
+    ITHACAstream::exportSolution(S2, name(1), "./ITHACAoutput/Online/");
+    // Evaluate the full order function and export it
+    HyperReduction_vectorFunction::evaluate_expression(S, par_new);
+    ITHACAstream::exportSolution(S, name(1), "./ITHACAoutput/Online/");
+    // Compute the L2 error and print it
+    Info << ITHACAutilities::errorL2Rel(S2, S) << endl;
+
+    Eigen::VectorXd vec = c.renormalizedBasisMatrix.col(2);
+    S = S*0;
+    S = Foam2Eigen::Eigen2field(S, vec);
+    ITHACAstream::exportSolution(S, name(1), "./basis/");
+}
+
+void test_vector_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime){
+    int n_modes = para->ITHACAdict->lookupOrDefault<int>("Modes", 15);
+    int n_nodes = para->ITHACAdict->lookupOrDefault<int>("Nodes", 15);
+    simpleControl simple(mesh);
+
+#include "createFields.H"
+    // List of volVectorField where the snapshots are stored
+    PtrList<volVectorField> Vp;
+    PtrList<volScalarField> Sp;
+    // Non linear function
+    volVectorField V
+    (
+        IOobject
+        (
+            "V",
+            runTime.timeName(),
+            mesh,
+            IOobject::NO_READ,
+            IOobject::AUTO_WRITE
+        ),
+        T.mesh(),
+        dimensionedVector("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), vector(0, 0, 0))
+    );
+    // Non linear function
+    volScalarField S
+    (
+        IOobject
+        (
+            "S",
+            runTime.timeName(),
+            mesh,
+            IOobject::NO_READ,
+            IOobject::AUTO_WRITE
+        ),
+        T.mesh(),
+        dimensionedScalar("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), 0)
+    );
+
+    // Parameters used to train the non-linear function
+    Eigen::MatrixXd pars = ITHACAutilities::rand(100, 2, -0.5, 0.5);
+
+    // Perform the offline phase
+    for (int i = 0; i < 100; i++)
+    {
+        HyperReduction_vectorScalarFunction::evaluate_expression(V, S, pars.row(i));
+        Vp.append((V).clone());
+        Sp.append((S).clone());
+        ITHACAstream::exportSolution(S, name(i + 1), "./ITHACAoutput/Offline/");
+        ITHACAstream::exportSolution(V, name(i + 1), "./ITHACAoutput/Offline/");
+    }
+
+    // Create HyperReduction object with given number of basis functions
+    Eigen::VectorXi initSeeds(0);
+
+    HyperReduction_vectorScalarFunction c(n_modes, n_nodes, initSeeds, "Gaussian_function", Vp, Sp);
+    c.offlineStage();
+
+    // Generate the submeshes with the depth of the layer
+    c.generateSubmesh(2, mesh);
+    auto vfield = c.interpolateField<volVectorField>(Vp[0]);
+    auto sfield = c.interpolateField<volScalarField>(Sp[0]);
+    // Define a new online parameter
+    Eigen::MatrixXd par_new(2, 1);
+    par_new(0, 0) = 0;
+    par_new(1, 0) = 0;
+    // Online evaluation of the non linear function
+    auto theta = c.onlineCoeffs(sfield(), par_new);
+    Eigen::VectorXd aprfield = c.renormalizedBasisMatrix*theta;
+    // Transform to an OpenFOAM field and export
+    Eigen::VectorXd recvec = aprfield.head(3*S.size());
+    Eigen::VectorXd recsca = aprfield.tail(S.size());
+    volVectorField V2("V_online", Foam2Eigen::Eigen2field(V, recvec));
+    volScalarField S2("S_online", Foam2Eigen::Eigen2field(S, recsca));
+
+    ITHACAstream::exportSolution(V2, name(1), "./ITHACAoutput/Online/");
+    ITHACAstream::exportSolution(S2, name(1), "./ITHACAoutput/Online/");
+    // Evaluate the full order function and export it
+    HyperReduction_vectorScalarFunction::evaluate_expression(V, S, par_new);
+    ITHACAstream::exportSolution(V, name(1), "./ITHACAoutput/Online/");
+    ITHACAstream::exportSolution(S, name(1), "./ITHACAoutput/Online/");
+    // Compute the L2 error and print it
+    Info << "Scalar L2 error: " << ITHACAutilities::errorL2Rel(S2, S) << endl;
+    Info << "Vector L2 error: " << ITHACAutilities::errorL2Rel(V2, V) << endl;
+}
+
+int main(int argc, char* argv[])
+{
+    // load stage to perform
+    argList::addOption("test", "scalar", "Perform scalar test");
+    argList::addOption("test", "vector", "Perform vector test");
+    argList::addOption("test", "vs", "Perform (vector, scalar) test");
+    // add options for parallel run
+    HashTable<string> validParOptions;
+    validParOptions.set
+    (
+        "test",
+        "scalar"
+    );
+    validParOptions.set
+    (
+        "test",
+        "vector"
+    );
+    validParOptions.set
+    (
+        "test",
+        "vs"
+    );
+
+    // Read parameters from ITHACAdict file
+#include "setRootCase.H"
+    Foam::Time runTime(Foam::Time::controlDictName, args);
+    Foam::fvMesh mesh
+    (
+        Foam::IOobject
+        (
+            Foam::fvMesh::defaultRegion,
+            runTime.timeName(),
+            runTime,
+            Foam::IOobject::MUST_READ
+        )
+    );
+    ITHACAparameters* para = ITHACAparameters::getInstance(mesh, runTime);
+
+    if (args.get("test").match("scalar"))
+    {   
+        Info << "Init scalar testcase\n";
+        test_scalar(para, mesh, runTime);
+    }
+    else if (args.get("test").match("vector"))
+    {
+        Info << "Init vector testcase\n";
+        test_vector(para, mesh, runTime);
+    }
+    else if (args.get("test").match("vs"))
+    {
+        Info << "Init vector scalar testcase\n";
+        test_vector_scalar(para, mesh, runTime);
+    }
+    else
+    {
+        Info << "Pass '-test scalar', '-test vector', '-test vs'" << endl;
+    }
+    
+    return 0;
+}
\ No newline at end of file
diff --git a/tutorials/CFD/24HyperReduction/Allclean b/tutorials/CFD/24HyperReduction/Allclean
new file mode 100755
index 000000000..b6c23a2ab
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/Allclean
@@ -0,0 +1,11 @@
+#!/bin/sh
+cd ${0%/*} || exit 1    # Run from this directory
+
+. $WM_PROJECT_DIR/bin/tools/RunFunctions
+
+# Source tutorial clean functions
+. $WM_PROJECT_DIR/bin/tools/CleanFunctions
+
+rm -r ITHACAoutput
+rm -r *.foam
+rm log.*
diff --git a/tutorials/CFD/24HyperReduction/Allrun b/tutorials/CFD/24HyperReduction/Allrun
new file mode 100755
index 000000000..d5b3083d6
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/Allrun
@@ -0,0 +1,7 @@
+#!/bin/sh
+cd ${0%/*} || exit 1    # Run from this directory
+
+# Source tutorial run functions
+. $WM_PROJECT_DIR/bin/tools/RunFunctions
+
+runApplication 24HyperReduction
diff --git a/tutorials/CFD/24HyperReduction/Make/.gitignore b/tutorials/CFD/24HyperReduction/Make/.gitignore
new file mode 100755
index 000000000..700e99f27
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/Make/.gitignore
@@ -0,0 +1 @@
+linux*
diff --git a/tutorials/CFD/24HyperReduction/Make/files b/tutorials/CFD/24HyperReduction/Make/files
new file mode 100644
index 000000000..3184b3373
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/Make/files
@@ -0,0 +1,3 @@
+24HyperReduction.C
+
+EXE = $(FOAM_USER_APPBIN)/24HyperReduction
diff --git a/tutorials/CFD/24HyperReduction/Make/options b/tutorials/CFD/24HyperReduction/Make/options
new file mode 100644
index 000000000..7d4e0e960
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/Make/options
@@ -0,0 +1,47 @@
+EXE_INC = \
+    -I$(LIB_SRC)/TurbulenceModels/turbulenceModels/lnInclude \
+    -I$(LIB_SRC)/TurbulenceModels/incompressible/lnInclude \
+    -I$(LIB_SRC)/transportModels \
+    -I$(LIB_SRC)/transportModels/incompressible/singlePhaseTransportModel \
+    -I$(LIB_SRC)/transportModels/incompressible/viscosityModels/viscosityModel \
+    -I$(LIB_SRC)/finiteVolume/lnInclude \
+    -I$(LIB_SRC)/meshTools/lnInclude \
+    -I$(LIB_SRC)/sampling/lnInclude \
+    -I$(LIB_SRC)/fvOptions/lnInclude \
+    -I$(LIB_SRC)/fileFormats/lnInclude \
+    -I$(LIB_SRC)/dynamicMesh/lnInclude \
+    -I$(LIB_SRC)/thermophysicalModels/basic/lnInclude \
+    -I$(LIB_SRC)/turbulenceModels/compressible/turbulenceModel \
+    -I$(LIB_SRC)/functionObjects/forces/lnInclude \
+    -I$(LIB_ITHACA_SRC)/ITHACA_HR \
+    -I$(LIB_ITHACA_SRC)/ITHACA_FOMPROBLEMS/lnInclude \
+    -I$(LIB_ITHACA_SRC)/ITHACA_ROMPROBLEMS/lnInclude \
+    -I$(LIB_ITHACA_SRC)/ITHACA_CORE/lnInclude \
+    -I$(LIB_ITHACA_SRC)/thirdparty/Eigen \
+    -I$(LIB_ITHACA_SRC)/thirdparty/spectra/include \
+    -I$(LIB_ITHACA_SRC)/ITHACA_THIRD_PARTY/splinter/include \
+    -Wno-comment \
+    -w \
+    -DOFVER=$${WM_PROJECT_VERSION%.*} \
+    -std=c++17
+
+
+EXE_LIBS = \
+    -lturbulenceModels \
+    -lfiniteVolume \
+    -ldynamicMesh \
+    -lmeshTools \
+    -lfvOptions \
+    -lsampling \
+    -lfluidThermophysicalModels \
+    -lradiationModels \
+    -lspecie \
+    -lforces \
+    -lfileFormats \
+    -L$(FOAM_USER_LIBBIN) \
+    -lITHACA_FOMPROBLEMS \
+    -lITHACA_ROMPROBLEMS \
+    -lITHACA_THIRD_PARTY \
+    -lITHACA_CORE \
+    -lITHACA_DEIM
+
diff --git a/tutorials/CFD/24HyperReduction/constant/polyMesh/blockMeshDict b/tutorials/CFD/24HyperReduction/constant/polyMesh/blockMeshDict
new file mode 100755
index 000000000..b589abcb2
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/constant/polyMesh/blockMeshDict
@@ -0,0 +1,91 @@
+FoamFile
+{
+version 2.0;
+format ascii;
+class dictionary;
+object blockMeshDict;
+}
+convertToMeters 1;
+vertices
+(
+    (0 0 0)
+    (1 0 0)
+    (1 -.5 0)
+    (2 -.5 0)
+    (2 0 0)
+    (2 1 0)
+    (1 1 0)
+    (0 1 0)
+    (0 0 0.1)
+    (1 0 0.1)
+    (1 -.5 0.1)
+    (2 -.5 0.1)
+    (2 0 0.1)
+    (2 1 0.1)
+    (1 1 0.1)
+    (0 1 0.1)
+);
+blocks
+(
+    hex (0 1 6 7 8 9 14 15) (100 100 1) simpleGrading (1 1 1)
+    hex (1 4 5 6 9 12 13 14) (100 100 1) simpleGrading (1 1 1)
+    hex (2 3 4 1 10 11 12 9) (100 50 1) simpleGrading (1 1 1)
+);
+edges
+(
+);
+boundary
+(
+    inlet
+    {
+        type patch;
+        faces
+        (
+            (0 8 15 7)
+        );
+    }
+    outlet
+    {
+        type patch;
+        faces
+        (
+            (3 11 12 4)
+            (4 12 13 5)
+        );
+    }
+    frontAndBack
+    {
+        type empty;
+        faces
+        (
+            (0 1 6 7)
+            (8 9 14 15)
+            (2 3 4 1)
+            (10 11 12 9)
+            (1 4 5 6)
+	        (9 12 13 14)
+        );
+    }
+    inlet2
+    {
+        type patch;
+        faces
+        (
+        	(2 10 9 1)
+        );
+    }
+    walls
+    {
+        type wall;
+        faces
+        (
+	(0 1 9 8)
+	(2 3 11 10)
+	(7 6 14 15)
+	(6 5 13 14)
+        );
+     }
+);
+mergePatchPairs
+(
+);
diff --git a/tutorials/CFD/24HyperReduction/constant/polyMesh/boundary b/tutorials/CFD/24HyperReduction/constant/polyMesh/boundary
new file mode 100755
index 000000000..e18baa99f
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/constant/polyMesh/boundary
@@ -0,0 +1,54 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  5.0                                   |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       polyBoundaryMesh;
+    location    "constant/polyMesh";
+    object      boundary;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+5
+(
+    inlet
+    {
+        type            patch;
+        nFaces          100;
+        startFace       49650;
+    }
+    outlet
+    {
+        type            patch;
+        nFaces          150;
+        startFace       49750;
+    }
+    frontAndBack
+    {
+        type            empty;
+        inGroups        1(empty);
+        nFaces          50000;
+        startFace       49900;
+    }
+    inlet2
+    {
+        type            patch;
+        nFaces          50;
+        startFace       99900;
+    }
+    walls
+    {
+        type            wall;
+        inGroups        1(wall);
+        nFaces          400;
+        startFace       99950;
+    }
+)
+
+// ************************************************************************* //
diff --git a/tutorials/CFD/24HyperReduction/constant/polyMesh/faces b/tutorials/CFD/24HyperReduction/constant/polyMesh/faces
new file mode 100755
index 000000000..628cac3b0
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/constant/polyMesh/faces
@@ -0,0 +1,100374 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  5.0                                   |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       faceList;
+    location    "constant/polyMesh";
+    object      faces;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+
+100350
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+
+
+// ************************************************************************* //
diff --git a/tutorials/CFD/24HyperReduction/constant/polyMesh/neighbour b/tutorials/CFD/24HyperReduction/constant/polyMesh/neighbour
new file mode 100755
index 000000000..695505f8e
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/constant/polyMesh/neighbour
@@ -0,0 +1,49675 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  5.0                                   |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       labelList;
+    note        "nPoints: 50702 nCells: 25000 nFaces: 100350 nInternalFaces: 49650";
+    location    "constant/polyMesh";
+    object      neighbour;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+
+49650
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+
+
+// ************************************************************************* //
diff --git a/tutorials/CFD/24HyperReduction/constant/polyMesh/owner b/tutorials/CFD/24HyperReduction/constant/polyMesh/owner
new file mode 100755
index 000000000..ed3378b8f
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/constant/polyMesh/owner
@@ -0,0 +1,100375 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  5.0                                   |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       labelList;
+    note        "nPoints: 50702 nCells: 25000 nFaces: 100350 nInternalFaces: 49650";
+    location    "constant/polyMesh";
+    object      owner;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+
+100350
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+
+
+// ************************************************************************* //
diff --git a/tutorials/CFD/24HyperReduction/constant/polyMesh/points b/tutorials/CFD/24HyperReduction/constant/polyMesh/points
new file mode 100755
index 000000000..dfc9c294a
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/constant/polyMesh/points
@@ -0,0 +1,50726 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  5.0                                   |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       vectorField;
+    location    "constant/polyMesh";
+    object      points;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
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+(1.7 -0.01 0.1)
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+(1.72 -0.01 0.1)
+(1.73 -0.01 0.1)
+(1.74 -0.01 0.1)
+(1.75 -0.01 0.1)
+(1.76 -0.01 0.1)
+(1.77 -0.01 0.1)
+(1.78 -0.01 0.1)
+(1.79 -0.01 0.1)
+(1.8 -0.01 0.1)
+(1.81 -0.01 0.1)
+(1.82 -0.01 0.1)
+(1.83 -0.01 0.1)
+(1.84 -0.01 0.1)
+(1.85 -0.01 0.1)
+(1.86 -0.01 0.1)
+(1.87 -0.01 0.1)
+(1.88 -0.01 0.1)
+(1.89 -0.01 0.1)
+(1.9 -0.01 0.1)
+(1.91 -0.01 0.1)
+(1.92 -0.01 0.1)
+(1.93 -0.01 0.1)
+(1.94 -0.01 0.1)
+(1.95 -0.01 0.1)
+(1.96 -0.01 0.1)
+(1.97 -0.01 0.1)
+(1.98 -0.01 0.1)
+(1.99 -0.01 0.1)
+(2 -0.01 0.1)
+)
+
+
+// ************************************************************************* //
diff --git a/tutorials/CFD/24HyperReduction/constant/transportProperties b/tutorials/CFD/24HyperReduction/constant/transportProperties
new file mode 100755
index 000000000..0445a58fe
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/constant/transportProperties
@@ -0,0 +1,19 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  1.5                                   |
+|   \\  /    A nd           | Web:      http://www.OpenFOAM.org               |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      transportProperties;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+DT              DT [0 2 -1 0 0 0 0] 1;
+/*f               f [0 0 0 0 0 0 0] 10000;*/
+// ************************************************************************* //
diff --git a/tutorials/CFD/24HyperReduction/createFields.H b/tutorials/CFD/24HyperReduction/createFields.H
new file mode 100755
index 000000000..de2ff4d44
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/createFields.H
@@ -0,0 +1,61 @@
+/*---------------------------------------------------------------------------*\
+     ██╗████████╗██╗  ██╗ █████╗  ██████╗ █████╗       ███████╗██╗   ██╗
+     ██║╚══██╔══╝██║  ██║██╔══██╗██╔════╝██╔══██╗      ██╔════╝██║   ██║
+     ██║   ██║   ███████║███████║██║     ███████║█████╗█████╗  ██║   ██║
+     ██║   ██║   ██╔══██║██╔══██║██║     ██╔══██║╚════╝██╔══╝  ╚██╗ ██╔╝
+     ██║   ██║   ██║  ██║██║  ██║╚██████╗██║  ██║      ██║      ╚████╔╝
+     ╚═╝   ╚═╝   ╚═╝  ╚═╝╚═╝  ╚═╝ ╚═════╝╚═╝  ╚═╝      ╚═╝       ╚═══╝
+
+ * In real Time Highly Advanced Computational Applications for Finite Volumes
+ * Copyright (C) 2017 by the ITHACA-FV authors
+-------------------------------------------------------------------------------
+  License
+  This file is part of ITHACA-FV
+  ITHACA-FV is free software: you can redistribute it and/or modify
+  it under the terms of the GNU Lesser General Public License as published by
+  the Free Software Foundation, either version 3 of the License, or
+  (at your option) any later version.
+  ITHACA-FV is distributed in the hope that it will be useful,
+  but WITHOUT ANY WARRANTY; without even the implied warranty of
+  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+  GNU Lesser General Public License for more details.
+  You should have received a copy of the GNU Lesser General Public License
+  along with ITHACA-FV. If not, see <http://www.gnu.org/licenses/>.
+\*---------------------------------------------------------------------------*/
+Info << "Reading field T\n" << endl;
+
+volScalarField T
+(
+    IOobject
+    (
+        "T",
+        runTime.timeName(),
+        mesh,
+        IOobject::MUST_READ,
+        IOobject::AUTO_WRITE
+    ),
+    mesh
+);
+
+
+Info << "Reading transportProperties\n" << endl;
+
+IOdictionary transportProperties
+(
+    IOobject
+    (
+        "transportProperties",
+        runTime.constant(),
+        mesh,
+        IOobject::MUST_READ_IF_MODIFIED,
+        IOobject::NO_WRITE
+    )
+);
+
+
+Info << "Reading diffusivity DT\n" << endl;
+
+dimensionedScalar DT
+(
+    transportProperties.lookup("DT")
+);
diff --git a/tutorials/CFD/24HyperReduction/system/ITHACAdict b/tutorials/CFD/24HyperReduction/system/ITHACAdict
new file mode 100755
index 000000000..4878925ab
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/system/ITHACAdict
@@ -0,0 +1,29 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  2.2.2                                 |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    location    "system";
+    object      ITHACAdict;
+}
+
+// EigenValue solver, can be eigen or spectra
+EigenSolver eigen;
+
+// Number of modes to output and to use for projection
+Nodes 200;
+Modes 80;
+
+// Output format to save market vectors.
+OutPrecision 20;
+OutType fixed;
+
+// HR
+HyperReduction GappyDEIM;
diff --git a/tutorials/CFD/24HyperReduction/system/PODsolverDict b/tutorials/CFD/24HyperReduction/system/PODsolverDict
new file mode 100755
index 000000000..0e8f6f0f3
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/system/PODsolverDict
@@ -0,0 +1,50 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  2.0.0                                 |
+|   \\  /    A nd           | Web:      http://www.OpenFOAM.org               |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      PODsolverDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+// Set simulation type 1 for Turbulent 0 for Laminar
+Turbulence 0;
+
+// Set Time from which you want to start taking the Snapshots
+InitialTime 0.1;
+
+// Set Time when you want to stop taking the Snapshots
+FinalTime 50;
+fields U;
+
+// Eventually you could set just InitalTime and Number of Snapshots you want    
+//Nsnapshots 40;
+
+// Field you want to use to construct the basis
+U 1;
+p 1;
+
+// Cumulative sum of the eigenvalues where you want to stop
+accuracy   1;
+
+// Number of modes you want to consider (used only during projection and reconstruction)
+nPODu       5;
+nPODp       5;
+nPODsup	    0;
+// Patch used to account for the boundary condition
+patchBC movingWall;
+
+writefields 1;
+twocoeffs 1;
+
+
+
+
+// ************************************************************************* //
diff --git a/tutorials/CFD/24HyperReduction/system/controlDict b/tutorials/CFD/24HyperReduction/system/controlDict
new file mode 100755
index 000000000..9b1624185
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/system/controlDict
@@ -0,0 +1,53 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  1.5                                   |
+|   \\  /    A nd           | Web:      http://www.OpenFOAM.org               |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      controlDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+application poissonFoam;
+
+startFrom       startTime;
+
+startTime       0;
+
+stopAt          endTime;
+
+/*endTime         3;*/
+endTime         1000;
+
+/*deltaT          0.005;*/
+deltaT          1;
+
+writeControl    timeStep;
+
+/*writeControl    runTime;*/
+
+writeInterval   10000000;
+
+/*writeInterval   0.1;*/
+
+purgeWrite      0;
+
+writeFormat     ascii;
+
+writePrecision  6;
+
+writeCompression uncompressed;
+
+timeFormat      general;
+
+timePrecision   6;
+
+runTimeModifiable yes;
+
+// ************************************************************************* //
diff --git a/tutorials/CFD/24HyperReduction/system/fvSchemes b/tutorials/CFD/24HyperReduction/system/fvSchemes
new file mode 100755
index 000000000..9a498f68d
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/system/fvSchemes
@@ -0,0 +1,56 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  1.5                                   |
+|   \\  /    A nd           | Web:      http://www.OpenFOAM.org               |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      fvSchemes;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+ddtSchemes
+{
+    default steadyState;
+}
+
+gradSchemes
+{
+    default         Gauss linear;
+    grad(T)         Gauss linear;
+}
+
+divSchemes
+{
+    default         Gauss linear;
+}
+
+laplacianSchemes
+{
+    default         Gauss linear orthogonal;
+    laplacian(DT,T)  Gauss linear orthogonal;
+    laplacian(DT,subsetT) Gauss linear;
+}
+
+interpolationSchemes
+{
+    default         linear;
+}
+
+snGradSchemes
+{
+    default         orthogonal;
+}
+
+fluxRequired
+{
+    default         no;
+    T;
+}
+
+// ************************************************************************* //
diff --git a/tutorials/CFD/24HyperReduction/system/fvSolution b/tutorials/CFD/24HyperReduction/system/fvSolution
new file mode 100755
index 000000000..b62619eb8
--- /dev/null
+++ b/tutorials/CFD/24HyperReduction/system/fvSolution
@@ -0,0 +1,47 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  1.5                                   |
+|   \\  /    A nd           | Web:      http://www.OpenFOAM.org               |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      fvSolution;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+solvers
+{
+    T 
+    {
+        solver           PCG;
+        preconditioner   DIC;
+        tolerance        1e-10;
+        relTol           0;
+    };
+
+    "(U|k|omega)"
+    {
+	    solver           GAMG;
+        tolerance        1e-10;
+        relTol           1e-10;
+        smoother         GaussSeidel;
+        nPreSweeps       0;
+        nPostSweeps      2;
+        cacheAgglomeration on;
+        agglomerator     faceAreaPair;
+        nCellsInCoarsestLevel 10;
+        mergeLevels      1;
+    }
+}
+
+SIMPLE
+{
+    nNonOrthogonalCorrectors 2;
+}
+
+// ************************************************************************* //

From bab2ee66270b850cf2297202ee432e5ad04a7192 Mon Sep 17 00:00:00 2001
From: fromor <francesco.romor@gmail.com>
Date: Tue, 25 Oct 2022 16:01:21 +0200
Subject: [PATCH 03/59] add SOPT and SOPTE hyperReduction methods, working on
 tutorial 24

---
 src/ITHACA_HR/Make/files                      |   3 -
 src/ITHACA_HR/Make/options                    |  34 --
 src/ITHACA_HR/hyperReduction.C                | 526 -----------------
 src/ITHACA_HR/hyperReduction.H                |  79 ++-
 src/ITHACA_HR/hyperReduction.templates.H      | 540 ++++++++++++------
 .../CFD/24HyperReduction/24HyperReduction.C   |  17 +-
 .../CFD/24HyperReduction/system/ITHACAdict    |   5 +-
 7 files changed, 443 insertions(+), 761 deletions(-)
 delete mode 100644 src/ITHACA_HR/Make/files
 delete mode 100644 src/ITHACA_HR/Make/options
 delete mode 100644 src/ITHACA_HR/hyperReduction.C

diff --git a/src/ITHACA_HR/Make/files b/src/ITHACA_HR/Make/files
deleted file mode 100644
index a30075081..000000000
--- a/src/ITHACA_HR/Make/files
+++ /dev/null
@@ -1,3 +0,0 @@
-hyperReduction.C
-
-LIB = $(FOAM_USER_LIBBIN)/libITHACA_HR
diff --git a/src/ITHACA_HR/Make/options b/src/ITHACA_HR/Make/options
deleted file mode 100644
index 2c343961d..000000000
--- a/src/ITHACA_HR/Make/options
+++ /dev/null
@@ -1,34 +0,0 @@
-sinclude $(GENERAL_RULES)/module-path-user
-
-/* Failsafe - user location */
-ifeq (,$(strip $(FOAM_MODULE_APPBIN)))
-    FOAM_MODULE_APPBIN = $(FOAM_USER_APPBIN)
-endif
-ifeq (,$(strip $(FOAM_MODULE_LIBBIN)))
-    FOAM_MODULE_LIBBIN = $(FOAM_USER_LIBBIN)
-endif
-
-EXE_INC = \
-    -I$(LIB_SRC)/finiteVolume/lnInclude \
-    -I$(LIB_SRC)/meshTools/lnInclude \
-    -I$(LIB_SRC)/dynamicMesh/lnInclude \
-    -I$(LIB_SRC)/dynamicFvMesh/lnInclude \
-    -I$(LIB_ITHACA_SRC)/ITHACA_DEIM/DEIM \
-    -I$(LIB_ITHACA_SRC)/thirdparty/Eigen \
-    -I$(LIB_ITHACA_SRC)/thirdparty/spectra/include \
-    -I$(LIB_ITHACA_SRC)/ITHACA_CORE/ITHACAutilities \
-    -I$(LIB_ITHACA_SRC)/ITHACA_CORE/ITHACAstream \
-    -I$(LIB_ITHACA_SRC)/ITHACA_CORE/ITHACAPOD \
-    -I$(LIB_ITHACA_SRC)/ITHACA_CORE/Foam2Eigen \
-    -I$(LIB_ITHACA_SRC)/ITHACA_CORE/EigenFunctions \
-    -I$(LIB_ITHACA_SRC)/ITHACA_CORE/Containers \
-    -Wno-comment \
-    -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++17 
-
-EXE_LIBS = \
-    -lITHACA-CORE \
-    -lmeshTools \
-    -lsampling \
-    -lfileFormats \
-    -lfiniteVolume
diff --git a/src/ITHACA_HR/hyperReduction.C b/src/ITHACA_HR/hyperReduction.C
deleted file mode 100644
index dfc1049ba..000000000
--- a/src/ITHACA_HR/hyperReduction.C
+++ /dev/null
@@ -1,526 +0,0 @@
-/*---------------------------------------------------------------------------*\
-     ██╗████████╗██╗  ██╗ █████╗  ██████╗ █████╗       ███████╗██╗   ██╗
-     ██║╚══██╔══╝██║  ██║██╔══██╗██╔════╝██╔══██╗      ██╔════╝██║   ██║
-     ██║   ██║   ███████║███████║██║     ███████║█████╗█████╗  ██║   ██║
-     ██║   ██║   ██╔══██║██╔══██║██║     ██╔══██║╚════╝██╔══╝  ╚██╗ ██╔╝
-     ██║   ██║   ██║  ██║██║  ██║╚██████╗██║  ██║      ██║      ╚████╔╝
-     ╚═╝   ╚═╝   ╚═╝  ╚═╝╚═╝  ╚═╝ ╚═════╝╚═╝  ╚═╝      ╚═╝       ╚═══╝
-
- * In real Time Highly Advanced Computational Applications for Finite Volumes
- * Copyright (C) 2017 by the ITHACA-FV authors
--------------------------------------------------------------------------------
-
-License
-    This file is part of ITHACA-FV
-
-    ITHACA-FV is free software: you can redistribute it and/or modify
-    it under the terms of the GNU Lesser General Public License as published by
-    the Free Software Foundation, either version 3 of the License, or
-    (at your option) any later version.
-
-    ITHACA-FV is distributed in the hope that it will be useful,
-    but WITHOUT ANY WARRANTY; without even the implied warranty of
-    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-    GNU Lesser General Public License for more details.
-
-    You should have received a copy of the GNU Lesser General Public License
-    along with ITHACA-FV. If not, see <http://www.gnu.org/licenses/>.
-
-\*---------------------------------------------------------------------------*/
-
-#include "hyperReduction.H"
-
-// Using the Eigen library, using the SVD decomposition method to solve the
-// matrix pseudo-inverse, the default error er is 0
-Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0) {
-  // perform svd decomposition
-  Eigen::JacobiSVD<Eigen::MatrixXd> svd_holder(origin, Eigen::ComputeThinU |
-                                                           Eigen::ComputeThinV);
-  // Build SVD decomposition results
-  Eigen::MatrixXd U = svd_holder.matrixU();
-  Eigen::MatrixXd V = svd_holder.matrixV();
-  Eigen::MatrixXd D = svd_holder.singularValues();
-
-  // Build the S matrix
-  Eigen::MatrixXd S(V.cols(), U.cols());
-  S.setZero();
-
-  for (unsigned int i = 0; i < D.size(); ++i) {
-
-    if (D(i, 0) > er) {
-      S(i, i) = 1 / D(i, 0);
-    } else {
-      S(i, i) = 0;
-    }
-  }
-
-  std::cout << "Condition number of inverse: " <<  D(D.size()-1, 0)/D(0, 0) << std::endl;
-
-  // pinv_matrix = V * S * U^T
-  return V * S * U.transpose();
-}
-
-// Template function constructor
-template <typename... SnapshotsLists>
-HyperReduction<SnapshotsLists...>::HyperReduction(HyperReductionMethod hrMethod,
-                                                  label n_modes,
-                                                  label n_nodes,
-                                                  Eigen::VectorXi initialSeeds,
-                                                  word functionName,
-                                                  SnapshotsLists &&...snapshotsLists)
-    :  methodName{methodNames[int(hrMethod)]},
-      vectorial_dim{compute_vectorial_dim(snapshotsLists...)},
-      n_modes{n_modes},
-      n_nodes{n_nodes},
-      initialSeeds{initialSeeds},
-      functionName{functionName},
-      snapshotsTuple{std::forward_as_tuple(snapshotsLists...)}
-{
-    Info << "Init HyperReduction class with vectorial dim: " << vectorial_dim << endl;
-    // check snapshotsLists is not empty
-    // check that the first snapshotsList is not empty (includes above)
-
-    // TODO initialize vectorial_dim only from SnapshotsLists type
-    // vectorial_dim = std::apply(compute_vectorial_dim<SnapshotsLists&&...>, snapshotsTuple);
-
-    ITHACAparameters *para(ITHACAparameters::getInstance());
-    Folder = "ITHACAoutput/" + methodName + "/" + functionName;
-    mkDir(Folder);
-
-    nodePoints = autoPtr<IOList<label>>(new IOList<label>(
-        IOobject("nodePoints", para->runTime.time().constant(), "../" + Folder,
-                 para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
-
-    n_snapshots = std::get<0>(snapshotsTuple).size();
-    Info << "The number of snapshots is: " << n_snapshots << endl;
-    n_cells = std::get<0>(snapshotsTuple)[0].size();
-    Info << "The number of cells is: " << n_cells << endl;
-    Info << "Initial seeds length: " << initialSeeds.rows() << endl;
-    
-    std::apply([this](auto& ...x){(..., compute_matrix_modes(x));}, snapshotsTuple);
-
-    if (!nodePoints().headerOk())
-    {
-        assert(n_modes > 0);
-        assert(n_nodes >= n_modes);
-
-        Eigen::VectorXd mp_not_mask = Eigen::VectorXd::Constant(n_cells * vectorial_dim, 1);
-        std::set<label> nodePointsSet;
-        std::deque<label> nodePointsDeque;
-
-        // set initialSeeds
-        if (initialSeeds.rows() > 0)
-        {
-          Info << "Add initialSeeds\n";
-          P.resize(n_cells * vectorial_dim, initialSeeds.rows() * vectorial_dim);
-          P.reserve(Eigen::VectorXi::Constant(initialSeeds.rows() * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
-
-          for (int i = 0; i < initialSeeds.rows(); i++)
-          {
-              for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-              {
-                P.insert(initialSeeds(i)+ith_field*n_cells, vectorial_dim*i+ith_field) = 1;
-                mp_not_mask(initialSeeds(i) + ith_field * n_cells) = 0;
-              }
-              
-              if (nodePointsSet.find(initialSeeds(i)) == nodePointsSet.end()){
-                nodePointsSet.insert(initialSeeds(i));
-                nodePointsDeque.push_back(initialSeeds(i));
-              }
-          }
-
-          P.makeCompressed();
-
-          for (int k = 0; k < initialSeeds.outerSize(); ++k) {
-            for (Eigen::SparseMatrix<double>::InnerIterator it(P, k); it; ++it) {
-              assert(it.value() == 1);
-              if (nodePointsSet.find(it.row() % n_cells) == nodePointsSet.end()){
-                nodePointsSet.insert(it.row() % n_cells);
-                nodePointsDeque.push_back(it.row() % n_cells);
-              }
-            }
-          }
-        }
-
-        int na = n_nodes - initialSeeds.rows();
-        if (na > 0)
-        {
-            int nb = 0;
-            int nit = std::min(n_modes, na);
-            int ncimin = std::floor(n_modes / nit);
-            int naimin = std::floor(na / n_modes);
-
-            Eigen::MatrixXd A;
-            Eigen::VectorXd b;
-            Eigen::VectorXd c;
-            Eigen::VectorXd r;
-            label ind_max, c1;
-
-            double max;
-
-            Info << "######## Begin Greedy GNAT ########" << endl;
-            Info << "######## Modes=" <<  n_modes
-                 << ", nodePoints=" << n_nodes << " ########"
-                 << endl;
-
-            for (int i = 1; i <= nit; i++)
-            {
-                int nci = ncimin;
-                // add the remaining modes in the quotien n_modes / nite
-                if (i <= n_modes % nit)
-                {
-                    nci = ncimin + 1;
-                }
-                int nai = naimin;
-                // add the remaining nodePoints_xyz in the quotien na / n_modes
-                if (i <= na % n_modes)
-                {
-                    nai = naimin + 1;
-                }
-
-                Eigen::MatrixXd V;
-
-                // select basis
-                if (i == 1)
-                {
-                    V = matrixModes.leftCols(nci);
-                }
-                else
-                {
-                  for (int q = 1; q <= nci; q++)
-                  {
-                      A = P.transpose() * basisMatrix;
-                      b = P.transpose() * matrixModes.col(nb + q - 1);
-                      c = A.fullPivLu().solve(b);
-                      r = matrixModes.col(nb + q - 1) - basisMatrix * c;
-                      V.conservativeResize(matrixModes.rows(), q);
-                      V.col(q - 1) = r;
-                  }
-                }
-
-                // select nodePoints_xyz
-                for (int j = 1; j <= nai; j++)
-                {
-                    // TODO: implement as in Carlberg paper taking into account degrees
-                    // of freedom associated to each node
-                    // auto Id = Eigen::MatrixXd::Identity(P.rows(), P.rows());
-                    
-                    if (P.cols() > 0)
-                    {
-                        // std::cout << mp_not_mask.asDiagonal().rows() << " " << V.rows() << V.cols() << std::endl;
-                        max = (mp_not_mask.asDiagonal() * V)
-                                  .rowwise()
-                                  .lpNorm<2>()
-                                  .maxCoeff(&ind_max, &c1);
-                    }
-                    else
-                    {
-                        // max = V.topRows(2*n_cells).rowwise().lpNorm<2>().maxCoeff(&ind_max, &c1);
-                        max = V.rowwise().lpNorm<2>().maxCoeff(&ind_max, &c1);
-                    }
-
-                    // std::cout << "Maximum found: " << max << " at " << ind_max
-                    //           << std::endl;
-
-                    int idxes = P.cols();
-                    int maxFirstMesh = ind_max % n_cells;
-                    P.conservativeResize(matrixModes.rows(), idxes + vectorial_dim);
-                    
-                    for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-                    {
-                        P.insert(maxFirstMesh + ith_field * n_cells, idxes + ith_field) = 1;
-                        mp_not_mask(maxFirstMesh + ith_field * n_cells) = 0;
-                    }
-
-                    if (nodePointsSet.find(maxFirstMesh) == nodePointsSet.end()){
-                      nodePointsSet.insert(maxFirstMesh);
-                      nodePointsDeque.push_back(maxFirstMesh);
-                    }
-
-                }
-
-                nb += nci;
-                basisMatrix = matrixModes.leftCols(nb);
-            }
-        }
-        else
-        {
-            basisMatrix = matrixModes;
-        }
-
-        Info << "######## End of greedy GNAT ########\n";
-        cnpy::save(basisMatrix, Folder +"/basisMatrix.npy");
-        cnpy::save(P, Folder +"/projectionMatrix.npy");
-        std::cout << "P: " << P.rows() << " " << P.cols() << std::endl;
-        std::cout << "basisMatrix: " << basisMatrix.rows() << " " << basisMatrix.cols() << std::endl;
-
-        // convert nodePointsSet to nodePoints i.e. list
-        for (auto &x : nodePointsDeque)
-        {
-          nodePoints().append(x);
-        }
-
-        int i{0};
-        Eigen::VectorXi nodes(nodePoints().size());
-        for (int &x : nodePoints())
-        {
-            nodes(i) = x;
-            i++;
-        }
-        cnpy::save(nodes, Folder + "/mp.npy");
-
-        evaluatePinv(P, basisMatrix);
-
-        // std::cout << "Reconstruction : " << (basisMatrix*((P.transpose() * basisMatrix).fullPivLu().inverse())*P.transpose()-Eigen::MatrixXd::Identity(basisMatrix.rows(), basisMatrix.rows())).norm() << std::endl;
-
-        // pinvPU =((P.transpose() * basisMatrix).fullPivLu().inverse());
-        std::cout << "pinvPU: " << pinvPU.rows() << " " << pinvPU.cols() << std::endl;
-
-        cnpy::save(pinvPU, Folder + "/pinvPU.npy");
-        nodePoints().write();
-    }
-    else
-    {
-        cnpy::load(pinvPU, Folder + "/basisMatrix.npy");
-    }
-}
-
-template <typename... SnapshotsLists>
-template <typename SnapshotsList>
-void HyperReduction<SnapshotsLists...>::compute_matrix_modes(SnapshotsList sList)
-{
-    Info << "####### Compute hyper-reduction basis #######\n";
-    // TODO normalization
-    // Eigen::MatrixXf::Index maxIndex;
-    // double maxVal = modes.col(0).cwiseAbs().maxCoeff(&maxIndex);
-    // std::cout << "MaxValues: " << maxVal << std::endl;
-
-    // modes = modes / maxVal;
-
-    // maxVal = modes.col(0).cwiseAbs().maxCoeff(&maxIndex);
-    // std::cout << "MaxValues: " << maxVal << std::endl;
-
-    word fieldName = sList[0].name();
-    unsigned int field_dim = get_field_dim<typename SnapshotsList::value_type>();
-
-    auto tmp_modes = ITHACAPOD::DEIMmodes(sList, n_modes, "GNAT/" + functionName + "V", fieldName);
-
-    matrixModes.conservativeResize(n_cells * field_dim, n_modes);
-    matrixModes.bottomRows(n_cells * field_dim) = Foam2Eigen::PtrList2Eigen(tmp_modes);
-
-    Info << "####### End of computing hyper-reduction basis #######\n";
-}
-
-template<typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::evaluatePinv(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes) {
-  assert(Projector.cols() > 0);
-  Eigen::MatrixXd restricted = Projector.transpose() * Modes;
-
-//   Info << "Restricted modes matrix: " << restricted.rows() << " x "
-//             << restricted.cols() << endl;
-
-  // int ssize = restricted.rows()/3;
-  // int vsize = 2*ssize;
-  
-  pinvPU = pinv_eigen_based(restricted);
-//   Eigen::MatrixXd PUV = restricted.topRows(vsize);
-//   Eigen::MatrixXd PUS = restricted.bottomRows(ssize);
-//   cnpy::save(restricted, "./numpy_datasets/restricted.npy");
-//   pinvPUV = pinv_eigen_based(PUV, 1e-10);
-//   pinvPUS = pinv_eigen_based(PUS, 1e-10);
-//   Info << "PUV: " << PUV.rows() << " " << PUV.cols() << endl;
-//   Info << "PUS: " << PUS.rows() << " " << PUS.cols() << endl;
-
-//   pinvPU.resize(restricted.cols(), ssize*3);
-//   pinvPU.leftCols(vsize) = pinvPUV;
-//   pinvPU.rightCols(ssize) = pinvPUS;
-  // Info << "pinvPU: " << pinvPU << endl;
-
-//   Info << "Pseudo inverse of restricted modes: " << pinvPU.rows() << " x "
-//             << pinvPU.cols() << endl;
-
-  // Eigen::MatrixXd UpinvPU_ = restricted * pinvPU;
-  // Info << "Pseudo inverse of restricted modes: " << UpinvPU_.rows()
-  //           << " x " << UpinvPU_.cols() << endl;
-
-  // maskingAux = Modes * pinvPU;
-//   Info << "Masking auxiliary matrix: " << maskingAux.rows() << " x "
-//             << maskingAux.cols() << endl;
-
-  // auto ret = std::make_pair<Eigen::MatrixXd, Eigen::MatrixXd>(UpinvPU, maskingAux);
-}
-
-template<typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::generateSubmesh(label layers, fvMesh &mesh) {
-
-  Info << "####### Extract submesh #######\n";
-  ITHACAparameters *para(ITHACAparameters::getInstance());
-
-  totalNodePoints = autoPtr<IOList<labelList>>(new IOList<labelList>(IOobject(
-      "totalNodePoints", para->runTime.time().constant(),  "../" + Folder,
-      para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
-
-  uniqueNodePoints = autoPtr<IOList<label>>(new IOList<label>(IOobject(
-      "uniqueNodePoints", para->runTime.time().constant(),  "../" + Folder,
-      para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
-
-  volScalarField Indici(
-      IOobject(functionName + "_indices", mesh.time().timeName(), mesh,
-               IOobject::NO_READ, IOobject::NO_WRITE),
-      mesh,
-      dimensionedScalar(functionName + "_indices",
-                        dimensionSet(0, 0, 0, 0, 0, 0, 0), 0.0));
-
-  submesh = autoPtr<fvMeshSubset>(new fvMeshSubset(mesh));
-
-  if (!totalNodePoints().headerOk()) {
-    List<label> indices;
-
-    for (label i = 0; i < nodePoints().size(); i++) {
-      indices = ITHACAutilities::getIndices(mesh, nodePoints()[i], layers);
-      totalNodePoints().append(indices);
-    }
-
-    labelList a = ListListOps::combine<labelList>(totalNodePoints(),
-                                                  accessOp<labelList>());
-
-    inplaceUniqueSort(a);
-    uniqueNodePoints() = a;
-
-    scalar zerodot25 = 0.25;
-    ITHACAutilities::assignIF(Indici, zerodot25,
-                              uniqueNodePoints().List<label>::clone()());
-    ITHACAutilities::assignONE(Indici, nodePoints());
-
-    totalNodePoints().write();
-    uniqueNodePoints().write();
-  }
-
-  submesh->setCellSubset(uniqueNodePoints());
-  submesh->subMesh().fvSchemes::readOpt() = mesh.fvSchemes::readOpt();
-  submesh->subMesh().fvSolution::readOpt() = mesh.fvSolution::readOpt();
-  submesh->subMesh().fvSchemes::read();
-  submesh->subMesh().fvSolution::read();
-  std::cout.clear();
-
-  localNodePoints = global2local(nodePoints(), submesh());
-  ITHACAstream::exportSolution(Indici, "1", "./ITHACAoutput/" + methodName + "/");
-
-  n_cellsSubfields = submesh().cellMap().size();
-  createMasks();
-  Info << "####### End extract submesh #######\n";
-}
-
-template<typename... SnapshotsLists>
-List<label> HyperReduction<SnapshotsLists...>::global2local(List<label> &points, fvMeshSubset &submesh) {
-  List<label> localPoints;
-
-  for (label i = 0; i < points.size(); i++) {
-    for (label j = 0; j < submesh.cellMap().size(); j++) {
-      if (submesh.cellMap()[j] == points[i]) {
-        localPoints.append(j);
-        break;
-      }
-    }
-  }
-
-  return localPoints;
-}
-
-template<typename... SnapshotsLists>
-template<typename FieldType>
-autoPtr<FieldType> HyperReduction<SnapshotsLists...>::interpolateField(FieldType& field) {
-    return autoPtr<FieldType>(new FieldType(submesh->interpolate(field)));
-}
-
-template<typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::createMasks() {
-  assert(uniqueNodePoints().size() > 0);
-
-  // initialize uniqueNodePointsVector
-  uniqueNodePointsVector.resize(uniqueNodePoints().size());
-  int vector_idx{0};
-  for (int &x : uniqueNodePoints()) {
-    uniqueNodePointsVector(vector_idx) = x;
-    vector_idx++;
-  }
-
-  // initialize uniqueNodePointsVector_xy
-  uniqueNodePointsVector_xy.resize(uniqueNodePoints().size() * vectorial_dim);
-  for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-  {
-    uniqueNodePointsVector_xy.segment(ith_field * uniqueNodePoints().size(), uniqueNodePoints().size()*(ith_field + 1)) =
-      (ith_field  * n_cells + uniqueNodePointsVector.array()).matrix();
-  }
-
-//   // initialize P_xymp_mp
-//   // due to the fact that x, y coordinates of the residual in a single cell are
-//   // computed at the same time in OF, if two nodePoints_xy refer to the same
-//   // cell, the residual can be evaluated just once. In case only one coordinate
-//   // is a magicPoint the following mask will be used to distinguish the two
-//   // cases
-//   cnpy::load(nodePoints, "./numpy_datasets/mp.npy");
-//   // std::cout << nodePoints << std::endl;
-
-//   P_xymp_submesh.resize(2 * nodePoints.rows(), 2 * NcellsSubfields);
-//   P_xymp_submesh_scalar.resize(nodePoints.rows(), NcellsSubfields);
-
-
-//   // ITHACAparameters *para(ITHACAparameters::getInstance());
-//   // nodePoints.clear();
-//   // nodePoints = autoPtr<IOList<label>>(new IOList<label>(
-//   //     IOobject("nodePoints", para->runTime.time().constant(), "../ITHACAoutput/GNAT/" + FunctionName,
-//   //              para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
-
-//   // for (int i{0}; i< nodePoints().size(); i++){
-//   //   std::cout << nodePoints()[i] << " ";
-//   // }
-
-//   int index_row = 0;
-//   int index_col = 0;
-//   for (const int &cell : submesh().cellMap()) {
-//     for (int mpxy{0}; mpxy < nodePoints.rows(); mpxy++) {
-//       // std::cout << "cell: "<< cell << " mp: " << nodePoints(mpxy) << std::endl;
-//       if (cell == int(nodePoints(mpxy))) {
-//         P_xymp_submesh.insert(index_row, index_col) = 1;
-//         P_xymp_submesh.insert(index_row + nodePoints.rows(), index_col + NcellsSubfields) = 1;
-
-//         P_xymp_submesh_scalar.insert(index_row, index_col) = 1;
-//       }
-
-//       index_row++;volVectorField fieldV, volScalarField fieldS
-//     }
-//     index_row = 0;
-//     index_col++;
-//   }
-// //   Info << " # DEBUG GNAT.C, line 429 # " << P_xymp_submesh.rows() << " " << P_xymp_submesh.cols() << endl;
-// // //   Info << " # DEBUG GNAT.C, line 430 # " << P_xymp_submesh_scalar.rows() << " " << P_xymp_submesh_scalar.cols() << endl;
-
-//   Eigen::MatrixXd P_xymp_submesh_ = P_xymp_submesh;
-//   Eigen::MatrixXd P_xymp_submesh_scalar_ = P_xymp_submesh_scalar;
-//   cnpy::save(P_xymp_submesh_, "./numpy_datasets/submesh_vector.npy");
-//   cnpy::save(P_xymp_submesh_scalar_, "./numpy_datasets/submesh_scalar.npy");
-}
-
-
-template HyperReduction<PtrList<volScalarField>&>::HyperReduction(HyperReductionMethod hrMethod,
-                                                        label maxModes,
-                                                        label maxNodes,
-                                                        Eigen::VectorXi initialSeeds,
-                                                        word functionName,
-                                                        PtrList<volScalarField>& snapshotsLists1);
-
-template HyperReduction<PtrList<volVectorField>&>::HyperReduction(HyperReductionMethod hrMethod,
-                                                        label maxModes,
-                                                        label maxNodes,
-                                                        Eigen::VectorXi initialSeeds,
-                                                        word functionName,
-                                                        PtrList<volVectorField>& snapshotsLists1);
-
-template HyperReduction<PtrList<volVectorField>&, PtrList<volScalarField>&>::HyperReduction(HyperReductionMethod hrMethod,
-                                                        label maxModes,
-                                                        label maxNodes,
-                                                        Eigen::VectorXi initialSeeds,
-                                                        word functionName,
-                                                        PtrList<volVectorField>& snapshotsLists1,
-                                                        PtrList<volScalarField>&snapshotsLists2);
\ No newline at end of file
diff --git a/src/ITHACA_HR/hyperReduction.H b/src/ITHACA_HR/hyperReduction.H
index b13432729..cb1d16276 100644
--- a/src/ITHACA_HR/hyperReduction.H
+++ b/src/ITHACA_HR/hyperReduction.H
@@ -49,17 +49,17 @@ class HyperReduction
 {
 public:
     const word methodNames[1] = {"GappyDEIM"};
-    const word methodName;
+    word methodName;
 
-    using SnapshotsTuple = std::tuple<std::decay_t<SnapshotsLists>...>;
-    using FieldsTuple = std::tuple<std::decay_t<SnapshotsLists>...>;
+    using SnapshotsListTuple = std::tuple<std::decay_t<SnapshotsLists>...>;
+    using FieldsTuple = std::tuple<typename std::decay_t<SnapshotsLists>::value_type ...>;
     static constexpr auto n_fields = sizeof...(SnapshotsLists);
 
     // TODO get vectorial dim from class template parameters
     unsigned int vectorial_dim;
 
     template <std::size_t N>
-    using NthFieldListType = typename std::tuple_element<N, SnapshotsTuple>::type;
+    using NthFieldListType = typename std::tuple_element<N, SnapshotsListTuple>::type;
 
     template <std::size_t N>
     using NthFieldType = typename NthFieldListType<N>::value_type;
@@ -79,6 +79,9 @@ public:
                    Eigen::VectorXi initialSeeds,
                    word problemName,
                    SnapshotsLists &&...snapshotsLists);
+    
+    // ITHACA parameters dict
+    ITHACAparameters* para;
 
     /// The maximum number of modes to be considered
     label n_modes;
@@ -96,7 +99,7 @@ public:
     word problemName;
 
     /// The snapshots matrix containing the nonlinear function or operator
-    SnapshotsTuple snapshotsTuple;
+    SnapshotsListTuple snapshotsListTuple;
 
     /// Names of the fields
     List<word> fieldNames;
@@ -146,18 +149,37 @@ public:
     
     /// Submeshes
     autoPtr<volVectorField> submesh_field;
+
     //----------------------------------------------------------------------
     /// @brief      TODO
     ///
     void offlineStage();
+    
+    //----------------------------------------------------------------------
+    /// @brief      TODO
+    ///
+    void offlineGappyDEIM();
 
+    //----------------------------------------------------------------------
+    /// @brief      TODO
+    ///
+    void offlineEQP();
+
+    //----------------------------------------------------------------------
+    /// @brief      TODO
+    ///
+    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+    /// @param[in]  sList  The list of snapshots
+    ///
+    void getModesSVD(SnapshotsListTuple &SnapshotsListTuple, Eigen::MatrixXd &modesSVD, Eigen::VectorXd &fieldWeights);
+    
     //----------------------------------------------------------------------
     /// @brief      TODO
     ///
     /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
     /// @param[in]  sList  The list of snapshots
     ///
-    void getModesSVD(SnapshotsTuple &snapshotsTuple, Eigen::MatrixXd &modesSVD, Eigen::VectorXd &fieldWeights);
+    void updateNodes(Eigen::SparseMatrix<double>& P, label& ind_max, Eigen::VectorXd& mp_not_mask, std::deque<label>& nodePointsDeque);
 
     //----------------------------------------------------------------------
     /// @brief      TODO
@@ -175,7 +197,9 @@ public:
     /// @param[in]  sList  The list of snapshots
     ///
     template <typename SnapshotsList>
-    void stackNames(SnapshotsList sList);
+    void stackNames(SnapshotsList sList){
+        fieldNames.append(sList[0].name());
+    }
 
     //----------------------------------------------------------------------
     /// @brief      TODO
@@ -184,7 +208,8 @@ public:
     /// @param[in]  sList  The list of snapshots
     ///
     template <typename SnapshotsList>
-    void stackDimensions(SnapshotsList sList);
+    inline void stackDimensions(SnapshotsList sList){
+        fieldDims.append(get_field_dim<typename SnapshotsList::value_type>());}
 
     //----------------------------------------------------------------------
     /// @brief      Compute the pseudo-inverse of the matrix M restricted with the projector P
@@ -218,7 +243,9 @@ public:
     /// @param[in]  sList  The list of snapshots
     ///
     template <typename FieldType>
-    autoPtr<FieldType> interpolateField(FieldType &field);
+    inline autoPtr<FieldType> interpolateField(FieldType &field){
+    return autoPtr<FieldType>(new FieldType(submesh->interpolate(field)));
+}
 
     /// @brief      TODO
     ///
@@ -250,6 +277,40 @@ public:
     {
         return get_field_dim<typename std::decay_t<List>::value_type>() + compute_vectorial_dim<RemainingLists...>(tail...);
     }
+
+    /// @brief      TODO
+    ///
+    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+    /// @param[in]  sList  The list of snapshots
+    ///
+    static inline double s_optimality(Eigen::MatrixXd& A)
+    {   
+        return std::pow(
+            std::sqrt((A.transpose()*A).determinant())/\
+            A.colwise().lpNorm<2>().prod(),
+            1.0/A.cols());
+    }
+
+    /// @brief      TODO
+    ///
+    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+    /// @param[in]  sList  The list of snapshots
+    ///
+    template <typename... FieldsArgs>
+    void eigen2fields(Eigen::VectorXd& eFields, FieldsArgs&&... oFields)
+    {   
+        unsigned int cumulativeSize{0}, ith_field{0};
+        
+        ([&](auto& oFieldsArg)
+            {
+                double ith_fieldSize = fieldDims[ith_field]*n_cells;
+                Eigen::VectorXd vec = eFields.segment(cumulativeSize, ith_fieldSize);
+                Foam2Eigen::Eigen2field(oFieldsArg, vec);
+                cumulativeSize+=ith_fieldSize;
+                ith_field++;
+            }(oFields), ...);
+
+    }
 };
 
 #endif
diff --git a/src/ITHACA_HR/hyperReduction.templates.H b/src/ITHACA_HR/hyperReduction.templates.H
index 4440caea3..80f91c9bc 100644
--- a/src/ITHACA_HR/hyperReduction.templates.H
+++ b/src/ITHACA_HR/hyperReduction.templates.H
@@ -14,7 +14,7 @@ License
     This file is part of ITHACA-FV
 
     ITHACA-FV is free software: you can redistribute it and/or modify
-    it under the terms of the GNU Lesser General Public License as published by
+    it under the terms of the GN3U Lesser General Public License as published by
     the Free Software Foundation, either version 3 of the License, or
     (at your option) any later version.
 
@@ -60,14 +60,14 @@ Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0) {
 
 template <typename... SnapshotsLists>
 void HyperReduction<SnapshotsLists...>::getModesSVD(
-    SnapshotsTuple& snapshotsTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights)
+    SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights)
 {
   ITHACAparameters* para(ITHACAparameters::getInstance());
   if (!ITHACAutilities::check_folder(Folder + "/Modes/"))
   {
     // Initialize stacked snapshotsMatrix and normalizing weights
     Eigen::MatrixXd snapMatrix;
-    std::apply([this, &snapMatrix, &fieldWeights](auto& ...snapList){(..., stackSnapshots(snapList, snapMatrix, fieldWeights));}, snapshotsTuple);
+    std::apply([this, &snapMatrix, &fieldWeights](auto& ...snapList){(..., stackSnapshots(snapList, snapMatrix, fieldWeights));}, snapshotsListTuple);
 
     Info << "####### Performing SVD for " << problemName << " #######" << endl;
 
@@ -124,7 +124,7 @@ HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
       n_nodes{n_nodes},
       initialSeeds{initialSeeds},
       problemName{problemName},
-      snapshotsTuple{std::forward_as_tuple(snapshotsLists...)}
+      snapshotsListTuple{std::forward_as_tuple(snapshotsLists...)}
 {
   Info << "Init HyperReduction class with vectorial dim: " << vectorial_dim << endl;
 
@@ -132,13 +132,13 @@ HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
   // TODO check that the first snapshotsList is not empty (includes above)
 
   // TODO initialize vectorial_dim only from SnapshotsLists type
-  // vectorial_dim = std::apply(compute_vectorial_dim<SnapshotsLists&&...>, snapshotsTuple);
+  // vectorial_dim = std::apply(compute_vectorial_dim<SnapshotsLists&&...>, snapshotsListTuple);
 
   // Get fields' names
-  std::apply([this](auto& ...snapList){(..., stackNames(snapList));}, snapshotsTuple);
+  std::apply([this](auto& ...snapList){(..., stackNames(snapList));}, snapshotsListTuple);
 
   // Get fields' dimensions
-  std::apply([this](auto& ...snapList){(..., stackDimensions(snapList));}, snapshotsTuple);
+  std::apply([this](auto& ...snapList){(..., stackDimensions(snapList));}, snapshotsListTuple);
 
   Info << "Fields names: ";
   for (unsigned int ith_field = 0; ith_field < fieldNames.size(); ith_field++)
@@ -147,9 +147,9 @@ HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
   }
   Info << endl;
   
-  n_snapshots = std::get<0>(snapshotsTuple).size();
+  n_snapshots = std::get<0>(snapshotsListTuple).size();
   Info << "The number of snapshots is: " << n_snapshots << endl;
-  n_cells = std::get<0>(snapshotsTuple)[0].size();
+  n_cells = std::get<0>(snapshotsListTuple)[0].size();
   Info << "The number of cells is: " << n_cells << endl;
   Info << "Initial seeds length: " << initialSeeds.rows() << endl;
 }
@@ -157,196 +157,397 @@ HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
 template <typename... SnapshotsLists>
 void HyperReduction<SnapshotsLists...>::offlineStage()
 {
-  ITHACAparameters *para(ITHACAparameters::getInstance());
-  word methodName = para->ITHACAdict->lookupOrDefault<word>("HyperReduction", "GappyDEIM");
+  para = ITHACAparameters::getInstance();
+  methodName = para->ITHACAdict->lookupOrDefault<word>("HyperReduction", "GappyDEIM");
   
   if (methodName=="GappyDEIM")
   {
-    Folder = "ITHACAoutput/" + problemName + "/" + methodName;
+    offlineGappyDEIM();
+  }
+  else if (methodName=="EQP")
+  {
+    offlineEQP();
+  }
+  else
+  {
+    M_Assert(false, "Offline stage not performed. Invalid HR method.\n");
+  }
+}
+
+template <typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
+{
+  Folder = "ITHACAoutput/" + problemName + "/" + methodName;
     mkDir(Folder);
 
-    nodePoints = autoPtr<IOList<label>>(new IOList<label>(
-        IOobject("nodePoints", para->runTime.time().constant(), "../" + Folder,
-                  para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
+  nodePoints = autoPtr<IOList<label>>(new IOList<label>(
+      IOobject("nodePoints", para->runTime.time().constant(), "../" + Folder,
+                para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
+
+  Eigen::MatrixXd snapshotsModes;
+  getModesSVD(snapshotsListTuple, snapshotsModes, normalizingWeights);  
 
-    Eigen::MatrixXd snapshotsModes;
-    getModesSVD(snapshotsTuple, snapshotsModes, normalizingWeights);  
+  auto greedyMetric = para->ITHACAdict->lookupOrDefault<word>("GreedyMetric", "l2");
 
-    if (!nodePoints().headerOk())
+  if (!nodePoints().headerOk())
+  {
+    assert(n_modes > 0);
+    assert(n_nodes >= n_modes);
+
+    Eigen::VectorXd mp_not_mask = Eigen::VectorXd::Constant(n_cells * vectorial_dim, 1);
+    std::set<label> nodePointsSet;
+    std::deque<label> nodePointsDeque;
+
+    // set initialSeeds
+    if (initialSeeds.rows() > 0)
     {
-        assert(n_modes > 0);
-        assert(n_nodes >= n_modes);
+      P.resize(n_cells * vectorial_dim, initialSeeds.rows() * vectorial_dim);
+      P.reserve(Eigen::VectorXi::Constant(initialSeeds.rows() * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
+
+      for (int i = 0; i < initialSeeds.rows(); i++)
+      {
+        unsigned int index = initialSeeds(i) % n_cells;
+        for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+        {
+          P.insert(index+ith_field*n_cells, vectorial_dim*i+ith_field) = 1;
+          mp_not_mask(index + ith_field * n_cells) = 0;
+        }
+        
+        // check that are not repeated nodes in initialSeeds
+        if (nodePointsSet.find(index) == nodePointsSet.end()){
+          nodePointsSet.insert(index);
+          nodePointsDeque.push_back(index);
+        }
+      }
 
-        Eigen::VectorXd mp_not_mask = Eigen::VectorXd::Constant(n_cells * vectorial_dim, 1);
-        std::set<label> nodePointsSet;
-        std::deque<label> nodePointsDeque;
+      P.makeCompressed();
+    }
+
+    int na = n_nodes - initialSeeds.rows();
+    if (na > 0)
+    {
+      Eigen::SparseMatrix<double> reshapeMat;
+      reshapeMat.resize(n_cells, n_cells*vectorial_dim);
+      reshapeMat.reserve(Eigen::VectorXi::Constant(n_cells * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
 
-        // set initialSeeds
-        if (initialSeeds.rows() > 0)
+      for (unsigned int i = 0; i < n_cells; i++)
+      {
+        for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
         {
-          Info << "Add initialSeeds\n";
-          P.resize(n_cells * vectorial_dim, initialSeeds.rows() * vectorial_dim);
-          P.reserve(Eigen::VectorXi::Constant(initialSeeds.rows() * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
+          reshapeMat.insert(i, i+n_cells*ith_field) = 1;
+        }
+      }
+        
+      reshapeMat.makeCompressed();
+
+      if (greedyMetric=="L2")
+      {
+        Info << "####### Begin Greedy-L2 GappyDEIM #######" << endl;
+        Info << "####### Modes=" <<  n_modes
+              << ", nodePoints=" << n_nodes << " #######"
+              << endl;
+
+        int nb = 0;
+        int nit = std::min(n_modes, na);
+        int ncimin = std::floor(n_modes / nit);
+        int naimin = std::floor(na / n_modes);
+
+        Eigen::MatrixXd A;
+        Eigen::VectorXd b;
+        Eigen::VectorXd c;
+        Eigen::VectorXd r;
+        label ind_max, c1;
 
-          for (int i = 0; i < initialSeeds.rows(); i++)
+        double max;
+
+
+        for (int i = 1; i <= nit; i++)
+        {
+          int nci = ncimin;
+          // add the remaining modes in the quotient n_modes / nite
+          if (i <= n_modes % nit)
           {
-            unsigned int index = initialSeeds(i) % n_cells;
-            for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+              nci = ncimin + 1;
+          }
+          int nai = naimin;
+          // add the remaining nodePoints in the quotient na / n_modes
+          if (i <= na % n_modes)
+          {
+              nai = naimin + 1;
+          }
+
+          Eigen::MatrixXd V;
+
+          // select basis
+          if (i == 1)
+          {
+              V = snapshotsModes.leftCols(nci);
+          }
+          else
+          {
+            for (int q = 1; q <= nci; q++)
             {
-              P.insert(index+ith_field*n_cells, vectorial_dim*i+ith_field) = 1;
-              mp_not_mask(index + ith_field * n_cells) = 0;
+                A = P.transpose() * basisMatrix;
+                b = P.transpose() * snapshotsModes.col(nb + q - 1);
+                c = A.fullPivLu().solve(b);
+                r = snapshotsModes.col(nb + q - 1) - basisMatrix * c;
+                V.conservativeResize(snapshotsModes.rows(), q);
+                V.col(q - 1) = r;
             }
-            
-            // check that are not repeated nodes in initialSeeds
-            if (nodePointsSet.find(index) == nodePointsSet.end()){
-              nodePointsSet.insert(index);
-              nodePointsDeque.push_back(index);
+          }
+
+          for (int j = 1; j <= nai; j++)
+          {
+            if (P.cols() > 0)
+            {
+              max = (reshapeMat*(mp_not_mask.asDiagonal() * V)
+                      .rowwise()
+                      .lpNorm<2>().array().square().matrix())
+                      .maxCoeff(&ind_max, &c1);
             }
+            else
+            {
+              max = (reshapeMat*V.rowwise().lpNorm<2>().array().square().matrix()).maxCoeff(&ind_max, &c1);
+            }
+            
+            updateNodes(P, ind_max, mp_not_mask, nodePointsDeque);
           }
 
-          P.makeCompressed();
+          nb += nci;
+          basisMatrix = snapshotsModes.leftCols(nb);
         }
+        Info << "####### End of greedy GappyDEIM #######\n";
+      }
+      else if (greedyMetric=="SOPT")
+      {
+        Info << "####### Begin SOPT GappyDEIM #######" << endl;
+        Info << "####### Modes=" <<  n_modes
+              << ", nodePoints=" << n_nodes << " #######"
+              << endl;
+
+        label ind_max, c1;
+        double max;
+        Eigen::MatrixXd V = snapshotsModes.leftCols(n_modes);
+
+        for (unsigned int ith_node = 0; ith_node < na; ith_node++)
+        {
+          if (P.cols() > 0)
+          {
+            // TODO make efficient
+            Eigen::MatrixXd tmp = P.transpose()*V;
+            Eigen::MatrixXd R = mp_not_mask.asDiagonal() * V;
+            Eigen::MatrixXd inv = (tmp.transpose()*tmp).fullPivLu().inverse();
+            Eigen::VectorXd num = 1 + (reshapeMat*((R * inv).array()*R.array()).rowwise().sum().matrix()).array();
+            Eigen::VectorXd norma = (tmp.array().square()).colwise().sum();
+            Eigen::MatrixXd adding = reshapeMat*R.array().square().matrix();
+            adding.rowwise() += norma.transpose();
+            Eigen::VectorXd denom = (adding.array().pow(1./V.cols()).matrix()).rowwise().prod();
+
+            max = ((mp_not_mask.head(n_cells).asDiagonal()*num).array()/denom.array()).maxCoeff(&ind_max, &c1);
+          }
+          else
+          {
+            max = (reshapeMat*V.rowwise().lpNorm<2>().array().square().matrix()).maxCoeff(&ind_max, &c1);
+          }
 
-        int na = n_nodes - initialSeeds.rows();
-        if (na > 0)
+          updateNodes(P, ind_max, mp_not_mask, nodePointsDeque);
+        }
+        basisMatrix = V;
+        Info << "####### End of SOPT GappyDEIM #######\n";
+      }
+      else if (greedyMetric=="SOPTE")
+      {
+        Info << "####### Begin SOPT-exact GappyDEIM #######" << endl;
+        Info << "####### Modes=" <<  n_modes
+              << ", nodePoints=" << n_nodes << " #######"
+              << endl;
+
+        label ind_max, c1;
+        double max;
+        Eigen::MatrixXd A;
+        Eigen::VectorXd b;
+        Eigen::VectorXd c;
+        Eigen::VectorXd r;
+        Eigen::MatrixXd V = snapshotsModes.col(0);
+
+        max = (reshapeMat*snapshotsModes.leftCols(n_modes).rowwise().lpNorm<2>().array().square().matrix()).maxCoeff(&ind_max, &c1);
+        updateNodes(P, ind_max, mp_not_mask, nodePointsDeque);
+
+        for (unsigned int ith_node = 1; ith_node < na; ith_node++)
         {
-            int nb = 0;
-            int nit = std::min(n_modes, na);
-            int ncimin = std::floor(n_modes / nit);
-            int naimin = std::floor(na / n_modes);
-
-            Eigen::MatrixXd A;
-            Eigen::VectorXd b;
-            Eigen::VectorXd c;
-            Eigen::VectorXd r;
-            label ind_max, c1;
-
-            double max;
-
-            Info << "####### Begin Greedy GappyDEIM #######" << endl;
-            Info << "####### Modes=" <<  n_modes
-                  << ", nodePoints=" << n_nodes << " #######"
-                  << endl;
-            
+          if (ith_node<n_modes)
+          {
+            A = P.transpose() * V;
+            b = P.transpose() * snapshotsModes.col(ith_node);
+            c = A.fullPivLu().solve(b);
+            r = snapshotsModes.col(ith_node) - V * c;
 
+            max = (reshapeMat*r.rowwise().lpNorm<2>().array().square().matrix()).maxCoeff(&ind_max, &c1);
 
-            Eigen::SparseMatrix<double> reshapeMat;
-            reshapeMat.resize(n_cells, n_cells*vectorial_dim);
-            reshapeMat.reserve(Eigen::VectorXi::Constant(n_cells * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
+            V.conservativeResize(snapshotsModes.rows(), ith_node + 1);
+            V.col(ith_node) =  snapshotsModes.col(ith_node);
+          }
+          else
+          {
+            // TODO optimize
+            Eigen::MatrixXd tmp = P.transpose()*snapshotsModes.leftCols(n_modes);
+            Info << "SOPT: " << s_optimality(tmp) << endl;
+            tmp.conservativeResize(tmp.rows()+vectorial_dim, tmp.cols());
+            
+            Eigen::MatrixXd masked = mp_not_mask.asDiagonal()*snapshotsModes.leftCols(n_modes);
+
+            Eigen::VectorXd results(n_cells);
 
-            for (unsigned int i = 0; i < n_cells; i++)
+            for (unsigned int ith_cell = 0; ith_cell < n_cells; ith_cell++)
             {
               for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
               {
-                reshapeMat.insert(i, i+n_cells*ith_field) = 1;
+                tmp.row(tmp.rows()-vectorial_dim+ith_field) = masked.row(ith_cell +  ith_field*n_cells);
               }
+              results(ith_cell) = s_optimality(tmp);
             }
-              
-            reshapeMat.makeCompressed();
+            max = results.maxCoeff(&ind_max, &c1);
+          }
 
-            for (int i = 1; i <= nit; i++)
-            {
-                int nci = ncimin;
-                // add the remaining modes in the quotient n_modes / nite
-                if (i <= n_modes % nit)
-                {
-                    nci = ncimin + 1;
-                }
-                int nai = naimin;
-                // add the remaining nodePoints_xyz in the quotient na / n_modes
-                if (i <= na % n_modes)
-                {
-                    nai = naimin + 1;
-                }
-
-                Eigen::MatrixXd V;
-
-                // select basis
-                if (i == 1)
-                {
-                    V = snapshotsModes.leftCols(nci);
-                }
-                else
-                {
-                  for (int q = 1; q <= nci; q++)
-                  {
-                      A = P.transpose() * basisMatrix;
-                      b = P.transpose() * snapshotsModes.col(nb + q - 1);
-                      c = A.fullPivLu().solve(b);
-                      r = snapshotsModes.col(nb + q - 1) - basisMatrix * c;
-                      V.conservativeResize(snapshotsModes.rows(), q);
-                      V.col(q - 1) = r;
-                  }
-                }
-
-                for (int j = 1; j <= nai; j++)
-                {
-                  
-                  if (P.cols() > 0)
-                  {
-                    max = (reshapeMat*(mp_not_mask.asDiagonal() * V)
-                              .rowwise()
-                              .lpNorm<2>())
-                              .maxCoeff(&ind_max, &c1);
-                  }
-                  else
-                  {
-                    max = V.rowwise().lpNorm<2>().maxCoeff(&ind_max, &c1);
-                  }
-                  int idxes = P.cols();
-                  int maxFirstMesh = ind_max % n_cells;
-                  P.conservativeResize(snapshotsModes.rows(), idxes + vectorial_dim);
-                  
-                  for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-                  {
-                    P.insert(maxFirstMesh + ith_field * n_cells, idxes + ith_field) = 1;
-                    mp_not_mask(maxFirstMesh + ith_field * n_cells) = 0;
-                  }
-
-                  nodePointsDeque.push_back(maxFirstMesh);
-                }
-
-                nb += nci;
-                basisMatrix = snapshotsModes.leftCols(nb);
-            }
-        }
-        else
-        {
-            basisMatrix = snapshotsModes;
+          updateNodes(P, ind_max, mp_not_mask, nodePointsDeque);
         }
+        basisMatrix = snapshotsModes.leftCols(n_modes);
+        Info << "####### End of SOPTE GappyDEIM #######\n";
+      }
+    }
+    else
+    {
+      basisMatrix = snapshotsModes.leftCols(n_modes);
+      Info << "####### InitialSeeds equal to n_nodes #######\n";
+    }
 
-        Info << "####### End of greedy GappyDEIM #######\n";
-        cnpy::save(basisMatrix, Folder +"/basisMatrix.npy");
-        cnpy::save(P, Folder +"/projectionMatrix.npy");
-        Info << "Projection Matrix shape: " << P.rows() << " " << P.cols() << endl;
-        Info << "Basis Matrix shape: " << basisMatrix.rows() << " " << basisMatrix.cols() << endl;
-
-        evaluatePinv(P, basisMatrix, normalizingWeights);
-        renormalizedBasisMatrix = normalizingWeights.asDiagonal()*basisMatrix;
-        Info << "Pseudo Inverse Matrix shape: " << pinvPU.rows() << " " << pinvPU.cols() << endl;
-
-        // convert nodePointsSet to nodePoints i.e. list
-        Eigen::VectorXi nodes(nodePointsDeque.size());
-        unsigned int i{0};
-        for (auto &x : nodePointsDeque)
+    cnpy::save(basisMatrix, Folder +"/basisMatrix.npy");
+    cnpy::save(P, Folder +"/projectionMatrix.npy");
+    Info << "Projection Matrix shape: " << P.rows() << " " << P.cols() << endl;
+    Info << "Basis Matrix shape: " << basisMatrix.rows() << " " << basisMatrix.cols() << endl;
+
+    evaluatePinv(P, basisMatrix, normalizingWeights);
+    renormalizedBasisMatrix = normalizingWeights.asDiagonal()*basisMatrix;
+    Info << "Pseudo Inverse Matrix shape: " << pinvPU.rows() << " " << pinvPU.cols() << endl;
+
+    // convert nodePointsSet to nodePoints i.e. list
+    Eigen::VectorXi nodes(nodePointsDeque.size());
+    unsigned int i{0};
+    for (auto &x : nodePointsDeque)
+    {
+      nodePoints().append(x);
+      nodes(i) = x;
+      i++;
+    }
+    cnpy::save(nodes, Folder + "/mp.npy");
+    cnpy::save(pinvPU, Folder + "/pinvPU.npy");
+    nodePoints().write();
+  }
+  else
+  {
+    cnpy::load(pinvPU, Folder + "/pinvPU.npy");
+    cnpy::load(basisMatrix, Folder +"/basisMatrix.npy");
+  }
+}
+
+template <typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::updateNodes(Eigen::SparseMatrix<double>& P, label& ind_max, Eigen::VectorXd& mp_not_mask, std::deque<label>& nodePointsDeque)
+{
+  unsigned int last_col{0};
+  
+  if (P.rows()==0)
+  {
+    P.resize(n_cells*vectorial_dim, vectorial_dim);
+  }
+  else
+  {
+    last_col = P.cols();
+    P.conservativeResize(P.rows(), P.cols() + vectorial_dim);
+  }
+
+  for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+  {
+    P.insert(ind_max + ith_field * n_cells, last_col + ith_field) = 1;
+    mp_not_mask(ind_max + ith_field * n_cells) = 0;
+  }
+
+  nodePointsDeque.push_back(ind_max);
+}
+
+template <typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::offlineEQP()
+{
+  Folder = "ITHACAoutput/" + problemName + "/" + methodName;
+    mkDir(Folder);
+
+  nodePoints = autoPtr<IOList<label>>(new IOList<label>(
+      IOobject("nodePoints", para->runTime.time().constant(), "../" + Folder,
+                para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
+
+  Eigen::MatrixXd snapshotsModes;
+  getModesSVD(snapshotsListTuple, snapshotsModes, normalizingWeights);  
+
+  if (!nodePoints().headerOk())
+  {
+    assert(n_modes > 0);
+    assert(n_nodes >= n_modes);
+
+    Eigen::VectorXd mp_not_mask = Eigen::VectorXd::Constant(n_cells * vectorial_dim, 1);
+    std::set<label> nodePointsSet;
+    std::deque<label> nodePointsDeque;
+
+    // set initialSeeds
+    if (initialSeeds.rows() > 0)
+    {
+      P.resize(n_cells * vectorial_dim, initialSeeds.rows() * vectorial_dim);
+      P.reserve(Eigen::VectorXi::Constant(initialSeeds.rows() * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
+
+      for (int i = 0; i < initialSeeds.rows(); i++)
+      {
+        unsigned int index = initialSeeds(i) % n_cells;
+        for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
         {
-          nodePoints().append(x);
-          nodes(i) = x;
-          i++;
+          P.insert(index+ith_field*n_cells, vectorial_dim*i+ith_field) = 1;
+          mp_not_mask(index + ith_field * n_cells) = 0;
+        }
+        
+        // check that are not repeated nodes in initialSeeds
+        if (nodePointsSet.find(index) == nodePointsSet.end()){
+          nodePointsSet.insert(index);
+          nodePointsDeque.push_back(index);
         }
-        cnpy::save(nodes, Folder + "/mp.npy");
-        cnpy::save(pinvPU, Folder + "/pinvPU.npy");
-        nodePoints().write();
+      }
+
+      P.makeCompressed();
     }
-    else
+
+    Info << "####### End of greedy GappyDEIM #######\n";
+    cnpy::save(basisMatrix, Folder +"/basisMatrix.npy");
+    cnpy::save(P, Folder +"/projectionMatrix.npy");
+    Info << "Projection Matrix shape: " << P.rows() << " " << P.cols() << endl;
+    Info << "Basis Matrix shape: " << basisMatrix.rows() << " " << basisMatrix.cols() << endl;
+
+    evaluatePinv(P, basisMatrix, normalizingWeights);
+    renormalizedBasisMatrix = normalizingWeights.asDiagonal()*basisMatrix;
+    Info << "Pseudo Inverse Matrix shape: " << pinvPU.rows() << " " << pinvPU.cols() << endl;
+
+    // convert nodePointsSet to nodePoints i.e. list
+    Eigen::VectorXi nodes(nodePointsDeque.size());
+    unsigned int i{0};
+    for (auto &x : nodePointsDeque)
     {
-        cnpy::load(pinvPU, Folder + "/pinvPU.npy");
-        cnpy::load(basisMatrix, Folder +"/basisMatrix.npy");
+      nodePoints().append(x);
+      nodes(i) = x;
+      i++;
     }
+    cnpy::save(nodes, Folder + "/mp.npy");
+    cnpy::save(pinvPU, Folder + "/pinvPU.npy");
+    nodePoints().write();
   }
   else
   {
-    Info << "Offline stage not performed. Invalid HR method.\n";
+    cnpy::load(pinvPU, Folder + "/pinvPU.npy");
+    cnpy::load(basisMatrix, Folder +"/basisMatrix.npy");
   }
 }
 
@@ -375,24 +576,11 @@ void HyperReduction<SnapshotsLists...>::stackSnapshots(SnapshotsList sList, Eige
   Info << "####### End of computing hyper-reduction basis #######\n";
 }
 
-template <typename... SnapshotsLists>
-template<typename SnapshotsList>
-void HyperReduction<SnapshotsLists...>::stackNames(SnapshotsList sList)
-{
-  fieldNames.append(sList[0].name());
-}
-
-template <typename... SnapshotsLists>
-template<typename SnapshotsList>
-void HyperReduction<SnapshotsLists...>::stackDimensions(SnapshotsList sList)
-{
-  fieldDims.append(get_field_dim<typename SnapshotsList::value_type>());
-}
-
 template<typename... SnapshotsLists>
 void HyperReduction<SnapshotsLists...>::evaluatePinv(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd &fieldWeights) {
   assert(Projector.cols() > 0);
   Eigen::MatrixXd restricted = Projector.transpose() * Modes;
+  Info << "S-Optimalty: " << s_optimality(restricted) << endl;
   pinvPU = pinv_eigen_based(restricted);
   pinvPU = pinvPU*(Projector.transpose() * fieldWeights.array().cwiseInverse().matrix()).asDiagonal();
 }
@@ -479,10 +667,4 @@ List<label> HyperReduction<SnapshotsLists...>::global2local(List<label> &points,
   return localPoints;
 }
 
-template<typename... SnapshotsLists>
-template<typename FieldType>
-autoPtr<FieldType> HyperReduction<SnapshotsLists...>::interpolateField(FieldType& field) {
-    return autoPtr<FieldType>(new FieldType(submesh->interpolate(field)));
-}
-
 #endif
diff --git a/tutorials/CFD/24HyperReduction/24HyperReduction.C b/tutorials/CFD/24HyperReduction/24HyperReduction.C
index d7266ea65..ce7b3e4c7 100644
--- a/tutorials/CFD/24HyperReduction/24HyperReduction.C
+++ b/tutorials/CFD/24HyperReduction/24HyperReduction.C
@@ -205,7 +205,8 @@ void test_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
         dimensionedScalar("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), 0)
     );
     // Parameters used to train the non-linear function
-    Eigen::MatrixXd pars = ITHACAutilities::rand(100, 2, -0.5, 0.5);
+    Eigen::MatrixXd pars;
+    cnpy::load(pars, "trainingPars.npy");
 
     // Perform the offline phase
     for (int i = 0; i < 100; i++)
@@ -263,7 +264,8 @@ void test_vector(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
         dimensionedVector("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), vector(0, 0, 0))
     );
     // Parameters used to train the non-linear function
-    Eigen::MatrixXd pars = ITHACAutilities::rand(100, 2, -0.5, 0.5);
+    Eigen::MatrixXd pars;
+    cnpy::load(pars, "trainingPars.npy");
 
     // Perform the offline phase
     for (int i = 0; i < 100; i++)
@@ -296,11 +298,6 @@ void test_vector(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
     ITHACAstream::exportSolution(S, name(1), "./ITHACAoutput/Online/");
     // Compute the L2 error and print it
     Info << ITHACAutilities::errorL2Rel(S2, S) << endl;
-
-    Eigen::VectorXd vec = c.renormalizedBasisMatrix.col(2);
-    S = S*0;
-    S = Foam2Eigen::Eigen2field(S, vec);
-    ITHACAstream::exportSolution(S, name(1), "./basis/");
 }
 
 void test_vector_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime){
@@ -342,7 +339,8 @@ void test_vector_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time&
     );
 
     // Parameters used to train the non-linear function
-    Eigen::MatrixXd pars = ITHACAutilities::rand(100, 2, -0.5, 0.5);
+    Eigen::MatrixXd pars;
+    cnpy::load(pars, "trainingPars.npy");
 
     // Perform the offline phase
     for (int i = 0; i < 100; i++)
@@ -372,6 +370,9 @@ void test_vector_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time&
     auto theta = c.onlineCoeffs(sfield(), par_new);
     Eigen::VectorXd aprfield = c.renormalizedBasisMatrix*theta;
     // Transform to an OpenFOAM field and export
+    // c.eigen2fields(aprfield, V, S);
+    // volVectorField V2("V_online", V);
+    // volScalarField S2("S_online", S);
     Eigen::VectorXd recvec = aprfield.head(3*S.size());
     Eigen::VectorXd recsca = aprfield.tail(S.size());
     volVectorField V2("V_online", Foam2Eigen::Eigen2field(V, recvec));
diff --git a/tutorials/CFD/24HyperReduction/system/ITHACAdict b/tutorials/CFD/24HyperReduction/system/ITHACAdict
index 4878925ab..8c1b4218a 100755
--- a/tutorials/CFD/24HyperReduction/system/ITHACAdict
+++ b/tutorials/CFD/24HyperReduction/system/ITHACAdict
@@ -18,8 +18,8 @@ FoamFile
 EigenSolver eigen;
 
 // Number of modes to output and to use for projection
-Nodes 200;
-Modes 80;
+Nodes 50;
+Modes 20;
 
 // Output format to save market vectors.
 OutPrecision 20;
@@ -27,3 +27,4 @@ OutType fixed;
 
 // HR
 HyperReduction GappyDEIM;
+GreedyMetric SOPTE;//L2, SOPT, SOPTE

From e6e12b9be0ce8fbe96226287b48ab565ff17cf7e Mon Sep 17 00:00:00 2001
From: fromor <francesco.romor@gmail.com>
Date: Fri, 28 Oct 2022 16:24:43 +0200
Subject: [PATCH 04/59] add ECP working scalar, vector

---
 src/ITHACA_HR/hyperReduction.H                |  49 +-
 src/ITHACA_HR/hyperReduction.templates.H      | 353 ++++++++++---
 .../CFD/24HyperReduction/24HyperReduction.C   | 464 +++++++++++-------
 .../CFD/24HyperReduction/system/ITHACAdict    |   8 +-
 4 files changed, 617 insertions(+), 257 deletions(-)

diff --git a/src/ITHACA_HR/hyperReduction.H b/src/ITHACA_HR/hyperReduction.H
index cb1d16276..f3db6cdb3 100644
--- a/src/ITHACA_HR/hyperReduction.H
+++ b/src/ITHACA_HR/hyperReduction.H
@@ -37,18 +37,13 @@ SourceFiles
 #include "EigenFunctions.H"
 #include "ITHACAutilities.H"
 #include "fvMeshSubset.H"
+#include <unsupported/Eigen/NNLS>
 #include <set>
 
-enum class HyperReductionMethod
-{
-    GappyDEIM
-};
-
 template <typename... SnapshotsLists>
 class HyperReduction
 {
 public:
-    const word methodNames[1] = {"GappyDEIM"};
     word methodName;
 
     using SnapshotsListTuple = std::tuple<std::decay_t<SnapshotsLists>...>;
@@ -95,6 +90,9 @@ public:
     // Initial nodes
     Eigen::VectorXi initialSeeds;
 
+    // nodes
+    Eigen::VectorXi nodes;
+
     /// The name of the non-linear function e.g. HR_method/residual
     word problemName;
 
@@ -138,12 +136,21 @@ public:
     // TODO
     Eigen::MatrixXd pinvPU;
 
-    /// The P matrix of the HyperReduction method
+    // TODO
+    Eigen::MatrixXd wPU;
+
+    // TODO
+    Eigen::VectorXd eigenValueseig;
+
+    /// The P matrix of the HyperReduction method. The nodes are ordered in the order of insertion during the greedy procedure. The components related to the same node follow immediately.
     Eigen::SparseMatrix<double> P;
 
     /// Normalizing weights of the offline snapshots
     Eigen::VectorXd normalizingWeights;
 
+    /// Quadrature weights. Ordered in the same order of matrix P.
+    Eigen::VectorXd quadratureWeights;
+
     /// Submesh of the HyperReduction method
     autoPtr<fvMeshSubset> submesh;
     
@@ -163,7 +170,7 @@ public:
     //----------------------------------------------------------------------
     /// @brief      TODO
     ///
-    void offlineEQP();
+    void offlineECP();
 
     //----------------------------------------------------------------------
     /// @brief      TODO
@@ -171,7 +178,7 @@ public:
     /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
     /// @param[in]  sList  The list of snapshots
     ///
-    void getModesSVD(SnapshotsListTuple &SnapshotsListTuple, Eigen::MatrixXd &modesSVD, Eigen::VectorXd &fieldWeights);
+    void getModesSVD(SnapshotsListTuple &SnapshotsListTuple, Eigen::MatrixXd &modesSVD, Eigen::VectorXd &fieldWeights, bool saveModesFlag = false);
     
     //----------------------------------------------------------------------
     /// @brief      TODO
@@ -189,6 +196,15 @@ public:
     ///
     template <typename SnapshotsList>
     void stackSnapshots(SnapshotsList sList, Eigen::MatrixXd &snapshotsMatrix, Eigen::VectorXd &fieldWeights);
+    
+    //----------------------------------------------------------------------
+    /// @brief      TODO
+    ///
+    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+    /// @param[in]  sList  The list of snapshots
+    ///
+    template <typename SnapshotsList>
+    void saveModes(SnapshotsList sList, Eigen::MatrixXd& snapshotsMatrix, unsigned int &rowIndex, unsigned int &modeIndex);
 
     //----------------------------------------------------------------------
     /// @brief      TODO
@@ -219,6 +235,14 @@ public:
     ///
     void evaluatePinv(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd& fieldWeights);
 
+     //----------------------------------------------------------------------
+    /// @brief      Compute the pseudo-inverse of the matrix M restricted with the projector P
+    ///
+    /// @param[in]  Projector  projector into interpolation nodes
+    /// @param[in]  Modes      matrix to restrict and invert
+    ///
+    void evaluateWPU(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd& fieldWeights, Eigen::VectorXd& quadratureWeights);
+
     //----------------------------------------------------------------------
     /// @brief      Compute the submesh common to all fields in SnapshotsLists
     ///
@@ -311,6 +335,13 @@ public:
             }(oFields), ...);
 
     }
+
+    /// @brief      TODO
+    ///
+    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+    /// @param[in]  sList  The list of snapshots
+    ///
+    void initReshapeMat(Eigen::SparseMatrix<double> &reshapeMat);
 };
 
 #endif
diff --git a/src/ITHACA_HR/hyperReduction.templates.H b/src/ITHACA_HR/hyperReduction.templates.H
index 80f91c9bc..0dd4d2694 100644
--- a/src/ITHACA_HR/hyperReduction.templates.H
+++ b/src/ITHACA_HR/hyperReduction.templates.H
@@ -33,6 +33,8 @@ License
 
 #include "hyperReduction.H"
 
+// TODO increase modularity to avoid heavy compiling costs
+
 // Using the Eigen library, using the SVD decomposition method to solve the
 // matrix pseudo-inverse, the default error er is 0
 Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0) {
@@ -60,8 +62,9 @@ Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0) {
 
 template <typename... SnapshotsLists>
 void HyperReduction<SnapshotsLists...>::getModesSVD(
-    SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights)
+    SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights, bool saveModesFlag)
 {
+  // TODO possibility to save openfoam modes fields
   ITHACAparameters* para(ITHACAparameters::getInstance());
   if (!ITHACAutilities::check_folder(Folder + "/Modes/"))
   {
@@ -77,7 +80,6 @@ void HyperReduction<SnapshotsLists...>::getModesSVD(
     Info << "####### End of SVD for " << problemName << " #######" <<
           endl;
 
-    Eigen::VectorXd eigenValueseig;
     Eigen::MatrixXd eigenVectoreig;
     eigenValueseig = svd.singularValues().real();
     eigenVectoreig = svd.matrixU().real();
@@ -103,6 +105,17 @@ void HyperReduction<SnapshotsLists...>::getModesSVD(
                             para->outytpe);
     cnpy::save(modesSVD, Folder + "/Modes/modes.npy");
     cnpy::save(fieldWeights, Folder + "/Modes/normalizingWeights.npy");
+
+
+    if (saveModesFlag)
+    {
+      unsigned int rowIndex{0};
+      for (unsigned int modeIndex = 0; modeIndex < modesSVD.cols(); modeIndex++)
+      {
+        std::apply([this, &modesSVD, &rowIndex, &modeIndex](auto& ...snapList){(..., saveModes(snapList, modesSVD, rowIndex, modeIndex));}, snapshotsListTuple);
+        rowIndex = 0;
+      }
+    }
   }
   else
   {
@@ -112,6 +125,20 @@ void HyperReduction<SnapshotsLists...>::getModesSVD(
   }
 }
 
+template <typename... SnapshotsLists>
+template <typename SnapshotsList>
+void HyperReduction<SnapshotsLists...>::saveModes(SnapshotsList sList, Eigen::MatrixXd& snapshotsMatrix, unsigned int &rowIndex, unsigned int &modeIndex)
+{
+  unsigned int field_dim = get_field_dim<typename SnapshotsList::value_type>();
+  auto fieldName = sList[0].name();
+  unsigned int fieldSize = field_dim*sList[0].size();
+  Eigen::VectorXd fieldBlock = snapshotsMatrix.block(rowIndex, modeIndex, fieldSize, 1);
+  auto fieldOut = Foam2Eigen::Eigen2field(sList[0], fieldBlock , true);
+  rowIndex +=fieldSize;
+  modeIndex++;
+  ITHACAstream::exportSolution(fieldOut, name(modeIndex), Folder + "/Modes/");
+}
+
 // Template function constructor
 template <typename... SnapshotsLists>
 HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
@@ -127,7 +154,7 @@ HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
       snapshotsListTuple{std::forward_as_tuple(snapshotsLists...)}
 {
   Info << "Init HyperReduction class with vectorial dim: " << vectorial_dim << endl;
-
+  para = ITHACAparameters::getInstance();
   // TODO check snapshotsLists is not empty
   // TODO check that the first snapshotsList is not empty (includes above)
 
@@ -159,24 +186,25 @@ void HyperReduction<SnapshotsLists...>::offlineStage()
 {
   para = ITHACAparameters::getInstance();
   methodName = para->ITHACAdict->lookupOrDefault<word>("HyperReduction", "GappyDEIM");
-  
+
   if (methodName=="GappyDEIM")
   {
     offlineGappyDEIM();
   }
-  else if (methodName=="EQP")
+  else if (methodName=="ECP")
   {
-    offlineEQP();
+    offlineECP();
   }
   else
   {
-    M_Assert(false, "Offline stage not performed. Invalid HR method.\n");
+    M_Assert(false, "Offline stage hyper-reduction not performed. Invalid HR method. Possible methods are: 'GappyDEIM', 'ECP.'\n");
   }
 }
 
 template <typename... SnapshotsLists>
 void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
 {
+  methodName = "GappyDEIM";
   Folder = "ITHACAoutput/" + problemName + "/" + methodName;
     mkDir(Folder);
 
@@ -204,41 +232,34 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
       P.resize(n_cells * vectorial_dim, initialSeeds.rows() * vectorial_dim);
       P.reserve(Eigen::VectorXi::Constant(initialSeeds.rows() * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
 
+      unsigned int trueSeeds{0};
       for (int i = 0; i < initialSeeds.rows(); i++)
       {
         unsigned int index = initialSeeds(i) % n_cells;
-        for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-        {
-          P.insert(index+ith_field*n_cells, vectorial_dim*i+ith_field) = 1;
-          mp_not_mask(index + ith_field * n_cells) = 0;
-        }
-        
-        // check that are not repeated nodes in initialSeeds
+        // check that there are not repeated nodes in initialSeeds
         if (nodePointsSet.find(index) == nodePointsSet.end()){
           nodePointsSet.insert(index);
           nodePointsDeque.push_back(index);
+
+          for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+          {
+            P.insert(index+ith_field*n_cells, vectorial_dim*trueSeeds+ith_field) = 1;
+            mp_not_mask(index + ith_field * n_cells) = 0;
+          }
+          trueSeeds++;
         }
       }
 
+      P.conservativeResize(P.rows(), nodePointsDeque.size()*vectorial_dim);
       P.makeCompressed();
+      M_Assert(nodePointsDeque.size()<=n_nodes, "Size of 'initialSeeds' is greater than 'n_nodes'");
     }
 
     int na = n_nodes - initialSeeds.rows();
     if (na > 0)
     {
       Eigen::SparseMatrix<double> reshapeMat;
-      reshapeMat.resize(n_cells, n_cells*vectorial_dim);
-      reshapeMat.reserve(Eigen::VectorXi::Constant(n_cells * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
-
-      for (unsigned int i = 0; i < n_cells; i++)
-      {
-        for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-        {
-          reshapeMat.insert(i, i+n_cells*ith_field) = 1;
-        }
-      }
-        
-      reshapeMat.makeCompressed();
+      initReshapeMat(reshapeMat);
 
       if (greedyMetric=="L2")
       {
@@ -370,7 +391,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
         Eigen::VectorXd r;
         Eigen::MatrixXd V = snapshotsModes.col(0);
 
-        max = (reshapeMat*snapshotsModes.leftCols(n_modes).rowwise().lpNorm<2>().array().square().matrix()).maxCoeff(&ind_max, &c1);
+        max = (reshapeMat* (mp_not_mask.asDiagonal()*snapshotsModes.leftCols(n_modes)).rowwise().lpNorm<2>().array().square().matrix()).maxCoeff(&ind_max, &c1);
         updateNodes(P, ind_max, mp_not_mask, nodePointsDeque);
 
         for (unsigned int ith_node = 1; ith_node < na; ith_node++)
@@ -431,13 +452,9 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
     Info << "Pseudo Inverse Matrix shape: " << pinvPU.rows() << " " << pinvPU.cols() << endl;
 
     // convert nodePointsSet to nodePoints i.e. list
-    Eigen::VectorXi nodes(nodePointsDeque.size());
-    unsigned int i{0};
     for (auto &x : nodePointsDeque)
     {
       nodePoints().append(x);
-      nodes(i) = x;
-      i++;
     }
     cnpy::save(nodes, Folder + "/mp.npy");
     cnpy::save(pinvPU, Folder + "/pinvPU.npy");
@@ -451,7 +468,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
 }
 
 template <typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::updateNodes(Eigen::SparseMatrix<double>& P, label& ind_max, Eigen::VectorXd& mp_not_mask, std::deque<label>& nodePointsDeque)
+void HyperReduction<SnapshotsLists...>::updateNodes(Eigen::SparseMatrix<double>& P, label& ind, Eigen::VectorXd& mp_not_mask, std::deque<label>& nodePointsDeque)
 {
   unsigned int last_col{0};
   
@@ -467,16 +484,28 @@ void HyperReduction<SnapshotsLists...>::updateNodes(Eigen::SparseMatrix<double>&
 
   for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
   {
-    P.insert(ind_max + ith_field * n_cells, last_col + ith_field) = 1;
-    mp_not_mask(ind_max + ith_field * n_cells) = 0;
+    P.insert(ind + ith_field * n_cells, last_col + ith_field) = 1;
+    mp_not_mask(ind + ith_field * n_cells) = 0;
   }
 
-  nodePointsDeque.push_back(ind_max);
+  nodePointsDeque.push_back(ind);
+
+  nodes.conservativeResize(nodes.rows()+1);
+  nodes(nodes.rows()-1) = ind;
 }
 
 template <typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::offlineEQP()
+void HyperReduction<SnapshotsLists...>::offlineECP()
 {
+  methodName = "ECP";
+
+  n_nodes = n_modes + 1;
+
+  Info << "####### Begin ECP #######" << endl;
+  Info << "####### Modes=" <<  n_modes
+            << ", nodePoints=" << n_nodes << " #######"
+            << endl;
+
   Folder = "ITHACAoutput/" + problemName + "/" + methodName;
     mkDir(Folder);
 
@@ -485,13 +514,43 @@ void HyperReduction<SnapshotsLists...>::offlineEQP()
                 para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
 
   Eigen::MatrixXd snapshotsModes;
-  getModesSVD(snapshotsListTuple, snapshotsModes, normalizingWeights);  
+  getModesSVD(snapshotsListTuple, snapshotsModes, normalizingWeights, true);  
 
   if (!nodePoints().headerOk())
   {
     assert(n_modes > 0);
     assert(n_nodes >= n_modes);
 
+    // matrices for quadratureWeights evaluation
+    Eigen::MatrixXd J;//shape: (vectorial_dim * (n_modes + 1), nodePointsDeque.size())
+    Eigen::MatrixXd Jwhole(vectorial_dim * (n_modes + 1), n_cells);
+    Eigen::VectorXd q(vectorial_dim * (n_modes + 1));
+
+    // matrices for greedy selection of the nodes
+    Eigen::MatrixXd A(vectorial_dim*n_modes, n_cells);
+    Eigen::VectorXd b = Eigen::VectorXd::Constant(vectorial_dim*n_modes, 1);
+
+    Eigen::VectorXd volumes = ITHACAutilities::getMassMatrixFV(std::get<0>(snapshotsListTuple)[0]);
+    double volume = volumes.array().sum();
+
+    for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+    {
+      Eigen::MatrixXd block = snapshotsModes.block(ith_field*n_cells, 0, n_cells, n_modes).transpose();
+
+      q.segment(ith_field*(n_modes+1), n_modes) = block.rowwise().sum();
+      q(ith_field*(n_modes+1)+n_modes) = volume;
+
+      Jwhole.middleRows(ith_field*(n_modes+1), n_modes) = block;
+      Jwhole.row(ith_field*(n_modes+1)+n_modes) = Eigen::VectorXd::Constant(n_cells, 1);
+
+      Eigen::VectorXd mean = block.rowwise().mean();
+      block.colwise() -= mean;
+      Eigen::VectorXd Anorm = block.colwise().lpNorm<2>();
+      block.array().rowwise() /= Anorm.transpose().array();
+
+      A.middleRows(ith_field*n_modes, n_modes) = block;
+    }
+
     Eigen::VectorXd mp_not_mask = Eigen::VectorXd::Constant(n_cells * vectorial_dim, 1);
     std::set<label> nodePointsSet;
     std::deque<label> nodePointsDeque;
@@ -499,56 +558,208 @@ void HyperReduction<SnapshotsLists...>::offlineEQP()
     // set initialSeeds
     if (initialSeeds.rows() > 0)
     {
+      // TODO init matrix P from initialSeeds
       P.resize(n_cells * vectorial_dim, initialSeeds.rows() * vectorial_dim);
       P.reserve(Eigen::VectorXi::Constant(initialSeeds.rows() * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
 
+      unsigned int trueSeeds{0};
       for (int i = 0; i < initialSeeds.rows(); i++)
       {
         unsigned int index = initialSeeds(i) % n_cells;
-        for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-        {
-          P.insert(index+ith_field*n_cells, vectorial_dim*i+ith_field) = 1;
-          mp_not_mask(index + ith_field * n_cells) = 0;
-        }
-        
-        // check that are not repeated nodes in initialSeeds
+        // check that there are not repeated nodes in initialSeeds
         if (nodePointsSet.find(index) == nodePointsSet.end()){
           nodePointsSet.insert(index);
           nodePointsDeque.push_back(index);
+
+          for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+          {
+            P.insert(index+ith_field*n_cells, vectorial_dim*trueSeeds+ith_field) = 1;
+            mp_not_mask(index + ith_field * n_cells) = 0;
+          }
+          trueSeeds++;
         }
       }
 
+      P.conservativeResize(P.rows(), nodePointsDeque.size()*vectorial_dim);
       P.makeCompressed();
+      M_Assert(nodePointsDeque.size()<=n_nodes, "Size of 'initialSeeds' is greater than 'n_nodes'");
+      
+      // TODO fix with only positive weights (NNLS)
+      // Init quadratureWeights
+      J.resize(vectorial_dim * (n_modes + 1), nodePointsDeque.size());
+      J = Jwhole(Eigen::indexing::all, nodes);
+      // J = Jwhole*P;
+      // for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+      // {
+      //   Eigen::MatrixXd block = APtmp(Eigen::indexing::all, Eigen::seqN(ith_field, nodePointsDeque.size(), vectorial_dim));
+      //   J.middleRows(n_modes*ith_field, n_modes) = block;
+      // }
+
+      // J.row(J.rows()-1) = Eigen::VectorXd::Constant(J.cols(), 1);
+
+      quadratureWeights.resize(nodePointsDeque.size()*vectorial_dim);
+      for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+      {
+        quadratureWeights.segment(ith_field*nodePointsDeque.size(), nodePointsDeque.size()) = J.middleRows(ith_field*(n_modes+1), n_modes+1).colPivHouseholderQr().solve(q.segment(ith_field*(n_modes+1), n_modes+1));
+        b.segment(ith_field*n_modes, n_modes) = q.segment(ith_field*(n_modes+1), n_modes)-J.middleRows(ith_field*(n_modes+1), n_modes)*quadratureWeights.segment(ith_field*nodePointsDeque.size(), nodePointsDeque.size());
+      }
+      Info << "Tol: " << b.lpNorm<2>()/q.lpNorm<2>() << endl;
+      Info << "ECP Error: " << b.maxCoeff() << endl;
+      b = b/b.lpNorm<2>();
+
+      Info << "weights: " << quadratureWeights << endl;
     }
 
-    Info << "####### End of greedy GappyDEIM #######\n";
-    cnpy::save(basisMatrix, Folder +"/basisMatrix.npy");
-    cnpy::save(P, Folder +"/projectionMatrix.npy");
-    Info << "Projection Matrix shape: " << P.rows() << " " << P.cols() << endl;
-    Info << "Basis Matrix shape: " << basisMatrix.rows() << " " << basisMatrix.cols() << endl;
+    int na = n_nodes - initialSeeds.rows();
+    Eigen::SparseMatrix<double> reshapeMat;
+    initReshapeMat(reshapeMat);
 
-    evaluatePinv(P, basisMatrix, normalizingWeights);
-    renormalizedBasisMatrix = normalizingWeights.asDiagonal()*basisMatrix;
-    Info << "Pseudo Inverse Matrix shape: " << pinvPU.rows() << " " << pinvPU.cols() << endl;
+    if (na > 0)
+    {
+      std::cout << "DEBUG ~/projects/ITHACA-FV/src/ITHACA_HR/hyperReduction.templates.H at Line 616 " << std::endl;
+      label ind_max, r1;
+      double max;
+      
+      // Eigen::MatrixXd Aw = A*mp_not_mask.asDiagonal();
+      // for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+      // {
+      //   Aw.middleCols(n_cells*ith_field, n_cells).array().colwise()*=b.segment(n_modes*ith_field, n_modes).array();
+      // }
+      std::cout << "DEBUG ~/projects/ITHACA-FV/src/ITHACA_HR/hyperReduction.templates.H at Line 625 " << b.rows() << " " << A.rows() << " " << A.cols() << " " << mp_not_mask.head(n_cells).rows() << std::endl;
+      max = ((b.transpose()*A*mp_not_mask.head(n_cells).asDiagonal()).colwise().sum()).maxCoeff(&r1, &ind_max);
+
+      updateNodes(P, ind_max, mp_not_mask, nodePointsDeque);
+      
+      Info << "Max ind init: " << ind_max << " Deque size: " << nodePointsDeque.size() << endl;
+
+      // TODO encapsulate update quadratureWeights
+      J.resize(vectorial_dim * (n_modes + 1), nodePointsDeque.size());
+      std::cout << "DEBUG ~/projects/ITHACA-FV/src/ITHACA_HR/hyperReduction.templates.H at Line 634 " << P.bottomRows(nodePointsDeque.size()).rows() << " " << P.bottomRows(nodePointsDeque.size()).cols() << std::endl;
+      J = Jwhole(Eigen::indexing::all, nodes);
+      // J = Jwhole*P;
+      std::cout << "DEBUG ~/projects/ITHACA-FV/src/ITHACA_HR/hyperReduction.templates.H at Line 636 " << std::endl;
+      
+      quadratureWeights.resize(nodePointsDeque.size()*vectorial_dim);
+      for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+      {
+        quadratureWeights.segment(ith_field*nodePointsDeque.size(), nodePointsDeque.size()) = J.middleRows(ith_field*(n_modes+1), n_modes+1).colPivHouseholderQr().solve(q.segment(ith_field*(n_modes+1), n_modes+1));
+        b.segment(ith_field*n_modes, n_modes) = q.segment(ith_field*(n_modes+1), n_modes)-J.middleRows(ith_field*(n_modes+1), n_modes)*quadratureWeights.segment(ith_field*nodePointsDeque.size(), nodePointsDeque.size());
+      }
+      Info << "DEBUG: " << b << endl;
+      Info << "Tol: " << b.lpNorm<2>()/q.lpNorm<2>() << endl;
+      Info << "ECP Error: " << b.maxCoeff() << endl;
+      b = b/b.lpNorm<2>();
+
+      // quadratureWeights.resize(nodePointsDeque.size());
+      // quadratureWeights = J.colPivHouseholderQr().solve(q);
+
+      // // auto ECPSolver = Eigen::NNLS(J);
+      // // quadratureWeights = ECPSolver.solve(q);
+      // // std::cout << "Info NNLS: " << ECPSolver.info() << endl;
+      // Info << quadratureWeights << endl;
+
+      // b = q-J*quadratureWeights;
+      // Info << "Tol: " << b.lpNorm<2>()/q.lpNorm<2>() << endl;
+      // Info << "ECP Error: " << b.maxCoeff(&ind_max, &c1) << " " << ind_max << " vol: " << b(b.rows()-1) << endl;
+      // b = b/b.lpNorm<2>();
+
+      for (unsigned int ith_node = 1; ith_node < na; ith_node++)
+      {
+        max = ((b.transpose()*A*mp_not_mask.head(n_cells).asDiagonal()).colwise().sum()).maxCoeff(&r1, &ind_max);
+
+        updateNodes(P, ind_max, mp_not_mask, nodePointsDeque);
+        
+        Info << "Max ind init: " << ind_max << " Deque size: " << nodePointsDeque.size() << endl;
+
+        // TODO encapsulate update quadratureWeights
+        J.resize(vectorial_dim * (n_modes + 1), nodePointsDeque.size());
+        J = Jwhole(Eigen::indexing::all, nodes);
+        // J = Jwhole*P;
+
+        quadratureWeights.resize(nodePointsDeque.size()*vectorial_dim);
+        for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+        {
+          quadratureWeights.segment(ith_field*nodePointsDeque.size(), nodePointsDeque.size()) = J.middleRows(ith_field*(n_modes+1), n_modes+1).colPivHouseholderQr().solve(q.segment(ith_field*(n_modes+1), n_modes+1));
+          b.segment(ith_field*n_modes, n_modes) = q.segment(ith_field*(n_modes+1), n_modes)-J.middleRows(ith_field*(n_modes+1), n_modes)*quadratureWeights.segment(ith_field*nodePointsDeque.size(), nodePointsDeque.size());
+        }
+        Info << "Tol: " << b.lpNorm<2>()/q.lpNorm<2>() << endl;
+        Info << "ECP Error: " << b.maxCoeff() << endl;
+        b = b/b.lpNorm<2>();
+        Info << "DEBUG quad size: " << quadratureWeights.rows() << endl;
+        
+        // Aw = A*mp_not_mask.asDiagonal();
+        // for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+        // {
+        //   Aw.middleCols(n_cells*ith_field, n_cells).array().colwise()*=b.segment(n_modes*ith_field, n_modes).array();
+        // }
+        // max = (Aw.colwise().sum()*reshapeMat).transpose().maxCoeff(&ind_max, &c1);
+
+        // updateNodes(P, ind_max, mp_not_mask, nodePointsDeque);
+        
+        // Info << "Max ind: " << ind_max << " Deque size: " << nodePointsDeque.size() << endl;
+
+        // // TODO encapsulate update quadratureWeights
+        // J.resize(n_modes*vectorial_dim+1, nodePointsDeque.size());
+
+        // Eigen::MatrixXd APtmp = (snapshotsModes).leftCols(n_modes).transpose()*P;
+
+        // // block transpose (M, nodes.size()*vectorial_dim)->(M*vectorial_dim, nodes.size()) if vectorial_dim > 1
+        // for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+        // {
+        //   Eigen::MatrixXd block = APtmp(Eigen::indexing::all, Eigen::seqN(ith_field, nodePointsDeque.size(), vectorial_dim));
+        //   J.middleRows(n_modes*ith_field, n_modes) = block;
+        // }
+
+        // J.row(J.rows()-1) = Eigen::VectorXd::Constant(J.cols(), 1);
+        // // J.array().colwise() /= q.array();
+
+        // quadratureWeights.resize(nodePointsDeque.size());
+        // quadratureWeights = J.colPivHouseholderQr().solve(q);
+
+        // b = q-J*quadratureWeights;
+        // Info << "Tol: " << b.lpNorm<2>()/q.lpNorm<2>() << endl;
+        // Info << "ECP Error: " << b.maxCoeff(&ind_max, &c1) << " " << ind_max << " vol: " << b(b.rows()-1) << endl << endl;
+        // b = b/b.lpNorm<2>();
+        // Info << "weights: " << quadratureWeights << endl;
+      }
+    }
+
+    basisMatrix = snapshotsModes.leftCols(n_modes);
+    cnpy::save(basisMatrix, Folder +"/basisMatrix.npy");
+    cnpy::save(quadratureWeights, Folder +"/quadratureWeights.npy");
+    nodePoints().write();
 
-    // convert nodePointsSet to nodePoints i.e. list
-    Eigen::VectorXi nodes(nodePointsDeque.size());
-    unsigned int i{0};
     for (auto &x : nodePointsDeque)
     {
       nodePoints().append(x);
-      nodes(i) = x;
-      i++;
     }
     cnpy::save(nodes, Folder + "/mp.npy");
-    cnpy::save(pinvPU, Folder + "/pinvPU.npy");
-    nodePoints().write();
+
+    evaluateWPU(P, basisMatrix, normalizingWeights, quadratureWeights);
+    cnpy::save(wPU, Folder + "/wPU.npy");
   }
   else
   {
     cnpy::load(pinvPU, Folder + "/pinvPU.npy");
     cnpy::load(basisMatrix, Folder +"/basisMatrix.npy");
+    cnpy::load(quadratureWeights, Folder +"/quadratureWeights.npy");
+  }
+}
+
+template<typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::initReshapeMat(Eigen::SparseMatrix<double> &reshapeMat)
+{
+  reshapeMat.resize(n_cells, n_cells*vectorial_dim);
+  reshapeMat.reserve(Eigen::VectorXi::Constant(n_cells * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
+
+  for (unsigned int i = 0; i < n_cells; i++)
+  {
+    for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+    {
+      reshapeMat.insert(i, i+n_cells*ith_field) = 1;
+    }
   }
+  reshapeMat.makeCompressed();
 }
 
 template <typename... SnapshotsLists>
@@ -585,6 +796,30 @@ void HyperReduction<SnapshotsLists...>::evaluatePinv(Eigen::SparseMatrix<double>
   pinvPU = pinvPU*(Projector.transpose() * fieldWeights.array().cwiseInverse().matrix()).asDiagonal();
 }
 
+template<typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::evaluateWPU(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd &fieldWeights, Eigen::VectorXd& quadratureWeights) {
+  assert(Projector.cols() > 0);
+  // Eigen::MatrixXd restricted = Projector.transpose() * Modes;
+
+  // restricted.array().rowwise()*= quadratureWeights.transpose().array();
+
+  // wPU = restricted.transpose()*(Projector.transpose() * fieldWeights.array().cwiseInverse().matrix()).asDiagonal();
+  Eigen::VectorXd quadratureWeightsOrderedAsProjector(quadratureWeights.rows());
+  unsigned int n_weightsPerField = quadratureWeights.rows()/vectorial_dim;
+  unsigned int reorderIndex{0};
+  
+  for (unsigned int ith_weight = 0; ith_weight < n_weightsPerField; ith_weight++)
+  {
+    for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+    {
+      quadratureWeightsOrderedAsProjector(reorderIndex) = quadratureWeights(ith_weight + ith_field * n_weightsPerField);
+      reorderIndex++;
+    }
+  }
+  
+  wPU = quadratureWeightsOrderedAsProjector.asDiagonal()*(Projector.transpose() * fieldWeights.array().cwiseInverse().matrix()).asDiagonal();
+}
+
 template<typename... SnapshotsLists>
 void HyperReduction<SnapshotsLists...>::generateSubmesh(label layers, fvMesh &mesh) {
 
diff --git a/tutorials/CFD/24HyperReduction/24HyperReduction.C b/tutorials/CFD/24HyperReduction/24HyperReduction.C
index ce7b3e4c7..2e8e45b36 100644
--- a/tutorials/CFD/24HyperReduction/24HyperReduction.C
+++ b/tutorials/CFD/24HyperReduction/24HyperReduction.C
@@ -72,7 +72,7 @@ class HyperReduction_function : public HyperReduction<PtrList<volScalarField>&>
             return ret;
         }
         
-        Eigen::VectorXd onlineCoeffs(volScalarField& S, Eigen::MatrixXd mu, volScalarField& SS)
+        Eigen::VectorXd onlineCoeffs(volScalarField& S, Eigen::MatrixXd mu)
         {
             Eigen::VectorXd f = evaluate_expression(S, mu, localNodePoints);
             return pinvPU*f;
@@ -129,64 +129,66 @@ class HyperReduction_vectorFunction : public HyperReduction<PtrList<volVectorFie
 
 };
 
-class HyperReduction_vectorScalarFunction : public HyperReduction<PtrList<volVectorField>&, PtrList<volScalarField>&>
-{
-    public:
-    using HyperReduction::HyperReduction;
-        static std::pair<volVectorField, volScalarField> evaluate_expression(volVectorField& V, volScalarField& S, Eigen::MatrixXd mu)
-        {
-            volScalarField yPos = S.mesh().C().component(vector::Y).ref();
-            volScalarField xPos = S.mesh().C().component(vector::X).ref();
-
-            for (auto i = 0; i < S.size(); i++)
-            {
-                V[i][0] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1,
-                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
-                V[i][1] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 0.5,
-                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
-                V[i][2] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1.5,
-                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0., 2));
-                S[i] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1,
-                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
-            }
-
-            return std::make_pair(V, S);
-        }
-
-        static Eigen::VectorXd evaluate_expression(volScalarField& S, Eigen::MatrixXd mu, List<label> nodesList)
-        {
-            Eigen::VectorXd ret(nodesList.size()*4);
-            volScalarField yPos = S.mesh().C().component(vector::Y).ref();
-            volScalarField xPos = S.mesh().C().component(vector::X).ref();
-
-            for (auto i = 0; i < nodesList.size(); i++)
-            {
-                ret(i*4) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
-                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
-                ret(i*4 + 1) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 0.5,
-                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
-                ret(i*4 + 2) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1.5,
-                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0., 2));
-                ret(i*4 + 3) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
-                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
-            }
-
-            return ret;
-        }
+// class HyperReduction_vectorScalarFunction : public HyperReduction<PtrList<volVectorField>&, PtrList<volScalarField>&>
+// {
+//     public:
+//     using HyperReduction::HyperReduction;
+//         static std::pair<volVectorField, volScalarField> evaluate_expression(volVectorField& V, volScalarField& S, Eigen::MatrixXd mu)
+//         {
+//             volScalarField yPos = S.mesh().C().component(vector::Y).ref();
+//             volScalarField xPos = S.mesh().C().component(vector::X).ref();
+
+//             for (auto i = 0; i < S.size(); i++)
+//             {
+//                 V[i][0] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1,
+//                                                 2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
+//                 V[i][1] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 0.5,
+//                                                 2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
+//                 V[i][2] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1.5,
+//                                                 2) - 2 * std::pow(yPos[i] - mu(1) - 0., 2));
+//                 S[i] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1,
+//                                                 2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
+//             }
+
+//             return std::make_pair(V, S);
+//         }
+
+//         static Eigen::VectorXd evaluate_expression(volScalarField& S, Eigen::MatrixXd mu, List<label> nodesList)
+//         {
+//             Eigen::VectorXd ret(nodesList.size()*4);
+//             volScalarField yPos = S.mesh().C().component(vector::Y).ref();
+//             volScalarField xPos = S.mesh().C().component(vector::X).ref();
+
+//             for (auto i = 0; i < nodesList.size(); i++)
+//             {
+//                 ret(i*4) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
+//                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
+//                 ret(i*4 + 1) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 0.5,
+//                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
+//                 ret(i*4 + 2) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1.5,
+//                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0., 2));
+//                 ret(i*4 + 3) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
+//                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
+//             }
+
+//             return ret;
+//         }
         
-        Eigen::VectorXd onlineCoeffs(volScalarField& S, Eigen::MatrixXd mu)
-        {
-            Eigen::VectorXd f = evaluate_expression(S, mu, localNodePoints);
-            return pinvPU*f;
-        }
+//         Eigen::VectorXd onlineCoeffs(volScalarField& S, Eigen::MatrixXd mu)
+//         {
+//             Eigen::VectorXd f = evaluate_expression(S, mu, localNodePoints);
+//             return pinvPU*f;
+//         }
 
-};
+// };
 
 void test_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime){
     int n_modes = para->ITHACAdict->lookupOrDefault<int>("Modes", 15);
     int n_nodes = para->ITHACAdict->lookupOrDefault<int>("Nodes", 15);
     simpleControl simple(mesh);
 
+    word methodName = para->ITHACAdict->lookupOrDefault<word>("HyperReduction", "GappyDEIM");
+
 #include "createFields.H"
     // List of volScalarField where the snapshots are stored
     PtrList<volScalarField> Sp;
@@ -216,35 +218,81 @@ void test_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
         ITHACAstream::exportSolution(S, name(i + 1), "./ITHACAoutput/Offline/");
     }
 
+    // Define new online parameters
+    Eigen::MatrixXd parTest;// = ITHACAutilities::rand(100, 2, -0.5, 0.5);
+    cnpy::load(parTest, "testingPars.npy");
+
     // Create HyperReduction object with given number of basis functions
-    Eigen::VectorXi initSeeds(0);
-
-    HyperReduction_function c(n_modes, n_nodes, initSeeds, "Gaussian_function", Sp);
-    c.offlineStage();
-
-    // Generate the submeshes with the depth of the layer
-    c.generateSubmesh(2, mesh);
-    auto sfield = c.interpolateField<volScalarField>(Sp[0]);
-    // Define a new online parameter
-    Eigen::MatrixXd par_new(2, 1);
-    par_new(0, 0) = 0;
-    par_new(1, 0) = 0;
-    // Online evaluation of the non linear function
-    Eigen::VectorXd aprfield = c.renormalizedBasisMatrix*c.onlineCoeffs(sfield(), par_new, Sp[0]);
-    // Transform to an OpenFOAM field and export
-    volScalarField S2("S_online", Foam2Eigen::Eigen2field(S, aprfield));
-    ITHACAstream::exportSolution(S2, name(1), "./ITHACAoutput/Online/");
-    // Evaluate the full order function and export it
-    HyperReduction_function::evaluate_expression(S, par_new);
-    ITHACAstream::exportSolution(S, name(1), "./ITHACAoutput/Online/");
-    // Compute the L2 error and print it
-    Info << ITHACAutilities::errorL2Rel(S2, S) << endl;
+    Eigen::VectorXi initSeeds;
+    // initSeeds = cnpy::load(initSeeds, "./mp.npy");//load mp to test initialSeeds
+
+    if (methodName=="GappyDEIM")
+    {
+        HyperReduction_function c(n_modes, n_nodes, initSeeds, "Gaussian_function", Sp);
+        c.offlineGappyDEIM();
+
+        // Generate the submeshes with the depth of the layer
+        unsigned int layers{2};
+        c.generateSubmesh(layers, mesh);
+        auto sfield = c.interpolateField<volScalarField>(Sp[0]);
+        
+        PtrList<volScalarField> testTrueFields;
+        PtrList<volScalarField> testRecFields;
+        for (unsigned int idTest = 0; idTest < parTest.rows(); idTest++)
+        {        
+            // Online evaluation of the non linear function
+            Eigen::VectorXd aprfield = c.renormalizedBasisMatrix*c.onlineCoeffs(sfield(), parTest.row(idTest));
+            // Transform to an OpenFOAM field and export
+            volScalarField S2("S_online", Foam2Eigen::Eigen2field(S, aprfield));
+            // Evaluate the full order function and export it
+            HyperReduction_function::evaluate_expression(S, parTest.row(idTest));
+            
+            testRecFields.append(S2.clone());
+            testTrueFields.append(S.clone());
+
+            ITHACAstream::exportSolution(S2, name(idTest), "./ITHACAoutput/Online/");
+            ITHACAstream::exportSolution(S, name(idTest), "./ITHACAoutput/Online/");
+        }
+
+        // Compute the L2 error and print it
+        auto err = ITHACAutilities::errorL2Rel(testRecFields, testTrueFields);
+        Info << "GappyDEIM max relative error: " << err.maxCoeff() << endl;
+        Info << "GappyDEIM mean relative error: " << err.array().mean() << endl;
+    }
+    else if (methodName=="ECP")
+    {
+        HyperReduction_function c(n_modes, n_nodes, initSeeds, "Gaussian_function", Sp);
+        c.offlineECP();
+
+        // Generate the submeshes with the depth of the layer
+        unsigned int layers{2};
+        c.generateSubmesh(layers, mesh);
+        auto sfield = c.interpolateField<volScalarField>(Sp[0]);
+        
+        Eigen::VectorXd results(parTest.rows());
+        for (unsigned int idTest = 0; idTest < parTest.rows(); idTest++)
+        {
+            // Online evaluation of the non linear function            
+            Eigen::VectorXd f = c.evaluate_expression(sfield(), parTest.row(idTest), c.localNodePoints);
+            Eigen::VectorXd ff = Foam2Eigen::field2Eigen(c.evaluate_expression(Sp[0], parTest.row(idTest)));
+            
+            double trueIntegral = (c.normalizingWeights.array().cwiseInverse().matrix().asDiagonal()*ff).array().sum();
+            double testIntegral = (c.wPU*f).array().sum();
+            Info << "Integral: " << trueIntegral << endl;
+            Info << "Reconstructed Integral: " << testIntegral << endl;
+
+            results(idTest) = trueIntegral-testIntegral;
+        }
+        Info << "ECP max error: " << results.cwiseAbs().maxCoeff() << endl;
+        Info << "ECP mean error: " << results.cwiseAbs().mean() << endl;
+    }
 }
 
 void test_vector(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime){
     int n_modes = para->ITHACAdict->lookupOrDefault<int>("Modes", 15);
     int n_nodes = para->ITHACAdict->lookupOrDefault<int>("Nodes", 15);
     simpleControl simple(mesh);
+    word methodName = para->ITHACAdict->lookupOrDefault<word>("HyperReduction", "GappyDEIM");
 
 #include "createFields.H"
     // List of volVectorField where the snapshots are stored
@@ -263,10 +311,10 @@ void test_vector(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
         T.mesh(),
         dimensionedVector("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), vector(0, 0, 0))
     );
+
     // Parameters used to train the non-linear function
     Eigen::MatrixXd pars;
     cnpy::load(pars, "trainingPars.npy");
-
     // Perform the offline phase
     for (int i = 0; i < 100; i++)
     {
@@ -275,120 +323,166 @@ void test_vector(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
         ITHACAstream::exportSolution(S, name(i + 1), "./ITHACAoutput/Offline/");
     }
 
-    // Create HyperReduction object with given number of basis functions
-    Eigen::VectorXi initSeeds(0);
-
-    HyperReduction_vectorFunction c(n_modes, n_nodes, initSeeds, "Gaussian_function", Sp);
-    c.offlineStage();
-
-    // Generate the submeshes with the depth of the layer
-    c.generateSubmesh(2, mesh);
-    auto sfield = c.interpolateField<volVectorField>(Sp[0]);
-    // Define a new online parameter
-    Eigen::MatrixXd par_new(2, 1);
-    par_new(0, 0) = 0;
-    par_new(1, 0) = 0;
-    // Online evaluation of the non linear function
-    Eigen::VectorXd aprfield = c.renormalizedBasisMatrix*c.onlineCoeffs(sfield(), par_new);
-    // Transform to an OpenFOAM field and export
-    volVectorField S2("S_online", Foam2Eigen::Eigen2field(S, aprfield));
-    ITHACAstream::exportSolution(S2, name(1), "./ITHACAoutput/Online/");
-    // Evaluate the full order function and export it
-    HyperReduction_vectorFunction::evaluate_expression(S, par_new);
-    ITHACAstream::exportSolution(S, name(1), "./ITHACAoutput/Online/");
-    // Compute the L2 error and print it
-    Info << ITHACAutilities::errorL2Rel(S2, S) << endl;
-}
+    // Define new online parameters
+    Eigen::MatrixXd parTest;// = ITHACAutilities::rand(100, 2, -0.5, 0.5);
+    cnpy::load(parTest, "testingPars.npy");
 
-void test_vector_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime){
-    int n_modes = para->ITHACAdict->lookupOrDefault<int>("Modes", 15);
-    int n_nodes = para->ITHACAdict->lookupOrDefault<int>("Nodes", 15);
-    simpleControl simple(mesh);
+    // Create HyperReduction object with given number of basis functions
+    Eigen::VectorXi initSeeds;
+    // initSeeds = cnpy::load(initSeeds, "./mp.npy");//load mp to test initialSeeds
 
-#include "createFields.H"
-    // List of volVectorField where the snapshots are stored
-    PtrList<volVectorField> Vp;
-    PtrList<volScalarField> Sp;
-    // Non linear function
-    volVectorField V
-    (
-        IOobject
-        (
-            "V",
-            runTime.timeName(),
-            mesh,
-            IOobject::NO_READ,
-            IOobject::AUTO_WRITE
-        ),
-        T.mesh(),
-        dimensionedVector("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), vector(0, 0, 0))
-    );
-    // Non linear function
-    volScalarField S
-    (
-        IOobject
-        (
-            "S",
-            runTime.timeName(),
-            mesh,
-            IOobject::NO_READ,
-            IOobject::AUTO_WRITE
-        ),
-        T.mesh(),
-        dimensionedScalar("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), 0)
-    );
+    if (methodName=="GappyDEIM")
+    {
+        HyperReduction_vectorFunction c(n_modes, n_nodes, initSeeds, "Gaussian_function", Sp);
+        c.offlineGappyDEIM();
 
-    // Parameters used to train the non-linear function
-    Eigen::MatrixXd pars;
-    cnpy::load(pars, "trainingPars.npy");
+        // Generate the submeshes with the depth of the layer
+        unsigned int layers{2};
+        c.generateSubmesh(layers, mesh);
+        auto sfield = c.interpolateField<volVectorField>(Sp[0]);
+        
+        PtrList<volVectorField> testTrueFields;
+        PtrList<volVectorField> testRecFields;
+        for (unsigned int idTest = 0; idTest < parTest.rows(); idTest++)
+        {        
+            // Online evaluation of the non linear function
+            Eigen::VectorXd aprfield = c.renormalizedBasisMatrix*c.onlineCoeffs(sfield(), parTest.row(idTest));
+            // Transform to an OpenFOAM field and export
+            volVectorField S2("S_online", Foam2Eigen::Eigen2field(S, aprfield));
+            // Evaluate the full order function and export it
+            HyperReduction_vectorFunction::evaluate_expression(S, parTest.row(idTest));
+            
+            testRecFields.append(S2.clone());
+            testTrueFields.append(S.clone());
+
+            ITHACAstream::exportSolution(S2, name(idTest), "./ITHACAoutput/Online/");
+            ITHACAstream::exportSolution(S, name(idTest), "./ITHACAoutput/Online/");
+        }
 
-    // Perform the offline phase
-    for (int i = 0; i < 100; i++)
-    {
-        HyperReduction_vectorScalarFunction::evaluate_expression(V, S, pars.row(i));
-        Vp.append((V).clone());
-        Sp.append((S).clone());
-        ITHACAstream::exportSolution(S, name(i + 1), "./ITHACAoutput/Offline/");
-        ITHACAstream::exportSolution(V, name(i + 1), "./ITHACAoutput/Offline/");
+        // Compute the L2 error and print it
+        auto err = ITHACAutilities::errorL2Rel(testRecFields, testTrueFields);
+        Info << "GappyDEIM max relative error: " << err.maxCoeff() << endl;
+        Info << "GappyDEIM mean relative error: " << err.array().mean() << endl;
     }
+    else if (methodName=="ECP")
+    {
+        HyperReduction_vectorFunction c(n_modes, n_nodes, initSeeds, "Gaussian_function", Sp);
+        c.offlineECP();
 
-    // Create HyperReduction object with given number of basis functions
-    Eigen::VectorXi initSeeds(0);
-
-    HyperReduction_vectorScalarFunction c(n_modes, n_nodes, initSeeds, "Gaussian_function", Vp, Sp);
-    c.offlineStage();
-
-    // Generate the submeshes with the depth of the layer
-    c.generateSubmesh(2, mesh);
-    auto vfield = c.interpolateField<volVectorField>(Vp[0]);
-    auto sfield = c.interpolateField<volScalarField>(Sp[0]);
-    // Define a new online parameter
-    Eigen::MatrixXd par_new(2, 1);
-    par_new(0, 0) = 0;
-    par_new(1, 0) = 0;
-    // Online evaluation of the non linear function
-    auto theta = c.onlineCoeffs(sfield(), par_new);
-    Eigen::VectorXd aprfield = c.renormalizedBasisMatrix*theta;
-    // Transform to an OpenFOAM field and export
-    // c.eigen2fields(aprfield, V, S);
-    // volVectorField V2("V_online", V);
-    // volScalarField S2("S_online", S);
-    Eigen::VectorXd recvec = aprfield.head(3*S.size());
-    Eigen::VectorXd recsca = aprfield.tail(S.size());
-    volVectorField V2("V_online", Foam2Eigen::Eigen2field(V, recvec));
-    volScalarField S2("S_online", Foam2Eigen::Eigen2field(S, recsca));
-
-    ITHACAstream::exportSolution(V2, name(1), "./ITHACAoutput/Online/");
-    ITHACAstream::exportSolution(S2, name(1), "./ITHACAoutput/Online/");
-    // Evaluate the full order function and export it
-    HyperReduction_vectorScalarFunction::evaluate_expression(V, S, par_new);
-    ITHACAstream::exportSolution(V, name(1), "./ITHACAoutput/Online/");
-    ITHACAstream::exportSolution(S, name(1), "./ITHACAoutput/Online/");
-    // Compute the L2 error and print it
-    Info << "Scalar L2 error: " << ITHACAutilities::errorL2Rel(S2, S) << endl;
-    Info << "Vector L2 error: " << ITHACAutilities::errorL2Rel(V2, V) << endl;
+        // Generate the submeshes with the depth of the layer
+        unsigned int layers{2};
+        c.generateSubmesh(layers, mesh);
+        auto sfield = c.interpolateField<volVectorField>(Sp[0]);
+        
+        Eigen::VectorXd results(parTest.rows());
+        for (unsigned int idTest = 0; idTest < parTest.rows(); idTest++)
+        {
+            // Online evaluation of the non linear function            
+            Eigen::VectorXd f = c.evaluate_expression(sfield(), parTest.row(idTest), c.localNodePoints);
+            auto wholeField = c.evaluate_expression(Sp[0], parTest.row(idTest));
+            Eigen::VectorXd ff = Foam2Eigen::field2Eigen(wholeField);
+            
+            double trueIntegral = (c.normalizingWeights.array().cwiseInverse().matrix().asDiagonal()*ff).array().sum();
+            double testIntegral = (c.wPU*f).array().sum();
+            Info << "Integral: " << trueIntegral << endl;
+            Info << "Reconstructed Integral: " << testIntegral << endl;
+
+            results(idTest) = trueIntegral-testIntegral;
+        }
+        Info << "ECP max error: " << results.cwiseAbs().maxCoeff() << endl;
+        Info << "ECP mean error: " << results.cwiseAbs().mean() << endl;
+    }
 }
 
+// void test_vector_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime){
+//     int n_modes = para->ITHACAdict->lookupOrDefault<int>("Modes", 15);
+//     int n_nodes = para->ITHACAdict->lookupOrDefault<int>("Nodes", 15);
+//     simpleControl simple(mesh);
+
+// #include "createFields.H"
+//     // List of volVectorField where the snapshots are stored
+//     PtrList<volVectorField> Vp;
+//     PtrList<volScalarField> Sp;
+//     // Non linear function
+//     volVectorField V
+//     (
+//         IOobject
+//         (
+//             "V",
+//             runTime.timeName(),
+//             mesh,
+//             IOobject::NO_READ,
+//             IOobject::AUTO_WRITE
+//         ),
+//         T.mesh(),
+//         dimensionedVector("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), vector(0, 0, 0))
+//     );
+//     // Non linear function
+//     volScalarField S
+//     (
+//         IOobject
+//         (
+//             "S",
+//             runTime.timeName(),
+//             mesh,
+//             IOobject::NO_READ,
+//             IOobject::AUTO_WRITE
+//         ),
+//         T.mesh(),
+//         dimensionedScalar("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), 0)
+//     );
+
+//     // Parameters used to train the non-linear function
+//     Eigen::MatrixXd pars;
+//     cnpy::load(pars, "trainingPars.npy");
+
+//     // Perform the offline phase
+//     for (int i = 0; i < 100; i++)
+//     {
+//         HyperReduction_vectorScalarFunction::evaluate_expression(V, S, pars.row(i));
+//         Vp.append((V).clone());
+//         Sp.append((S).clone());
+//         ITHACAstream::exportSolution(S, name(i + 1), "./ITHACAoutput/Offline/");
+//         ITHACAstream::exportSolution(V, name(i + 1), "./ITHACAoutput/Offline/");
+//     }
+
+//     // Create HyperReduction object with given number of basis functions
+//     Eigen::VectorXi initSeeds(0);
+
+//     HyperReduction_vectorScalarFunction c(n_modes, n_nodes, initSeeds, "Gaussian_function", Vp, Sp);
+//     c.offlineStage();
+
+//     // Generate the submeshes with the depth of the layer
+//     c.generateSubmesh(2, mesh);
+//     auto vfield = c.interpolateField<volVectorField>(Vp[0]);
+//     auto sfield = c.interpolateField<volScalarField>(Sp[0]);
+//     // Define a new online parameter
+//     Eigen::MatrixXd par_new(2, 1);
+//     par_new(0, 0) = 0;
+//     par_new(1, 0) = 0;
+//     // Online evaluation of the non linear function
+//     auto theta = c.onlineCoeffs(sfield(), par_new);
+//     Eigen::VectorXd aprfield = c.renormalizedBasisMatrix*theta;
+//     // Transform to an OpenFOAM field and export
+//     // c.eigen2fields(aprfield, V, S);
+//     // volVectorField V2("V_online", V);
+//     // volScalarField S2("S_online", S);
+//     Eigen::VectorXd recvec = aprfield.head(3*S.size());
+//     Eigen::VectorXd recsca = aprfield.tail(S.size());
+//     volVectorField V2("V_online", Foam2Eigen::Eigen2field(V, recvec));
+//     volScalarField S2("S_online", Foam2Eigen::Eigen2field(S, recsca));
+
+//     ITHACAstream::exportSolution(V2, name(1), "./ITHACAoutput/Online/");
+//     ITHACAstream::exportSolution(S2, name(1), "./ITHACAoutput/Online/");
+//     // Evaluate the full order function and export it
+//     HyperReduction_vectorScalarFunction::evaluate_expression(V, S, par_new);
+//     ITHACAstream::exportSolution(V, name(1), "./ITHACAoutput/Online/");
+//     ITHACAstream::exportSolution(S, name(1), "./ITHACAoutput/Online/");
+//     // Compute the L2 error and print it
+//     Info << "Scalar L2 error: " << ITHACAutilities::errorL2Rel(S2, S) << endl;
+//     Info << "Vector L2 error: " << ITHACAutilities::errorL2Rel(V2, V) << endl;
+// }
+
 int main(int argc, char* argv[])
 {
     // load stage to perform
@@ -438,11 +532,11 @@ int main(int argc, char* argv[])
         Info << "Init vector testcase\n";
         test_vector(para, mesh, runTime);
     }
-    else if (args.get("test").match("vs"))
-    {
-        Info << "Init vector scalar testcase\n";
-        test_vector_scalar(para, mesh, runTime);
-    }
+    // else if (args.get("test").match("vs"))
+    // {
+    //     Info << "Init vector scalar testcase\n";
+    //     test_vector_scalar(para, mesh, runTime);
+    // }
     else
     {
         Info << "Pass '-test scalar', '-test vector', '-test vs'" << endl;
diff --git a/tutorials/CFD/24HyperReduction/system/ITHACAdict b/tutorials/CFD/24HyperReduction/system/ITHACAdict
index 8c1b4218a..b29c5901d 100755
--- a/tutorials/CFD/24HyperReduction/system/ITHACAdict
+++ b/tutorials/CFD/24HyperReduction/system/ITHACAdict
@@ -18,13 +18,13 @@ FoamFile
 EigenSolver eigen;
 
 // Number of modes to output and to use for projection
-Nodes 50;
-Modes 20;
+Nodes 31;
+Modes 30;
 
 // Output format to save market vectors.
 OutPrecision 20;
 OutType fixed;
 
 // HR
-HyperReduction GappyDEIM;
-GreedyMetric SOPTE;//L2, SOPT, SOPTE
+HyperReduction ECP;//GreedyDEIM, ECP
+GreedyMetric SOPT;//L2, SOPT, SOPTE
\ No newline at end of file

From d9237a3aee505374a1b42c6e0880fb99e7a62f2f Mon Sep 17 00:00:00 2001
From: fromor <francesco.romor@gmail.com>
Date: Fri, 28 Oct 2022 17:15:37 +0200
Subject: [PATCH 05/59] working HR, tutorial 24 with ECP

---
 src/ITHACA_HR/hyperReduction.H                |  18 +-
 src/ITHACA_HR/hyperReduction.templates.H      | 489 ++++++------------
 .../CFD/24HyperReduction/24HyperReduction.C   | 366 +++++++------
 .../CFD/24HyperReduction/system/ITHACAdict    |   4 +-
 4 files changed, 396 insertions(+), 481 deletions(-)

diff --git a/src/ITHACA_HR/hyperReduction.H b/src/ITHACA_HR/hyperReduction.H
index f3db6cdb3..5f49e4af8 100644
--- a/src/ITHACA_HR/hyperReduction.H
+++ b/src/ITHACA_HR/hyperReduction.H
@@ -37,9 +37,10 @@ SourceFiles
 #include "EigenFunctions.H"
 #include "ITHACAutilities.H"
 #include "fvMeshSubset.H"
-#include <unsupported/Eigen/NNLS>
 #include <set>
 
+Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
+
 template <typename... SnapshotsLists>
 class HyperReduction
 {
@@ -156,21 +157,26 @@ public:
     
     /// Submeshes
     autoPtr<volVectorField> submesh_field;
+    
+    //----------------------------------------------------------------------
+    /// @brief      TODO
+    ///
+    void offlineGappyDEIM();
 
     //----------------------------------------------------------------------
     /// @brief      TODO
     ///
-    void offlineStage();
+    void offlineECP(Eigen::MatrixXd snapshotsModes);
     
     //----------------------------------------------------------------------
     /// @brief      TODO
     ///
-    void offlineGappyDEIM();
+    void initSeeds(Eigen::VectorXd mp_not_mask, std::set<label> nodePointsSet);
 
     //----------------------------------------------------------------------
     /// @brief      TODO
     ///
-    void offlineECP();
+    void computeLS(Eigen::MatrixXd& J, Eigen::MatrixXd& JWhole, Eigen::VectorXd& b, Eigen::VectorXd& q);
 
     //----------------------------------------------------------------------
     /// @brief      TODO
@@ -186,7 +192,7 @@ public:
     /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
     /// @param[in]  sList  The list of snapshots
     ///
-    void updateNodes(Eigen::SparseMatrix<double>& P, label& ind_max, Eigen::VectorXd& mp_not_mask, std::deque<label>& nodePointsDeque);
+    void updateNodes(Eigen::SparseMatrix<double>& P, label& ind_max, Eigen::VectorXd& mp_not_mask);
 
     //----------------------------------------------------------------------
     /// @brief      TODO
@@ -204,7 +210,7 @@ public:
     /// @param[in]  sList  The list of snapshots
     ///
     template <typename SnapshotsList>
-    void saveModes(SnapshotsList sList, Eigen::MatrixXd& snapshotsMatrix, unsigned int &rowIndex, unsigned int &modeIndex);
+    void saveModes(SnapshotsList sList, Eigen::MatrixXd& snapshotsMatrix, unsigned int &rowIndex, unsigned int &modeIndex, word folder);
 
     //----------------------------------------------------------------------
     /// @brief      TODO
diff --git a/src/ITHACA_HR/hyperReduction.templates.H b/src/ITHACA_HR/hyperReduction.templates.H
index 0dd4d2694..b90806989 100644
--- a/src/ITHACA_HR/hyperReduction.templates.H
+++ b/src/ITHACA_HR/hyperReduction.templates.H
@@ -35,6 +35,51 @@ License
 
 // TODO increase modularity to avoid heavy compiling costs
 
+// Template function constructor
+template <typename... SnapshotsLists>
+HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
+                                                  label n_nodes,
+                                                  Eigen::VectorXi initialSeeds,
+                                                  word problemName,
+                                                  SnapshotsLists &&...snapshotsLists)
+    : vectorial_dim{compute_vectorial_dim(snapshotsLists...)},
+      n_modes{n_modes},
+      n_nodes{n_nodes},
+      initialSeeds{initialSeeds},
+      problemName{problemName},
+      snapshotsListTuple{std::forward_as_tuple(snapshotsLists...)}
+{
+  Info << "Init HyperReduction class with vectorial dim: " << vectorial_dim << endl;
+  para = ITHACAparameters::getInstance();
+  Folder = "ITHACAoutput/" + problemName;
+  mkDir(Folder);
+
+  // TODO check snapshotsLists is not empty
+  // TODO check that the first snapshotsList is not empty (includes above)
+
+  // TODO initialize vectorial_dim only from SnapshotsLists type
+  // vectorial_dim = std::apply(compute_vectorial_dim<SnapshotsLists&&...>, snapshotsListTuple);
+
+  // Get fields' names
+  std::apply([this](auto& ...snapList){(..., stackNames(snapList));}, snapshotsListTuple);
+
+  // Get fields' dimensions
+  std::apply([this](auto& ...snapList){(..., stackDimensions(snapList));}, snapshotsListTuple);
+
+  Info << "Fields names: ";
+  for (unsigned int ith_field = 0; ith_field < fieldNames.size(); ith_field++)
+  {
+    Info << fieldNames[ith_field] << " (dim=" << fieldDims[ith_field] << "); ";
+  }
+  Info << endl;
+  
+  n_snapshots = std::get<0>(snapshotsListTuple).size();
+  Info << "The number of snapshots is: " << n_snapshots << endl;
+  n_cells = std::get<0>(snapshotsListTuple)[0].size();
+  Info << "The number of cells is: " << n_cells << endl;
+  Info << "Initial seeds length: " << initialSeeds.rows() << endl;
+}
+
 // Using the Eigen library, using the SVD decomposition method to solve the
 // matrix pseudo-inverse, the default error er is 0
 Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0) {
@@ -64,9 +109,10 @@ template <typename... SnapshotsLists>
 void HyperReduction<SnapshotsLists...>::getModesSVD(
     SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights, bool saveModesFlag)
 {
-  // TODO possibility to save openfoam modes fields
+  // TODO move inside ITHACAPOD
   ITHACAparameters* para(ITHACAparameters::getInstance());
-  if (!ITHACAutilities::check_folder(Folder + "/Modes/"))
+  word folderSVD = "ITHACAoutput/" + problemName + "/ModesSVD/";
+  if (!ITHACAutilities::check_folder(folderSVD))
   {
     // Initialize stacked snapshotsMatrix and normalizing weights
     Eigen::MatrixXd snapMatrix;
@@ -96,15 +142,15 @@ void HyperReduction<SnapshotsLists...>::getModesSVD(
         cumEigenValues(j) += cumEigenValues(j - 1);
     }
 
-    mkDir(Folder + "/Modes/");
+    mkDir(folderSVD);
     Eigen::saveMarketVector(eigenValueseig,
-                            Folder+"/Modes/Eigenvalues_" + problemName, para->precision,
+                            "ITHACAoutput/" + problemName + "/ModesSVD/Eigenvalues_" + problemName, para->precision,
                             para->outytpe);
     Eigen::saveMarketVector(cumEigenValues,
-                            Folder+"/Modes/CumEigenvalues_" + problemName, para->precision,
+                            "ITHACAoutput/" + problemName + "/ModesSVD/CumEigenvalues_" + problemName, para->precision,
                             para->outytpe);
-    cnpy::save(modesSVD, Folder + "/Modes/modes.npy");
-    cnpy::save(fieldWeights, Folder + "/Modes/normalizingWeights.npy");
+    cnpy::save(modesSVD, "ITHACAoutput/" + problemName + "/ModesSVD/modes.npy");
+    cnpy::save(fieldWeights, "ITHACAoutput/" + problemName + "/ModesSVD/normalizingWeights.npy");
 
 
     if (saveModesFlag)
@@ -112,7 +158,7 @@ void HyperReduction<SnapshotsLists...>::getModesSVD(
       unsigned int rowIndex{0};
       for (unsigned int modeIndex = 0; modeIndex < modesSVD.cols(); modeIndex++)
       {
-        std::apply([this, &modesSVD, &rowIndex, &modeIndex](auto& ...snapList){(..., saveModes(snapList, modesSVD, rowIndex, modeIndex));}, snapshotsListTuple);
+        std::apply([this, &modesSVD, &rowIndex, &modeIndex, &folderSVD](auto& ...snapList){(..., saveModes(snapList, modesSVD, rowIndex, modeIndex, folderSVD));}, snapshotsListTuple);
         rowIndex = 0;
       }
     }
@@ -120,14 +166,14 @@ void HyperReduction<SnapshotsLists...>::getModesSVD(
   else
   {
     Info << "Reading the existing modes" << endl;
-    cnpy::load(modesSVD, Folder + "/Modes/modes.npy");
-    cnpy::load(fieldWeights, Folder + "/Modes/normalizingWeights.npy");
+    cnpy::load(modesSVD, folderSVD + "/modes.npy");
+    cnpy::load(fieldWeights, folderSVD + "/normalizingWeights.npy");
   }
 }
 
 template <typename... SnapshotsLists>
 template <typename SnapshotsList>
-void HyperReduction<SnapshotsLists...>::saveModes(SnapshotsList sList, Eigen::MatrixXd& snapshotsMatrix, unsigned int &rowIndex, unsigned int &modeIndex)
+void HyperReduction<SnapshotsLists...>::saveModes(SnapshotsList sList, Eigen::MatrixXd& snapshotsMatrix, unsigned int &rowIndex, unsigned int &modeIndex, word folder)
 {
   unsigned int field_dim = get_field_dim<typename SnapshotsList::value_type>();
   auto fieldName = sList[0].name();
@@ -135,70 +181,7 @@ void HyperReduction<SnapshotsLists...>::saveModes(SnapshotsList sList, Eigen::Ma
   Eigen::VectorXd fieldBlock = snapshotsMatrix.block(rowIndex, modeIndex, fieldSize, 1);
   auto fieldOut = Foam2Eigen::Eigen2field(sList[0], fieldBlock , true);
   rowIndex +=fieldSize;
-  modeIndex++;
-  ITHACAstream::exportSolution(fieldOut, name(modeIndex), Folder + "/Modes/");
-}
-
-// Template function constructor
-template <typename... SnapshotsLists>
-HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
-                                                  label n_nodes,
-                                                  Eigen::VectorXi initialSeeds,
-                                                  word problemName,
-                                                  SnapshotsLists &&...snapshotsLists)
-    : vectorial_dim{compute_vectorial_dim(snapshotsLists...)},
-      n_modes{n_modes},
-      n_nodes{n_nodes},
-      initialSeeds{initialSeeds},
-      problemName{problemName},
-      snapshotsListTuple{std::forward_as_tuple(snapshotsLists...)}
-{
-  Info << "Init HyperReduction class with vectorial dim: " << vectorial_dim << endl;
-  para = ITHACAparameters::getInstance();
-  // TODO check snapshotsLists is not empty
-  // TODO check that the first snapshotsList is not empty (includes above)
-
-  // TODO initialize vectorial_dim only from SnapshotsLists type
-  // vectorial_dim = std::apply(compute_vectorial_dim<SnapshotsLists&&...>, snapshotsListTuple);
-
-  // Get fields' names
-  std::apply([this](auto& ...snapList){(..., stackNames(snapList));}, snapshotsListTuple);
-
-  // Get fields' dimensions
-  std::apply([this](auto& ...snapList){(..., stackDimensions(snapList));}, snapshotsListTuple);
-
-  Info << "Fields names: ";
-  for (unsigned int ith_field = 0; ith_field < fieldNames.size(); ith_field++)
-  {
-    Info << fieldNames[ith_field] << " (dim=" << fieldDims[ith_field] << "); ";
-  }
-  Info << endl;
-  
-  n_snapshots = std::get<0>(snapshotsListTuple).size();
-  Info << "The number of snapshots is: " << n_snapshots << endl;
-  n_cells = std::get<0>(snapshotsListTuple)[0].size();
-  Info << "The number of cells is: " << n_cells << endl;
-  Info << "Initial seeds length: " << initialSeeds.rows() << endl;
-}
-
-template <typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::offlineStage()
-{
-  para = ITHACAparameters::getInstance();
-  methodName = para->ITHACAdict->lookupOrDefault<word>("HyperReduction", "GappyDEIM");
-
-  if (methodName=="GappyDEIM")
-  {
-    offlineGappyDEIM();
-  }
-  else if (methodName=="ECP")
-  {
-    offlineECP();
-  }
-  else
-  {
-    M_Assert(false, "Offline stage hyper-reduction not performed. Invalid HR method. Possible methods are: 'GappyDEIM', 'ECP.'\n");
-  }
+  ITHACAstream::exportSolution(fieldOut, name(modeIndex), folder);
 }
 
 template <typename... SnapshotsLists>
@@ -206,7 +189,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
 {
   methodName = "GappyDEIM";
   Folder = "ITHACAoutput/" + problemName + "/" + methodName;
-    mkDir(Folder);
+  mkDir(Folder);
 
   nodePoints = autoPtr<IOList<label>>(new IOList<label>(
       IOobject("nodePoints", para->runTime.time().constant(), "../" + Folder,
@@ -224,35 +207,11 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
 
     Eigen::VectorXd mp_not_mask = Eigen::VectorXd::Constant(n_cells * vectorial_dim, 1);
     std::set<label> nodePointsSet;
-    std::deque<label> nodePointsDeque;
 
     // set initialSeeds
     if (initialSeeds.rows() > 0)
     {
-      P.resize(n_cells * vectorial_dim, initialSeeds.rows() * vectorial_dim);
-      P.reserve(Eigen::VectorXi::Constant(initialSeeds.rows() * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
-
-      unsigned int trueSeeds{0};
-      for (int i = 0; i < initialSeeds.rows(); i++)
-      {
-        unsigned int index = initialSeeds(i) % n_cells;
-        // check that there are not repeated nodes in initialSeeds
-        if (nodePointsSet.find(index) == nodePointsSet.end()){
-          nodePointsSet.insert(index);
-          nodePointsDeque.push_back(index);
-
-          for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-          {
-            P.insert(index+ith_field*n_cells, vectorial_dim*trueSeeds+ith_field) = 1;
-            mp_not_mask(index + ith_field * n_cells) = 0;
-          }
-          trueSeeds++;
-        }
-      }
-
-      P.conservativeResize(P.rows(), nodePointsDeque.size()*vectorial_dim);
-      P.makeCompressed();
-      M_Assert(nodePointsDeque.size()<=n_nodes, "Size of 'initialSeeds' is greater than 'n_nodes'");
+      initSeeds(mp_not_mask, nodePointsSet);
     }
 
     int na = n_nodes - initialSeeds.rows();
@@ -272,16 +231,13 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
         int nit = std::min(n_modes, na);
         int ncimin = std::floor(n_modes / nit);
         int naimin = std::floor(na / n_modes);
-
         Eigen::MatrixXd A;
         Eigen::VectorXd b;
         Eigen::VectorXd c;
         Eigen::VectorXd r;
         label ind_max, c1;
-
         double max;
 
-
         for (int i = 1; i <= nit; i++)
         {
           int nci = ncimin;
@@ -331,7 +287,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
               max = (reshapeMat*V.rowwise().lpNorm<2>().array().square().matrix()).maxCoeff(&ind_max, &c1);
             }
             
-            updateNodes(P, ind_max, mp_not_mask, nodePointsDeque);
+            updateNodes(P, ind_max, mp_not_mask);
           }
 
           nb += nci;
@@ -371,7 +327,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
             max = (reshapeMat*V.rowwise().lpNorm<2>().array().square().matrix()).maxCoeff(&ind_max, &c1);
           }
 
-          updateNodes(P, ind_max, mp_not_mask, nodePointsDeque);
+          updateNodes(P, ind_max, mp_not_mask);
         }
         basisMatrix = V;
         Info << "####### End of SOPT GappyDEIM #######\n";
@@ -392,7 +348,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
         Eigen::MatrixXd V = snapshotsModes.col(0);
 
         max = (reshapeMat* (mp_not_mask.asDiagonal()*snapshotsModes.leftCols(n_modes)).rowwise().lpNorm<2>().array().square().matrix()).maxCoeff(&ind_max, &c1);
-        updateNodes(P, ind_max, mp_not_mask, nodePointsDeque);
+        updateNodes(P, ind_max, mp_not_mask);
 
         for (unsigned int ith_node = 1; ith_node < na; ith_node++)
         {
@@ -402,11 +358,10 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
             b = P.transpose() * snapshotsModes.col(ith_node);
             c = A.fullPivLu().solve(b);
             r = snapshotsModes.col(ith_node) - V * c;
-
-            max = (reshapeMat*r.rowwise().lpNorm<2>().array().square().matrix()).maxCoeff(&ind_max, &c1);
-
             V.conservativeResize(snapshotsModes.rows(), ith_node + 1);
             V.col(ith_node) =  snapshotsModes.col(ith_node);
+
+            max = (reshapeMat*r.rowwise().lpNorm<2>().array().square().matrix()).maxCoeff(&ind_max, &c1);
           }
           else
           {
@@ -430,7 +385,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
             max = results.maxCoeff(&ind_max, &c1);
           }
 
-          updateNodes(P, ind_max, mp_not_mask, nodePointsDeque);
+          updateNodes(P, ind_max, mp_not_mask);
         }
         basisMatrix = snapshotsModes.leftCols(n_modes);
         Info << "####### End of SOPTE GappyDEIM #######\n";
@@ -442,63 +397,32 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
       Info << "####### InitialSeeds equal to n_nodes #######\n";
     }
 
-    cnpy::save(basisMatrix, Folder +"/basisMatrix.npy");
-    cnpy::save(P, Folder +"/projectionMatrix.npy");
-    Info << "Projection Matrix shape: " << P.rows() << " " << P.cols() << endl;
-    Info << "Basis Matrix shape: " << basisMatrix.rows() << " " << basisMatrix.cols() << endl;
-
     evaluatePinv(P, basisMatrix, normalizingWeights);
     renormalizedBasisMatrix = normalizingWeights.asDiagonal()*basisMatrix;
-    Info << "Pseudo Inverse Matrix shape: " << pinvPU.rows() << " " << pinvPU.cols() << endl;
 
-    // convert nodePointsSet to nodePoints i.e. list
-    for (auto &x : nodePointsDeque)
-    {
-      nodePoints().append(x);
-    }
+    cnpy::save(basisMatrix, Folder +"/basisMatrix.npy");
+    cnpy::save(P, Folder +"/projectionMatrix.npy");
     cnpy::save(nodes, Folder + "/mp.npy");
     cnpy::save(pinvPU, Folder + "/pinvPU.npy");
     nodePoints().write();
+
+    Info << "Projection Matrix shape: " << P.rows() << " " << P.cols() << endl;
+    Info << "Basis Matrix shape: " << basisMatrix.rows() << " " << basisMatrix.cols() << endl;
+    Info << "Pseudo Inverse Matrix shape: " << pinvPU.rows() << " " << pinvPU.cols() << endl;
   }
   else
   {
-    cnpy::load(pinvPU, Folder + "/pinvPU.npy");
     cnpy::load(basisMatrix, Folder +"/basisMatrix.npy");
+    cnpy::load(P, Folder +"/projectionMatrix.npy");
+    cnpy::load(nodes, Folder + "/mp.npy");
+    cnpy::load(pinvPU, Folder + "/pinvPU.npy");
   }
 }
 
 template <typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::updateNodes(Eigen::SparseMatrix<double>& P, label& ind, Eigen::VectorXd& mp_not_mask, std::deque<label>& nodePointsDeque)
-{
-  unsigned int last_col{0};
-  
-  if (P.rows()==0)
-  {
-    P.resize(n_cells*vectorial_dim, vectorial_dim);
-  }
-  else
-  {
-    last_col = P.cols();
-    P.conservativeResize(P.rows(), P.cols() + vectorial_dim);
-  }
-
-  for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-  {
-    P.insert(ind + ith_field * n_cells, last_col + ith_field) = 1;
-    mp_not_mask(ind + ith_field * n_cells) = 0;
-  }
-
-  nodePointsDeque.push_back(ind);
-
-  nodes.conservativeResize(nodes.rows()+1);
-  nodes(nodes.rows()-1) = ind;
-}
-
-template <typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::offlineECP()
+void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd snapshotsModes)
 {
   methodName = "ECP";
-
   n_nodes = n_modes + 1;
 
   Info << "####### Begin ECP #######" << endl;
@@ -507,14 +431,11 @@ void HyperReduction<SnapshotsLists...>::offlineECP()
             << endl;
 
   Folder = "ITHACAoutput/" + problemName + "/" + methodName;
-    mkDir(Folder);
+  mkDir(Folder);
 
   nodePoints = autoPtr<IOList<label>>(new IOList<label>(
       IOobject("nodePoints", para->runTime.time().constant(), "../" + Folder,
-                para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
-
-  Eigen::MatrixXd snapshotsModes;
-  getModesSVD(snapshotsListTuple, snapshotsModes, normalizingWeights, true);  
+                para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE))); 
 
   if (!nodePoints().headerOk())
   {
@@ -522,7 +443,7 @@ void HyperReduction<SnapshotsLists...>::offlineECP()
     assert(n_nodes >= n_modes);
 
     // matrices for quadratureWeights evaluation
-    Eigen::MatrixXd J;//shape: (vectorial_dim * (n_modes + 1), nodePointsDeque.size())
+    Eigen::MatrixXd J;//shape: (vectorial_dim * (n_modes + 1), nodePoints->size())
     Eigen::MatrixXd Jwhole(vectorial_dim * (n_modes + 1), n_cells);
     Eigen::VectorXd q(vectorial_dim * (n_modes + 1));
 
@@ -553,61 +474,12 @@ void HyperReduction<SnapshotsLists...>::offlineECP()
 
     Eigen::VectorXd mp_not_mask = Eigen::VectorXd::Constant(n_cells * vectorial_dim, 1);
     std::set<label> nodePointsSet;
-    std::deque<label> nodePointsDeque;
 
     // set initialSeeds
     if (initialSeeds.rows() > 0)
     {
-      // TODO init matrix P from initialSeeds
-      P.resize(n_cells * vectorial_dim, initialSeeds.rows() * vectorial_dim);
-      P.reserve(Eigen::VectorXi::Constant(initialSeeds.rows() * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
-
-      unsigned int trueSeeds{0};
-      for (int i = 0; i < initialSeeds.rows(); i++)
-      {
-        unsigned int index = initialSeeds(i) % n_cells;
-        // check that there are not repeated nodes in initialSeeds
-        if (nodePointsSet.find(index) == nodePointsSet.end()){
-          nodePointsSet.insert(index);
-          nodePointsDeque.push_back(index);
-
-          for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-          {
-            P.insert(index+ith_field*n_cells, vectorial_dim*trueSeeds+ith_field) = 1;
-            mp_not_mask(index + ith_field * n_cells) = 0;
-          }
-          trueSeeds++;
-        }
-      }
-
-      P.conservativeResize(P.rows(), nodePointsDeque.size()*vectorial_dim);
-      P.makeCompressed();
-      M_Assert(nodePointsDeque.size()<=n_nodes, "Size of 'initialSeeds' is greater than 'n_nodes'");
-      
-      // TODO fix with only positive weights (NNLS)
-      // Init quadratureWeights
-      J.resize(vectorial_dim * (n_modes + 1), nodePointsDeque.size());
-      J = Jwhole(Eigen::indexing::all, nodes);
-      // J = Jwhole*P;
-      // for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-      // {
-      //   Eigen::MatrixXd block = APtmp(Eigen::indexing::all, Eigen::seqN(ith_field, nodePointsDeque.size(), vectorial_dim));
-      //   J.middleRows(n_modes*ith_field, n_modes) = block;
-      // }
-
-      // J.row(J.rows()-1) = Eigen::VectorXd::Constant(J.cols(), 1);
-
-      quadratureWeights.resize(nodePointsDeque.size()*vectorial_dim);
-      for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-      {
-        quadratureWeights.segment(ith_field*nodePointsDeque.size(), nodePointsDeque.size()) = J.middleRows(ith_field*(n_modes+1), n_modes+1).colPivHouseholderQr().solve(q.segment(ith_field*(n_modes+1), n_modes+1));
-        b.segment(ith_field*n_modes, n_modes) = q.segment(ith_field*(n_modes+1), n_modes)-J.middleRows(ith_field*(n_modes+1), n_modes)*quadratureWeights.segment(ith_field*nodePointsDeque.size(), nodePointsDeque.size());
-      }
-      Info << "Tol: " << b.lpNorm<2>()/q.lpNorm<2>() << endl;
-      Info << "ECP Error: " << b.maxCoeff() << endl;
-      b = b/b.lpNorm<2>();
-
-      Info << "weights: " << quadratureWeights << endl;
+      initialSeeds(mp_not_mask, nodePointsSet);
+      computeLS(J, Jwhole, b, q);
     }
 
     int na = n_nodes - initialSeeds.rows();
@@ -616,134 +488,108 @@ void HyperReduction<SnapshotsLists...>::offlineECP()
 
     if (na > 0)
     {
-      std::cout << "DEBUG ~/projects/ITHACA-FV/src/ITHACA_HR/hyperReduction.templates.H at Line 616 " << std::endl;
       label ind_max, r1;
       double max;
-      
-      // Eigen::MatrixXd Aw = A*mp_not_mask.asDiagonal();
-      // for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-      // {
-      //   Aw.middleCols(n_cells*ith_field, n_cells).array().colwise()*=b.segment(n_modes*ith_field, n_modes).array();
-      // }
-      std::cout << "DEBUG ~/projects/ITHACA-FV/src/ITHACA_HR/hyperReduction.templates.H at Line 625 " << b.rows() << " " << A.rows() << " " << A.cols() << " " << mp_not_mask.head(n_cells).rows() << std::endl;
-      max = ((b.transpose()*A*mp_not_mask.head(n_cells).asDiagonal()).colwise().sum()).maxCoeff(&r1, &ind_max);
-
-      updateNodes(P, ind_max, mp_not_mask, nodePointsDeque);
-      
-      Info << "Max ind init: " << ind_max << " Deque size: " << nodePointsDeque.size() << endl;
-
-      // TODO encapsulate update quadratureWeights
-      J.resize(vectorial_dim * (n_modes + 1), nodePointsDeque.size());
-      std::cout << "DEBUG ~/projects/ITHACA-FV/src/ITHACA_HR/hyperReduction.templates.H at Line 634 " << P.bottomRows(nodePointsDeque.size()).rows() << " " << P.bottomRows(nodePointsDeque.size()).cols() << std::endl;
-      J = Jwhole(Eigen::indexing::all, nodes);
-      // J = Jwhole*P;
-      std::cout << "DEBUG ~/projects/ITHACA-FV/src/ITHACA_HR/hyperReduction.templates.H at Line 636 " << std::endl;
-      
-      quadratureWeights.resize(nodePointsDeque.size()*vectorial_dim);
-      for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-      {
-        quadratureWeights.segment(ith_field*nodePointsDeque.size(), nodePointsDeque.size()) = J.middleRows(ith_field*(n_modes+1), n_modes+1).colPivHouseholderQr().solve(q.segment(ith_field*(n_modes+1), n_modes+1));
-        b.segment(ith_field*n_modes, n_modes) = q.segment(ith_field*(n_modes+1), n_modes)-J.middleRows(ith_field*(n_modes+1), n_modes)*quadratureWeights.segment(ith_field*nodePointsDeque.size(), nodePointsDeque.size());
-      }
-      Info << "DEBUG: " << b << endl;
-      Info << "Tol: " << b.lpNorm<2>()/q.lpNorm<2>() << endl;
-      Info << "ECP Error: " << b.maxCoeff() << endl;
-      b = b/b.lpNorm<2>();
-
-      // quadratureWeights.resize(nodePointsDeque.size());
-      // quadratureWeights = J.colPivHouseholderQr().solve(q);
 
-      // // auto ECPSolver = Eigen::NNLS(J);
-      // // quadratureWeights = ECPSolver.solve(q);
-      // // std::cout << "Info NNLS: " << ECPSolver.info() << endl;
-      // Info << quadratureWeights << endl;
-
-      // b = q-J*quadratureWeights;
-      // Info << "Tol: " << b.lpNorm<2>()/q.lpNorm<2>() << endl;
-      // Info << "ECP Error: " << b.maxCoeff(&ind_max, &c1) << " " << ind_max << " vol: " << b(b.rows()-1) << endl;
-      // b = b/b.lpNorm<2>();
-
-      for (unsigned int ith_node = 1; ith_node < na; ith_node++)
+      for (unsigned int ith_node = 0; ith_node < na; ith_node++)
       {
         max = ((b.transpose()*A*mp_not_mask.head(n_cells).asDiagonal()).colwise().sum()).maxCoeff(&r1, &ind_max);
 
-        updateNodes(P, ind_max, mp_not_mask, nodePointsDeque);
-        
-        Info << "Max ind init: " << ind_max << " Deque size: " << nodePointsDeque.size() << endl;
-
-        // TODO encapsulate update quadratureWeights
-        J.resize(vectorial_dim * (n_modes + 1), nodePointsDeque.size());
-        J = Jwhole(Eigen::indexing::all, nodes);
-        // J = Jwhole*P;
-
-        quadratureWeights.resize(nodePointsDeque.size()*vectorial_dim);
-        for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-        {
-          quadratureWeights.segment(ith_field*nodePointsDeque.size(), nodePointsDeque.size()) = J.middleRows(ith_field*(n_modes+1), n_modes+1).colPivHouseholderQr().solve(q.segment(ith_field*(n_modes+1), n_modes+1));
-          b.segment(ith_field*n_modes, n_modes) = q.segment(ith_field*(n_modes+1), n_modes)-J.middleRows(ith_field*(n_modes+1), n_modes)*quadratureWeights.segment(ith_field*nodePointsDeque.size(), nodePointsDeque.size());
-        }
-        Info << "Tol: " << b.lpNorm<2>()/q.lpNorm<2>() << endl;
-        Info << "ECP Error: " << b.maxCoeff() << endl;
-        b = b/b.lpNorm<2>();
-        Info << "DEBUG quad size: " << quadratureWeights.rows() << endl;
-        
-        // Aw = A*mp_not_mask.asDiagonal();
-        // for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-        // {
-        //   Aw.middleCols(n_cells*ith_field, n_cells).array().colwise()*=b.segment(n_modes*ith_field, n_modes).array();
-        // }
-        // max = (Aw.colwise().sum()*reshapeMat).transpose().maxCoeff(&ind_max, &c1);
-
-        // updateNodes(P, ind_max, mp_not_mask, nodePointsDeque);
-        
-        // Info << "Max ind: " << ind_max << " Deque size: " << nodePointsDeque.size() << endl;
-
-        // // TODO encapsulate update quadratureWeights
-        // J.resize(n_modes*vectorial_dim+1, nodePointsDeque.size());
-
-        // Eigen::MatrixXd APtmp = (snapshotsModes).leftCols(n_modes).transpose()*P;
-
-        // // block transpose (M, nodes.size()*vectorial_dim)->(M*vectorial_dim, nodes.size()) if vectorial_dim > 1
-        // for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-        // {
-        //   Eigen::MatrixXd block = APtmp(Eigen::indexing::all, Eigen::seqN(ith_field, nodePointsDeque.size(), vectorial_dim));
-        //   J.middleRows(n_modes*ith_field, n_modes) = block;
-        // }
-
-        // J.row(J.rows()-1) = Eigen::VectorXd::Constant(J.cols(), 1);
-        // // J.array().colwise() /= q.array();
-
-        // quadratureWeights.resize(nodePointsDeque.size());
-        // quadratureWeights = J.colPivHouseholderQr().solve(q);
-
-        // b = q-J*quadratureWeights;
-        // Info << "Tol: " << b.lpNorm<2>()/q.lpNorm<2>() << endl;
-        // Info << "ECP Error: " << b.maxCoeff(&ind_max, &c1) << " " << ind_max << " vol: " << b(b.rows()-1) << endl << endl;
-        // b = b/b.lpNorm<2>();
-        // Info << "weights: " << quadratureWeights << endl;
+        updateNodes(P, ind_max, mp_not_mask);
+        computeLS(J, Jwhole, b, q);
       }
     }
 
+    Info << "####### End ECP #######" << endl;
+
     basisMatrix = snapshotsModes.leftCols(n_modes);
+    evaluateWPU(P, basisMatrix, normalizingWeights, quadratureWeights);
+
     cnpy::save(basisMatrix, Folder +"/basisMatrix.npy");
     cnpy::save(quadratureWeights, Folder +"/quadratureWeights.npy");
-    nodePoints().write();
-
-    for (auto &x : nodePointsDeque)
-    {
-      nodePoints().append(x);
-    }
     cnpy::save(nodes, Folder + "/mp.npy");
-
-    evaluateWPU(P, basisMatrix, normalizingWeights, quadratureWeights);
     cnpy::save(wPU, Folder + "/wPU.npy");
+    nodePoints().write();
   }
   else
   {
-    cnpy::load(pinvPU, Folder + "/pinvPU.npy");
     cnpy::load(basisMatrix, Folder +"/basisMatrix.npy");
     cnpy::load(quadratureWeights, Folder +"/quadratureWeights.npy");
+    cnpy::load(nodes, Folder + "/mp.npy");
+    cnpy::load(wPU, Folder + "/wPU.npy");
+  }
+}
+
+template<typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::initSeeds(Eigen::VectorXd mp_not_mask, std::set<label> nodePointsSet)
+{
+  P.resize(n_cells * vectorial_dim, initialSeeds.rows() * vectorial_dim);
+  P.reserve(Eigen::VectorXi::Constant(initialSeeds.rows() * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
+
+  unsigned int trueSeeds{0};
+  for (int i = 0; i < initialSeeds.rows(); i++)
+  {
+    unsigned int index = initialSeeds(i) % n_cells;
+    // check that there are not repeated nodes in initialSeeds
+    if (nodePointsSet.find(index) == nodePointsSet.end()){
+      nodePointsSet.insert(index);
+      nodePoints->append(index);
+
+      for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+      {
+        P.insert(index+ith_field*n_cells, vectorial_dim*trueSeeds+ith_field) = 1;
+        mp_not_mask(index + ith_field * n_cells) = 0;
+      }
+      trueSeeds++;
+    }
+  }
+
+  P.conservativeResize(P.rows(), nodePoints->size()*vectorial_dim);
+  P.makeCompressed();
+  M_Assert(nodePoints->size()<=n_nodes, "Size of 'initialSeeds' is greater than 'n_nodes'");
+}
+
+template <typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::updateNodes(Eigen::SparseMatrix<double>& P, label& ind, Eigen::VectorXd& mp_not_mask)
+{
+  unsigned int last_col{0};
+  
+  if (P.rows()==0)
+  {
+    P.resize(n_cells*vectorial_dim, vectorial_dim);
+  }
+  else
+  {
+    last_col = P.cols();
+    P.conservativeResize(P.rows(), P.cols() + vectorial_dim);
+  }
+
+  for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+  {
+    P.insert(ind + ith_field * n_cells, last_col + ith_field) = 1;
+    mp_not_mask(ind + ith_field * n_cells) = 0;
+  }
+
+  nodePoints->append(ind);
+
+  nodes.conservativeResize(nodes.rows()+1);
+  nodes(nodes.rows()-1) = ind;
+}
+
+template<typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::computeLS(Eigen::MatrixXd& J, Eigen::MatrixXd& Jwhole, Eigen::VectorXd& b, Eigen::VectorXd& q)
+{
+  // TODO fix with only positive weights (NNLS)
+  J.resize(vectorial_dim * (n_modes + 1), nodePoints->size());
+  J = Jwhole(Eigen::indexing::all, nodes);
+
+  quadratureWeights.resize(nodePoints->size()*vectorial_dim);
+  for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+  {
+    quadratureWeights.segment(ith_field*nodePoints->size(), nodePoints->size()) = J.middleRows(ith_field*(n_modes+1), n_modes+1).colPivHouseholderQr().solve(q.segment(ith_field*(n_modes+1), n_modes+1));
+    b.segment(ith_field*n_modes, n_modes) = q.segment(ith_field*(n_modes+1), n_modes)-J.middleRows(ith_field*(n_modes+1), n_modes)*quadratureWeights.segment(ith_field*nodePoints->size(), nodePoints->size());
   }
+  b = b/b.lpNorm<2>();
 }
 
 template<typename... SnapshotsLists>
@@ -799,15 +645,11 @@ void HyperReduction<SnapshotsLists...>::evaluatePinv(Eigen::SparseMatrix<double>
 template<typename... SnapshotsLists>
 void HyperReduction<SnapshotsLists...>::evaluateWPU(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd &fieldWeights, Eigen::VectorXd& quadratureWeights) {
   assert(Projector.cols() > 0);
-  // Eigen::MatrixXd restricted = Projector.transpose() * Modes;
-
-  // restricted.array().rowwise()*= quadratureWeights.transpose().array();
 
-  // wPU = restricted.transpose()*(Projector.transpose() * fieldWeights.array().cwiseInverse().matrix()).asDiagonal();
   Eigen::VectorXd quadratureWeightsOrderedAsProjector(quadratureWeights.rows());
   unsigned int n_weightsPerField = quadratureWeights.rows()/vectorial_dim;
   unsigned int reorderIndex{0};
-  
+
   for (unsigned int ith_weight = 0; ith_weight < n_weightsPerField; ith_weight++)
   {
     for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
@@ -816,8 +658,7 @@ void HyperReduction<SnapshotsLists...>::evaluateWPU(Eigen::SparseMatrix<double>
       reorderIndex++;
     }
   }
-  
-  wPU = quadratureWeightsOrderedAsProjector.asDiagonal()*(Projector.transpose() * fieldWeights.array().cwiseInverse().matrix()).asDiagonal();
+  wPU = quadratureWeightsOrderedAsProjector.transpose()*(Projector.transpose() * fieldWeights.array().cwiseInverse().matrix()).asDiagonal();
 }
 
 template<typename... SnapshotsLists>
diff --git a/tutorials/CFD/24HyperReduction/24HyperReduction.C b/tutorials/CFD/24HyperReduction/24HyperReduction.C
index 2e8e45b36..72ba31ee1 100644
--- a/tutorials/CFD/24HyperReduction/24HyperReduction.C
+++ b/tutorials/CFD/24HyperReduction/24HyperReduction.C
@@ -129,58 +129,58 @@ class HyperReduction_vectorFunction : public HyperReduction<PtrList<volVectorFie
 
 };
 
-// class HyperReduction_vectorScalarFunction : public HyperReduction<PtrList<volVectorField>&, PtrList<volScalarField>&>
-// {
-//     public:
-//     using HyperReduction::HyperReduction;
-//         static std::pair<volVectorField, volScalarField> evaluate_expression(volVectorField& V, volScalarField& S, Eigen::MatrixXd mu)
-//         {
-//             volScalarField yPos = S.mesh().C().component(vector::Y).ref();
-//             volScalarField xPos = S.mesh().C().component(vector::X).ref();
-
-//             for (auto i = 0; i < S.size(); i++)
-//             {
-//                 V[i][0] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1,
-//                                                 2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
-//                 V[i][1] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 0.5,
-//                                                 2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
-//                 V[i][2] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1.5,
-//                                                 2) - 2 * std::pow(yPos[i] - mu(1) - 0., 2));
-//                 S[i] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1,
-//                                                 2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
-//             }
-
-//             return std::make_pair(V, S);
-//         }
-
-//         static Eigen::VectorXd evaluate_expression(volScalarField& S, Eigen::MatrixXd mu, List<label> nodesList)
-//         {
-//             Eigen::VectorXd ret(nodesList.size()*4);
-//             volScalarField yPos = S.mesh().C().component(vector::Y).ref();
-//             volScalarField xPos = S.mesh().C().component(vector::X).ref();
-
-//             for (auto i = 0; i < nodesList.size(); i++)
-//             {
-//                 ret(i*4) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
-//                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
-//                 ret(i*4 + 1) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 0.5,
-//                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
-//                 ret(i*4 + 2) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1.5,
-//                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0., 2));
-//                 ret(i*4 + 3) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
-//                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
-//             }
-
-//             return ret;
-//         }
+class HyperReduction_vectorScalarFunction : public HyperReduction<PtrList<volVectorField>&, PtrList<volScalarField>&>
+{
+    public:
+    using HyperReduction::HyperReduction;
+        static std::pair<volVectorField, volScalarField> evaluate_expression(volVectorField& V, volScalarField& S, Eigen::MatrixXd mu)
+        {
+            volScalarField yPos = S.mesh().C().component(vector::Y).ref();
+            volScalarField xPos = S.mesh().C().component(vector::X).ref();
+
+            for (auto i = 0; i < S.size(); i++)
+            {
+                V[i][0] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1,
+                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
+                V[i][1] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 0.5,
+                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
+                V[i][2] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1.5,
+                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0., 2));
+                S[i] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1,
+                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
+            }
+
+            return std::make_pair(V, S);
+        }
+
+        static Eigen::VectorXd evaluate_expression(volScalarField& S, Eigen::MatrixXd mu, List<label> nodesList)
+        {
+            Eigen::VectorXd ret(nodesList.size()*4);
+            volScalarField yPos = S.mesh().C().component(vector::Y).ref();
+            volScalarField xPos = S.mesh().C().component(vector::X).ref();
+
+            for (auto i = 0; i < nodesList.size(); i++)
+            {
+                ret(i*4) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
+                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
+                ret(i*4 + 1) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 0.5,
+                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
+                ret(i*4 + 2) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1.5,
+                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0., 2));
+                ret(i*4 + 3) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
+                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
+            }
+
+            return ret;
+        }
         
-//         Eigen::VectorXd onlineCoeffs(volScalarField& S, Eigen::MatrixXd mu)
-//         {
-//             Eigen::VectorXd f = evaluate_expression(S, mu, localNodePoints);
-//             return pinvPU*f;
-//         }
+        Eigen::VectorXd onlineCoeffs(volScalarField& S, Eigen::MatrixXd mu)
+        {
+            Eigen::VectorXd f = evaluate_expression(S, mu, localNodePoints);
+            return pinvPU*f;
+        }
 
-// };
+};
 
 void test_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime){
     int n_modes = para->ITHACAdict->lookupOrDefault<int>("Modes", 15);
@@ -262,7 +262,11 @@ void test_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
     else if (methodName=="ECP")
     {
         HyperReduction_function c(n_modes, n_nodes, initSeeds, "Gaussian_function", Sp);
-        c.offlineECP();
+
+        Eigen::MatrixXd snapshotsModes;
+        bool saveOFModes{true};
+        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, c.normalizingWeights, saveOFModes); 
+        c.offlineECP(snapshotsModes);
 
         // Generate the submeshes with the depth of the layer
         unsigned int layers{2};
@@ -278,8 +282,8 @@ void test_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
             
             double trueIntegral = (c.normalizingWeights.array().cwiseInverse().matrix().asDiagonal()*ff).array().sum();
             double testIntegral = (c.wPU*f).array().sum();
-            Info << "Integral: " << trueIntegral << endl;
-            Info << "Reconstructed Integral: " << testIntegral << endl;
+            // Info << "Integral: " << trueIntegral << endl;
+            // Info << "Reconstructed Integral: " << testIntegral << endl;
 
             results(idTest) = trueIntegral-testIntegral;
         }
@@ -367,7 +371,11 @@ void test_vector(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
     else if (methodName=="ECP")
     {
         HyperReduction_vectorFunction c(n_modes, n_nodes, initSeeds, "Gaussian_function", Sp);
-        c.offlineECP();
+        
+        Eigen::MatrixXd snapshotsModes;
+        bool saveOFModes{true};
+        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, c.normalizingWeights, saveOFModes); 
+        c.offlineECP(snapshotsModes);
 
         // Generate the submeshes with the depth of the layer
         unsigned int layers{2};
@@ -384,8 +392,8 @@ void test_vector(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
             
             double trueIntegral = (c.normalizingWeights.array().cwiseInverse().matrix().asDiagonal()*ff).array().sum();
             double testIntegral = (c.wPU*f).array().sum();
-            Info << "Integral: " << trueIntegral << endl;
-            Info << "Reconstructed Integral: " << testIntegral << endl;
+            // Info << "Integral: " << trueIntegral << endl;
+            // Info << "Reconstructed Integral: " << testIntegral << endl;
 
             results(idTest) = trueIntegral-testIntegral;
         }
@@ -394,94 +402,154 @@ void test_vector(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
     }
 }
 
-// void test_vector_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime){
-//     int n_modes = para->ITHACAdict->lookupOrDefault<int>("Modes", 15);
-//     int n_nodes = para->ITHACAdict->lookupOrDefault<int>("Nodes", 15);
-//     simpleControl simple(mesh);
-
-// #include "createFields.H"
-//     // List of volVectorField where the snapshots are stored
-//     PtrList<volVectorField> Vp;
-//     PtrList<volScalarField> Sp;
-//     // Non linear function
-//     volVectorField V
-//     (
-//         IOobject
-//         (
-//             "V",
-//             runTime.timeName(),
-//             mesh,
-//             IOobject::NO_READ,
-//             IOobject::AUTO_WRITE
-//         ),
-//         T.mesh(),
-//         dimensionedVector("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), vector(0, 0, 0))
-//     );
-//     // Non linear function
-//     volScalarField S
-//     (
-//         IOobject
-//         (
-//             "S",
-//             runTime.timeName(),
-//             mesh,
-//             IOobject::NO_READ,
-//             IOobject::AUTO_WRITE
-//         ),
-//         T.mesh(),
-//         dimensionedScalar("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), 0)
-//     );
-
-//     // Parameters used to train the non-linear function
-//     Eigen::MatrixXd pars;
-//     cnpy::load(pars, "trainingPars.npy");
-
-//     // Perform the offline phase
-//     for (int i = 0; i < 100; i++)
-//     {
-//         HyperReduction_vectorScalarFunction::evaluate_expression(V, S, pars.row(i));
-//         Vp.append((V).clone());
-//         Sp.append((S).clone());
-//         ITHACAstream::exportSolution(S, name(i + 1), "./ITHACAoutput/Offline/");
-//         ITHACAstream::exportSolution(V, name(i + 1), "./ITHACAoutput/Offline/");
-//     }
-
-//     // Create HyperReduction object with given number of basis functions
-//     Eigen::VectorXi initSeeds(0);
-
-//     HyperReduction_vectorScalarFunction c(n_modes, n_nodes, initSeeds, "Gaussian_function", Vp, Sp);
-//     c.offlineStage();
-
-//     // Generate the submeshes with the depth of the layer
-//     c.generateSubmesh(2, mesh);
-//     auto vfield = c.interpolateField<volVectorField>(Vp[0]);
-//     auto sfield = c.interpolateField<volScalarField>(Sp[0]);
-//     // Define a new online parameter
-//     Eigen::MatrixXd par_new(2, 1);
-//     par_new(0, 0) = 0;
-//     par_new(1, 0) = 0;
-//     // Online evaluation of the non linear function
-//     auto theta = c.onlineCoeffs(sfield(), par_new);
-//     Eigen::VectorXd aprfield = c.renormalizedBasisMatrix*theta;
-//     // Transform to an OpenFOAM field and export
-//     // c.eigen2fields(aprfield, V, S);
-//     // volVectorField V2("V_online", V);
-//     // volScalarField S2("S_online", S);
-//     Eigen::VectorXd recvec = aprfield.head(3*S.size());
-//     Eigen::VectorXd recsca = aprfield.tail(S.size());
-//     volVectorField V2("V_online", Foam2Eigen::Eigen2field(V, recvec));
-//     volScalarField S2("S_online", Foam2Eigen::Eigen2field(S, recsca));
-
-//     ITHACAstream::exportSolution(V2, name(1), "./ITHACAoutput/Online/");
-//     ITHACAstream::exportSolution(S2, name(1), "./ITHACAoutput/Online/");
-//     // Evaluate the full order function and export it
-//     HyperReduction_vectorScalarFunction::evaluate_expression(V, S, par_new);
-//     ITHACAstream::exportSolution(V, name(1), "./ITHACAoutput/Online/");
-//     ITHACAstream::exportSolution(S, name(1), "./ITHACAoutput/Online/");
-//     // Compute the L2 error and print it
-//     Info << "Scalar L2 error: " << ITHACAutilities::errorL2Rel(S2, S) << endl;
-//     Info << "Vector L2 error: " << ITHACAutilities::errorL2Rel(V2, V) << endl;
-// }
+void test_vector_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime){
+    int n_modes = para->ITHACAdict->lookupOrDefault<int>("Modes", 15);
+    int n_nodes = para->ITHACAdict->lookupOrDefault<int>("Nodes", 15);
+    simpleControl simple(mesh);
+    word methodName = para->ITHACAdict->lookupOrDefault<word>("HyperReduction", "GappyDEIM");
+
+#include "createFields.H"
+    // List of volVectorField where the snapshots are stored
+    PtrList<volVectorField> Vp;
+    PtrList<volScalarField> Sp;
+    // Non linear function
+    volVectorField V
+    (
+        IOobject
+        (
+            "V",
+            runTime.timeName(),
+            mesh,
+            IOobject::NO_READ,
+            IOobject::AUTO_WRITE
+        ),
+        T.mesh(),
+        dimensionedVector("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), vector(0, 0, 0))
+    );
+    // Non linear function
+    volScalarField S
+    (
+        IOobject
+        (
+            "S",
+            runTime.timeName(),
+            mesh,
+            IOobject::NO_READ,
+            IOobject::AUTO_WRITE
+        ),
+        T.mesh(),
+        dimensionedScalar("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), 0)
+    );
+    
+    // Parameters used to train the non-linear function
+    Eigen::MatrixXd pars;
+    cnpy::load(pars, "trainingPars.npy");
+    // Perform the offline phase
+    for (int i = 0; i < 100; i++)
+    {
+        HyperReduction_vectorScalarFunction::evaluate_expression(V, S, pars.row(i));
+        Vp.append((V).clone());
+        Sp.append((S).clone());
+        ITHACAstream::exportSolution(V, name(i + 1), "./ITHACAoutput/Offline/");
+        ITHACAstream::exportSolution(S, name(i + 1), "./ITHACAoutput/Offline/");
+    }
+
+    // Define new online parameters
+    Eigen::MatrixXd parTest;// = ITHACAutilities::rand(100, 2, -0.5, 0.5);
+    cnpy::load(parTest, "testingPars.npy");
+
+    // Create HyperReduction object with given number of basis functions
+    Eigen::VectorXi initSeeds;
+    // initSeeds = cnpy::load(initSeeds, "./mp.npy");//load mp to test initialSeeds
+
+    if (methodName=="GappyDEIM")
+    {
+        HyperReduction_vectorScalarFunction c(n_modes, n_nodes, initSeeds, "Gaussian_function", Vp, Sp);
+        c.offlineGappyDEIM();
+
+        // Generate the submeshes with the depth of the layer
+        unsigned int layers{2};
+        c.generateSubmesh(layers, mesh);
+        auto vfield = c.interpolateField<volVectorField>(Vp[0]);
+        auto sfield = c.interpolateField<volScalarField>(Sp[0]);
+        
+        PtrList<volVectorField> testTrueFieldsV;
+        PtrList<volVectorField> testRecFieldsV;
+        PtrList<volScalarField> testTrueFieldsS;
+        PtrList<volScalarField> testRecFieldsS;
+        for (unsigned int idTest = 0; idTest < parTest.rows(); idTest++)
+        {        
+            // Online evaluation of the non linear function
+            auto theta = c.onlineCoeffs(sfield(), parTest.row(idTest));
+            Eigen::VectorXd aprfield = c.renormalizedBasisMatrix*theta;
+            Eigen::VectorXd recvec = aprfield.head(3*S.size());
+            Eigen::VectorXd recsca = aprfield.tail(S.size());
+            // Transform to an OpenFOAM field and export
+            volVectorField V2("V_online", Foam2Eigen::Eigen2field(V, recvec));
+            volScalarField S2("S_online", Foam2Eigen::Eigen2field(S, recsca));
+            // Evaluate the full order function and export it
+            HyperReduction_vectorScalarFunction::evaluate_expression(V, S, parTest.row(idTest));
+            
+            testRecFieldsV.append(V2.clone());
+            testTrueFieldsV.append(V.clone());
+
+            ITHACAstream::exportSolution(V2, name(idTest), "./ITHACAoutput/Online/");
+            ITHACAstream::exportSolution(V, name(idTest), "./ITHACAoutput/Online/");
+
+            testRecFieldsS.append(S2.clone());
+            testTrueFieldsS.append(S.clone());
+
+            ITHACAstream::exportSolution(S2, name(idTest), "./ITHACAoutput/Online/");
+            ITHACAstream::exportSolution(S, name(idTest), "./ITHACAoutput/Online/");
+        }
+
+        // Compute the L2 error and print it
+        auto errV = ITHACAutilities::errorL2Rel(testRecFieldsV, testTrueFieldsV);
+        Info << "GappyDEIM vector field max relative error: " << errV.maxCoeff() << endl;
+        Info << "GappyDEIM vector field mean relative error: " << errV.array().mean() << endl;
+
+        auto errS = ITHACAutilities::errorL2Rel(testRecFieldsS, testTrueFieldsS);
+        Info << "GappyDEIM scalar max relative error: " << errS.maxCoeff() << endl;
+        Info << "GappyDEIM scalar mean relative error: " << errS.array().mean() << endl;
+    }
+    else if (methodName=="ECP")
+    {
+        HyperReduction_vectorScalarFunction c(n_modes, n_nodes, initSeeds, "Gaussian_function", Vp, Sp);
+        
+        Eigen::MatrixXd snapshotsModes;
+        bool saveOFModes{true};
+        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, c.normalizingWeights, saveOFModes); 
+        c.offlineECP(snapshotsModes);
+
+        // Generate the submeshes with the depth of the layer
+        unsigned int layers{2};
+        c.generateSubmesh(layers, mesh);
+        auto vfield = c.interpolateField<volVectorField>(Vp[0]);
+        auto sfield = c.interpolateField<volScalarField>(Sp[0]);
+        
+        Eigen::VectorXd results(parTest.rows());
+        for (unsigned int idTest = 0; idTest < parTest.rows(); idTest++)
+        {
+            // Online evaluation of the non linear function            
+            Eigen::VectorXd f = c.evaluate_expression(sfield(), parTest.row(idTest), c.localNodePoints);
+            HyperReduction_vectorScalarFunction::evaluate_expression(V, S, parTest.row(idTest));
+            Eigen::VectorXd ffV = Foam2Eigen::field2Eigen(V);
+            Eigen::VectorXd ffS = Foam2Eigen::field2Eigen(S);
+            Eigen::VectorXd ff(ffV.rows() + ffS.rows());
+            ff.head(ffV.rows()) = ffV;
+            ff.tail(ffS.rows()) = ffS;
+            
+            double trueIntegral = (c.normalizingWeights.array().cwiseInverse().matrix().asDiagonal()*ff).array().sum();
+            double testIntegral = (c.wPU*f).array().sum();
+            // Info << "Integral: " << trueIntegral << endl;
+            // Info << "Reconstructed Integral: " << testIntegral << endl;
+
+            results(idTest) = trueIntegral-testIntegral;
+        }
+        Info << "ECP max error: " << results.cwiseAbs().maxCoeff() << endl;
+        Info << "ECP mean error: " << results.cwiseAbs().mean() << endl;
+    }
+}
 
 int main(int argc, char* argv[])
 {
@@ -532,11 +600,11 @@ int main(int argc, char* argv[])
         Info << "Init vector testcase\n";
         test_vector(para, mesh, runTime);
     }
-    // else if (args.get("test").match("vs"))
-    // {
-    //     Info << "Init vector scalar testcase\n";
-    //     test_vector_scalar(para, mesh, runTime);
-    // }
+    else if (args.get("test").match("vs"))
+    {
+        Info << "Init vector scalar testcase\n";
+        test_vector_scalar(para, mesh, runTime);
+    }
     else
     {
         Info << "Pass '-test scalar', '-test vector', '-test vs'" << endl;
diff --git a/tutorials/CFD/24HyperReduction/system/ITHACAdict b/tutorials/CFD/24HyperReduction/system/ITHACAdict
index b29c5901d..668de9635 100755
--- a/tutorials/CFD/24HyperReduction/system/ITHACAdict
+++ b/tutorials/CFD/24HyperReduction/system/ITHACAdict
@@ -26,5 +26,5 @@ OutPrecision 20;
 OutType fixed;
 
 // HR
-HyperReduction ECP;//GreedyDEIM, ECP
-GreedyMetric SOPT;//L2, SOPT, SOPTE
\ No newline at end of file
+HyperReduction ECP;//GappyDEIM, ECP
+GreedyMetric L2;//L2, SOPT, SOPTE
\ No newline at end of file

From 6ddf3913bf696b7527deac355abccf3e6daf3e11 Mon Sep 17 00:00:00 2001
From: fromor <francesco.romor@gmail.com>
Date: Mon, 31 Oct 2022 10:22:37 +0100
Subject: [PATCH 06/59] fix loading of HR methods

---
 src/ITHACA_HR/hyperReduction.H           |  7 ++-
 src/ITHACA_HR/hyperReduction.templates.H | 63 +++++++++++++-----------
 2 files changed, 40 insertions(+), 30 deletions(-)

diff --git a/src/ITHACA_HR/hyperReduction.H b/src/ITHACA_HR/hyperReduction.H
index 5f49e4af8..6c68271b1 100644
--- a/src/ITHACA_HR/hyperReduction.H
+++ b/src/ITHACA_HR/hyperReduction.H
@@ -121,8 +121,11 @@ public:
     /// List of the unique indices of the nodes that define the submesh
     autoPtr<IOList<label>> uniqueNodePoints;
 
-    /// Folder for nonlinear functions
-    word Folder;
+    /// Folder for the HR problem
+    word folderProblem;
+
+    /// Folder for the selected HR method
+    word folderMethod;
 
     /// Indices of the local node points in the subMesh
     List<label> localNodePoints;
diff --git a/src/ITHACA_HR/hyperReduction.templates.H b/src/ITHACA_HR/hyperReduction.templates.H
index b90806989..1825f1543 100644
--- a/src/ITHACA_HR/hyperReduction.templates.H
+++ b/src/ITHACA_HR/hyperReduction.templates.H
@@ -51,8 +51,8 @@ HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
 {
   Info << "Init HyperReduction class with vectorial dim: " << vectorial_dim << endl;
   para = ITHACAparameters::getInstance();
-  Folder = "ITHACAoutput/" + problemName;
-  mkDir(Folder);
+  folderProblem = "ITHACAoutput/" + problemName;
+  mkDir(folderProblem);
 
   // TODO check snapshotsLists is not empty
   // TODO check that the first snapshotsList is not empty (includes above)
@@ -82,7 +82,7 @@ HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
 
 // Using the Eigen library, using the SVD decomposition method to solve the
 // matrix pseudo-inverse, the default error er is 0
-Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0) {
+Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er) {
   // perform svd decomposition
   Eigen::JacobiSVD<Eigen::MatrixXd> svd_holder(origin, Eigen::ComputeThinU | Eigen::ComputeThinV);
   // Build SVD decomposition results
@@ -188,11 +188,11 @@ template <typename... SnapshotsLists>
 void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
 {
   methodName = "GappyDEIM";
-  Folder = "ITHACAoutput/" + problemName + "/" + methodName;
-  mkDir(Folder);
+  folderMethod = "ITHACAoutput/" + problemName + "/" + methodName;
+  mkDir(folderMethod);
 
   nodePoints = autoPtr<IOList<label>>(new IOList<label>(
-      IOobject("nodePoints", para->runTime.time().constant(), "../" + Folder,
+      IOobject("nodePoints", para->runTime.time().constant(), "../" + folderMethod,
                 para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
 
   Eigen::MatrixXd snapshotsModes;
@@ -400,10 +400,11 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
     evaluatePinv(P, basisMatrix, normalizingWeights);
     renormalizedBasisMatrix = normalizingWeights.asDiagonal()*basisMatrix;
 
-    cnpy::save(basisMatrix, Folder +"/basisMatrix.npy");
-    cnpy::save(P, Folder +"/projectionMatrix.npy");
-    cnpy::save(nodes, Folder + "/mp.npy");
-    cnpy::save(pinvPU, Folder + "/pinvPU.npy");
+    P.makeCompressed();
+    cnpy::save(basisMatrix, folderMethod +"/basisMatrix.npy");
+    cnpy::save(P, folderMethod +"/projectionMatrix.npz");
+    cnpy::save(nodes, folderMethod + "/mp.npy");
+    cnpy::save(pinvPU, folderMethod + "/pinvPU.npy");
     nodePoints().write();
 
     Info << "Projection Matrix shape: " << P.rows() << " " << P.cols() << endl;
@@ -412,10 +413,16 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
   }
   else
   {
-    cnpy::load(basisMatrix, Folder +"/basisMatrix.npy");
-    cnpy::load(P, Folder +"/projectionMatrix.npy");
-    cnpy::load(nodes, Folder + "/mp.npy");
-    cnpy::load(pinvPU, Folder + "/pinvPU.npy");
+    cnpy::load(basisMatrix, folderMethod +"/basisMatrix.npy");
+    cnpy::load(P, folderMethod +"/projectionMatrix.npz");
+    cnpy::load(nodes, folderMethod + "/mp.npy");
+    cnpy::load(pinvPU, folderMethod + "/pinvPU.npy");
+
+    renormalizedBasisMatrix = normalizingWeights.asDiagonal()*basisMatrix;
+    
+    Info << "Projection Matrix shape: " << P.rows() << " " << P.cols() << endl;
+    Info << "Basis Matrix shape: " << basisMatrix.rows() << " " << basisMatrix.cols() << endl;
+    Info << "Pseudo Inverse Matrix shape: " << pinvPU.rows() << " " << pinvPU.cols() << endl;
   }
 }
 
@@ -430,11 +437,11 @@ void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd snapshotsMode
             << ", nodePoints=" << n_nodes << " #######"
             << endl;
 
-  Folder = "ITHACAoutput/" + problemName + "/" + methodName;
-  mkDir(Folder);
+  folderMethod = "ITHACAoutput/" + problemName + "/" + methodName;
+  mkDir(folderMethod);
 
   nodePoints = autoPtr<IOList<label>>(new IOList<label>(
-      IOobject("nodePoints", para->runTime.time().constant(), "../" + Folder,
+      IOobject("nodePoints", para->runTime.time().constant(), "../" + folderMethod,
                 para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE))); 
 
   if (!nodePoints().headerOk())
@@ -505,18 +512,18 @@ void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd snapshotsMode
     basisMatrix = snapshotsModes.leftCols(n_modes);
     evaluateWPU(P, basisMatrix, normalizingWeights, quadratureWeights);
 
-    cnpy::save(basisMatrix, Folder +"/basisMatrix.npy");
-    cnpy::save(quadratureWeights, Folder +"/quadratureWeights.npy");
-    cnpy::save(nodes, Folder + "/mp.npy");
-    cnpy::save(wPU, Folder + "/wPU.npy");
+    cnpy::save(basisMatrix, folderMethod +"/basisMatrix.npy");
+    cnpy::save(quadratureWeights, folderMethod +"/quadratureWeights.npy");
+    cnpy::save(nodes, folderMethod + "/mp.npy");
+    cnpy::save(wPU, folderMethod + "/wPU.npy");
     nodePoints().write();
   }
   else
   {
-    cnpy::load(basisMatrix, Folder +"/basisMatrix.npy");
-    cnpy::load(quadratureWeights, Folder +"/quadratureWeights.npy");
-    cnpy::load(nodes, Folder + "/mp.npy");
-    cnpy::load(wPU, Folder + "/wPU.npy");
+    cnpy::load(basisMatrix, folderMethod +"/basisMatrix.npy");
+    cnpy::load(quadratureWeights, folderMethod +"/quadratureWeights.npy");
+    cnpy::load(nodes, folderMethod + "/mp.npy");
+    cnpy::load(wPU, folderMethod + "/wPU.npy");
   }
 }
 
@@ -668,11 +675,11 @@ void HyperReduction<SnapshotsLists...>::generateSubmesh(label layers, fvMesh &me
   ITHACAparameters *para(ITHACAparameters::getInstance());
 
   totalNodePoints = autoPtr<IOList<labelList>>(new IOList<labelList>(IOobject(
-      "totalNodePoints", para->runTime.time().constant(),  "../" + Folder,
+      "totalNodePoints", para->runTime.time().constant(),  "../" + folderMethod,
       para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
 
   uniqueNodePoints = autoPtr<IOList<label>>(new IOList<label>(IOobject(
-      "uniqueNodePoints", para->runTime.time().constant(),  "../" + Folder,
+      "uniqueNodePoints", para->runTime.time().constant(),  "../" + folderMethod,
       para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
 
   volScalarField Indici
@@ -721,7 +728,7 @@ void HyperReduction<SnapshotsLists...>::generateSubmesh(label layers, fvMesh &me
   std::cout.clear();
 
   localNodePoints = global2local(nodePoints(), submesh());
-  ITHACAstream::exportSolution(Indici, "1", Folder);
+  ITHACAstream::exportSolution(Indici, "1", folderMethod);
 
   n_cellsSubfields = submesh().cellMap().size();
   Info << "####### End extract submesh #######\n";

From 6378e4304604232f449377a7707e28ea52becf0d Mon Sep 17 00:00:00 2001
From: fromor <francesco.romor@gmail.com>
Date: Mon, 31 Oct 2022 16:38:17 +0100
Subject: [PATCH 07/59] separate modes computation from HR offline stages

---
 src/ITHACA_HR/hyperReduction.H                | 11 ++---
 src/ITHACA_HR/hyperReduction.templates.H      | 11 +++--
 .../CFD/24HyperReduction/24HyperReduction.C   | 42 ++++++++++++-------
 3 files changed, 36 insertions(+), 28 deletions(-)

diff --git a/src/ITHACA_HR/hyperReduction.H b/src/ITHACA_HR/hyperReduction.H
index 6c68271b1..7d1ef66ff 100644
--- a/src/ITHACA_HR/hyperReduction.H
+++ b/src/ITHACA_HR/hyperReduction.H
@@ -149,9 +149,6 @@ public:
     /// The P matrix of the HyperReduction method. The nodes are ordered in the order of insertion during the greedy procedure. The components related to the same node follow immediately.
     Eigen::SparseMatrix<double> P;
 
-    /// Normalizing weights of the offline snapshots
-    Eigen::VectorXd normalizingWeights;
-
     /// Quadrature weights. Ordered in the same order of matrix P.
     Eigen::VectorXd quadratureWeights;
 
@@ -162,14 +159,14 @@ public:
     autoPtr<volVectorField> submesh_field;
     
     //----------------------------------------------------------------------
-    /// @brief      TODO
+    /// @brief      Methods implemented: 'GappyDEIM'  from "DEIM, Chaturantabut, Saifon, and Danny C. Sorensen. "Nonlinear model reduction via discrete empirical interpolation." SIAM Journal on Scientific Computing 32.5 (2010): 2737-2764" and "GNAT, Carlberg, Kevin, et al. "The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows." Journal of Computational Physics 242 (2013): 623-647.". Quasi-optimal point selection algorithm 'SOPT' and optimal point selection 'SOPTE' from "Lauzon, Jessica T., Siu Wun Cheung, Yeonjong Shin, Youngsoo Choi, Dylan Matthew Copeland, and Kevin Huynh. "S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models." arXiv preprint arXiv:2203.16494 (2022).""
     ///
-    void offlineGappyDEIM();
+    void offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights);
 
     //----------------------------------------------------------------------
-    /// @brief      TODO
+    /// @brief      Methods implemented: 'ECP' from "ECP, Hernandez, Joaquin Alberto, Manuel Alejandro Caicedo, and Alex Ferrer. "Dimensional hyper-reduction of nonlinear finite element models via empirical cubature." Computer methods in applied mechanics and engineering 313 (2017): 687-722.". TODO implement non-negative LS.
     ///
-    void offlineECP(Eigen::MatrixXd snapshotsModes);
+    void offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights);
     
     //----------------------------------------------------------------------
     /// @brief      TODO
diff --git a/src/ITHACA_HR/hyperReduction.templates.H b/src/ITHACA_HR/hyperReduction.templates.H
index 1825f1543..bba2a086e 100644
--- a/src/ITHACA_HR/hyperReduction.templates.H
+++ b/src/ITHACA_HR/hyperReduction.templates.H
@@ -185,7 +185,7 @@ void HyperReduction<SnapshotsLists...>::saveModes(SnapshotsList sList, Eigen::Ma
 }
 
 template <typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
+void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights)
 {
   methodName = "GappyDEIM";
   folderMethod = "ITHACAoutput/" + problemName + "/" + methodName;
@@ -193,10 +193,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
 
   nodePoints = autoPtr<IOList<label>>(new IOList<label>(
       IOobject("nodePoints", para->runTime.time().constant(), "../" + folderMethod,
-                para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
-
-  Eigen::MatrixXd snapshotsModes;
-  getModesSVD(snapshotsListTuple, snapshotsModes, normalizingWeights);  
+                para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE))); 
 
   auto greedyMetric = para->ITHACAdict->lookupOrDefault<word>("GreedyMetric", "l2");
 
@@ -413,6 +410,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
   }
   else
   {
+    Info << "Read GappyDEIM\n";
     cnpy::load(basisMatrix, folderMethod +"/basisMatrix.npy");
     cnpy::load(P, folderMethod +"/projectionMatrix.npz");
     cnpy::load(nodes, folderMethod + "/mp.npy");
@@ -427,7 +425,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM()
 }
 
 template <typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd snapshotsModes)
+void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights)
 {
   methodName = "ECP";
   n_nodes = n_modes + 1;
@@ -520,6 +518,7 @@ void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd snapshotsMode
   }
   else
   {
+    Info << "Read ECP\n";
     cnpy::load(basisMatrix, folderMethod +"/basisMatrix.npy");
     cnpy::load(quadratureWeights, folderMethod +"/quadratureWeights.npy");
     cnpy::load(nodes, folderMethod + "/mp.npy");
diff --git a/tutorials/CFD/24HyperReduction/24HyperReduction.C b/tutorials/CFD/24HyperReduction/24HyperReduction.C
index 72ba31ee1..6cf4d6256 100644
--- a/tutorials/CFD/24HyperReduction/24HyperReduction.C
+++ b/tutorials/CFD/24HyperReduction/24HyperReduction.C
@@ -229,7 +229,10 @@ void test_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
     if (methodName=="GappyDEIM")
     {
         HyperReduction_function c(n_modes, n_nodes, initSeeds, "Gaussian_function", Sp);
-        c.offlineGappyDEIM();
+        Eigen::MatrixXd snapshotsModes;
+        Eigen::VectorXd normalizingWeights;
+        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights); 
+        c.offlineGappyDEIM(snapshotsModes, normalizingWeights);
 
         // Generate the submeshes with the depth of the layer
         unsigned int layers{2};
@@ -263,10 +266,11 @@ void test_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
     {
         HyperReduction_function c(n_modes, n_nodes, initSeeds, "Gaussian_function", Sp);
 
-        Eigen::MatrixXd snapshotsModes;
         bool saveOFModes{true};
-        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, c.normalizingWeights, saveOFModes); 
-        c.offlineECP(snapshotsModes);
+        Eigen::MatrixXd snapshotsModes;
+        Eigen::VectorXd normalizingWeights;
+        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights, saveOFModes); 
+        c.offlineECP(snapshotsModes, normalizingWeights);
 
         // Generate the submeshes with the depth of the layer
         unsigned int layers{2};
@@ -280,7 +284,7 @@ void test_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
             Eigen::VectorXd f = c.evaluate_expression(sfield(), parTest.row(idTest), c.localNodePoints);
             Eigen::VectorXd ff = Foam2Eigen::field2Eigen(c.evaluate_expression(Sp[0], parTest.row(idTest)));
             
-            double trueIntegral = (c.normalizingWeights.array().cwiseInverse().matrix().asDiagonal()*ff).array().sum();
+            double trueIntegral = (normalizingWeights.cwiseInverse().asDiagonal()*ff).array().sum();
             double testIntegral = (c.wPU*f).array().sum();
             // Info << "Integral: " << trueIntegral << endl;
             // Info << "Reconstructed Integral: " << testIntegral << endl;
@@ -338,7 +342,10 @@ void test_vector(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
     if (methodName=="GappyDEIM")
     {
         HyperReduction_vectorFunction c(n_modes, n_nodes, initSeeds, "Gaussian_function", Sp);
-        c.offlineGappyDEIM();
+        Eigen::MatrixXd snapshotsModes;
+        Eigen::VectorXd normalizingWeights;
+        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights); 
+        c.offlineGappyDEIM(snapshotsModes, normalizingWeights);
 
         // Generate the submeshes with the depth of the layer
         unsigned int layers{2};
@@ -372,10 +379,11 @@ void test_vector(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
     {
         HyperReduction_vectorFunction c(n_modes, n_nodes, initSeeds, "Gaussian_function", Sp);
         
-        Eigen::MatrixXd snapshotsModes;
         bool saveOFModes{true};
-        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, c.normalizingWeights, saveOFModes); 
-        c.offlineECP(snapshotsModes);
+        Eigen::MatrixXd snapshotsModes;
+        Eigen::VectorXd normalizingWeights;
+        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights, saveOFModes); 
+        c.offlineECP(snapshotsModes, normalizingWeights);
 
         // Generate the submeshes with the depth of the layer
         unsigned int layers{2};
@@ -390,7 +398,7 @@ void test_vector(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
             auto wholeField = c.evaluate_expression(Sp[0], parTest.row(idTest));
             Eigen::VectorXd ff = Foam2Eigen::field2Eigen(wholeField);
             
-            double trueIntegral = (c.normalizingWeights.array().cwiseInverse().matrix().asDiagonal()*ff).array().sum();
+            double trueIntegral = (normalizingWeights.cwiseInverse().asDiagonal()*ff).array().sum();
             double testIntegral = (c.wPU*f).array().sum();
             // Info << "Integral: " << trueIntegral << endl;
             // Info << "Reconstructed Integral: " << testIntegral << endl;
@@ -465,7 +473,10 @@ void test_vector_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time&
     if (methodName=="GappyDEIM")
     {
         HyperReduction_vectorScalarFunction c(n_modes, n_nodes, initSeeds, "Gaussian_function", Vp, Sp);
-        c.offlineGappyDEIM();
+        Eigen::MatrixXd snapshotsModes;
+        Eigen::VectorXd normalizingWeights;
+        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights); 
+        c.offlineGappyDEIM(snapshotsModes, normalizingWeights);
 
         // Generate the submeshes with the depth of the layer
         unsigned int layers{2};
@@ -516,10 +527,11 @@ void test_vector_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time&
     {
         HyperReduction_vectorScalarFunction c(n_modes, n_nodes, initSeeds, "Gaussian_function", Vp, Sp);
         
-        Eigen::MatrixXd snapshotsModes;
         bool saveOFModes{true};
-        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, c.normalizingWeights, saveOFModes); 
-        c.offlineECP(snapshotsModes);
+        Eigen::MatrixXd snapshotsModes;
+        Eigen::VectorXd normalizingWeights;
+        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights, saveOFModes); 
+        c.offlineECP(snapshotsModes, normalizingWeights);
 
         // Generate the submeshes with the depth of the layer
         unsigned int layers{2};
@@ -539,7 +551,7 @@ void test_vector_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time&
             ff.head(ffV.rows()) = ffV;
             ff.tail(ffS.rows()) = ffS;
             
-            double trueIntegral = (c.normalizingWeights.array().cwiseInverse().matrix().asDiagonal()*ff).array().sum();
+            double trueIntegral = (normalizingWeights.cwiseInverse().asDiagonal()*ff).array().sum();
             double testIntegral = (c.wPU*f).array().sum();
             // Info << "Integral: " << trueIntegral << endl;
             // Info << "Reconstructed Integral: " << testIntegral << endl;

From 949bd58611d9de67d986b58bbcf89ccc88569f24 Mon Sep 17 00:00:00 2001
From: fromor <francesco.romor@gmail.com>
Date: Thu, 3 Nov 2022 18:27:16 +0100
Subject: [PATCH 08/59] add redsvd

---
 src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.C     |  55 ++++
 src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.H     |  38 +++
 src/ITHACA_FOMPROBLEMS/Burgers/Burgers.C    |   5 +
 src/ITHACA_HR/hyperReduction.H              |  92 +++++-
 src/ITHACA_HR/hyperReduction.templates.H    | 328 ++++++++++++++++++--
 src/ITHACA_TORCH/torch2Eigen.C              |   4 +-
 tutorials/CFD/24HyperReduction/Make/options |   1 +
 7 files changed, 489 insertions(+), 34 deletions(-)

diff --git a/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.C b/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.C
index 761d4e02a..ec69c7d2f 100755
--- a/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.C
+++ b/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.C
@@ -266,6 +266,61 @@ List<Eigen::MatrixXd> Foam2Eigen::PtrList2EigenBC(
 template List<Eigen::MatrixXd> Foam2Eigen::PtrList2EigenBC(
     PtrList<volVectorField>& fields, label Nfields);
 
+template<template<class> class PatchField, class GeoMesh>
+GeometricField<vector, PatchField, GeoMesh> Foam2Eigen::Eigen2field(
+    GeometricField<vector, PatchField, GeoMesh>& field_in,
+    Eigen::VectorXd& eigen_vector, List<Eigen::VectorXd>& eigen_vector_boundary)
+{
+    GeometricField<vector, PatchField, GeoMesh> field_out(field_in);
+
+    for (auto i = 0; i < field_out.size(); i++)
+    {
+        field_out.ref()[i][0] = eigen_vector(i);
+        field_out.ref()[i][1] = eigen_vector(i + field_out.size());
+        field_out.ref()[i][2] = eigen_vector(i + field_out.size() * 2);
+    }
+
+    for(unsigned int id = 0; id < field_out.boundaryField().size(); id++)
+    {
+        unsigned int idBSize = field_out.boundaryField()[id].size();
+        for (unsigned int ith_bcell = 0; ith_bcell < idBSize; ith_bcell++)
+        {
+            ITHACAutilities::assignBC(field_out, id, eigen_vector_boundary[id]);
+        }
+    }
+
+    return field_out;
+}
+
+template volVectorField Foam2Eigen::Eigen2field(
+    volVectorField& field_in, Eigen::VectorXd& eigen_vector, List<Eigen::VectorXd>& eigen_vector_boundary);
+
+template<template<class> class PatchField, class GeoMesh>
+GeometricField<scalar, PatchField, GeoMesh> Foam2Eigen::Eigen2field(
+    GeometricField<scalar, PatchField, GeoMesh>& field_in,
+    Eigen::VectorXd& eigen_vector, List<Eigen::VectorXd>& eigen_vector_boundary)
+{
+    GeometricField<scalar, PatchField, GeoMesh> field_out(field_in);
+
+    for (auto i = 0; i < field_out.size(); i++)
+    {
+        field_out.ref()[i] = eigen_vector(i);
+    }
+
+    for(unsigned int id = 0; id < field_out.boundaryField().size(); id++)
+    {
+        for (unsigned int ith_bcell = 0; ith_bcell < field_out.boundaryField()[id].size(); ith_bcell++)
+        {
+            ITHACAutilities::assignBC(field_out, id, eigen_vector_boundary[id]);
+        }
+    }
+
+    return field_out;
+}
+
+template volScalarField Foam2Eigen::Eigen2field(
+    volScalarField& field_in, Eigen::VectorXd& eigen_vector, List<Eigen::VectorXd>& eigen_vector_boundary);
+
 template<template<class> class PatchField, class GeoMesh>
 GeometricField<vector, PatchField, GeoMesh> Foam2Eigen::Eigen2field(
     GeometricField<vector, PatchField, GeoMesh>& field_in,
diff --git a/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.H b/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.H
index 12d02f39c..8dd497571 100644
--- a/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.H
+++ b/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.H
@@ -40,6 +40,7 @@
 #include "fvCFD.H"
 #include "IOmanip.H"
 #include "ITHACAassert.H"
+#include "ITHACAutilities.H"
 #include <tuple>
 #include <sys/stat.h>
 #pragma GCC diagnostic push
@@ -295,6 +296,43 @@ class Foam2Eigen
         static GeometricField<vector, PatchField, GeoMesh> Eigen2field(
             GeometricField<vector, PatchField, GeoMesh>& field,
             Eigen::VectorXd& eigen_vector, bool correctBC = true);
+        
+        //----------------------------------------------------------------------
+        /// @brief         Convert a vector in Eigen format into an OpenFOAM
+        ///                scalar GeometricField
+        ///
+        /// @param[in/out] field         OpenFOAM GeometricField
+        /// @param[in]     eigen_vector  Vector in Eigen format
+        /// @param[in]     eigen_vector_boundary  Vector in Eigen format
+        ///
+        /// @tparam        PatchField    fvPatchField or fvsPatchField.
+        /// @tparam        GeoMesh       volMesh or surfaceMesh.
+        ///
+        /// @return        OpenFOAM GeometricField
+        ///
+        template<template<class> class PatchField, class GeoMesh>
+        static GeometricField<scalar, PatchField, GeoMesh> Eigen2field(
+            GeometricField<scalar, PatchField, GeoMesh>& field,
+            Eigen::VectorXd& eigen_vector, List<Eigen::VectorXd>& eigen_vector_boundary);
+
+        //----------------------------------------------------------------------
+        /// @brief         Convert a vector in Eigen format into an OpenFOAM
+        ///                vector GeometricField
+        ///
+        /// @param[in/out] field         OpenFOAM GeometricField
+        /// @param[in]     eigen_vector  Vector in Eigen format
+        /// @param[in]     eigen_vector_boundary  Vector in Eigen format
+        ///
+        /// @tparam        PatchField    fvPatchField or fvsPatchField.
+        /// @tparam        GeoMesh       volMesh or surfaceMesh.
+        ///
+        /// @return        OpenFOAM GeometricField
+        ///
+        template<template<class> class PatchField, class GeoMesh>
+        static GeometricField<vector, PatchField, GeoMesh> Eigen2field(
+            GeometricField<vector, PatchField, GeoMesh>& field,
+            Eigen::VectorXd& eigen_vector, List<Eigen::VectorXd>& eigen_vector_boundary);
+
 
         //----------------------------------------------------------------------
         /// @brief         Converts a matrix in Eigen format into an OpenFOAM
diff --git a/src/ITHACA_FOMPROBLEMS/Burgers/Burgers.C b/src/ITHACA_FOMPROBLEMS/Burgers/Burgers.C
index d1f935fbb..d201dbd71 100644
--- a/src/ITHACA_FOMPROBLEMS/Burgers/Burgers.C
+++ b/src/ITHACA_FOMPROBLEMS/Burgers/Burgers.C
@@ -98,6 +98,7 @@ void Burgers::truthSolve(word folder)
 
     while (_simple().loop())
     {
+        auto start = std::chrono::system_clock::now();
         Info << "Time = " << _runTime().timeName() << nl << endl;
 
         while (simple.correctNonOrthogonal())
@@ -112,6 +113,10 @@ void Burgers::truthSolve(word folder)
 
         phi = linearInterpolate(U) & mesh.Sf();
 
+        auto end = std::chrono::system_clock::now();
+        auto elapsed = std::chrono::duration_cast<std::chrono::microseconds>(end - start);
+        Info << "Elapsed: " << elapsed.count() << " microseconds\n";
+        
         if (checkWrite(runTime))
         {
             ITHACAstream::exportSolution(U, name(counter), folder + name(folderN));
diff --git a/src/ITHACA_HR/hyperReduction.H b/src/ITHACA_HR/hyperReduction.H
index 7d1ef66ff..6411b4338 100644
--- a/src/ITHACA_HR/hyperReduction.H
+++ b/src/ITHACA_HR/hyperReduction.H
@@ -38,9 +38,11 @@ SourceFiles
 #include "ITHACAutilities.H"
 #include "fvMeshSubset.H"
 #include <set>
+#include "redsvd"
 
 Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
 
+// TODO uniform style for separating offline and onlie stages
 template <typename... SnapshotsLists>
 class HyperReduction
 {
@@ -53,6 +55,7 @@ public:
 
     // TODO get vectorial dim from class template parameters
     unsigned int vectorial_dim;
+    unsigned int sumFieldsDim;
 
     template <std::size_t N>
     using NthFieldListType = typename std::tuple_element<N, SnapshotsListTuple>::type;
@@ -79,6 +82,15 @@ public:
     // ITHACA parameters dict
     ITHACAparameters* para;
 
+    //TODO
+    label n_boundary_patches;
+
+    //TODO
+    List<label> n_boundary_cells_list;
+
+    //TODO
+    label n_boundary_cells;
+
     /// The maximum number of modes to be considered
     label n_modes;
 
@@ -134,6 +146,9 @@ public:
     /// Orthonormal basis of HR
     Eigen::MatrixXd basisMatrix;
 
+    // Normalizing weights of SVD decomposition
+    Eigen::VectorXd normalizingWeights;
+
     /// Renormalized basis of HR
     Eigen::MatrixXd renormalizedBasisMatrix;
 
@@ -149,6 +164,15 @@ public:
     /// The P matrix of the HyperReduction method. The nodes are ordered in the order of insertion during the greedy procedure. The components related to the same node follow immediately.
     Eigen::SparseMatrix<double> P;
 
+    // Mask field to submesh
+    Eigen::SparseMatrix<double> field2submesh;
+
+    // Mask submesh to nodes
+    Eigen::SparseMatrix<double> submesh2nodes;
+
+    // Indices submesh to nodes
+    Eigen::VectorXi submesh2nodesMask;
+
     /// Quadrature weights. Ordered in the same order of matrix P.
     Eigen::VectorXd quadratureWeights;
 
@@ -185,6 +209,14 @@ public:
     /// @param[in]  sList  The list of snapshots
     ///
     void getModesSVD(SnapshotsListTuple &SnapshotsListTuple, Eigen::MatrixXd &modesSVD, Eigen::VectorXd &fieldWeights, bool saveModesFlag = false);
+
+    //----------------------------------------------------------------------
+    /// @brief      TODO
+    ///
+    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+    /// @param[in]  sList  The list of snapshots
+    ///
+    void getModesSVD(SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights, Eigen::MatrixXd& modesSVDBoundary, Eigen::VectorXd& fieldWeightsBoundary, bool saveModesFlag);
     
     //----------------------------------------------------------------------
     /// @brief      TODO
@@ -202,6 +234,15 @@ public:
     ///
     template <typename SnapshotsList>
     void stackSnapshots(SnapshotsList sList, Eigen::MatrixXd &snapshotsMatrix, Eigen::VectorXd &fieldWeights);
+
+    //----------------------------------------------------------------------
+    /// @brief      TODO
+    ///
+    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+    /// @param[in]  sList  The list of snapshots
+    ///
+    template <typename SnapshotsList>
+    void stackSnapshotsBoundary(SnapshotsList sList, List<Eigen::MatrixXd>& snapshotsMatrixBoundary, List<Eigen::VectorXd>& fieldWeightsBoundary);
     
     //----------------------------------------------------------------------
     /// @brief      TODO
@@ -212,6 +253,15 @@ public:
     template <typename SnapshotsList>
     void saveModes(SnapshotsList sList, Eigen::MatrixXd& snapshotsMatrix, unsigned int &rowIndex, unsigned int &modeIndex, word folder);
 
+    //----------------------------------------------------------------------
+    /// @brief      TODO
+    ///
+    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+    /// @param[in]  sList  The list of snapshots
+    ///
+    template <typename SnapshotsList>
+    void saveModes(SnapshotsList sList, Eigen::MatrixXd& snapshotsMatrix, Eigen::MatrixXd& snapshotsMatrixBoundary, unsigned int &rowIndex,  unsigned int& rowIndexBoundary, unsigned int &modeIndex, word folder);
+
     //----------------------------------------------------------------------
     /// @brief      TODO
     ///
@@ -233,6 +283,16 @@ public:
     inline void stackDimensions(SnapshotsList sList){
         fieldDims.append(get_field_dim<typename SnapshotsList::value_type>());}
 
+    //----------------------------------------------------------------------
+    /// @brief      TODO
+    ///
+    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+    /// @param[in]  sList  The list of snapshots
+    ///
+    template <typename SnapshotsList>
+    inline void sumDimensions(double sum, SnapshotsList sList){
+        sum+=get_field_dim<typename SnapshotsList::value_type>();}
+
     //----------------------------------------------------------------------
     /// @brief      Compute the pseudo-inverse of the matrix M restricted with the projector P
     ///
@@ -273,9 +333,10 @@ public:
     /// @param[in]  sList  The list of snapshots
     ///
     template <typename FieldType>
-    inline autoPtr<FieldType> interpolateField(FieldType &field){
-    return autoPtr<FieldType>(new FieldType(submesh->interpolate(field)));
-}
+    inline autoPtr<FieldType> interpolateField(const FieldType &field)
+    {
+        return autoPtr<FieldType>(new FieldType(submesh->interpolate(field)));
+    }
 
     /// @brief      TODO
     ///
@@ -333,9 +394,9 @@ public:
         
         ([&](auto& oFieldsArg)
             {
-                double ith_fieldSize = fieldDims[ith_field]*n_cells;
+                double ith_fieldSize = fieldDims[ith_field]*oFieldsArg.size();
                 Eigen::VectorXd vec = eFields.segment(cumulativeSize, ith_fieldSize);
-                Foam2Eigen::Eigen2field(oFieldsArg, vec);
+                oFieldsArg = Foam2Eigen::Eigen2field(oFieldsArg, vec);
                 cumulativeSize+=ith_fieldSize;
                 ith_field++;
             }(oFields), ...);
@@ -348,6 +409,27 @@ public:
     /// @param[in]  sList  The list of snapshots
     ///
     void initReshapeMat(Eigen::SparseMatrix<double> &reshapeMat);
+
+    /// @brief      TODO
+    ///
+    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+    /// @param[in]  sList  The list of snapshots
+    ///
+    void createMasks(bool offlineStage = true);
+
+    /// @brief      TODO
+    ///
+    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+    /// @param[in]  sList  The list of snapshots
+    ///
+    void getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights);
+
+    /// @brief      TODO
+    ///
+    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+    /// @param[in]  sList  The list of snapshots
+    ///
+    void getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights, List<Eigen::MatrixXd>& snapMatrixBoundary, List<Eigen::VectorXd>& fieldWeightsBoundary);
 };
 
 #endif
diff --git a/src/ITHACA_HR/hyperReduction.templates.H b/src/ITHACA_HR/hyperReduction.templates.H
index bba2a086e..90c37cc9a 100644
--- a/src/ITHACA_HR/hyperReduction.templates.H
+++ b/src/ITHACA_HR/hyperReduction.templates.H
@@ -66,6 +66,9 @@ HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
   // Get fields' dimensions
   std::apply([this](auto& ...snapList){(..., stackDimensions(snapList));}, snapshotsListTuple);
 
+  sumFieldsDim = 0;
+  std::apply([this](auto& ...snapList){(..., sumDimensions(this->sumFieldsDim, snapList));}, snapshotsListTuple);
+
   Info << "Fields names: ";
   for (unsigned int ith_field = 0; ith_field < fieldNames.size(); ith_field++)
   {
@@ -78,6 +81,18 @@ HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
   n_cells = std::get<0>(snapshotsListTuple)[0].size();
   Info << "The number of cells is: " << n_cells << endl;
   Info << "Initial seeds length: " << initialSeeds.rows() << endl;
+
+  // get boundaries info
+  n_boundary_patches = std::get<0>(snapshotsListTuple)[0].boundaryField().size();
+
+  n_boundary_cells_list.resize(n_boundary_patches);
+  n_boundary_cells = 0;
+  for (unsigned int ith_boundary_patch = 0; ith_boundary_patch < n_boundary_patches; ith_boundary_patch++)
+  {
+    n_boundary_cells_list[ith_boundary_patch] = std::get<0>(snapshotsListTuple)[0].boundaryField()[ith_boundary_patch].size();
+    n_boundary_cells = n_boundary_cells + n_boundary_cells_list[ith_boundary_patch];
+  }
+  Info << "Number of boundary cells: " << n_boundary_cells << endl;
 }
 
 // Using the Eigen library, using the SVD decomposition method to solve the
@@ -114,25 +129,46 @@ void HyperReduction<SnapshotsLists...>::getModesSVD(
   word folderSVD = "ITHACAoutput/" + problemName + "/ModesSVD/";
   if (!ITHACAutilities::check_folder(folderSVD))
   {
+    mkDir(folderSVD);
     // Initialize stacked snapshotsMatrix and normalizing weights
     Eigen::MatrixXd snapMatrix;
-    std::apply([this, &snapMatrix, &fieldWeights](auto& ...snapList){(..., stackSnapshots(snapList, snapMatrix, fieldWeights));}, snapshotsListTuple);
+    getSnapMatrix(snapMatrix, fieldWeights);
 
-    Info << "####### Performing SVD for " << problemName << " #######" << endl;
+    word dimensionReductionMethod = para->ITHACAdict->lookupOrDefault<word>("DimensionReductionMethod", "SVD");
 
-    Eigen::JacobiSVD<Eigen::MatrixXd> svd(fieldWeights.array().cwiseInverse().matrix().asDiagonal()*snapMatrix,
-                                          Eigen::ComputeThinU | Eigen::ComputeThinV);
+    Eigen::MatrixXd eigenVectoreig;
 
-    Info << "####### End of SVD for " << problemName << " #######" <<
-          endl;
+    if (dimensionReductionMethod == "RSVD")
+    {
+      Info << "####### Performing RSVD for " << problemName << " #######" << endl;
 
-    Eigen::MatrixXd eigenVectoreig;
-    eigenValueseig = svd.singularValues().real();
-    eigenVectoreig = svd.matrixU().real();
+      unsigned int r_modeSVD = para->ITHACAdict->lookupOrDefault<unsigned int>("RSVDdim", snapMatrix.cols());
+      RedSVD::RedSVD svd(fieldWeights.array().cwiseInverse().matrix().asDiagonal()*snapMatrix, r_modeSVD);
+
+      Info << "####### End of RSVD for " << problemName << " #######" <<
+            endl;
+
+      eigenValueseig = svd.singularValues().real();
+      eigenVectoreig = svd.matrixU().real();
+    }
+    else
+    {
+      Info << "####### Performing SVD for " << problemName << " #######" << endl;
+
+      Eigen::JacobiSVD<Eigen::MatrixXd> svd(fieldWeights.array().cwiseInverse().matrix().asDiagonal()*snapMatrix, Eigen::ComputeThinU | Eigen::ComputeThinV);
+
+      Info << "####### End of SVD for " << problemName << " #######" <<
+            endl;
+
+      eigenValueseig = svd.singularValues().real();
+      eigenVectoreig = svd.matrixU().real();
+    }
 
     modesSVD = eigenVectoreig;
 
     // TODO correct boundary conditions
+    
+    cnpy::save(eigenValueseig, "ITHACAoutput/" + problemName + "/ModesSVD/eigenvalues.npy");
 
     eigenValueseig = eigenValueseig / eigenValueseig.sum();
     Eigen::VectorXd cumEigenValues(eigenValueseig);
@@ -142,7 +178,6 @@ void HyperReduction<SnapshotsLists...>::getModesSVD(
         cumEigenValues(j) += cumEigenValues(j - 1);
     }
 
-    mkDir(folderSVD);
     Eigen::saveMarketVector(eigenValueseig,
                             "ITHACAoutput/" + problemName + "/ModesSVD/Eigenvalues_" + problemName, para->precision,
                             para->outytpe);
@@ -171,6 +206,129 @@ void HyperReduction<SnapshotsLists...>::getModesSVD(
   }
 }
 
+template <typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::getModesSVD(
+    SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights, Eigen::MatrixXd& modesSVDBoundary, Eigen::VectorXd& fieldWeightsBoundary, bool saveModesFlag)
+{
+  // TODO move inside ITHACAPOD
+  ITHACAparameters* para(ITHACAparameters::getInstance());
+  word folderSVD = "ITHACAoutput/" + problemName + "/ModesSVD/";
+  if (!ITHACAutilities::check_folder(folderSVD))
+  {
+    mkDir(folderSVD);
+    // Initialize stacked snapshotsMatrix and normalizing weights
+    Eigen::MatrixXd snapMatrix;
+    List<Eigen::MatrixXd> snapMatrixBoundary;
+    List<Eigen::VectorXd> fieldWeightsBoundaryList;
+    getSnapMatrix(snapMatrix, fieldWeights, snapMatrixBoundary, fieldWeightsBoundaryList);
+
+    for (unsigned int id = 0; id < n_boundary_patches; id++)
+    {
+      snapMatrix.conservativeResize(snapMatrix.rows()+snapMatrixBoundary[id].rows(), snapMatrix.cols());
+      snapMatrix.bottomRows(snapMatrixBoundary[id].rows()) = snapMatrixBoundary[id];
+
+      fieldWeightsBoundary.conservativeResize(fieldWeightsBoundary.rows()+snapMatrixBoundary[id].rows());
+      fieldWeightsBoundary.tail(fieldWeightsBoundaryList[id].rows()) = fieldWeightsBoundaryList[id];
+    }
+
+    cnpy::save(fieldWeights, "ITHACAoutput/" + problemName + "/ModesSVD/normalizingWeights.npy");
+    cnpy::save(fieldWeightsBoundary, "ITHACAoutput/" + problemName + "/ModesSVD/normalizingWeightsBoundary.npy");
+
+    fieldWeights.conservativeResize(fieldWeights.rows()+fieldWeightsBoundary.rows());
+    fieldWeights.tail(fieldWeightsBoundary.rows()) = fieldWeightsBoundary;
+    
+    word dimensionReductionMethod = para->ITHACAdict->lookupOrDefault<word>("DimensionReductionMethod", "SVD");
+
+    Eigen::MatrixXd eigenVectoreig;
+
+    if (dimensionReductionMethod == "RSVD")
+    {
+      Info << "####### Performing RSVD for " << problemName << " #######" << endl;
+
+      unsigned int r_modeSVD = para->ITHACAdict->lookupOrDefault<unsigned int>("RSVDdim", snapMatrix.cols());
+
+      RedSVD::RedSVD svd(fieldWeights.array().cwiseInverse().matrix().asDiagonal()*snapMatrix, r_modeSVD);
+
+      Info << "####### End of RSVD for " << problemName << " #######" << endl;
+
+      eigenValueseig = svd.singularValues().real();
+      eigenVectoreig = svd.matrixU().real();
+    }
+    else
+    {
+      Info << "####### Performing SVD for " << problemName << " #######" << endl;
+
+      Eigen::JacobiSVD<Eigen::MatrixXd> svd(fieldWeights.array().cwiseInverse().matrix().asDiagonal()*snapMatrix, Eigen::ComputeThinU | Eigen::ComputeThinV);
+
+      Info << "####### End of SVD for " << problemName << " #######" <<
+            endl;
+
+      eigenValueseig = svd.singularValues().real();
+      eigenVectoreig = svd.matrixU().real();
+    }
+
+    modesSVD = eigenVectoreig.bottomRows(vectorial_dim*n_cells);
+    modesSVDBoundary = eigenVectoreig.topRows(n_boundary_cells);
+    fieldWeights.conservativeResize(fieldWeights.rows()-fieldWeightsBoundary.rows());
+    
+    cnpy::save(eigenValueseig, "ITHACAoutput/" + problemName + "/ModesSVD/eigenvalues.npy");
+
+    eigenValueseig = eigenValueseig / eigenValueseig.sum();
+    Eigen::VectorXd cumEigenValues(eigenValueseig);
+
+    for (label j = 1; j < cumEigenValues.size(); ++j)
+    {
+        cumEigenValues(j) += cumEigenValues(j - 1);
+    }
+
+    Eigen::saveMarketVector(eigenValueseig,
+                            "ITHACAoutput/" + problemName + "/ModesSVD/Eigenvalues_" + problemName, para->precision,
+                            para->outytpe);
+    Eigen::saveMarketVector(cumEigenValues,
+                            "ITHACAoutput/" + problemName + "/ModesSVD/CumEigenvalues_" + problemName, para->precision,
+                            para->outytpe);
+    cnpy::save(modesSVD, "ITHACAoutput/" + problemName + "/ModesSVD/modes.npy");
+    cnpy::save(modesSVDBoundary, "ITHACAoutput/" + problemName + "/ModesSVD/modesBoundary.npy");
+
+    if (saveModesFlag)
+    {
+      unsigned int rowIndex{0};
+      unsigned int rowIndexBoundary{0};
+      for (unsigned int modeIndex = 0; modeIndex < modesSVD.cols(); modeIndex++)
+      {
+        std::apply([this, &modesSVD,  &modesSVDBoundary, &rowIndex, &modeIndex, &rowIndexBoundary, &folderSVD](auto& ...snapList){(..., saveModes(snapList, modesSVD, modesSVDBoundary, rowIndex, rowIndexBoundary, modeIndex, folderSVD));}, snapshotsListTuple);
+        rowIndex = 0;
+      }
+    }
+  }
+  else
+  {
+    Info << "Reading the existing modes" << endl;
+    cnpy::load(modesSVD, folderSVD + "/modes.npy");
+    cnpy::load(modesSVDBoundary, "ITHACAoutput/" + problemName + "/ModesSVD/modesBoundary.npy");
+    cnpy::load(fieldWeights, folderSVD + "/normalizingWeights.npy");
+    cnpy::load(fieldWeightsBoundary, "ITHACAoutput/" + problemName + "/ModesSVD/normalizingWeightsBoundary.npy");
+  }
+}
+
+template <typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights)
+{
+  std::apply([this, &fieldWeights, &snapMatrix](auto& ...snapList){(..., stackSnapshots(snapList, snapMatrix, fieldWeights));}, snapshotsListTuple);
+}
+
+template <typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights, List<Eigen::MatrixXd>& snapMatrixBoundary, List<Eigen::VectorXd>& fieldWeightsBoundary)
+{
+  fieldWeightsBoundary.resize(n_boundary_patches);
+  snapMatrixBoundary.resize(n_boundary_patches);
+
+  std::apply([this, &fieldWeights, &snapMatrix, &fieldWeightsBoundary, &snapMatrixBoundary](auto& ...snapList){
+    (..., stackSnapshots(snapList, snapMatrix, fieldWeights));
+    (..., stackSnapshotsBoundary(snapList, snapMatrixBoundary, fieldWeightsBoundary));},
+  snapshotsListTuple);
+}
+
 template <typename... SnapshotsLists>
 template <typename SnapshotsList>
 void HyperReduction<SnapshotsLists...>::saveModes(SnapshotsList sList, Eigen::MatrixXd& snapshotsMatrix, unsigned int &rowIndex, unsigned int &modeIndex, word folder)
@@ -185,19 +343,48 @@ void HyperReduction<SnapshotsLists...>::saveModes(SnapshotsList sList, Eigen::Ma
 }
 
 template <typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights)
+template <typename SnapshotsList>
+void HyperReduction<SnapshotsLists...>::saveModes(SnapshotsList sList, Eigen::MatrixXd& snapshotsMatrix, Eigen::MatrixXd& snapshotsMatrixBoundary, unsigned int &rowIndex,  unsigned int& rowIndexBoundary, unsigned int &modeIndex, word folder)
+{
+  unsigned int field_dim = get_field_dim<typename SnapshotsList::value_type>();
+  auto fieldName = sList[0].name();
+  unsigned int fieldSize = field_dim*sList[0].size();
+
+  Eigen::VectorXd fieldBlock = snapshotsMatrix.block(rowIndex, modeIndex, fieldSize, 1);
+
+  List<Eigen::VectorXd> fieldBlockBoundary;
+  fieldBlockBoundary.resize(n_boundary_patches);
+  for (unsigned int id = 0; id < n_boundary_patches; id++)
+  {
+    unsigned int bfieldDim = field_dim*int(n_boundary_cells_list[id]);
+    fieldBlockBoundary[id] = snapshotsMatrixBoundary.block(rowIndexBoundary, modeIndex, bfieldDim, 1);
+    rowIndexBoundary+=bfieldDim;
+  }
+
+  auto fieldOut = Foam2Eigen::Eigen2field(sList[0], fieldBlock, fieldBlockBoundary);
+  rowIndex +=fieldSize;
+  
+  ITHACAstream::exportSolution(fieldOut, name(modeIndex), folder);
+}
+
+template <typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights)
 {
   methodName = "GappyDEIM";
   folderMethod = "ITHACAoutput/" + problemName + "/" + methodName;
   mkDir(folderMethod);
 
+  normalizingWeights = weights;
+
   nodePoints = autoPtr<IOList<label>>(new IOList<label>(
       IOobject("nodePoints", para->runTime.time().constant(), "../" + folderMethod,
                 para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE))); 
 
   auto greedyMetric = para->ITHACAdict->lookupOrDefault<word>("GreedyMetric", "l2");
+  
+  bool offlineStage = !nodePoints().headerOk();
 
-  if (!nodePoints().headerOk())
+  if (offlineStage)
   {
     assert(n_modes > 0);
     assert(n_nodes >= n_modes);
@@ -400,6 +587,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
     P.makeCompressed();
     cnpy::save(basisMatrix, folderMethod +"/basisMatrix.npy");
     cnpy::save(P, folderMethod +"/projectionMatrix.npz");
+    cnpy::save(normalizingWeights, folderMethod + "/normalizingWeights.npy");
     cnpy::save(nodes, folderMethod + "/mp.npy");
     cnpy::save(pinvPU, folderMethod + "/pinvPU.npy");
     nodePoints().write();
@@ -412,6 +600,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
   {
     Info << "Read GappyDEIM\n";
     cnpy::load(basisMatrix, folderMethod +"/basisMatrix.npy");
+    cnpy::load(normalizingWeights, folderMethod + "/normalizingWeights.npy");
     cnpy::load(P, folderMethod +"/projectionMatrix.npz");
     cnpy::load(nodes, folderMethod + "/mp.npy");
     cnpy::load(pinvPU, folderMethod + "/pinvPU.npy");
@@ -425,11 +614,13 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
 }
 
 template <typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights)
+void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights)
 {
   methodName = "ECP";
   n_nodes = n_modes + 1;
 
+  normalizingWeights = weights;
+
   Info << "####### Begin ECP #######" << endl;
   Info << "####### Modes=" <<  n_modes
             << ", nodePoints=" << n_nodes << " #######"
@@ -441,8 +632,10 @@ void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd& snapshotsMod
   nodePoints = autoPtr<IOList<label>>(new IOList<label>(
       IOobject("nodePoints", para->runTime.time().constant(), "../" + folderMethod,
                 para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE))); 
+  
+  bool offlineStage = !nodePoints().headerOk();
 
-  if (!nodePoints().headerOk())
+  if (offlineStage)
   {
     assert(n_modes > 0);
     assert(n_nodes >= n_modes);
@@ -458,7 +651,6 @@ void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd& snapshotsMod
 
     Eigen::VectorXd volumes = ITHACAutilities::getMassMatrixFV(std::get<0>(snapshotsListTuple)[0]);
     double volume = volumes.array().sum();
-
     for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
     {
       Eigen::MatrixXd block = snapshotsModes.block(ith_field*n_cells, 0, n_cells, n_modes).transpose();
@@ -472,11 +664,13 @@ void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd& snapshotsMod
       Eigen::VectorXd mean = block.rowwise().mean();
       block.colwise() -= mean;
       Eigen::VectorXd Anorm = block.colwise().lpNorm<2>();
-      block.array().rowwise() /= Anorm.transpose().array();
+      if (Anorm.minCoeff()> 0)
+      {
+        block.array().rowwise() /= Anorm.transpose().array();
+      }
 
       A.middleRows(ith_field*n_modes, n_modes) = block;
     }
-
     Eigen::VectorXd mp_not_mask = Eigen::VectorXd::Constant(n_cells * vectorial_dim, 1);
     std::set<label> nodePointsSet;
 
@@ -512,6 +706,7 @@ void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd& snapshotsMod
 
     cnpy::save(basisMatrix, folderMethod +"/basisMatrix.npy");
     cnpy::save(quadratureWeights, folderMethod +"/quadratureWeights.npy");
+    cnpy::save(normalizingWeights, folderMethod +"/normalizingWeights.npy");
     cnpy::save(nodes, folderMethod + "/mp.npy");
     cnpy::save(wPU, folderMethod + "/wPU.npy");
     nodePoints().write();
@@ -521,6 +716,7 @@ void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd& snapshotsMod
     Info << "Read ECP\n";
     cnpy::load(basisMatrix, folderMethod +"/basisMatrix.npy");
     cnpy::load(quadratureWeights, folderMethod +"/quadratureWeights.npy");
+    cnpy::load(normalizingWeights, folderMethod +"/normalizingWeights.npy");
     cnpy::load(nodes, folderMethod + "/mp.npy");
     cnpy::load(wPU, folderMethod + "/wPU.npy");
   }
@@ -618,25 +814,48 @@ template <typename... SnapshotsLists>
 template <typename SnapshotsList>
 void HyperReduction<SnapshotsLists...>::stackSnapshots(SnapshotsList sList, Eigen::MatrixXd& snapshotsMatrix, Eigen::VectorXd& fieldWeights)
 {
-  Info << "####### Compute hyper-reduction basis #######\n";
-
   unsigned int field_dim = get_field_dim<typename SnapshotsList::value_type>();
 
   Eigen::MatrixXd tmpSnapshots = Foam2Eigen::PtrList2Eigen(sList);
-  auto fieldName = sList[0].name();
-
-  double maxVal = std::sqrt(tmpSnapshots.colwise().lpNorm<2>().maxCoeff());
-
   // get volumes
   Eigen::VectorXd V = ITHACAutilities::getMassMatrixFV(sList[0]);
 
+
+  double maxVal = std::sqrt(tmpSnapshots.colwise().lpNorm<2>().maxCoeff());
+
   fieldWeights.conservativeResize(fieldWeights.rows()+field_dim*n_cells);
   fieldWeights.tail(n_cells * field_dim) = V.array().sqrt().cwiseInverse()*maxVal;
 
   snapshotsMatrix.conservativeResize(snapshotsMatrix.rows() + n_cells * field_dim, n_snapshots);
   snapshotsMatrix.bottomRows(n_cells * field_dim) = tmpSnapshots;
+}
 
-  Info << "####### End of computing hyper-reduction basis #######\n";
+template <typename... SnapshotsLists>
+template <typename SnapshotsList>
+void HyperReduction<SnapshotsLists...>::stackSnapshotsBoundary(SnapshotsList sList, List<Eigen::MatrixXd>& snapshotsMatrixBoundary, List<Eigen::VectorXd>& fieldWeightsBoundary)
+{
+  unsigned int field_dim = get_field_dim<typename SnapshotsList::value_type>();
+
+  List<Eigen::MatrixXd> tmpBoundarySnapshots = Foam2Eigen::PtrList2EigenBC(sList);
+
+  List<double> maxVal;
+  maxVal.resize(n_boundary_patches);
+  
+  for (label id = 0; id < n_boundary_patches; id++)
+  {
+    maxVal[id] = std::sqrt(tmpBoundarySnapshots[id].colwise().lpNorm<2>().maxCoeff());
+
+    // get surface areas
+    Eigen::VectorXd S = Foam2Eigen::field2Eigen(sList[0].mesh().magSf().boundaryField()[id]);
+    S = S.replicate(field_dim, 1);
+
+    unsigned int bSize = field_dim*int(n_boundary_cells_list[id]);
+    fieldWeightsBoundary[id].conservativeResize(fieldWeightsBoundary[id].rows()+bSize);
+    fieldWeightsBoundary[id].tail(bSize) = S.array().pow(3/4)*maxVal[id];
+
+    snapshotsMatrixBoundary[id].conservativeResize(snapshotsMatrixBoundary[id].rows() + bSize, n_snapshots);
+    snapshotsMatrixBoundary[id].bottomRows(bSize) = tmpBoundarySnapshots[id];
+  }
 }
 
 template<typename... SnapshotsLists>
@@ -696,8 +915,9 @@ void HyperReduction<SnapshotsLists...>::generateSubmesh(label layers, fvMesh &me
                         dimensionSet(0, 0, 0, 0, 0, 0, 0), 0.0));
 
   submesh = autoPtr<fvMeshSubset>(new fvMeshSubset(mesh));
+  bool offlineStage = !totalNodePoints().headerOk();
 
-  if (!totalNodePoints().headerOk()) {
+  if (offlineStage) {
     List<label> indices;
     for (label i = 0; i < nodePoints().size(); i++) {
       indices = ITHACAutilities::getIndices(mesh, nodePoints()[i], layers);
@@ -717,6 +937,7 @@ void HyperReduction<SnapshotsLists...>::generateSubmesh(label layers, fvMesh &me
 
     totalNodePoints().write();
     uniqueNodePoints().write();
+    ITHACAstream::exportSolution(Indici, "1", folderMethod);
   }
 
   submesh->setCellSubset(uniqueNodePoints());
@@ -727,10 +948,63 @@ void HyperReduction<SnapshotsLists...>::generateSubmesh(label layers, fvMesh &me
   std::cout.clear();
 
   localNodePoints = global2local(nodePoints(), submesh());
-  ITHACAstream::exportSolution(Indici, "1", folderMethod);
 
   n_cellsSubfields = submesh().cellMap().size();
-  Info << "####### End extract submesh #######\n";
+  Info << "####### End extract submesh size = " << n_cellsSubfields <<" #######\n";
+
+  createMasks(offlineStage);
+  Info << "####### End create masks #######\n";
+}
+
+template<typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::createMasks(bool offlineStage)
+{ 
+  if (offlineStage)
+  {
+    field2submesh.resize(submesh().cellMap().size() * vectorial_dim, n_cells*vectorial_dim);
+    field2submesh.reserve(Eigen::VectorXi::Constant(n_cells*vectorial_dim, 1));
+
+    for (unsigned int ith_subCell{0} ; ith_subCell <submesh().cellMap().size(); ith_subCell++)
+    {
+        for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+        {
+          field2submesh.insert(ith_subCell+ith_field*submesh().cellMap().size(), submesh().cellMap()[ith_subCell]+n_cells*ith_field) = 1;
+        }
+    }
+    field2submesh.makeCompressed();
+
+    submesh2nodes.resize(nodePoints().size() * vectorial_dim, submesh().cellMap().size()*vectorial_dim);
+    submesh2nodes.reserve(Eigen::VectorXi::Constant(submesh().cellMap().size()*vectorial_dim, 1));
+    submesh2nodesMask.resize(nodePoints().size() * vectorial_dim);
+
+    int index_col = 0;
+    for (unsigned int ith_node{0} ; ith_node <nodePoints().size(); ith_node++) {
+      for (unsigned int ith_subCell{0} ; ith_subCell <submesh().cellMap().size(); ith_subCell++) {
+        if (nodePoints()[ith_node] == submesh().cellMap()[ith_subCell]) {
+          for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+          {
+            submesh2nodes.insert(ith_node + nodePoints().size()*ith_field, index_col + ith_field*submesh().cellMap().size()) = 1;
+            submesh2nodesMask(ith_node + nodePoints().size()*ith_field) = index_col + ith_field*submesh().cellMap().size();
+          }
+          break;
+        } else {
+          index_col++;
+        }
+      }
+      index_col = 0;
+    }
+    submesh2nodes.makeCompressed();
+
+    cnpy::save(field2submesh, folderMethod +"/field2submesh.npz");
+    cnpy::save(submesh2nodes, folderMethod +"/submesh2nodes.npz");
+    cnpy::save(submesh2nodesMask, folderMethod +"/submesh2nodesMask.npy");
+  }
+  else
+  {
+    cnpy::load(field2submesh, folderMethod +"/field2submesh.npz");
+    cnpy::load(submesh2nodes, folderMethod +"/submesh2nodes.npz");
+    cnpy::load(submesh2nodesMask, folderMethod +"/submesh2nodesMask.npy");
+  }
 }
 
 template<typename... SnapshotsLists>
diff --git a/src/ITHACA_TORCH/torch2Eigen.C b/src/ITHACA_TORCH/torch2Eigen.C
index 23a7eda5e..1f2270c33 100755
--- a/src/ITHACA_TORCH/torch2Eigen.C
+++ b/src/ITHACA_TORCH/torch2Eigen.C
@@ -81,12 +81,12 @@ Eigen::Matrix<type, Eigen::Dynamic, Eigen::Dynamic> torchTensor2eigenMatrix(
 
     typedef Eigen::Matrix<type, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>
     MatrixXf_rm;
-    float* data_p = torchTensor.data_ptr<float>();
+    type* data_p = torchTensor.data_ptr<type>();
     std::vector<type> raw(nElem);
 
     for (int i = 0; i < nElem; i++)
     {
-        float d(*(data_p + i));
+        type d(*(data_p + i));
         type a = static_cast <type>(d);
         raw[i] = a;
     }
diff --git a/tutorials/CFD/24HyperReduction/Make/options b/tutorials/CFD/24HyperReduction/Make/options
index 7d4e0e960..2157192a1 100644
--- a/tutorials/CFD/24HyperReduction/Make/options
+++ b/tutorials/CFD/24HyperReduction/Make/options
@@ -18,6 +18,7 @@ EXE_INC = \
     -I$(LIB_ITHACA_SRC)/ITHACA_ROMPROBLEMS/lnInclude \
     -I$(LIB_ITHACA_SRC)/ITHACA_CORE/lnInclude \
     -I$(LIB_ITHACA_SRC)/thirdparty/Eigen \
+    -I$(LIB_ITHACA_SRC)/thirdparty/redsvd \
     -I$(LIB_ITHACA_SRC)/thirdparty/spectra/include \
     -I$(LIB_ITHACA_SRC)/ITHACA_THIRD_PARTY/splinter/include \
     -Wno-comment \

From 64a230c1a3b3f3be81d2e9db32c44806ecac2c4d Mon Sep 17 00:00:00 2001
From: giovastabile <giovanni.stabile87@gmail.com>
Date: Tue, 23 May 2023 10:30:43 +0200
Subject: [PATCH 09/59] FIX: adding funding section readme

---
 README.md | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index b9f9526ad..9cbeecfa7 100644
--- a/README.md
+++ b/README.md
@@ -204,9 +204,14 @@ Year                     = {2018},
 Doi                      = {10.1016/j.compfluid.2018.01.035}}
 ```
 
-
 and cite the [ITHACA-FV website](https://ithaca-fv.github.io/ITHACA-FV).
 
+### 8. Funding
+A significant part of PyDMD has been written either as a by-product for other projects people were funded for, or by people on university-funded positions. There are probably many of such projects that have led to some development of PyDMD. We are very grateful for this support!
+
+Beyond this, PyDMD has also been supported by some dedicated projects that have allowed us to work on extensions, documentation, training and dissemination that would otherwise not have been possible. In particular, we acknowledge the following sources of support with great gratitude:
+
+* [H2020 ERC CoG 2015 AROMA-CFD project 681447](https://people.sissa.it/~grozza/aroma-cfd/), P.I. Professor [Gianluigi Rozza](https://people.sissa.it/~grozza) at [SISSA mathLab](https://mathlab.sissa.it/).
 
 ### 8. License
 **ITHACA-FV** is freely available under the GNU LGPL, version 3.

From da94a37e875911875389270899b38acc97d03d88 Mon Sep 17 00:00:00 2001
From: Giovanni Stabile <giovanni.stabile87@gmail.com>
Date: Wed, 28 Jun 2023 10:37:35 +0200
Subject: [PATCH 10/59] Update README.md

---
 README.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 9cbeecfa7..ef06511ed 100644
--- a/README.md
+++ b/README.md
@@ -22,7 +22,7 @@
 </p>
 
 ### 0. Introduction
-**ITHACA-FV** is an implementation in **OpenFOAM** of several reduced order modelling techniques. **ITHACA-FV** is designed for [**OpenFOAM v2106**](https://www.openfoam.com/releases/openfoam-v2106/) and older openfoam.com versions but it can be easily adapted also to other versions of OpenFOAM.
+**ITHACA-FV** is an implementation in **OpenFOAM** of several reduced order modelling techniques. **ITHACA-FV** is designed for [**OpenFOAM v2212**](https://www.openfoam.com/releases/openfoam-v2212/) and older openfoam.com versions but it can be easily adapted also to other versions of OpenFOAM.
 
 **ITHACA-FV** can also be used as a basis for more advanced projects that would like to assess the capability of reduced order models in their existing **OpenFOAM**-based software, thanks to the availability of several reduced order methods and algorithms.
 
@@ -38,6 +38,7 @@ Linear and non-linear algebra operations which are not already implemented in Op
 *   [**OpenFOAM 2006**](https://www.openfoam.com/releases/openfoam-v2006/) or
 *   [**OpenFOAM 2012**](https://www.openfoam.com/releases/openfoam-v2012/) or
 *   [**OpenFOAM 2106**](https://www.openfoam.com/news/main-news/openfoam-v2106)
+*   [**OpenFOAM 2212**](https://www.openfoam.com/news/main-news/openfoam-v2212)
 
 
 ### 2. Installation and usage

From 90a7c65207f8fbf9166c1c292ecf633919556354 Mon Sep 17 00:00:00 2001
From: Giovanni Stabile <giovanni.stabile87@gmail.com>
Date: Wed, 28 Jun 2023 10:39:38 +0200
Subject: [PATCH 11/59] Update README.md

---
 README.md | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/README.md b/README.md
index ef06511ed..056a82323 100644
--- a/README.md
+++ b/README.md
@@ -22,7 +22,7 @@
 </p>
 
 ### 0. Introduction
-**ITHACA-FV** is an implementation in **OpenFOAM** of several reduced order modelling techniques. **ITHACA-FV** is designed for [**OpenFOAM v2212**](https://www.openfoam.com/releases/openfoam-v2212/) and older openfoam.com versions but it can be easily adapted also to other versions of OpenFOAM.
+**ITHACA-FV** is an implementation in **OpenFOAM** of several reduced order modelling techniques. **ITHACA-FV** is designed for [**OpenFOAM v2212**](https://www.openfoam.com/news/main-news/openfoam-v2212/) and older openfoam.com versions but it can be easily adapted also to other versions of OpenFOAM.
 
 **ITHACA-FV** can also be used as a basis for more advanced projects that would like to assess the capability of reduced order models in their existing **OpenFOAM**-based software, thanks to the availability of several reduced order methods and algorithms.
 
@@ -32,12 +32,12 @@ Linear and non-linear algebra operations which are not already implemented in Op
 
 ### 1. Prerequisites
 **ITHACA-FV** requires
-*   [**OpenFOAM 1812**](https://www.openfoam.com/releases/openfoam-v1812/) or
-*   [**OpenFOAM 1906**](https://www.openfoam.com/releases/openfoam-v1906/) or
-*   [**OpenFOAM 1912**](https://www.openfoam.com/releases/openfoam-v1912/) or
-*   [**OpenFOAM 2006**](https://www.openfoam.com/releases/openfoam-v2006/) or
-*   [**OpenFOAM 2012**](https://www.openfoam.com/releases/openfoam-v2012/) or
-*   [**OpenFOAM 2106**](https://www.openfoam.com/news/main-news/openfoam-v2106)
+*   [**OpenFOAM 1812**](https://www.openfoam.com/news/main-news/openfoam-v1812/) or
+*   [**OpenFOAM 1906**](https://www.openfoam.com/news/main-news/openfoam-v1906/) or
+*   [**OpenFOAM 1912**](https://www.openfoam.com/news/main-news/openfoam-v1912/) or
+*   [**OpenFOAM 2006**](https://www.openfoam.com/news/main-news/openfoam-v2006/) or
+*   [**OpenFOAM 2012**](https://www.openfoam.com/news/main-news/openfoam-v2012/) or
+*   [**OpenFOAM 2106**](https://www.openfoam.com/news/main-news/openfoam-v2106) or
 *   [**OpenFOAM 2212**](https://www.openfoam.com/news/main-news/openfoam-v2212)
 
 

From 6c4dc57b4171356606a993fbd5c7436014064d98 Mon Sep 17 00:00:00 2001
From: Tom Protin <tom.protin@scalian.com>
Date: Fri, 7 Jul 2023 12:30:30 +0200
Subject: [PATCH 12/59] added new functions for surface interpolations related
 to jump and average calculations : added surfaceIndexInt, surfaceIndexExt,
 surfaceValuesInt and surfaceValuesExt

---
 .../ITHACAutilities/ITHACAsurfacetools.C      | 111 ++++++++++++++++++
 .../ITHACAutilities/ITHACAsurfacetools.H      |  66 +++++++++++
 src/ITHACA_CORE/Make/files                    |   1 +
 3 files changed, 178 insertions(+)
 create mode 100644 src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C
 create mode 100644 src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.H

diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C
new file mode 100644
index 000000000..e3519422a
--- /dev/null
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C
@@ -0,0 +1,111 @@
+/*---------------------------------------------------------------------------*\
+     ██╗████████╗██╗  ██╗ █████╗  ██████╗ █████╗       ███████╗██╗   ██╗
+     ██║╚══██╔══╝██║  ██║██╔══██╗██╔════╝██╔══██╗      ██╔════╝██║   ██║
+     ██║   ██║   ███████║███████║██║     ███████║█████╗█████╗  ██║   ██║
+     ██║   ██║   ██╔══██║██╔══██║██║     ██╔══██║╚════╝██╔══╝  ╚██╗ ██╔╝
+     ██║   ██║   ██║  ██║██║  ██║╚██████╗██║  ██║      ██║      ╚████╔╝
+     ╚═╝   ╚═╝   ╚═╝  ╚═╝╚═╝  ╚═╝ ╚═════╝╚═╝  ╚═╝      ╚═╝       ╚═══╝
+
+ * In real Time Highly Advanced Computational Applications for Finite Volumes
+ * Copyright (C) 2017 by the ITHACA-FV authors
+-------------------------------------------------------------------------------
+
+License
+    This file is part of ITHACA-FV
+
+    ITHACA-FV is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    ITHACA-FV is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU Lesser General Public License for more details.
+
+
+    You should have received a copy of the GNU Lesser General Public License
+    along with ITHACA-FV. If not, see <http://www.gnu.org/licenses/>.
+\*---------------------------------------------------------------------------*/
+
+#include "ITHACAsurfacetools.H"
+
+
+namespace ITHACAutilities
+{
+namespace ITHACAsurfacetools
+{
+
+  template<typename T>
+  List<label> surfaceIndexInt(T& field, const label patchInt, const label patchExt)
+  {
+    if (field.mesh().boundaryMesh()[patchInt].type() != "cyclic") {
+      Info << "PATCH TYPE MUST BE cyclic, not " << field.mesh().boundaryMesh()[patchInt].type() <<endl;
+      return *(new List<label>);
+    }
+
+    List<label>* result = new List<label>;
+
+    for (size_t i = 0; i < field.mesh().boundaryMesh()[patchInt].size(); i++) {
+      result->append(field.mesh().boundaryMesh()[patchInt].faceCells()[i]);
+    }
+
+    return *result;
+  }
+
+  template List<label> surfaceIndexInt(volScalarField& field, const label patchInt, const label patchExt);
+  template List<label> surfaceIndexInt(volVectorField& field, const label patchInt, const label patchExt);
+  template List<label> surfaceIndexInt(volTensorField& field, const label patchInt, const label patchExt);
+
+  template<typename T>
+  List<label> surfaceIndexExt(T& field, const label patchInt, const label patchExt)
+  {
+    return surfaceIndexInt(field, patchExt, patchInt);
+  }
+
+  template List<label> surfaceIndexExt(volScalarField& field, const label patchInt, const label patchExt);
+  template List<label> surfaceIndexExt(volVectorField& field, const label patchInt, const label patchExt);
+  template List<label> surfaceIndexExt(volTensorField& field, const label patchInt, const label patchExt);
+
+  template<typename T, typename V>
+  void surfaceValuesInt(T& field, const label patchInt, const label patchExt, List<V>& result)
+  {
+    if (field.mesh().boundaryMesh()[patchInt].type() != "cyclic") {
+      Info << "PATCH TYPE MUST BE cyclic, not " << field.mesh().boundaryMesh()[patchInt].type() <<endl;
+    }
+    else
+    {
+      List<label> indexes = surfaceIndexInt(field, patchInt, patchExt);
+
+      for (size_t i = 0; i < indexes.size(); i++) {
+        result.append(field[indexes[i]]);
+      }
+    }
+  }
+
+  template void surfaceValuesInt(volScalarField& field, const label patchInt, const label patchExt, List<scalar>& result);
+  template void surfaceValuesInt(volVectorField& field, const label patchInt, const label patchExt, List<Foam::Vector<scalar>>& result);
+  template void surfaceValuesInt(volTensorField& field, const label patchInt, const label patchExt, List<Foam::Tensor<scalar>>& result);
+
+  template<typename T, typename V>
+  void surfaceValuesExt(T& field, const label patchInt, const label patchExt, List<V>& result)
+  {
+    if (field.mesh().boundaryMesh()[patchInt].type() != "cyclic") {
+      Info << "PATCH TYPE MUST BE cyclic, not " << field.mesh().boundaryMesh()[patchInt].type() <<endl;
+    }
+    else
+    {
+      surfaceValuesInt(field, patchExt, patchInt, result);
+    }
+  }
+
+  template void surfaceValuesExt(volScalarField& field, const label patchInt, const label patchExt, List<scalar>& result);
+  template void surfaceValuesExt(volVectorField& field, const label patchInt, const label patchExt, List<Foam::Vector<scalar>>& result);
+  template void surfaceValuesExt(volTensorField& field, const label patchInt, const label patchExt, List<Foam::Tensor<scalar>>& result);
+
+} // End namespace ITHACAsurfacetools
+} // End namespace ITHACAutilities
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+// ************************************************************************* //
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.H b/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.H
new file mode 100644
index 000000000..299a8d57c
--- /dev/null
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.H
@@ -0,0 +1,66 @@
+/*---------------------------------------------------------------------------*\
+     ██╗████████╗██╗  ██╗ █████╗  ██████╗ █████╗       ███████╗██╗   ██╗
+     ██║╚══██╔══╝██║  ██║██╔══██╗██╔════╝██╔══██╗      ██╔════╝██║   ██║
+     ██║   ██║   ███████║███████║██║     ███████║█████╗█████╗  ██║   ██║
+     ██║   ██║   ██╔══██║██╔══██║██║     ██╔══██║╚════╝██╔══╝  ╚██╗ ██╔╝
+     ██║   ██║   ██║  ██║██║  ██║╚██████╗██║  ██║      ██║      ╚████╔╝
+     ╚═╝   ╚═╝   ╚═╝  ╚═╝╚═╝  ╚═╝ ╚═════╝╚═╝  ╚═╝      ╚═╝       ╚═══╝
+
+ * In real Time Highly Advanced Computational Applications for Finite Volumes
+ * Copyright (C) 2017 by the ITHACA-FV authors
+-------------------------------------------------------------------------------
+License
+    This file is part of ITHACA-FV
+    ITHACA-FV is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+    ITHACA-FV is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU Lesser General Public License for more details.
+    You should have received a copy of the GNU Lesser General Public License
+    along with ITHACA-FV. If not, see <http://www.gnu.org/licenses/>.
+\*---------------------------------------------------------------------------*/
+
+#ifndef functionObjects_ITHACAsurfacetools_H
+#define functionObjects_ITHACAsurfacetools_H
+
+#include <Eigen/Eigen>
+#include "Foam2Eigen.H"
+#include "fvMesh.H"
+#include "fvMeshSubset.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace ITHACAutilities
+{
+namespace ITHACAsurfacetools
+{
+
+  template<typename T>
+  List<label> surfaceIndexInt(T& field, const label patchInt, const label patchExt);
+
+  template<typename T>
+  List<label> surfaceIndexExt(T& field, const label patchInt, const label patchExt);
+
+  template<typename T, typename V>
+  void surfaceValuesInt(T& field, const label patchInt, const label patchExt, List<V>& result);
+
+  template<typename T, typename V>
+  void surfaceValuesExt(T& field, const label patchInt, const label patchExt, List<V>& result);
+/*
+  template<typename T>
+  List<Eigen::vector> surfaceAverage(T& field, const label patch);
+
+  template<typename T>
+  List<Eigen::vector> surfaceJump(T& field, const label patch);
+*/
+}; // End namespace ITHACAsurfacetools
+} // End namespace ITHACAutilities
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //
diff --git a/src/ITHACA_CORE/Make/files b/src/ITHACA_CORE/Make/files
index 24868373b..8966153c0 100644
--- a/src/ITHACA_CORE/Make/files
+++ b/src/ITHACA_CORE/Make/files
@@ -9,6 +9,7 @@ ITHACAutilities/ITHACAassign.C
 ITHACAutilities/ITHACAcoeffsMass.C
 ITHACAparallel/ITHACAparallel.C
 ITHACAutilities/ITHACAforces.C
+ITHACAutilities/ITHACAsurfacetools.C
 ITHACAPOD/ITHACAPOD.C
 ITHACAPOD/incrementalPOD.C
 ITHACADMD/ITHACADMD.C

From 314c03aaccff54f5dbdf9652641cbe9e646c12dc Mon Sep 17 00:00:00 2001
From: Tom Protin <tom.protin@scalian.com>
Date: Fri, 7 Jul 2023 12:32:07 +0200
Subject: [PATCH 13/59] added a new unit test to test surfacetools functions

---
 unitTests/ITHACAsurfacetools/Make/files       |   3 +
 unitTests/ITHACAsurfacetools/Make/options     |  30 ++++++
 .../ITHACAsurfacetools/SurfacetoolsTest.C     |  55 ++++++++++
 unitTests/ITHACAsurfacetools/createFields.H   |  28 +++++
 unitTests/ITHACAsurfacetools/createMesh.H     | 102 ++++++++++++++++++
 unitTests/ITHACAsurfacetools/createTime.H     |   3 +
 6 files changed, 221 insertions(+)
 create mode 100644 unitTests/ITHACAsurfacetools/Make/files
 create mode 100644 unitTests/ITHACAsurfacetools/Make/options
 create mode 100644 unitTests/ITHACAsurfacetools/SurfacetoolsTest.C
 create mode 100644 unitTests/ITHACAsurfacetools/createFields.H
 create mode 100644 unitTests/ITHACAsurfacetools/createMesh.H
 create mode 100644 unitTests/ITHACAsurfacetools/createTime.H

diff --git a/unitTests/ITHACAsurfacetools/Make/files b/unitTests/ITHACAsurfacetools/Make/files
new file mode 100644
index 000000000..156fe17ef
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/Make/files
@@ -0,0 +1,3 @@
+SurfacetoolsTest.C
+
+EXE = $(FOAM_USER_APPBIN)/SurfacetoolsTest
diff --git a/unitTests/ITHACAsurfacetools/Make/options b/unitTests/ITHACAsurfacetools/Make/options
new file mode 100644
index 000000000..17c1e0f12
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/Make/options
@@ -0,0 +1,30 @@
+EXE_INC = \
+    -I$(LIB_SRC)/finiteVolume/lnInclude \
+    -I$(LIB_SRC)/meshTools/lnInclude \
+    -I$(LIB_SRC)/sampling/lnInclude \
+    -I$(LIB_SRC)/fvOptions/lnInclude \
+    -I$(LIB_SRC)/fileFormats/lnInclude \
+    -I$(LIB_SRC)/dynamicFvMesh/lnInclude \
+    -I$(LIB_SRC)/dynamicMesh/lnInclude \
+    -I$(LIB_SRC)/fileFormats/lnInclude \
+    -I$(LIB_ITHACA_SRC)/ITHACA_CORE/lnInclude \
+    -I$(LIB_ITHACA_SRC)/thirdparty/Eigen \
+    -I$(LIB_ITHACA_SRC)/thirdparty/spectra-0.6.1/include \
+    -I$(LIB_ITHACA_SRC)/thirdparty/splinter/include \
+    -w \
+    -DOFVER=$${WM_PROJECT_VERSION%.*} \
+    -std=c++11
+
+EXE_LIBS = \
+    -lturbulenceModels \
+    -lincompressibleTransportModels \
+    -lincompressibleTurbulenceModels \
+    -lfiniteVolume \
+    -lmeshTools \
+    -lfvOptions \
+    -lsampling \
+    -lforces \
+    -lITHACA_CORE \
+    -L$(FOAM_USER_LIBBIN) \
+
+ 
diff --git a/unitTests/ITHACAsurfacetools/SurfacetoolsTest.C b/unitTests/ITHACAsurfacetools/SurfacetoolsTest.C
new file mode 100644
index 000000000..d2f5e6c8f
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/SurfacetoolsTest.C
@@ -0,0 +1,55 @@
+#include "ITHACAstream.H"
+#include "ITHACAsurfacetools.H"
+#include "fvCFD.H"
+#include "volPointInterpolation.H"
+#include "fvOptions.H"
+#include <complex>
+#include <cstdlib>
+#include <iostream>
+#include <map>
+#include <string>
+#include <tuple>
+
+using namespace ITHACAutilities;
+using namespace ITHACAsurfacetools;
+
+int main(int argc, char **argv)
+{
+  #include "setRootCaseLists.H"
+  #include "createTime.H"
+  #include "createMesh.H"
+  #include "createFields.H"
+
+  IOdictionary ITHACAdict
+  (
+    IOobject
+    (
+      "ITHACAdict",
+      runTime.system(),
+      mesh,
+      IOobject::MUST_READ,
+      IOobject::NO_WRITE
+    )
+  );
+
+  Info << runTime.timeName() << endl;
+
+  label patchInt = ITHACAdict.lookupOrDefault<label>("patchInt", 0);
+  label patchExt = ITHACAdict.lookupOrDefault<label>("patchExt", 0);
+
+  List<label> indexesInt = surfaceIndexInt(U, patchInt, patchExt);
+  List<label> indexesExt = surfaceIndexExt(U, patchInt, patchExt);
+  List<Foam::Vector<double>> patchValuesInt = *(new List<Foam::Vector<double>>);
+  surfaceValuesInt(U, patchInt, patchExt, patchValuesInt);
+  List<Foam::Vector<double>> patchValuesExt = *(new List<Foam::Vector<double>>);
+  surfaceValuesExt(U, patchInt, patchExt, patchValuesExt);
+
+  Info << "surfaceIndexInt(U, 6) = " << indexesInt << endl;
+  Info << "surfaceIndexExt(U, 6) = " << indexesExt << endl;
+  Info << "surfaceValuesInt(U, 6) = " << patchValuesInt << endl;
+  Info << "surfaceValuesExt(U, 6) = " << patchValuesExt << endl;
+  Info << "surfaceAverage(U, 6) = " << "" << endl;
+  Info << "surfaceJump(U, 6) = " << "" << endl;
+
+  return 0;
+}
diff --git a/unitTests/ITHACAsurfacetools/createFields.H b/unitTests/ITHACAsurfacetools/createFields.H
new file mode 100644
index 000000000..d62ba40d3
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/createFields.H
@@ -0,0 +1,28 @@
+Info<< "Reading field p\n" << endl;
+
+volScalarField p
+(
+    IOobject
+    (
+        "p",
+        runTime.timeName(),
+        mesh,
+        IOobject::MUST_READ,
+        IOobject::AUTO_WRITE
+    ),
+    mesh
+);
+
+Info<< "Reading field U\n" << endl;
+volVectorField U
+(
+    IOobject
+    (
+        "U",
+        runTime.timeName(),
+        mesh,
+        IOobject::MUST_READ,
+        IOobject::AUTO_WRITE
+    ),
+    mesh
+);
diff --git a/unitTests/ITHACAsurfacetools/createMesh.H b/unitTests/ITHACAsurfacetools/createMesh.H
new file mode 100644
index 000000000..67dc3e911
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/createMesh.H
@@ -0,0 +1,102 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2018-2021 OpenCFD Ltd.
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM, distributed under GPL-3.0-or-later.
+
+Description
+    Create a fvMesh (specified region or defaultRegion) with
+    additional handling of -dry-run and -dry-run-write options.
+
+Required Variables
+    - args [argList]
+    - runTime [Time]
+
+Provided Variables
+    - regionName [word]
+    - mesh [fvMesh]
+    - meshPtr [autoPtr<fvMesh>]
+
+\*---------------------------------------------------------------------------*/
+
+Foam::autoPtr<Foam::fvMesh> meshPtr(nullptr);
+Foam::word regionName(Foam::polyMesh::defaultRegion);
+
+if (args.found("dry-run") || args.found("dry-run-write"))
+{
+    Foam::Info
+        << "Operating in 'dry-run' mode: case will run for 1 time step.  "
+        << "All checks assumed OK on a clean exit" << Foam::endl;
+
+    // Allow region in combination with dry-run
+    args.readIfPresent("region", regionName);
+
+    Foam::FieldBase::allowConstructFromLargerSize = true;
+
+    // Create a simplified 1D mesh and attempt to re-create boundary conditions
+    meshPtr.reset
+    (
+        new Foam::simplifiedMeshes::columnFvMesh(runTime, regionName)
+    );
+
+    // Stop after 1 iteration of the simplified mesh
+
+    if (args.found("dry-run-write"))
+    {
+        // Using saWriteNow triggers function objects execute(), write()
+        runTime.stopAt(Foam::Time::saWriteNow);
+
+        // Make sure mesh gets output to the current time (since instance
+        // no longer constant)
+        meshPtr().setInstance(runTime.timeName());
+    }
+    else
+    {
+        // Using saNoWriteNow triggers function objects execute(),
+        // but not write()
+        runTime.stopAt(Foam::Time::saNoWriteNow);
+    }
+
+    Foam::functionObject::outputPrefix = "postProcessing-dry-run";
+}
+else
+{
+    if (args.readIfPresent("region", regionName))
+    {
+        Foam::Info << "Create mesh " << regionName;
+    }
+    else
+    {
+        Foam::Info << "Create mesh";
+    }
+    Foam::Info << " for time = " << runTime.timeName() << Foam::nl;
+
+    meshPtr.reset
+    (
+        new Foam::fvMesh
+        (
+            Foam::IOobject
+            (
+                regionName,
+                runTime.timeName(),
+                runTime,
+                Foam::IOobject::MUST_READ
+            ),
+            false
+        )
+    );
+    meshPtr().init(true);   // initialise all (lower levels and current)
+
+    Foam::Info << Foam::endl;
+}
+
+Foam::fvMesh& mesh = meshPtr();
+
+
+// ************************************************************************* //
diff --git a/unitTests/ITHACAsurfacetools/createTime.H b/unitTests/ITHACAsurfacetools/createTime.H
new file mode 100644
index 000000000..4ea4a6be6
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/createTime.H
@@ -0,0 +1,3 @@
+Foam::Info<< "Create time\n" << Foam::endl;
+
+Foam::Time runTime(Foam::Time::controlDictName, args);

From 0b5c1ec78f7b14052607c146d0a93c0ba55901aa Mon Sep 17 00:00:00 2001
From: Tom Protin <tom.protin@scalian.com>
Date: Fri, 7 Jul 2023 12:32:43 +0200
Subject: [PATCH 14/59] changed Allwmake file to compile unittests

---
 Allwmake | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Allwmake b/Allwmake
index 6c2efdf93..a4e19e14b 100755
--- a/Allwmake
+++ b/Allwmake
@@ -6,7 +6,7 @@ tutorial_flag=''
 torch_flag=''
 muq_flag=''
 applications_flag=''
-unit_tests_flag=''
+unit_tests_flag='true'
 
 has_wmake="$(command -v wmake)"
 

From e82baf6c37a19ffb5746d19c323aca8c318a3b3a Mon Sep 17 00:00:00 2001
From: Tom Protin <tom.protin@scalian.com>
Date: Mon, 10 Jul 2023 15:31:40 +0200
Subject: [PATCH 15/59] added jump and average support in ITHACAsurfacetools;
 added helper functions

---
 .../ITHACAutilities/ITHACAsurfacetools.C      | 102 ++++++++++++++----
 .../ITHACAutilities/ITHACAsurfacetools.H      |  15 ++-
 2 files changed, 92 insertions(+), 25 deletions(-)

diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C
index e3519422a..636034b67 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C
@@ -39,11 +39,6 @@ namespace ITHACAsurfacetools
   template<typename T>
   List<label> surfaceIndexInt(T& field, const label patchInt, const label patchExt)
   {
-    if (field.mesh().boundaryMesh()[patchInt].type() != "cyclic") {
-      Info << "PATCH TYPE MUST BE cyclic, not " << field.mesh().boundaryMesh()[patchInt].type() <<endl;
-      return *(new List<label>);
-    }
-
     List<label>* result = new List<label>;
 
     for (size_t i = 0; i < field.mesh().boundaryMesh()[patchInt].size(); i++) {
@@ -70,16 +65,10 @@ namespace ITHACAsurfacetools
   template<typename T, typename V>
   void surfaceValuesInt(T& field, const label patchInt, const label patchExt, List<V>& result)
   {
-    if (field.mesh().boundaryMesh()[patchInt].type() != "cyclic") {
-      Info << "PATCH TYPE MUST BE cyclic, not " << field.mesh().boundaryMesh()[patchInt].type() <<endl;
-    }
-    else
-    {
-      List<label> indexes = surfaceIndexInt(field, patchInt, patchExt);
+    List<label> indexes = surfaceIndexInt(field, patchInt, patchExt);
 
-      for (size_t i = 0; i < indexes.size(); i++) {
-        result.append(field[indexes[i]]);
-      }
+    for (size_t i = 0; i < indexes.size(); i++) {
+      result.append(field[indexes[i]]);
     }
   }
 
@@ -90,19 +79,90 @@ namespace ITHACAsurfacetools
   template<typename T, typename V>
   void surfaceValuesExt(T& field, const label patchInt, const label patchExt, List<V>& result)
   {
-    if (field.mesh().boundaryMesh()[patchInt].type() != "cyclic") {
-      Info << "PATCH TYPE MUST BE cyclic, not " << field.mesh().boundaryMesh()[patchInt].type() <<endl;
-    }
-    else
-    {
-      surfaceValuesInt(field, patchExt, patchInt, result);
-    }
+    surfaceValuesInt(field, patchExt, patchInt, result);
   }
 
   template void surfaceValuesExt(volScalarField& field, const label patchInt, const label patchExt, List<scalar>& result);
   template void surfaceValuesExt(volVectorField& field, const label patchInt, const label patchExt, List<Foam::Vector<scalar>>& result);
   template void surfaceValuesExt(volTensorField& field, const label patchInt, const label patchExt, List<Foam::Tensor<scalar>>& result);
 
+  template<typename T>
+  Foam::Vector<scalar> surfaceFindMirrorPoint(T& field, const label patchInt, const label patchExt, const label cellID)
+  {
+    Foam::Vector<scalar> result = *(new Foam::Vector<scalar>);
+    List<label> indexesInt = surfaceIndexInt(field, patchInt, patchExt);
+
+    result = 2 * field.mesh().boundaryMesh()[patchInt].faceCentres()[cellID] - field.mesh().C()[indexesInt[cellID]];
+
+    return result;
+  }
+
+  template Foam::Vector<scalar> surfaceFindMirrorPoint(volScalarField& field, const label patchInt, const label patchExt, const label cellID);
+  template Foam::Vector<scalar> surfaceFindMirrorPoint(volVectorField& field, const label patchInt, const label patchExt, const label cellID);
+  template Foam::Vector<scalar> surfaceFindMirrorPoint(volTensorField& field, const label patchInt, const label patchExt, const label cellID);
+
+  template<typename T>
+  label surfaceFindClosest(T& field, const label patchInt, const label patchExt, Foam::Vector<scalar> point)
+  {
+    label result = 0;
+    scalar dist = 0;
+    List<label> indexesExt = surfaceIndexExt(field, patchInt, patchExt);
+
+    dist = mag(point - field.mesh().C()[indexesExt[0]]);
+
+    for(int i = 1; i < indexesExt.size(); i++)
+    {
+      scalar temp = mag(point - field.mesh().C()[indexesExt[i]]);
+      if(temp <= dist)
+      {
+        dist = temp;
+        result = i;
+      }
+    }
+    result = indexesExt[result];
+    return result;
+  }
+
+  template label surfaceFindClosest(volScalarField& field, const label patchInt, const label patchExt, Foam::Vector<scalar> point);
+  template label surfaceFindClosest(volVectorField& field, const label patchInt, const label patchExt, Foam::Vector<scalar> point);
+  template label surfaceFindClosest(volTensorField& field, const label patchInt, const label patchExt, Foam::Vector<scalar> point);
+
+  template<typename T, typename V>
+  void surfaceAverage(T& field, const label patchInt, const label patchExt, List<V>& result)
+  {
+    List<label> indexesInt = surfaceIndexInt(field, patchInt, patchExt);
+    result.resize(0);
+
+    for(int i = 0; i < indexesInt.size(); i++)
+    {
+        Foam::Vector<scalar> mirror = surfaceFindMirrorPoint(field, patchInt, patchExt, i);
+        label closest = surfaceFindClosest(field, patchInt, patchExt, mirror);
+        result.append(0.5 * field[closest] + 0.5 * field[indexesInt[i]]);
+    }
+  }
+
+  template void surfaceAverage(volScalarField& field, const label patchInt, const label patchExt, List<scalar>& result);
+  template void surfaceAverage(volVectorField& field, const label patchInt, const label patchExt, List<Foam::Vector<scalar>>& result);
+  template void surfaceAverage(volTensorField& field, const label patchInt, const label patchExt, List<Foam::Tensor<scalar>>& result);
+
+  template<typename T, typename V>
+  void surfaceJump(T& field, const label patchInt, const label patchExt, List<V>& result)
+  {
+    List<label> indexesInt = surfaceIndexInt(field, patchInt, patchExt);
+    result.resize(0);
+    Info << indexesInt.size() << endl;
+
+    for(int i = 0; i < indexesInt.size(); i++)
+    {
+        Foam::Vector<scalar> mirror = surfaceFindMirrorPoint(field, patchInt, patchExt, i);
+        label closest = surfaceFindClosest(field, patchInt, patchExt, mirror);
+        result.append(field[closest] - field[indexesInt[i]]);
+    }
+  }
+
+  template void surfaceJump(volScalarField& field, const label patchInt, const label patchExt, List<scalar>& result);
+  template void surfaceJump(volVectorField& field, const label patchInt, const label patchExt, List<Foam::Vector<scalar>>& result);
+  template void surfaceJump(volTensorField& field, const label patchInt, const label patchExt, List<Foam::Tensor<scalar>>& result);
 } // End namespace ITHACAsurfacetools
 } // End namespace ITHACAutilities
 
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.H b/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.H
index 299a8d57c..1ef379bdf 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.H
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.H
@@ -27,6 +27,7 @@ License
 #define functionObjects_ITHACAsurfacetools_H
 
 #include <Eigen/Eigen>
+#include "volPointInterpolation.H"
 #include "Foam2Eigen.H"
 #include "fvMesh.H"
 #include "fvMeshSubset.H"
@@ -49,13 +50,19 @@ namespace ITHACAsurfacetools
 
   template<typename T, typename V>
   void surfaceValuesExt(T& field, const label patchInt, const label patchExt, List<V>& result);
-/*
+
   template<typename T>
-  List<Eigen::vector> surfaceAverage(T& field, const label patch);
+  Foam::Vector<scalar> surfaceFindMirrorPoint(T& field, const label patchInt, const label patchExt, const label cellID);
 
   template<typename T>
-  List<Eigen::vector> surfaceJump(T& field, const label patch);
-*/
+  label surfaceFindClosest(T& field, const label patchInt, const label patchExt, Foam::Vector<scalar> point);
+
+  template<typename T, typename V>
+  void surfaceAverage(T& field, const label patchInt, const label patchExt, List<V>& result);
+
+  template<typename T, typename V>
+  void surfaceJump(T& field, const label patchInt, const label patchExt, List<V>& result);
+
 }; // End namespace ITHACAsurfacetools
 } // End namespace ITHACAutilities
 

From d94f04ad1bd2d1606476eff04f108578697e2f25 Mon Sep 17 00:00:00 2001
From: Tom Protin <tom.protin@scalian.com>
Date: Mon, 10 Jul 2023 15:32:18 +0200
Subject: [PATCH 16/59] changed unit test to test new jump and average
 functions

---
 unitTests/ITHACAsurfacetools/SurfacetoolsTest.C | 10 ++++++----
 1 file changed, 6 insertions(+), 4 deletions(-)

diff --git a/unitTests/ITHACAsurfacetools/SurfacetoolsTest.C b/unitTests/ITHACAsurfacetools/SurfacetoolsTest.C
index d2f5e6c8f..9f6317b1e 100644
--- a/unitTests/ITHACAsurfacetools/SurfacetoolsTest.C
+++ b/unitTests/ITHACAsurfacetools/SurfacetoolsTest.C
@@ -32,8 +32,6 @@ int main(int argc, char **argv)
     )
   );
 
-  Info << runTime.timeName() << endl;
-
   label patchInt = ITHACAdict.lookupOrDefault<label>("patchInt", 0);
   label patchExt = ITHACAdict.lookupOrDefault<label>("patchExt", 0);
 
@@ -43,13 +41,17 @@ int main(int argc, char **argv)
   surfaceValuesInt(U, patchInt, patchExt, patchValuesInt);
   List<Foam::Vector<double>> patchValuesExt = *(new List<Foam::Vector<double>>);
   surfaceValuesExt(U, patchInt, patchExt, patchValuesExt);
+  List<Foam::Vector<double>> average = *(new List<Foam::Vector<double>>);
+  surfaceAverage(U, patchInt, patchExt, average);
+  List<Foam::Vector<double>> jump = *(new List<Foam::Vector<double>>);
+  surfaceJump(U, patchInt, patchExt, jump);
 
   Info << "surfaceIndexInt(U, 6) = " << indexesInt << endl;
   Info << "surfaceIndexExt(U, 6) = " << indexesExt << endl;
   Info << "surfaceValuesInt(U, 6) = " << patchValuesInt << endl;
   Info << "surfaceValuesExt(U, 6) = " << patchValuesExt << endl;
-  Info << "surfaceAverage(U, 6) = " << "" << endl;
-  Info << "surfaceJump(U, 6) = " << "" << endl;
+  Info << "surfaceAverage(U, 6) = " << average << endl;
+  Info << "surfaceJump(U, 6) = " << jump << endl;
 
   return 0;
 }

From 231cc55a3c4f707b23531c6ef907ae1d21e76ac2 Mon Sep 17 00:00:00 2001
From: Giovanni Stabile <giovanni.stabile87@gmail.com>
Date: Tue, 18 Jul 2023 14:28:55 +0200
Subject: [PATCH 17/59] Update README.md

---
 README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index 056a82323..6b68d8951 100644
--- a/README.md
+++ b/README.md
@@ -208,9 +208,9 @@ Doi                      = {10.1016/j.compfluid.2018.01.035}}
 and cite the [ITHACA-FV website](https://ithaca-fv.github.io/ITHACA-FV).
 
 ### 8. Funding
-A significant part of PyDMD has been written either as a by-product for other projects people were funded for, or by people on university-funded positions. There are probably many of such projects that have led to some development of PyDMD. We are very grateful for this support!
+A significant part of ITHACA-FV has been written either as a by-product for other projects people were funded for, or by people on university-funded positions. There are probably many of such projects that have led to some development of ITHACA-FV. We are very grateful for this support!
 
-Beyond this, PyDMD has also been supported by some dedicated projects that have allowed us to work on extensions, documentation, training and dissemination that would otherwise not have been possible. In particular, we acknowledge the following sources of support with great gratitude:
+Beyond this, ITHACA-FV has also been supported by some dedicated projects that have allowed us to work on extensions, documentation, training and dissemination that would otherwise not have been possible. In particular, we acknowledge the following sources of support with great gratitude:
 
 * [H2020 ERC CoG 2015 AROMA-CFD project 681447](https://people.sissa.it/~grozza/aroma-cfd/), P.I. Professor [Gianluigi Rozza](https://people.sissa.it/~grozza) at [SISSA mathLab](https://mathlab.sissa.it/).
 

From 0424138876c131d160ebf32ed5a8f27bb0cb947d Mon Sep 17 00:00:00 2001
From: Valentin Resseguier <valentin.resseguier@scalian.com>
Date: Mon, 31 Jul 2023 19:11:45 +0200
Subject: [PATCH 18/59] specialization of reconstructFromCoeff for
 volTensorFields

---
 src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
index 948487592..794b6857e 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
@@ -59,6 +59,10 @@ template PtrList<GeometricField<vector, fvPatchField, volMesh>>
 reconstructFromCoeff(
     PtrList<GeometricField<vector, fvPatchField, volMesh>>& modes,
     Eigen::MatrixXd& coeff_matrix, label Nmodes);
+template PtrList<GeometricField<tensor, fvPatchField, volMesh>>
+reconstructFromCoeff(
+    PtrList<GeometricField<tensor, fvPatchField, volMesh>>& modes,
+    Eigen::MatrixXd& coeff_matrix, label Nmodes);
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 Eigen::MatrixXd getMassMatrix(

From 9bcb499de5a766c30cb1ab0fd4a63849650c6613 Mon Sep 17 00:00:00 2001
From: Valentin Resseguier <valentin.resseguier@scalian.com>
Date: Tue, 1 Aug 2023 11:12:02 +0200
Subject: [PATCH 19/59] Update ITHACAsurfacetools.C use double

---
 src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C
index 636034b67..feeababea 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C
@@ -92,7 +92,7 @@ namespace ITHACAsurfacetools
     Foam::Vector<scalar> result = *(new Foam::Vector<scalar>);
     List<label> indexesInt = surfaceIndexInt(field, patchInt, patchExt);
 
-    result = 2 * field.mesh().boundaryMesh()[patchInt].faceCentres()[cellID] - field.mesh().C()[indexesInt[cellID]];
+    result = 2.0 * field.mesh().boundaryMesh()[patchInt].faceCentres()[cellID] - field.mesh().C()[indexesInt[cellID]];
 
     return result;
   }

From 25edc23592a1d6baeade21eb9836b480f168393c Mon Sep 17 00:00:00 2001
From: Tom Protin <tom.protin@scalian.com>
Date: Tue, 1 Aug 2023 11:14:21 +0200
Subject: [PATCH 20/59] removed useless print

---
 src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C | 1 -
 1 file changed, 1 deletion(-)

diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C
index 636034b67..d2ac35149 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C
@@ -150,7 +150,6 @@ namespace ITHACAsurfacetools
   {
     List<label> indexesInt = surfaceIndexInt(field, patchInt, patchExt);
     result.resize(0);
-    Info << indexesInt.size() << endl;
 
     for(int i = 0; i < indexesInt.size(); i++)
     {

From 09b81907c5f8490f0c91a06ab47cff6c49716919 Mon Sep 17 00:00:00 2001
From: Tom Protin <tom.protin@scalian.com>
Date: Tue, 1 Aug 2023 11:18:22 +0200
Subject: [PATCH 21/59] changed how unit test displays the results

---
 .../ITHACAsurfacetools/SurfacetoolsTest.C     | 35 +++++++++++++++----
 1 file changed, 29 insertions(+), 6 deletions(-)

diff --git a/unitTests/ITHACAsurfacetools/SurfacetoolsTest.C b/unitTests/ITHACAsurfacetools/SurfacetoolsTest.C
index 9f6317b1e..f4cd98b91 100644
--- a/unitTests/ITHACAsurfacetools/SurfacetoolsTest.C
+++ b/unitTests/ITHACAsurfacetools/SurfacetoolsTest.C
@@ -46,12 +46,35 @@ int main(int argc, char **argv)
   List<Foam::Vector<double>> jump = *(new List<Foam::Vector<double>>);
   surfaceJump(U, patchInt, patchExt, jump);
 
-  Info << "surfaceIndexInt(U, 6) = " << indexesInt << endl;
-  Info << "surfaceIndexExt(U, 6) = " << indexesExt << endl;
-  Info << "surfaceValuesInt(U, 6) = " << patchValuesInt << endl;
-  Info << "surfaceValuesExt(U, 6) = " << patchValuesExt << endl;
-  Info << "surfaceAverage(U, 6) = " << average << endl;
-  Info << "surfaceJump(U, 6) = " << jump << endl;
+  Info << "surfaceIndexInt(U, 6) = " << endl;
+  for (size_t i = 0; i < indexesInt.size(); i++) {
+    Info << "   " << indexesInt[i] << endl;
+  }
+
+  Info << endl << "surfaceIndexExt(U, 6) = " << endl;
+  for (size_t i = 0; i < indexesExt.size(); i++) {
+    Info << "   " << indexesExt[i] << endl;
+  }
+
+  Info << endl << "surfaceValuesInt(U, 6) = " << endl;
+  for (size_t i = 0; i < patchValuesInt.size(); i++) {
+    Info << "   " << patchValuesInt[i] << endl;
+  }
+
+  Info << endl << "surfaceValuesExt(U, 6) = " << endl;
+  for (size_t i = 0; i < patchValuesExt.size(); i++) {
+    Info << "   " << patchValuesExt[i] << endl;
+  }
+
+  Info << endl << "surfaceAverage(U, 6) = " << endl;
+  for (size_t i = 0; i < average.size(); i++) {
+    Info << "   " << average[i] << endl;
+  }
+
+  Info << endl << "surfaceJump(U, 6) = " << endl;
+  for (size_t i = 0; i < jump.size(); i++) {
+    Info << i << " :   " << jump[i] << endl;
+  }
 
   return 0;
 }

From 612074fd16475ae635cc514b0304ffe1520d8f4b Mon Sep 17 00:00:00 2001
From: Tom Protin <tom.protin@scalian.com>
Date: Tue, 1 Aug 2023 11:28:05 +0200
Subject: [PATCH 22/59] unit test changed initialization of some variables

---
 unitTests/ITHACAsurfacetools/SurfacetoolsTest.C | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/unitTests/ITHACAsurfacetools/SurfacetoolsTest.C b/unitTests/ITHACAsurfacetools/SurfacetoolsTest.C
index f4cd98b91..c615292d3 100644
--- a/unitTests/ITHACAsurfacetools/SurfacetoolsTest.C
+++ b/unitTests/ITHACAsurfacetools/SurfacetoolsTest.C
@@ -37,13 +37,13 @@ int main(int argc, char **argv)
 
   List<label> indexesInt = surfaceIndexInt(U, patchInt, patchExt);
   List<label> indexesExt = surfaceIndexExt(U, patchInt, patchExt);
-  List<Foam::Vector<double>> patchValuesInt = *(new List<Foam::Vector<double>>);
+  List<Foam::Vector<double>> patchValuesInt;
   surfaceValuesInt(U, patchInt, patchExt, patchValuesInt);
-  List<Foam::Vector<double>> patchValuesExt = *(new List<Foam::Vector<double>>);
+  List<Foam::Vector<double>> patchValuesExt;
   surfaceValuesExt(U, patchInt, patchExt, patchValuesExt);
-  List<Foam::Vector<double>> average = *(new List<Foam::Vector<double>>);
+  List<Foam::Vector<double>> average;
   surfaceAverage(U, patchInt, patchExt, average);
-  List<Foam::Vector<double>> jump = *(new List<Foam::Vector<double>>);
+  List<Foam::Vector<double>> jump;
   surfaceJump(U, patchInt, patchExt, jump);
 
   Info << "surfaceIndexInt(U, 6) = " << endl;

From 4c0a743736b707e2e5c4723d1cf44968c6d333a1 Mon Sep 17 00:00:00 2001
From: Tom Protin <tom.protin@scalian.com>
Date: Tue, 1 Aug 2023 11:28:13 +0200
Subject: [PATCH 23/59] Revert "changed Allwmake file to compile unittests"

This reverts commit 0b5c1ec78f7b14052607c146d0a93c0ba55901aa.
---
 Allwmake | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Allwmake b/Allwmake
index a4e19e14b..6c2efdf93 100755
--- a/Allwmake
+++ b/Allwmake
@@ -6,7 +6,7 @@ tutorial_flag=''
 torch_flag=''
 muq_flag=''
 applications_flag=''
-unit_tests_flag='true'
+unit_tests_flag=''
 
 has_wmake="$(command -v wmake)"
 

From 36a00742c9351451cff36199b6c3cdf49ffcee58 Mon Sep 17 00:00:00 2001
From: Tom Protin <tom.protin@scalian.com>
Date: Tue, 1 Aug 2023 11:33:53 +0200
Subject: [PATCH 24/59] improved how unit test displays results

---
 unitTests/ITHACAsurfacetools/SurfacetoolsTest.C | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/unitTests/ITHACAsurfacetools/SurfacetoolsTest.C b/unitTests/ITHACAsurfacetools/SurfacetoolsTest.C
index c615292d3..eefe583de 100644
--- a/unitTests/ITHACAsurfacetools/SurfacetoolsTest.C
+++ b/unitTests/ITHACAsurfacetools/SurfacetoolsTest.C
@@ -46,32 +46,32 @@ int main(int argc, char **argv)
   List<Foam::Vector<double>> jump;
   surfaceJump(U, patchInt, patchExt, jump);
 
-  Info << "surfaceIndexInt(U, 6) = " << endl;
+  Info << "surfaceIndexInt(U, patchInt, patchExt) = " << endl;
   for (size_t i = 0; i < indexesInt.size(); i++) {
     Info << "   " << indexesInt[i] << endl;
   }
 
-  Info << endl << "surfaceIndexExt(U, 6) = " << endl;
+  Info << endl << "surfaceIndexExt(U, patchInt, patchExt) = " << endl;
   for (size_t i = 0; i < indexesExt.size(); i++) {
     Info << "   " << indexesExt[i] << endl;
   }
 
-  Info << endl << "surfaceValuesInt(U, 6) = " << endl;
+  Info << endl << "surfaceValuesInt(U, patchInt, patchExt, patchValuesInt) = " << endl;
   for (size_t i = 0; i < patchValuesInt.size(); i++) {
     Info << "   " << patchValuesInt[i] << endl;
   }
 
-  Info << endl << "surfaceValuesExt(U, 6) = " << endl;
+  Info << endl << "surfaceValuesExt(U, patchInt, patchExt, patchValuesExt) = " << endl;
   for (size_t i = 0; i < patchValuesExt.size(); i++) {
     Info << "   " << patchValuesExt[i] << endl;
   }
 
-  Info << endl << "surfaceAverage(U, 6) = " << endl;
+  Info << endl << "surfaceAverage(U, patchInt, patchExt, average) = " << endl;
   for (size_t i = 0; i < average.size(); i++) {
     Info << "   " << average[i] << endl;
   }
 
-  Info << endl << "surfaceJump(U, 6) = " << endl;
+  Info << endl << "surfaceJump(U, patchInt, patchExt, jump) = " << endl;
   for (size_t i = 0; i < jump.size(); i++) {
     Info << i << " :   " << jump[i] << endl;
   }

From 2e6db530b7c4c2e632ebee95744865c100548903 Mon Sep 17 00:00:00 2001
From: Tom Protin <tom.protin@scalian.com>
Date: Tue, 1 Aug 2023 11:43:37 +0200
Subject: [PATCH 25/59] added test case in the unit test for surface tools

---
 unitTests/ITHACAsurfacetools/0/U              |  391 +++++
 unitTests/ITHACAsurfacetools/0/cellToRegion   |   21 +
 unitTests/ITHACAsurfacetools/0/p              |   67 +
 .../constant/polyMesh/boundary                |   87 ++
 .../constant/polyMesh/faces                   | 1275 ++++++++++++++++
 .../constant/polyMesh/neighbour               |  576 ++++++++
 .../constant/polyMesh/owner                   | 1276 +++++++++++++++++
 .../constant/polyMesh/points                  |  729 ++++++++++
 .../constant/transportProperties              |   22 +
 .../ITHACAsurfacetools/system/ITHACAdict      |   15 +
 .../system/PDRblockMeshDict                   |   61 +
 .../ITHACAsurfacetools/system/blockMeshDict   |  124 ++
 .../ITHACAsurfacetools/system/controlDict     |   48 +
 .../system/decomposeParDict                   |   27 +
 unitTests/ITHACAsurfacetools/system/fvSchemes |   51 +
 .../ITHACAsurfacetools/system/fvSolution      |   59 +
 .../ITHACAsurfacetools/system/setFieldsDict   |   35 +
 17 files changed, 4864 insertions(+)
 create mode 100644 unitTests/ITHACAsurfacetools/0/U
 create mode 100644 unitTests/ITHACAsurfacetools/0/cellToRegion
 create mode 100644 unitTests/ITHACAsurfacetools/0/p
 create mode 100644 unitTests/ITHACAsurfacetools/constant/polyMesh/boundary
 create mode 100644 unitTests/ITHACAsurfacetools/constant/polyMesh/faces
 create mode 100644 unitTests/ITHACAsurfacetools/constant/polyMesh/neighbour
 create mode 100644 unitTests/ITHACAsurfacetools/constant/polyMesh/owner
 create mode 100644 unitTests/ITHACAsurfacetools/constant/polyMesh/points
 create mode 100644 unitTests/ITHACAsurfacetools/constant/transportProperties
 create mode 100644 unitTests/ITHACAsurfacetools/system/ITHACAdict
 create mode 100644 unitTests/ITHACAsurfacetools/system/PDRblockMeshDict
 create mode 100644 unitTests/ITHACAsurfacetools/system/blockMeshDict
 create mode 100644 unitTests/ITHACAsurfacetools/system/controlDict
 create mode 100644 unitTests/ITHACAsurfacetools/system/decomposeParDict
 create mode 100644 unitTests/ITHACAsurfacetools/system/fvSchemes
 create mode 100644 unitTests/ITHACAsurfacetools/system/fvSolution
 create mode 100644 unitTests/ITHACAsurfacetools/system/setFieldsDict

diff --git a/unitTests/ITHACAsurfacetools/0/U b/unitTests/ITHACAsurfacetools/0/U
new file mode 100644
index 000000000..021a135ee
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/0/U
@@ -0,0 +1,391 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  2106                                  |
+|   \\  /    A nd           | Website:  www.openfoam.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
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+    inlet
+    {
+        type            fixedValue;
+        value           uniform (5 0 0);
+    }
+    outlet
+    {
+        type            zeroGradient;
+    }
+    fixedWallsLeft
+    {
+        type            noSlip;
+    }
+    fixedWallsRight
+    {
+        type            noSlip;
+    }
+    frontAndBackLeft
+    {
+        type            empty;
+    }
+    frontAndBackRight
+    {
+        type            empty;
+    }
+    left
+    {
+        type            cyclicAMI;
+        value           nonuniform List<vector> 10((1.66259 0.0728993 0) (4.24936 0.114087 0) (5.82185 0.17936 0) (6.52527 0.157219 0) (6.74186 0.0606261 0) (6.74186 -0.0606262 0) (6.52527 -0.157219 0) (5.82185 -0.17936 0) (4.24936 -0.114087 0) (1.66259 -0.0728993 0));
+    }
+    right
+    {
+        type            cyclicAMI;
+        value           nonuniform List<vector> 
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+)
+;
+    }
+}
+
+
+// ************************************************************************* //
diff --git a/unitTests/ITHACAsurfacetools/0/cellToRegion b/unitTests/ITHACAsurfacetools/0/cellToRegion
new file mode 100644
index 000000000..e658eb81f
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/0/cellToRegion
@@ -0,0 +1,21 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  2106                                  |
+|   \\  /    A nd           | Website:  www.openfoam.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    arch        "LSB;label=32;scalar=64";
+    class       labelList;
+    location    "0";
+    object      cellToRegion;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+3(0 0 1)
+
+// ************************************************************************* //
diff --git a/unitTests/ITHACAsurfacetools/0/p b/unitTests/ITHACAsurfacetools/0/p
new file mode 100644
index 000000000..101f324a7
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/0/p
@@ -0,0 +1,67 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  v2106                                 |
+|   \\  /    A nd           | Website:  www.openfoam.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       volScalarField;
+    location	"0";
+    object      p;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dimensions      [0 2 -2 0 0 0 0];
+
+internalField   uniform 0;
+
+boundaryField
+{
+    inlet
+    {
+        type            zeroGradient;
+    }
+    
+    outlet
+    {
+    	type            fixedValue;
+        value           uniform 0;
+    }
+    
+    fixedWallsLeft
+    {
+    	type		zeroGradient;
+    }
+    
+    fixedWallsRight
+    {
+    	type		zeroGradient;
+    }
+
+    frontAndBackLeft
+    {
+        type            empty;
+    }
+    
+    frontAndBackRight
+    {
+        type            empty;
+    }
+    
+    left
+    {
+    	type		cyclicAMI;
+    }
+    
+    right
+    {
+    	type		cyclicAMI;
+    }
+}
+
+
+// ************************************************************************* //
diff --git a/unitTests/ITHACAsurfacetools/constant/polyMesh/boundary b/unitTests/ITHACAsurfacetools/constant/polyMesh/boundary
new file mode 100644
index 000000000..7560ce846
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/constant/polyMesh/boundary
@@ -0,0 +1,87 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  2106                                  |
+|   \\  /    A nd           | Website:  www.openfoam.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    arch        "LSB;label=32;scalar=64";
+    class       polyBoundaryMesh;
+    location    "constant/polyMesh";
+    object      boundary;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+8
+(
+    inlet
+    {
+        type            patch;
+        nFaces          10;
+        startFace       550;
+    }
+    outlet
+    {
+        type            patch;
+        nFaces          20;
+        startFace       560;
+    }
+    fixedWallsLeft
+    {
+        type            wall;
+        inGroups        1(wall);
+        nFaces          20;
+        startFace       580;
+    }
+    fixedWallsRight
+    {
+        type            wall;
+        inGroups        1(wall);
+        nFaces          20;
+        startFace       600;
+    }
+    frontAndBackLeft
+    {
+        type            empty;
+        inGroups        1(empty);
+        nFaces          200;
+        startFace       620;
+    }
+    frontAndBackRight
+    {
+        type            empty;
+        inGroups        1(empty);
+        nFaces          400;
+        startFace       820;
+    }
+    left
+    {
+        type            cyclicAMI;
+        inGroups        1(cyclicAMI);
+        nFaces          10;
+        startFace       1220;
+        matchTolerance  0.0001;
+        transform       unknown;
+        neighbourPatch  right;
+        AMIMethod       faceAreaWeightAMI;
+        restartUncoveredSourceFace 1;
+    }
+    right
+    {
+        type            cyclicAMI;
+        inGroups        1(cyclicAMI);
+        nFaces          20;
+        startFace       1230;
+        matchTolerance  0.0001;
+        transform       unknown;
+        neighbourPatch  left;
+        AMIMethod       faceAreaWeightAMI;
+        restartUncoveredSourceFace 1;
+    }
+)
+
+// ************************************************************************* //
diff --git a/unitTests/ITHACAsurfacetools/constant/polyMesh/faces b/unitTests/ITHACAsurfacetools/constant/polyMesh/faces
new file mode 100644
index 000000000..b6af090ad
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/constant/polyMesh/faces
@@ -0,0 +1,1275 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  2106                                  |
+|   \\  /    A nd           | Website:  www.openfoam.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    arch        "LSB;label=32;scalar=64";
+    class       faceList;
+    location    "constant/polyMesh";
+    object      faces;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+
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+
+
+// ************************************************************************* //
diff --git a/unitTests/ITHACAsurfacetools/constant/polyMesh/neighbour b/unitTests/ITHACAsurfacetools/constant/polyMesh/neighbour
new file mode 100644
index 000000000..b6bd8252c
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/constant/polyMesh/neighbour
@@ -0,0 +1,576 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  2106                                  |
+|   \\  /    A nd           | Website:  www.openfoam.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    arch        "LSB;label=32;scalar=64";
+    note        "nPoints:704  nCells:300  nFaces:1250  nInternalFaces:550";
+    class       labelList;
+    location    "constant/polyMesh";
+    object      neighbour;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
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+
+
+// ************************************************************************* //
diff --git a/unitTests/ITHACAsurfacetools/constant/polyMesh/owner b/unitTests/ITHACAsurfacetools/constant/polyMesh/owner
new file mode 100644
index 000000000..e8ed08685
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/constant/polyMesh/owner
@@ -0,0 +1,1276 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  2106                                  |
+|   \\  /    A nd           | Website:  www.openfoam.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    arch        "LSB;label=32;scalar=64";
+    note        "nPoints:704  nCells:300  nFaces:1250  nInternalFaces:550";
+    class       labelList;
+    location    "constant/polyMesh";
+    object      owner;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
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+
+
+// ************************************************************************* //
diff --git a/unitTests/ITHACAsurfacetools/constant/polyMesh/points b/unitTests/ITHACAsurfacetools/constant/polyMesh/points
new file mode 100644
index 000000000..d9c8a6562
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/constant/polyMesh/points
@@ -0,0 +1,729 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  2106                                  |
+|   \\  /    A nd           | Website:  www.openfoam.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    arch        "LSB;label=32;scalar=64";
+    class       vectorField;
+    location    "constant/polyMesh";
+    object      points;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
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+(0.19 0.09 0.01)
+(0.2 0.09 0.01)
+(0.1 0.095 0.01)
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+(0.12 0.095 0.01)
+(0.13 0.095 0.01)
+(0.14 0.095 0.01)
+(0.15 0.095 0.01)
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+(0.2 0.095 0.01)
+(0.1 0.1 0.01)
+(0.11 0.1 0.01)
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+(0.18 0.1 0.01)
+(0.19 0.1 0.01)
+(0.2 0.1 0.01)
+)
+
+
+// ************************************************************************* //
diff --git a/unitTests/ITHACAsurfacetools/constant/transportProperties b/unitTests/ITHACAsurfacetools/constant/transportProperties
new file mode 100644
index 000000000..fde80dfcb
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/constant/transportProperties
@@ -0,0 +1,22 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  v2106                                 |
+|   \\  /    A nd           | Website:  www.openfoam.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      transportProperties;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+nu              0.01;
+
+nu_2		15;
+
+
+// ************************************************************************* //
diff --git a/unitTests/ITHACAsurfacetools/system/ITHACAdict b/unitTests/ITHACAsurfacetools/system/ITHACAdict
new file mode 100644
index 000000000..d5705888e
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/system/ITHACAdict
@@ -0,0 +1,15 @@
+FoamFile
+{
+    version     5.0;
+    format      ascii;
+    class       dictionary;
+    object      ITHACAPODdict;
+}
+
+patchInt 6;
+patchExt 7;
+
+
+
+
+// ************************************************************************* //
diff --git a/unitTests/ITHACAsurfacetools/system/PDRblockMeshDict b/unitTests/ITHACAsurfacetools/system/PDRblockMeshDict
new file mode 100644
index 000000000..b609e2f7b
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/system/PDRblockMeshDict
@@ -0,0 +1,61 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  v2106                                 |
+|   \\  /    A nd           | Website:  www.openfoam.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      PDRblockMeshDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+scale   0.1;
+
+x
+{
+    points  (0 1);
+    nCells  (20);
+    ratios  (1);
+}
+
+y
+{
+    points  (0 1);
+    nCells  (20);
+    ratios  (1);
+}
+
+z
+{
+    points  (0 0.1);
+    nCells  (1);
+    ratios  (1);
+}
+
+
+boundary
+(
+    movingWall
+    {
+        type  wall;
+        faces (3);
+    }
+    fixedWalls
+    {
+        type  wall;
+        faces (0 1 2);
+    }
+    frontAndBack
+    {
+        type  empty;
+        faces (4 5);
+    }
+);
+
+
+// ************************************************************************* //
diff --git a/unitTests/ITHACAsurfacetools/system/blockMeshDict b/unitTests/ITHACAsurfacetools/system/blockMeshDict
new file mode 100644
index 000000000..468f781eb
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/system/blockMeshDict
@@ -0,0 +1,124 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  v2106                                 |
+|   \\  /    A nd           | Website:  www.openfoam.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      blockMeshDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+scale   0.1;
+
+vertices
+(
+    (0 0 0)
+    (1 0 0)
+    (1 1 0)
+    (0 1 0)
+    (0 0 0.1)
+    (1 0 0.1)
+    (1 1 0.1)
+    (0 1 0.1)
+    (1 0 0)
+    (2 0 0)
+    (2 1 0)
+    (1 1 0)
+    (1 0 0.1)
+    (2 0 0.1)
+    (2 1 0.1)
+    (1 1 0.1)
+);
+
+blocks
+(
+    hex (0 1 2 3 4 5 6 7) (10 10 1) simpleGrading (1 1 1)
+    hex (8 9 10 11 12 13 14 15) (10 20 1) simpleGrading (1 1 1)
+);
+
+edges
+(
+);
+
+boundary
+(
+    inlet
+    {
+    	type patch;
+    	faces
+    	(
+            (0 4 7 3)
+    	);
+    }
+    outlet
+    {
+    	type patch;
+    	faces
+    	(
+            (10 14 13 9)
+    	);
+    }
+    fixedWallsLeft
+    {
+        type wall;
+        faces
+        (
+            (1 5 4 0)
+            (3 7 6 2)
+        );
+    }
+    fixedWallsRight
+    {
+        type wall;
+        faces
+        (
+            (9 13 12 8)
+            (11 15 14 10)
+        );
+    }
+    frontAndBackLeft
+    {
+        type empty;
+        faces
+        (
+            (0 3 2 1)
+            (4 5 6 7)
+        );
+    }
+    frontAndBackRight
+    {
+        type empty;
+        faces
+        (
+            (8 11 10 9)
+            (12 13 14 15)
+        );
+    }
+    left
+    {
+    	type cyclicAMI;
+    	neighbourPatch right;
+    	faces
+    	(
+    	    (2 6 5 1)
+    	);
+    }
+    right
+    {
+    	type cyclicAMI;
+    	neighbourPatch left;
+    	faces
+    	(
+    	    (8 12 15 11)
+    	);
+    }
+);
+
+
+// ************************************************************************* //
diff --git a/unitTests/ITHACAsurfacetools/system/controlDict b/unitTests/ITHACAsurfacetools/system/controlDict
new file mode 100644
index 000000000..49e8514d9
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/system/controlDict
@@ -0,0 +1,48 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  v2106                                 |
+|   \\  /    A nd           | Website:  www.openfoam.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      controlDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+application     icoFoam;
+
+startFrom       startTime;
+
+startTime       0;
+
+stopAt          endTime;
+
+endTime         0.05;
+
+deltaT          0.0001;
+
+writeControl    runTime;
+
+writeInterval   0.0015;
+
+purgeWrite      0;
+
+writeFormat     ascii;
+
+writePrecision  6;
+
+writeCompression off;
+
+timeFormat      general;
+
+timePrecision   6;
+
+runTimeModifiable true;
+
+
+// ************************************************************************* //
diff --git a/unitTests/ITHACAsurfacetools/system/decomposeParDict b/unitTests/ITHACAsurfacetools/system/decomposeParDict
new file mode 100644
index 000000000..1516a7179
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/system/decomposeParDict
@@ -0,0 +1,27 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  v2106                                 |
+|   \\  /    A nd           | Website:  www.openfoam.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      decomposeParDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+numberOfSubdomains  9;
+
+method  hierarchical;
+
+coeffs
+{
+    n   (3 3 1);
+}
+
+
+// ************************************************************************* //
diff --git a/unitTests/ITHACAsurfacetools/system/fvSchemes b/unitTests/ITHACAsurfacetools/system/fvSchemes
new file mode 100644
index 000000000..04699f23a
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/system/fvSchemes
@@ -0,0 +1,51 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  v2106                                 |
+|   \\  /    A nd           | Website:  www.openfoam.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      fvSchemes;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+ddtSchemes
+{
+    default         Euler;
+}
+
+gradSchemes
+{
+    default         Gauss linear;
+    grad(p)         Gauss linear;
+}
+
+divSchemes
+{
+    default         none;
+    div(phi,U)      Gauss linear;
+    div(phi,s)      Gauss linearUpwind grad(U);
+}
+
+laplacianSchemes
+{
+    default         Gauss linear orthogonal;
+}
+
+interpolationSchemes
+{
+    default         linear;
+}
+
+snGradSchemes
+{
+    default         orthogonal;
+}
+
+
+// ************************************************************************* //
diff --git a/unitTests/ITHACAsurfacetools/system/fvSolution b/unitTests/ITHACAsurfacetools/system/fvSolution
new file mode 100644
index 000000000..2ef1c5025
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/system/fvSolution
@@ -0,0 +1,59 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  v2106                                 |
+|   \\  /    A nd           | Website:  www.openfoam.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      fvSolution;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+solvers
+{
+    p
+    {
+        solver          PCG;
+        preconditioner  DIC;
+        tolerance       1e-06;
+        relTol          0.05;
+    }
+
+    pFinal
+    {
+        $p;
+        relTol          0;
+    }
+
+    U
+    {
+        solver          smoothSolver;
+        smoother        symGaussSeidel;
+        tolerance       1e-05;
+        relTol          0;
+    }
+    
+    s
+    {
+        solver          smoothSolver;
+        smoother        symGaussSeidel;
+        tolerance       1e-05;
+        relTol          0;
+    }
+}
+
+PISO
+{
+    nCorrectors     2;
+    nNonOrthogonalCorrectors 0;
+    pRefCell        0;
+    pRefValue       0;
+}
+
+
+// ************************************************************************* //
diff --git a/unitTests/ITHACAsurfacetools/system/setFieldsDict b/unitTests/ITHACAsurfacetools/system/setFieldsDict
new file mode 100644
index 000000000..8e501e2b3
--- /dev/null
+++ b/unitTests/ITHACAsurfacetools/system/setFieldsDict
@@ -0,0 +1,35 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  v2106                                 |
+|   \\  /    A nd           | Website:  www.openfoam.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      setFieldsDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+defaultFieldValues
+(
+    volVectorFieldValue U (0 0 0)
+);
+
+regions
+(
+    boxToCell
+    {
+        box (0 0 0) (0.1 0.1 0.01);
+        fieldValues
+        (
+            volVectorFieldValue U (1 0 0)
+        );
+    }
+);
+
+
+// ************************************************************************* //

From e2d71a916651197a92377d7f559e329f6ae0cae1 Mon Sep 17 00:00:00 2001
From: Valentin Resseguier <valentin.resseguier@scalian.com>
Date: Thu, 31 Aug 2023 13:47:24 +0200
Subject: [PATCH 26/59] Define the symetric diffusive term projection

---
 src/ITHACA_FOMPROBLEMS/steadyNS/steadyNS.C | 31 ++++++++++++++++++++++
 src/ITHACA_FOMPROBLEMS/steadyNS/steadyNS.H | 12 +++++++++
 2 files changed, 43 insertions(+)

diff --git a/src/ITHACA_FOMPROBLEMS/steadyNS/steadyNS.C b/src/ITHACA_FOMPROBLEMS/steadyNS/steadyNS.C
index 8799c149b..7abab9cb6 100644
--- a/src/ITHACA_FOMPROBLEMS/steadyNS/steadyNS.C
+++ b/src/ITHACA_FOMPROBLEMS/steadyNS/steadyNS.C
@@ -889,6 +889,37 @@ Eigen::MatrixXd steadyNS::diffusive_term(label NUmodes, label NPmodes,
     return B_matrix;
 }
 
+Eigen::MatrixXd steadyNS::diffusive_term_sym(label NUmodes, label NPmodes,
+        label NSUPmodes)
+{
+    label Bsize = NUmodes + NSUPmodes + liftfield.size();
+    Eigen::MatrixXd B_matrix;
+    B_matrix.resize(Bsize, Bsize);
+
+    // Project everything
+    for (label i = 0; i < Bsize; i++)
+    {
+        for (label j = 0; j < Bsize; j++)
+        {
+            B_matrix(i, j) = - fvc::domainIntegrate(fvc::grad(L_U_SUPmodes[i])
+                                        && fvc::grad(L_U_SUPmodes[j])).value();
+        }
+    }
+
+    if (Pstream::parRun())
+    {
+        reduce(B_matrix, sumOp<Eigen::MatrixXd>());
+    }
+
+    if (Pstream::master())
+    {
+        ITHACAstream::SaveDenseMatrix(B_matrix, "./ITHACAoutput/Matrices/",
+                                      "B_" + name(liftfield.size()) + "_" + name(NUmodes) + "_" + name(NSUPmodes));
+    }
+
+    return B_matrix;
+}
+
 Eigen::MatrixXd steadyNS::pressure_gradient_term(label NUmodes, label NPmodes,
         label NSUPmodes)
 {
diff --git a/src/ITHACA_FOMPROBLEMS/steadyNS/steadyNS.H b/src/ITHACA_FOMPROBLEMS/steadyNS/steadyNS.H
index f5f7d0a79..d158c549c 100644
--- a/src/ITHACA_FOMPROBLEMS/steadyNS/steadyNS.H
+++ b/src/ITHACA_FOMPROBLEMS/steadyNS/steadyNS.H
@@ -385,6 +385,18 @@ class steadyNS: public reductionProblem
         ///
         Eigen::MatrixXd diffusive_term(label NUmodes, label NPmodes, label NSUPmodes);
 
+        //--------------------------------------------------------------------------
+        //  Projection Methods Momentum Equation
+        /// Symetric diffusive Term
+        ///
+        /// @param[in]  NUmodes    The number of velocity modes.
+        /// @param[in]  NPmodes    The number of pressure modes.
+        /// @param[in]  NSUPmodes  The number of supremizer modes.
+        ///
+        /// @return     reduced matrix in Eigen::MatrixXd format for the diffusion term.
+        ///
+        Eigen::MatrixXd diffusive_term_sym(label NUmodes, label NPmodes, label NSUPmodes);
+
         //--------------------------------------------------------------------------
         /// Gradient of pressure
         ///

From b43354e668644d2b4c2c743e5200e647ba883679 Mon Sep 17 00:00:00 2001
From: carpemonf <carpemonf@gmail.com>
Date: Wed, 6 Sep 2023 07:46:48 +0200
Subject: [PATCH 27/59] Fix UnsteadyNSTurb FOM solution

Update and passing of fields fixed. UEqn and pEqn files changed to match OpenFOAM ones (v2212).
---
 .../UnsteadyNSTurb/UnsteadyNSTurb.C           | 37 ++++++++++++-------
 .../UnsteadyNSTurb/UnsteadyNSTurb.H           |  9 +++++
 .../UnsteadyNSTurb/createFields.H             |  7 ++--
 .../UnsteadyNSTurb/createUfIfPresent.H        | 20 ++++++++++
 src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/pEqn.H  | 29 +++++++++++----
 5 files changed, 76 insertions(+), 26 deletions(-)
 create mode 100644 src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/createUfIfPresent.H

diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UnsteadyNSTurb.C b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UnsteadyNSTurb.C
index 32b5e1d8d..4f39df00e 100644
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UnsteadyNSTurb.C
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UnsteadyNSTurb.C
@@ -62,6 +62,7 @@ UnsteadyNSTurb::UnsteadyNSTurb(int argc, char* argv[])
                   )
               );
 #include "createFields.H"
+#include "createUfIfPresent.H"
 #include "createFvOptions.H"
     ITHACAdict = new IOdictionary
     (
@@ -114,38 +115,45 @@ void UnsteadyNSTurb::truthSolve(List<scalar> mu_now, std::string& offlinepath)
 #include "initContinuityErrs.H"
     fv::options& fvOptions = _fvOptions();
     pimpleControl& pimple = _pimple();
-    volScalarField p = _p();
-    volVectorField U = _U();
-    volScalarField nut = _nut();
+    volScalarField& p = _p();
+    volVectorField& U = _U();
+    volScalarField& nut = _nut();
     IOMRFZoneList& MRF = _MRF();
     singlePhaseTransportModel& laminarTransport = _laminarTransport();
     instantList Times = runTime.times();
+    label& pRefCell = _pRefCell;
+    scalar& pRefValue = _pRefValue;
+
+    mesh.setFluxRequired(p.name());
+
     runTime.setEndTime(finalTime);
-    // Perform a TruthSolve
     runTime.setTime(Times[1], 1);
     runTime.setDeltaT(timeStep);
-    nextWrite = startTime;
+    nextWrite = startTime + writeEvery;
+
     // Initialize Nsnapshots
     label nsnapshots = 0;
 
+
     // Start the time loop
     while (runTime.run())
     {
-#include "readTimeControls.H"
-#include "CourantNo.H"
-#include "setDeltaT.H"
-        runTime.setEndTime(finalTime + timeStep);
+        #include "readTimeControls.H"
+        #include "CourantNo.H"
+        #include "setDeltaT.H"
+
+        ++runTime;
+
         Info << "Time = " << runTime.timeName() << nl << endl;
 
         // --- Pressure-velocity PIMPLE corrector loop
         while (pimple.loop())
         {
-#include "UEqn.H"
-
+            #include "UEqn.H"
             // --- Pressure corrector loop
             while (pimple.correct())
             {
-#include "pEqn.H"
+                #include "pEqn.H"
             }
 
             if (pimple.turbCorr())
@@ -153,6 +161,7 @@ void UnsteadyNSTurb::truthSolve(List<scalar> mu_now, std::string& offlinepath)
                 laminarTransport.correct();
                 turbulence->correct();
             }
+
         }
 
         Info << "ExecutionTime = " << runTime.elapsedCpuTime() << " s"
@@ -164,6 +173,8 @@ void UnsteadyNSTurb::truthSolve(List<scalar> mu_now, std::string& offlinepath)
             nsnapshots += 1;
             // Produces error when uncommented
             // volScalarField nut = turbulence->nut().ref();
+            nut = turbulence->nut();
+
             ITHACAstream::exportSolution(U, name(counter), offlinepath);
             ITHACAstream::exportSolution(p, name(counter), offlinepath);
             ITHACAstream::exportSolution(nut, name(counter), offlinepath);
@@ -184,8 +195,6 @@ void UnsteadyNSTurb::truthSolve(List<scalar> mu_now, std::string& offlinepath)
                 mu_samples(mu_samples.rows() - 1, i + 1) = mu_now[i];
             }
         }
-
-        runTime++;
     }
 
     // Resize to Unitary if not initialized by user (i.e. non-parametric problem)
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UnsteadyNSTurb.H b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UnsteadyNSTurb.H
index f84750b7b..a78044dd8 100755
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UnsteadyNSTurb.H
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UnsteadyNSTurb.H
@@ -157,6 +157,15 @@ class UnsteadyNSTurb: public unsteadyNS
         /// Eddy viscosity field
         autoPtr<volScalarField> _nut;
 
+        /// Face velocity field
+        autoPtr<surfaceVectorField> _Uf;
+
+        /// Pressure reference cell
+        label _pRefCell;
+
+        /// Pressure reference value
+        scalar _pRefValue;
+
         //--------------------------------------------------------------------------
         /// @brief      bt added matrix for the turbulence treatement
         ///
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/createFields.H b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/createFields.H
index aab9ede40..ec304d455 100755
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/createFields.H
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/createFields.H
@@ -76,10 +76,9 @@ _nut = autoPtr<volScalarField>
 
 #include "createPhi.H"
 
-
-label pRefCell = 0;
-scalar pRefValue = 0.0;
-setRefCell(p, mesh.solutionDict().subDict("SIMPLE"), pRefCell, pRefValue);
+_pRefCell = 0;
+_pRefValue = 0.0;
+setRefCell(p, mesh.solutionDict().subDict("PIMPLE"), _pRefCell, _pRefValue);
 
 _laminarTransport = autoPtr<singlePhaseTransportModel>
                     (
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/createUfIfPresent.H b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/createUfIfPresent.H
new file mode 100644
index 000000000..a4b819fe3
--- /dev/null
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/createUfIfPresent.H
@@ -0,0 +1,20 @@
+if (mesh.dynamic())
+{
+    Info<< "Constructing face velocity Uf\n" << endl;
+
+    _Uf.reset
+    (
+        new surfaceVectorField
+        (
+            IOobject
+            (
+                "Uf",
+                runTime.timeName(),
+                mesh,
+                IOobject::READ_IF_PRESENT,
+                IOobject::AUTO_WRITE
+            ),
+            fvc::interpolate(U)
+        )
+    );
+}
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/pEqn.H b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/pEqn.H
index 443200815..b64152168 100755
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/pEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/pEqn.H
@@ -24,17 +24,24 @@
 \*---------------------------------------------------------------------------*/
 // Solve pressure equation
 volScalarField rAU(1.0 / UEqn.A());
-volVectorField HbyA(constrainHbyA(rAU* UEqn.H(), U, p));
-surfaceScalarField phiHbyA
-(
-    "phiHbyA",
-    fvc::flux(HbyA)
-    + fvc::interpolate(rAU)*fvc::ddtCorr(U, phi)
-    );
+
+volVectorField HbyA(constrainHbyA(rAU * UEqn.H(), U, p));
+surfaceScalarField phiHbyA("phiHbyA", fvc::flux(HbyA));
+
+if (pimple.ddtCorr())
+{
+    phiHbyA += MRF.zeroFilter(fvc::interpolate(rAU) * fvc::ddtCorr(U, phi, _Uf));
+}
+
 
 MRF.makeRelative(phiHbyA);
 
-adjustPhi(phiHbyA, U, p);
+if (p.needReference())
+{
+    fvc::makeRelative(phiHbyA, U);
+    adjustPhi(phiHbyA, U, p);
+    fvc::makeAbsolute(phiHbyA, U);
+}
 
 tmp<volScalarField> rAtU(rAU);
 
@@ -79,3 +86,9 @@ p.relax();
 U = HbyA - rAtU() * fvc::grad(p);
 U.correctBoundaryConditions();
 fvOptions.correct(U);
+
+// Correct Uf if the mesh is moving
+fvc::correctUf(_Uf, U, phi);
+
+// Make the fluxes relative to the mesh motion
+fvc::makeRelative(phi, U);

From 47a205b2b820bd83677f0608088d65702c994a6e Mon Sep 17 00:00:00 2001
From: carpemonf <carpemonf@gmail.com>
Date: Wed, 6 Sep 2023 07:51:32 +0200
Subject: [PATCH 28/59] Remove extra line break

---
 src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UnsteadyNSTurb.C | 2 --
 1 file changed, 2 deletions(-)

diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UnsteadyNSTurb.C b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UnsteadyNSTurb.C
index 4f39df00e..6f8ff894e 100644
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UnsteadyNSTurb.C
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UnsteadyNSTurb.C
@@ -131,10 +131,8 @@ void UnsteadyNSTurb::truthSolve(List<scalar> mu_now, std::string& offlinepath)
     runTime.setDeltaT(timeStep);
     nextWrite = startTime + writeEvery;
 
-    // Initialize Nsnapshots
     label nsnapshots = 0;
 
-
     // Start the time loop
     while (runTime.run())
     {

From ea5d0f34c12155ad07f4a963616e5538bb51ff5c Mon Sep 17 00:00:00 2001
From: carpemonf <carpemonf@gmail.com>
Date: Wed, 6 Sep 2023 12:27:25 +0200
Subject: [PATCH 29/59] Fixing unsteady correction term for version
 compatibility

---
 src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/pEqn.H | 13 ++++++-------
 1 file changed, 6 insertions(+), 7 deletions(-)

diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/pEqn.H b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/pEqn.H
index b64152168..b374b900e 100755
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/pEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/pEqn.H
@@ -26,13 +26,12 @@
 volScalarField rAU(1.0 / UEqn.A());
 
 volVectorField HbyA(constrainHbyA(rAU * UEqn.H(), U, p));
-surfaceScalarField phiHbyA("phiHbyA", fvc::flux(HbyA));
-
-if (pimple.ddtCorr())
-{
-    phiHbyA += MRF.zeroFilter(fvc::interpolate(rAU) * fvc::ddtCorr(U, phi, _Uf));
-}
-
+surfaceScalarField phiHbyA
+(
+    "phiHbyA",
+    fvc::flux(HbyA)
+  + MRF.zeroFilter(fvc::interpolate(rAU)*fvc::ddtCorr(U, phi, _Uf))
+);
 
 MRF.makeRelative(phiHbyA);
 

From cb6e85800f2b64ef50ef51a5337a13cd6b21c3c8 Mon Sep 17 00:00:00 2001
From: vressegu <valentin.resseguier@inrae.fr>
Date: Wed, 3 Jan 2024 13:18:45 +0100
Subject: [PATCH 30/59] specialization of getMassMatrix for tensor

---
 src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
index 794b6857e..f75f2951f 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
@@ -116,6 +116,10 @@ template Eigen::MatrixXd getMassMatrix(
     PtrList<GeometricField<vector, fvPatchField, volMesh>>& modes, label Nmodes,
     bool consider_volumes);
 
+template Eigen::MatrixXd getMassMatrix(
+    PtrList<GeometricField<tensor, fvPatchField, volMesh>>& modes, label Nmodes,
+    bool consider_volumes);
+
 template<class Type, template<class> class PatchField, class GeoMesh>
 Eigen::VectorXd getMassMatrixFV(
     GeometricField<Type, PatchField, GeoMesh>& snapshot)
@@ -131,6 +135,8 @@ template Eigen::VectorXd getMassMatrixFV(
     GeometricField<scalar, fvPatchField, volMesh>& snapshot);
 template Eigen::VectorXd getMassMatrixFV(
     GeometricField<vector, fvPatchField, volMesh>& snapshot);
+template Eigen::VectorXd getMassMatrixFV(
+    GeometricField<tensor, fvPatchField, volMesh>& snapshot);
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 Eigen::VectorXd getCoeffs(GeometricField<Type, PatchField, GeoMesh>&

From dc54db43db590290e00aacfa9c563c31052473e8 Mon Sep 17 00:00:00 2001
From: vressegu <valentin.resseguier@inrae.fr>
Date: Wed, 3 Jan 2024 13:21:28 +0100
Subject: [PATCH 31/59] cross mass matrix between two PtrLists

---
 .../ITHACAutilities/ITHACAcoeffsMass.C        | 65 +++++++++++++++++++
 .../ITHACAutilities/ITHACAcoeffsMass.H        | 19 ++++++
 2 files changed, 84 insertions(+)

diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
index f75f2951f..0a131b3cf 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
@@ -120,6 +120,71 @@ template Eigen::MatrixXd getMassMatrix(
     PtrList<GeometricField<tensor, fvPatchField, volMesh>>& modes, label Nmodes,
     bool consider_volumes);
 
+template<class Type, template<class> class PatchField, class GeoMesh>
+Eigen::MatrixXd getMassMatrix(
+    PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes2, label Nmodes,
+    bool consider_volumes)
+{
+    label Msize,Msize2;
+    if (Nmodes == 0)
+    {
+        Msize =  modes.size();
+        Msize2 =  modes2.size();
+    }
+    else
+    {
+        Msize = Nmodes;
+        Msize2 = Nmodes;
+    }
+    M_Assert(modes.size() >= Msize,
+             "The Number of requested modes is larger then the available quantity.");
+    M_Assert(modes2.size() >= Msize2,
+             "The Number of requested modes is larger then the available quantity.");
+
+    Eigen::MatrixXd F = Foam2Eigen::PtrList2Eigen(modes);
+    Eigen::MatrixXd F2 = Foam2Eigen::PtrList2Eigen(modes2);
+    Eigen::MatrixXd M;
+
+    if (consider_volumes)
+    {
+        Eigen::VectorXd V = getMassMatrixFV(modes[0]);
+        M = F.transpose().topRows(Msize) * V.asDiagonal() * F2.leftCols(Msize2);
+    }
+    else
+    {
+        M = F.transpose().topRows(Msize) * F2.leftCols(Msize2);
+    }
+
+    if (Pstream::parRun())
+    {
+        reduce(M, sumOp<Eigen::MatrixXd>());
+    }
+
+    return M;
+}
+
+template Eigen::MatrixXd getMassMatrix(
+    PtrList<GeometricField<scalar, fvPatchField, volMesh>>& modes,
+    PtrList<GeometricField<scalar, fvPatchField, volMesh>>& modes2, label Nmodes,
+    bool consider_volumes);
+
+template Eigen::MatrixXd getMassMatrix(
+    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>>& modes,
+    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>>& modes2,
+    label Nmodes,
+    bool consider_volumes = false);
+
+template Eigen::MatrixXd getMassMatrix(
+    PtrList<GeometricField<vector, fvPatchField, volMesh>>& modes,
+    PtrList<GeometricField<vector, fvPatchField, volMesh>>& modes2, label Nmodes,
+    bool consider_volumes);
+
+template Eigen::MatrixXd getMassMatrix(
+    PtrList<GeometricField<tensor, fvPatchField, volMesh>>& modes,
+    PtrList<GeometricField<tensor, fvPatchField, volMesh>>& modes2, label Nmodes,
+    bool consider_volumes);
+
 template<class Type, template<class> class PatchField, class GeoMesh>
 Eigen::VectorXd getMassMatrixFV(
     GeometricField<Type, PatchField, GeoMesh>& snapshot)
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.H b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.H
index ee374f3fb..6e6519517 100755
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.H
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.H
@@ -96,6 +96,25 @@ Eigen::MatrixXd getMassMatrix(PtrList<GeometricField<Type, PatchField, GeoMesh>>
                               fields, label nModes = 0,
                               bool consider_volumes = true);
 
+//-----------------------------------------------------------------------------
+/// Gets the cross mass matrix using the eigen routine
+///
+/// @param[in]  fields            The openFoam fields
+/// @param[in]  consider_volumes  True if you want to consider the volumes
+///
+/// @tparam     Type        vector or scalar.
+/// @tparam     PatchField  fvPatchField or fvsPatchField.
+/// @tparam     GeoMesh     volMesh or surfaceMesh.
+///
+/// @return     The cross mass matrix eigen.
+///
+template<class Type, template<class> class PatchField, class GeoMesh>
+Eigen::MatrixXd getMassMatrix(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
+                              fields,
+                              PtrList<GeometricField<Type, PatchField, GeoMesh>>&
+                              fields2, label nModes = 0,
+                              bool consider_volumes = true);
+
 //--------------------------------------------------------------------------
 /// Gets a vector containing the volumes of each cell of the mesh.
 ///

From ba81626421377f691676fed3834214995169bc79 Mon Sep 17 00:00:00 2001
From: vressegu <valentin.resseguier@inrae.fr>
Date: Wed, 3 Jan 2024 19:06:17 +0100
Subject: [PATCH 32/59] sparse volume matrix for massMatrix

To alleviate RAM issue with large meshes
---
 src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C | 14 ++++++++++++--
 1 file changed, 12 insertions(+), 2 deletions(-)

diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
index 0a131b3cf..5e64cae91 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
@@ -88,7 +88,12 @@ Eigen::MatrixXd getMassMatrix(
     if (consider_volumes)
     {
         Eigen::VectorXd V = getMassMatrixFV(modes[0]);
-        M = F.transpose().topRows(Msize) * V.asDiagonal() * F.leftCols(Msize);
+        Eigen::SparseMatrix<double> Vmat(V.size(),V.size());
+        for (int i=0; i<V.size(); i++)
+        {
+          Vmat.insert(i,i)=V(i);
+        }
+        M = F.transpose().topRows(Msize) * Vmat * F.leftCols(Msize);
     }
     else
     {
@@ -149,7 +154,12 @@ Eigen::MatrixXd getMassMatrix(
     if (consider_volumes)
     {
         Eigen::VectorXd V = getMassMatrixFV(modes[0]);
-        M = F.transpose().topRows(Msize) * V.asDiagonal() * F2.leftCols(Msize2);
+        Eigen::SparseMatrix<double> Vmat(V.size(),V.size());
+        for (int i=0; i<V.size(); i++)
+        {
+          Vmat.insert(i,i)=V(i);
+        }
+        M = F.transpose().topRows(Msize) * Vmat * F2.leftCols(Msize2);
     }
     else
     {

From 2774c7141278125fa7f6ba505250cdaa23d74c68 Mon Sep 17 00:00:00 2001
From: vressegu <valentin.resseguier@inrae.fr>
Date: Thu, 4 Jan 2024 13:42:51 +0100
Subject: [PATCH 33/59] use loop instead of sparse matrix

---
 src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C | 12 ++++--------
 1 file changed, 4 insertions(+), 8 deletions(-)

diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
index 5e64cae91..76a09ac03 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
@@ -83,17 +83,15 @@ Eigen::MatrixXd getMassMatrix(
     M_Assert(modes.size() >= Msize,
              "The Number of requested modes is larger then the available quantity.");
     Eigen::MatrixXd F = Foam2Eigen::PtrList2Eigen(modes);
-    Eigen::MatrixXd M;
+    Eigen::MatrixXd M = Eigen::MatrixXd::Zero(Msize,Msize);
 
     if (consider_volumes)
     {
         Eigen::VectorXd V = getMassMatrixFV(modes[0]);
-        Eigen::SparseMatrix<double> Vmat(V.size(),V.size());
         for (int i=0; i<V.size(); i++)
         {
-          Vmat.insert(i,i)=V(i);
+          M += V(i) * F.transpose().topRows(Msize).col(i) * F.leftCols(Msize).row(i);
         }
-        M = F.transpose().topRows(Msize) * Vmat * F.leftCols(Msize);
     }
     else
     {
@@ -149,17 +147,15 @@ Eigen::MatrixXd getMassMatrix(
 
     Eigen::MatrixXd F = Foam2Eigen::PtrList2Eigen(modes);
     Eigen::MatrixXd F2 = Foam2Eigen::PtrList2Eigen(modes2);
-    Eigen::MatrixXd M;
+    Eigen::MatrixXd M = Eigen::MatrixXd::Zero(Msize,Msize2);
 
     if (consider_volumes)
     {
         Eigen::VectorXd V = getMassMatrixFV(modes[0]);
-        Eigen::SparseMatrix<double> Vmat(V.size(),V.size());
         for (int i=0; i<V.size(); i++)
         {
-          Vmat.insert(i,i)=V(i);
+          M += V(i) * F.transpose().topRows(Msize).col(i) * F2.leftCols(Msize2).row(i);
         }
-        M = F.transpose().topRows(Msize) * Vmat * F2.leftCols(Msize2);
     }
     else
     {

From a50be89a0b9f14aca3a7e30eac995478193506e4 Mon Sep 17 00:00:00 2001
From: Matthieu Petit <matthieu.petit@scalian.com>
Date: Fri, 1 Mar 2024 16:12:37 +0100
Subject: [PATCH 34/59] Usefool changes to HyperReduction class for
 compatibility with RedLum v1.0

---
 src/ITHACA_HR/hyperReduction.H           | 27 +++++++--
 src/ITHACA_HR/hyperReduction.templates.H | 72 +++++++++++++++++-------
 2 files changed, 74 insertions(+), 25 deletions(-)

diff --git a/src/ITHACA_HR/hyperReduction.H b/src/ITHACA_HR/hyperReduction.H
index 6411b4338..e7e686573 100644
--- a/src/ITHACA_HR/hyperReduction.H
+++ b/src/ITHACA_HR/hyperReduction.H
@@ -40,8 +40,6 @@ SourceFiles
 #include <set>
 #include "redsvd"
 
-Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
-
 // TODO uniform style for separating offline and onlie stages
 template <typename... SnapshotsLists>
 class HyperReduction
@@ -78,7 +76,26 @@ public:
                    Eigen::VectorXi initialSeeds,
                    word problemName,
                    SnapshotsLists &&...snapshotsLists);
-    
+
+
+      //----------------------------------------------------------------------
+    /// @brief      Construct HyperReduction class, interpolation-based.`SnapshotsLists` is a variadic argument of PtrLists of fields e.g. for incompressible Navier-Stokes PtrList<volVectorField>, PtrList<volScalarField> for velocity and pressure.
+    ///
+    /// @param[in]  n_modes           dimension of the HR basis
+    /// @param[in]  n_nodes           number of nodes
+    /// @param[in]  problemName       name of the function to be hyper-reduced
+    /// @param[in]  modes             lists of modes
+    ///
+    HyperReduction(label n_modes,
+                   label n_nodes, 
+                   label n_cells, 
+                   word folderMethod, 
+                   word problemName);//, 
+                //    unsigned int vectorialDim); 
+
+
+    Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
+                    
     // ITHACA parameters dict
     ITHACAparameters* para;
 
@@ -181,7 +198,7 @@ public:
     
     /// Submeshes
     autoPtr<volVectorField> submesh_field;
-    
+
     //----------------------------------------------------------------------
     /// @brief      Methods implemented: 'GappyDEIM'  from "DEIM, Chaturantabut, Saifon, and Danny C. Sorensen. "Nonlinear model reduction via discrete empirical interpolation." SIAM Journal on Scientific Computing 32.5 (2010): 2737-2764" and "GNAT, Carlberg, Kevin, et al. "The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows." Journal of Computational Physics 242 (2013): 623-647.". Quasi-optimal point selection algorithm 'SOPT' and optimal point selection 'SOPTE' from "Lauzon, Jessica T., Siu Wun Cheung, Yeonjong Shin, Youngsoo Choi, Dylan Matthew Copeland, and Kevin Huynh. "S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models." arXiv preprint arXiv:2203.16494 (2022).""
     ///
@@ -315,7 +332,7 @@ public:
     /// @param[in]  layers          projector into interpolation nodes
     /// @param[in]  mesh            matrix to restrict and invert
     ///
-    void generateSubmesh(label layers, fvMesh &mesh);
+    void generateSubmesh(label layers, const fvMesh &mesh);
 
     //----------------------------------------------------------------------
     /// @brief      Get local indices in the submesh from indices in the global ones
diff --git a/src/ITHACA_HR/hyperReduction.templates.H b/src/ITHACA_HR/hyperReduction.templates.H
index 90c37cc9a..51e8e9b56 100644
--- a/src/ITHACA_HR/hyperReduction.templates.H
+++ b/src/ITHACA_HR/hyperReduction.templates.H
@@ -31,6 +31,11 @@ License
 #ifndef hyperReduction_templates_H
 #define hyperReduction_templates_H
 
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wold-style-cast"
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+#pragma GCC diagnostic ignored "-Wreorder"
+
 #include "hyperReduction.H"
 
 // TODO increase modularity to avoid heavy compiling costs
@@ -95,9 +100,38 @@ HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
   Info << "Number of boundary cells: " << n_boundary_cells << endl;
 }
 
+// Template function constructor
+template <typename... SnapshotsLists>
+HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
+                                                  label n_nodes,
+                                                  label nbcells, 
+                                                  word folderMethod, 
+                                                  word problemName)//,
+                                                  // unsigned int vectorialDim)
+    : n_modes{n_modes},
+      n_nodes{n_nodes},
+      n_cells{nbcells},
+      folderMethod{folderMethod},
+      problemName{problemName}
+      // vectorial_dim{vectorialDim}
+{
+  para = ITHACAparameters::getInstance();
+  mkDir(folderMethod);
+
+  // folderProblem = "ITHACAoutput/" + problemName;
+  // mkDir(folderProblem);
+
+  Info << "The number of cells is: " << n_cells << endl;
+  n_snapshots = n_modes;
+  Info << "The number of modes is: " << n_modes << endl;
+}
+
+
 // Using the Eigen library, using the SVD decomposition method to solve the
 // matrix pseudo-inverse, the default error er is 0
-Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er) {
+template <typename... SnapshotsLists>
+Eigen::MatrixXd 
+HyperReduction<SnapshotsLists...>::pinv_eigen_based(Eigen::MatrixXd &origin, const float er) {
   // perform svd decomposition
   Eigen::JacobiSVD<Eigen::MatrixXd> svd_holder(origin, Eigen::ComputeThinU | Eigen::ComputeThinV);
   // Build SVD decomposition results
@@ -109,7 +143,7 @@ Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er) {
   Eigen::MatrixXd S(V.cols(), U.cols());
   S.setZero();
 
-  for (unsigned int i = 0; i < D.size(); ++i) {
+  for (int i = 0; i < D.size(); ++i) {
 
     if (D(i, 0) > er) {
       S(i, i) = 1 / D(i, 0);
@@ -370,9 +404,8 @@ void HyperReduction<SnapshotsLists...>::saveModes(SnapshotsList sList, Eigen::Ma
 template <typename... SnapshotsLists>
 void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights)
 {
-  methodName = "GappyDEIM";
-  folderMethod = "ITHACAoutput/" + problemName + "/" + methodName;
-  mkDir(folderMethod);
+  // methodName = "GappyDEIM";
+  // folderMethod = "ITHACAoutput/" + problemName + "/" + methodName;
 
   normalizingWeights = weights;
 
@@ -391,7 +424,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
 
     Eigen::VectorXd mp_not_mask = Eigen::VectorXd::Constant(n_cells * vectorial_dim, 1);
     std::set<label> nodePointsSet;
-
+    double max;
     // set initialSeeds
     if (initialSeeds.rows() > 0)
     {
@@ -420,7 +453,6 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
         Eigen::VectorXd c;
         Eigen::VectorXd r;
         label ind_max, c1;
-        double max;
 
         for (int i = 1; i <= nit; i++)
         {
@@ -487,10 +519,9 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
               << endl;
 
         label ind_max, c1;
-        double max;
         Eigen::MatrixXd V = snapshotsModes.leftCols(n_modes);
 
-        for (unsigned int ith_node = 0; ith_node < na; ith_node++)
+        for (int ith_node = 0; ith_node < na; ith_node++)
         {
           if (P.cols() > 0)
           {
@@ -524,7 +555,6 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
               << endl;
 
         label ind_max, c1;
-        double max;
         Eigen::MatrixXd A;
         Eigen::VectorXd b;
         Eigen::VectorXd c;
@@ -534,7 +564,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
         max = (reshapeMat* (mp_not_mask.asDiagonal()*snapshotsModes.leftCols(n_modes)).rowwise().lpNorm<2>().array().square().matrix()).maxCoeff(&ind_max, &c1);
         updateNodes(P, ind_max, mp_not_mask);
 
-        for (unsigned int ith_node = 1; ith_node < na; ith_node++)
+        for (int ith_node = 1; ith_node < na; ith_node++)
         {
           if (ith_node<n_modes)
           {
@@ -558,7 +588,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
 
             Eigen::VectorXd results(n_cells);
 
-            for (unsigned int ith_cell = 0; ith_cell < n_cells; ith_cell++)
+            for (int ith_cell = 0; ith_cell < n_cells; ith_cell++)
             {
               for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
               {
@@ -583,7 +613,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
 
     evaluatePinv(P, basisMatrix, normalizingWeights);
     renormalizedBasisMatrix = normalizingWeights.asDiagonal()*basisMatrix;
-
+    
     P.makeCompressed();
     cnpy::save(basisMatrix, folderMethod +"/basisMatrix.npy");
     cnpy::save(P, folderMethod +"/projectionMatrix.npz");
@@ -606,7 +636,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
     cnpy::load(pinvPU, folderMethod + "/pinvPU.npy");
 
     renormalizedBasisMatrix = normalizingWeights.asDiagonal()*basisMatrix;
-    
+
     Info << "Projection Matrix shape: " << P.rows() << " " << P.cols() << endl;
     Info << "Basis Matrix shape: " << basisMatrix.rows() << " " << basisMatrix.cols() << endl;
     Info << "Pseudo Inverse Matrix shape: " << pinvPU.rows() << " " << pinvPU.cols() << endl;
@@ -800,7 +830,7 @@ void HyperReduction<SnapshotsLists...>::initReshapeMat(Eigen::SparseMatrix<doubl
   reshapeMat.resize(n_cells, n_cells*vectorial_dim);
   reshapeMat.reserve(Eigen::VectorXi::Constant(n_cells * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
 
-  for (unsigned int i = 0; i < n_cells; i++)
+  for (int i = 0; i < n_cells; i++)
   {
     for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
     {
@@ -887,7 +917,7 @@ void HyperReduction<SnapshotsLists...>::evaluateWPU(Eigen::SparseMatrix<double>
 }
 
 template<typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::generateSubmesh(label layers, fvMesh &mesh) {
+void HyperReduction<SnapshotsLists...>::generateSubmesh(label layers, const fvMesh &mesh) {
 
   Info << "####### Extract submesh #######\n";
   ITHACAparameters *para(ITHACAparameters::getInstance());
@@ -937,7 +967,7 @@ void HyperReduction<SnapshotsLists...>::generateSubmesh(label layers, fvMesh &me
 
     totalNodePoints().write();
     uniqueNodePoints().write();
-    ITHACAstream::exportSolution(Indici, "1", folderMethod);
+    ITHACAstream::exportSolution(Indici, "1", problemName);
   }
 
   submesh->setCellSubset(uniqueNodePoints());
@@ -964,7 +994,7 @@ void HyperReduction<SnapshotsLists...>::createMasks(bool offlineStage)
     field2submesh.resize(submesh().cellMap().size() * vectorial_dim, n_cells*vectorial_dim);
     field2submesh.reserve(Eigen::VectorXi::Constant(n_cells*vectorial_dim, 1));
 
-    for (unsigned int ith_subCell{0} ; ith_subCell <submesh().cellMap().size(); ith_subCell++)
+    for (int ith_subCell{0} ; ith_subCell <submesh().cellMap().size(); ith_subCell++)
     {
         for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
         {
@@ -978,8 +1008,8 @@ void HyperReduction<SnapshotsLists...>::createMasks(bool offlineStage)
     submesh2nodesMask.resize(nodePoints().size() * vectorial_dim);
 
     int index_col = 0;
-    for (unsigned int ith_node{0} ; ith_node <nodePoints().size(); ith_node++) {
-      for (unsigned int ith_subCell{0} ; ith_subCell <submesh().cellMap().size(); ith_subCell++) {
+    for (int ith_node{0} ; ith_node <nodePoints().size(); ith_node++) {
+      for (int ith_subCell{0} ; ith_subCell <submesh().cellMap().size(); ith_subCell++) {
         if (nodePoints()[ith_node] == submesh().cellMap()[ith_subCell]) {
           for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
           {
@@ -1023,4 +1053,6 @@ List<label> HyperReduction<SnapshotsLists...>::global2local(List<label> &points,
   return localPoints;
 }
 
+#pragma GCC diagnostic pop
+
 #endif

From a6c9fdbe19d5168d95f07b2468fbc553222ae8b0 Mon Sep 17 00:00:00 2001
From: Matthieu Petit <matthieu.petit@scalian.com>
Date: Fri, 8 Mar 2024 17:44:04 +0100
Subject: [PATCH 35/59] Usefool changes to HyperReduction class for
 compatibility with RedLum v1.0

---
 src/ITHACA_HR/hyperReduction.H           |  28 +-
 src/ITHACA_HR/hyperReduction.templates.H | 365 +++++++++++++++++++++--
 tutorials/CFD/08DEIM/08DEIM.C            |   3 +
 tutorials/CFD/08DEIM/HR08DEIM.C          | 244 +++++++++++++++
 tutorials/CFD/08DEIM/Make/files          |   2 +-
 tutorials/CFD/08DEIM/Make/options        |   7 +-
 tutorials/CFD/08DEIM/system/ITHACAdict   |   7 +-
 7 files changed, 612 insertions(+), 44 deletions(-)
 create mode 100644 tutorials/CFD/08DEIM/HR08DEIM.C

diff --git a/src/ITHACA_HR/hyperReduction.H b/src/ITHACA_HR/hyperReduction.H
index e7e686573..7bced8268 100644
--- a/src/ITHACA_HR/hyperReduction.H
+++ b/src/ITHACA_HR/hyperReduction.H
@@ -40,6 +40,10 @@ SourceFiles
 #include <set>
 #include "redsvd"
 
+
+Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
+Eigen::MatrixXd half_pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
+
 // TODO uniform style for separating offline and onlie stages
 template <typename... SnapshotsLists>
 class HyperReduction
@@ -78,23 +82,19 @@ public:
                    SnapshotsLists &&...snapshotsLists);
 
 
-      //----------------------------------------------------------------------
+    //----------------------------------------------------------------------
     /// @brief      Construct HyperReduction class, interpolation-based.`SnapshotsLists` is a variadic argument of PtrLists of fields e.g. for incompressible Navier-Stokes PtrList<volVectorField>, PtrList<volScalarField> for velocity and pressure.
     ///
     /// @param[in]  n_modes           dimension of the HR basis
     /// @param[in]  n_nodes           number of nodes
     /// @param[in]  problemName       name of the function to be hyper-reduced
-    /// @param[in]  modes             lists of modes
+    /// @param[in]  modeLists             lists of modes
     ///
     HyperReduction(label n_modes,
                    label n_nodes, 
-                   label n_cells, 
                    word folderMethod, 
-                   word problemName);//, 
-                //    unsigned int vectorialDim); 
-
-
-    Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
+                   word problemName,
+                   SnapshotsLists &...modeLists);
                     
     // ITHACA parameters dict
     ITHACAparameters* para;
@@ -199,10 +199,20 @@ public:
     /// Submeshes
     autoPtr<volVectorField> submesh_field;
 
+    /// Online Matrice
+    Eigen::MatrixXd MatrixOnline;
+
     //----------------------------------------------------------------------
     /// @brief      Methods implemented: 'GappyDEIM'  from "DEIM, Chaturantabut, Saifon, and Danny C. Sorensen. "Nonlinear model reduction via discrete empirical interpolation." SIAM Journal on Scientific Computing 32.5 (2010): 2737-2764" and "GNAT, Carlberg, Kevin, et al. "The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows." Journal of Computational Physics 242 (2013): 623-647.". Quasi-optimal point selection algorithm 'SOPT' and optimal point selection 'SOPTE' from "Lauzon, Jessica T., Siu Wun Cheung, Yeonjong Shin, Youngsoo Choi, Dylan Matthew Copeland, and Kevin Huynh. "S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models." arXiv preprint arXiv:2203.16494 (2022).""
     ///
-    void offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights);
+    void offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights){
+        methodName = "GappyDEIM";
+        word name = "ITHACAoutput/" + problemName + "/" + methodName;
+        offlineGappyDEIM(snapshotsModes, normalizingWeights, name);
+    }
+
+    void offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights, word folderMethodName);
+
 
     //----------------------------------------------------------------------
     /// @brief      Methods implemented: 'ECP' from "ECP, Hernandez, Joaquin Alberto, Manuel Alejandro Caicedo, and Alex Ferrer. "Dimensional hyper-reduction of nonlinear finite element models via empirical cubature." Computer methods in applied mechanics and engineering 313 (2017): 687-722.". TODO implement non-negative LS.
diff --git a/src/ITHACA_HR/hyperReduction.templates.H b/src/ITHACA_HR/hyperReduction.templates.H
index 51e8e9b56..2b49cba45 100644
--- a/src/ITHACA_HR/hyperReduction.templates.H
+++ b/src/ITHACA_HR/hyperReduction.templates.H
@@ -31,11 +31,6 @@ License
 #ifndef hyperReduction_templates_H
 #define hyperReduction_templates_H
 
-#pragma GCC diagnostic push
-#pragma GCC diagnostic ignored "-Wold-style-cast"
-#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
-#pragma GCC diagnostic ignored "-Wreorder"
-
 #include "hyperReduction.H"
 
 // TODO increase modularity to avoid heavy compiling costs
@@ -100,38 +95,69 @@ HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
   Info << "Number of boundary cells: " << n_boundary_cells << endl;
 }
 
-// Template function constructor
+
+// Template function constructor to directly pass modes 
 template <typename... SnapshotsLists>
 HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
                                                   label n_nodes,
-                                                  label nbcells, 
-                                                  word folderMethod, 
-                                                  word problemName)//,
-                                                  // unsigned int vectorialDim)
-    : n_modes{n_modes},
+                                                  word folderProblem, 
+                                                  word problemName,
+                                                  SnapshotsLists &...modeLists)
+    : vectorial_dim{compute_vectorial_dim(modeLists...)},
+      n_modes{n_modes},
       n_nodes{n_nodes},
-      n_cells{nbcells},
-      folderMethod{folderMethod},
-      problemName{problemName}
-      // vectorial_dim{vectorialDim}
+      folderProblem{folderProblem},
+      problemName{problemName},
+      snapshotsListTuple{std::forward_as_tuple(modeLists...)}
 {
+  Info << "Init HyperReduction class with vectorial dim: " << vectorial_dim << endl;
   para = ITHACAparameters::getInstance();
-  mkDir(folderMethod);
+  mkDir(folderProblem);
+
+  // TODO check snapshotsLists is not empty
+  // TODO check that the first snapshotsList is not empty (includes above)
 
-  // folderProblem = "ITHACAoutput/" + problemName;
-  // mkDir(folderProblem);
+  // TODO initialize vectorial_dim only from SnapshotsLists type
+  // vectorial_dim = std::apply(compute_vectorial_dim<modeLists...>, snapshotsListTuple);
 
-  Info << "The number of cells is: " << n_cells << endl;
-  n_snapshots = n_modes;
+  // Get fields' names
+  std::apply([this](auto& ...snapList){(..., stackNames(snapList));}, snapshotsListTuple);
+
+  // Get fields' dimensions
+  std::apply([this](auto& ...snapList){(..., stackDimensions(snapList));}, snapshotsListTuple);
+
+  sumFieldsDim = 0;
+  std::apply([this](auto& ...snapList){(..., sumDimensions(this->sumFieldsDim, snapList));}, snapshotsListTuple);
+
+  Info << "Fields names: ";
+  for (unsigned int ith_field = 0; ith_field < fieldNames.size(); ith_field++)
+  {
+    Info << fieldNames[ith_field] << " (dim=" << fieldDims[ith_field] << "); ";
+  }
+  Info << endl;
+  
   Info << "The number of modes is: " << n_modes << endl;
+  n_cells = std::get<0>(snapshotsListTuple)[0].size();
+  Info << "The number of cells is: " << n_cells << endl;
+  Info << "Initial seeds length: " << initialSeeds.rows() << endl;
+
+  // get boundaries info
+  n_boundary_patches = std::get<0>(snapshotsListTuple)[0].boundaryField().size();
+
+  n_boundary_cells_list.resize(n_boundary_patches);
+  n_boundary_cells = 0;
+  for (unsigned int ith_boundary_patch = 0; ith_boundary_patch < n_boundary_patches; ith_boundary_patch++)
+  {
+    n_boundary_cells_list[ith_boundary_patch] = std::get<0>(snapshotsListTuple)[0].boundaryField()[ith_boundary_patch].size();
+    n_boundary_cells = n_boundary_cells + n_boundary_cells_list[ith_boundary_patch];
+  }
+  Info << "Number of boundary cells: " << n_boundary_cells << endl;
 }
 
 
 // Using the Eigen library, using the SVD decomposition method to solve the
 // matrix pseudo-inverse, the default error er is 0
-template <typename... SnapshotsLists>
-Eigen::MatrixXd 
-HyperReduction<SnapshotsLists...>::pinv_eigen_based(Eigen::MatrixXd &origin, const float er) {
+Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er) {
   // perform svd decomposition
   Eigen::JacobiSVD<Eigen::MatrixXd> svd_holder(origin, Eigen::ComputeThinU | Eigen::ComputeThinV);
   // Build SVD decomposition results
@@ -154,6 +180,29 @@ HyperReduction<SnapshotsLists...>::pinv_eigen_based(Eigen::MatrixXd &origin, con
   return V * S * U.transpose();
 }
 
+Eigen::MatrixXd half_pinv_eigen_based(Eigen::MatrixXd &origin, const float er) {
+  // perform svd decomposition
+  Eigen::JacobiSVD<Eigen::MatrixXd> svd_holder(origin, Eigen::ComputeThinU | Eigen::ComputeThinV);
+  // Build SVD decomposition results
+  Eigen::MatrixXd U = svd_holder.matrixU();
+  Eigen::MatrixXd V = svd_holder.matrixV();
+  Eigen::MatrixXd D = svd_holder.singularValues();
+
+  // Build the S matrix
+  Eigen::MatrixXd S(V.cols(), U.cols());
+  S.setZero();
+
+  for (unsigned int i = 0; i < D.size(); ++i) {
+
+    if (D(i, 0) > er) {
+      S(i, i) = 1 / D(i, 0);
+    } else {
+      S(i, i) = 0;
+    }
+  }
+  return V * S;
+}
+
 template <typename... SnapshotsLists>
 void HyperReduction<SnapshotsLists...>::getModesSVD(
     SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights, bool saveModesFlag)
@@ -402,11 +451,12 @@ void HyperReduction<SnapshotsLists...>::saveModes(SnapshotsList sList, Eigen::Ma
 }
 
 template <typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights)
+void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights, word folderMethodName)
 {
-  // methodName = "GappyDEIM";
-  // folderMethod = "ITHACAoutput/" + problemName + "/" + methodName;
-
+  folderMethod = folderMethodName;
+  Info << "FolderMethod : " << folderMethod << endl;
+  mkDir(folderMethod);
+  
   normalizingWeights = weights;
 
   nodePoints = autoPtr<IOList<label>>(new IOList<label>(
@@ -613,13 +663,16 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
 
     evaluatePinv(P, basisMatrix, normalizingWeights);
     renormalizedBasisMatrix = normalizingWeights.asDiagonal()*basisMatrix;
-    
+
+    MatrixOnline = basisMatrix * ((P.transpose() * basisMatrix).completeOrthogonalDecomposition().pseudoInverse());
+
     P.makeCompressed();
     cnpy::save(basisMatrix, folderMethod +"/basisMatrix.npy");
     cnpy::save(P, folderMethod +"/projectionMatrix.npz");
     cnpy::save(normalizingWeights, folderMethod + "/normalizingWeights.npy");
     cnpy::save(nodes, folderMethod + "/mp.npy");
     cnpy::save(pinvPU, folderMethod + "/pinvPU.npy");
+    cnpy::save(MatrixOnline, folderMethod + "/MatrixOnline.npy");
     nodePoints().write();
 
     Info << "Projection Matrix shape: " << P.rows() << " " << P.cols() << endl;
@@ -630,6 +683,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
   {
     Info << "Read GappyDEIM\n";
     cnpy::load(basisMatrix, folderMethod +"/basisMatrix.npy");
+    cnpy::load(MatrixOnline, folderMethod +"/MatrixOnline.npy");
     cnpy::load(normalizingWeights, folderMethod + "/normalizingWeights.npy");
     cnpy::load(P, folderMethod +"/projectionMatrix.npz");
     cnpy::load(nodes, folderMethod + "/mp.npy");
@@ -967,7 +1021,7 @@ void HyperReduction<SnapshotsLists...>::generateSubmesh(label layers, const fvMe
 
     totalNodePoints().write();
     uniqueNodePoints().write();
-    ITHACAstream::exportSolution(Indici, "1", problemName);
+    ITHACAstream::exportSolution(Indici, "1", folderMethod);
   }
 
   submesh->setCellSubset(uniqueNodePoints());
@@ -1053,6 +1107,257 @@ List<label> HyperReduction<SnapshotsLists...>::global2local(List<label> &points,
   return localPoints;
 }
 
-#pragma GCC diagnostic pop
+
+// //---------- Specialization -----------//
+
+// // Specialization of the first constructor
+
+// template
+// HyperReduction<PtrList<volScalarField>&>::HyperReduction(label n_modes,
+//                                                         label n_nodes,
+//                                                         Eigen::VectorXi initialSeeds,
+//                                                         word problemName,
+//                                                         PtrList<volScalarField>& snapshotsList);
+
+// template<>
+// HyperReduction<PtrList<volVectorField>&>::HyperReduction(label n_modes,
+//                                                   label n_nodes,
+//                                                   Eigen::VectorXi initialSeeds,
+//                                                   word problemName,
+//                                                   PtrList<volVectorField>& snapshotsLists);
+
+// template
+// HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::HyperReduction(label n_modes,
+//                                                   label n_nodes,
+//                                                   Eigen::VectorXi initialSeeds,
+//                                                   word problemName,
+//                                                   PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>& snapshotsLists);
+
+// template HyperReduction<PtrList<volScalarField>&, PtrList<volScalarField>&>::HyperReduction(label n_modes,
+//                                                   label n_nodes,
+//                                                   Eigen::VectorXi initialSeeds,
+//                                                   word problemName,
+//                                                   PtrList<volVectorField>& snapshotsLists);
+
+
+// // Specialization of the second constructor
+
+// template 
+// HyperReduction<PtrList<volScalarField>&>::HyperReduction(label n_modes,
+//                                                             label n_nodes,
+//                                                             label nbcells, 
+//                                                             word folderMethod, 
+//                                                             word problemName);
+
+// template
+// HyperReduction<PtrList<volVectorField>&>::HyperReduction(label n_modes,
+//                                                               label n_nodes,
+//                                                               label nbcells, 
+//                                                               word folderMethod, 
+//                                                               word problemName);
+// // template
+// // HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::HyperReduction(label n_modes,
+// //                                                               label n_nodes,
+// //                                                               label nbcells, 
+// //                                                               word folderMethod, 
+// //                                                               word problemName);
+// // Specialization of pinv_eigen_based
+// template 
+// Eigen::MatrixXd HyperReduction<PtrList<volScalarField>&>::pinv_eigen_based(Eigen::MatrixXd &origin, const float er);
+// template 
+// Eigen::MatrixXd HyperReduction<PtrList<volVectorField>&>::pinv_eigen_based(Eigen::MatrixXd &origin, const float er);
+// // template 
+// // Eigen::MatrixXd HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::pinv_eigen_based(Eigen::MatrixXd &origin, const float er);
+
+// // Specialization of getModesSVD
+// template  
+// void HyperReduction<PtrList<volScalarField>&>::getModesSVD(
+//     SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights, bool saveModesFlag);
+// template  
+// void HyperReduction<PtrList<volVectorField>&>::getModesSVD(
+//     SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights, bool saveModesFlag);
+// // template 
+// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::getModesSVD(
+// //     SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights, bool saveModesFlag);
+
+
+// template  
+// void HyperReduction<PtrList<volScalarField>&>::getModesSVD(
+//     SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights, 
+//     Eigen::MatrixXd& modesSVDBoundary, Eigen::VectorXd& fieldWeightsBoundary, bool saveModesFlag);
+// template  
+// void HyperReduction<PtrList<volVectorField>&>::getModesSVD(
+//     SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights, 
+//     Eigen::MatrixXd& modesSVDBoundary, Eigen::VectorXd& fieldWeightsBoundary, bool saveModesFlag);
+// // template 
+// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::getModesSVD(
+// //     SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights, 
+// //     Eigen::MatrixXd& modesSVDBoundary, Eigen::VectorXd& fieldWeightsBoundary, bool saveModesFlag);
+
+
+// // Specialization of getSnapMatrix
+// template  
+// void HyperReduction<PtrList<volScalarField>&>::getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights);
+// template  
+// void HyperReduction<PtrList<volVectorField>&>::getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights);
+// // template 
+// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights);
+
+
+// template  
+// void HyperReduction<PtrList<volScalarField>&>::getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights, 
+//                   List<Eigen::MatrixXd>& snapMatrixBoundary, List<Eigen::VectorXd>& fieldWeightsBoundary);
+// template  
+// void HyperReduction<PtrList<volVectorField>&>::getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights, 
+//                   List<Eigen::MatrixXd>& snapMatrixBoundary, List<Eigen::VectorXd>& fieldWeightsBoundary);
+// // template 
+// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights, 
+// //                   List<Eigen::MatrixXd>& snapMatrixBoundary, List<Eigen::VectorXd>& fieldWeightsBoundary);
+
+
+// // Specialization of saveModes
+// template  <>
+// template <>
+// void HyperReduction<PtrList<volScalarField>&>::saveModes(PtrList<volScalarField>& sList, Eigen::MatrixXd& snapshotsMatrix, 
+//                                               unsigned int &rowIndex, unsigned int &modeIndex, word folder);
+// template  <>
+// template <>
+// void HyperReduction<PtrList<volVectorField>&>::saveModes(PtrList<volVectorField>& sList, Eigen::MatrixXd& snapshotsMatrix, 
+//                                               unsigned int &rowIndex, unsigned int &modeIndex, word folder);
+// // template 
+// // template 
+// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::saveModes(PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>> sList, Eigen::MatrixXd& snapshotsMatrix, 
+// //                                               unsigned int &rowIndex, unsigned int &modeIndex, word folder);
+
+
+// template  <>
+// template <>
+// void HyperReduction<PtrList<volScalarField>&>::saveModes(PtrList<volScalarField>& sList, Eigen::MatrixXd& snapshotsMatrix, 
+//       Eigen::MatrixXd& snapshotsMatrixBoundary, unsigned int &rowIndex,  unsigned int& rowIndexBoundary, unsigned int &modeIndex, word folder);
+// template  <>
+// template <>
+// void HyperReduction<PtrList<volVectorField>&>::saveModes(PtrList<volVectorField>& sList, Eigen::MatrixXd& snapshotsMatrix, 
+//       Eigen::MatrixXd& snapshotsMatrixBoundary, unsigned int &rowIndex,  unsigned int& rowIndexBoundary, unsigned int &modeIndex, word folder);
+// // template 
+// // template 
+// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::saveModes(PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>> sList, Eigen::MatrixXd& snapshotsMatrix, 
+// //       Eigen::MatrixXd& snapshotsMatrixBoundary, unsigned int &rowIndex,  unsigned int& rowIndexBoundary, unsigned int &modeIndex, word folder);
+
+
+// // Specialization of offlineGappyDEIM
+// template  
+// void HyperReduction<PtrList<volScalarField>&>::offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights);
+// template  
+// void HyperReduction<PtrList<volVectorField>&>::offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights);
+// // template 
+// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights);
+
+// // Specialization of offlineECP
+// template  
+// void HyperReduction<PtrList<volScalarField>&>::offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights);
+// template  
+// void HyperReduction<PtrList<volVectorField>&>::offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights);
+// // template 
+// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights);
+
+// // Specialization of initSeeds
+// template  
+// void HyperReduction<PtrList<volScalarField>&>::initSeeds(Eigen::VectorXd mp_not_mask, std::set<label> nodePointsSet);
+// template  
+// void HyperReduction<PtrList<volVectorField>&>::initSeeds(Eigen::VectorXd mp_not_mask, std::set<label> nodePointsSet);
+// // template 
+// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::initSeeds(Eigen::VectorXd mp_not_mask, std::set<label> nodePointsSet);
+
+// // Specialization of updateNodes
+// template  
+// void HyperReduction<PtrList<volScalarField>&>::updateNodes(Eigen::SparseMatrix<double>& P, label& ind, Eigen::VectorXd& mp_not_mask);
+// template  
+// void HyperReduction<PtrList<volVectorField>&>::updateNodes(Eigen::SparseMatrix<double>& P, label& ind, Eigen::VectorXd& mp_not_mask);
+// // template 
+// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::updateNodes(Eigen::SparseMatrix<double>& P, label& ind, Eigen::VectorXd& mp_not_mask);
+
+// // Specialization of computeLS
+// template  
+// void HyperReduction<PtrList<volScalarField>&>::computeLS(Eigen::MatrixXd& J, Eigen::MatrixXd& Jwhole, Eigen::VectorXd& b, Eigen::VectorXd& q);
+// template  
+// void HyperReduction<PtrList<volVectorField>&>::computeLS(Eigen::MatrixXd& J, Eigen::MatrixXd& Jwhole, Eigen::VectorXd& b, Eigen::VectorXd& q);
+// // template 
+// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::computeLS(Eigen::MatrixXd& J, Eigen::MatrixXd& Jwhole, Eigen::VectorXd& b, Eigen::VectorXd& q);
+
+// // Specialization of initReshapeMat
+// template  
+// void HyperReduction<PtrList<volScalarField>&>::initReshapeMat(Eigen::SparseMatrix<double> &reshapeMat);
+// template  
+// void HyperReduction<PtrList<volVectorField>&>::initReshapeMat(Eigen::SparseMatrix<double> &reshapeMat);
+// // template 
+// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::initReshapeMat(Eigen::SparseMatrix<double> &reshapeMat);
+
+// // Specialization of stackSnapshots
+// template  <>
+// template <>
+// void HyperReduction<PtrList<volScalarField>&>::stackSnapshots(PtrList<volScalarField>& sList, Eigen::MatrixXd& snapshotsMatrix, Eigen::VectorXd& fieldWeights);
+// template  <>
+// template <>
+// void HyperReduction<PtrList<volVectorField>&>::stackSnapshots(PtrList<volVectorField>& sList, Eigen::MatrixXd& snapshotsMatrix, Eigen::VectorXd& fieldWeights);
+// // template 
+// // template 
+// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::stackSnapshots(PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>> sList, Eigen::MatrixXd& snapshotsMatrix, Eigen::VectorXd& fieldWeights);
+
+// // Specialization of stackSnapshotsBoundary
+// template  <>
+// template <>
+// void HyperReduction<PtrList<volScalarField>&>::stackSnapshotsBoundary(PtrList<volScalarField>& sList, List<Eigen::MatrixXd>& snapshotsMatrixBoundary, List<Eigen::VectorXd>& fieldWeightsBoundary);
+// template  <>
+// template <>
+// void HyperReduction<PtrList<volVectorField>&>::stackSnapshotsBoundary(PtrList<volVectorField>& sList, List<Eigen::MatrixXd>& snapshotsMatrixBoundary, List<Eigen::VectorXd>& fieldWeightsBoundary);
+// // template 
+// // template 
+// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::stackSnapshotsBoundary(PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>> sList, List<Eigen::MatrixXd>& snapshotsMatrixBoundary, List<Eigen::VectorXd>& fieldWeightsBoundary);
+
+
+// // Specialization of evaluatePinv
+// template  
+// void HyperReduction<PtrList<volScalarField>&>::evaluatePinv(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd &fieldWeights);
+// template  
+// void HyperReduction<PtrList<volVectorField>&>::evaluatePinv(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd &fieldWeights);
+// // template 
+// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::evaluatePinv(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd &fieldWeights);
+
+// // Specialization of evaluateWPU
+// template  
+// void HyperReduction<PtrList<volScalarField>&>::evaluateWPU(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd &fieldWeights, Eigen::VectorXd& quadratureWeights);
+// template  
+// void HyperReduction<PtrList<volVectorField>&>::evaluateWPU(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd &fieldWeights, Eigen::VectorXd& quadratureWeights);
+// // template 
+// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::evaluateWPU(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd &fieldWeights, Eigen::VectorXd& quadratureWeights);
+
+// // Specialization of generateSubmesh
+// template  
+// void HyperReduction<PtrList<volScalarField>&>::generateSubmesh(label layers, const fvMesh &mesh);
+// template  
+// void HyperReduction<PtrList<volVectorField>&>::generateSubmesh(label layers, const fvMesh &mesh);
+// // template 
+// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::generateSubmesh(label layers, const fvMesh &mesh);
+
+// // Specialization of createMasks
+// template  
+// void HyperReduction<PtrList<volScalarField>&>::createMasks(bool offlineStage);
+// template  
+// void HyperReduction<PtrList<volVectorField>&>::createMasks(bool offlineStage);
+// // template 
+// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::createMasks(bool offlineStage);
+
+// // Specialization of global2local
+// template  
+// List<label> HyperReduction<PtrList<volScalarField>&>::global2local(List<label> &points, fvMeshSubset &submesh);
+// template  
+// List<label> HyperReduction<PtrList<volVectorField>&>::global2local(List<label> &points, fvMeshSubset &submesh);
+// // template 
+// // List<label> HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::global2local(List<label> &points, fvMeshSubset &submesh);
+
+
+
+
+
 
 #endif
diff --git a/tutorials/CFD/08DEIM/08DEIM.C b/tutorials/CFD/08DEIM/08DEIM.C
index 4a9b880fc..f305d6bb8 100644
--- a/tutorials/CFD/08DEIM/08DEIM.C
+++ b/tutorials/CFD/08DEIM/08DEIM.C
@@ -111,6 +111,9 @@ int main(int argc, char* argv[])
     );
     // Parameters used to train the non-linear function
     Eigen::MatrixXd pars = ITHACAutilities::rand(100, 2, -0.5, 0.5);
+    // Possible to create a file "random.npy" to compare both version 
+    // with cnpy::save(pars, "./random.npy");
+    // and load it with :  cnpy::load(pars, "./random.npy");
 
     // Perform the offline phase
     for (int i = 0; i < 100; i++)
diff --git a/tutorials/CFD/08DEIM/HR08DEIM.C b/tutorials/CFD/08DEIM/HR08DEIM.C
new file mode 100644
index 000000000..9ee865659
--- /dev/null
+++ b/tutorials/CFD/08DEIM/HR08DEIM.C
@@ -0,0 +1,244 @@
+/*---------------------------------------------------------------------------*\
+     ██╗████████╗██╗  ██╗ █████╗  ██████╗ █████╗       ███████╗██╗   ██╗
+     ██║╚══██╔══╝██║  ██║██╔══██╗██╔════╝██╔══██╗      ██╔════╝██║   ██║
+     ██║   ██║   ███████║███████║██║     ███████║█████╗█████╗  ██║   ██║
+     ██║   ██║   ██╔══██║██╔══██║██║     ██╔══██║╚════╝██╔══╝  ╚██╗ ██╔╝
+     ██║   ██║   ██║  ██║██║  ██║╚██████╗██║  ██║      ██║      ╚████╔╝
+     ╚═╝   ╚═╝   ╚═╝  ╚═╝╚═╝  ╚═╝ ╚═════╝╚═╝  ╚═╝      ╚═╝       ╚═══╝
+
+ * In real Time Highly Advanced Computational Applications for Finite Volumes
+ * Copyright (C) 2017 by the ITHACA-FV authors
+-------------------------------------------------------------------------------
+License
+    This file is part of ITHACA-FV
+    ITHACA-FV is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+    ITHACA-FV is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU Lesser General Public License for more details.
+    You should have received a copy of the GNU Lesser General Public License
+    along with ITHACA-FV. If not, see <http://www.gnu.org/licenses/>.
+Description
+    Example of the reconstruction of a non-linear function using the DEIM
+SourceFiles
+    08DEIM.C
+\*---------------------------------------------------------------------------*/
+
+#include "fvCFD.H"
+#include "fvOptions.H"
+#include "simpleControl.H"
+#include "simpleControl.H"
+#include "fvMeshSubset.H"
+#include "ITHACAutilities.H"
+#include "Foam2Eigen.H"
+#include "ITHACAstream.H"
+#include "ITHACAPOD.H"
+#include "hyperReduction.templates.H"
+// #include "DEIM.H"
+#include <chrono>
+
+
+class DEIM_function : public HyperReduction<PtrList<volScalarField>&>
+{
+    public:
+        using HyperReduction::HyperReduction;
+        static volScalarField evaluate_expression(volScalarField& S, Eigen::MatrixXd mu)
+        {
+            volScalarField yPos = S.mesh().C().component(vector::Y).ref();
+            volScalarField xPos = S.mesh().C().component(vector::X).ref();
+
+            for (auto i = 0; i < S.size(); i++)
+            {
+                S[i] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1,
+                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
+            }
+
+            return S;
+        }
+        Eigen::VectorXd onlineCoeffs(Eigen::MatrixXd mu)
+        {
+            theta.resize(nodePoints().size());
+            auto f = evaluate_expression(subField(), mu);
+
+            for (int i = 0; i < nodePoints().size(); i++)
+            {
+                // double on_coeff = f[localMagicPoints[i]];
+                theta(i) = f[localNodePoints[i]];
+            }
+
+            return theta;
+        }
+        
+        Eigen::VectorXd theta;
+        PtrList<volScalarField> fields;
+        autoPtr<volScalarField> subField;
+};
+
+int main(int argc, char* argv[])
+{
+    // Read parameters from ITHACAdict file
+#include "setRootCase.H"
+    Foam::Time runTime(Foam::Time::controlDictName, args);
+    Foam::fvMesh mesh
+    (
+        Foam::IOobject
+        (
+            Foam::fvMesh::defaultRegion,
+            runTime.timeName(),
+            runTime,
+            Foam::IOobject::MUST_READ
+        )
+    );
+    ITHACAparameters* para = ITHACAparameters::getInstance(mesh, runTime);
+    int NDEIM = para->ITHACAdict->lookupOrDefault<int>("NDEIM", 15);
+    simpleControl simple(mesh);
+#include "createFields.H"
+    // List of volScalarField where the snapshots are stored
+    PtrList<volScalarField> Sp;
+    // Non linear function
+    volScalarField S
+    (
+        IOobject
+        (
+            "S",
+            runTime.timeName(),
+            mesh,
+            IOobject::NO_READ,
+            IOobject::AUTO_WRITE
+        ),
+        T.mesh(),
+        dimensionedScalar("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), 0)
+    );
+    // Parameters used to train the non-linear function
+    Eigen::MatrixXd pars ;//= ITHACAutilities::rand(100, 2, -0.5, 0.5);
+    pars = cnpy::load(pars, "./random.npy");
+
+    // Perform the offline phase
+    for (int i = 0; i < 100; i++)
+    {
+        DEIM_function::evaluate_expression(S, pars.row(i));
+        Sp.append((S).clone());
+        ITHACAstream::exportSolution(S, name(i + 1), "./ITHACAoutput/Offline/");
+    }
+
+    // Create DEIM object with given number of basis functions
+    Eigen::VectorXi initSeeds;
+    DEIM_function c(NDEIM, NDEIM, initSeeds, "", Sp);
+    c.problemName = "Gaussian_function";
+    Eigen::MatrixXd snapshotsModes;
+    Eigen::VectorXd normalizingWeights = ITHACAutilities::getMassMatrixFV(Sp[0]).array().sqrt();
+    PtrList<volScalarField> modes = ITHACAPOD::DEIMmodes(Sp, NDEIM, "Gaussian_function",S.name());
+    
+    // c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights); 
+    snapshotsModes = Foam2Eigen::PtrList2Eigen(modes);
+    c.offlineGappyDEIM(snapshotsModes, normalizingWeights, "ITHACAoutput/DEIM/"+c.problemName);
+
+    // Generate the submeshes with the depth of the layer
+    c.generateSubmesh(2, mesh); 
+    c.subField = autoPtr<volScalarField>(new volScalarField(c.submesh->interpolate(S).ref()));
+    // Define a new online parameter
+    Eigen::MatrixXd par_new(2, 1);
+    par_new(0, 0) = 0;
+    par_new(1, 0) = 0;
+    // Online evaluation of the non linear function
+    Eigen::VectorXd aprfield = c.MatrixOnline * c.onlineCoeffs(par_new);
+    // Transform to an OpenFOAM field and export
+    volScalarField S2("S_online", Foam2Eigen::Eigen2field(S, aprfield));
+    ITHACAstream::exportSolution(S2, name(1), "./ITHACAoutput/Online/");
+    // Evaluate the full order function and export it
+    DEIM_function::evaluate_expression(S, par_new);
+    ITHACAstream::exportSolution(S, name(1), "./ITHACAoutput/Online/");
+    // Compute the L2 error and print it
+    Info << ITHACAutilities::errorL2Rel(S2, S) << endl;
+    return 0;
+}
+
+/// \dir 08DEIM Folder of the turorial 8
+/// \file
+/// \brief Implementation of tutorial 8 for DEIM reconstruction of a non linear function
+
+/// \example 08DEIM.C
+/// \section intro_08DEIM Introduction to tutorial 8
+/// In this tutorial we propose an example concerning the usage of the Discrete Empirical Interpolation Method (implemented in the DEIM class) for the approximation of a non-linear function.
+/// The following image illustrates the computational domain used to discretize the problem
+/// \htmlonly <style>div.image img[src="mesh.png"]{width:500px;}</style> \endhtmlonly @image html mesh.png "Computational Domain"
+///
+/// The non-liner function is described by a parametric Gaussian function:
+/// \f[
+/// S(\mathbf{x},\mathbf{\mu}) = e^{-2(x-\mu_x-1)^2 - 2(y-\mu_y-0.5)^2},
+///  \f]
+/// that is depending on the parameter vector \f$\mathbf{\mu} = [\mu_x, \mu_y] \f$ and on the location inside the domain \f$ \mathbf{x} = [x,y] \f$. A training set of 100 samples is used to construct the DEIM modes which are later used for the approximation.
+///
+/// \subsection header The necessary header files
+/// First of all let's have a look to the header files that needs to be included and what they are responsible for:
+/// The header files of ITHACA-FV necessary for this tutorial are: <Foam2Eigen.H> for Eigen to OpenFOAM conversion of objects, <ITHACAstream.H> for ITHACA-FV input-output operations. <ITHACAPOD.H> for the POD decomposition, <DEIM.H> for the DEIM approximation.
+///
+///
+/// \section code08 A detailed look into the code
+///
+/// \dontinclude 08DEIM.C
+/// The OpenFOAM header files:
+/// \skip #include "fvCFD.H"
+/// \until fvMeshSubset
+///
+/// ITHACA-FV header files
+///
+/// \until DEIM
+///
+/// chrono to compute the speedup
+/// \until chrono
+///
+/// Construction of the function to be approximated with the DEIM method.
+/// \skip class
+/// \until DEIM::DEIM
+///
+/// Method with the explicit definition of the non-linear function
+/// \skip evaluate_expression
+/// \until }
+/// \until }
+///
+/// Method with the expression for the evaluation of the online coefficients
+/// \skip onlineCoeffs
+/// \until }
+/// \until }
+///
+/// Now let's have a look to important command in the main function.
+/// Read parameters from the ITHACAdict file
+/// \skip ITHACApara
+/// \until int
+///
+/// Definition of the parameter samples to train the non-linear function
+/// \skipline Eigen
+/// Offline training of the function and assembly of the snapshots list
+/// \skip for
+/// \until }
+/// Construction of the DEIM object passing the list of snapshots Sp, the maximum number of DEIM modes NDEIM, and the name used to store the output "Gaussian_function".
+/// \skipline DEIM_function
+/// Command to generate the submeshes used for pointwise evaluation of the function
+/// \skipline c.
+/// Definition of a new sample value to test the accuracy of the method \f$ \mu* = (0,0) \f$
+/// \skip Eigen
+/// \until 1,
+///
+/// Evaluation of the function using DEIM and reconstruction of the field
+/// \skip Eigen
+/// \until volSca
+///
+/// Export the approximation
+///
+/// \skipline ITHACA
+///
+/// Evaluate the function on in \f$\mu*\f$ using the FOM
+/// \skipline DEIM
+/// Export the FOM field
+/// \skipline ITHACA
+/// Compute the error and print it
+/// \skipline Info
+///
+/// \section plaincode The plain program
+/// Here there's the plain code
+
+
diff --git a/tutorials/CFD/08DEIM/Make/files b/tutorials/CFD/08DEIM/Make/files
index fe9231886..029547431 100644
--- a/tutorials/CFD/08DEIM/Make/files
+++ b/tutorials/CFD/08DEIM/Make/files
@@ -1,3 +1,3 @@
-08DEIM.C
+HR08DEIM.C
 
 EXE = $(FOAM_USER_APPBIN)/08DEIM
diff --git a/tutorials/CFD/08DEIM/Make/options b/tutorials/CFD/08DEIM/Make/options
index d25ac44ef..08cdb4ae3 100644
--- a/tutorials/CFD/08DEIM/Make/options
+++ b/tutorials/CFD/08DEIM/Make/options
@@ -9,11 +9,13 @@ EXE_INC = \
     -I$(LIB_SRC)/sampling/lnInclude \
     -I$(LIB_SRC)/fvOptions/lnInclude \
     -I$(LIB_SRC)/fileFormats/lnInclude \
+    -I$(LIB_ITHACA_SRC)/thirdparty/redsvd \
     -I$(LIB_SRC)/dynamicMesh/lnInclude \
     -I$(LIB_SRC)/thermophysicalModels/basic/lnInclude \
     -I$(LIB_SRC)/turbulenceModels/compressible/turbulenceModel \
     -I$(LIB_SRC)/functionObjects/forces/lnInclude \
     -I$(LIB_ITHACA_SRC)/ITHACA_DEIM \
+    -I$(LIB_ITHACA_SRC)/ITHACA_HR \
     -I$(LIB_ITHACA_SRC)/ITHACA_FOMPROBLEMS/lnInclude \
     -I$(LIB_ITHACA_SRC)/ITHACA_ROMPROBLEMS/lnInclude \
     -I$(LIB_ITHACA_SRC)/ITHACA_CORE/lnInclude \
@@ -23,7 +25,7 @@ EXE_INC = \
     -Wno-comment \
     -w \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11 \
+    -std=c++17 \
 
 
 EXE_LIBS = \
@@ -43,5 +45,4 @@ EXE_LIBS = \
     -lITHACA_ROMPROBLEMS \
     -lITHACA_THIRD_PARTY \
     -lITHACA_CORE \
-    -lITHACA_DEIM
-
+    -lITHACA_DEIM 
diff --git a/tutorials/CFD/08DEIM/system/ITHACAdict b/tutorials/CFD/08DEIM/system/ITHACAdict
index ce42c6026..d733fd3e7 100755
--- a/tutorials/CFD/08DEIM/system/ITHACAdict
+++ b/tutorials/CFD/08DEIM/system/ITHACAdict
@@ -18,8 +18,13 @@ FoamFile
 EigenSolver eigen;
 
 // Number of modes to output and to use for projection
-NDEIM 80;
+NDEIM 50;
 
 // Output format to save market vectors.
 OutPrecision 20;
 OutType fixed;
+
+// HR
+HyperReduction GappyDEIM;//GappyDEIM, ECP
+GreedyMetric L2;//L2, SOPT, SOPTE
+

From df4a8e26adc72f404bca0b1bbfc0b392ba821558 Mon Sep 17 00:00:00 2001
From: Matthieu Petit <matthieu.petit@scalian.com>
Date: Mon, 11 Mar 2024 17:50:49 +0100
Subject: [PATCH 36/59] Update for the adaptation of tutorial 08 and second
 constructor of the HyperReduction class

---
 src/ITHACA_HR/hyperReduction.H           | 11 ++++++++---
 src/ITHACA_HR/hyperReduction.templates.H |  8 ++++++--
 tutorials/CFD/08DEIM/HR08DEIM.C          | 18 ++++++++++++------
 3 files changed, 26 insertions(+), 11 deletions(-)

diff --git a/src/ITHACA_HR/hyperReduction.H b/src/ITHACA_HR/hyperReduction.H
index 7bced8268..9e693c495 100644
--- a/src/ITHACA_HR/hyperReduction.H
+++ b/src/ITHACA_HR/hyperReduction.H
@@ -41,8 +41,8 @@ SourceFiles
 #include "redsvd"
 
 
-Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
-Eigen::MatrixXd half_pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
+// Eigen::MatrixXd half_pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
+// Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
 
 // TODO uniform style for separating offline and onlie stages
 template <typename... SnapshotsLists>
@@ -92,10 +92,15 @@ public:
     ///
     HyperReduction(label n_modes,
                    label n_nodes, 
+                   Eigen::VectorXi initialSeeds,
                    word folderMethod, 
                    word problemName,
                    SnapshotsLists &...modeLists);
-                    
+
+
+    Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
+    Eigen::MatrixXd half_pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
+          
     // ITHACA parameters dict
     ITHACAparameters* para;
 
diff --git a/src/ITHACA_HR/hyperReduction.templates.H b/src/ITHACA_HR/hyperReduction.templates.H
index 2b49cba45..8f0830b0d 100644
--- a/src/ITHACA_HR/hyperReduction.templates.H
+++ b/src/ITHACA_HR/hyperReduction.templates.H
@@ -100,12 +100,14 @@ HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
 template <typename... SnapshotsLists>
 HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
                                                   label n_nodes,
+                                                  Eigen::VectorXi initialSeeds,
                                                   word folderProblem, 
                                                   word problemName,
                                                   SnapshotsLists &...modeLists)
     : vectorial_dim{compute_vectorial_dim(modeLists...)},
       n_modes{n_modes},
       n_nodes{n_nodes},
+      initialSeeds{initialSeeds},
       folderProblem{folderProblem},
       problemName{problemName},
       snapshotsListTuple{std::forward_as_tuple(modeLists...)}
@@ -157,7 +159,8 @@ HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
 
 // Using the Eigen library, using the SVD decomposition method to solve the
 // matrix pseudo-inverse, the default error er is 0
-Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er) {
+template <typename... SnapshotsLists>
+Eigen::MatrixXd HyperReduction<SnapshotsLists...>::pinv_eigen_based(Eigen::MatrixXd &origin, const float er) {
   // perform svd decomposition
   Eigen::JacobiSVD<Eigen::MatrixXd> svd_holder(origin, Eigen::ComputeThinU | Eigen::ComputeThinV);
   // Build SVD decomposition results
@@ -180,7 +183,8 @@ Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er) {
   return V * S * U.transpose();
 }
 
-Eigen::MatrixXd half_pinv_eigen_based(Eigen::MatrixXd &origin, const float er) {
+template <typename... SnapshotsLists>
+Eigen::MatrixXd HyperReduction<SnapshotsLists...>::half_pinv_eigen_based(Eigen::MatrixXd &origin, const float er) {
   // perform svd decomposition
   Eigen::JacobiSVD<Eigen::MatrixXd> svd_holder(origin, Eigen::ComputeThinU | Eigen::ComputeThinV);
   // Build SVD decomposition results
diff --git a/tutorials/CFD/08DEIM/HR08DEIM.C b/tutorials/CFD/08DEIM/HR08DEIM.C
index 9ee865659..9adbc2638 100644
--- a/tutorials/CFD/08DEIM/HR08DEIM.C
+++ b/tutorials/CFD/08DEIM/HR08DEIM.C
@@ -72,7 +72,7 @@ class DEIM_function : public HyperReduction<PtrList<volScalarField>&>
             return theta;
         }
         
-        Eigen::VectorXd theta;
+        Eigen::VectorXd theta; // Necessary to add inside the HyperReduction class ?
         PtrList<volScalarField> fields;
         autoPtr<volScalarField> subField;
 };
@@ -114,7 +114,7 @@ int main(int argc, char* argv[])
     );
     // Parameters used to train the non-linear function
     Eigen::MatrixXd pars ;//= ITHACAutilities::rand(100, 2, -0.5, 0.5);
-    pars = cnpy::load(pars, "./random.npy");
+    cnpy::load(pars, "./random.npy");
 
     // Perform the offline phase
     for (int i = 0; i < 100; i++)
@@ -127,13 +127,19 @@ int main(int argc, char* argv[])
     // Create DEIM object with given number of basis functions
     Eigen::VectorXi initSeeds;
     DEIM_function c(NDEIM, NDEIM, initSeeds, "", Sp);
-    c.problemName = "Gaussian_function";
+    c.problemName = "Gaussian_function"; // To access the same folder as before
     Eigen::MatrixXd snapshotsModes;
-    Eigen::VectorXd normalizingWeights = ITHACAutilities::getMassMatrixFV(Sp[0]).array().sqrt();
+
+    // To use the DEIMmodes methode from ITHACAPOD :
     PtrList<volScalarField> modes = ITHACAPOD::DEIMmodes(Sp, NDEIM, "Gaussian_function",S.name());
-    
-    // c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights); 
     snapshotsModes = Foam2Eigen::PtrList2Eigen(modes);
+    Eigen::VectorXd normalizingWeights = ITHACAutilities::getMassMatrixFV(Sp[0]).array();
+
+    // To use the SVD modes from the hyperReduction class : 
+    // Eigen::VectorXd normalizingWeights;
+    // c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights); 
+    
+
     c.offlineGappyDEIM(snapshotsModes, normalizingWeights, "ITHACAoutput/DEIM/"+c.problemName);
 
     // Generate the submeshes with the depth of the layer

From b6e61653acbe854c6a8d7fa89a447fa1dcca4beb Mon Sep 17 00:00:00 2001
From: Matthieu Petit <matthieu.petit@scalian.com>
Date: Fri, 15 Mar 2024 14:57:30 +0100
Subject: [PATCH 37/59] Changes and cleanup of the hyperReduction class and
 tutorial 08 with the new results folder hierarchy

---
 src/ITHACA_HR/hyperReduction.H           |  17 --
 src/ITHACA_HR/hyperReduction.templates.H | 315 +----------------------
 tutorials/CFD/08DEIM/HR08DEIM.C          |  19 +-
 3 files changed, 11 insertions(+), 340 deletions(-)

diff --git a/src/ITHACA_HR/hyperReduction.H b/src/ITHACA_HR/hyperReduction.H
index 9e693c495..19c4acf44 100644
--- a/src/ITHACA_HR/hyperReduction.H
+++ b/src/ITHACA_HR/hyperReduction.H
@@ -81,23 +81,6 @@ public:
                    word problemName,
                    SnapshotsLists &&...snapshotsLists);
 
-
-    //----------------------------------------------------------------------
-    /// @brief      Construct HyperReduction class, interpolation-based.`SnapshotsLists` is a variadic argument of PtrLists of fields e.g. for incompressible Navier-Stokes PtrList<volVectorField>, PtrList<volScalarField> for velocity and pressure.
-    ///
-    /// @param[in]  n_modes           dimension of the HR basis
-    /// @param[in]  n_nodes           number of nodes
-    /// @param[in]  problemName       name of the function to be hyper-reduced
-    /// @param[in]  modeLists             lists of modes
-    ///
-    HyperReduction(label n_modes,
-                   label n_nodes, 
-                   Eigen::VectorXi initialSeeds,
-                   word folderMethod, 
-                   word problemName,
-                   SnapshotsLists &...modeLists);
-
-
     Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
     Eigen::MatrixXd half_pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
           
diff --git a/src/ITHACA_HR/hyperReduction.templates.H b/src/ITHACA_HR/hyperReduction.templates.H
index 8f0830b0d..704b3665e 100644
--- a/src/ITHACA_HR/hyperReduction.templates.H
+++ b/src/ITHACA_HR/hyperReduction.templates.H
@@ -96,67 +96,6 @@ HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
 }
 
 
-// Template function constructor to directly pass modes 
-template <typename... SnapshotsLists>
-HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
-                                                  label n_nodes,
-                                                  Eigen::VectorXi initialSeeds,
-                                                  word folderProblem, 
-                                                  word problemName,
-                                                  SnapshotsLists &...modeLists)
-    : vectorial_dim{compute_vectorial_dim(modeLists...)},
-      n_modes{n_modes},
-      n_nodes{n_nodes},
-      initialSeeds{initialSeeds},
-      folderProblem{folderProblem},
-      problemName{problemName},
-      snapshotsListTuple{std::forward_as_tuple(modeLists...)}
-{
-  Info << "Init HyperReduction class with vectorial dim: " << vectorial_dim << endl;
-  para = ITHACAparameters::getInstance();
-  mkDir(folderProblem);
-
-  // TODO check snapshotsLists is not empty
-  // TODO check that the first snapshotsList is not empty (includes above)
-
-  // TODO initialize vectorial_dim only from SnapshotsLists type
-  // vectorial_dim = std::apply(compute_vectorial_dim<modeLists...>, snapshotsListTuple);
-
-  // Get fields' names
-  std::apply([this](auto& ...snapList){(..., stackNames(snapList));}, snapshotsListTuple);
-
-  // Get fields' dimensions
-  std::apply([this](auto& ...snapList){(..., stackDimensions(snapList));}, snapshotsListTuple);
-
-  sumFieldsDim = 0;
-  std::apply([this](auto& ...snapList){(..., sumDimensions(this->sumFieldsDim, snapList));}, snapshotsListTuple);
-
-  Info << "Fields names: ";
-  for (unsigned int ith_field = 0; ith_field < fieldNames.size(); ith_field++)
-  {
-    Info << fieldNames[ith_field] << " (dim=" << fieldDims[ith_field] << "); ";
-  }
-  Info << endl;
-  
-  Info << "The number of modes is: " << n_modes << endl;
-  n_cells = std::get<0>(snapshotsListTuple)[0].size();
-  Info << "The number of cells is: " << n_cells << endl;
-  Info << "Initial seeds length: " << initialSeeds.rows() << endl;
-
-  // get boundaries info
-  n_boundary_patches = std::get<0>(snapshotsListTuple)[0].boundaryField().size();
-
-  n_boundary_cells_list.resize(n_boundary_patches);
-  n_boundary_cells = 0;
-  for (unsigned int ith_boundary_patch = 0; ith_boundary_patch < n_boundary_patches; ith_boundary_patch++)
-  {
-    n_boundary_cells_list[ith_boundary_patch] = std::get<0>(snapshotsListTuple)[0].boundaryField()[ith_boundary_patch].size();
-    n_boundary_cells = n_boundary_cells + n_boundary_cells_list[ith_boundary_patch];
-  }
-  Info << "Number of boundary cells: " << n_boundary_cells << endl;
-}
-
-
 // Using the Eigen library, using the SVD decomposition method to solve the
 // matrix pseudo-inverse, the default error er is 0
 template <typename... SnapshotsLists>
@@ -668,7 +607,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
     evaluatePinv(P, basisMatrix, normalizingWeights);
     renormalizedBasisMatrix = normalizingWeights.asDiagonal()*basisMatrix;
 
-    MatrixOnline = basisMatrix * ((P.transpose() * basisMatrix).completeOrthogonalDecomposition().pseudoInverse());
+    MatrixOnline = renormalizedBasisMatrix * pinvPU;
 
     P.makeCompressed();
     cnpy::save(basisMatrix, folderMethod +"/basisMatrix.npy");
@@ -726,7 +665,7 @@ void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd& snapshotsMod
   if (offlineStage)
   {
     assert(n_modes > 0);
-    assert(n_nodes >= n_modes);
+    assert(n_nodes >= n_modes); 
 
     // matrices for quadratureWeights evaluation
     Eigen::MatrixXd J;//shape: (vectorial_dim * (n_modes + 1), nodePoints->size())
@@ -1112,256 +1051,6 @@ List<label> HyperReduction<SnapshotsLists...>::global2local(List<label> &points,
 }
 
 
-// //---------- Specialization -----------//
-
-// // Specialization of the first constructor
-
-// template
-// HyperReduction<PtrList<volScalarField>&>::HyperReduction(label n_modes,
-//                                                         label n_nodes,
-//                                                         Eigen::VectorXi initialSeeds,
-//                                                         word problemName,
-//                                                         PtrList<volScalarField>& snapshotsList);
-
-// template<>
-// HyperReduction<PtrList<volVectorField>&>::HyperReduction(label n_modes,
-//                                                   label n_nodes,
-//                                                   Eigen::VectorXi initialSeeds,
-//                                                   word problemName,
-//                                                   PtrList<volVectorField>& snapshotsLists);
-
-// template
-// HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::HyperReduction(label n_modes,
-//                                                   label n_nodes,
-//                                                   Eigen::VectorXi initialSeeds,
-//                                                   word problemName,
-//                                                   PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>& snapshotsLists);
-
-// template HyperReduction<PtrList<volScalarField>&, PtrList<volScalarField>&>::HyperReduction(label n_modes,
-//                                                   label n_nodes,
-//                                                   Eigen::VectorXi initialSeeds,
-//                                                   word problemName,
-//                                                   PtrList<volVectorField>& snapshotsLists);
-
-
-// // Specialization of the second constructor
-
-// template 
-// HyperReduction<PtrList<volScalarField>&>::HyperReduction(label n_modes,
-//                                                             label n_nodes,
-//                                                             label nbcells, 
-//                                                             word folderMethod, 
-//                                                             word problemName);
-
-// template
-// HyperReduction<PtrList<volVectorField>&>::HyperReduction(label n_modes,
-//                                                               label n_nodes,
-//                                                               label nbcells, 
-//                                                               word folderMethod, 
-//                                                               word problemName);
-// // template
-// // HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::HyperReduction(label n_modes,
-// //                                                               label n_nodes,
-// //                                                               label nbcells, 
-// //                                                               word folderMethod, 
-// //                                                               word problemName);
-// // Specialization of pinv_eigen_based
-// template 
-// Eigen::MatrixXd HyperReduction<PtrList<volScalarField>&>::pinv_eigen_based(Eigen::MatrixXd &origin, const float er);
-// template 
-// Eigen::MatrixXd HyperReduction<PtrList<volVectorField>&>::pinv_eigen_based(Eigen::MatrixXd &origin, const float er);
-// // template 
-// // Eigen::MatrixXd HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::pinv_eigen_based(Eigen::MatrixXd &origin, const float er);
-
-// // Specialization of getModesSVD
-// template  
-// void HyperReduction<PtrList<volScalarField>&>::getModesSVD(
-//     SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights, bool saveModesFlag);
-// template  
-// void HyperReduction<PtrList<volVectorField>&>::getModesSVD(
-//     SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights, bool saveModesFlag);
-// // template 
-// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::getModesSVD(
-// //     SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights, bool saveModesFlag);
-
-
-// template  
-// void HyperReduction<PtrList<volScalarField>&>::getModesSVD(
-//     SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights, 
-//     Eigen::MatrixXd& modesSVDBoundary, Eigen::VectorXd& fieldWeightsBoundary, bool saveModesFlag);
-// template  
-// void HyperReduction<PtrList<volVectorField>&>::getModesSVD(
-//     SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights, 
-//     Eigen::MatrixXd& modesSVDBoundary, Eigen::VectorXd& fieldWeightsBoundary, bool saveModesFlag);
-// // template 
-// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::getModesSVD(
-// //     SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights, 
-// //     Eigen::MatrixXd& modesSVDBoundary, Eigen::VectorXd& fieldWeightsBoundary, bool saveModesFlag);
-
-
-// // Specialization of getSnapMatrix
-// template  
-// void HyperReduction<PtrList<volScalarField>&>::getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights);
-// template  
-// void HyperReduction<PtrList<volVectorField>&>::getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights);
-// // template 
-// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights);
-
-
-// template  
-// void HyperReduction<PtrList<volScalarField>&>::getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights, 
-//                   List<Eigen::MatrixXd>& snapMatrixBoundary, List<Eigen::VectorXd>& fieldWeightsBoundary);
-// template  
-// void HyperReduction<PtrList<volVectorField>&>::getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights, 
-//                   List<Eigen::MatrixXd>& snapMatrixBoundary, List<Eigen::VectorXd>& fieldWeightsBoundary);
-// // template 
-// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights, 
-// //                   List<Eigen::MatrixXd>& snapMatrixBoundary, List<Eigen::VectorXd>& fieldWeightsBoundary);
-
-
-// // Specialization of saveModes
-// template  <>
-// template <>
-// void HyperReduction<PtrList<volScalarField>&>::saveModes(PtrList<volScalarField>& sList, Eigen::MatrixXd& snapshotsMatrix, 
-//                                               unsigned int &rowIndex, unsigned int &modeIndex, word folder);
-// template  <>
-// template <>
-// void HyperReduction<PtrList<volVectorField>&>::saveModes(PtrList<volVectorField>& sList, Eigen::MatrixXd& snapshotsMatrix, 
-//                                               unsigned int &rowIndex, unsigned int &modeIndex, word folder);
-// // template 
-// // template 
-// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::saveModes(PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>> sList, Eigen::MatrixXd& snapshotsMatrix, 
-// //                                               unsigned int &rowIndex, unsigned int &modeIndex, word folder);
-
-
-// template  <>
-// template <>
-// void HyperReduction<PtrList<volScalarField>&>::saveModes(PtrList<volScalarField>& sList, Eigen::MatrixXd& snapshotsMatrix, 
-//       Eigen::MatrixXd& snapshotsMatrixBoundary, unsigned int &rowIndex,  unsigned int& rowIndexBoundary, unsigned int &modeIndex, word folder);
-// template  <>
-// template <>
-// void HyperReduction<PtrList<volVectorField>&>::saveModes(PtrList<volVectorField>& sList, Eigen::MatrixXd& snapshotsMatrix, 
-//       Eigen::MatrixXd& snapshotsMatrixBoundary, unsigned int &rowIndex,  unsigned int& rowIndexBoundary, unsigned int &modeIndex, word folder);
-// // template 
-// // template 
-// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::saveModes(PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>> sList, Eigen::MatrixXd& snapshotsMatrix, 
-// //       Eigen::MatrixXd& snapshotsMatrixBoundary, unsigned int &rowIndex,  unsigned int& rowIndexBoundary, unsigned int &modeIndex, word folder);
-
-
-// // Specialization of offlineGappyDEIM
-// template  
-// void HyperReduction<PtrList<volScalarField>&>::offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights);
-// template  
-// void HyperReduction<PtrList<volVectorField>&>::offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights);
-// // template 
-// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights);
-
-// // Specialization of offlineECP
-// template  
-// void HyperReduction<PtrList<volScalarField>&>::offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights);
-// template  
-// void HyperReduction<PtrList<volVectorField>&>::offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights);
-// // template 
-// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights);
-
-// // Specialization of initSeeds
-// template  
-// void HyperReduction<PtrList<volScalarField>&>::initSeeds(Eigen::VectorXd mp_not_mask, std::set<label> nodePointsSet);
-// template  
-// void HyperReduction<PtrList<volVectorField>&>::initSeeds(Eigen::VectorXd mp_not_mask, std::set<label> nodePointsSet);
-// // template 
-// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::initSeeds(Eigen::VectorXd mp_not_mask, std::set<label> nodePointsSet);
-
-// // Specialization of updateNodes
-// template  
-// void HyperReduction<PtrList<volScalarField>&>::updateNodes(Eigen::SparseMatrix<double>& P, label& ind, Eigen::VectorXd& mp_not_mask);
-// template  
-// void HyperReduction<PtrList<volVectorField>&>::updateNodes(Eigen::SparseMatrix<double>& P, label& ind, Eigen::VectorXd& mp_not_mask);
-// // template 
-// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::updateNodes(Eigen::SparseMatrix<double>& P, label& ind, Eigen::VectorXd& mp_not_mask);
-
-// // Specialization of computeLS
-// template  
-// void HyperReduction<PtrList<volScalarField>&>::computeLS(Eigen::MatrixXd& J, Eigen::MatrixXd& Jwhole, Eigen::VectorXd& b, Eigen::VectorXd& q);
-// template  
-// void HyperReduction<PtrList<volVectorField>&>::computeLS(Eigen::MatrixXd& J, Eigen::MatrixXd& Jwhole, Eigen::VectorXd& b, Eigen::VectorXd& q);
-// // template 
-// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::computeLS(Eigen::MatrixXd& J, Eigen::MatrixXd& Jwhole, Eigen::VectorXd& b, Eigen::VectorXd& q);
-
-// // Specialization of initReshapeMat
-// template  
-// void HyperReduction<PtrList<volScalarField>&>::initReshapeMat(Eigen::SparseMatrix<double> &reshapeMat);
-// template  
-// void HyperReduction<PtrList<volVectorField>&>::initReshapeMat(Eigen::SparseMatrix<double> &reshapeMat);
-// // template 
-// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::initReshapeMat(Eigen::SparseMatrix<double> &reshapeMat);
-
-// // Specialization of stackSnapshots
-// template  <>
-// template <>
-// void HyperReduction<PtrList<volScalarField>&>::stackSnapshots(PtrList<volScalarField>& sList, Eigen::MatrixXd& snapshotsMatrix, Eigen::VectorXd& fieldWeights);
-// template  <>
-// template <>
-// void HyperReduction<PtrList<volVectorField>&>::stackSnapshots(PtrList<volVectorField>& sList, Eigen::MatrixXd& snapshotsMatrix, Eigen::VectorXd& fieldWeights);
-// // template 
-// // template 
-// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::stackSnapshots(PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>> sList, Eigen::MatrixXd& snapshotsMatrix, Eigen::VectorXd& fieldWeights);
-
-// // Specialization of stackSnapshotsBoundary
-// template  <>
-// template <>
-// void HyperReduction<PtrList<volScalarField>&>::stackSnapshotsBoundary(PtrList<volScalarField>& sList, List<Eigen::MatrixXd>& snapshotsMatrixBoundary, List<Eigen::VectorXd>& fieldWeightsBoundary);
-// template  <>
-// template <>
-// void HyperReduction<PtrList<volVectorField>&>::stackSnapshotsBoundary(PtrList<volVectorField>& sList, List<Eigen::MatrixXd>& snapshotsMatrixBoundary, List<Eigen::VectorXd>& fieldWeightsBoundary);
-// // template 
-// // template 
-// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::stackSnapshotsBoundary(PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>> sList, List<Eigen::MatrixXd>& snapshotsMatrixBoundary, List<Eigen::VectorXd>& fieldWeightsBoundary);
-
-
-// // Specialization of evaluatePinv
-// template  
-// void HyperReduction<PtrList<volScalarField>&>::evaluatePinv(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd &fieldWeights);
-// template  
-// void HyperReduction<PtrList<volVectorField>&>::evaluatePinv(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd &fieldWeights);
-// // template 
-// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::evaluatePinv(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd &fieldWeights);
-
-// // Specialization of evaluateWPU
-// template  
-// void HyperReduction<PtrList<volScalarField>&>::evaluateWPU(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd &fieldWeights, Eigen::VectorXd& quadratureWeights);
-// template  
-// void HyperReduction<PtrList<volVectorField>&>::evaluateWPU(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd &fieldWeights, Eigen::VectorXd& quadratureWeights);
-// // template 
-// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::evaluateWPU(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd &fieldWeights, Eigen::VectorXd& quadratureWeights);
-
-// // Specialization of generateSubmesh
-// template  
-// void HyperReduction<PtrList<volScalarField>&>::generateSubmesh(label layers, const fvMesh &mesh);
-// template  
-// void HyperReduction<PtrList<volVectorField>&>::generateSubmesh(label layers, const fvMesh &mesh);
-// // template 
-// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::generateSubmesh(label layers, const fvMesh &mesh);
-
-// // Specialization of createMasks
-// template  
-// void HyperReduction<PtrList<volScalarField>&>::createMasks(bool offlineStage);
-// template  
-// void HyperReduction<PtrList<volVectorField>&>::createMasks(bool offlineStage);
-// // template 
-// // void HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::createMasks(bool offlineStage);
-
-// // Specialization of global2local
-// template  
-// List<label> HyperReduction<PtrList<volScalarField>&>::global2local(List<label> &points, fvMeshSubset &submesh);
-// template  
-// List<label> HyperReduction<PtrList<volVectorField>&>::global2local(List<label> &points, fvMeshSubset &submesh);
-// // template 
-// // List<label> HyperReduction<PtrList<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh>>&>::global2local(List<label> &points, fvMeshSubset &submesh);
-
-
-
-
 
 
 #endif
diff --git a/tutorials/CFD/08DEIM/HR08DEIM.C b/tutorials/CFD/08DEIM/HR08DEIM.C
index 9adbc2638..df7b4b43b 100644
--- a/tutorials/CFD/08DEIM/HR08DEIM.C
+++ b/tutorials/CFD/08DEIM/HR08DEIM.C
@@ -37,10 +37,8 @@ SourceFiles
 #include "ITHACAstream.H"
 #include "ITHACAPOD.H"
 #include "hyperReduction.templates.H"
-// #include "DEIM.H"
 #include <chrono>
 
-
 class DEIM_function : public HyperReduction<PtrList<volScalarField>&>
 {
     public:
@@ -126,22 +124,23 @@ int main(int argc, char* argv[])
 
     // Create DEIM object with given number of basis functions
     Eigen::VectorXi initSeeds;
-    DEIM_function c(NDEIM, NDEIM, initSeeds, "", Sp);
-    c.problemName = "Gaussian_function"; // To access the same folder as before
+    DEIM_function c(NDEIM, NDEIM, initSeeds, "DEIM", Sp);
+    // c.problemName = "Gaussian_function"; // To access the same folder as before
+
     Eigen::MatrixXd snapshotsModes;
 
-    // To use the DEIMmodes methode from ITHACAPOD :
-    PtrList<volScalarField> modes = ITHACAPOD::DEIMmodes(Sp, NDEIM, "Gaussian_function",S.name());
-    snapshotsModes = Foam2Eigen::PtrList2Eigen(modes);
+    // To use the DEIMmodes method from ITHACAPOD :
     Eigen::VectorXd normalizingWeights = ITHACAutilities::getMassMatrixFV(Sp[0]).array();
+    PtrList<volScalarField> modes = ITHACAPOD::DEIMmodes(Sp, NDEIM, "Gaussian_function", S.name());
+    snapshotsModes = Foam2Eigen::PtrList2Eigen(modes);
 
     // To use the SVD modes from the hyperReduction class : 
     // Eigen::VectorXd normalizingWeights;
     // c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights); 
-    
-
-    c.offlineGappyDEIM(snapshotsModes, normalizingWeights, "ITHACAoutput/DEIM/"+c.problemName);
 
+    c.offlineGappyDEIM(snapshotsModes, normalizingWeights);//, "ITHACAoutput/DEIM/"+c.problemName);
+                                                           // To access the same folder as before
+                                                           
     // Generate the submeshes with the depth of the layer
     c.generateSubmesh(2, mesh); 
     c.subField = autoPtr<volScalarField>(new volScalarField(c.submesh->interpolate(S).ref()));

From 48d82f548c998c097c450110c8c73874924eec94 Mon Sep 17 00:00:00 2001
From: Matthieu Petit <matthieu.petit@scalian.com>
Date: Tue, 19 Mar 2024 11:00:01 +0100
Subject: [PATCH 38/59] Small changes and comments before validation of the
 08DEIM tutorial

---
 tutorials/CFD/08DEIM/08DEIM.C   |  9 +++++----
 tutorials/CFD/08DEIM/HR08DEIM.C | 15 +++++++++------
 2 files changed, 14 insertions(+), 10 deletions(-)

diff --git a/tutorials/CFD/08DEIM/08DEIM.C b/tutorials/CFD/08DEIM/08DEIM.C
index f305d6bb8..a1efdc675 100644
--- a/tutorials/CFD/08DEIM/08DEIM.C
+++ b/tutorials/CFD/08DEIM/08DEIM.C
@@ -111,10 +111,11 @@ int main(int argc, char* argv[])
     );
     // Parameters used to train the non-linear function
     Eigen::MatrixXd pars = ITHACAutilities::rand(100, 2, -0.5, 0.5);
-    // Possible to create a file "random.npy" to compare both version 
-    // with cnpy::save(pars, "./random.npy");
-    // and load it with :  cnpy::load(pars, "./random.npy");
-
+    // It's possible to create a file "random.npy" to compare both version 
+    // save it and load it with : 
+    // cnpy::save(pars, "./random.npy");
+    // cnpy::load(pars, "./random.npy");
+    
     // Perform the offline phase
     for (int i = 0; i < 100; i++)
     {
diff --git a/tutorials/CFD/08DEIM/HR08DEIM.C b/tutorials/CFD/08DEIM/HR08DEIM.C
index df7b4b43b..db136f28e 100644
--- a/tutorials/CFD/08DEIM/HR08DEIM.C
+++ b/tutorials/CFD/08DEIM/HR08DEIM.C
@@ -111,8 +111,10 @@ int main(int argc, char* argv[])
         dimensionedScalar("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), 0)
     );
     // Parameters used to train the non-linear function
-    Eigen::MatrixXd pars ;//= ITHACAutilities::rand(100, 2, -0.5, 0.5);
-    cnpy::load(pars, "./random.npy");
+    Eigen::MatrixXd pars = ITHACAutilities::rand(100, 2, -0.5, 0.5);
+    // To compare with the same parameters, save data and then load it 
+    // cnpy::load(pars, "./random.npy");
+    // cnpy::save(pars, "./random.npy");
 
     // Perform the offline phase
     for (int i = 0; i < 100; i++)
@@ -125,7 +127,6 @@ int main(int argc, char* argv[])
     // Create DEIM object with given number of basis functions
     Eigen::VectorXi initSeeds;
     DEIM_function c(NDEIM, NDEIM, initSeeds, "DEIM", Sp);
-    // c.problemName = "Gaussian_function"; // To access the same folder as before
 
     Eigen::MatrixXd snapshotsModes;
 
@@ -134,12 +135,14 @@ int main(int argc, char* argv[])
     PtrList<volScalarField> modes = ITHACAPOD::DEIMmodes(Sp, NDEIM, "Gaussian_function", S.name());
     snapshotsModes = Foam2Eigen::PtrList2Eigen(modes);
 
-    // To use the SVD modes from the hyperReduction class : 
+    // To use the SVD modes from the HyperReduction class : 
     // Eigen::VectorXd normalizingWeights;
     // c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights); 
 
-    c.offlineGappyDEIM(snapshotsModes, normalizingWeights);//, "ITHACAoutput/DEIM/"+c.problemName);
-                                                           // To access the same folder as before
+    c.offlineGappyDEIM(snapshotsModes, normalizingWeights);
+    // To access the same folder hierarchy as before : 
+    // c.problemName = "Gaussian_function";
+    // c.offlineGappyDEIM(snapshotsModes, normalizingWeights, "ITHACAoutput/DEIM/"+c.problemName);
                                                            
     // Generate the submeshes with the depth of the layer
     c.generateSubmesh(2, mesh); 

From d3a76d510f84be971184ecf9cd9dfd8c50a1af89 Mon Sep 17 00:00:00 2001
From: Matthieu Petit <matthieu.petit@scalian.com>
Date: Tue, 23 Apr 2024 12:16:12 +0200
Subject: [PATCH 39/59] Modifications in the HyperReduction class, changes
 convention in the coordinate choice which has been changed in the tutorial
 24HyperReduction too. Modifications in the tutorial 08DEIM to use the
 HyperReduction class

---
 .../ITHACAutilities/ITHACAutilities.C         |  77 +++++++++++++
 .../ITHACAutilities/ITHACAutilities.H         |  21 ++++
 src/ITHACA_HR/hyperReduction.H                |  40 ++++++-
 src/ITHACA_HR/hyperReduction.templates.H      | 102 ++++++++++--------
 tutorials/CFD/08DEIM/08DEIM.C                 |  80 ++++++++++----
 tutorials/CFD/08DEIM/Make/options             |   6 +-
 tutorials/CFD/08DEIM/system/ITHACAdict        |  11 ++
 .../CFD/24HyperReduction/24HyperReduction.C   |  14 +--
 tutorials/CFD/24HyperReduction/Allrun         |   4 +-
 .../CFD/24HyperReduction/system/ITHACAdict    |   7 +-
 10 files changed, 278 insertions(+), 84 deletions(-)

diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.C
index 78b610580..84d7e0d46 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.C
@@ -133,4 +133,81 @@ List<T> combineList(List<List<T>>& doubleList)
 template List<label> combineList(List<List<label>>& doubleList);
 
 
+// Using the Eigen library, using the SVD decomposition method to solve the
+// matrix pseudo-inverse, the default error er is 0
+Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er) {
+  // perform svd decomposition
+  Eigen::JacobiSVD<Eigen::MatrixXd> svd_holder(origin, Eigen::ComputeThinU | Eigen::ComputeThinV);
+  // Build SVD decomposition results
+  Eigen::MatrixXd U = svd_holder.matrixU();
+  Eigen::MatrixXd V = svd_holder.matrixV();
+  Eigen::MatrixXd D = svd_holder.singularValues();
+
+  // Build the S matrix
+  Eigen::MatrixXd S(V.cols(), U.cols());
+  S.setZero();
+
+  for (unsigned int i = 0; i < D.size(); ++i) {
+
+    if (D(i, 0) > er) {
+      S(i, i) = 1 / D(i, 0);
+    } else {
+      S(i, i) = 0;
+    }
+  }
+  return V * S * U.transpose();
+}
+
+
+Eigen::MatrixXd invertMatrix(Eigen::MatrixXd& matrixToInvert, const word inversionMethod){
+
+  Info << "Inversion method : " << inversionMethod << endl;
+  if(inversionMethod == "pinv_eigen_based"){
+    return pinv_eigen_based(matrixToInvert);
+  }
+  else if(inversionMethod == "direct"){
+    return matrixToInvert.inverse();
+  }
+  else if(inversionMethod == "fullPivLu"){
+    return matrixToInvert.fullPivLu().inverse();
+  }
+  else if(inversionMethod == "partialPivLu"){
+    return matrixToInvert.partialPivLu().inverse();
+  }
+  else if(inversionMethod == "householderQr"){
+    return matrixToInvert.householderQr().solve(Eigen::MatrixXd::Identity(matrixToInvert.rows(), matrixToInvert.cols()));
+  }
+  else if(inversionMethod == "colPivHouseholderQr"){
+    return matrixToInvert.colPivHouseholderQr().inverse();
+  }
+  else if(inversionMethod == "fullPivHouseholderQr"){
+    return matrixToInvert.fullPivHouseholderQr().inverse();
+  }
+  else if(inversionMethod == "completeOrthogonalDecomposition"){
+    return matrixToInvert.completeOrthogonalDecomposition().pseudoInverse();
+  }
+  else if(inversionMethod == "jacobiSvd")
+  {
+    return matrixToInvert.jacobiSvd(Eigen::ComputeThinU | Eigen::ComputeThinV).solve(Eigen::MatrixXd::Identity(matrixToInvert.rows(), matrixToInvert.cols()));
+  }
+  else if(inversionMethod == "llt")
+  {
+    return matrixToInvert.llt().solve(Eigen::MatrixXd::Identity(matrixToInvert.rows(), matrixToInvert.cols()));
+  }
+  else if(inversionMethod == "ldlt")
+  {
+    Eigen::LLT<Eigen::MatrixXd> lltOfA(matrixToInvert);
+    return lltOfA.solve(Eigen::MatrixXd::Identity(matrixToInvert.rows(), matrixToInvert.cols()));
+  }
+  else if(inversionMethod == "bdcSvd")
+  {
+    return matrixToInvert.bdcSvd(Eigen::ComputeThinU | Eigen::ComputeThinV).solve(Eigen::MatrixXd::Identity(matrixToInvert.rows(), matrixToInvert.cols()));
+  } 
+  else{
+    Info << "Unkwown inversion method, solving with : completeOrthogonalDecomposition" << endl;
+    return matrixToInvert.completeOrthogonalDecomposition().pseudoInverse();
+  }
 }
+
+
+}
\ No newline at end of file
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.H b/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.H
index f4ebdf1b4..90041cd14 100755
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.H
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.H
@@ -125,6 +125,27 @@ bool isTurbulent();
 template<typename T>
 List<T> combineList(List<List<T>>& doubleList);
 
+//------------------------------------------------------------------------------
+/// @brief      Using the Eigen library, using the SVD decomposition method to solve the
+///             matrix pseudo-inverse, the default error er is 0
+///
+/// @param      origin  Matrix to invert
+/// @param      er      Error
+///
+/// @return     Inversed matrix
+///
+Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
+
+//------------------------------------------------------------------------------
+/// @brief      Invert a matrix given the method name in the ITHACAdict
+///
+/// @param[in]      matrixToInvert  Matrix to invert
+/// @param[in]      methodName      Method 
+///
+/// @return         Inversed matrix
+///
+Eigen::MatrixXd invertMatrix(Eigen::MatrixXd& matrixToInvert, const word inversionMethod);
+
 
 };
 #endif
diff --git a/src/ITHACA_HR/hyperReduction.H b/src/ITHACA_HR/hyperReduction.H
index 6411b4338..26ec277a3 100644
--- a/src/ITHACA_HR/hyperReduction.H
+++ b/src/ITHACA_HR/hyperReduction.H
@@ -40,7 +40,7 @@ SourceFiles
 #include <set>
 #include "redsvd"
 
-Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
+
 
 // TODO uniform style for separating offline and onlie stages
 template <typename... SnapshotsLists>
@@ -79,6 +79,23 @@ public:
                    word problemName,
                    SnapshotsLists &&...snapshotsLists);
     
+    //----------------------------------------------------------------------
+    /// @brief      Construct HyperReduction class
+    ///
+    /// @param[in]  n_modes           Dimension of the HR basis
+    /// @param[in]  n_nodes           Number of nodes
+    /// @param[in]  vectorial_dim     Field dimension (1 for volScalarField 3 for volVectorField)
+    /// @param[in]  n_cells           Number of cells
+    /// @param[in]  initialSeeds      Initial nodes
+    /// @param[in]  problemName       Name of the function to be hyper-reduced
+    ///
+    HyperReduction(label n_modes,
+                   label n_nodes,
+                   unsigned int vectorial_dim, 
+                   label n_cells,
+                   Eigen::VectorXi initialSeeds,
+                   word problemName);
+    
     // ITHACA parameters dict
     ITHACAparameters* para;
 
@@ -181,16 +198,31 @@ public:
     
     /// Submeshes
     autoPtr<volVectorField> submesh_field;
+
+    /// Online Matrix
+    Eigen::MatrixXd MatrixOnline;
     
     //----------------------------------------------------------------------
     /// @brief      Methods implemented: 'GappyDEIM'  from "DEIM, Chaturantabut, Saifon, and Danny C. Sorensen. "Nonlinear model reduction via discrete empirical interpolation." SIAM Journal on Scientific Computing 32.5 (2010): 2737-2764" and "GNAT, Carlberg, Kevin, et al. "The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows." Journal of Computational Physics 242 (2013): 623-647.". Quasi-optimal point selection algorithm 'SOPT' and optimal point selection 'SOPTE' from "Lauzon, Jessica T., Siu Wun Cheung, Yeonjong Shin, Youngsoo Choi, Dylan Matthew Copeland, and Kevin Huynh. "S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models." arXiv preprint arXiv:2203.16494 (2022).""
     ///
-    void offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights);
+    void offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights){
+        methodName = "GappyDEIM";
+        word name = "ITHACAoutput/" + problemName + "/" + methodName;
+        offlineGappyDEIM(snapshotsModes, normalizingWeights, name);
+    }
+
+    void offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights, word folderMethodName);
 
     //----------------------------------------------------------------------
     /// @brief      Methods implemented: 'ECP' from "ECP, Hernandez, Joaquin Alberto, Manuel Alejandro Caicedo, and Alex Ferrer. "Dimensional hyper-reduction of nonlinear finite element models via empirical cubature." Computer methods in applied mechanics and engineering 313 (2017): 687-722.". TODO implement non-negative LS.
     ///
-    void offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights);
+    void offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights){
+        methodName = "ECP";
+        word name = "ITHACAoutput/" + problemName + "/" + methodName;
+        offlineECP(snapshotsModes, normalizingWeights, name);
+    }
+
+    void offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights, word folderMethodName);
     
     //----------------------------------------------------------------------
     /// @brief      TODO
@@ -315,7 +347,7 @@ public:
     /// @param[in]  layers          projector into interpolation nodes
     /// @param[in]  mesh            matrix to restrict and invert
     ///
-    void generateSubmesh(label layers, fvMesh &mesh);
+    void generateSubmesh(label layers, const fvMesh &mesh);
 
     //----------------------------------------------------------------------
     /// @brief      Get local indices in the submesh from indices in the global ones
diff --git a/src/ITHACA_HR/hyperReduction.templates.H b/src/ITHACA_HR/hyperReduction.templates.H
index 90c37cc9a..d3f0e383d 100644
--- a/src/ITHACA_HR/hyperReduction.templates.H
+++ b/src/ITHACA_HR/hyperReduction.templates.H
@@ -95,29 +95,29 @@ HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
   Info << "Number of boundary cells: " << n_boundary_cells << endl;
 }
 
-// Using the Eigen library, using the SVD decomposition method to solve the
-// matrix pseudo-inverse, the default error er is 0
-Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er) {
-  // perform svd decomposition
-  Eigen::JacobiSVD<Eigen::MatrixXd> svd_holder(origin, Eigen::ComputeThinU | Eigen::ComputeThinV);
-  // Build SVD decomposition results
-  Eigen::MatrixXd U = svd_holder.matrixU();
-  Eigen::MatrixXd V = svd_holder.matrixV();
-  Eigen::MatrixXd D = svd_holder.singularValues();
-
-  // Build the S matrix
-  Eigen::MatrixXd S(V.cols(), U.cols());
-  S.setZero();
-
-  for (unsigned int i = 0; i < D.size(); ++i) {
-
-    if (D(i, 0) > er) {
-      S(i, i) = 1 / D(i, 0);
-    } else {
-      S(i, i) = 0;
-    }
-  }
-  return V * S * U.transpose();
+
+// Template function constructor
+template <typename... SnapshotsLists>
+HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
+                                                  label n_nodes,
+                                                  unsigned int vectorialDim,
+                                                  label n_cells,
+                                                  Eigen::VectorXi initialSeeds,
+                                                  word problemName)
+    : n_modes{n_modes},
+      n_nodes{n_nodes},
+      vectorial_dim{vectorialDim},
+      n_cells{n_cells},
+      initialSeeds{initialSeeds},
+      problemName{problemName}
+{
+  Info << "Init HyperReduction class with vectorial dim: " << vectorial_dim << endl;
+  para = ITHACAparameters::getInstance();
+  folderProblem = problemName;
+  mkDir(folderProblem);
+
+  Info << "Initial seeds length: " << initialSeeds.rows() << endl;
+
 }
 
 template <typename... SnapshotsLists>
@@ -368,10 +368,10 @@ void HyperReduction<SnapshotsLists...>::saveModes(SnapshotsList sList, Eigen::Ma
 }
 
 template <typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights)
+void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights, word folderMethodName)
 {
-  methodName = "GappyDEIM";
-  folderMethod = "ITHACAoutput/" + problemName + "/" + methodName;
+  folderMethod = folderMethodName;
+  Info << "FolderMethod : " << folderMethod << endl;
   mkDir(folderMethod);
 
   normalizingWeights = weights;
@@ -380,7 +380,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
       IOobject("nodePoints", para->runTime.time().constant(), "../" + folderMethod,
                 para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE))); 
 
-  auto greedyMetric = para->ITHACAdict->lookupOrDefault<word>("GreedyMetric", "l2");
+  auto greedyMetric = para->ITHACAdict->lookupOrDefault<word>("GreedyMetric", "L2");
   
   bool offlineStage = !nodePoints().headerOk();
 
@@ -584,12 +584,15 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
     evaluatePinv(P, basisMatrix, normalizingWeights);
     renormalizedBasisMatrix = normalizingWeights.asDiagonal()*basisMatrix;
 
+    MatrixOnline = renormalizedBasisMatrix * pinvPU;
+
     P.makeCompressed();
     cnpy::save(basisMatrix, folderMethod +"/basisMatrix.npy");
     cnpy::save(P, folderMethod +"/projectionMatrix.npz");
     cnpy::save(normalizingWeights, folderMethod + "/normalizingWeights.npy");
     cnpy::save(nodes, folderMethod + "/mp.npy");
     cnpy::save(pinvPU, folderMethod + "/pinvPU.npy");
+    cnpy::save(MatrixOnline, folderMethod + "/MatrixOnline.npy");
     nodePoints().write();
 
     Info << "Projection Matrix shape: " << P.rows() << " " << P.cols() << endl;
@@ -600,6 +603,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
   {
     Info << "Read GappyDEIM\n";
     cnpy::load(basisMatrix, folderMethod +"/basisMatrix.npy");
+    cnpy::load(MatrixOnline, folderMethod +"/MatrixOnline.npy");
     cnpy::load(normalizingWeights, folderMethod + "/normalizingWeights.npy");
     cnpy::load(P, folderMethod +"/projectionMatrix.npz");
     cnpy::load(nodes, folderMethod + "/mp.npy");
@@ -614,9 +618,12 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
 }
 
 template <typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights)
+void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights, word folderMethodName)
 {
-  methodName = "ECP";
+  folderMethod = folderMethodName;
+  Info << "FolderMethod : " << folderMethod << endl;
+  mkDir(folderMethod);
+
   n_nodes = n_modes + 1;
 
   normalizingWeights = weights;
@@ -626,9 +633,6 @@ void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd& snapshotsMod
             << ", nodePoints=" << n_nodes << " #######"
             << endl;
 
-  folderMethod = "ITHACAoutput/" + problemName + "/" + methodName;
-  mkDir(folderMethod);
-
   nodePoints = autoPtr<IOList<label>>(new IOList<label>(
       IOobject("nodePoints", para->runTime.time().constant(), "../" + folderMethod,
                 para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE))); 
@@ -754,8 +758,13 @@ void HyperReduction<SnapshotsLists...>::initSeeds(Eigen::VectorXd mp_not_mask, s
 template <typename... SnapshotsLists>
 void HyperReduction<SnapshotsLists...>::updateNodes(Eigen::SparseMatrix<double>& P, label& ind, Eigen::VectorXd& mp_not_mask)
 {
+  nodePoints->append(ind);
+
+  nodes.conservativeResize(nodes.rows()+1);
+  nodes(nodes.rows()-1) = ind;
+
   unsigned int last_col{0};
-  
+
   if (P.rows()==0)
   {
     P.resize(n_cells*vectorial_dim, vectorial_dim);
@@ -763,19 +772,22 @@ void HyperReduction<SnapshotsLists...>::updateNodes(Eigen::SparseMatrix<double>&
   else
   {
     last_col = P.cols();
-    P.conservativeResize(P.rows(), P.cols() + vectorial_dim);
+    P.resize(P.rows(), P.cols() + vectorial_dim);
+  }
+  int step = P.cols() / vectorial_dim - 1;
+  
+  for (int ith_node=0; ith_node <= step; ith_node++)
+  {
+    for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+    {
+      P.insert(nodes[ith_node]+ith_field*n_cells,ith_node+ith_field*(step+1))=1;
+    }
   }
 
   for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
   {
-    P.insert(ind + ith_field * n_cells, last_col + ith_field) = 1;
     mp_not_mask(ind + ith_field * n_cells) = 0;
   }
-
-  nodePoints->append(ind);
-
-  nodes.conservativeResize(nodes.rows()+1);
-  nodes(nodes.rows()-1) = ind;
 }
 
 template<typename... SnapshotsLists>
@@ -863,7 +875,7 @@ void HyperReduction<SnapshotsLists...>::evaluatePinv(Eigen::SparseMatrix<double>
   assert(Projector.cols() > 0);
   Eigen::MatrixXd restricted = Projector.transpose() * Modes;
   Info << "S-Optimalty: " << s_optimality(restricted) << endl;
-  pinvPU = pinv_eigen_based(restricted);
+  pinvPU = ITHACAutilities::invertMatrix(restricted, para->ITHACAdict->lookupOrDefault<word>("InversionMethod", "completeOrthogonalDecomposition"));
   pinvPU = pinvPU*(Projector.transpose() * fieldWeights.array().cwiseInverse().matrix()).asDiagonal();
 }
 
@@ -875,9 +887,9 @@ void HyperReduction<SnapshotsLists...>::evaluateWPU(Eigen::SparseMatrix<double>
   unsigned int n_weightsPerField = quadratureWeights.rows()/vectorial_dim;
   unsigned int reorderIndex{0};
 
-  for (unsigned int ith_weight = 0; ith_weight < n_weightsPerField; ith_weight++)
-  {
-    for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+  for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+  {  
+    for (unsigned int ith_weight = 0; ith_weight < n_weightsPerField; ith_weight++)
     {
       quadratureWeightsOrderedAsProjector(reorderIndex) = quadratureWeights(ith_weight + ith_field * n_weightsPerField);
       reorderIndex++;
@@ -887,7 +899,7 @@ void HyperReduction<SnapshotsLists...>::evaluateWPU(Eigen::SparseMatrix<double>
 }
 
 template<typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::generateSubmesh(label layers, fvMesh &mesh) {
+void HyperReduction<SnapshotsLists...>::generateSubmesh(label layers, const fvMesh &mesh) {
 
   Info << "####### Extract submesh #######\n";
   ITHACAparameters *para(ITHACAparameters::getInstance());
diff --git a/tutorials/CFD/08DEIM/08DEIM.C b/tutorials/CFD/08DEIM/08DEIM.C
index 4a9b880fc..3ea6fbd4d 100644
--- a/tutorials/CFD/08DEIM/08DEIM.C
+++ b/tutorials/CFD/08DEIM/08DEIM.C
@@ -36,13 +36,12 @@ SourceFiles
 #include "Foam2Eigen.H"
 #include "ITHACAstream.H"
 #include "ITHACAPOD.H"
-#include "DEIM.H"
+#include "hyperReduction.templates.H"
 #include <chrono>
-
-class DEIM_function : public DEIM<volScalarField>
+class DEIM_function : public HyperReduction<PtrList<volScalarField>&>
 {
     public:
-        using DEIM::DEIM;
+        using HyperReduction::HyperReduction;
         static volScalarField evaluate_expression(volScalarField& S, Eigen::MatrixXd mu)
         {
             volScalarField yPos = S.mesh().C().component(vector::Y).ref();
@@ -58,18 +57,19 @@ class DEIM_function : public DEIM<volScalarField>
         }
         Eigen::VectorXd onlineCoeffs(Eigen::MatrixXd mu)
         {
-            theta.resize(magicPoints().size());
+            theta.resize(nodePoints().size());
             auto f = evaluate_expression(subField(), mu);
 
-            for (int i = 0; i < magicPoints().size(); i++)
+            for (int i = 0; i < nodePoints().size(); i++)
             {
                 // double on_coeff = f[localMagicPoints[i]];
-                theta(i) = f[localMagicPoints[i]];
+                theta(i) = f[localNodePoints[i]];
             }
 
             return theta;
         }
-
+        
+        Eigen::VectorXd theta; 
         PtrList<volScalarField> fields;
         autoPtr<volScalarField> subField;
 };
@@ -111,6 +111,10 @@ int main(int argc, char* argv[])
     );
     // Parameters used to train the non-linear function
     Eigen::MatrixXd pars = ITHACAutilities::rand(100, 2, -0.5, 0.5);
+    
+    // To compare with the same parameters, save data and then load it 
+    // cnpy::load(pars, "./random100.npy");
+    // cnpy::save(pars, "./random100.npy");
 
     // Perform the offline phase
     for (int i = 0; i < 100; i++)
@@ -120,11 +124,31 @@ int main(int argc, char* argv[])
         ITHACAstream::exportSolution(S, name(i + 1), "./ITHACAoutput/Offline/");
     }
 
+    Eigen::MatrixXd snapshotsModes;
+
+    // To use the DEIMmodes method from ITHACAPOD :
+    Eigen::VectorXd normalizingWeights = ITHACAutilities::getMassMatrixFV(Sp[0]).array();
+    PtrList<volScalarField> modes = ITHACAPOD::DEIMmodes(Sp, NDEIM, "GappyDEIM", S.name());
+    snapshotsModes = Foam2Eigen::PtrList2Eigen(modes);
+
+    // To use the SVD modes from the HyperReduction class : 
+    // Eigen::VectorXd normalizingWeights;
+    // c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights); 
+
     // Create DEIM object with given number of basis functions
-    DEIM_function c(Sp, NDEIM, "Gaussian_function", S.name());
+    Eigen::VectorXi initSeeds(0);
+    DEIM_function c(NDEIM, NDEIM, initSeeds, "DEIM", Sp);
+
+    // Compute the DEIM 
+    c.offlineGappyDEIM(snapshotsModes, normalizingWeights);
+    // To access the same folder hierarchy as before : 
+    // c.problemName = "Gaussian_function";
+    // c.offlineGappyDEIM(snapshotsModes, normalizingWeights, "ITHACAoutput/DEIM/"+c.problemName);
+                                                           
     // Generate the submeshes with the depth of the layer
-    c.subField = autoPtr<volScalarField>(new volScalarField(c.generateSubmesh(2,
-                                         mesh, S)));
+    c.generateSubmesh(2, mesh); 
+    c.subField = c.interpolateField<volScalarField>(Sp[0]);
+
     // Define a new online parameter
     Eigen::MatrixXd par_new(2, 1);
     par_new(0, 0) = 0;
@@ -148,19 +172,19 @@ int main(int argc, char* argv[])
 
 /// \example 08DEIM.C
 /// \section intro_08DEIM Introduction to tutorial 8
-/// In this tutorial we propose an example concerning the usage of the Discrete Empirical Interpolation Method (implemented in the DEIM class) for the approximation of a non-linear function.
+/// In this tutorial we propose an example concerning the usage of the Discrete Empirical Interpolation Method (implemented in the HyperReduction class) for the approximation of a non-linear function.
 /// The following image illustrates the computational domain used to discretize the problem
 /// \htmlonly <style>div.image img[src="mesh.png"]{width:500px;}</style> \endhtmlonly @image html mesh.png "Computational Domain"
 ///
-/// The non-liner function is described by a parametric Gaussian function:
+/// The non-linear function is described by a parametric Gaussian function:
 /// \f[
 /// S(\mathbf{x},\mathbf{\mu}) = e^{-2(x-\mu_x-1)^2 - 2(y-\mu_y-0.5)^2},
 ///  \f]
-/// that is depending on the parameter vector \f$\mathbf{\mu} = [\mu_x, \mu_y] \f$ and on the location inside the domain \f$ \mathbf{x} = [x,y] \f$. A training set of 100 samples is used to construct the DEIM modes which are later used for the approximation.
+/// that is depending on the parameter vector \f$\mathbf{\mu} = [\mu_x, \mu_y] \f$ and on the location inside the domain \f$ \mathbf{x} = [x,y] \f$. A training set of 100 samples is used to construct the "DEIM" modes which are later used for the approximation.
 ///
 /// \subsection header The necessary header files
 /// First of all let's have a look to the header files that needs to be included and what they are responsible for:
-/// The header files of ITHACA-FV necessary for this tutorial are: <Foam2Eigen.H> for Eigen to OpenFOAM conversion of objects, <ITHACAstream.H> for ITHACA-FV input-output operations. <ITHACAPOD.H> for the POD decomposition, <DEIM.H> for the DEIM approximation.
+/// The header files of ITHACA-FV necessary for this tutorial are: <Foam2Eigen.H> for Eigen to OpenFOAM conversion of objects, <ITHACAstream.H> for ITHACA-FV input-output operations. <ITHACAPOD.H> for the POD decomposition, <hyperReduction.templates.H> for the "DEIM" approximation.
 ///
 ///
 /// \section code08 A detailed look into the code
@@ -172,14 +196,14 @@ int main(int argc, char* argv[])
 ///
 /// ITHACA-FV header files
 ///
-/// \until DEIM
+/// \until hyperReduction
 ///
 /// chrono to compute the speedup
 /// \until chrono
 ///
-/// Construction of the function to be approximated with the DEIM method.
+/// Construction of the function to be approximated with the "DEIM" method from the HyperReduction class.
 /// \skip class
-/// \until DEIM::DEIM
+/// \until HyperReduction::HyperReduction
 ///
 /// Method with the explicit definition of the non-linear function
 /// \skip evaluate_expression
@@ -201,15 +225,27 @@ int main(int argc, char* argv[])
 /// Offline training of the function and assembly of the snapshots list
 /// \skip for
 /// \until }
-/// Construction of the DEIM object passing the list of snapshots Sp, the maximum number of DEIM modes NDEIM, and the name used to store the output "Gaussian_function".
-/// \skipline DEIM_function
+///
+/// Compute the "DEIM" modes using the ITHACAPOD class 
+/// \skip normalizingWeights
+/// \until snapshotsModes
+///
+/// Construction of the HyperReduction object passing the maximum number of "DEIM" modes NDEIM, the initSeeds (none in this tutorial), the name used to store the output "DEIM" and the list of snapshots Sp. The constructor is taking the number of modes and the number of point to compute, for the "DEIM" method these numbers are equal. 
+/// \skip initSeeds 
+/// \until DEIM_function
+///
+/// Compute the "DEIM" method HyperReduction::offlineGappyDEIM passing the "DEIM" modes and the normalizingWeights
+/// \skipline c.offlineGappyDEIM
+///
 /// Command to generate the submeshes used for pointwise evaluation of the function
-/// \skipline c.
+/// \skip c.generateSubmesh
+/// \until c.subField
+///
 /// Definition of a new sample value to test the accuracy of the method \f$ \mu* = (0,0) \f$
 /// \skip Eigen
 /// \until 1,
 ///
-/// Evaluation of the function using DEIM and reconstruction of the field
+/// Evaluation of the function using "DEIM" and reconstruction of the field
 /// \skip Eigen
 /// \until volSca
 ///
diff --git a/tutorials/CFD/08DEIM/Make/options b/tutorials/CFD/08DEIM/Make/options
index d25ac44ef..6ce109619 100644
--- a/tutorials/CFD/08DEIM/Make/options
+++ b/tutorials/CFD/08DEIM/Make/options
@@ -13,18 +13,18 @@ EXE_INC = \
     -I$(LIB_SRC)/thermophysicalModels/basic/lnInclude \
     -I$(LIB_SRC)/turbulenceModels/compressible/turbulenceModel \
     -I$(LIB_SRC)/functionObjects/forces/lnInclude \
-    -I$(LIB_ITHACA_SRC)/ITHACA_DEIM \
+    -I$(LIB_ITHACA_SRC)/ITHACA_HR \
     -I$(LIB_ITHACA_SRC)/ITHACA_FOMPROBLEMS/lnInclude \
     -I$(LIB_ITHACA_SRC)/ITHACA_ROMPROBLEMS/lnInclude \
     -I$(LIB_ITHACA_SRC)/ITHACA_CORE/lnInclude \
     -I$(LIB_ITHACA_SRC)/thirdparty/Eigen \
+    -I$(LIB_ITHACA_SRC)/thirdparty/redsvd \
     -I$(LIB_ITHACA_SRC)/thirdparty/spectra/include \
     -I$(LIB_ITHACA_SRC)/ITHACA_THIRD_PARTY/splinter/include \
     -Wno-comment \
     -w \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11 \
-
+    -std=c++17 \
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/tutorials/CFD/08DEIM/system/ITHACAdict b/tutorials/CFD/08DEIM/system/ITHACAdict
index ce42c6026..84ac7599c 100755
--- a/tutorials/CFD/08DEIM/system/ITHACAdict
+++ b/tutorials/CFD/08DEIM/system/ITHACAdict
@@ -23,3 +23,14 @@ NDEIM 80;
 // Output format to save market vectors.
 OutPrecision 20;
 OutType fixed;
+
+// HR
+HyperReduction GappyDEIM;
+GreedyMetric L2;//L2, SOPT, SOPTE
+
+// Inversion method 
+// Possibilities : pinv_eigen_based, half_pinv_eigen_based, direct, fullPivLu, 
+// partialPivLu, householderQr, colPivHouseholderQr, fullPivHouseholderQr, 
+// completeOrthogonalDecomposition, jacobiSvd, llt, ldlt, bdcSvd  
+InversionMethod completeOrthogonalDecomposition;
+
diff --git a/tutorials/CFD/24HyperReduction/24HyperReduction.C b/tutorials/CFD/24HyperReduction/24HyperReduction.C
index 6cf4d6256..d7013bda6 100644
--- a/tutorials/CFD/24HyperReduction/24HyperReduction.C
+++ b/tutorials/CFD/24HyperReduction/24HyperReduction.C
@@ -110,11 +110,11 @@ class HyperReduction_vectorFunction : public HyperReduction<PtrList<volVectorFie
 
             for (auto i = 0; i < nodesList.size(); i++)
             {
-                ret(i*3) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
+                ret(i) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
-                ret(i*3 + 1) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 0.5,
+                ret(i + nodesList.size()) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 0.5,
                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
-                ret(i*3 + 2) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1.5,
+                ret(i + 2 * nodesList.size()) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1.5,
                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0., 2));
             }
 
@@ -161,13 +161,13 @@ class HyperReduction_vectorScalarFunction : public HyperReduction<PtrList<volVec
 
             for (auto i = 0; i < nodesList.size(); i++)
             {
-                ret(i*4) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
+                ret(i) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
-                ret(i*4 + 1) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 0.5,
+                ret(i + nodesList.size()) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 0.5,
                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
-                ret(i*4 + 2) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1.5,
+                ret(i + 2 * nodesList.size()) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1.5,
                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0., 2));
-                ret(i*4 + 3) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
+                ret(i + 3 * nodesList.size()) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
             }
 
diff --git a/tutorials/CFD/24HyperReduction/Allrun b/tutorials/CFD/24HyperReduction/Allrun
index d5b3083d6..009c45b14 100755
--- a/tutorials/CFD/24HyperReduction/Allrun
+++ b/tutorials/CFD/24HyperReduction/Allrun
@@ -4,4 +4,6 @@ cd ${0%/*} || exit 1    # Run from this directory
 # Source tutorial run functions
 . $WM_PROJECT_DIR/bin/tools/RunFunctions
 
-runApplication 24HyperReduction
+# To test scalar : -test scalar 
+# To test vector + scalar : -test vs 
+runApplication 24HyperReduction -test vector 
diff --git a/tutorials/CFD/24HyperReduction/system/ITHACAdict b/tutorials/CFD/24HyperReduction/system/ITHACAdict
index 668de9635..6bd532ce5 100755
--- a/tutorials/CFD/24HyperReduction/system/ITHACAdict
+++ b/tutorials/CFD/24HyperReduction/system/ITHACAdict
@@ -26,5 +26,8 @@ OutPrecision 20;
 OutType fixed;
 
 // HR
-HyperReduction ECP;//GappyDEIM, ECP
-GreedyMetric L2;//L2, SOPT, SOPTE
\ No newline at end of file
+HyperReduction GappyDEIM;//GappyDEIM, ECP
+GreedyMetric L2;//L2, SOPT, SOPTE
+
+// Inversion Method 
+InversionMethod completeOrthogonalDecomposition;

From a018608af96150f25e9de76d778f92892f08e553 Mon Sep 17 00:00:00 2001
From: giovastabile <giovanni.stabile87@gmail.com>
Date: Sat, 18 May 2024 09:16:19 +0200
Subject: [PATCH 40/59] removed old workflows

---
 .github/workflows/of1812.yml | 27 ---------------------------
 .github/workflows/of1906.yml | 27 ---------------------------
 .github/workflows/of1912.yml | 27 ---------------------------
 .github/workflows/of2006.yml | 27 ---------------------------
 4 files changed, 108 deletions(-)
 delete mode 100755 .github/workflows/of1812.yml
 delete mode 100755 .github/workflows/of1906.yml
 delete mode 100755 .github/workflows/of1912.yml
 delete mode 100755 .github/workflows/of2006.yml

diff --git a/.github/workflows/of1812.yml b/.github/workflows/of1812.yml
deleted file mode 100755
index c3a428093..000000000
--- a/.github/workflows/of1812.yml
+++ /dev/null
@@ -1,27 +0,0 @@
-name: OF1812
-
-on:
-  push:
-    branches: [ master ]
-  pull_request:
-    branches: [ master ]
-
-jobs:
-  build:
-
-    runs-on: ubuntu-latest
-    
-    strategy:
-      matrix:
-        include:
-          - name: "OpenFOAM 1812"
-            install: "cd ."
-            compile: ./.compileOF1812.sh
-
-    steps:
-    - name: Checkout
-      uses: actions/checkout@v1
-    - name: install OF
-      run: ${{ matrix.install}}
-    - name: make
-      run: ${{ matrix.compile}}
diff --git a/.github/workflows/of1906.yml b/.github/workflows/of1906.yml
deleted file mode 100755
index 9b8adef8f..000000000
--- a/.github/workflows/of1906.yml
+++ /dev/null
@@ -1,27 +0,0 @@
-name: OF1906
-
-on:
-  push:
-    branches: [ master ]
-  pull_request:
-    branches: [ master ]
-
-jobs:
-  build:
-
-    runs-on: ubuntu-latest
-    
-    strategy:
-      matrix:
-        include:
-          - name: "OpenFOAM 1906"
-            install: "cd ."
-            compile: ./.compileOF1906.sh
-
-    steps:
-    - name: Checkout
-      uses: actions/checkout@v1
-    - name: install OF
-      run: ${{ matrix.install}}
-    - name: make
-      run: ${{ matrix.compile}}
diff --git a/.github/workflows/of1912.yml b/.github/workflows/of1912.yml
deleted file mode 100755
index 6cff9bcd2..000000000
--- a/.github/workflows/of1912.yml
+++ /dev/null
@@ -1,27 +0,0 @@
-name: OF1912
-
-on:
-  push:
-    branches: [ master ]
-  pull_request:
-    branches: [ master ]
-
-jobs:
-  build:
-
-    runs-on: ubuntu-latest
-    
-    strategy:
-      matrix:
-        include:
-          - name: "OpenFOAM 1912"
-            install: "cd ."
-            compile: ./.compileOF1912.sh
-
-    steps:
-    - name: Checkout
-      uses: actions/checkout@v1
-    - name: install OF
-      run: ${{ matrix.install}}
-    - name: make
-      run: ${{ matrix.compile}}
diff --git a/.github/workflows/of2006.yml b/.github/workflows/of2006.yml
deleted file mode 100755
index 4910f0bc3..000000000
--- a/.github/workflows/of2006.yml
+++ /dev/null
@@ -1,27 +0,0 @@
-name: OF2006
-
-on:
-  push:
-    branches: [ master ]
-  pull_request:
-    branches: [ master ]
-
-jobs:
-  build:
-
-    runs-on: ubuntu-latest
-    
-    strategy:
-      matrix:
-        include:
-          - name: "OpenFOAM 2006"
-            install: "cd ."
-            compile: ./.compileOF2006.sh
-
-    steps:
-    - name: Checkout
-      uses: actions/checkout@v1
-    - name: install OF
-      run: ${{ matrix.install}}
-    - name: make
-      run: ${{ matrix.compile}}

From fd7e41860e961dcc860773ef01313ccef8f2789d Mon Sep 17 00:00:00 2001
From: giovastabile <giovanni.stabile87@gmail.com>
Date: Sat, 18 May 2024 09:21:55 +0200
Subject: [PATCH 41/59] changing doc

---
 src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblem.H | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblem.H b/src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblem.H
index 111bff205..916bec211 100755
--- a/src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblem.H
+++ b/src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblem.H
@@ -348,8 +348,8 @@ class reductionProblem
  * ITHACA-FV (In real Time Highly Advanced Computational Applications for
 Finite Volumes) is C++ library based on the finite volume solver
 [<b> OpenFOAM </b>](https://openfoam.org/). It consists of the implementation of several reduced order
-modeling techniques for parametrized problems. ITHACA-FV is developed and maintained by
-[<b> Dr. Giovanni Stabile </b>](https://www.giovannistabile.com/) at the [<b>University of Urbino Carlo Bo](https://www.uniurb.it/) and at [<b> SISSA mathLab </b>](https://mathlab.sissa.it/) in collaboration with [<b> Prof. Gianluigi Rozza's Group </b>](http://people.sissa.it/~grozza/). Check also the GitHub [webpage](https://github.com/ITHACA-FV/ITHACA-FV) for more info.
+modeling techniques for parametrized problems. ITHACA-FV is developed and maintained by the group of 
+[<b> Dr. Giovanni Stabile </b>](https://www.giovannistabile.com/) at the [<b>Sant'Anna School of Advanced Studies](https://www.santannapisa.it/en) and at [<b> SISSA mathLab </b>](https://mathlab.sissa.it/) in collaboration with [<b> Prof. Gianluigi Rozza's Group </b>](http://people.sissa.it/~grozza/). Check also the GitHub [webpage](https://github.com/ITHACA-FV/ITHACA-FV) for more info.
 
  *
  * \section structure ITHACA-FV directory structure

From d68efca5b8fd4ee462fbf84e65307d163be6aadb Mon Sep 17 00:00:00 2001
From: giovastabile <giovanni.stabile87@gmail.com>
Date: Sat, 18 May 2024 09:29:33 +0200
Subject: [PATCH 42/59] Fixing docs

---
 README.md                                     | 20 +++++++------------
 .../reductionProblem/reductionProblem.H       |  4 ++--
 2 files changed, 9 insertions(+), 15 deletions(-)

diff --git a/README.md b/README.md
index 6b68d8951..3cb6c7edd 100644
--- a/README.md
+++ b/README.md
@@ -15,30 +15,24 @@
 </a>
 </p>
 <p align="center">
-<a href="https://github.com/ithaca-fv/ITHACA-FV/actions?query=workflow%3AOF1812"><img alt="OF1812" src="https://github.com/ithaca-fv/ITHACA-FV/workflows/OF1812/badge.svg"></a>
-<a href="https://github.com/ithaca-fv/ITHACA-FV/actions?query=workflow%3AOF1906"><img alt="OF1906" src="https://github.com/ithaca-fv/ITHACA-FV/workflows/OF1906/badge.svg"></a>
-<a href="https://github.com/ithaca-fv/ITHACA-FV/actions?query=workflow%3AOF1912"><img alt="OF1912" src="https://github.com/ithaca-fv/ITHACA-FV/workflows/OF1912/badge.svg"></a>
-<a href="https://github.com/ithaca-fv/ITHACA-FV/actions?query=workflow%3AOF2006"><img alt="OF2006" src="https://github.com/ithaca-fv/ITHACA-FV/workflows/OF2006/badge.svg"></a>
+<a href="https://github.com/ithaca-fv/ITHACA-FV/actions?query=workflow%3AOF1812"><img alt="OF1812" src="https://github.com/ithaca-fv/ITHACA-FV/workflows/OF2212/badge.svg"></a>
 </p>
 
 ### 0. Introduction
-**ITHACA-FV** is an implementation in **OpenFOAM** of several reduced order modelling techniques. **ITHACA-FV** is designed for [**OpenFOAM v2212**](https://www.openfoam.com/news/main-news/openfoam-v2212/) and older openfoam.com versions but it can be easily adapted also to other versions of OpenFOAM.
+**ITHACA-FV** is an implementation in **OpenFOAM** of several reduced order modelling techniques. **ITHACA-FV** is designed for [**OpenFOAM v2212**](https://www.openfoam.com/news/main-news/openfoam-v2212/) but it can be easily adapted also to other versions of OpenFOAM.
 
 **ITHACA-FV** can also be used as a basis for more advanced projects that would like to assess the capability of reduced order models in their existing **OpenFOAM**-based software, thanks to the availability of several reduced order methods and algorithms.
 
 Linear and non-linear algebra operations which are not already implemented in OpenFOAM are performed with the external library [**Eigen**](http://eigen.tuxfamily.org/index.php?title=Main_Page). The source code of Eigen 3.3.7 is provided together with ITHACA-FV and is located in the [src/thirdyparty/Eigen](./src/thirdparty/Eigen) folder.  For the EigenValue decomposition it is also possible to rely on the [**Spectra-0.7.0**](https://spectralib.org/) library and the source code is provided in the [src/thirdyparty/spectra](./src//thirdparty/spectra) folder. Numerical optimization can be performed using the external library [**OptimLib**](https://www.kthohr.com/optimlib.html) and the header based source code is provided in the [src/thirdyparty/OptimLib](./src/thirdparty/OptimLib) folder.
 
-**ITHACA-FV** has been tested on ubuntu 16.04, CentOS 7, ArchLinux but can be easily compiled on any linux distribution with a compiled version of OpenFOAM 1812, OpenFOAM 1906, OpenFOAM 1912, OpenFOAM 2006, OpenFOAM 2012 and OpenFOAM 2106.
+**ITHACA-FV** has been tested on ubuntu 16.04, CentOS 7, ArchLinux but can be easily compiled on any linux distribution with a compiled version of OpenFOAM 2106, OpenFOAM 2212, OpenFOAM 2306, and OpenFOAM 2312.
 
 ### 1. Prerequisites
 **ITHACA-FV** requires
-*   [**OpenFOAM 1812**](https://www.openfoam.com/news/main-news/openfoam-v1812/) or
-*   [**OpenFOAM 1906**](https://www.openfoam.com/news/main-news/openfoam-v1906/) or
-*   [**OpenFOAM 1912**](https://www.openfoam.com/news/main-news/openfoam-v1912/) or
-*   [**OpenFOAM 2006**](https://www.openfoam.com/news/main-news/openfoam-v2006/) or
-*   [**OpenFOAM 2012**](https://www.openfoam.com/news/main-news/openfoam-v2012/) or
 *   [**OpenFOAM 2106**](https://www.openfoam.com/news/main-news/openfoam-v2106) or
-*   [**OpenFOAM 2212**](https://www.openfoam.com/news/main-news/openfoam-v2212)
+*   [**OpenFOAM 2212**](https://www.openfoam.com/news/main-news/openfoam-v2212) or 
+*   [**OpenFOAM 2306**](https://www.openfoam.com/news/main-news/openfoam-v2306) or
+*   [**OpenFOAM 2312**](https://www.openfoam.com/news/main-news/openfoam-v2312) or
 
 
 ### 2. Installation and usage
@@ -177,7 +171,7 @@ Several tutorials are provided in the [**tutorials** subfolder](./tutorials).
 
 
 ### 6. Authors and contributors
-**ITHACA-FV** is currently developed and maintained at the [University of Urbino Carlo Bo](https://www.uniurb.it/) by [Dr. Giovanni Stabile](www.giovannistabile.com) and at [SISSA mathLab](http://mathlab.sissa.it/) in collaboration with [Prof. Gianluigi Rozza](https://people.sissa.it/~grozza/)'s group.
+**ITHACA-FV** is currently developed and maintained mainly at the [Sant'Anna School of Advanced Studies](https://www.santannapisa.it/en) by the group of [Prof. Giovanni Stabile](www.giovannistabile.com) and partially at [SISSA mathLab](http://mathlab.sissa.it/) in collaboration with [Prof. Gianluigi Rozza](https://people.sissa.it/~grozza/)'s group.
 
 Contact us by email for further information or questions about **ITHACA-FV**, or open an ''Issue'' on this website. **ITHACA-FV** is at an early development stage, so contributions improving either the code or the documentation are welcome, both as patches or merge requests on this website. If you are willing to contribute please follow the [developer instructions](https://github.com/ithaca-fv/ITHACA-FV/tree/master/src).
 
diff --git a/src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblem.H b/src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblem.H
index 916bec211..b4d754858 100755
--- a/src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblem.H
+++ b/src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblem.H
@@ -348,8 +348,8 @@ class reductionProblem
  * ITHACA-FV (In real Time Highly Advanced Computational Applications for
 Finite Volumes) is C++ library based on the finite volume solver
 [<b> OpenFOAM </b>](https://openfoam.org/). It consists of the implementation of several reduced order
-modeling techniques for parametrized problems. ITHACA-FV is developed and maintained by the group of 
-[<b> Dr. Giovanni Stabile </b>](https://www.giovannistabile.com/) at the [<b>Sant'Anna School of Advanced Studies](https://www.santannapisa.it/en) and at [<b> SISSA mathLab </b>](https://mathlab.sissa.it/) in collaboration with [<b> Prof. Gianluigi Rozza's Group </b>](http://people.sissa.it/~grozza/). Check also the GitHub [webpage](https://github.com/ITHACA-FV/ITHACA-FV) for more info.
+modeling techniques for parametrized problems. ITHACA-FV is developed and maintained mainly by the group of 
+[<b> Prof. Giovanni Stabile </b>](https://www.giovannistabile.com/) at the [<b>Sant'Anna School of Advanced Studies](https://www.santannapisa.it/en) and partially at [<b> SISSA mathLab </b>](https://mathlab.sissa.it/) in collaboration with [<b> Prof. Gianluigi Rozza's Group </b>](http://people.sissa.it/~grozza/). Check also the GitHub [webpage](https://github.com/ITHACA-FV/ITHACA-FV) for more info.
 
  *
  * \section structure ITHACA-FV directory structure

From 3106f16a4bbd03c565839f459d8e2215434810cd Mon Sep 17 00:00:00 2001
From: Giovanni Stabile <giovanni.stabile87@gmail.com>
Date: Sat, 18 May 2024 10:40:40 +0200
Subject: [PATCH 43/59] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 3cb6c7edd..f4e00e36f 100644
--- a/README.md
+++ b/README.md
@@ -171,7 +171,7 @@ Several tutorials are provided in the [**tutorials** subfolder](./tutorials).
 
 
 ### 6. Authors and contributors
-**ITHACA-FV** is currently developed and maintained mainly at the [Sant'Anna School of Advanced Studies](https://www.santannapisa.it/en) by the group of [Prof. Giovanni Stabile](www.giovannistabile.com) and partially at [SISSA mathLab](http://mathlab.sissa.it/) in collaboration with [Prof. Gianluigi Rozza](https://people.sissa.it/~grozza/)'s group.
+**ITHACA-FV** is currently developed and maintained mainly at the [Sant'Anna School of Advanced Studies](https://www.santannapisa.it/en) by the group of [Prof. Giovanni Stabile](https://www.giovannistabile.com) and partially at [SISSA mathLab](http://mathlab.sissa.it/) in collaboration with [Prof. Gianluigi Rozza](https://people.sissa.it/~grozza/)'s group.
 
 Contact us by email for further information or questions about **ITHACA-FV**, or open an ''Issue'' on this website. **ITHACA-FV** is at an early development stage, so contributions improving either the code or the documentation are welcome, both as patches or merge requests on this website. If you are willing to contribute please follow the [developer instructions](https://github.com/ithaca-fv/ITHACA-FV/tree/master/src).
 

From f12174601f3c20622416965dbe0edb8cab084e41 Mon Sep 17 00:00:00 2001
From: Matthieu Petit <matthieu.petit@scalian.com>
Date: Wed, 22 May 2024 16:17:21 +0200
Subject: [PATCH 44/59] Update to devMattPullRequest branch + new scalar
 product for the hyper-reduction on $\delta \nu_t$ (getMassMatrix
 ITHACAcoeffsMass)

---
 .../ITHACAutilities/ITHACAcoeffsMass.C        |  78 ++++++
 .../ITHACAutilities/ITHACAcoeffsMass.H        |  22 ++
 .../ITHACAutilities/ITHACAutilities.C         |  77 ++++++
 .../ITHACAutilities/ITHACAutilities.H         |  21 ++
 src/ITHACA_HR/hyperReduction.H                |  37 ++-
 src/ITHACA_HR/hyperReduction.templates.H      | 138 +++++-----
 tutorials/CFD/08DEIM/08DEIM.C                 |  84 ++++--
 tutorials/CFD/08DEIM/HR08DEIM.C               | 252 ------------------
 tutorials/CFD/08DEIM/Make/files               |   2 +-
 tutorials/CFD/08DEIM/Make/options             |   7 +-
 tutorials/CFD/08DEIM/system/ITHACAdict        |   6 +
 .../CFD/24HyperReduction/24HyperReduction.C   |  14 +-
 tutorials/CFD/24HyperReduction/Allrun         |   4 +-
 .../CFD/24HyperReduction/system/ITHACAdict    |   7 +-
 14 files changed, 368 insertions(+), 381 deletions(-)
 mode change 100755 => 100644 src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.H
 delete mode 100644 tutorials/CFD/08DEIM/HR08DEIM.C

diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
index 76a09ac03..2425d0243 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
@@ -191,6 +191,84 @@ template Eigen::MatrixXd getMassMatrix(
     PtrList<GeometricField<tensor, fvPatchField, volMesh>>& modes2, label Nmodes,
     bool consider_volumes);
 
+
+template<class Type, template<class> class PatchField, class GeoMesh>
+Eigen::MatrixXd getMassMatrix(PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes,
+                              PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes2, 
+                              Eigen::VectorXd weights,
+                              label Nmodes,
+                              bool consider_volumes)
+{
+    label Msize,Msize2;
+    if (Nmodes == 0)
+    {
+        Msize =  modes.size();
+        Msize2 =  modes2.size();
+    }
+    else
+    {
+        Msize = Nmodes;
+        Msize2 = Nmodes;
+    }
+    M_Assert(modes.size() >= Msize,
+             "The Number of requested modes is larger then the available quantity.");
+    M_Assert(modes2.size() >= Msize2,
+             "The Number of requested modes is larger then the available quantity.");
+
+    Eigen::MatrixXd F = Foam2Eigen::PtrList2Eigen(modes);
+    Eigen::MatrixXd F2 = Foam2Eigen::PtrList2Eigen(modes2);
+    Eigen::MatrixXd M = Eigen::MatrixXd::Zero(Msize,Msize2);
+    
+    if (consider_volumes)
+    {
+        Eigen::VectorXd V = getMassMatrixFV(modes[0]);
+        for (int i=0; i<weights.size(); i++)
+        {
+          M += (V(i) * weights(i)) * F.transpose().topRows(Msize).col(i) * F2.leftCols(Msize2).row(i);
+        }
+    }
+    else
+    {
+        M = weights.asDiagonal() * F.transpose().topRows(Msize) * F2.leftCols(Msize2);
+    }
+
+    if (Pstream::parRun())
+    {
+        reduce(M, sumOp<Eigen::MatrixXd>());
+    }
+
+    return M;
+}
+
+template Eigen::MatrixXd getMassMatrix(
+    PtrList<GeometricField<scalar, fvPatchField, volMesh>>& modes,
+    PtrList<GeometricField<scalar, fvPatchField, volMesh>>& modes2, 
+    Eigen::VectorXd weights,
+    label Nmodes = 0,
+    bool consider_volumes);
+
+template Eigen::MatrixXd getMassMatrix(
+    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>>& modes,
+    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>>& modes2,
+    Eigen::VectorXd weights,
+    label Nmodes = 0,
+    bool consider_volumes);
+
+template Eigen::MatrixXd getMassMatrix(
+    PtrList<GeometricField<vector, fvPatchField, volMesh>>& modes,
+    PtrList<GeometricField<vector, fvPatchField, volMesh>>& modes2, 
+    Eigen::VectorXd weights,
+    label Nmodes = 0,
+    bool consider_volumes);
+
+template Eigen::MatrixXd getMassMatrix(
+    PtrList<GeometricField<tensor, fvPatchField, volMesh>>& modes,
+    PtrList<GeometricField<tensor, fvPatchField, volMesh>>& modes2, 
+    Eigen::VectorXd weights,
+    label Nmodes = 0,
+    bool consider_volumes);
+
+
 template<class Type, template<class> class PatchField, class GeoMesh>
 Eigen::VectorXd getMassMatrixFV(
     GeometricField<Type, PatchField, GeoMesh>& snapshot)
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.H b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.H
old mode 100755
new mode 100644
index 6e6519517..26bf78639
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.H
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.H
@@ -115,6 +115,28 @@ Eigen::MatrixXd getMassMatrix(PtrList<GeometricField<Type, PatchField, GeoMesh>>
                               fields2, label nModes = 0,
                               bool consider_volumes = true);
 
+//-----------------------------------------------------------------------------
+/// Gets the cross mass matrix using the eigen routine
+///
+/// @param[in]  fields            The openFoam fields
+/// @param[in]  fields2           The second openFoam fields
+/// @param[in]  weights           Weights 
+/// @param[in]  consider_volumes  True if you want to consider the volumes
+///
+/// @tparam     Type        vector or scalar.
+/// @tparam     PatchField  fvPatchField or fvsPatchField.
+/// @tparam     GeoMesh     volMesh or surfaceMesh.
+///
+/// @return     The cross mass matrix eigen.
+///
+template<class Type, template<class> class PatchField, class GeoMesh>
+Eigen::MatrixXd getMassMatrix(PtrList<GeometricField<Type, PatchField, GeoMesh>>& fields,
+                              PtrList<GeometricField<Type, PatchField, GeoMesh>>& fields2, 
+                              Eigen::VectorXd weights,
+                              label Nmodes = 0,
+                              bool consider_volumes = true);
+
+
 //--------------------------------------------------------------------------
 /// Gets a vector containing the volumes of each cell of the mesh.
 ///
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.C
index 78b610580..84d7e0d46 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.C
@@ -133,4 +133,81 @@ List<T> combineList(List<List<T>>& doubleList)
 template List<label> combineList(List<List<label>>& doubleList);
 
 
+// Using the Eigen library, using the SVD decomposition method to solve the
+// matrix pseudo-inverse, the default error er is 0
+Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er) {
+  // perform svd decomposition
+  Eigen::JacobiSVD<Eigen::MatrixXd> svd_holder(origin, Eigen::ComputeThinU | Eigen::ComputeThinV);
+  // Build SVD decomposition results
+  Eigen::MatrixXd U = svd_holder.matrixU();
+  Eigen::MatrixXd V = svd_holder.matrixV();
+  Eigen::MatrixXd D = svd_holder.singularValues();
+
+  // Build the S matrix
+  Eigen::MatrixXd S(V.cols(), U.cols());
+  S.setZero();
+
+  for (unsigned int i = 0; i < D.size(); ++i) {
+
+    if (D(i, 0) > er) {
+      S(i, i) = 1 / D(i, 0);
+    } else {
+      S(i, i) = 0;
+    }
+  }
+  return V * S * U.transpose();
+}
+
+
+Eigen::MatrixXd invertMatrix(Eigen::MatrixXd& matrixToInvert, const word inversionMethod){
+
+  Info << "Inversion method : " << inversionMethod << endl;
+  if(inversionMethod == "pinv_eigen_based"){
+    return pinv_eigen_based(matrixToInvert);
+  }
+  else if(inversionMethod == "direct"){
+    return matrixToInvert.inverse();
+  }
+  else if(inversionMethod == "fullPivLu"){
+    return matrixToInvert.fullPivLu().inverse();
+  }
+  else if(inversionMethod == "partialPivLu"){
+    return matrixToInvert.partialPivLu().inverse();
+  }
+  else if(inversionMethod == "householderQr"){
+    return matrixToInvert.householderQr().solve(Eigen::MatrixXd::Identity(matrixToInvert.rows(), matrixToInvert.cols()));
+  }
+  else if(inversionMethod == "colPivHouseholderQr"){
+    return matrixToInvert.colPivHouseholderQr().inverse();
+  }
+  else if(inversionMethod == "fullPivHouseholderQr"){
+    return matrixToInvert.fullPivHouseholderQr().inverse();
+  }
+  else if(inversionMethod == "completeOrthogonalDecomposition"){
+    return matrixToInvert.completeOrthogonalDecomposition().pseudoInverse();
+  }
+  else if(inversionMethod == "jacobiSvd")
+  {
+    return matrixToInvert.jacobiSvd(Eigen::ComputeThinU | Eigen::ComputeThinV).solve(Eigen::MatrixXd::Identity(matrixToInvert.rows(), matrixToInvert.cols()));
+  }
+  else if(inversionMethod == "llt")
+  {
+    return matrixToInvert.llt().solve(Eigen::MatrixXd::Identity(matrixToInvert.rows(), matrixToInvert.cols()));
+  }
+  else if(inversionMethod == "ldlt")
+  {
+    Eigen::LLT<Eigen::MatrixXd> lltOfA(matrixToInvert);
+    return lltOfA.solve(Eigen::MatrixXd::Identity(matrixToInvert.rows(), matrixToInvert.cols()));
+  }
+  else if(inversionMethod == "bdcSvd")
+  {
+    return matrixToInvert.bdcSvd(Eigen::ComputeThinU | Eigen::ComputeThinV).solve(Eigen::MatrixXd::Identity(matrixToInvert.rows(), matrixToInvert.cols()));
+  } 
+  else{
+    Info << "Unkwown inversion method, solving with : completeOrthogonalDecomposition" << endl;
+    return matrixToInvert.completeOrthogonalDecomposition().pseudoInverse();
+  }
 }
+
+
+}
\ No newline at end of file
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.H b/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.H
index f4ebdf1b4..90041cd14 100755
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.H
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.H
@@ -125,6 +125,27 @@ bool isTurbulent();
 template<typename T>
 List<T> combineList(List<List<T>>& doubleList);
 
+//------------------------------------------------------------------------------
+/// @brief      Using the Eigen library, using the SVD decomposition method to solve the
+///             matrix pseudo-inverse, the default error er is 0
+///
+/// @param      origin  Matrix to invert
+/// @param      er      Error
+///
+/// @return     Inversed matrix
+///
+Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
+
+//------------------------------------------------------------------------------
+/// @brief      Invert a matrix given the method name in the ITHACAdict
+///
+/// @param[in]      matrixToInvert  Matrix to invert
+/// @param[in]      methodName      Method 
+///
+/// @return         Inversed matrix
+///
+Eigen::MatrixXd invertMatrix(Eigen::MatrixXd& matrixToInvert, const word inversionMethod);
+
 
 };
 #endif
diff --git a/src/ITHACA_HR/hyperReduction.H b/src/ITHACA_HR/hyperReduction.H
index 19c4acf44..26ec277a3 100644
--- a/src/ITHACA_HR/hyperReduction.H
+++ b/src/ITHACA_HR/hyperReduction.H
@@ -41,8 +41,6 @@ SourceFiles
 #include "redsvd"
 
 
-// Eigen::MatrixXd half_pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
-// Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
 
 // TODO uniform style for separating offline and onlie stages
 template <typename... SnapshotsLists>
@@ -80,10 +78,24 @@ public:
                    Eigen::VectorXi initialSeeds,
                    word problemName,
                    SnapshotsLists &&...snapshotsLists);
-
-    Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
-    Eigen::MatrixXd half_pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
-          
+    
+    //----------------------------------------------------------------------
+    /// @brief      Construct HyperReduction class
+    ///
+    /// @param[in]  n_modes           Dimension of the HR basis
+    /// @param[in]  n_nodes           Number of nodes
+    /// @param[in]  vectorial_dim     Field dimension (1 for volScalarField 3 for volVectorField)
+    /// @param[in]  n_cells           Number of cells
+    /// @param[in]  initialSeeds      Initial nodes
+    /// @param[in]  problemName       Name of the function to be hyper-reduced
+    ///
+    HyperReduction(label n_modes,
+                   label n_nodes,
+                   unsigned int vectorial_dim, 
+                   label n_cells,
+                   Eigen::VectorXi initialSeeds,
+                   word problemName);
+    
     // ITHACA parameters dict
     ITHACAparameters* para;
 
@@ -187,9 +199,9 @@ public:
     /// Submeshes
     autoPtr<volVectorField> submesh_field;
 
-    /// Online Matrice
+    /// Online Matrix
     Eigen::MatrixXd MatrixOnline;
-
+    
     //----------------------------------------------------------------------
     /// @brief      Methods implemented: 'GappyDEIM'  from "DEIM, Chaturantabut, Saifon, and Danny C. Sorensen. "Nonlinear model reduction via discrete empirical interpolation." SIAM Journal on Scientific Computing 32.5 (2010): 2737-2764" and "GNAT, Carlberg, Kevin, et al. "The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows." Journal of Computational Physics 242 (2013): 623-647.". Quasi-optimal point selection algorithm 'SOPT' and optimal point selection 'SOPTE' from "Lauzon, Jessica T., Siu Wun Cheung, Yeonjong Shin, Youngsoo Choi, Dylan Matthew Copeland, and Kevin Huynh. "S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models." arXiv preprint arXiv:2203.16494 (2022).""
     ///
@@ -201,11 +213,16 @@ public:
 
     void offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights, word folderMethodName);
 
-
     //----------------------------------------------------------------------
     /// @brief      Methods implemented: 'ECP' from "ECP, Hernandez, Joaquin Alberto, Manuel Alejandro Caicedo, and Alex Ferrer. "Dimensional hyper-reduction of nonlinear finite element models via empirical cubature." Computer methods in applied mechanics and engineering 313 (2017): 687-722.". TODO implement non-negative LS.
     ///
-    void offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights);
+    void offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights){
+        methodName = "ECP";
+        word name = "ITHACAoutput/" + problemName + "/" + methodName;
+        offlineECP(snapshotsModes, normalizingWeights, name);
+    }
+
+    void offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights, word folderMethodName);
     
     //----------------------------------------------------------------------
     /// @brief      TODO
diff --git a/src/ITHACA_HR/hyperReduction.templates.H b/src/ITHACA_HR/hyperReduction.templates.H
index 704b3665e..d3f0e383d 100644
--- a/src/ITHACA_HR/hyperReduction.templates.H
+++ b/src/ITHACA_HR/hyperReduction.templates.H
@@ -96,54 +96,28 @@ HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
 }
 
 
-// Using the Eigen library, using the SVD decomposition method to solve the
-// matrix pseudo-inverse, the default error er is 0
+// Template function constructor
 template <typename... SnapshotsLists>
-Eigen::MatrixXd HyperReduction<SnapshotsLists...>::pinv_eigen_based(Eigen::MatrixXd &origin, const float er) {
-  // perform svd decomposition
-  Eigen::JacobiSVD<Eigen::MatrixXd> svd_holder(origin, Eigen::ComputeThinU | Eigen::ComputeThinV);
-  // Build SVD decomposition results
-  Eigen::MatrixXd U = svd_holder.matrixU();
-  Eigen::MatrixXd V = svd_holder.matrixV();
-  Eigen::MatrixXd D = svd_holder.singularValues();
-
-  // Build the S matrix
-  Eigen::MatrixXd S(V.cols(), U.cols());
-  S.setZero();
-
-  for (int i = 0; i < D.size(); ++i) {
-
-    if (D(i, 0) > er) {
-      S(i, i) = 1 / D(i, 0);
-    } else {
-      S(i, i) = 0;
-    }
-  }
-  return V * S * U.transpose();
-}
+HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
+                                                  label n_nodes,
+                                                  unsigned int vectorialDim,
+                                                  label n_cells,
+                                                  Eigen::VectorXi initialSeeds,
+                                                  word problemName)
+    : n_modes{n_modes},
+      n_nodes{n_nodes},
+      vectorial_dim{vectorialDim},
+      n_cells{n_cells},
+      initialSeeds{initialSeeds},
+      problemName{problemName}
+{
+  Info << "Init HyperReduction class with vectorial dim: " << vectorial_dim << endl;
+  para = ITHACAparameters::getInstance();
+  folderProblem = problemName;
+  mkDir(folderProblem);
+
+  Info << "Initial seeds length: " << initialSeeds.rows() << endl;
 
-template <typename... SnapshotsLists>
-Eigen::MatrixXd HyperReduction<SnapshotsLists...>::half_pinv_eigen_based(Eigen::MatrixXd &origin, const float er) {
-  // perform svd decomposition
-  Eigen::JacobiSVD<Eigen::MatrixXd> svd_holder(origin, Eigen::ComputeThinU | Eigen::ComputeThinV);
-  // Build SVD decomposition results
-  Eigen::MatrixXd U = svd_holder.matrixU();
-  Eigen::MatrixXd V = svd_holder.matrixV();
-  Eigen::MatrixXd D = svd_holder.singularValues();
-
-  // Build the S matrix
-  Eigen::MatrixXd S(V.cols(), U.cols());
-  S.setZero();
-
-  for (unsigned int i = 0; i < D.size(); ++i) {
-
-    if (D(i, 0) > er) {
-      S(i, i) = 1 / D(i, 0);
-    } else {
-      S(i, i) = 0;
-    }
-  }
-  return V * S;
 }
 
 template <typename... SnapshotsLists>
@@ -399,14 +373,14 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
   folderMethod = folderMethodName;
   Info << "FolderMethod : " << folderMethod << endl;
   mkDir(folderMethod);
-  
+
   normalizingWeights = weights;
 
   nodePoints = autoPtr<IOList<label>>(new IOList<label>(
       IOobject("nodePoints", para->runTime.time().constant(), "../" + folderMethod,
                 para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE))); 
 
-  auto greedyMetric = para->ITHACAdict->lookupOrDefault<word>("GreedyMetric", "l2");
+  auto greedyMetric = para->ITHACAdict->lookupOrDefault<word>("GreedyMetric", "L2");
   
   bool offlineStage = !nodePoints().headerOk();
 
@@ -417,7 +391,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
 
     Eigen::VectorXd mp_not_mask = Eigen::VectorXd::Constant(n_cells * vectorial_dim, 1);
     std::set<label> nodePointsSet;
-    double max;
+
     // set initialSeeds
     if (initialSeeds.rows() > 0)
     {
@@ -446,6 +420,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
         Eigen::VectorXd c;
         Eigen::VectorXd r;
         label ind_max, c1;
+        double max;
 
         for (int i = 1; i <= nit; i++)
         {
@@ -512,9 +487,10 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
               << endl;
 
         label ind_max, c1;
+        double max;
         Eigen::MatrixXd V = snapshotsModes.leftCols(n_modes);
 
-        for (int ith_node = 0; ith_node < na; ith_node++)
+        for (unsigned int ith_node = 0; ith_node < na; ith_node++)
         {
           if (P.cols() > 0)
           {
@@ -548,6 +524,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
               << endl;
 
         label ind_max, c1;
+        double max;
         Eigen::MatrixXd A;
         Eigen::VectorXd b;
         Eigen::VectorXd c;
@@ -557,7 +534,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
         max = (reshapeMat* (mp_not_mask.asDiagonal()*snapshotsModes.leftCols(n_modes)).rowwise().lpNorm<2>().array().square().matrix()).maxCoeff(&ind_max, &c1);
         updateNodes(P, ind_max, mp_not_mask);
 
-        for (int ith_node = 1; ith_node < na; ith_node++)
+        for (unsigned int ith_node = 1; ith_node < na; ith_node++)
         {
           if (ith_node<n_modes)
           {
@@ -581,7 +558,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
 
             Eigen::VectorXd results(n_cells);
 
-            for (int ith_cell = 0; ith_cell < n_cells; ith_cell++)
+            for (unsigned int ith_cell = 0; ith_cell < n_cells; ith_cell++)
             {
               for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
               {
@@ -633,7 +610,7 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
     cnpy::load(pinvPU, folderMethod + "/pinvPU.npy");
 
     renormalizedBasisMatrix = normalizingWeights.asDiagonal()*basisMatrix;
-
+    
     Info << "Projection Matrix shape: " << P.rows() << " " << P.cols() << endl;
     Info << "Basis Matrix shape: " << basisMatrix.rows() << " " << basisMatrix.cols() << endl;
     Info << "Pseudo Inverse Matrix shape: " << pinvPU.rows() << " " << pinvPU.cols() << endl;
@@ -641,9 +618,12 @@ void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapsh
 }
 
 template <typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights)
+void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights, word folderMethodName)
 {
-  methodName = "ECP";
+  folderMethod = folderMethodName;
+  Info << "FolderMethod : " << folderMethod << endl;
+  mkDir(folderMethod);
+
   n_nodes = n_modes + 1;
 
   normalizingWeights = weights;
@@ -653,9 +633,6 @@ void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd& snapshotsMod
             << ", nodePoints=" << n_nodes << " #######"
             << endl;
 
-  folderMethod = "ITHACAoutput/" + problemName + "/" + methodName;
-  mkDir(folderMethod);
-
   nodePoints = autoPtr<IOList<label>>(new IOList<label>(
       IOobject("nodePoints", para->runTime.time().constant(), "../" + folderMethod,
                 para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE))); 
@@ -665,7 +642,7 @@ void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd& snapshotsMod
   if (offlineStage)
   {
     assert(n_modes > 0);
-    assert(n_nodes >= n_modes); 
+    assert(n_nodes >= n_modes);
 
     // matrices for quadratureWeights evaluation
     Eigen::MatrixXd J;//shape: (vectorial_dim * (n_modes + 1), nodePoints->size())
@@ -781,8 +758,13 @@ void HyperReduction<SnapshotsLists...>::initSeeds(Eigen::VectorXd mp_not_mask, s
 template <typename... SnapshotsLists>
 void HyperReduction<SnapshotsLists...>::updateNodes(Eigen::SparseMatrix<double>& P, label& ind, Eigen::VectorXd& mp_not_mask)
 {
+  nodePoints->append(ind);
+
+  nodes.conservativeResize(nodes.rows()+1);
+  nodes(nodes.rows()-1) = ind;
+
   unsigned int last_col{0};
-  
+
   if (P.rows()==0)
   {
     P.resize(n_cells*vectorial_dim, vectorial_dim);
@@ -790,19 +772,22 @@ void HyperReduction<SnapshotsLists...>::updateNodes(Eigen::SparseMatrix<double>&
   else
   {
     last_col = P.cols();
-    P.conservativeResize(P.rows(), P.cols() + vectorial_dim);
+    P.resize(P.rows(), P.cols() + vectorial_dim);
+  }
+  int step = P.cols() / vectorial_dim - 1;
+  
+  for (int ith_node=0; ith_node <= step; ith_node++)
+  {
+    for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+    {
+      P.insert(nodes[ith_node]+ith_field*n_cells,ith_node+ith_field*(step+1))=1;
+    }
   }
 
   for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
   {
-    P.insert(ind + ith_field * n_cells, last_col + ith_field) = 1;
     mp_not_mask(ind + ith_field * n_cells) = 0;
   }
-
-  nodePoints->append(ind);
-
-  nodes.conservativeResize(nodes.rows()+1);
-  nodes(nodes.rows()-1) = ind;
 }
 
 template<typename... SnapshotsLists>
@@ -827,7 +812,7 @@ void HyperReduction<SnapshotsLists...>::initReshapeMat(Eigen::SparseMatrix<doubl
   reshapeMat.resize(n_cells, n_cells*vectorial_dim);
   reshapeMat.reserve(Eigen::VectorXi::Constant(n_cells * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
 
-  for (int i = 0; i < n_cells; i++)
+  for (unsigned int i = 0; i < n_cells; i++)
   {
     for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
     {
@@ -890,7 +875,7 @@ void HyperReduction<SnapshotsLists...>::evaluatePinv(Eigen::SparseMatrix<double>
   assert(Projector.cols() > 0);
   Eigen::MatrixXd restricted = Projector.transpose() * Modes;
   Info << "S-Optimalty: " << s_optimality(restricted) << endl;
-  pinvPU = pinv_eigen_based(restricted);
+  pinvPU = ITHACAutilities::invertMatrix(restricted, para->ITHACAdict->lookupOrDefault<word>("InversionMethod", "completeOrthogonalDecomposition"));
   pinvPU = pinvPU*(Projector.transpose() * fieldWeights.array().cwiseInverse().matrix()).asDiagonal();
 }
 
@@ -902,9 +887,9 @@ void HyperReduction<SnapshotsLists...>::evaluateWPU(Eigen::SparseMatrix<double>
   unsigned int n_weightsPerField = quadratureWeights.rows()/vectorial_dim;
   unsigned int reorderIndex{0};
 
-  for (unsigned int ith_weight = 0; ith_weight < n_weightsPerField; ith_weight++)
-  {
-    for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+  for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+  {  
+    for (unsigned int ith_weight = 0; ith_weight < n_weightsPerField; ith_weight++)
     {
       quadratureWeightsOrderedAsProjector(reorderIndex) = quadratureWeights(ith_weight + ith_field * n_weightsPerField);
       reorderIndex++;
@@ -991,7 +976,7 @@ void HyperReduction<SnapshotsLists...>::createMasks(bool offlineStage)
     field2submesh.resize(submesh().cellMap().size() * vectorial_dim, n_cells*vectorial_dim);
     field2submesh.reserve(Eigen::VectorXi::Constant(n_cells*vectorial_dim, 1));
 
-    for (int ith_subCell{0} ; ith_subCell <submesh().cellMap().size(); ith_subCell++)
+    for (unsigned int ith_subCell{0} ; ith_subCell <submesh().cellMap().size(); ith_subCell++)
     {
         for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
         {
@@ -1005,8 +990,8 @@ void HyperReduction<SnapshotsLists...>::createMasks(bool offlineStage)
     submesh2nodesMask.resize(nodePoints().size() * vectorial_dim);
 
     int index_col = 0;
-    for (int ith_node{0} ; ith_node <nodePoints().size(); ith_node++) {
-      for (int ith_subCell{0} ; ith_subCell <submesh().cellMap().size(); ith_subCell++) {
+    for (unsigned int ith_node{0} ; ith_node <nodePoints().size(); ith_node++) {
+      for (unsigned int ith_subCell{0} ; ith_subCell <submesh().cellMap().size(); ith_subCell++) {
         if (nodePoints()[ith_node] == submesh().cellMap()[ith_subCell]) {
           for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
           {
@@ -1050,7 +1035,4 @@ List<label> HyperReduction<SnapshotsLists...>::global2local(List<label> &points,
   return localPoints;
 }
 
-
-
-
 #endif
diff --git a/tutorials/CFD/08DEIM/08DEIM.C b/tutorials/CFD/08DEIM/08DEIM.C
index a1efdc675..3ea6fbd4d 100644
--- a/tutorials/CFD/08DEIM/08DEIM.C
+++ b/tutorials/CFD/08DEIM/08DEIM.C
@@ -36,13 +36,12 @@ SourceFiles
 #include "Foam2Eigen.H"
 #include "ITHACAstream.H"
 #include "ITHACAPOD.H"
-#include "DEIM.H"
+#include "hyperReduction.templates.H"
 #include <chrono>
-
-class DEIM_function : public DEIM<volScalarField>
+class DEIM_function : public HyperReduction<PtrList<volScalarField>&>
 {
     public:
-        using DEIM::DEIM;
+        using HyperReduction::HyperReduction;
         static volScalarField evaluate_expression(volScalarField& S, Eigen::MatrixXd mu)
         {
             volScalarField yPos = S.mesh().C().component(vector::Y).ref();
@@ -58,18 +57,19 @@ class DEIM_function : public DEIM<volScalarField>
         }
         Eigen::VectorXd onlineCoeffs(Eigen::MatrixXd mu)
         {
-            theta.resize(magicPoints().size());
+            theta.resize(nodePoints().size());
             auto f = evaluate_expression(subField(), mu);
 
-            for (int i = 0; i < magicPoints().size(); i++)
+            for (int i = 0; i < nodePoints().size(); i++)
             {
                 // double on_coeff = f[localMagicPoints[i]];
-                theta(i) = f[localMagicPoints[i]];
+                theta(i) = f[localNodePoints[i]];
             }
 
             return theta;
         }
-
+        
+        Eigen::VectorXd theta; 
         PtrList<volScalarField> fields;
         autoPtr<volScalarField> subField;
 };
@@ -111,11 +111,11 @@ int main(int argc, char* argv[])
     );
     // Parameters used to train the non-linear function
     Eigen::MatrixXd pars = ITHACAutilities::rand(100, 2, -0.5, 0.5);
-    // It's possible to create a file "random.npy" to compare both version 
-    // save it and load it with : 
-    // cnpy::save(pars, "./random.npy");
-    // cnpy::load(pars, "./random.npy");
     
+    // To compare with the same parameters, save data and then load it 
+    // cnpy::load(pars, "./random100.npy");
+    // cnpy::save(pars, "./random100.npy");
+
     // Perform the offline phase
     for (int i = 0; i < 100; i++)
     {
@@ -124,11 +124,31 @@ int main(int argc, char* argv[])
         ITHACAstream::exportSolution(S, name(i + 1), "./ITHACAoutput/Offline/");
     }
 
+    Eigen::MatrixXd snapshotsModes;
+
+    // To use the DEIMmodes method from ITHACAPOD :
+    Eigen::VectorXd normalizingWeights = ITHACAutilities::getMassMatrixFV(Sp[0]).array();
+    PtrList<volScalarField> modes = ITHACAPOD::DEIMmodes(Sp, NDEIM, "GappyDEIM", S.name());
+    snapshotsModes = Foam2Eigen::PtrList2Eigen(modes);
+
+    // To use the SVD modes from the HyperReduction class : 
+    // Eigen::VectorXd normalizingWeights;
+    // c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights); 
+
     // Create DEIM object with given number of basis functions
-    DEIM_function c(Sp, NDEIM, "Gaussian_function", S.name());
+    Eigen::VectorXi initSeeds(0);
+    DEIM_function c(NDEIM, NDEIM, initSeeds, "DEIM", Sp);
+
+    // Compute the DEIM 
+    c.offlineGappyDEIM(snapshotsModes, normalizingWeights);
+    // To access the same folder hierarchy as before : 
+    // c.problemName = "Gaussian_function";
+    // c.offlineGappyDEIM(snapshotsModes, normalizingWeights, "ITHACAoutput/DEIM/"+c.problemName);
+                                                           
     // Generate the submeshes with the depth of the layer
-    c.subField = autoPtr<volScalarField>(new volScalarField(c.generateSubmesh(2,
-                                         mesh, S)));
+    c.generateSubmesh(2, mesh); 
+    c.subField = c.interpolateField<volScalarField>(Sp[0]);
+
     // Define a new online parameter
     Eigen::MatrixXd par_new(2, 1);
     par_new(0, 0) = 0;
@@ -152,19 +172,19 @@ int main(int argc, char* argv[])
 
 /// \example 08DEIM.C
 /// \section intro_08DEIM Introduction to tutorial 8
-/// In this tutorial we propose an example concerning the usage of the Discrete Empirical Interpolation Method (implemented in the DEIM class) for the approximation of a non-linear function.
+/// In this tutorial we propose an example concerning the usage of the Discrete Empirical Interpolation Method (implemented in the HyperReduction class) for the approximation of a non-linear function.
 /// The following image illustrates the computational domain used to discretize the problem
 /// \htmlonly <style>div.image img[src="mesh.png"]{width:500px;}</style> \endhtmlonly @image html mesh.png "Computational Domain"
 ///
-/// The non-liner function is described by a parametric Gaussian function:
+/// The non-linear function is described by a parametric Gaussian function:
 /// \f[
 /// S(\mathbf{x},\mathbf{\mu}) = e^{-2(x-\mu_x-1)^2 - 2(y-\mu_y-0.5)^2},
 ///  \f]
-/// that is depending on the parameter vector \f$\mathbf{\mu} = [\mu_x, \mu_y] \f$ and on the location inside the domain \f$ \mathbf{x} = [x,y] \f$. A training set of 100 samples is used to construct the DEIM modes which are later used for the approximation.
+/// that is depending on the parameter vector \f$\mathbf{\mu} = [\mu_x, \mu_y] \f$ and on the location inside the domain \f$ \mathbf{x} = [x,y] \f$. A training set of 100 samples is used to construct the "DEIM" modes which are later used for the approximation.
 ///
 /// \subsection header The necessary header files
 /// First of all let's have a look to the header files that needs to be included and what they are responsible for:
-/// The header files of ITHACA-FV necessary for this tutorial are: <Foam2Eigen.H> for Eigen to OpenFOAM conversion of objects, <ITHACAstream.H> for ITHACA-FV input-output operations. <ITHACAPOD.H> for the POD decomposition, <DEIM.H> for the DEIM approximation.
+/// The header files of ITHACA-FV necessary for this tutorial are: <Foam2Eigen.H> for Eigen to OpenFOAM conversion of objects, <ITHACAstream.H> for ITHACA-FV input-output operations. <ITHACAPOD.H> for the POD decomposition, <hyperReduction.templates.H> for the "DEIM" approximation.
 ///
 ///
 /// \section code08 A detailed look into the code
@@ -176,14 +196,14 @@ int main(int argc, char* argv[])
 ///
 /// ITHACA-FV header files
 ///
-/// \until DEIM
+/// \until hyperReduction
 ///
 /// chrono to compute the speedup
 /// \until chrono
 ///
-/// Construction of the function to be approximated with the DEIM method.
+/// Construction of the function to be approximated with the "DEIM" method from the HyperReduction class.
 /// \skip class
-/// \until DEIM::DEIM
+/// \until HyperReduction::HyperReduction
 ///
 /// Method with the explicit definition of the non-linear function
 /// \skip evaluate_expression
@@ -205,15 +225,27 @@ int main(int argc, char* argv[])
 /// Offline training of the function and assembly of the snapshots list
 /// \skip for
 /// \until }
-/// Construction of the DEIM object passing the list of snapshots Sp, the maximum number of DEIM modes NDEIM, and the name used to store the output "Gaussian_function".
-/// \skipline DEIM_function
+///
+/// Compute the "DEIM" modes using the ITHACAPOD class 
+/// \skip normalizingWeights
+/// \until snapshotsModes
+///
+/// Construction of the HyperReduction object passing the maximum number of "DEIM" modes NDEIM, the initSeeds (none in this tutorial), the name used to store the output "DEIM" and the list of snapshots Sp. The constructor is taking the number of modes and the number of point to compute, for the "DEIM" method these numbers are equal. 
+/// \skip initSeeds 
+/// \until DEIM_function
+///
+/// Compute the "DEIM" method HyperReduction::offlineGappyDEIM passing the "DEIM" modes and the normalizingWeights
+/// \skipline c.offlineGappyDEIM
+///
 /// Command to generate the submeshes used for pointwise evaluation of the function
-/// \skipline c.
+/// \skip c.generateSubmesh
+/// \until c.subField
+///
 /// Definition of a new sample value to test the accuracy of the method \f$ \mu* = (0,0) \f$
 /// \skip Eigen
 /// \until 1,
 ///
-/// Evaluation of the function using DEIM and reconstruction of the field
+/// Evaluation of the function using "DEIM" and reconstruction of the field
 /// \skip Eigen
 /// \until volSca
 ///
diff --git a/tutorials/CFD/08DEIM/HR08DEIM.C b/tutorials/CFD/08DEIM/HR08DEIM.C
deleted file mode 100644
index db136f28e..000000000
--- a/tutorials/CFD/08DEIM/HR08DEIM.C
+++ /dev/null
@@ -1,252 +0,0 @@
-/*---------------------------------------------------------------------------*\
-     ██╗████████╗██╗  ██╗ █████╗  ██████╗ █████╗       ███████╗██╗   ██╗
-     ██║╚══██╔══╝██║  ██║██╔══██╗██╔════╝██╔══██╗      ██╔════╝██║   ██║
-     ██║   ██║   ███████║███████║██║     ███████║█████╗█████╗  ██║   ██║
-     ██║   ██║   ██╔══██║██╔══██║██║     ██╔══██║╚════╝██╔══╝  ╚██╗ ██╔╝
-     ██║   ██║   ██║  ██║██║  ██║╚██████╗██║  ██║      ██║      ╚████╔╝
-     ╚═╝   ╚═╝   ╚═╝  ╚═╝╚═╝  ╚═╝ ╚═════╝╚═╝  ╚═╝      ╚═╝       ╚═══╝
-
- * In real Time Highly Advanced Computational Applications for Finite Volumes
- * Copyright (C) 2017 by the ITHACA-FV authors
--------------------------------------------------------------------------------
-License
-    This file is part of ITHACA-FV
-    ITHACA-FV is free software: you can redistribute it and/or modify
-    it under the terms of the GNU Lesser General Public License as published by
-    the Free Software Foundation, either version 3 of the License, or
-    (at your option) any later version.
-    ITHACA-FV is distributed in the hope that it will be useful,
-    but WITHOUT ANY WARRANTY; without even the implied warranty of
-    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-    GNU Lesser General Public License for more details.
-    You should have received a copy of the GNU Lesser General Public License
-    along with ITHACA-FV. If not, see <http://www.gnu.org/licenses/>.
-Description
-    Example of the reconstruction of a non-linear function using the DEIM
-SourceFiles
-    08DEIM.C
-\*---------------------------------------------------------------------------*/
-
-#include "fvCFD.H"
-#include "fvOptions.H"
-#include "simpleControl.H"
-#include "simpleControl.H"
-#include "fvMeshSubset.H"
-#include "ITHACAutilities.H"
-#include "Foam2Eigen.H"
-#include "ITHACAstream.H"
-#include "ITHACAPOD.H"
-#include "hyperReduction.templates.H"
-#include <chrono>
-
-class DEIM_function : public HyperReduction<PtrList<volScalarField>&>
-{
-    public:
-        using HyperReduction::HyperReduction;
-        static volScalarField evaluate_expression(volScalarField& S, Eigen::MatrixXd mu)
-        {
-            volScalarField yPos = S.mesh().C().component(vector::Y).ref();
-            volScalarField xPos = S.mesh().C().component(vector::X).ref();
-
-            for (auto i = 0; i < S.size(); i++)
-            {
-                S[i] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1,
-                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
-            }
-
-            return S;
-        }
-        Eigen::VectorXd onlineCoeffs(Eigen::MatrixXd mu)
-        {
-            theta.resize(nodePoints().size());
-            auto f = evaluate_expression(subField(), mu);
-
-            for (int i = 0; i < nodePoints().size(); i++)
-            {
-                // double on_coeff = f[localMagicPoints[i]];
-                theta(i) = f[localNodePoints[i]];
-            }
-
-            return theta;
-        }
-        
-        Eigen::VectorXd theta; // Necessary to add inside the HyperReduction class ?
-        PtrList<volScalarField> fields;
-        autoPtr<volScalarField> subField;
-};
-
-int main(int argc, char* argv[])
-{
-    // Read parameters from ITHACAdict file
-#include "setRootCase.H"
-    Foam::Time runTime(Foam::Time::controlDictName, args);
-    Foam::fvMesh mesh
-    (
-        Foam::IOobject
-        (
-            Foam::fvMesh::defaultRegion,
-            runTime.timeName(),
-            runTime,
-            Foam::IOobject::MUST_READ
-        )
-    );
-    ITHACAparameters* para = ITHACAparameters::getInstance(mesh, runTime);
-    int NDEIM = para->ITHACAdict->lookupOrDefault<int>("NDEIM", 15);
-    simpleControl simple(mesh);
-#include "createFields.H"
-    // List of volScalarField where the snapshots are stored
-    PtrList<volScalarField> Sp;
-    // Non linear function
-    volScalarField S
-    (
-        IOobject
-        (
-            "S",
-            runTime.timeName(),
-            mesh,
-            IOobject::NO_READ,
-            IOobject::AUTO_WRITE
-        ),
-        T.mesh(),
-        dimensionedScalar("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), 0)
-    );
-    // Parameters used to train the non-linear function
-    Eigen::MatrixXd pars = ITHACAutilities::rand(100, 2, -0.5, 0.5);
-    // To compare with the same parameters, save data and then load it 
-    // cnpy::load(pars, "./random.npy");
-    // cnpy::save(pars, "./random.npy");
-
-    // Perform the offline phase
-    for (int i = 0; i < 100; i++)
-    {
-        DEIM_function::evaluate_expression(S, pars.row(i));
-        Sp.append((S).clone());
-        ITHACAstream::exportSolution(S, name(i + 1), "./ITHACAoutput/Offline/");
-    }
-
-    // Create DEIM object with given number of basis functions
-    Eigen::VectorXi initSeeds;
-    DEIM_function c(NDEIM, NDEIM, initSeeds, "DEIM", Sp);
-
-    Eigen::MatrixXd snapshotsModes;
-
-    // To use the DEIMmodes method from ITHACAPOD :
-    Eigen::VectorXd normalizingWeights = ITHACAutilities::getMassMatrixFV(Sp[0]).array();
-    PtrList<volScalarField> modes = ITHACAPOD::DEIMmodes(Sp, NDEIM, "Gaussian_function", S.name());
-    snapshotsModes = Foam2Eigen::PtrList2Eigen(modes);
-
-    // To use the SVD modes from the HyperReduction class : 
-    // Eigen::VectorXd normalizingWeights;
-    // c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights); 
-
-    c.offlineGappyDEIM(snapshotsModes, normalizingWeights);
-    // To access the same folder hierarchy as before : 
-    // c.problemName = "Gaussian_function";
-    // c.offlineGappyDEIM(snapshotsModes, normalizingWeights, "ITHACAoutput/DEIM/"+c.problemName);
-                                                           
-    // Generate the submeshes with the depth of the layer
-    c.generateSubmesh(2, mesh); 
-    c.subField = autoPtr<volScalarField>(new volScalarField(c.submesh->interpolate(S).ref()));
-    // Define a new online parameter
-    Eigen::MatrixXd par_new(2, 1);
-    par_new(0, 0) = 0;
-    par_new(1, 0) = 0;
-    // Online evaluation of the non linear function
-    Eigen::VectorXd aprfield = c.MatrixOnline * c.onlineCoeffs(par_new);
-    // Transform to an OpenFOAM field and export
-    volScalarField S2("S_online", Foam2Eigen::Eigen2field(S, aprfield));
-    ITHACAstream::exportSolution(S2, name(1), "./ITHACAoutput/Online/");
-    // Evaluate the full order function and export it
-    DEIM_function::evaluate_expression(S, par_new);
-    ITHACAstream::exportSolution(S, name(1), "./ITHACAoutput/Online/");
-    // Compute the L2 error and print it
-    Info << ITHACAutilities::errorL2Rel(S2, S) << endl;
-    return 0;
-}
-
-/// \dir 08DEIM Folder of the turorial 8
-/// \file
-/// \brief Implementation of tutorial 8 for DEIM reconstruction of a non linear function
-
-/// \example 08DEIM.C
-/// \section intro_08DEIM Introduction to tutorial 8
-/// In this tutorial we propose an example concerning the usage of the Discrete Empirical Interpolation Method (implemented in the DEIM class) for the approximation of a non-linear function.
-/// The following image illustrates the computational domain used to discretize the problem
-/// \htmlonly <style>div.image img[src="mesh.png"]{width:500px;}</style> \endhtmlonly @image html mesh.png "Computational Domain"
-///
-/// The non-liner function is described by a parametric Gaussian function:
-/// \f[
-/// S(\mathbf{x},\mathbf{\mu}) = e^{-2(x-\mu_x-1)^2 - 2(y-\mu_y-0.5)^2},
-///  \f]
-/// that is depending on the parameter vector \f$\mathbf{\mu} = [\mu_x, \mu_y] \f$ and on the location inside the domain \f$ \mathbf{x} = [x,y] \f$. A training set of 100 samples is used to construct the DEIM modes which are later used for the approximation.
-///
-/// \subsection header The necessary header files
-/// First of all let's have a look to the header files that needs to be included and what they are responsible for:
-/// The header files of ITHACA-FV necessary for this tutorial are: <Foam2Eigen.H> for Eigen to OpenFOAM conversion of objects, <ITHACAstream.H> for ITHACA-FV input-output operations. <ITHACAPOD.H> for the POD decomposition, <DEIM.H> for the DEIM approximation.
-///
-///
-/// \section code08 A detailed look into the code
-///
-/// \dontinclude 08DEIM.C
-/// The OpenFOAM header files:
-/// \skip #include "fvCFD.H"
-/// \until fvMeshSubset
-///
-/// ITHACA-FV header files
-///
-/// \until DEIM
-///
-/// chrono to compute the speedup
-/// \until chrono
-///
-/// Construction of the function to be approximated with the DEIM method.
-/// \skip class
-/// \until DEIM::DEIM
-///
-/// Method with the explicit definition of the non-linear function
-/// \skip evaluate_expression
-/// \until }
-/// \until }
-///
-/// Method with the expression for the evaluation of the online coefficients
-/// \skip onlineCoeffs
-/// \until }
-/// \until }
-///
-/// Now let's have a look to important command in the main function.
-/// Read parameters from the ITHACAdict file
-/// \skip ITHACApara
-/// \until int
-///
-/// Definition of the parameter samples to train the non-linear function
-/// \skipline Eigen
-/// Offline training of the function and assembly of the snapshots list
-/// \skip for
-/// \until }
-/// Construction of the DEIM object passing the list of snapshots Sp, the maximum number of DEIM modes NDEIM, and the name used to store the output "Gaussian_function".
-/// \skipline DEIM_function
-/// Command to generate the submeshes used for pointwise evaluation of the function
-/// \skipline c.
-/// Definition of a new sample value to test the accuracy of the method \f$ \mu* = (0,0) \f$
-/// \skip Eigen
-/// \until 1,
-///
-/// Evaluation of the function using DEIM and reconstruction of the field
-/// \skip Eigen
-/// \until volSca
-///
-/// Export the approximation
-///
-/// \skipline ITHACA
-///
-/// Evaluate the function on in \f$\mu*\f$ using the FOM
-/// \skipline DEIM
-/// Export the FOM field
-/// \skipline ITHACA
-/// Compute the error and print it
-/// \skipline Info
-///
-/// \section plaincode The plain program
-/// Here there's the plain code
-
-
diff --git a/tutorials/CFD/08DEIM/Make/files b/tutorials/CFD/08DEIM/Make/files
index 029547431..fe9231886 100644
--- a/tutorials/CFD/08DEIM/Make/files
+++ b/tutorials/CFD/08DEIM/Make/files
@@ -1,3 +1,3 @@
-HR08DEIM.C
+08DEIM.C
 
 EXE = $(FOAM_USER_APPBIN)/08DEIM
diff --git a/tutorials/CFD/08DEIM/Make/options b/tutorials/CFD/08DEIM/Make/options
index 08cdb4ae3..6ce109619 100644
--- a/tutorials/CFD/08DEIM/Make/options
+++ b/tutorials/CFD/08DEIM/Make/options
@@ -9,17 +9,16 @@ EXE_INC = \
     -I$(LIB_SRC)/sampling/lnInclude \
     -I$(LIB_SRC)/fvOptions/lnInclude \
     -I$(LIB_SRC)/fileFormats/lnInclude \
-    -I$(LIB_ITHACA_SRC)/thirdparty/redsvd \
     -I$(LIB_SRC)/dynamicMesh/lnInclude \
     -I$(LIB_SRC)/thermophysicalModels/basic/lnInclude \
     -I$(LIB_SRC)/turbulenceModels/compressible/turbulenceModel \
     -I$(LIB_SRC)/functionObjects/forces/lnInclude \
-    -I$(LIB_ITHACA_SRC)/ITHACA_DEIM \
     -I$(LIB_ITHACA_SRC)/ITHACA_HR \
     -I$(LIB_ITHACA_SRC)/ITHACA_FOMPROBLEMS/lnInclude \
     -I$(LIB_ITHACA_SRC)/ITHACA_ROMPROBLEMS/lnInclude \
     -I$(LIB_ITHACA_SRC)/ITHACA_CORE/lnInclude \
     -I$(LIB_ITHACA_SRC)/thirdparty/Eigen \
+    -I$(LIB_ITHACA_SRC)/thirdparty/redsvd \
     -I$(LIB_ITHACA_SRC)/thirdparty/spectra/include \
     -I$(LIB_ITHACA_SRC)/ITHACA_THIRD_PARTY/splinter/include \
     -Wno-comment \
@@ -27,7 +26,6 @@ EXE_INC = \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
     -std=c++17 \
 
-
 EXE_LIBS = \
     -lturbulenceModels \
     -lfiniteVolume \
@@ -45,4 +43,5 @@ EXE_LIBS = \
     -lITHACA_ROMPROBLEMS \
     -lITHACA_THIRD_PARTY \
     -lITHACA_CORE \
-    -lITHACA_DEIM 
+    -lITHACA_DEIM
+
diff --git a/tutorials/CFD/08DEIM/system/ITHACAdict b/tutorials/CFD/08DEIM/system/ITHACAdict
index d733fd3e7..e1d4b2812 100755
--- a/tutorials/CFD/08DEIM/system/ITHACAdict
+++ b/tutorials/CFD/08DEIM/system/ITHACAdict
@@ -28,3 +28,9 @@ OutType fixed;
 HyperReduction GappyDEIM;//GappyDEIM, ECP
 GreedyMetric L2;//L2, SOPT, SOPTE
 
+// Inversion method 
+// Possibilities : pinv_eigen_based, half_pinv_eigen_based, direct, fullPivLu, 
+// partialPivLu, householderQr, colPivHouseholderQr, fullPivHouseholderQr, 
+// completeOrthogonalDecomposition, jacobiSvd, llt, ldlt, bdcSvd  
+InversionMethod completeOrthogonalDecomposition;
+
diff --git a/tutorials/CFD/24HyperReduction/24HyperReduction.C b/tutorials/CFD/24HyperReduction/24HyperReduction.C
index 6cf4d6256..d7013bda6 100644
--- a/tutorials/CFD/24HyperReduction/24HyperReduction.C
+++ b/tutorials/CFD/24HyperReduction/24HyperReduction.C
@@ -110,11 +110,11 @@ class HyperReduction_vectorFunction : public HyperReduction<PtrList<volVectorFie
 
             for (auto i = 0; i < nodesList.size(); i++)
             {
-                ret(i*3) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
+                ret(i) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
-                ret(i*3 + 1) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 0.5,
+                ret(i + nodesList.size()) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 0.5,
                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
-                ret(i*3 + 2) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1.5,
+                ret(i + 2 * nodesList.size()) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1.5,
                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0., 2));
             }
 
@@ -161,13 +161,13 @@ class HyperReduction_vectorScalarFunction : public HyperReduction<PtrList<volVec
 
             for (auto i = 0; i < nodesList.size(); i++)
             {
-                ret(i*4) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
+                ret(i) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
-                ret(i*4 + 1) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 0.5,
+                ret(i + nodesList.size()) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 0.5,
                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
-                ret(i*4 + 2) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1.5,
+                ret(i + 2 * nodesList.size()) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1.5,
                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0., 2));
-                ret(i*4 + 3) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
+                ret(i + 3 * nodesList.size()) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
                                                 2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
             }
 
diff --git a/tutorials/CFD/24HyperReduction/Allrun b/tutorials/CFD/24HyperReduction/Allrun
index d5b3083d6..009c45b14 100755
--- a/tutorials/CFD/24HyperReduction/Allrun
+++ b/tutorials/CFD/24HyperReduction/Allrun
@@ -4,4 +4,6 @@ cd ${0%/*} || exit 1    # Run from this directory
 # Source tutorial run functions
 . $WM_PROJECT_DIR/bin/tools/RunFunctions
 
-runApplication 24HyperReduction
+# To test scalar : -test scalar 
+# To test vector + scalar : -test vs 
+runApplication 24HyperReduction -test vector 
diff --git a/tutorials/CFD/24HyperReduction/system/ITHACAdict b/tutorials/CFD/24HyperReduction/system/ITHACAdict
index 668de9635..6bd532ce5 100755
--- a/tutorials/CFD/24HyperReduction/system/ITHACAdict
+++ b/tutorials/CFD/24HyperReduction/system/ITHACAdict
@@ -26,5 +26,8 @@ OutPrecision 20;
 OutType fixed;
 
 // HR
-HyperReduction ECP;//GappyDEIM, ECP
-GreedyMetric L2;//L2, SOPT, SOPTE
\ No newline at end of file
+HyperReduction GappyDEIM;//GappyDEIM, ECP
+GreedyMetric L2;//L2, SOPT, SOPTE
+
+// Inversion Method 
+InversionMethod completeOrthogonalDecomposition;

From bca512844069c8d798c8dc240d918eb86425acc5 Mon Sep 17 00:00:00 2001
From: Florian Regnault <florian.regnault@scalian.com>
Date: Fri, 24 May 2024 15:52:08 +0200
Subject: [PATCH 45/59] Changing M computation to handle RAM issues for high
 resolution runs

---
 .../ITHACAutilities/ITHACAcoeffsMass.C        | 31 ++++++++++++++-----
 1 file changed, 24 insertions(+), 7 deletions(-)

diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
index 76a09ac03..2708e6508 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
@@ -88,9 +88,17 @@ Eigen::MatrixXd getMassMatrix(
     if (consider_volumes)
     {
         Eigen::VectorXd V = getMassMatrixFV(modes[0]);
-        for (int i=0; i<V.size(); i++)
+        // If V is too big then we need a for loop to avoid RAM overload
+        if (V.size() > 1e6)
         {
-          M += V(i) * F.transpose().topRows(Msize).col(i) * F.leftCols(Msize).row(i);
+            for (int i=0; i<V.size(); i++)
+            {
+                M += V(i) * F.transpose().topRows(Msize).col(i) * F.leftCols(Msize).row(i);
+            }
+        }
+        else
+        {
+            M = F.transpose().topRows(Msize) * V.asDiagonal() * F.leftCols(Msize);
         }
     }
     else
@@ -148,13 +156,22 @@ Eigen::MatrixXd getMassMatrix(
     Eigen::MatrixXd F = Foam2Eigen::PtrList2Eigen(modes);
     Eigen::MatrixXd F2 = Foam2Eigen::PtrList2Eigen(modes2);
     Eigen::MatrixXd M = Eigen::MatrixXd::Zero(Msize,Msize2);
-
+    
     if (consider_volumes)
     {
-        Eigen::VectorXd V = getMassMatrixFV(modes[0]);
-        for (int i=0; i<V.size(); i++)
-        {
-          M += V(i) * F.transpose().topRows(Msize).col(i) * F2.leftCols(Msize2).row(i);
+       Eigen::VectorXd V = getMassMatrixFV(modes[0]);
+       // If V is too big then we need a for loop to avoid RAM overload
+       if (V.size() > 1e6)
+       {
+            for (int i=0; i<V.size(); i++)
+            {
+             M += V(i) * F.transpose().topRows(Msize).col(i) * F2.leftCols(Msize2).row(i);
+            }
+       }
+       else
+       {
+        // Classical M computation
+        M = F.transpose().topRows(Msize) * V.asDiagonal() * F2.leftCols(Msize2);
         }
     }
     else

From 53ba70627ab22be7afd0c1d2f6f40051e4793bdb Mon Sep 17 00:00:00 2001
From: vressegu <valentin.resseguier@inrae.fr>
Date: Wed, 29 May 2024 18:22:38 +0200
Subject: [PATCH 46/59] correct weight without volume in coefMass

---
 src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
index 7b08b10f5..624df8f38 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
@@ -246,7 +246,7 @@ Eigen::MatrixXd getMassMatrix(PtrList<GeometricField<Type, PatchField, GeoMesh>>
     }
     else
     {
-        M = weights.asDiagonal() * F.transpose().topRows(Msize) * F2.leftCols(Msize2);
+        M = F.transpose().topRows(Msize) * weights.asDiagonal() * F2.leftCols(Msize2);
     }
 
     if (Pstream::parRun())

From 39e1f5443fdf373021fef8a0f1215a42d4d1b15f Mon Sep 17 00:00:00 2001
From: vressegu <valentin.resseguier@inrae.fr>
Date: Wed, 29 May 2024 18:27:06 +0200
Subject: [PATCH 47/59] compromise RAM speed for weighted getMassMatrix

---
 .../ITHACAutilities/ITHACAcoeffsMass.C        | 19 ++++++++++++++-----
 1 file changed, 14 insertions(+), 5 deletions(-)

diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
index 624df8f38..cec4e3956 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
@@ -238,11 +238,20 @@ Eigen::MatrixXd getMassMatrix(PtrList<GeometricField<Type, PatchField, GeoMesh>>
     
     if (consider_volumes)
     {
-        Eigen::VectorXd V = getMassMatrixFV(modes[0]);
-        for (int i=0; i<weights.size(); i++)
-        {
-          M += (V(i) * weights(i)) * F.transpose().topRows(Msize).col(i) * F2.leftCols(Msize2).row(i);
-        }
+       Eigen::VectorXd V = getMassMatrixFV(modes[0]);
+       // If V is too big then we need a for loop to avoid RAM overload
+       if (V.size() > 1e6)
+       {
+            for (int i=0; i<V.size(); i++)
+            {
+             M += (V(i) * weights(i)) * F.transpose().topRows(Msize).col(i) * F2.leftCols(Msize2).row(i);
+            }
+       }
+       else
+       {
+        // Classical M computation
+        M = F.transpose().topRows(Msize) * ( V * weights ).asDiagonal() * F2.leftCols(Msize2);
+       }
     }
     else
     {

From fd17a8c1937402e90be97a4b05731365b4e295da Mon Sep 17 00:00:00 2001
From: "Shenhui,Ruan" <shenhui.ruan@outlook.com>
Date: Fri, 21 Jun 2024 11:15:52 +0200
Subject: [PATCH 48/59] 1-Add two functions, read_last_fields and
 readLastFields, to the ITHACAstream. The two functions allow to parallel read
 the converged fields in the subfolders. 2-The solver, 18simpleTurbNS, is also
 modified.

---
 src/ITHACA_CORE/ITHACAstream/ITHACAstream.C   | 92 +++++++++++++++++++
 src/ITHACA_CORE/ITHACAstream/ITHACAstream.H   | 38 ++++++++
 tutorials/CFD/18simpleTurbNS/18simpleTurbNS.C |  2 +-
 3 files changed, 131 insertions(+), 1 deletion(-)

diff --git a/src/ITHACA_CORE/ITHACAstream/ITHACAstream.C b/src/ITHACA_CORE/ITHACAstream/ITHACAstream.C
index e782b0697..b0f96e663 100644
--- a/src/ITHACA_CORE/ITHACAstream/ITHACAstream.C
+++ b/src/ITHACA_CORE/ITHACAstream/ITHACAstream.C
@@ -691,6 +691,77 @@ void readConvergedFields(
     }
 }
 
+template<class Type, template<class> class PatchField, class GeoMesh>
+void read_last_fields(
+    PtrList<GeometricField<Type, PatchField, GeoMesh>>& Lfield,
+    GeometricField<Type, PatchField, GeoMesh>& field,
+    fileName casename)
+{
+    if (!Pstream::parRun())
+    {
+        Info << "######### Reading the Data for " << field.name() << " #########" <<
+             endl;
+        fileName rootpath(".");
+        Foam::Time runTime2(Foam::Time::controlDictName, rootpath, casename);
+        int last_s (runTime2.times().size());
+
+        GeometricField<Type, PatchField, GeoMesh> tmp_field(
+            IOobject
+            (
+                field.name(),
+                casename + runTime2.times()[last_s-1].name(),
+                field.mesh(),
+                IOobject::MUST_READ
+            ),
+            field.mesh()
+        );
+        Lfield.append(tmp_field.clone());
+
+        std::cout << std::endl;
+    }
+    else
+    {
+        Info << "######### Reading the Data for " << field.name() << " #########" <<
+             endl;
+        word timename(field.mesh().time().rootPath() + "/" +
+                      field.mesh().time().caseName() );
+        timename = timename.substr(0, timename.find_last_of("\\/"));
+        timename = timename + "/" + casename + "processor" + name(Pstream::myProcNo());
+        int last_s = numberOfFiles(casename,
+                                   "processor" + name(Pstream::myProcNo()) + "/");
+
+        GeometricField<Type, PatchField, GeoMesh> tmp_field(
+            IOobject
+            (
+                field.name(),
+                timename + "/" + name(last_s-1),
+                field.mesh(),
+                IOobject::MUST_READ
+            ),
+            field.mesh()
+        );
+        Lfield.append(tmp_field.clone());
+
+        Info << endl;
+    }
+}
+
+template<class Type, template<class> class PatchField, class GeoMesh>
+void readLastFields(
+    PtrList<GeometricField<Type, PatchField, GeoMesh>>& Lfield,
+    GeometricField<Type, PatchField, GeoMesh>& field, fileName casename)
+{
+    int par = 1;
+    M_Assert(ITHACAutilities::check_folder(casename + name(par)) != 0,
+             "No parameter dependent solutions stored into Offline folder");
+
+    while (ITHACAutilities::check_folder(casename + name(par)))
+    {
+        read_last_fields(Lfield, field, casename + name(par) + "/");
+        par++;
+    } 
+}
+
 int numberOfFiles(word folder, word MatrixName, word ext)
 {
     int number_of_files = 0;
@@ -952,6 +1023,27 @@ template void readConvergedFields(PtrList<surfaceScalarField>&
 template void readConvergedFields(PtrList<surfaceVectorField>&
                                   Lfield, surfaceVectorField& field, fileName casename);
 
+template void read_last_fields(PtrList<volScalarField>& Lfield,
+                          volScalarField& field, fileName casename);
+template void read_last_fields(PtrList<volVectorField>& Lfield,
+                          volVectorField& field, fileName casename);
+template void read_last_fields(PtrList<volTensorField>& Lfield,
+                          volTensorField& field, fileName casename);
+template void read_last_fields(PtrList<surfaceScalarField>& Lfield,
+                          surfaceScalarField& field, fileName casename);
+template void read_last_fields(PtrList<surfaceVectorField>& Lfield,
+                          surfaceVectorField& field, fileName casename);
+template void readLastFields(PtrList<volScalarField>& Lfield,
+                               volScalarField& field, fileName casename);
+template void readLastFields(PtrList<volVectorField>& Lfield,
+                               volVectorField& field, fileName casename);
+template void readLastFields(PtrList<volTensorField>& Lfield,
+                               volTensorField& field, fileName casename);
+template void readLastFields(PtrList<surfaceScalarField>&
+                               Lfield, surfaceScalarField& field, fileName casename);
+template void readLastFields(PtrList<surfaceVectorField>&
+                               Lfield, surfaceVectorField& field, fileName casename);
+
 template<typename T>
 void exportList(T& list, word folder, word filename)
 {
diff --git a/src/ITHACA_CORE/ITHACAstream/ITHACAstream.H b/src/ITHACA_CORE/ITHACAstream/ITHACAstream.H
index 410721dc3..fa944d44d 100644
--- a/src/ITHACA_CORE/ITHACAstream/ITHACAstream.H
+++ b/src/ITHACA_CORE/ITHACAstream/ITHACAstream.H
@@ -229,6 +229,44 @@ void readConvergedFields(
     GeometricField<Type, PatchField, GeoMesh>& field,
     fileName casename);
 
+//----------------------------------------------------------------------
+/// Function to read a list of fields from the name of the field including only the last snapshot
+///
+/// @param[in]  Lfield      a PtrList of OpenFOAM fields where you want
+///                         to store the field.
+/// @param[in]  field       The field used as template to read other
+///                         fields.
+/// @param[in]  casename    The folder where the field is stored.
+
+/// @tparam     Type        vector or scalar.
+/// @tparam     PatchField  fvPatchField or fvsPatchField.
+/// @tparam     GeoMesh     volMesh or surfaceMesh.
+///
+template<class Type, template<class> class PatchField, class GeoMesh>
+void read_last_fields(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
+                 Lfield,
+                 GeometricField<Type, PatchField, GeoMesh>& field,
+                 fileName casename); 
+
+//----------------------------------------------------------------------
+/// Funtion to read a list of volVectorField from name of the field including only the last snapshots
+///
+/// @param[in]  Lfield      a PtrList of OpenFOAM fields where you want
+///                         to store the field.
+/// @param[in]  field       The field used as template to read other
+///                         fields.
+/// @param[in]  casename    The folder where the field is stored.
+///
+/// @tparam     Type        vector or scalar.
+/// @tparam     PatchField  fvPatchField or fvsPatchField.
+/// @tparam     GeoMesh     volMesh or surfaceMesh.
+///
+template<class Type, template<class> class PatchField, class GeoMesh>
+void readLastFields(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
+                      Lfield,
+                      GeometricField<Type, PatchField, GeoMesh>& field,
+                      fileName casename);
+
 //--------------------------------------------------------------------------
 /// Function to export a scalar of vector field
 ///
diff --git a/tutorials/CFD/18simpleTurbNS/18simpleTurbNS.C b/tutorials/CFD/18simpleTurbNS/18simpleTurbNS.C
index 056cf9cd8..9304dca1f 100755
--- a/tutorials/CFD/18simpleTurbNS/18simpleTurbNS.C
+++ b/tutorials/CFD/18simpleTurbNS/18simpleTurbNS.C
@@ -66,7 +66,7 @@ class tutorial18 : public SteadyNSSimple
                 ITHACAstream::readMiddleFields(Ufield, U, "./ITHACAoutput/Offline/");
                 ITHACAstream::readMiddleFields(Pfield, p, "./ITHACAoutput/Offline/");
                 auto nut = _mesh().lookupObject<volScalarField>("nut");
-                ITHACAstream::readConvergedFields(nutFields, nut, "./ITHACAoutput/Offline/");
+                ITHACAstream::readLastFields(nutFields, nut, "./ITHACAoutput/Offline/");
                 mu_samples =
                     ITHACAstream::readMatrix("./ITHACAoutput/Offline/mu_samples_mat.txt");
             }

From c1705d4effe8649105b94a181a5a3e380380e7cc Mon Sep 17 00:00:00 2001
From: "Shenhui,Ruan" <shenhui.ruan@outlook.com>
Date: Mon, 24 Jun 2024 11:12:32 +0200
Subject: [PATCH 49/59] 1-Declear as _const_ for those immutable variables in
 the _read_last_fields_ function; 2-Use pointer to improve the efficiency of
 the code; 3-Add  to activate _emplace_back_ function for new OF version;
 4-Use  instead of  in the  function to reduce repeating print.

---
 src/ITHACA_CORE/ITHACAstream/ITHACAstream.C   | 66 ++++++++++++++-----
 src/ITHACA_CORE/ITHACAstream/ITHACAstream.H   |  8 +--
 .../SteadyNSSimple/SteadyNSSimple.C           |  6 +-
 3 files changed, 57 insertions(+), 23 deletions(-)

diff --git a/src/ITHACA_CORE/ITHACAstream/ITHACAstream.C b/src/ITHACA_CORE/ITHACAstream/ITHACAstream.C
index b0f96e663..fc7d3863c 100644
--- a/src/ITHACA_CORE/ITHACAstream/ITHACAstream.C
+++ b/src/ITHACA_CORE/ITHACAstream/ITHACAstream.C
@@ -694,8 +694,8 @@ void readConvergedFields(
 template<class Type, template<class> class PatchField, class GeoMesh>
 void read_last_fields(
     PtrList<GeometricField<Type, PatchField, GeoMesh>>& Lfield,
-    GeometricField<Type, PatchField, GeoMesh>& field,
-    fileName casename)
+    const GeometricField<Type, PatchField, GeoMesh>& field,
+    const fileName casename)
 {
     if (!Pstream::parRun())
     {
@@ -705,7 +705,9 @@ void read_last_fields(
         Foam::Time runTime2(Foam::Time::controlDictName, rootpath, casename);
         int last_s (runTime2.times().size());
 
-        GeometricField<Type, PatchField, GeoMesh> tmp_field(
+        #if defined(OFVER) && (OFVER >= 2212)
+        Lfield.emplace_back
+        (
             IOobject
             (
                 field.name(),
@@ -715,7 +717,21 @@ void read_last_fields(
             ),
             field.mesh()
         );
-        Lfield.append(tmp_field.clone());
+        #else 
+        auto tfld =
+            autoPtr<GeometricField<Type, PatchField, GeoMesh>>::New
+            (
+                IOobject
+                (
+                    field.name(),
+                    casename + runTime2.times()[last_s-1].name(),
+                    field.mesh(),
+                    IOobject::MUST_READ
+                ),
+                field.mesh()
+            );
+        Lfield.append(std::move(tfld));
+        #endif
 
         std::cout << std::endl;
     }
@@ -730,7 +746,9 @@ void read_last_fields(
         int last_s = numberOfFiles(casename,
                                    "processor" + name(Pstream::myProcNo()) + "/");
 
-        GeometricField<Type, PatchField, GeoMesh> tmp_field(
+        #if defined(OFVER) && (OFVER >= 2212)
+        Lfield.emplace_back
+        (
             IOobject
             (
                 field.name(),
@@ -740,7 +758,21 @@ void read_last_fields(
             ),
             field.mesh()
         );
-        Lfield.append(tmp_field.clone());
+        #else
+        auto tfld =
+            autoPtr<GeometricField<Type, PatchField, GeoMesh>>::New
+            (
+                IOobject
+                (
+                    field.name(),
+                    timename + "/" + name(last_s-1),
+                    field.mesh(),
+                    IOobject::MUST_READ
+                ),
+                field.mesh()
+            );
+        Lfield.append(std::move(tfld));
+        #endif
 
         Info << endl;
     }
@@ -749,7 +781,7 @@ void read_last_fields(
 template<class Type, template<class> class PatchField, class GeoMesh>
 void readLastFields(
     PtrList<GeometricField<Type, PatchField, GeoMesh>>& Lfield,
-    GeometricField<Type, PatchField, GeoMesh>& field, fileName casename)
+    const GeometricField<Type, PatchField, GeoMesh>& field, const fileName casename)
 {
     int par = 1;
     M_Assert(ITHACAutilities::check_folder(casename + name(par)) != 0,
@@ -1024,25 +1056,25 @@ template void readConvergedFields(PtrList<surfaceVectorField>&
                                   Lfield, surfaceVectorField& field, fileName casename);
 
 template void read_last_fields(PtrList<volScalarField>& Lfield,
-                          volScalarField& field, fileName casename);
+                         const volScalarField& field, const fileName casename);
 template void read_last_fields(PtrList<volVectorField>& Lfield,
-                          volVectorField& field, fileName casename);
+                         const volVectorField& field, const fileName casename);
 template void read_last_fields(PtrList<volTensorField>& Lfield,
-                          volTensorField& field, fileName casename);
+                         const volTensorField& field, const fileName casename);
 template void read_last_fields(PtrList<surfaceScalarField>& Lfield,
-                          surfaceScalarField& field, fileName casename);
+                         const surfaceScalarField& field, const fileName casename);
 template void read_last_fields(PtrList<surfaceVectorField>& Lfield,
-                          surfaceVectorField& field, fileName casename);
+                         const surfaceVectorField& field, const fileName casename);
 template void readLastFields(PtrList<volScalarField>& Lfield,
-                               volScalarField& field, fileName casename);
+                              const volScalarField& field, const fileName casename);
 template void readLastFields(PtrList<volVectorField>& Lfield,
-                               volVectorField& field, fileName casename);
+                              const volVectorField& field, const fileName casename);
 template void readLastFields(PtrList<volTensorField>& Lfield,
-                               volTensorField& field, fileName casename);
+                              const volTensorField& field, const fileName casename);
 template void readLastFields(PtrList<surfaceScalarField>&
-                               Lfield, surfaceScalarField& field, fileName casename);
+                               Lfield, const surfaceScalarField& field, const fileName casename);
 template void readLastFields(PtrList<surfaceVectorField>&
-                               Lfield, surfaceVectorField& field, fileName casename);
+                               Lfield, const surfaceVectorField& field, const fileName casename);
 
 template<typename T>
 void exportList(T& list, word folder, word filename)
diff --git a/src/ITHACA_CORE/ITHACAstream/ITHACAstream.H b/src/ITHACA_CORE/ITHACAstream/ITHACAstream.H
index fa944d44d..f3329ec99 100644
--- a/src/ITHACA_CORE/ITHACAstream/ITHACAstream.H
+++ b/src/ITHACA_CORE/ITHACAstream/ITHACAstream.H
@@ -245,8 +245,8 @@ void readConvergedFields(
 template<class Type, template<class> class PatchField, class GeoMesh>
 void read_last_fields(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
                  Lfield,
-                 GeometricField<Type, PatchField, GeoMesh>& field,
-                 fileName casename); 
+                 const GeometricField<Type, PatchField, GeoMesh>& field,
+                 const fileName casename); 
 
 //----------------------------------------------------------------------
 /// Funtion to read a list of volVectorField from name of the field including only the last snapshots
@@ -264,8 +264,8 @@ void read_last_fields(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
 template<class Type, template<class> class PatchField, class GeoMesh>
 void readLastFields(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
                       Lfield,
-                      GeometricField<Type, PatchField, GeoMesh>& field,
-                      fileName casename);
+                      const GeometricField<Type, PatchField, GeoMesh>& field,
+                      const fileName casename);
 
 //--------------------------------------------------------------------------
 /// Function to export a scalar of vector field
diff --git a/src/ITHACA_FOMPROBLEMS/SteadyNSSimple/SteadyNSSimple.C b/src/ITHACA_FOMPROBLEMS/SteadyNSSimple/SteadyNSSimple.C
index 46ad8d16a..81261c481 100644
--- a/src/ITHACA_FOMPROBLEMS/SteadyNSSimple/SteadyNSSimple.C
+++ b/src/ITHACA_FOMPROBLEMS/SteadyNSSimple/SteadyNSSimple.C
@@ -88,7 +88,8 @@ void SteadyNSSimple::getTurbRBF(label NNutModes)
             ITHACAstream::ReadDenseMatrix(weights, "./ITHACAoutput/weights/", weightName);
             rbfSplines[i] = new SPLINTER::RBFSpline(*samples[i],
                                                     SPLINTER::RadialBasisFunctionType::GAUSSIAN, weights);
-            std::cout << "Constructing RadialBasisFunction for mode " << i + 1 << std::endl;
+            // std::cout << "Constructing RadialBasisFunction for mode " << i + 1 << std::endl;
+            Info<< "Constructing RadialBasisFunction for mode " << i + 1 << endl;
         }
         else
         {
@@ -104,7 +105,8 @@ void SteadyNSSimple::getTurbRBF(label NNutModes)
                                                     SPLINTER::RadialBasisFunctionType::GAUSSIAN);
             ITHACAstream::SaveDenseMatrix(rbfSplines[i]->weights,
                                           "./ITHACAoutput/weights/", weightName);
-            std::cout << "Constructing RadialBasisFunction for mode " << i + 1 << std::endl;
+            // std::cout << "Constructing RadialBasisFunction for mode " << i + 1 << std::endl;
+            Info<< "Constructing RadialBasisFunction for mode " << i + 1 << endl;
         }
     }
 }

From 594d24e24761db2ae617eb1007146f42053b3354 Mon Sep 17 00:00:00 2001
From: Giovanni Stabile <giovanni.stabile87@gmail.com>
Date: Wed, 26 Jun 2024 15:06:47 +0200
Subject: [PATCH 50/59] FIX: added correctBC as an output parameter

---
 applications/POD/perform_POD.C                  | 4 ++--
 src/ITHACA_CORE/ITHACAstream/ITHACAparameters.C | 1 +
 src/ITHACA_CORE/ITHACAstream/ITHACAparameters.H | 1 +
 3 files changed, 4 insertions(+), 2 deletions(-)

diff --git a/applications/POD/perform_POD.C b/applications/POD/perform_POD.C
index 7d2656d2e..4ddd3bbd6 100755
--- a/applications/POD/perform_POD.C
+++ b/applications/POD/perform_POD.C
@@ -217,11 +217,11 @@ int main(int argc, char *argv[])
 
         if (field_type == "vector")
         {
-            ITHACAPOD::getModes(Vfield, Vmodes, field_name, 0, 0, 0, nmodes);
+            ITHACAPOD::getModes(Vfield, Vmodes, field_name, 0, 0, 0, nmodes, para->correctBC);
         }
         if (field_type == "scalar")
         {
-            ITHACAPOD::getModes(Sfield, Smodes, field_name, 0, 0, 0, nmodes);
+            ITHACAPOD::getModes(Sfield, Smodes, field_name, 0, 0, 0, nmodes, para->correctBC);
         }
 
         Vfield.clear();
diff --git a/src/ITHACA_CORE/ITHACAstream/ITHACAparameters.C b/src/ITHACA_CORE/ITHACAstream/ITHACAparameters.C
index 08c6cc0dd..668e15df4 100755
--- a/src/ITHACA_CORE/ITHACAstream/ITHACAparameters.C
+++ b/src/ITHACA_CORE/ITHACAstream/ITHACAparameters.C
@@ -38,6 +38,7 @@ ITHACAparameters::ITHACAparameters(fvMesh& mesh, Time& localTime)
     exportTxt = ITHACAdict->lookupOrDefault<bool>("exportTxt", 0);
     debug = ITHACAdict->lookupOrDefault<bool>("debug", 0);
     warnings = ITHACAdict->lookupOrDefault<bool>("warnings", 0);
+    correctBC = ITHACAdict->lookupOrDefault<bool>("correctBC", 1);
 }
 
 ITHACAparameters* ITHACAparameters::getInstance(fvMesh& mesh,
diff --git a/src/ITHACA_CORE/ITHACAstream/ITHACAparameters.H b/src/ITHACA_CORE/ITHACAstream/ITHACAparameters.H
index 42ed0efa4..5de67119d 100755
--- a/src/ITHACA_CORE/ITHACAstream/ITHACAparameters.H
+++ b/src/ITHACA_CORE/ITHACAstream/ITHACAparameters.H
@@ -55,6 +55,7 @@ class ITHACAparameters
         bool exportTxt;
         bool debug;
         bool warnings;
+        bool correctBC;
 
         /// type of output format can be fixed or scientific
         std::_Ios_Fmtflags outytpe;

From 2de10168484d78d50cf3ff2386ebc49bea38c0fd Mon Sep 17 00:00:00 2001
From: Giovanni Stabile <giovanni.stabile87@gmail.com>
Date: Wed, 26 Jun 2024 16:19:40 +0200
Subject: [PATCH 51/59] ENH: add map function also for BCs

---
 src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.C |  8 ++++++++
 src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.H | 16 ++++++++++++++++
 2 files changed, 24 insertions(+)

diff --git a/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.C b/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.C
index f7784fe65..7069e7a85 100644
--- a/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.C
+++ b/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.C
@@ -101,6 +101,14 @@ Eigen::Map<Eigen::MatrixXd> Foam2Eigen::field2EigenMap(
     return std::move(output);
 }
 
+template <template <class> class PatchField, class GeoMesh>
+Eigen::Map<Eigen::MatrixXd> Foam2Eigen::field2EigenMapBC(
+    GeometricField<scalar, PatchField, GeoMesh>& field, int BC_index)
+{
+    Eigen::Map<Eigen::MatrixXd> output(field.boundaryFieldRef()[BC_index].data(), field.boundaryField()[BC_index].size(), 1);
+    return std::move(output);
+}
+
 template Eigen::Map<Eigen::MatrixXd> Foam2Eigen::field2EigenMap(
     volScalarField& field);
 
diff --git a/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.H b/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.H
index 0120518f0..60aa07b3d 100644
--- a/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.H
+++ b/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.H
@@ -199,6 +199,22 @@ class Foam2Eigen
         static Eigen::Map<Eigen::MatrixXd> field2EigenMap(
             GeometricField<scalar, PatchField, GeoMesh>&
             field);
+        
+        //----------------------------------------------------------------------
+        /// @brief      Map a scalar OpenFOAM field boundary into an Eigen Matrix
+        ///
+        /// @param[in]  field       The field
+        /// @param[in]  BC_index    The index of the BC you want to Map
+        ///
+        /// @tparam     PatchField  fvPatchField or fvsPatchField.
+        /// @tparam     GeoMesh     volMesh or surfaceMesh.
+        ///
+        /// @return     Dense Eigen Map Matrix
+        ///
+        template<template<class> class PatchField, class GeoMesh>
+        static Eigen::Map<Eigen::MatrixXd> field2EigenMapBC(
+            GeometricField<scalar, PatchField, GeoMesh>&
+            field, int BC_index);
 
         //----------------------------------------------------------------------
         /// @brief      Convert an OpenFOAM field into an Eigen Vector

From 486070f4dc23f029872eeee9acb1d6381a64035b Mon Sep 17 00:00:00 2001
From: Giovanni Stabile <giovanni.stabile87@gmail.com>
Date: Fri, 28 Jun 2024 12:03:06 +0200
Subject: [PATCH 52/59] ENH: adding test to deform a geometry with RBF

---
 unitTests/RBF_def/.gitignore                  |      1 +
 unitTests/RBF_def/0/U                         |     53 +
 unitTests/RBF_def/0/p                         |     52 +
 unitTests/RBF_def/0/pointDisplacement         |     55 +
 unitTests/RBF_def/Make/.gitignore             |      1 +
 unitTests/RBF_def/Make/files                  |      3 +
 unitTests/RBF_def/Make/options                |     47 +
 unitTests/RBF_def/constant/RASProperties      |     24 +
 unitTests/RBF_def/constant/dynamicMeshDictRBF |     69 +
 unitTests/RBF_def/constant/polyMesh/boundary  |     62 +
 unitTests/RBF_def/constant/polyMesh/cellLevel | 124425 +++++
 unitTests/RBF_def/constant/polyMesh/cellZones |     21 +
 unitTests/RBF_def/constant/polyMesh/faceZones |     21 +
 unitTests/RBF_def/constant/polyMesh/faces     |  47176 ++
 .../RBF_def/constant/polyMesh/level0Edge      |     23 +
 unitTests/RBF_def/constant/polyMesh/neighbour |  23291 +
 unitTests/RBF_def/constant/polyMesh/owner     |  47177 ++
 .../RBF_def/constant/polyMesh/pointLevel      | 148819 ++++++
 .../RBF_def/constant/polyMesh/pointZones      |     21 +
 unitTests/RBF_def/constant/polyMesh/points    |  24464 +
 .../RBF_def/constant/polyMesh/surfaceIndex    | 397045 +++++++++++++++
 .../RBF_def/constant/transportProperties      |     21 +
 .../RBF_def/constant/turbulenceProperties     |     21 +
 unitTests/RBF_def/defGeom.C                   |    120 +
 unitTests/RBF_def/system/ITHACAdict           |     32 +
 unitTests/RBF_def/system/blockMeshDict        |    116 +
 unitTests/RBF_def/system/controlDict          |     54 +
 unitTests/RBF_def/system/decomposeParDict     |     30 +
 unitTests/RBF_def/system/extrudeMeshDict      |     53 +
 unitTests/RBF_def/system/fvSchemes            |     73 +
 unitTests/RBF_def/system/fvSolution           |    113 +
 unitTests/RBF_def/system/meshQualityDict      |     22 +
 unitTests/RBF_def/system/snappyHexMeshDict    |    237 +
 .../RBF_def/system/surfaceFeatureExtractDict  |     35 +
 34 files changed, 813777 insertions(+)
 create mode 100644 unitTests/RBF_def/.gitignore
 create mode 100755 unitTests/RBF_def/0/U
 create mode 100755 unitTests/RBF_def/0/p
 create mode 100755 unitTests/RBF_def/0/pointDisplacement
 create mode 100755 unitTests/RBF_def/Make/.gitignore
 create mode 100755 unitTests/RBF_def/Make/files
 create mode 100755 unitTests/RBF_def/Make/options
 create mode 100755 unitTests/RBF_def/constant/RASProperties
 create mode 100755 unitTests/RBF_def/constant/dynamicMeshDictRBF
 create mode 100755 unitTests/RBF_def/constant/polyMesh/boundary
 create mode 100755 unitTests/RBF_def/constant/polyMesh/cellLevel
 create mode 100755 unitTests/RBF_def/constant/polyMesh/cellZones
 create mode 100755 unitTests/RBF_def/constant/polyMesh/faceZones
 create mode 100755 unitTests/RBF_def/constant/polyMesh/faces
 create mode 100755 unitTests/RBF_def/constant/polyMesh/level0Edge
 create mode 100755 unitTests/RBF_def/constant/polyMesh/neighbour
 create mode 100755 unitTests/RBF_def/constant/polyMesh/owner
 create mode 100755 unitTests/RBF_def/constant/polyMesh/pointLevel
 create mode 100755 unitTests/RBF_def/constant/polyMesh/pointZones
 create mode 100755 unitTests/RBF_def/constant/polyMesh/points
 create mode 100755 unitTests/RBF_def/constant/polyMesh/surfaceIndex
 create mode 100755 unitTests/RBF_def/constant/transportProperties
 create mode 100755 unitTests/RBF_def/constant/turbulenceProperties
 create mode 100755 unitTests/RBF_def/defGeom.C
 create mode 100755 unitTests/RBF_def/system/ITHACAdict
 create mode 100755 unitTests/RBF_def/system/blockMeshDict
 create mode 100755 unitTests/RBF_def/system/controlDict
 create mode 100755 unitTests/RBF_def/system/decomposeParDict
 create mode 100755 unitTests/RBF_def/system/extrudeMeshDict
 create mode 100755 unitTests/RBF_def/system/fvSchemes
 create mode 100755 unitTests/RBF_def/system/fvSolution
 create mode 100755 unitTests/RBF_def/system/meshQualityDict
 create mode 100755 unitTests/RBF_def/system/snappyHexMeshDict
 create mode 100755 unitTests/RBF_def/system/surfaceFeatureExtractDict

diff --git a/unitTests/RBF_def/.gitignore b/unitTests/RBF_def/.gitignore
new file mode 100644
index 000000000..3e25c2870
--- /dev/null
+++ b/unitTests/RBF_def/.gitignore
@@ -0,0 +1 @@
+defGeoms
\ No newline at end of file
diff --git a/unitTests/RBF_def/0/U b/unitTests/RBF_def/0/U
new file mode 100755
index 000000000..d820cf114
--- /dev/null
+++ b/unitTests/RBF_def/0/U
@@ -0,0 +1,53 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  5.0                                   |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       volVectorField;
+    location    "41.8500000000178005";
+    object      U;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dimensions      [0 1 -1 0 0 0 0];
+
+internalField   uniform (1 0 0);
+
+boundaryField
+{
+    inlet
+    {
+        type            fixedValue;
+        value           uniform (1 0 0);
+    }
+    outlet
+    {
+        type            zeroGradient;
+    }
+    down
+    {
+        type            empty;
+    }
+    up
+    {
+        type            empty;
+    }
+    sides
+    {
+        type            slip;
+    }
+    cylinder1
+    {
+        type            fixedValue;
+        value           uniform (0 0 0);
+    }
+}
+
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/0/p b/unitTests/RBF_def/0/p
new file mode 100755
index 000000000..1985b26f7
--- /dev/null
+++ b/unitTests/RBF_def/0/p
@@ -0,0 +1,52 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  5.0                                   |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       volScalarField;
+    location    "41.8500000000178005";
+    object      p;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dimensions      [0 2 -2 0 0 0 0];
+
+internalField   uniform 0;
+
+boundaryField
+{
+    inlet
+    {
+        type            zeroGradient;
+    }
+    outlet
+    {
+        type            fixedValue;
+        value           uniform 0;
+    }
+    down
+    {
+        type            empty;
+    }
+    up
+    {
+        type            empty;
+    }
+    sides
+    {
+        type            zeroGradient;
+    }
+    cylinder1
+    {
+        type            zeroGradient;
+    }
+}
+
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/0/pointDisplacement b/unitTests/RBF_def/0/pointDisplacement
new file mode 100755
index 000000000..f4e0125a8
--- /dev/null
+++ b/unitTests/RBF_def/0/pointDisplacement
@@ -0,0 +1,55 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  5.0                                   |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       pointVectorField;
+    location    "0";
+    object      T;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dimensions      [0 0 0 1 0 0 0];
+
+internalField   uniform (0 0 0);
+
+boundaryField
+{
+    inlet
+    {
+        type            fixedValue;
+        value        uniform (0 0 0);
+    }
+    outlet
+    {
+        type            fixedValue;
+        value        uniform (0 0 0);
+    }
+    cylinder1
+    {
+        type            fixedValue;
+        value        uniform (0 0 0);
+    }
+    sides
+    {
+        type            fixedValue;
+        value        uniform (0 0 0);
+    }    
+    down
+    {
+        type            empty;
+    }
+    up
+    {
+        type            empty;
+    }
+}
+
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/Make/.gitignore b/unitTests/RBF_def/Make/.gitignore
new file mode 100755
index 000000000..700e99f27
--- /dev/null
+++ b/unitTests/RBF_def/Make/.gitignore
@@ -0,0 +1 @@
+linux*
diff --git a/unitTests/RBF_def/Make/files b/unitTests/RBF_def/Make/files
new file mode 100755
index 000000000..b1e4289b2
--- /dev/null
+++ b/unitTests/RBF_def/Make/files
@@ -0,0 +1,3 @@
+defGeom.C
+
+EXE = $(FOAM_USER_APPBIN)/defGeom
diff --git a/unitTests/RBF_def/Make/options b/unitTests/RBF_def/Make/options
new file mode 100755
index 000000000..d66d80c5c
--- /dev/null
+++ b/unitTests/RBF_def/Make/options
@@ -0,0 +1,47 @@
+EXE_INC = \
+    -I$(LIB_SRC)/TurbulenceModels/turbulenceModels/lnInclude \
+    -I$(LIB_SRC)/TurbulenceModels/incompressible/lnInclude \
+    -I$(LIB_SRC)/transportModels \
+    -I$(LIB_SRC)/transportModels/incompressible/singlePhaseTransportModel \
+    -I$(LIB_SRC)/finiteVolume/lnInclude \
+    -I$(LIB_SRC)/meshTools/lnInclude \
+    -I$(LIB_SRC)/sampling/lnInclude \
+    -I$(LIB_SRC)/fvOptions/lnInclude \
+    -I$(LIB_SRC)/fileFormats/lnInclude \
+    -I$(LIB_SRC)/dynamicFvMesh/lnInclude \
+    -I$(LIB_SRC)/thermophysicalModels/basic/lnInclude \
+    -I$(LIB_SRC)/thermophysicalModels/radiation/lnInclude \
+    -I$(LIB_SRC)/turbulenceModels/compressible/turbulenceModel \
+    -I$(FOAM_SRC)/functionObjects/forces/lnInclude \
+    -I$(LIB_SRC)/fileFormats/lnInclude \
+    -I$(LIB_SRC)/dynamicMesh/lnInclude \
+    -I$(LIB_ITHACA_SRC)/OF_EXT/lnInclude \
+    -I$(LIB_ITHACA_SRC)/ITHACA_FOMPROBLEMS/lnInclude \    
+    -I$(LIB_ITHACA_SRC)/ITHACA_ROMPROBLEMS/lnInclude \   
+    -I$(LIB_ITHACA_SRC)/ITHACA_CORE/lnInclude \    
+    -I$(LIB_ITHACA_SRC)/thirdparty/Eigen \
+    -I$(LIB_ITHACA_SRC)/ITHACA_CORE/Foam2Eigen \
+    -I$(LIB_ITHACA_SRC)/ITHACA_CORE/EigenFunctions \
+    -I$(LIB_ITHACA_SRC)/thirdparty/spectra/include \
+    -I$(LIB_ITHACA_SRC)/ITHACA_THIRD_PARTY/splinter/include \
+    -w \
+    -DOFVER=$${WM_PROJECT_VERSION%.*} \
+    -std=c++11
+
+EXE_LIBS = \
+    -lturbulenceModels \
+    -lincompressibleTransportModels \
+    -lincompressibleTurbulenceModels \
+    -lfiniteVolume \
+    -lmeshTools \
+    -lfvOptions \
+    -lsampling \
+    -lforces \
+    -lITHACA_ROMPROBLEMS \
+    -lITHACA_FOMPROBLEMS \
+    -lITHACA_THIRD_PARTY \
+    -lITHACA_CORE \
+    -lITHACA_DEIM \
+    -L$(FOAM_USER_LIBBIN) \
+    -lRBFMotionSolver 
+ 
diff --git a/unitTests/RBF_def/constant/RASProperties b/unitTests/RBF_def/constant/RASProperties
new file mode 100755
index 000000000..81473b042
--- /dev/null
+++ b/unitTests/RBF_def/constant/RASProperties
@@ -0,0 +1,24 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  2.2.0                                 |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      RASProperties;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+RASModel           laminar;
+
+turbulence          off;
+
+printCoeffs         on;
+
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/constant/dynamicMeshDictRBF b/unitTests/RBF_def/constant/dynamicMeshDictRBF
new file mode 100755
index 000000000..fa77187bf
--- /dev/null
+++ b/unitTests/RBF_def/constant/dynamicMeshDictRBF
@@ -0,0 +1,69 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  5                                     |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    location    "constant";
+    object      dynamicMeshDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  5                                     |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      dynamicMeshDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dynamicFvMesh      dynamicMotionSolverFvMesh;
+
+motionSolverLibs ("libRBFMotionSolver.so");
+motionSolver    RBFMotionSolver;
+movingPatches (cylinder1);
+staticPatches (inlet outlet sides);
+coarseningRatio 5;
+
+includeStaticPatches   true;
+frozenInterpolation    true;
+
+interpolation
+{
+    RBF W2;
+    focalPoint (0 0 0);
+    innerRadius 0.0;//5.0
+    outerRadius 10;
+    polynomials true;
+
+    W2Coeffs
+    {
+        radius     5;
+    }
+    TPSCoeffs
+    {
+        radius     4;
+    }
+    GaussCoeffs
+    {
+        radius     1;
+    }
+    IMQBCoeffs
+    {
+        radius     0.1;
+    }
+}
diff --git a/unitTests/RBF_def/constant/polyMesh/boundary b/unitTests/RBF_def/constant/polyMesh/boundary
new file mode 100755
index 000000000..25e319efe
--- /dev/null
+++ b/unitTests/RBF_def/constant/polyMesh/boundary
@@ -0,0 +1,62 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  6
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       polyBoundaryMesh;
+    location    "constant/polyMesh";
+    object      boundary;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+6
+(
+    inlet
+    {
+        type            patch;
+        nFaces          40;
+        startFace       23266;
+    }
+    outlet
+    {
+        type            patch;
+        nFaces          40;
+        startFace       23306;
+    }
+    down
+    {
+        type            empty;
+        inGroups        1(empty);
+        nFaces          11644;
+        startFace       23346;
+    }
+    up
+    {
+        type            empty;
+        inGroups        1(empty);
+        nFaces          11644;
+        startFace       34990;
+    }
+    sides
+    {
+        type            wall;
+        inGroups        1(wall);
+        nFaces          200;
+        startFace       46634;
+    }
+    cylinder1
+    {
+        type            wall;
+        inGroups        1(wall);
+        nFaces          318;
+        startFace       46834;
+    }
+)
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/constant/polyMesh/cellLevel b/unitTests/RBF_def/constant/polyMesh/cellLevel
new file mode 100755
index 000000000..b57322e0c
--- /dev/null
+++ b/unitTests/RBF_def/constant/polyMesh/cellLevel
@@ -0,0 +1,124425 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  6
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       labelList;
+    location    "constant/polyMesh";
+    object      cellLevel;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+
+124401
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+)
+
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/constant/polyMesh/cellZones b/unitTests/RBF_def/constant/polyMesh/cellZones
new file mode 100755
index 000000000..1ff21bfb2
--- /dev/null
+++ b/unitTests/RBF_def/constant/polyMesh/cellZones
@@ -0,0 +1,21 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  6
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       regIOobject;
+    location    "constant/polyMesh";
+    object      cellZones;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+0
+()
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/constant/polyMesh/faceZones b/unitTests/RBF_def/constant/polyMesh/faceZones
new file mode 100755
index 000000000..1e7975b8a
--- /dev/null
+++ b/unitTests/RBF_def/constant/polyMesh/faceZones
@@ -0,0 +1,21 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  6
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       regIOobject;
+    location    "constant/polyMesh";
+    object      faceZones;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+0
+()
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/constant/polyMesh/faces b/unitTests/RBF_def/constant/polyMesh/faces
new file mode 100755
index 000000000..f5445607e
--- /dev/null
+++ b/unitTests/RBF_def/constant/polyMesh/faces
@@ -0,0 +1,47176 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  6
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       faceList;
+    location    "constant/polyMesh";
+    object      faces;
+}
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+)
+
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/constant/polyMesh/level0Edge b/unitTests/RBF_def/constant/polyMesh/level0Edge
new file mode 100755
index 000000000..9fbc8c812
--- /dev/null
+++ b/unitTests/RBF_def/constant/polyMesh/level0Edge
@@ -0,0 +1,23 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  6
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       uniformDimensionedScalarField;
+    location    "constant/polyMesh";
+    object      level0Edge;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dimensions      [0 1 0 0 0 0 0];
+value           0.2;
+
+
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/constant/polyMesh/neighbour b/unitTests/RBF_def/constant/polyMesh/neighbour
new file mode 100755
index 000000000..42ace1060
--- /dev/null
+++ b/unitTests/RBF_def/constant/polyMesh/neighbour
@@ -0,0 +1,23291 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  6
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       labelList;
+    note        "nPoints:24440  nCells:11644  nFaces:47152  nInternalFaces:23266";
+    location    "constant/polyMesh";
+    object      neighbour;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+
+23266
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+
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/constant/polyMesh/owner b/unitTests/RBF_def/constant/polyMesh/owner
new file mode 100755
index 000000000..de5362d91
--- /dev/null
+++ b/unitTests/RBF_def/constant/polyMesh/owner
@@ -0,0 +1,47177 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  6
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       labelList;
+    note        "nPoints:24440  nCells:11644  nFaces:47152  nInternalFaces:23266";
+    location    "constant/polyMesh";
+    object      owner;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+
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+
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/constant/polyMesh/pointLevel b/unitTests/RBF_def/constant/polyMesh/pointLevel
new file mode 100755
index 000000000..eea2ff5a7
--- /dev/null
+++ b/unitTests/RBF_def/constant/polyMesh/pointLevel
@@ -0,0 +1,148819 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  6
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       labelList;
+    location    "constant/polyMesh";
+    object      pointLevel;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+
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+
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/constant/polyMesh/pointZones b/unitTests/RBF_def/constant/polyMesh/pointZones
new file mode 100755
index 000000000..f5f63c5ad
--- /dev/null
+++ b/unitTests/RBF_def/constant/polyMesh/pointZones
@@ -0,0 +1,21 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  6
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       regIOobject;
+    location    "constant/polyMesh";
+    object      pointZones;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+0
+()
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/constant/polyMesh/points b/unitTests/RBF_def/constant/polyMesh/points
new file mode 100755
index 000000000..24026e5ef
--- /dev/null
+++ b/unitTests/RBF_def/constant/polyMesh/points
@@ -0,0 +1,24464 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  6
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       vectorField;
+    location    "constant/polyMesh";
+    object      points;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+
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+// ************************************************************************* //
diff --git a/unitTests/RBF_def/constant/polyMesh/surfaceIndex b/unitTests/RBF_def/constant/polyMesh/surfaceIndex
new file mode 100755
index 000000000..1c2e82132
--- /dev/null
+++ b/unitTests/RBF_def/constant/polyMesh/surfaceIndex
@@ -0,0 +1,397045 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  6
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       labelList;
+    location    "constant/polyMesh";
+    object      surfaceIndex;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
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+)
+
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/constant/transportProperties b/unitTests/RBF_def/constant/transportProperties
new file mode 100755
index 000000000..139d4bdab
--- /dev/null
+++ b/unitTests/RBF_def/constant/transportProperties
@@ -0,0 +1,21 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  2.4.0                                 |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      transportProperties;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+transportModel  Newtonian;
+
+nu              nu [ 0 2 -1 0 0 0 0 ] 0.07;
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/constant/turbulenceProperties b/unitTests/RBF_def/constant/turbulenceProperties
new file mode 100755
index 000000000..9cfc50a3d
--- /dev/null
+++ b/unitTests/RBF_def/constant/turbulenceProperties
@@ -0,0 +1,21 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  1.6                                   |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    location    "constant";
+    object      turbulenceProperties;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+simulationType  laminar;
+
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/defGeom.C b/unitTests/RBF_def/defGeom.C
new file mode 100755
index 000000000..712ebab76
--- /dev/null
+++ b/unitTests/RBF_def/defGeom.C
@@ -0,0 +1,120 @@
+#include<iostream>
+#include "argList.H"
+#include "Time.H"
+#include "fvMesh.H"
+#include "RBFMotionSolver.H"
+#include "dictionary.H"
+#include "fvCFD.H"
+#include "IOmanip.H"
+#include "SteadyNSSimple.H"
+#include <Eigen/Dense>
+#define _USE_MATH_DEFINES
+#include <cmath>
+#include "pointPatchField.H"
+
+class geomPar : public SteadyNSSimple
+{
+public:
+    explicit geomPar(int argc, char* argv[])
+        :
+        SteadyNSSimple(argc, argv)
+    {
+        fvMesh& mesh = _mesh();
+        IOdictionary* dyndict = new IOdictionary
+        (
+            IOobject
+            (
+                "dynamicMeshDictRBF",
+                "./constant",
+                mesh,
+                IOobject::MUST_READ,
+                IOobject::NO_WRITE
+            )
+        );
+        //ITHACAutilities::getPointsFromPatch(mesh, 6, ahmed, ahmedInd);
+        ms = new RBFMotionSolver(mesh, *dyndict);
+        vectorField motion(ms->movingPoints().size(), vector::zero);
+        movingIDs = ms->movingIDs();
+        x0 = ms->movingPoints();
+        curX = x0;
+        point0 = ms->curPoints();
+    }
+
+    List<vector> x0;
+    vectorField point0;
+    List<vector> curX;
+    IOdictionary* dyndict;
+    RBFMotionSolver* ms;
+    labelList movingIDs;
+
+    labelList getIndicesFromBox(fvMesh& mesh, label ind, Eigen::MatrixXd Box,
+                                List<vector>& points2Move)
+    {
+        points2Move.resize(0);
+        pointField meshPoints(mesh.points());
+        const polyPatch& patchFound = mesh.boundaryMesh()[ind];
+        labelList labelPatchFound(patchFound.meshPoints());
+        labelList boxIndices;
+
+        for (int i = 0; i < labelPatchFound.size(); i++)
+        {
+            auto px = meshPoints[labelPatchFound[i]].component(0);
+            auto py = meshPoints[labelPatchFound[i]].component(1);
+            auto pz = meshPoints[labelPatchFound[i]].component(2);
+
+            if (px >= min(Box(0, 0), Box(1, 0)) && py >= min(Box(0, 1), Box(1, 1)) &&
+                    pz >= min(Box(0, 2), Box(1, 2)) && px <= max(Box(0, 0), Box(1, 0))
+                    && py <= max(Box(0, 1), Box(1, 1)) && pz <= max(Box(0, 2), Box(1, 2)) )
+            {
+                boxIndices.append(labelPatchFound[i]);
+                points2Move.append(meshPoints[labelPatchFound[i]]);
+            }
+        }
+
+        return boxIndices;
+    }
+
+    void movePts(double dis, List<vector>& points2Move)
+    {
+        for (label i = 0; i < points2Move.size(); i++)
+        {
+            points2Move[i].component(1) = points2Move[i].component(1) + dis;
+        }
+    }
+};
+
+int main(int argc, char* argv[])
+{
+    geomPar example(argc, argv);
+    fvMesh& mesh = example._mesh();
+    Eigen::VectorXd beta = Eigen::VectorXd::LinSpaced(50,0,1);
+    Eigen::MatrixXd Box(2, 3);
+
+    // Setting the box where you want to serach for boundary
+    // Box << x0, y0, z0, x1, y1, z1;
+    Box << -7, -7, -1,
+        7, 7, 1;
+    mkDir("./defGeoms/");
+    system("cp -r constant defGeoms/constant");
+    system("cp -r system defGeoms/system");
+    system("cp -r 0 defGeoms/0");// Box << x0, y0, z0, x1, y1, z1;
+
+    for (int k = 0; k < beta.size(); k++)
+    {
+        mkDir("./defGeoms/" + name(k + 1));
+        mesh.movePoints(example.point0);
+        List<vector> points2Move;
+        // The cylinder patch is number 5
+        labelList boxIndices = example.getIndicesFromBox(mesh, 5, Box, points2Move);
+        // Move the points of the cylinder according to a prescribed law (in this case constant vertical displacement)
+        example.movePts(beta(k), points2Move);
+        ITHACAutilities::setIndices2Value(boxIndices, points2Move, example.movingIDs,
+                                          example.curX);
+        example.ms->setMotion(example.curX - example.x0);
+        // Move any other point (not belonging to the patch) using RBF (see dynamicMeshDictRBF for settings)
+        mesh.movePoints(example.ms->curPoints());
+        // Write the points in a dedicated folder to visualize geometries
+        ITHACAstream::writePoints(mesh.points(), "defGeoms/", name(k + 1) + "/polyMesh/");
+
+    }
+}
\ No newline at end of file
diff --git a/unitTests/RBF_def/system/ITHACAdict b/unitTests/RBF_def/system/ITHACAdict
new file mode 100755
index 000000000..9c6108d82
--- /dev/null
+++ b/unitTests/RBF_def/system/ITHACAdict
@@ -0,0 +1,32 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  2.2.2                                 |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    location    "system";
+    object      ITHACAdict;
+}
+
+// EigenValue solver, can be eigen or spectra
+EigenSolver eigen;
+
+// Number of modes to output and to use for projection
+NmodesUout 50;
+NmodesUproj 10;
+
+NmodesPout 50;
+NmodesPproj 8;
+
+NmodesSUPout 50;
+NmodesSUPproj 10;
+
+// Output format to save market vectors.
+OutPrecision 20;
+OutType fixed;
diff --git a/unitTests/RBF_def/system/blockMeshDict b/unitTests/RBF_def/system/blockMeshDict
new file mode 100755
index 000000000..369a016cd
--- /dev/null
+++ b/unitTests/RBF_def/system/blockMeshDict
@@ -0,0 +1,116 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  2.4.0                                 |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      blockMeshDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+backgroundMesh
+{
+    xMin    -4;
+    xMax    30;
+    yMin    -5;
+    yMax     5;
+    zMin    -0.1;
+    zMax     0.1;
+    xCells  100;
+    yCells  40;
+    zCells  1;
+}
+
+convertToMeters 1;
+
+vertices
+(
+    ($:backgroundMesh.xMin $:backgroundMesh.yMin $:backgroundMesh.zMin)
+    ($:backgroundMesh.xMax $:backgroundMesh.yMin $:backgroundMesh.zMin)
+    ($:backgroundMesh.xMax $:backgroundMesh.yMax $:backgroundMesh.zMin)
+    ($:backgroundMesh.xMin $:backgroundMesh.yMax $:backgroundMesh.zMin)
+
+    ($:backgroundMesh.xMin $:backgroundMesh.yMin $:backgroundMesh.zMax)
+    ($:backgroundMesh.xMax $:backgroundMesh.yMin $:backgroundMesh.zMax)
+    ($:backgroundMesh.xMax $:backgroundMesh.yMax $:backgroundMesh.zMax)
+    ($:backgroundMesh.xMin $:backgroundMesh.yMax $:backgroundMesh.zMax)
+);
+
+blocks
+(
+    hex (0 1 2 3 4 5 6 7)
+    (
+        $:backgroundMesh.xCells
+        $:backgroundMesh.yCells
+        $:backgroundMesh.zCells
+    )
+    simpleGrading (1 1 1)
+);
+
+edges
+(
+);
+
+boundary
+(
+    inlet
+{
+	type patch;
+	faces
+	(
+	    (0 3 7 4)
+	);
+
+}
+
+outlet
+{
+	type patch;
+	faces
+	(
+	    (1 2 6 5)
+	);
+}
+
+	down
+	{
+		type empty;
+		faces
+		(
+            (0 1 2 3)
+
+		);
+	}
+	up
+	{
+		type empty;
+		faces
+		(
+            (4 5 6 7)
+
+		);
+	}
+	sides
+	{
+		type wall;
+		faces
+		(
+            (0 1 5 4)
+            (3 2 6 7)
+		);
+	}
+
+    
+);
+
+mergePatchPairs
+(
+);
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/system/controlDict b/unitTests/RBF_def/system/controlDict
new file mode 100755
index 000000000..a2a382a84
--- /dev/null
+++ b/unitTests/RBF_def/system/controlDict
@@ -0,0 +1,54 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  3.0.x                                 |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+|*---------------------------------------------------------------------------*|
+|  File created by CFD support s.r.o., Wed Jan 25 11:27:58 2017               |
+|                    http://www.cdfsupport.com                                |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     3.0;
+    format      ascii;
+    class       dictionary;
+    location    "system";
+    object      controlDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+application     pimpleFoam;
+
+startFrom       startTime;
+
+startTime       0;
+
+stopAt          endTime;
+
+endTime         200;
+
+deltaT          0.005;
+
+writeControl    timeStep;
+
+writeInterval   10000000;
+
+purgeWrite      500;
+
+writeFormat     ascii;
+
+writePrecision  6;
+
+writeCompression off;
+
+timeFormat      general;
+
+timePrecision   6;
+
+runTimeModifiable false;
+
+adjustTimeStep off; 
+
+maxCo 1;
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/system/decomposeParDict b/unitTests/RBF_def/system/decomposeParDict
new file mode 100755
index 000000000..0debe3ee9
--- /dev/null
+++ b/unitTests/RBF_def/system/decomposeParDict
@@ -0,0 +1,30 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  4.x                                   |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      decomposeParDict;
+}
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+numberOfSubdomains 4;
+
+method          simple;
+// method          ptscotch;
+
+simpleCoeffs
+{
+    n               (4 1 1);
+    delta           0.001;
+}
+
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/system/extrudeMeshDict b/unitTests/RBF_def/system/extrudeMeshDict
new file mode 100755
index 000000000..7735184cf
--- /dev/null
+++ b/unitTests/RBF_def/system/extrudeMeshDict
@@ -0,0 +1,53 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  2.2.0                                 |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      extrudeMeshDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+// What to extrude:
+//      patch   : from patch of another case ('sourceCase')
+//      mesh    : as above but with original case included
+//      surface : from externally read surface
+
+constructFrom patch;
+sourceCase ".";
+sourcePatches (up);
+
+// If construct from patch: patch to use for back (can be same as sourcePatch)
+exposedPatchName down;
+
+// Flip surface normals before usage. Valid only for extrude from surface or
+// patch.
+flipNormals false;
+
+//- Linear extrusion in point-normal direction
+extrudeModel        linearNormal;
+
+nLayers             1;
+
+expansionRatio      1.0;
+
+linearNormalCoeffs
+{
+    thickness       0.025;
+}
+
+// Do front and back need to be merged? Usually only makes sense for 360
+// degree wedges.
+mergeFaces false;   //true;
+
+// Merge small edges. Fraction of bounding box.
+mergeTol 0;
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
diff --git a/unitTests/RBF_def/system/fvSchemes b/unitTests/RBF_def/system/fvSchemes
new file mode 100755
index 000000000..34a8e60b9
--- /dev/null
+++ b/unitTests/RBF_def/system/fvSchemes
@@ -0,0 +1,73 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  3.0.x                                 |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+|*---------------------------------------------------------------------------*|
+|  File created by CFD support s.r.o., Wed Jan 25 11:27:58 2017               |
+|                    http://www.cdfsupport.com                                |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     3.0;
+    format      ascii;
+    class       dictionary;
+    location    "system";
+    object      fvSchemes;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+ddtSchemes
+{
+    default         backward;
+}
+
+gradSchemes
+{
+    default         cellMDLimited Gauss linear 0.5;
+}
+
+divSchemes
+{
+    default         Gauss linear;
+/*    div(phi,U)      Gauss linear; //linearUpwind grad(U);*/
+/*    div((nuEff*dev(T(grad(U))))) Gauss linear;*/
+/*    div((nuEff*dev2(T(grad(U))))) Gauss linear;*/
+/*    div((nuEff*dev2(T(grad(Ua))))) Gauss linear;*/
+/*    div((interpolate(U)&S),U) Gauss linearUpwind grad(U);*/
+/*    div((interpolate(U)&S),Usup) Gauss linearUpwind grad(Usup);*/
+/*    div((interpolate(U)&S),Ulift0) Gauss linearUpwind grad(Ulift0);*/
+/*    div((interpolate(Usup)&S),U) Gauss linearUpwind grad(U);*/
+/*    div((interpolate(Usup)&S),Usup) Gauss linearUpwind grad(Usup);*/
+/*    div((interpolate(Usup)&S),Ulift0) Gauss linearUpwind grad(Ulift0);*/
+/*    div((interpolate(Ulift0)&S),U) Gauss linearUpwind grad(U);*/
+/*    div((interpolate(Ulift0)&S),Usup) Gauss linearUpwind grad(Usup);*/
+/*    div((interpolate(Ulift0)&S),Ulift0) Gauss linearUpwind grad(Ulift0);*/
+}
+
+laplacianSchemes
+{
+    default        Gauss linear limited 1.0;
+}
+
+interpolationSchemes
+{
+    default         linear;
+}
+
+snGradSchemes
+{
+    default         limited 1;
+}
+
+fluxRequired
+{
+    default         no;
+    p;
+    Phi;
+}
+
+
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/system/fvSolution b/unitTests/RBF_def/system/fvSolution
new file mode 100755
index 000000000..e41b91759
--- /dev/null
+++ b/unitTests/RBF_def/system/fvSolution
@@ -0,0 +1,113 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  3.0.x                                 |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+|*---------------------------------------------------------------------------*|
+|  File created by CFD support s.r.o., Wed Jan 25 11:27:58 2017               |
+|                    http://www.cdfsupport.com                                |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     3.0;
+    format      ascii;
+    class       dictionary;
+    location    "system";
+    object      fvSolution;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+solvers
+{
+    "(p|pa)"
+    {
+        solver          GAMG;
+        tolerance       1e-08;
+        relTol          0.01;
+        smoother        GaussSeidel;
+        nPreSweeps      0;
+        nPostSweeps     2;
+        cacheAgglomeration true;
+        nCellsInCoarsestLevel 10;
+        agglomerator    faceAreaPair;
+        mergeLevels     1;
+    }
+
+    "(U|Ua|k|epsilon)"
+    {
+        solver          smoothSolver;
+        smoother        GaussSeidel;
+        nSweeps         2;
+        tolerance       1e-08;
+        relTol          0.1;
+    }
+
+    "(U|k|epsilon)Final"
+    {
+        $U;
+        relTol          0;
+    }
+    pFinal
+    {
+        $p;
+        relTol          0;
+    }
+
+    Usup
+    {
+	    solver           GAMG;
+        tolerance        1e-7;
+        relTol           0.001;
+        smoother         GaussSeidel;
+        nPreSweeps       0;
+        nPostSweeps      2;
+        cacheAgglomeration on;
+        agglomerator     faceAreaPair;
+        nCellsInCoarsestLevel 10;
+        mergeLevels      1;
+    }
+    Phi
+    {
+        $p;
+    }
+}
+
+SIMPLE
+{
+    nNonOrthogonalCorrectors 2;
+    pRefCell 0;
+    pRefValue 0;
+}
+
+PIMPLE
+{
+    nNonOrthogonalCorrectors 1;
+    nCorrectors 3;
+}
+
+potentialFlow
+{
+    nNonOrthogonalCorrectors 10;
+}
+
+
+relaxationFactors
+{
+    p 0.3;
+    U 0.7;    
+
+    fields
+    {
+        "(p|pa)"        0.3;
+        alpha           0.1;
+    }
+    equations
+    {
+        "(U|Ua)"        0.7;
+        "(k|epsilon)"   0.7;
+    }
+}
+
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/system/meshQualityDict b/unitTests/RBF_def/system/meshQualityDict
new file mode 100755
index 000000000..f5f47a62f
--- /dev/null
+++ b/unitTests/RBF_def/system/meshQualityDict
@@ -0,0 +1,22 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  2.4.0                                 |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      meshQualityDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#includeEtc "caseDicts/mesh/generation/meshQualityDict.cfg"
+
+//- minFaceWeight (0 -> 0.5)
+//minFaceWeight 0.02;
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/system/snappyHexMeshDict b/unitTests/RBF_def/system/snappyHexMeshDict
new file mode 100755
index 000000000..864325757
--- /dev/null
+++ b/unitTests/RBF_def/system/snappyHexMeshDict
@@ -0,0 +1,237 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  2.0.0                                 |
+|   \\  /    A nd           | Web:      www.OpenFOAM.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      snappyHexMeshDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+// Which of the steps to run
+castellatedMesh true;
+snap            true;
+addLayers       true;
+debug 0;
+mergeTolerance 1e-6;
+
+
+geometry
+{
+    cylinder1
+    {
+        type searchableCylinder;
+        point1 (0 0 -2.5);    // Height
+        point2 (0 0 2.5);    // Vector
+        radius 0.5; 
+    }
+
+/*    cylinder2*/
+/*    {*/
+/*        type searchableCylinder;*/
+/*        point1 (9 0 -2.5);    // Height*/
+/*        point2 (9 0 2.5);    // Vector*/
+/*        radius 0.5; */
+/*    }*/
+
+    refinementBox                      //USER DEFINED REGION NAME
+    {
+          type searchableBox;          //REGION DEFINED BY BOUNDING BOX
+          min ( -1 -1 -3);    //parameters
+          max (3 1 3);    
+    }
+
+    suprefinementBox1                      //USER DEFINED REGION NAME
+    {
+          type searchableBox;          //REGION DEFINED BY BOUNDING BOX
+          min ( -1 -1 -6);    //parameters
+          max (1 1 6);    
+    }  
+
+/*    suprefinementBox2                      //USER DEFINED REGION NAME*/
+/*    {*/
+/*          type searchableBox;          //REGION DEFINED BY BOUNDING BOX*/
+/*          min (8 -1 -6);    //parameters*/
+/*          max (10 1 6);    */
+/*    }      */
+
+    suprefinementCylinder1
+    {
+        type searchableCylinder;
+        point1 (0 0 -2.7);    // Height
+        point2 (0 0 2.7);    // Vector
+        radius 0.8; 
+    }
+
+/*    suprefinementCylinder2*/
+/*    {*/
+/*        type searchableCylinder;*/
+/*        point1 (9 0 -2.7);    // Height*/
+/*        point2 (9 0 2.7);    // Vector*/
+/*        radius 0.8; */
+/*    }*/
+};
+castellatedMeshControls
+{
+    maxLocalCells 3000000;
+    maxGlobalCells 5000000;
+    minRefinementCells 50;
+    //maxLoadUnbalance 0.50;
+    nCellsBetweenLevels 6;
+    features
+    (
+    );
+    refinementSurfaces
+    {  
+        cylinder1
+        {
+            level (5 6);
+
+            patchInfo
+            {
+                type wall;
+            }
+        }
+        
+    }
+    refinementSurfaces
+    {  
+        cylinder2
+        {
+            level (5 6);
+
+            patchInfo
+            {
+                type wall;
+            }
+        }
+        
+    }
+
+    resolveFeatureAngle 30;
+/*    refinementRegions*/
+/*    {*/
+/*    	cylinder*/
+/*    	{*/
+/*    		mode distance;*/
+/*    		levels ((0.01 5) (0.2 2) (1 1));*/
+/*    	}*/
+/*    }*/
+
+    refinementRegions
+    {
+      
+       refinementBox
+        {
+            mode inside;
+            levels ((2 2));
+        }
+       suprefinementBox1
+        {
+            mode inside;
+            levels ((3 3));
+        }
+/*       suprefinementBox2*/
+/*        {*/
+/*            mode inside;*/
+/*            levels ((3 3));*/
+/*        }*/
+       
+        suprefinementCylinder1
+        {
+            mode inside;
+            levels ((4 4));
+        }
+
+/*        suprefinementCylinder2*/
+/*        {*/
+/*            mode inside;*/
+/*            levels ((4 4));*/
+/*        }*/
+    }
+    
+    
+    locationInMesh (8 0 0);
+    allowFreeStandingZoneFaces true;
+}
+
+
+snapControls
+{
+    nSmoothPatch 5;
+    tolerance 1.0;
+    nSolveIter 300;
+    nRelaxIter 5;
+}
+
+addLayersControls
+{
+    relativeSizes false;
+
+    layers
+    {
+        cylinder1
+        {
+            nSurfaceLayers 40;
+        }
+    }
+
+    layers
+    {
+        cylinder2
+        {
+            nSurfaceLayers 40;
+        }
+    }
+
+    expansionRatio 1.2;
+//    finalLayerThickness 1e-9;
+    finalLayerThickness 0.015e-7;
+  //  finalLayerRatio 0.01;
+    minThickness 0.001e-7;
+    nGrow 0;
+    featureAngle 30;
+    nRelaxIter 10;
+    nSmoothSurfaceNormals 1;
+    nSmoothNormals 3;
+    nSmoothThickness 10;
+    maxFaceThicknessRatio 0.8;
+    maxThicknessToMedialRatio 0.8;
+    minMedianAxisAngle 40;
+    nBufferCellsNoExtrude 0;
+    nLayerIter 100;
+    nRelaxedIter 20;
+}
+
+meshQualityControls
+{
+    maxNonOrtho 65;
+    maxBoundarySkewness 20;
+    maxInternalSkewness 4;
+    maxConcave 80;
+    minVol 1e-250;
+    minTetQuality 1e-25;
+    minArea -1;
+    minTwist 0.05;
+    minDeterminant 0.001;
+    minFaceWeight 0.05;
+    minVolRatio 1e-1;
+    minTriangleTwist -1;
+    nSmoothScale 4;
+    errorReduction 0.75;
+
+    relaxed
+    {
+        maxNonOrtho 75;
+    }
+}
+
+
+
+// ************************************************************************* //
diff --git a/unitTests/RBF_def/system/surfaceFeatureExtractDict b/unitTests/RBF_def/system/surfaceFeatureExtractDict
new file mode 100755
index 000000000..fab26191a
--- /dev/null
+++ b/unitTests/RBF_def/system/surfaceFeatureExtractDict
@@ -0,0 +1,35 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  2.4.0                                 |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       dictionary;
+    object      surfaceFeatureExtractDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+CAD.obj
+{
+    extractionMethod     extractFromSurface;
+
+    extractFromSurfaceCoeffs
+    {
+        includedAngle    150;
+    }
+
+    subsetFeatures
+    {
+        nonManifoldEdges yes;
+        openEdges        yes;
+    }
+
+    writeObj             yes;
+}
+
+// ************************************************************************* //

From 62922d70a315500816f92ced30bbfc9b4120ecde Mon Sep 17 00:00:00 2001
From: Giovanni Stabile <giovanni.stabile87@gmail.com>
Date: Fri, 28 Jun 2024 12:04:57 +0200
Subject: [PATCH 53/59] FIX: added compilation for field2EigenMapBC function
 using volScalarField

---
 src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.C | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.C b/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.C
index 7069e7a85..176b89021 100644
--- a/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.C
+++ b/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.C
@@ -112,6 +112,9 @@ Eigen::Map<Eigen::MatrixXd> Foam2Eigen::field2EigenMapBC(
 template Eigen::Map<Eigen::MatrixXd> Foam2Eigen::field2EigenMap(
     volScalarField& field);
 
+template Eigen::Map<Eigen::MatrixXd> Foam2Eigen::field2EigenMapBC(
+    volScalarField& field, int BC_index);
+
 template Eigen::VectorXd Foam2Eigen::field2Eigen(
     volScalarField& field);
 template Eigen::VectorXd Foam2Eigen::field2Eigen(

From 1ec445a0f6bf178b8410b4680f0d014e7d089c24 Mon Sep 17 00:00:00 2001
From: shehzadmazhar <shehzadmazhar9@gmail.com>
Date: Wed, 17 Jul 2024 10:02:15 +0200
Subject: [PATCH 54/59] ENH: Added the possibly to simply switch from
 Supremizer to PPE and from Lift to penalty by selecting it in ITHACADict

---
 .../unsteadyNS/unsteadyNS.C                   |   5 +
 .../unsteadyNS/unsteadyNS.H                   |   2 +
 tutorials/CFD/04unsteadyNS/04unsteadyNS.C     | 154 +++++++++++-------
 tutorials/CFD/04unsteadyNS/system/ITHACAdict  |  25 ++-
 4 files changed, 119 insertions(+), 67 deletions(-)

diff --git a/src/ITHACA_FOMPROBLEMS/unsteadyNS/unsteadyNS.C b/src/ITHACA_FOMPROBLEMS/unsteadyNS/unsteadyNS.C
index 453a9e214..4443995f8 100644
--- a/src/ITHACA_FOMPROBLEMS/unsteadyNS/unsteadyNS.C
+++ b/src/ITHACA_FOMPROBLEMS/unsteadyNS/unsteadyNS.C
@@ -77,9 +77,14 @@ unsteadyNS::unsteadyNS(int argc, char* argv[])
 #include "createFields.H"
 #include "createFvOptions.H"
     para = ITHACAparameters::getInstance(mesh, runTime);
+    
+    method = ITHACAdict->lookupOrDefault<word>("method", "supremizer");
+    M_Assert(method == "supremizer" || method == "PPE", "The method must be set to supremizer or PPE in ITHACAdict");
+    
     bcMethod = ITHACAdict->lookupOrDefault<word>("bcMethod", "lift");
     M_Assert(bcMethod == "lift" || bcMethod == "penalty",
              "The BC method must be set to lift or penalty in ITHACAdict");
+    
     timedepbcMethod = ITHACAdict->lookupOrDefault<word>("timedepbcMethod", "no");
     M_Assert(timedepbcMethod == "yes" || timedepbcMethod == "no",
              "The BC method can be set to yes or no");
diff --git a/src/ITHACA_FOMPROBLEMS/unsteadyNS/unsteadyNS.H b/src/ITHACA_FOMPROBLEMS/unsteadyNS/unsteadyNS.H
index 8eb066e5c..93024860f 100755
--- a/src/ITHACA_FOMPROBLEMS/unsteadyNS/unsteadyNS.H
+++ b/src/ITHACA_FOMPROBLEMS/unsteadyNS/unsteadyNS.H
@@ -86,6 +86,8 @@ class unsteadyNS: public steadyNS, public UnsteadyProblem
 
         // Counter used for the time-dependent boundary conditions
         label counter2 = 1;
+        
+        word method;
 
         /// Time-dependent Boundary Method
         word timedepbcMethod;
diff --git a/tutorials/CFD/04unsteadyNS/04unsteadyNS.C b/tutorials/CFD/04unsteadyNS/04unsteadyNS.C
index fa8cf2e0c..4494743e3 100755
--- a/tutorials/CFD/04unsteadyNS/04unsteadyNS.C
+++ b/tutorials/CFD/04unsteadyNS/04unsteadyNS.C
@@ -32,46 +32,42 @@ SourceFiles
 #include "ReducedUnsteadyNS.H"
 #include "ITHACAstream.H"
 #include <chrono>
-#include<math.h>
-#include<iomanip>
+#include <math.h>
+#include <iomanip>
+#include <iostream>
 
-class tutorial04: public unsteadyNS
+class tutorial04 : public unsteadyNS
 {
-    public:
-        explicit tutorial04(int argc, char* argv[])
-            :
-            unsteadyNS(argc, argv),
-            U(_U()),
-            p(_p())
-        {}
+public:
+    explicit tutorial04(int argc, char* argv[])
+        : unsteadyNS(argc, argv), U(_U()), p(_p()) {}
 
-        // Fields To Perform
-        volVectorField& U;
-        volScalarField& p;
+    // Fields To Perform
+    volVectorField& U;
+    volScalarField& p;
 
-        void offlineSolve()
-        {
-            Vector<double> inl(1, 0, 0);
-            List<scalar> mu_now(1);
+    void offlineSolve()
+    {
+        Vector<double> inl(1, 0, 0);
+        List<scalar> mu_now(1);
+        label BCind = 0;
 
-            if (offline)
-            {
-                ITHACAstream::read_fields(Ufield, U, "./ITHACAoutput/Offline/");
-                ITHACAstream::read_fields(Pfield, p, "./ITHACAoutput/Offline/");
-            }
-            else
+        if (offline)
+        {
+            ITHACAstream::read_fields(Ufield, U, "./ITHACAoutput/Offline/");
+            ITHACAstream::read_fields(Pfield, p, "./ITHACAoutput/Offline/");
+        }
+        else
+        {
+            for (label i = 0; i < mu.cols(); i++)
             {
-                for (label i = 0; i < mu.cols(); i++)
-                {
-                    //inl[0] = mu(0, i);
-                    mu_now[0] = mu(0, i);
-                    //assignBC(U, BCind, inl);
-                    assignIF(U, inl);
-                    change_viscosity( mu(0, i));
-                    truthSolve(mu_now);
-                }
+                mu_now[0] = mu(0, i);
+                assignIF(U, inl);
+                change_viscosity(mu(0, i));
+                truthSolve(mu_now);
             }
         }
+    }
 };
 
 /*---------------------------------------------------------------------------*\
@@ -81,20 +77,21 @@ int main(int argc, char* argv[])
 {
     // Construct the tutorial04 object
     tutorial04 example(argc, argv);
+
     // Read parameters from ITHACAdict file
-    ITHACAparameters* para = ITHACAparameters::getInstance(example._mesh(),
-                             example._runTime());
+    ITHACAparameters* para = ITHACAparameters::getInstance(example._mesh(), example._runTime());
     int NmodesUout = para->ITHACAdict->lookupOrDefault<int>("NmodesUout", 15);
     int NmodesPout = para->ITHACAdict->lookupOrDefault<int>("NmodesPout", 15);
     int NmodesSUPout = para->ITHACAdict->lookupOrDefault<int>("NmodesSUPout", 15);
     int NmodesUproj = para->ITHACAdict->lookupOrDefault<int>("NmodesUproj", 10);
     int NmodesPproj = para->ITHACAdict->lookupOrDefault<int>("NmodesPproj", 10);
     int NmodesSUPproj = para->ITHACAdict->lookupOrDefault<int>("NmodesSUPproj", 10);
-    /// Set the number of parameters
+
+    // Set the number of parameters
     example.Pnumber = 1;
-    /// Set samples
+    // Set samples
     example.Tnumber = 1;
-    /// Set the parameters infos
+    // Set the parameters infos
     example.setParameters();
     // Set the parameter ranges
     example.mu_range(0, 0) = 0.005;
@@ -106,50 +103,85 @@ int main(int argc, char* argv[])
     example.inletIndex(0, 0) = 0;
     example.inletIndex(0, 1) = 0;
     // Time parameters
-    example.startTime = 50;
+    example.startTime = 60;
     example.finalTime = 70;
     example.timeStep = 0.01;
     example.writeEvery = 0.1;
-    // Perform The Offline Solve;
+    // Perform The Offline Solve
     example.offlineSolve();
-    // Solve the supremizer problem
-    example.solvesupremizer();
-    // Search the lift function
-    example.liftSolve();
-    // Normalize the lifting function
-    ITHACAutilities::normalizeFields(example.liftfield);
-    // Create homogeneous basis functions for velocity
-    example.computeLift(example.Ufield, example.liftfield, example.Uomfield);
-    // Perform a POD decomposition for velocity and pressure
-    ITHACAPOD::getModes(example.Uomfield, example.Umodes, example._U().name(),
-                        example.podex, 0, 0,
-                        NmodesUout);
-    ITHACAPOD::getModes(example.Pfield, example.Pmodes, example._p().name(),
-                        example.podex, 0, 0,
-                        NmodesPout);
-    ITHACAPOD::getModes(example.supfield, example.supmodes, example._U().name(),
-                        example.podex,
-                        example.supex, 1, NmodesSUPout);
-    example.projectSUP("./Matrices", NmodesUproj, NmodesPproj, NmodesSUPproj);
+
+    // Check if lift or penalty method should be used
+    if (example.bcMethod == "lift")
+    {
+        // Search the lift function
+        example.liftSolve();
+        // Normalize the lifting function
+        ITHACAutilities::normalizeFields(example.liftfield);
+        // Create homogeneous basis functions for velocity
+        example.computeLift(example.Ufield, example.liftfield, example.Uomfield);
+        // Perform a POD decomposition for velocity and pressure
+        ITHACAPOD::getModes(example.Uomfield, example.Umodes, example._U().name(), example.podex, 0, 0, NmodesUout);
+        ITHACAPOD::getModes(example.Pfield, example.Pmodes, example._p().name(), example.podex, 0, 0, NmodesPout);
+    }
+    else
+    {
+        // Perform a POD decomposition for velocity and pressure without lifting function
+        ITHACAPOD::getModes(example.Ufield, example.Umodes, example._U().name(), example.podex, 0, 0, NmodesUout);
+        ITHACAPOD::getModes(example.Pfield, example.Pmodes, example._p().name(), example.podex, 0, 0, NmodesPout);
+    }
+    // Check the method and perform the appropriate projection
+    if (example.method == "supremizer")
+    {
+        example.solvesupremizer(); 
+        ITHACAPOD::getModes(example.supfield, example.supmodes, example._U().name(), example.podex, example.supex, 1, NmodesSUPout);
+        example.projectSUP("./Matrices", NmodesUproj, NmodesPproj, NmodesSUPproj);
+    }
+    else if (example.method == "PPE")
+    {
+        example.projectPPE("./Matrices", NmodesUproj, NmodesPproj);
+    }
+
     reducedUnsteadyNS reduced(example);
+
     // Set values of the reduced stuff
     reduced.nu = 0.005;
-    reduced.tstart = 50;
+    reduced.tstart = 60;
     reduced.finalTime = 70;
     reduced.dt = 0.005;
     reduced.storeEvery = 0.005;
     reduced.exportEvery = 0.1;
+
     // Set the online velocity
     Eigen::MatrixXd vel_now(1, 1);
     vel_now(0, 0) = 1;
-    reduced.solveOnline_sup(vel_now, 1);
+
+    // If using the penalty method, set tauU
+    if (example.bcMethod == "penalty")
+    {
+        reduced.tauU = Eigen::MatrixXd::Zero(1, 1);
+        reduced.tauU(0, 0) = 1e-1;  // Example penalty coefficient
+    }
+
+    // Perform the online solve based on the method
+    if (example.method == "supremizer")
+    {
+        reduced.solveOnline_sup(vel_now, 1);
+    }
+    else if (example.method == "PPE")
+    {
+        reduced.solveOnline_PPE(vel_now, 1);
+    }
+
     // Reconstruct the solution and export it
-    reduced.reconstruct(true, "./ITHACAoutput/ReconstructionSUP/");
+    reduced.reconstruct(true, "./ITHACAoutput/Reconstruction" + example.method + "/");
+
     exit(0);
 }
 
 
 
+
+
 /// \dir 04unsteadyNS Folder of the turorial 4
 /// \file
 /// \brief Implementation of tutorial 4 for an unsteady Navier-Stokes problem
diff --git a/tutorials/CFD/04unsteadyNS/system/ITHACAdict b/tutorials/CFD/04unsteadyNS/system/ITHACAdict
index 9c6108d82..5c4986e95 100755
--- a/tutorials/CFD/04unsteadyNS/system/ITHACAdict
+++ b/tutorials/CFD/04unsteadyNS/system/ITHACAdict
@@ -18,15 +18,28 @@ FoamFile
 EigenSolver eigen;
 
 // Number of modes to output and to use for projection
-NmodesUout 50;
+NmodesUout 10;
 NmodesUproj 10;
-
-NmodesPout 50;
-NmodesPproj 8;
-
-NmodesSUPout 50;
+NmodesPout 10;
+NmodesPproj 10;
+NmodesSUPout 10;
 NmodesSUPproj 10;
 
 // Output format to save market vectors.
 OutPrecision 20;
 OutType fixed;
+
+// Specific problem of a stationary case
+// Boundary condition method, can be "lift" or "penalty"
+method  PPE;  // or "PPE"
+bcMethod penalty;
+
+
+// Time-dependent boundary condition method, can be "yes" or "no"
+timedepbcMethod no;
+
+// Time derivative scheme order, can be "first" or "second"
+timeDerivativeSchemeOrder second;
+
+
+

From 84182b2187cb6a7e2e8550cc6c01d8d76a3455ca Mon Sep 17 00:00:00 2001
From: giovastabile <giovanni.stabile87@gmail.com>
Date: Fri, 19 Jul 2024 15:36:53 +0200
Subject: [PATCH 55/59] porting to std14 to make it compiling with of2406

---
 applications/POD/Make/options                                   | 2 +-
 applications/extract_time_evolution/Make/options                | 2 +-
 gtest/Make/options                                              | 2 +-
 src/ITHACA_CORE/Make/options                                    | 2 +-
 src/ITHACA_DEIM/Make/options                                    | 2 +-
 src/ITHACA_FOMPROBLEMS/Make/options                             | 2 +-
 src/ITHACA_MUQ/Make/options                                     | 2 +-
 src/ITHACA_ROMPROBLEMS/Make/options                             | 2 +-
 src/ITHACA_THIRD_PARTY/Make/options                             | 2 +-
 src/OF_EXT/Make/options                                         | 2 +-
 tutorials/CFD/02thermalBlock/Make/options                       | 2 +-
 tutorials/CFD/03steadyNS/Make/options                           | 2 +-
 tutorials/CFD/04unsteadyNS/Make/options                         | 2 +-
 tutorials/CFD/05PODI/Make/options                               | 2 +-
 tutorials/CFD/06POD_RBF/Make/options                            | 2 +-
 tutorials/CFD/07NonIsothermalMixingElbow/Make/options           | 2 +-
 tutorials/CFD/09DEIM_ROM/Make/options                           | 2 +-
 tutorials/CFD/10unsteadyBB_enclosed/Make/options                | 2 +-
 tutorials/CFD/11UnsteadyBBOpen/Make/options                     | 2 +-
 tutorials/CFD/12simpleSteadyNS/Make/options                     | 2 +-
 tutorials/CFD/14DMDexample/Make/options                         | 2 +-
 tutorials/CFD/15MSR_cavity/Make/options                         | 2 +-
 tutorials/CFD/16MSR_FOMSA/Make/options                          | 2 +-
 tutorials/CFD/17YJunction/Make/options                          | 2 +-
 tutorials/CFD/18simpleTurbNS/Make/options                       | 2 +-
 tutorials/CFD/19UnsteadyNSExplicit/Make/options                 | 2 +-
 tutorials/CFD/20incrementalPOD/Make/options                     | 2 +-
 tutorials/CFD/21unsteadyNSTurb_RBF/Make/options                 | 2 +-
 tutorials/CFD/22datadriven_corrections/Make/options             | 2 +-
 tutorials/CFD/23burgers/Make/options                            | 2 +-
 .../inverseHeatTransfer/IHTP01inverseLaplacian/Make/options     | 2 +-
 unitTests/ITHACAstream/Make/options                             | 2 +-
 unitTests/ITHACAsurfacetools/Make/options                       | 2 +-
 unitTests/ITHACAutilities/Make/options                          | 2 +-
 unitTests/OptimLib/ADAM/Make/options                            | 2 +-
 unitTests/RBF_def/Make/options                                  | 2 +-
 unitTests/UQ/quantileTest/Make/options                          | 2 +-
 unitTests/pybind11/Eigen/Make/options                           | 2 +-
 unitTests/pybind11/of_pybind/Make/options                       | 2 +-
 unitTests/pybind11/residual_of/Make/options                     | 2 +-
 unitTests/splinter/Make/options                                 | 2 +-
 41 files changed, 41 insertions(+), 41 deletions(-)

diff --git a/applications/POD/Make/options b/applications/POD/Make/options
index 5f147629f..421af160b 100644
--- a/applications/POD/Make/options
+++ b/applications/POD/Make/options
@@ -34,7 +34,7 @@ EXE_INC = \
     -I$(LIB_ITHACA_SRC)/thirdparty/spectra/include \
     -Wno-comment \
     -w \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/applications/extract_time_evolution/Make/options b/applications/extract_time_evolution/Make/options
index e5580efe7..c047e7cda 100644
--- a/applications/extract_time_evolution/Make/options
+++ b/applications/extract_time_evolution/Make/options
@@ -25,7 +25,7 @@ EXE_INC = \
     -I$(LIB_SRC)/turbulenceModels/compressible/turbulenceModel \
     -I$(LIB_SRC)/functionObjects/forces/lnInclude \
     -w \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/gtest/Make/options b/gtest/Make/options
index dd66e7a2a..12747fdf6 100755
--- a/gtest/Make/options
+++ b/gtest/Make/options
@@ -13,7 +13,7 @@ EXE_INC = \
     -I$(LIB_ITHACA_SRC)/thirdparty/splinter/include \
     -w \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/src/ITHACA_CORE/Make/options b/src/ITHACA_CORE/Make/options
index 4a31fbdc6..e6baf2c81 100644
--- a/src/ITHACA_CORE/Make/options
+++ b/src/ITHACA_CORE/Make/options
@@ -42,7 +42,7 @@ EXE_INC = \
     -O2 \
     -Wno-comment \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11
+    -std=c++14
 
 
 EXE_LIBS = \
diff --git a/src/ITHACA_DEIM/Make/options b/src/ITHACA_DEIM/Make/options
index 0380b8b3b..3dae8efea 100644
--- a/src/ITHACA_DEIM/Make/options
+++ b/src/ITHACA_DEIM/Make/options
@@ -24,7 +24,7 @@ EXE_INC = \
     -I$(LIB_ITHACA_SRC)/ITHACA_CORE/Containers \
     -Wno-comment \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lITHACA-CORE \
diff --git a/src/ITHACA_FOMPROBLEMS/Make/options b/src/ITHACA_FOMPROBLEMS/Make/options
index bcee910b4..897ea6871 100644
--- a/src/ITHACA_FOMPROBLEMS/Make/options
+++ b/src/ITHACA_FOMPROBLEMS/Make/options
@@ -37,7 +37,7 @@ EXE_INC = \
     -Wno-comment \
     -w \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11
+    -std=c++14
 
 
 EXE_LIBS = \
diff --git a/src/ITHACA_MUQ/Make/options b/src/ITHACA_MUQ/Make/options
index 4ee3875bb..28ab167d5 100644
--- a/src/ITHACA_MUQ/Make/options
+++ b/src/ITHACA_MUQ/Make/options
@@ -45,7 +45,7 @@ EXE_INC = \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
     -Wno-comment \
     -g \
-    -std=c++11 \
+    -std=c++14 \
     -Wall \
     -Wno-maybe-uninitialized \
     -Wno-sign-compare \
diff --git a/src/ITHACA_ROMPROBLEMS/Make/options b/src/ITHACA_ROMPROBLEMS/Make/options
index 274cbf168..a484012c0 100644
--- a/src/ITHACA_ROMPROBLEMS/Make/options
+++ b/src/ITHACA_ROMPROBLEMS/Make/options
@@ -40,7 +40,7 @@ EXE_INC = \
     -Wno-comment \
     -w \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11
+    -std=c++14
 
 
 EXE_LIBS = \
diff --git a/src/ITHACA_THIRD_PARTY/Make/options b/src/ITHACA_THIRD_PARTY/Make/options
index 7e3580466..fc75967ff 100644
--- a/src/ITHACA_THIRD_PARTY/Make/options
+++ b/src/ITHACA_THIRD_PARTY/Make/options
@@ -13,7 +13,7 @@ EXE_INC = \
     -I$(LIB_ITHACA_SRC)/ITHACA_THIRD_PARTY/cnpy \
     -I$(LIB_ITHACA_SRC)/thirdparty/Eigen \
     -I$(LIB_ITHACA_SRC)/thirdparty/redsvd \
-    -std=c++11 \
+    -std=c++14 \
     -ftemplate-depth=500 \
     -w \
     -Wno-old-style-cast \
diff --git a/src/OF_EXT/Make/options b/src/OF_EXT/Make/options
index fab5b184d..99beca644 100644
--- a/src/OF_EXT/Make/options
+++ b/src/OF_EXT/Make/options
@@ -18,7 +18,7 @@ EXE_INC = \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
     -Wno-comment \
     -w \
-    -std=c++11
+    -std=c++14
 
 LIB_LIBS = \
     -lmeshTools \
diff --git a/tutorials/CFD/02thermalBlock/Make/options b/tutorials/CFD/02thermalBlock/Make/options
index 856bf7f23..a810cf258 100644
--- a/tutorials/CFD/02thermalBlock/Make/options
+++ b/tutorials/CFD/02thermalBlock/Make/options
@@ -26,7 +26,7 @@ EXE_INC = \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
     -Wno-comment \
     -w \
-    -std=c++11 \
+    -std=c++14 \
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/tutorials/CFD/03steadyNS/Make/options b/tutorials/CFD/03steadyNS/Make/options
index 890209f8d..f9592d243 100644
--- a/tutorials/CFD/03steadyNS/Make/options
+++ b/tutorials/CFD/03steadyNS/Make/options
@@ -24,7 +24,7 @@ EXE_INC = \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
     -Wno-comment \
     -w \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/tutorials/CFD/04unsteadyNS/Make/options b/tutorials/CFD/04unsteadyNS/Make/options
index c04847826..bf582f3c0 100644
--- a/tutorials/CFD/04unsteadyNS/Make/options
+++ b/tutorials/CFD/04unsteadyNS/Make/options
@@ -24,7 +24,7 @@ EXE_INC = \
     -Wno-comment \
     -w \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/tutorials/CFD/05PODI/Make/options b/tutorials/CFD/05PODI/Make/options
index ff32a24ba..d5719e69f 100644
--- a/tutorials/CFD/05PODI/Make/options
+++ b/tutorials/CFD/05PODI/Make/options
@@ -24,7 +24,7 @@ EXE_INC = \
     -Wno-comment \
     -w \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/tutorials/CFD/06POD_RBF/Make/options b/tutorials/CFD/06POD_RBF/Make/options
index 8d753cfae..65c72e01d 100644
--- a/tutorials/CFD/06POD_RBF/Make/options
+++ b/tutorials/CFD/06POD_RBF/Make/options
@@ -23,7 +23,7 @@ EXE_INC = \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
     -Wno-comment \
     -w \
-    -std=c++11 \
+    -std=c++14 \
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/tutorials/CFD/07NonIsothermalMixingElbow/Make/options b/tutorials/CFD/07NonIsothermalMixingElbow/Make/options
index 7a6a5b51d..0e1a8e7ad 100644
--- a/tutorials/CFD/07NonIsothermalMixingElbow/Make/options
+++ b/tutorials/CFD/07NonIsothermalMixingElbow/Make/options
@@ -24,7 +24,7 @@ EXE_INC = \
     -Wno-comment \
     -w \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/tutorials/CFD/09DEIM_ROM/Make/options b/tutorials/CFD/09DEIM_ROM/Make/options
index cdb52b73e..757e52242 100644
--- a/tutorials/CFD/09DEIM_ROM/Make/options
+++ b/tutorials/CFD/09DEIM_ROM/Make/options
@@ -23,7 +23,7 @@ EXE_INC = \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
     -Wno-comment \
     -w \
-    -std=c++11 \
+    -std=c++14 \
 
 
 EXE_LIBS = \
diff --git a/tutorials/CFD/10unsteadyBB_enclosed/Make/options b/tutorials/CFD/10unsteadyBB_enclosed/Make/options
index b3f76bda7..cfa661cd0 100644
--- a/tutorials/CFD/10unsteadyBB_enclosed/Make/options
+++ b/tutorials/CFD/10unsteadyBB_enclosed/Make/options
@@ -24,7 +24,7 @@ EXE_INC = \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
     -Wno-comment \
     -w \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/tutorials/CFD/11UnsteadyBBOpen/Make/options b/tutorials/CFD/11UnsteadyBBOpen/Make/options
index b3f76bda7..cfa661cd0 100644
--- a/tutorials/CFD/11UnsteadyBBOpen/Make/options
+++ b/tutorials/CFD/11UnsteadyBBOpen/Make/options
@@ -24,7 +24,7 @@ EXE_INC = \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
     -Wno-comment \
     -w \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/tutorials/CFD/12simpleSteadyNS/Make/options b/tutorials/CFD/12simpleSteadyNS/Make/options
index 9ef8fcc4b..0a43096ea 100644
--- a/tutorials/CFD/12simpleSteadyNS/Make/options
+++ b/tutorials/CFD/12simpleSteadyNS/Make/options
@@ -23,7 +23,7 @@ EXE_INC = \
     -I$(LIB_ITHACA_SRC)/ITHACA_THIRD_PARTY/splinter/include \
     -w \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/tutorials/CFD/14DMDexample/Make/options b/tutorials/CFD/14DMDexample/Make/options
index 0c07888b4..25f6b953d 100644
--- a/tutorials/CFD/14DMDexample/Make/options
+++ b/tutorials/CFD/14DMDexample/Make/options
@@ -25,7 +25,7 @@ EXE_INC = \
     -Wno-comment \
     -w \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/tutorials/CFD/15MSR_cavity/Make/options b/tutorials/CFD/15MSR_cavity/Make/options
index 7ef594070..84ae293f5 100644
--- a/tutorials/CFD/15MSR_cavity/Make/options
+++ b/tutorials/CFD/15MSR_cavity/Make/options
@@ -23,7 +23,7 @@ EXE_INC = \
     -I$(LIB_ITHACA_SRC)/ITHACA_THIRD_PARTY/splinter/include \
     -w \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/tutorials/CFD/16MSR_FOMSA/Make/options b/tutorials/CFD/16MSR_FOMSA/Make/options
index 7ef594070..84ae293f5 100644
--- a/tutorials/CFD/16MSR_FOMSA/Make/options
+++ b/tutorials/CFD/16MSR_FOMSA/Make/options
@@ -23,7 +23,7 @@ EXE_INC = \
     -I$(LIB_ITHACA_SRC)/ITHACA_THIRD_PARTY/splinter/include \
     -w \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/tutorials/CFD/17YJunction/Make/options b/tutorials/CFD/17YJunction/Make/options
index c04847826..bf582f3c0 100644
--- a/tutorials/CFD/17YJunction/Make/options
+++ b/tutorials/CFD/17YJunction/Make/options
@@ -24,7 +24,7 @@ EXE_INC = \
     -Wno-comment \
     -w \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/tutorials/CFD/18simpleTurbNS/Make/options b/tutorials/CFD/18simpleTurbNS/Make/options
index 9ef8fcc4b..0a43096ea 100644
--- a/tutorials/CFD/18simpleTurbNS/Make/options
+++ b/tutorials/CFD/18simpleTurbNS/Make/options
@@ -23,7 +23,7 @@ EXE_INC = \
     -I$(LIB_ITHACA_SRC)/ITHACA_THIRD_PARTY/splinter/include \
     -w \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/tutorials/CFD/19UnsteadyNSExplicit/Make/options b/tutorials/CFD/19UnsteadyNSExplicit/Make/options
index c04847826..bf582f3c0 100644
--- a/tutorials/CFD/19UnsteadyNSExplicit/Make/options
+++ b/tutorials/CFD/19UnsteadyNSExplicit/Make/options
@@ -24,7 +24,7 @@ EXE_INC = \
     -Wno-comment \
     -w \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/tutorials/CFD/20incrementalPOD/Make/options b/tutorials/CFD/20incrementalPOD/Make/options
index 856bf7f23..a810cf258 100644
--- a/tutorials/CFD/20incrementalPOD/Make/options
+++ b/tutorials/CFD/20incrementalPOD/Make/options
@@ -26,7 +26,7 @@ EXE_INC = \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
     -Wno-comment \
     -w \
-    -std=c++11 \
+    -std=c++14 \
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/tutorials/CFD/21unsteadyNSTurb_RBF/Make/options b/tutorials/CFD/21unsteadyNSTurb_RBF/Make/options
index c04847826..bf582f3c0 100644
--- a/tutorials/CFD/21unsteadyNSTurb_RBF/Make/options
+++ b/tutorials/CFD/21unsteadyNSTurb_RBF/Make/options
@@ -24,7 +24,7 @@ EXE_INC = \
     -Wno-comment \
     -w \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/tutorials/CFD/22datadriven_corrections/Make/options b/tutorials/CFD/22datadriven_corrections/Make/options
index c04847826..bf582f3c0 100644
--- a/tutorials/CFD/22datadriven_corrections/Make/options
+++ b/tutorials/CFD/22datadriven_corrections/Make/options
@@ -24,7 +24,7 @@ EXE_INC = \
     -Wno-comment \
     -w \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/tutorials/CFD/23burgers/Make/options b/tutorials/CFD/23burgers/Make/options
index 8350c47bd..750161e84 100644
--- a/tutorials/CFD/23burgers/Make/options
+++ b/tutorials/CFD/23burgers/Make/options
@@ -25,7 +25,7 @@ EXE_INC = \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
     -Wno-comment \
     -w \
-    -std=c++11 \
+    -std=c++14 \
 
 EXE_LIBS = \
     -lfiniteVolume \
diff --git a/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/Make/options b/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/Make/options
index 8bfb8bc21..be6d2824e 100644
--- a/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/Make/options
+++ b/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/Make/options
@@ -26,7 +26,7 @@ EXE_INC = \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
     -Wno-comment \
     -g \
-    -std=c++11 \
+    -std=c++14 \
     -Wno-int-in-bool-context \
     -Wno-maybe-uninitialized \
     -Wno-sign-compare \
diff --git a/unitTests/ITHACAstream/Make/options b/unitTests/ITHACAstream/Make/options
index 17c1e0f12..8030afac1 100755
--- a/unitTests/ITHACAstream/Make/options
+++ b/unitTests/ITHACAstream/Make/options
@@ -13,7 +13,7 @@ EXE_INC = \
     -I$(LIB_ITHACA_SRC)/thirdparty/splinter/include \
     -w \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/unitTests/ITHACAsurfacetools/Make/options b/unitTests/ITHACAsurfacetools/Make/options
index 17c1e0f12..8030afac1 100644
--- a/unitTests/ITHACAsurfacetools/Make/options
+++ b/unitTests/ITHACAsurfacetools/Make/options
@@ -13,7 +13,7 @@ EXE_INC = \
     -I$(LIB_ITHACA_SRC)/thirdparty/splinter/include \
     -w \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/unitTests/ITHACAutilities/Make/options b/unitTests/ITHACAutilities/Make/options
index fc7bbcb94..9b8a1a073 100755
--- a/unitTests/ITHACAutilities/Make/options
+++ b/unitTests/ITHACAutilities/Make/options
@@ -12,7 +12,7 @@ EXE_INC = \
     -I$(LIB_ITHACA_SRC)/thirdparty/spectra-0.6.1/include \
     -w \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/unitTests/OptimLib/ADAM/Make/options b/unitTests/OptimLib/ADAM/Make/options
index 0d10caf70..945aae164 100755
--- a/unitTests/OptimLib/ADAM/Make/options
+++ b/unitTests/OptimLib/ADAM/Make/options
@@ -2,7 +2,7 @@ EXE_INC = \
     -I$(LIB_ITHACA_SRC)/thirdparty/Eigen \
     -I$(LIB_ITHACA_SRC)/thirdparty/OptimLib \
     -w \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -L$(FOAM_USER_LIBBIN) \
diff --git a/unitTests/RBF_def/Make/options b/unitTests/RBF_def/Make/options
index d66d80c5c..f200cd60a 100755
--- a/unitTests/RBF_def/Make/options
+++ b/unitTests/RBF_def/Make/options
@@ -26,7 +26,7 @@ EXE_INC = \
     -I$(LIB_ITHACA_SRC)/ITHACA_THIRD_PARTY/splinter/include \
     -w \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -lturbulenceModels \
diff --git a/unitTests/UQ/quantileTest/Make/options b/unitTests/UQ/quantileTest/Make/options
index 433aa0e4b..199f78e03 100755
--- a/unitTests/UQ/quantileTest/Make/options
+++ b/unitTests/UQ/quantileTest/Make/options
@@ -10,7 +10,7 @@ EXE_INC = \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
     -Wno-comment \
     -g \
-    -std=c++11 \
+    -std=c++14 \
     -Wno-maybe-uninitialized \
     -Wno-sign-compare \
     -Wno-unknown-pragmas \
diff --git a/unitTests/pybind11/Eigen/Make/options b/unitTests/pybind11/Eigen/Make/options
index 784fb353e..0c6284b58 100755
--- a/unitTests/pybind11/Eigen/Make/options
+++ b/unitTests/pybind11/Eigen/Make/options
@@ -3,7 +3,7 @@ EXE_INC = \
     -I$(includepybind1) \
     -I$(includepybind2) \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11 \
+    -std=c++14 \
     -O3 \
     -w \
     -shared \
diff --git a/unitTests/pybind11/of_pybind/Make/options b/unitTests/pybind11/of_pybind/Make/options
index e53dc790b..74b25aa84 100644
--- a/unitTests/pybind11/of_pybind/Make/options
+++ b/unitTests/pybind11/of_pybind/Make/options
@@ -52,7 +52,7 @@ EXE_INC = \
     -I$(includepybind1) \
     -I$(includepybind2) \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11 \
+    -std=c++14 \
     -O3 \
     -w \
     -shared \
diff --git a/unitTests/pybind11/residual_of/Make/options b/unitTests/pybind11/residual_of/Make/options
index e53dc790b..74b25aa84 100644
--- a/unitTests/pybind11/residual_of/Make/options
+++ b/unitTests/pybind11/residual_of/Make/options
@@ -52,7 +52,7 @@ EXE_INC = \
     -I$(includepybind1) \
     -I$(includepybind2) \
     -DOFVER=$${WM_PROJECT_VERSION%.*} \
-    -std=c++11 \
+    -std=c++14 \
     -O3 \
     -w \
     -shared \
diff --git a/unitTests/splinter/Make/options b/unitTests/splinter/Make/options
index bb183f14e..6eabb20c5 100755
--- a/unitTests/splinter/Make/options
+++ b/unitTests/splinter/Make/options
@@ -2,7 +2,7 @@ EXE_INC = \
     -I$(LIB_ITHACA_SRC)/thirdparty/Eigen \
     -I$(LIB_ITHACA_SRC)/ITHACA_THIRD_PARTY/splinter/include \
     -w \
-    -std=c++11
+    -std=c++14
 
 EXE_LIBS = \
     -L$(FOAM_USER_LIBBIN) \

From 1475379129f53691b6c81dd78f37b1f2599d059f Mon Sep 17 00:00:00 2001
From: Giovanni Stabile <giovanni.stabile87@gmail.com>
Date: Fri, 4 Oct 2024 17:33:14 +0200
Subject: [PATCH 56/59] adding npy export inside steady NS and adding flag
 inside ithacaparameters

---
 src/ITHACA_CORE/Containers/Modes.C            |   54 +-
 src/ITHACA_CORE/Containers/Modes.H            |   32 +-
 .../EigenFunctions/EigenFunctions.C           |   23 +-
 .../EigenFunctions/EigenFunctions.H           |   96 +-
 src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.C       |  217 ++-
 src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.H       |   71 +-
 src/ITHACA_CORE/ITHACADMD/ITHACADMD.C         |   20 +-
 src/ITHACA_CORE/ITHACADMD/ITHACADMD.H         |    2 +-
 src/ITHACA_CORE/ITHACAPOD/ITHACAPOD.C         |  149 +-
 src/ITHACA_CORE/ITHACAPOD/ITHACAPOD.H         |   42 +-
 src/ITHACA_CORE/ITHACAPOD/incrementalPOD.C    |   23 +-
 src/ITHACA_CORE/ITHACAPOD/incrementalPOD.H    |   17 +-
 .../ITHACAparallel/ITHACAparallel.C           |    4 +-
 .../ITHACAparallel/ITHACAparallel.H           |    5 +-
 .../ITHACAregularization.C                    |    4 +-
 .../FiguresOfMerit/Tm_time.H                  |    1 +
 .../ITHACAsensitivity/LRSensitivity.C         |    2 +-
 .../ITHACAsensitivity/LRSensitivity.H         |    3 +-
 .../ITHACAstream/ITHACAparameters.C           |    1 +
 .../ITHACAstream/ITHACAparameters.H           |    1 +
 src/ITHACA_CORE/ITHACAstream/ITHACAstream.C   |  193 +-
 src/ITHACA_CORE/ITHACAstream/ITHACAstream.H   |  120 +-
 src/ITHACA_CORE/ITHACAstream/cnpy.C           |  132 +-
 src/ITHACA_CORE/ITHACAstream/cnpy.H           |   62 +-
 .../ITHACAutilities/ITHACAassign.C            |  180 +-
 .../ITHACAutilities/ITHACAassign.H            |   69 +-
 .../ITHACAutilities/ITHACAcoeffsMass.C        |  176 +-
 .../ITHACAutilities/ITHACAcoeffsMass.H        |   29 +-
 src/ITHACA_CORE/ITHACAutilities/ITHACAerror.C |  175 +-
 src/ITHACA_CORE/ITHACAutilities/ITHACAerror.H |   50 +-
 .../ITHACAutilities/ITHACAforces.C            |   52 +-
 .../ITHACAutilities/ITHACAforces18.H          |    6 +-
 .../ITHACAutilities/ITHACAgeometry.C          |   57 +-
 .../ITHACAutilities/ITHACAgeometry.H          |   12 +-
 .../ITHACAutilities/ITHACAsurfacetools.C      |  218 ++-
 .../ITHACAutilities/ITHACAsurfacetools.H      |   40 +-
 .../ITHACAutilities/ITHACAsystem.C            |    2 +-
 .../ITHACAutilities/ITHACAutilities.C         |  167 +-
 .../ITHACAutilities/ITHACAutilities.H         |   10 +-
 src/ITHACA_CORE/ITHACAutilities/colormod.H    |    1 +
 src/ITHACA_DEIM/DEIM.C                        |   30 +-
 src/ITHACA_DEIM/DEIM.H                        |    8 +-
 src/ITHACA_FOMPROBLEMS/Burgers/Burgers.C      |    6 +-
 .../SteadyNSSimple/SteadyNSSimple.C           |   14 +-
 src/ITHACA_FOMPROBLEMS/SteadyNSSimple/UEqn.H  |    2 +-
 src/ITHACA_FOMPROBLEMS/SteadyNSSimple/pEqn.H  |    2 +-
 .../SteadyNSTurb/NLsolveSteadyNSTurb.H        |    1 +
 .../SteadyNSTurb/SteadyNSTurb.C               |   17 +-
 src/ITHACA_FOMPROBLEMS/SteadyNSTurb/UEqn.H    |    2 +-
 src/ITHACA_FOMPROBLEMS/SteadyNSTurb/pEqn.H    |    2 +-
 .../NLsolveSteadyNSTurbIntrusive.H            |    1 +
 .../SteadyNSTurbIntrusive.C                   |    1 +
 .../SteadyNSTurbIntrusive/UEqn.H              |    2 +-
 .../SteadyNSTurbIntrusive/pEqn.H              |    2 +-
 src/ITHACA_FOMPROBLEMS/UnsteadyBB/TEqn.H      |    2 +-
 src/ITHACA_FOMPROBLEMS/UnsteadyBB/UEqn.H      |    6 +-
 .../UnsteadyBB/UnsteadyBB.C                   |   12 +-
 src/ITHACA_FOMPROBLEMS/UnsteadyBB/pEqn.H      |   12 +-
 .../UnsteadyNSExplicit/CFM.H                  |    8 +-
 .../UnsteadyNSExplicit/IFM.H                  |    8 +-
 .../UnsteadyNSExplicit/UnsteadyNSExplicit.C   |    2 +-
 .../UnsteadyNSExplicit/UnsteadyNSExplicit.H   |    1 +
 src/ITHACA_FOMPROBLEMS/UnsteadyNSTTurb/UEqn.H |    2 +-
 .../UnsteadyNSTTurb/UnsteadyNSTTurb.C         |    9 +-
 src/ITHACA_FOMPROBLEMS/UnsteadyNSTTurb/pEqn.H |    6 +-
 src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UEqn.H  |    2 +-
 .../UnsteadyNSTurb/UnsteadyNSTurb.C           |   66 +-
 .../UnsteadyNSTurb/createUfIfPresent.H        |    4 +-
 src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/pEqn.H  |    4 +-
 .../UnsteadyNSTurbIntrusive/UEqn.H            |    2 +-
 .../UnsteadyNSTurbIntrusive.C                 |   16 +-
 .../UnsteadyNSTurbIntrusive/pEqn.H            |    4 +-
 .../inverseLaplacianProblem.C                 |   21 +-
 ...verseLaplacianProblemTotalHeatMeasure_CG.C |    7 +-
 ...LaplacianProblemTotalHeatMeasure_paramBC.C |    6 +-
 .../inverseLaplacianProblem_CG.C              |   44 +-
 .../thermocouplesPlane.H                      |    1 +
 .../inverseLaplacianProblem_paramBC.C         |   11 +-
 .../laplacianProblem/laplacianProblem.C       |    4 +-
 src/ITHACA_FOMPROBLEMS/msrProblem/DiffEqn.H   |    2 +-
 .../msrProblem/NLmsrProblem.H                 |    5 +-
 src/ITHACA_FOMPROBLEMS/msrProblem/TEqn.H      |    6 +-
 src/ITHACA_FOMPROBLEMS/msrProblem/UEqn.H      |    2 +-
 src/ITHACA_FOMPROBLEMS/msrProblem/decEqns.H   |    6 +-
 .../msrProblem/msrProblem.C                   |   47 +-
 src/ITHACA_FOMPROBLEMS/msrProblem/pEqn.H      |    2 +-
 src/ITHACA_FOMPROBLEMS/msrProblem/precEqns.H  |   16 +-
 .../msrProblem/steadySolver.H                 |   13 +-
 .../msrProblem/updateConsts.H                 |    2 +-
 src/ITHACA_FOMPROBLEMS/msrProblem/updateK.H   |    2 +-
 .../reductionProblem/reductionProblem.C       |   29 +-
 .../reductionProblem/reductionProblem.H       |   20 +-
 .../reductionProblemTemplates.C               |    8 +-
 .../steadyNS/NLsolvesteadyNS.H                |    1 +
 src/ITHACA_FOMPROBLEMS/steadyNS/UEqn.H        |    2 +-
 src/ITHACA_FOMPROBLEMS/steadyNS/pEqn.H        |    2 +-
 src/ITHACA_FOMPROBLEMS/steadyNS/steadyNS.C    |   80 +-
 src/ITHACA_FOMPROBLEMS/steadyNS/steadyNS.H    |    3 +-
 src/ITHACA_FOMPROBLEMS/unsteadyNS/UEqn.H      |    2 +-
 src/ITHACA_FOMPROBLEMS/unsteadyNS/pEqn.H      |    4 +-
 .../unsteadyNS/unsteadyNS.C                   |   13 +-
 .../unsteadyNS/unsteadyNS.H                   |    3 +-
 src/ITHACA_FOMPROBLEMS/unsteadyNST/TEqn.H     |    2 +-
 src/ITHACA_FOMPROBLEMS/unsteadyNST/UEqn.H     |    2 +-
 src/ITHACA_FOMPROBLEMS/unsteadyNST/pEqn.H     |    6 +-
 .../unsteadyNST/unsteadyNST.C                 |    7 +-
 .../unsteadymsrProblem/DiffEqn.H              |    2 +-
 .../unsteadymsrProblem/TEqn.H                 |    6 +-
 .../unsteadymsrProblem/UEqn.H                 |    2 +-
 .../unsteadymsrProblem/decEqns.H              |    6 +-
 .../unsteadymsrProblem/pEqn.H                 |    4 +-
 .../unsteadymsrProblem/precEqns.H             |   16 +-
 .../unsteadymsrProblem/updateConsts.H         |    2 +-
 .../unsteadymsrProblem/updateK.H              |    2 +-
 .../unsteadymsrProblem/usmsrProblem.C         |   34 +-
 src/ITHACA_HR/hyperReduction.H                |  860 ++++----
 src/ITHACA_HR/hyperReduction.templates.H      | 1733 +++++++++--------
 src/ITHACA_MUQ/muq2ithaca.C                   |   36 +-
 src/ITHACA_MUQ/muq2ithaca.H                   |    2 +-
 .../ReducedLaplacian/ReducedLaplacian.C       |    4 +-
 .../ReducedMSR/ReducedMSR.C                   |  102 +-
 .../ReducedMSR/ReducedMSR.H                   |   12 +-
 .../ReducedProblem/ReducedProblem.C           |    2 +-
 .../ReducedProblem/ReducedProblem.H           |    2 +-
 .../ReducedSimpleSteadyNS.C                   |    8 +-
 .../ReducedSteadyNS/ReducedSteadyNS.C         |   12 +-
 .../ReducedSteadyNS/ReducedSteadyNS.H         |    3 +-
 .../ReducedSteadyNSTurb/ReducedSteadyNSTurb.C |   31 +-
 .../ReducedSteadyNSTurb/ReducedSteadyNSTurb.H |    6 +-
 .../ReducedSteadyNSTurbIntrusive.C            |   13 +-
 .../ReducedSteadyNSTurbIntrusive.H            |    3 +-
 .../ReducedUnsteadyBB/ReducedUnsteadyBB.C     |   44 +-
 .../ReducedUnsteadyBB/ReducedUnsteadyBB.H     |    6 +-
 .../ReducedUnsteadyMSR/ReducedUnsteadyMSR.C   |  130 +-
 .../ReducedUnsteadyMSR/ReducedUnsteadyMSR.H   |   12 +-
 .../ReducedUnsteadyNS/ReducedUnsteadyNS.C     |   33 +-
 .../ReducedUnsteadyNS/ReducedUnsteadyNS.H     |    6 +-
 .../ReducedUnsteadyNSExplicit.C               |   42 +-
 .../ReducedUnsteadyNST/ReducedUnsteadyNST.C   |   19 +-
 .../ReducedUnsteadyNST/ReducedUnsteadyNST.H   |    7 +-
 .../ReducedUnsteadyNSTTurb.C                  |   20 +-
 .../ReducedUnsteadyNSTTurb.H                  |    6 +-
 .../ReducedUnsteadyNSTurb.C                   |   75 +-
 .../ReducedUnsteadyNSTurb.H                   |   12 +-
 .../ReducedUnsteadyNSTurbIntrusive.C          |   34 +-
 .../ReducedUnsteadyNSTurbIntrusive.H          |    6 +-
 src/ITHACA_THIRD_PARTY/splinter/src/bspline.C |   18 +-
 .../splinter/src/bsplinebasis.C               |   12 +-
 .../splinter/src/bsplinebasis1d.C             |   39 +-
 .../splinter/src/bsplinebuilder.C             |   28 +-
 .../splinter/src/datapoint.C                  |    2 +-
 .../splinter/src/datatable.C                  |   18 +-
 .../splinter/src/function.C                   |   12 +-
 src/ITHACA_THIRD_PARTY/splinter/src/knots.C   |   14 +-
 .../splinter/src/mykroneckerproduct.C         |   17 +-
 .../splinter/src/rbfspline.C                  |   12 +-
 .../splinter/src/serializer.C                 |    8 +-
 .../splinter/src/utilities.C                  |    8 +-
 src/ITHACA_TORCH/ConvLayer.C                  |   10 +-
 src/ITHACA_TORCH/ConvLayer.H                  |    5 +-
 src/ITHACA_TORCH/Filters/Filter.H             |    4 +-
 src/ITHACA_TORCH/Filters/IntegralFilter.C     |    4 +-
 src/ITHACA_TORCH/Filters/IntegralFilter.H     |    4 +-
 src/ITHACA_TORCH/torch2Eigen.C                |    6 +-
 src/ITHACA_TORCH/torch2Foam.C                 |   20 +-
 src/ITHACA_TORCH/torch2Foam.H                 |    4 +-
 src/ITHACA_TORCH/torchUTILITIES.C             |    6 +-
 src/ITHACA_TORCH/torchUTILITIES.H             |    4 +-
 src/OF_EXT/RBFFunctions/TPS/TPS.C             |    1 +
 src/OF_EXT/RBFInterpolation.C                 |    2 +-
 src/OF_EXT/RBFInterpolation.H                 |    4 +-
 src/OF_EXT/RBFInterpolationTemplates.C        |   17 +-
 src/OF_EXT/RBFMotionSolver.C                  |   13 +
 ...entHeatFluxTemperatureFvPatchScalarField.C |   14 +-
 ...entHeatFluxTemperatureFvPatchScalarField.H |   14 +-
 tutorials/CFD/02thermalBlock/02thermalBlock.C |    2 +
 tutorials/CFD/04unsteadyNS/04unsteadyNS.C     |   77 +-
 tutorials/CFD/06POD_RBF/06POD_RBF.C           |    3 +
 tutorials/CFD/06POD_RBF/NLsolveSteadyNSTurb.H |    1 +
 tutorials/CFD/06POD_RBF/UEqn.H                |    2 +-
 tutorials/CFD/06POD_RBF/pEqn.H                |    2 +-
 tutorials/CFD/08DEIM/08DEIM.C                 |   41 +-
 tutorials/CFD/09DEIM_ROM/09DEIM_ROM.C         |    2 +-
 .../CFD/11UnsteadyBBOpen/11UnsteadyBBOpen.C   |    7 +-
 tutorials/CFD/15MSR_cavity/15MSR_cavity.C     |   70 +-
 tutorials/CFD/16MSR_FOMSA/16MSR_FOMSA.C       |   20 +-
 tutorials/CFD/17YJunction/17YJunction.C       |    2 +-
 .../CFD/20incrementalPOD/20incrementalPOD.C   |    2 +
 .../CFD/22datadriven_corrections/offline.C    |    1 +
 .../CFD/24HyperReduction/24HyperReduction.C   |  270 +--
 .../01simpleTurbGeomClosed.C                  |   12 +-
 tutorials/UQ/01enKF/01enKF.C                  |    8 +-
 .../02enKF_1DinverseHeatTransfer.C            |    1 +
 .../02enKF_1DinverseHeatTransfer.H            |    5 +-
 .../IHTP01inverseLaplacian/CGtest.H           |    1 +
 .../IHTP01inverseLaplacian.C                  |    7 +-
 .../IHTP01inverseLaplacian.H                  |   12 +-
 .../IHTP01inverseLaplacian/directBC.H         |   15 +-
 .../parameterizedBCtest.H                     |    1 +
 .../IHTP01inverseLaplacian/postProcess.H      |    1 +
 .../thermocouplesLocation_paramBC.H           |    2 +-
 .../thermocouplesNumberTest_paramBC.H         |    2 +-
 unitTests/RBF_def/defGeom.C                   |    2 +-
 .../residual_of/lnInclude/createFields.H      |  109 +-
 .../residual_of/lnInclude/createMesh.H        |   46 +-
 .../residual_of/lnInclude/createTime.H        |   32 +-
 206 files changed, 4107 insertions(+), 3481 deletions(-)
 mode change 100755 => 100644 src/ITHACA_CORE/Containers/Modes.H
 mode change 100755 => 100644 src/ITHACA_CORE/EigenFunctions/EigenFunctions.C
 mode change 100755 => 100644 src/ITHACA_CORE/EigenFunctions/EigenFunctions.H
 mode change 100755 => 100644 src/ITHACA_CORE/ITHACADMD/ITHACADMD.H
 mode change 100755 => 100644 src/ITHACA_CORE/ITHACAPOD/ITHACAPOD.H
 mode change 100755 => 100644 src/ITHACA_CORE/ITHACAPOD/incrementalPOD.C
 mode change 100755 => 100644 src/ITHACA_CORE/ITHACAPOD/incrementalPOD.H
 mode change 100755 => 100644 src/ITHACA_CORE/ITHACAregularization/ITHACAregularization.C
 mode change 100755 => 100644 src/ITHACA_CORE/ITHACAsensitivity/FiguresOfMerit/Tm_time.H
 mode change 100755 => 100644 src/ITHACA_CORE/ITHACAsensitivity/LRSensitivity.C
 mode change 100755 => 100644 src/ITHACA_CORE/ITHACAsensitivity/LRSensitivity.H
 mode change 100755 => 100644 src/ITHACA_CORE/ITHACAutilities/ITHACAforces.C
 mode change 100755 => 100644 src/ITHACA_CORE/ITHACAutilities/ITHACAforces18.H
 mode change 100755 => 100644 src/ITHACA_CORE/ITHACAutilities/ITHACAgeometry.H
 mode change 100755 => 100644 src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.H
 mode change 100755 => 100644 src/ITHACA_CORE/ITHACAutilities/colormod.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/SteadyNSSimple/UEqn.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/SteadyNSSimple/pEqn.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/SteadyNSTurb/UEqn.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/SteadyNSTurb/pEqn.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/SteadyNSTurbIntrusive/SteadyNSTurbIntrusive.C
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/SteadyNSTurbIntrusive/UEqn.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/SteadyNSTurbIntrusive/pEqn.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/UnsteadyBB/TEqn.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/UnsteadyBB/UEqn.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/UnsteadyBB/pEqn.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/UnsteadyNSExplicit/CFM.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/UnsteadyNSExplicit/IFM.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/UnsteadyNSExplicit/UnsteadyNSExplicit.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/UnsteadyNSTTurb/UEqn.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/UnsteadyNSTTurb/UnsteadyNSTTurb.C
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/UnsteadyNSTTurb/pEqn.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UEqn.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/pEqn.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/UnsteadyNSTurbIntrusive/UEqn.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/UnsteadyNSTurbIntrusive/UnsteadyNSTurbIntrusive.C
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/UnsteadyNSTurbIntrusive/pEqn.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/inverseLaplacianProblemTotalHeatMeasure_CG/inverseLaplacianProblemTotalHeatMeasure_CG.C
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/inverseLaplacianProblemTotalHeatMeasure_paramBC/inverseLaplacianProblemTotalHeatMeasure_paramBC.C
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/inverseLaplacianProblem_CG/thermocouplesPlane.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/laplacianProblem/laplacianProblem.C
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/msrProblem/DiffEqn.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/msrProblem/TEqn.H
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 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/msrProblem/decEqns.H
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 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/msrProblem/updateConsts.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/msrProblem/updateK.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblem.C
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblem.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblemTemplates.C
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/steadyNS/UEqn.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/steadyNS/pEqn.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/unsteadyNS/UEqn.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/unsteadyNS/pEqn.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/unsteadyNS/unsteadyNS.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/unsteadyNST/TEqn.H
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 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/unsteadyNST/pEqn.H
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 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/DiffEqn.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/TEqn.H
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 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/updateConsts.H
 mode change 100755 => 100644 src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/updateK.H
 mode change 100755 => 100644 src/ITHACA_MUQ/muq2ithaca.C
 mode change 100755 => 100644 src/ITHACA_MUQ/muq2ithaca.H
 mode change 100755 => 100644 src/ITHACA_ROMPROBLEMS/ReducedLaplacian/ReducedLaplacian.C
 mode change 100755 => 100644 src/ITHACA_ROMPROBLEMS/ReducedMSR/ReducedMSR.C
 mode change 100755 => 100644 src/ITHACA_ROMPROBLEMS/ReducedMSR/ReducedMSR.H
 mode change 100755 => 100644 src/ITHACA_ROMPROBLEMS/ReducedSimpleSteadyNS/ReducedSimpleSteadyNS.C
 mode change 100755 => 100644 src/ITHACA_ROMPROBLEMS/ReducedSteadyNS/ReducedSteadyNS.H
 mode change 100755 => 100644 src/ITHACA_ROMPROBLEMS/ReducedSteadyNSTurbIntrusive/ReducedSteadyNSTurbIntrusive.C
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 mode change 100755 => 100644 src/ITHACA_ROMPROBLEMS/ReducedUnsteadyBB/ReducedUnsteadyBB.H
 mode change 100755 => 100644 src/ITHACA_ROMPROBLEMS/ReducedUnsteadyMSR/ReducedUnsteadyMSR.C
 mode change 100755 => 100644 src/ITHACA_ROMPROBLEMS/ReducedUnsteadyMSR/ReducedUnsteadyMSR.H
 mode change 100755 => 100644 src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNS/ReducedUnsteadyNS.C
 mode change 100755 => 100644 src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNS/ReducedUnsteadyNS.H
 mode change 100755 => 100644 src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNST/ReducedUnsteadyNST.C
 mode change 100755 => 100644 src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNST/ReducedUnsteadyNST.H
 mode change 100755 => 100644 src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTTurb/ReducedUnsteadyNSTTurb.C
 mode change 100755 => 100644 src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTTurb/ReducedUnsteadyNSTTurb.H
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 mode change 100755 => 100644 src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTurbIntrusive/ReducedUnsteadyNSTurbIntrusive.C
 mode change 100755 => 100644 src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTurbIntrusive/ReducedUnsteadyNSTurbIntrusive.H
 mode change 100755 => 100644 src/ITHACA_THIRD_PARTY/splinter/src/bspline.C
 mode change 100755 => 100644 src/ITHACA_THIRD_PARTY/splinter/src/bsplinebasis.C
 mode change 100755 => 100644 src/ITHACA_THIRD_PARTY/splinter/src/bsplinebasis1d.C
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 mode change 100755 => 100644 src/ITHACA_THIRD_PARTY/splinter/src/knots.C
 mode change 100755 => 100644 src/ITHACA_THIRD_PARTY/splinter/src/mykroneckerproduct.C
 mode change 100755 => 100644 src/ITHACA_THIRD_PARTY/splinter/src/rbfspline.C
 mode change 100755 => 100644 src/ITHACA_THIRD_PARTY/splinter/src/serializer.C
 mode change 100755 => 100644 src/ITHACA_THIRD_PARTY/splinter/src/utilities.C
 mode change 100755 => 100644 src/ITHACA_TORCH/torch2Eigen.C
 mode change 100755 => 100644 src/ITHACA_TORCH/torch2Foam.C
 mode change 100755 => 100644 src/ITHACA_TORCH/torch2Foam.H
 mode change 100755 => 100644 src/ITHACA_TORCH/torchUTILITIES.H
 mode change 100755 => 100644 src/OF_EXT/RBFFunctions/TPS/TPS.C
 mode change 100755 => 100644 src/OF_EXT/RBFInterpolation.C
 mode change 100755 => 100644 src/OF_EXT/RBFInterpolation.H
 mode change 100755 => 100644 src/OF_EXT/RBFInterpolationTemplates.C
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 mode change 100755 => 100644 src/OF_EXT/fvPatchFields/basic/turbulentHeatFluxTemperature/turbulentHeatFluxTemperatureFvPatchScalarField.C
 mode change 100755 => 100644 src/OF_EXT/fvPatchFields/basic/turbulentHeatFluxTemperature/turbulentHeatFluxTemperatureFvPatchScalarField.H
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 mode change 100755 => 100644 tutorials/UQ/02enKF_1DinverseHeatTransfer/02enKF_1DinverseHeatTransfer.H
 mode change 100755 => 100644 tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/directBC.H
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 mode change 120000 => 100755 unitTests/pybind11/residual_of/lnInclude/createFields.H
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diff --git a/src/ITHACA_CORE/Containers/Modes.C b/src/ITHACA_CORE/Containers/Modes.C
index acc060b58..d7fc35a46 100644
--- a/src/ITHACA_CORE/Containers/Modes.C
+++ b/src/ITHACA_CORE/Containers/Modes.C
@@ -61,7 +61,7 @@ List<Eigen::MatrixXd> Modes<Type, PatchField, GeoMesh>::toEigen()
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 List<Eigen::MatrixXd> Modes<Type, PatchField, GeoMesh>::project(
-    fvMatrix<Type>& Af, label numberOfModes,
+    fvMatrix<Type> & Af, label numberOfModes,
     word projType)
 {
     M_Assert(projType == "G" || projType == "PG",
@@ -82,14 +82,14 @@ List<Eigen::MatrixXd> Modes<Type, PatchField, GeoMesh>::project(
     {
         if (projType == "G")
         {
-            LinSys[0] = EigenModes[0].transpose() * Ae * EigenModes[0];
+            LinSys[0] = EigenModes[0].transpose() * Ae* EigenModes[0];
             LinSys[1] = EigenModes[0].transpose() * be;
         }
 
         if (projType == "PG")
         {
-            LinSys[0] = (Ae * EigenModes[0]).transpose() * Ae * EigenModes[0];
-            LinSys[1] = (Ae * EigenModes[0]).transpose() * be;
+            LinSys[0] = (Ae* EigenModes[0]).transpose() * Ae* EigenModes[0];
+            LinSys[1] = (Ae* EigenModes[0]).transpose() * be;
         }
     }
     else
@@ -117,7 +117,7 @@ List<Eigen::MatrixXd> Modes<Type, PatchField, GeoMesh>::project(
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 Eigen::MatrixXd Modes<Type, PatchField, GeoMesh>::project(
-    GeometricField<Type, PatchField, GeoMesh>&
+    GeometricField<Type, PatchField, GeoMesh> &
     field, label numberOfModes, word projType, fvMatrix<Type>* Af)
 {
     M_Assert(projType == "F" || projType == "G" || projType == "PG",
@@ -152,8 +152,8 @@ Eigen::MatrixXd Modes<Type, PatchField, GeoMesh>::project(
                      "Using a Petrov-Galerkin projection you have to provide also the system matrix");
             Eigen::SparseMatrix<double> Ae;
             Eigen::VectorXd be;
-            Foam2Eigen::fvMatrix2Eigen(*Af, Ae, be);
-            projField = (Ae * EigenModes[0]).transpose() * vol.asDiagonal() * fieldEig;
+            Foam2Eigen::fvMatrix2Eigen( * Af, Ae, be);
+            projField = (Ae* EigenModes[0]).transpose() * vol.asDiagonal() * fieldEig;
         }
     }
     else
@@ -181,7 +181,7 @@ Eigen::MatrixXd Modes<Type, PatchField, GeoMesh>::project(
                      "Using a Petrov-Galerkin projection you have to provide also the system matrix");
             Eigen::SparseMatrix<double> Ae;
             Eigen::VectorXd be;
-            Foam2Eigen::fvMatrix2Eigen(*Af, Ae, be);
+            Foam2Eigen::fvMatrix2Eigen( * Af, Ae, be);
             projField = (Ae * ((EigenModes[0]).leftCols(numberOfModes))).transpose() *
                         vol.asDiagonal() * fieldEig;
         }
@@ -193,7 +193,7 @@ Eigen::MatrixXd Modes<Type, PatchField, GeoMesh>::project(
 template<class Type, template<class> class PatchField, class GeoMesh>
 GeometricField<Type, PatchField, GeoMesh>
 Modes<Type, PatchField, GeoMesh>::projectSnapshot(
-    GeometricField<Type, PatchField, GeoMesh>&
+    GeometricField<Type, PatchField, GeoMesh> &
     field, label numberOfModes, word projType, fvMatrix<Type>* Af)
 {
     Eigen::MatrixXd proj = project(field, numberOfModes, projType, Af);
@@ -204,7 +204,7 @@ Modes<Type, PatchField, GeoMesh>::projectSnapshot(
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 Eigen::MatrixXd Modes<Type, PatchField, GeoMesh>::project(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>&
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> &
     fields,
     label numberOfModes, word projType, fvMatrix<Type>* Af)
 {
@@ -236,8 +236,8 @@ Eigen::MatrixXd Modes<Type, PatchField, GeoMesh>::project(
                      "Using a Petrov-Galerkin projection you have to provide also the system matrix");
             Eigen::SparseMatrix<double> Ae;
             Eigen::VectorXd be;
-            Foam2Eigen::fvMatrix2Eigen(*Af, Ae, be);
-            projField = (Ae * EigenModes[0]).transpose() * vol.asDiagonal() * fieldEig;
+            Foam2Eigen::fvMatrix2Eigen( * Af, Ae, be);
+            projField = (Ae* EigenModes[0]).transpose() * vol.asDiagonal() * fieldEig;
         }
     }
     else
@@ -262,7 +262,7 @@ Eigen::MatrixXd Modes<Type, PatchField, GeoMesh>::project(
                      "Using a Petrov-Galerkin projection you have to provide also the system matrix");
             Eigen::SparseMatrix<double> Ae;
             Eigen::VectorXd be;
-            Foam2Eigen::fvMatrix2Eigen(*Af, Ae, be);
+            Foam2Eigen::fvMatrix2Eigen( * Af, Ae, be);
             projField = (Ae * ((EigenModes[0]).leftCols(numberOfModes))).transpose() *
                         vol.asDiagonal() * fieldEig;
         }
@@ -270,10 +270,11 @@ Eigen::MatrixXd Modes<Type, PatchField, GeoMesh>::project(
 
     return projField;
 }
+
 template<class Type, template<class> class PatchField, class GeoMesh>
 GeometricField<Type, PatchField, GeoMesh>
 Modes<Type, PatchField, GeoMesh>::reconstruct(
-    GeometricField<Type, PatchField, GeoMesh>& inputField,
+    GeometricField<Type, PatchField, GeoMesh> & inputField,
     Eigen::MatrixXd Coeff,
     word Name)
 {
@@ -307,12 +308,13 @@ Modes<Type, PatchField, GeoMesh>::reconstruct(
 
     return inputField;
 }
+
 template<class Type, template<class> class PatchField, class GeoMesh>
 PtrList<GeometricField<Type, PatchField, GeoMesh>>
-        Modes<Type, PatchField, GeoMesh>::reconstruct(
-            GeometricField<Type, PatchField, GeoMesh>& inputField,
-            List < Eigen::MatrixXd> Coeff,
-            word Name)
+Modes<Type, PatchField, GeoMesh>::reconstruct(
+    GeometricField<Type, PatchField, GeoMesh> & inputField,
+    List < Eigen::MatrixXd> Coeff,
+    word Name)
 {
     PtrList<GeometricField<Type, PatchField, GeoMesh>> inputFields;
     inputFields.resize(0);
@@ -330,7 +332,7 @@ PtrList<GeometricField<Type, PatchField, GeoMesh>>
 template<class Type, template<class> class PatchField, class GeoMesh>
 void Modes<Type, PatchField, GeoMesh>::projectSnapshots(
     PtrList<GeometricField<Type, PatchField, GeoMesh>> snapshots,
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& projSnapshots,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & projSnapshots,
     PtrList<volScalarField> Volumes,
     label numberOfModes,
     word innerProduct)
@@ -349,7 +351,7 @@ void Modes<Type, PatchField, GeoMesh>::projectSnapshots(
     projSnapshots.resize(snapshots.size());
     label dim = std::nearbyint(EigenModes[0].rows() /
                                Volumes[0].size()); //Checking if volumes and modes have the same size that means check if the problem is vector or scalar
-    Eigen::MatrixXd totVolumes(Volumes[0].size()*dim, Volumes.size());
+    Eigen::MatrixXd totVolumes(Volumes[0].size() * dim, Volumes.size());
 
     for (label i = 0; i < Volumes.size(); i++)
     {
@@ -393,10 +395,11 @@ void Modes<Type, PatchField, GeoMesh>::projectSnapshots(
         projSnapshots.set(i, Fr.clone());
     }
 }
+
 template<class Type, template<class> class PatchField, class GeoMesh>
 void Modes<Type, PatchField, GeoMesh>::projectSnapshots(
     PtrList<GeometricField<Type, PatchField, GeoMesh>> snapshots,
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& projSnapshots,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & projSnapshots,
     PtrList<volScalarField> Volumes, word innerProduct)
 {
     label numberOfModes = 0;
@@ -407,7 +410,7 @@ void Modes<Type, PatchField, GeoMesh>::projectSnapshots(
 template<class Type, template<class> class PatchField, class GeoMesh>
 void Modes<Type, PatchField, GeoMesh>::projectSnapshots(
     PtrList<GeometricField<Type, PatchField, GeoMesh>> snapshots,
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& projSnapshots,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & projSnapshots,
     label numberOfModes,
     word innerProduct)
 {
@@ -463,10 +466,11 @@ void Modes<Type, PatchField, GeoMesh>::projectSnapshots(
         projSnapshots.set(i, Fr.clone());
     }
 }
+
 template<class Type, template<class> class PatchField, class GeoMesh>
 void Modes<Type, PatchField, GeoMesh>::projectSnapshots(
     PtrList<GeometricField<Type, PatchField, GeoMesh>> snapshots,
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& projSnapshots,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & projSnapshots,
     word innerProduct)
 {
     label numberOfModes = 0;
@@ -475,13 +479,13 @@ void Modes<Type, PatchField, GeoMesh>::projectSnapshots(
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 void Modes<Type, PatchField, GeoMesh>::operator=(const
-        PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes)
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes)
 {
     this->resize(modes.size());
 
     for (label i = 0; i < modes.size(); i++)
     {
-        (*this).set(i, modes[i].clone());
+        ( * this).set(i, modes[i].clone());
     }
 }
 
diff --git a/src/ITHACA_CORE/Containers/Modes.H b/src/ITHACA_CORE/Containers/Modes.H
old mode 100755
new mode 100644
index c250bf23f..df0ba2a9a
--- a/src/ITHACA_CORE/Containers/Modes.H
+++ b/src/ITHACA_CORE/Containers/Modes.H
@@ -83,9 +83,10 @@ class Modes : public PtrList<GeometricField<Type, PatchField, GeoMesh>>
         ///
         /// @return     The PtrList containing the modes
         ///
-        PtrList<GeometricField<Type, PatchField, GeoMesh>>& toPtrList()
+        PtrList<GeometricField<Type, PatchField, GeoMesh>> & toPtrList()
         {
-            return static_cast<PtrList<GeometricField<Type, PatchField, GeoMesh>>&>(*this);
+            return static_cast<PtrList<GeometricField<Type, PatchField, GeoMesh>>&>
+                   ( * this);
         }
 
         //----------------------------------------------------------------------
@@ -110,7 +111,7 @@ class Modes : public PtrList<GeometricField<Type, PatchField, GeoMesh>>
         ///             system, the second element is the reduced source term of
         ///             the linear system.
         ///
-        List<Eigen::MatrixXd> project(fvMatrix<Type>& Af, label numberOfModes = 0,
+        List<Eigen::MatrixXd> project(fvMatrix<Type> & Af, label numberOfModes = 0,
                                       word projType = "G");
 
         //----------------------------------------------------------------------
@@ -130,7 +131,7 @@ class Modes : public PtrList<GeometricField<Type, PatchField, GeoMesh>>
         ///
         /// @return     An Eigen MatrixXd.
         ///
-        Eigen::MatrixXd project(GeometricField<Type, PatchField, GeoMesh>& field,
+        Eigen::MatrixXd project(GeometricField<Type, PatchField, GeoMesh> & field,
                                 label numberOfModes = 0, word projType = "G", fvMatrix<Type>* Af = NULL);
 
         //----------------------------------------------------------------------
@@ -150,7 +151,7 @@ class Modes : public PtrList<GeometricField<Type, PatchField, GeoMesh>>
         ///
         /// @return     An Eigen MatricxXd list.
         ///
-        Eigen::MatrixXd project(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
+        Eigen::MatrixXd project(PtrList<GeometricField<Type, PatchField, GeoMesh>> &
                                 fields,
                                 label numberOfModes = 0, word projType = "G", fvMatrix<Type>* Af = NULL);
 
@@ -165,7 +166,7 @@ class Modes : public PtrList<GeometricField<Type, PatchField, GeoMesh>>
         /// @return     The projected snapshot
         ///
         GeometricField<Type, PatchField, GeoMesh> projectSnapshot(
-            GeometricField<Type, PatchField, GeoMesh>& field,
+            GeometricField<Type, PatchField, GeoMesh> & field,
             label numberOfModes = 0, word projType = "G", fvMatrix<Type>* Af = NULL);
 
         //----------------------------------------------------------------------
@@ -181,7 +182,7 @@ class Modes : public PtrList<GeometricField<Type, PatchField, GeoMesh>>
         ///             reconstruction.
         ///
         GeometricField<Type, PatchField, GeoMesh> reconstruct(
-            GeometricField<Type, PatchField, GeoMesh>& inputField, Eigen::MatrixXd Coeff,
+            GeometricField<Type, PatchField, GeoMesh> & inputField, Eigen::MatrixXd Coeff,
             word Name);
 
         //----------------------------------------------------------------------
@@ -197,9 +198,9 @@ class Modes : public PtrList<GeometricField<Type, PatchField, GeoMesh>>
         ///             reconstruction.
         ///
         PtrList<GeometricField<Type, PatchField, GeoMesh>> reconstruct(
-                    GeometricField<Type, PatchField, GeoMesh>& inputField,
-                    List < Eigen::MatrixXd> Coeff,
-                    word Name);
+            GeometricField<Type, PatchField, GeoMesh> & inputField,
+            List < Eigen::MatrixXd> Coeff,
+            word Name);
 
         //----------------------------------------------------------------------
         /// @brief      Function to project a list of fields into the modes manifold
@@ -209,7 +210,7 @@ class Modes : public PtrList<GeometricField<Type, PatchField, GeoMesh>>
         /// @param[in]  innerProduct        The inner product to be applied
         ///
         void projectSnapshots(PtrList<GeometricField<Type, PatchField, GeoMesh>>
-                              snapshots, PtrList<GeometricField<Type, PatchField, GeoMesh>>& projSnapshots,
+                              snapshots, PtrList<GeometricField<Type, PatchField, GeoMesh>> & projSnapshots,
                               label numberOfModes = 0, word innerProduct = "L2");
 
         //----------------------------------------------------------------------
@@ -219,7 +220,7 @@ class Modes : public PtrList<GeometricField<Type, PatchField, GeoMesh>>
         /// @param[in]  innerProduct        The inner product to be applied
         ///
         void projectSnapshots(PtrList<GeometricField<Type, PatchField, GeoMesh>>
-                              snapshots, PtrList<GeometricField<Type, PatchField, GeoMesh>>& projSnapshots,
+                              snapshots, PtrList<GeometricField<Type, PatchField, GeoMesh>> & projSnapshots,
                               word innerProduct = "L2");
 
         //----------------------------------------------------------------------
@@ -231,7 +232,7 @@ class Modes : public PtrList<GeometricField<Type, PatchField, GeoMesh>>
         /// @param[in]  innerProduct        The inner product to be applied
         ///
         void projectSnapshots(PtrList<GeometricField<Type, PatchField, GeoMesh>>
-                              snapshots, PtrList<GeometricField<Type, PatchField, GeoMesh>>& projSnapshots,
+                              snapshots, PtrList<GeometricField<Type, PatchField, GeoMesh>> & projSnapshots,
                               PtrList<volScalarField> Volumes,
                               label numberOfModes = 0, word innerProduct = "L2");
 
@@ -243,11 +244,12 @@ class Modes : public PtrList<GeometricField<Type, PatchField, GeoMesh>>
         /// @param[in]  innerProduct        The inner product to be applied
         ///
         void projectSnapshots(PtrList<GeometricField<Type, PatchField, GeoMesh>>
-                              snapshots, PtrList<GeometricField<Type, PatchField, GeoMesh>>& projSnapshots,
+                              snapshots, PtrList<GeometricField<Type, PatchField, GeoMesh>> & projSnapshots,
                               PtrList<volScalarField> Volumes,
                               word innerProduct);
 
-        void operator=(const PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes);
+        void operator=(const PtrList<GeometricField<Type, PatchField, GeoMesh>> &
+                       modes);
 };
 
 typedef Modes<scalar, fvPatchField, volMesh> volScalarModes;
diff --git a/src/ITHACA_CORE/EigenFunctions/EigenFunctions.C b/src/ITHACA_CORE/EigenFunctions/EigenFunctions.C
old mode 100755
new mode 100644
index 0b602ad41..afc8b5fb4
--- a/src/ITHACA_CORE/EigenFunctions/EigenFunctions.C
+++ b/src/ITHACA_CORE/EigenFunctions/EigenFunctions.C
@@ -86,10 +86,10 @@ Eigen::VectorXd ExpSpaced(double first, double last, int n)
 
 template <typename T>
 Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>
-vectorTensorProduct(const Eigen::Matrix<T, Eigen::Dynamic, 1>&
+vectorTensorProduct(const Eigen::Matrix<T, Eigen::Dynamic, 1> &
                     g,
-                    const Eigen::Tensor<T, 3 >& c,
-                    const Eigen::Matrix<T, Eigen::Dynamic, 1>& a)
+                    const Eigen::Tensor<T, 3 > & c,
+                    const Eigen::Matrix<T, Eigen::Dynamic, 1> & a)
 {
     int prodDim = c.dimension(0);
     Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> prod;
@@ -106,18 +106,19 @@ vectorTensorProduct(const Eigen::Matrix<T, Eigen::Dynamic, 1>&
 
 template Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>
 vectorTensorProduct<>(
-    const Eigen::Matrix<double, Eigen::Dynamic, 1>& g,
-    const Eigen::Tensor<double, 3 >& c,
-    const Eigen::Matrix<double, Eigen::Dynamic, 1>& a);
+    const Eigen::Matrix<double, Eigen::Dynamic, 1> & g,
+    const Eigen::Tensor<double, 3 > & c,
+    const Eigen::Matrix<double, Eigen::Dynamic, 1> & a);
 
 template Eigen::Matrix<int, Eigen::Dynamic, Eigen::Dynamic>
 vectorTensorProduct(
-    const Eigen::Matrix<int, Eigen::Dynamic, 1>& g, const Eigen::Tensor<int, 3 >& c,
-    const Eigen::Matrix<int, Eigen::Dynamic, 1>& a);
+    const Eigen::Matrix<int, Eigen::Dynamic, 1> & g,
+    const Eigen::Tensor<int, 3 > & c,
+    const Eigen::Matrix<int, Eigen::Dynamic, 1> & a);
 
 template Eigen::Matrix<float, Eigen::Dynamic, Eigen::Dynamic>
 vectorTensorProduct(
-    const Eigen::Matrix<float, Eigen::Dynamic, 1>& g,
-    const Eigen::Tensor<float, 3 >& c,
-    const Eigen::Matrix<float, Eigen::Dynamic, 1>& a);
+    const Eigen::Matrix<float, Eigen::Dynamic, 1> & g,
+    const Eigen::Tensor<float, 3 > & c,
+    const Eigen::Matrix<float, Eigen::Dynamic, 1> & a);
 }
diff --git a/src/ITHACA_CORE/EigenFunctions/EigenFunctions.H b/src/ITHACA_CORE/EigenFunctions/EigenFunctions.H
old mode 100755
new mode 100644
index c2c939c60..84cedc185
--- a/src/ITHACA_CORE/EigenFunctions/EigenFunctions.H
+++ b/src/ITHACA_CORE/EigenFunctions/EigenFunctions.H
@@ -67,7 +67,7 @@ namespace EigenFunctions
 /// @return     The Sparse Vector
 ///
 template <typename T>
-Eigen::SparseMatrix<T> vectorize(Eigen::SparseMatrix<T>& Matrix);
+Eigen::SparseMatrix<T> vectorize(Eigen::SparseMatrix<T> & Matrix);
 
 //--------------------------------------------------------------------------
 /// @brief      Find the maximum of a sparse Matrix (Useful for DEIM)
@@ -81,7 +81,7 @@ Eigen::SparseMatrix<T> vectorize(Eigen::SparseMatrix<T>& Matrix);
 /// @return     the maximum
 ///
 template <typename T>
-T max(Eigen::SparseMatrix<T>& mat, label& ind_row, label& ind_col);
+T max(Eigen::SparseMatrix<T> & mat, label& ind_row, label& ind_col);
 
 //--------------------------------------------------------------------------
 /// @brief           Find the minimum of a sparse Matrix (Useful for DEIM)
@@ -95,7 +95,7 @@ T max(Eigen::SparseMatrix<T>& mat, label& ind_row, label& ind_col);
 /// @return     the minimum
 ///
 template <typename T>
-T min(Eigen::SparseMatrix<T>& mat, label& ind_row, label& ind_col);
+T min(Eigen::SparseMatrix<T> & mat, label& ind_row, label& ind_col);
 
 //--------------------------------------------------------------------------
 /// @brief      sort eigenvalues
@@ -120,7 +120,7 @@ void sortEigenvalues(Eigen::VectorXd& eigenvalues,
 ///
 template <typename T>
 Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> innerProduct(
-    List <Eigen::SparseMatrix<T>>& A, List <Eigen::SparseMatrix<T>>& B);
+    List <Eigen::SparseMatrix<T>> & A, List <Eigen::SparseMatrix<T>> & B);
 
 //--------------------------------------------------------------------------
 /// @brief      Perform Frobenius inner Product between a list of sparse matrices A and a sparse matrix B
@@ -136,7 +136,7 @@ Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> innerProduct(
 ///
 template <typename T>
 Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> innerProduct(
-    List <Eigen::SparseMatrix<T>>& A, Eigen::SparseMatrix<T>& B);
+    List <Eigen::SparseMatrix<T>> & A, Eigen::SparseMatrix<T> & B);
 
 //--------------------------------------------------------------------------
 /// @brief      Perform Frobenius inner Product between two sparse matrices A and B
@@ -152,7 +152,7 @@ Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> innerProduct(
 /// @return     out Value of the inner products between the two matrices
 ///
 template <typename T>
-T innerProduct(Eigen::SparseMatrix<T>& A, Eigen::SparseMatrix<T>& B);
+T innerProduct(Eigen::SparseMatrix<T> & A, Eigen::SparseMatrix<T> & B);
 
 //--------------------------------------------------------------------------
 /// @brief      Sparse Matrix-Vector product between a list of sparse matrices and a vector of coefficients
@@ -169,8 +169,8 @@ T innerProduct(Eigen::SparseMatrix<T>& A, Eigen::SparseMatrix<T>& B);
 /// @return     out Sparse Matrix containing the sum of all the matrices multiplied by the vector coefficients
 ///
 template <typename T>
-Eigen::SparseMatrix<T> MVproduct(List<Eigen::SparseMatrix<T>>& A,
-                                 Eigen::DenseBase<Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>>& C);
+Eigen::SparseMatrix<T> MVproduct(List<Eigen::SparseMatrix<T>> & A,
+                                 Eigen::DenseBase<Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>> & C);
 
 //--------------------------------------------------------------------------
 /// @brief      Dense Matrix-Vector product between a list of sparse matrices and a vector of coefficients
@@ -188,8 +188,8 @@ Eigen::SparseMatrix<T> MVproduct(List<Eigen::SparseMatrix<T>>& A,
 ///
 template <typename T>
 Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> MVproduct(
-    const std::vector< Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>>& A,
-    Eigen::DenseBase<Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>>& C);
+    const std::vector< Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>> & A,
+    Eigen::DenseBase<Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>> & C);
 
 //--------------------------------------------------------------------------
 /// @brief      Sparse Matrix - Dense Matrix product between a list of sparse matrices and a dense matrix
@@ -206,8 +206,8 @@ Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> MVproduct(
 /// @return     List of Sparse Matrices containing the sum of all the matrices multiplied by the matrix coefficients by columns
 ///
 template <typename T>
-List<Eigen::SparseMatrix<T>> MMproduct(List<Eigen::SparseMatrix<T>>& A,
-                                       Eigen::DenseBase<Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>>& C);
+List<Eigen::SparseMatrix<T>> MMproduct(List<Eigen::SparseMatrix<T>> & A,
+                                       Eigen::DenseBase<Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>> & C);
 
 //--------------------------------------------------------------------------
 /// @brief      Conditioning number of a dense matrix
@@ -219,7 +219,7 @@ List<Eigen::SparseMatrix<T>> MMproduct(List<Eigen::SparseMatrix<T>>& A,
 /// @return     Conditioning number
 ///
 template <typename T>
-T condNumber(Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>& A);
+T condNumber(Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> & A);
 
 //--------------------------------------------------------------------------
 /// @brief      Returns exponentially spaced vector
@@ -245,14 +245,15 @@ Eigen::VectorXd ExpSpaced(double first, double last, int n);
 ///
 template <typename T>
 Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> vectorTensorProduct(
-    const Eigen::Matrix<T, Eigen::Dynamic, 1>& g,
-    const Eigen::Tensor<T, 3 >& c,
-    const Eigen::Matrix<T, Eigen::Dynamic, 1>& a);
+    const Eigen::Matrix<T, Eigen::Dynamic, 1> & g,
+    const Eigen::Tensor<T, 3 > & c,
+    const Eigen::Matrix<T, Eigen::Dynamic, 1> & a);
 
 };
 
 template <typename T>
-Eigen::SparseMatrix<T> EigenFunctions::vectorize(Eigen::SparseMatrix<T>& Matrix)
+Eigen::SparseMatrix<T> EigenFunctions::vectorize(Eigen::SparseMatrix<T> &
+        Matrix)
 {
     typedef Eigen::Triplet<double> Trip;
     std::vector<Trip> tripletList;
@@ -265,7 +266,7 @@ Eigen::SparseMatrix<T> EigenFunctions::vectorize(Eigen::SparseMatrix<T>& Matrix)
     {
         for (Eigen::SparseMatrix<double>::InnerIterator it(Matrix, k); it; ++it)
         {
-            tripletList.push_back(Trip(0, it.row() + it.col()*Matrix.rows(), it.value()));
+            tripletList.push_back(Trip(0, it.row() + it.col() * Matrix.rows(), it.value()));
         }
     }
 
@@ -273,7 +274,7 @@ Eigen::SparseMatrix<T> EigenFunctions::vectorize(Eigen::SparseMatrix<T>& Matrix)
 }
 
 template <typename T>
-T EigenFunctions::max(Eigen::SparseMatrix<T>& mat, label& ind_row,
+T EigenFunctions::max(Eigen::SparseMatrix<T> & mat, label& ind_row,
                       label& ind_col)
 {
     label i = 0;
@@ -297,7 +298,7 @@ T EigenFunctions::max(Eigen::SparseMatrix<T>& mat, label& ind_row,
 }
 
 template <typename T>
-T EigenFunctions::min(Eigen::SparseMatrix<T>& mat, label& ind_row,
+T EigenFunctions::min(Eigen::SparseMatrix<T> & mat, label& ind_row,
                       label& ind_col)
 {
     label i = 0;
@@ -322,7 +323,7 @@ T EigenFunctions::min(Eigen::SparseMatrix<T>& mat, label& ind_row,
 
 template <typename T>
 Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> EigenFunctions::innerProduct(
-    List <Eigen::SparseMatrix<T>>& A, List <Eigen::SparseMatrix<T>>& B)
+    List <Eigen::SparseMatrix<T>> & A, List <Eigen::SparseMatrix<T>> & B)
 {
     label rows = A.size();
     label cols = B.size();
@@ -342,7 +343,7 @@ Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> EigenFunctions::innerProduct(
 
 template <typename T>
 Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> EigenFunctions::innerProduct(
-    List<Eigen::SparseMatrix<T>>& A, Eigen::SparseMatrix<T>& B)
+    List<Eigen::SparseMatrix<T>> & A, Eigen::SparseMatrix<T> & B)
 {
     label rows = A.size();
     label cols = 1;
@@ -358,8 +359,8 @@ Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> EigenFunctions::innerProduct(
 }
 
 template <typename T>
-T EigenFunctions::innerProduct(Eigen::SparseMatrix<T>& A,
-                               Eigen::SparseMatrix<T>& B)
+T EigenFunctions::innerProduct(Eigen::SparseMatrix<T> & A,
+                               Eigen::SparseMatrix<T> & B)
 {
     T res = 0;
 
@@ -372,8 +373,9 @@ T EigenFunctions::innerProduct(Eigen::SparseMatrix<T>& A,
 }
 
 template <typename T>
-Eigen::SparseMatrix<T> EigenFunctions::MVproduct(List<Eigen::SparseMatrix<T>>& A
-        , Eigen::DenseBase<Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>>& C)
+Eigen::SparseMatrix<T> EigenFunctions::MVproduct(List<Eigen::SparseMatrix<T>> &
+        A
+        , Eigen::DenseBase<Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>> & C)
 {
     Eigen::SparseMatrix<T> out;
     out = A[0] * C(0);
@@ -388,8 +390,8 @@ Eigen::SparseMatrix<T> EigenFunctions::MVproduct(List<Eigen::SparseMatrix<T>>& A
 
 template <typename T>
 Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> EigenFunctions::MVproduct(
-    const std::vector< Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>>& A,
-    Eigen::DenseBase<Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>>& C)
+    const std::vector< Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>> & A,
+    Eigen::DenseBase<Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>> & C)
 {
     Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> out;
     out = A[0] * C(0);
@@ -406,8 +408,8 @@ Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> EigenFunctions::MVproduct(
 
 template <typename T>
 List<Eigen::SparseMatrix<T>> EigenFunctions::MMproduct(
-                              List<Eigen::SparseMatrix<T>>& A,
-                              Eigen::DenseBase<Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>>& C)
+    List<Eigen::SparseMatrix<T>> & A,
+    Eigen::DenseBase<Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>> & C)
 {
     List<Eigen::SparseMatrix<T>> out;
     out.resize(C.cols());
@@ -423,7 +425,7 @@ List<Eigen::SparseMatrix<T>> EigenFunctions::MMproduct(
 }
 
 template <typename T>
-T EigenFunctions::condNumber(Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>&
+T EigenFunctions::condNumber(Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> &
                              A)
 {
     Eigen::JacobiSVD<Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>> svd(A);
@@ -475,33 +477,33 @@ bool saveMarketVector (const VectorType& vec, const std::string& filename,
 
 template<typename VectorType>
 Matrix<VectorType, Dynamic, Dynamic> SliceFromTensor(
-    Eigen::Tensor<VectorType, 3>& tensor, label dim, label index1)
+    Eigen::Tensor<VectorType, 3> & tensor, label dim, label index1)
 {
     Eigen::Tensor<VectorType, 2> t2 = tensor.chip(index1, dim);
     Matrix<VectorType, Dynamic, Dynamic> m = Eigen::Map<Eigen::Matrix<
-            VectorType,           /* scalar element type */
-            Eigen::Dynamic,  /* num_rows is a run-time value */
-            Eigen::Dynamic,  /* num_cols is a run-time value */
-            Eigen::ColMajor  /* tensorflow::Tensor is always row-major */>>(
-                t2.data(),  /* ptr to data */
-                t2.dimensions()[0],           /* num_rows */
-                t2.dimensions()[1]            /* num_cols */);
+        VectorType,           /* scalar element type */
+        Eigen::Dynamic,  /* num_rows is a run-time value */
+        Eigen::Dynamic,  /* num_cols is a run-time value */
+        Eigen::ColMajor  /* tensorflow::Tensor is always row-major */>>(
+            t2.data(),  /* ptr to data */
+            t2.dimensions()[0],           /* num_rows */
+            t2.dimensions()[1]            /* num_cols */);
     return m;
 }
 
 template<typename VectorType>
 Matrix<VectorType, Dynamic, Dynamic> SliceFromTensor(
-    const Eigen::Tensor<VectorType, 3>& tensor, label dim, label index1)
+    const Eigen::Tensor<VectorType, 3> & tensor, label dim, label index1)
 {
     Eigen::Tensor<VectorType, 2> t2 = tensor.chip(index1, dim);
     Matrix<VectorType, Dynamic, Dynamic> m = Eigen::Map<Eigen::Matrix<
-            VectorType,           /* scalar element type */
-            Eigen::Dynamic,  /* num_rows is a run-time value */
-            Eigen::Dynamic,  /* num_cols is a run-time value */
-            Eigen::ColMajor  /* tensorflow::Tensor is always row-major */>>(
-                t2.data(),  /* ptr to data */
-                t2.dimensions()[0],           /* num_rows */
-                t2.dimensions()[1]            /* num_cols */);
+        VectorType,           /* scalar element type */
+        Eigen::Dynamic,  /* num_rows is a run-time value */
+        Eigen::Dynamic,  /* num_cols is a run-time value */
+        Eigen::ColMajor  /* tensorflow::Tensor is always row-major */>>(
+            t2.data(),  /* ptr to data */
+            t2.dimensions()[0],           /* num_rows */
+            t2.dimensions()[1]            /* num_cols */);
     return m;
 }
 
diff --git a/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.C b/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.C
index 176b89021..9ff220519 100644
--- a/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.C
+++ b/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.C
@@ -38,17 +38,17 @@ License
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 template <template <class> class PatchField, class GeoMesh>
 Eigen::VectorXd Foam2Eigen::field2Eigen(
-    GeometricField<tensor, PatchField, GeoMesh>& field)
+    GeometricField<tensor, PatchField, GeoMesh> & field)
 {
     Eigen::VectorXd out;
     out.resize(label(field.size() * 9));
 
     for (label l = 0; l < field.size(); l++)
     {
-      for (label j = 0; j < 9; j++)
-      {
-          out(j * field.size() + l) = field[l][j];
-      }
+        for (label j = 0; j < 9; j++)
+        {
+            out(j* field.size() + l) = field[l][j];
+        }
     }
 
     return out;
@@ -59,17 +59,17 @@ template Eigen::VectorXd Foam2Eigen::field2Eigen(
 
 template <template <class> class PatchField, class GeoMesh>
 Eigen::VectorXd Foam2Eigen::field2Eigen(
-    GeometricField<vector, PatchField, GeoMesh>& field)
+    GeometricField<vector, PatchField, GeoMesh> & field)
 {
     Eigen::VectorXd out;
     out.resize(label(field.size() * 3));
 
     for (label l = 0; l < field.size(); l++)
     {
-      for (label j = 0; j < 3; j++)
-      {
-          out(j * field.size() + l) = field[l][j];
-      }
+        for (label j = 0; j < 3; j++)
+        {
+            out(j* field.size() + l) = field[l][j];
+        }
     }
 
     return out;
@@ -80,7 +80,7 @@ template Eigen::VectorXd Foam2Eigen::field2Eigen(
 
 template <template <class> class PatchField, class GeoMesh>
 Eigen::VectorXd Foam2Eigen::field2Eigen(
-    GeometricField<scalar, PatchField, GeoMesh>& field)
+    GeometricField<scalar, PatchField, GeoMesh> & field)
 {
     Eigen::VectorXd out;
     out.resize(label(field.size()));
@@ -95,7 +95,7 @@ Eigen::VectorXd Foam2Eigen::field2Eigen(
 
 template <template <class> class PatchField, class GeoMesh>
 Eigen::Map<Eigen::MatrixXd> Foam2Eigen::field2EigenMap(
-    GeometricField<scalar, PatchField, GeoMesh>& field)
+    GeometricField<scalar, PatchField, GeoMesh> & field)
 {
     Eigen::Map<Eigen::MatrixXd> output(field.ref().data(), field.size(), 1);
     return std::move(output);
@@ -103,9 +103,10 @@ Eigen::Map<Eigen::MatrixXd> Foam2Eigen::field2EigenMap(
 
 template <template <class> class PatchField, class GeoMesh>
 Eigen::Map<Eigen::MatrixXd> Foam2Eigen::field2EigenMapBC(
-    GeometricField<scalar, PatchField, GeoMesh>& field, int BC_index)
+    GeometricField<scalar, PatchField, GeoMesh> & field, int BC_index)
 {
-    Eigen::Map<Eigen::MatrixXd> output(field.boundaryFieldRef()[BC_index].data(), field.boundaryField()[BC_index].size(), 1);
+    Eigen::Map<Eigen::MatrixXd> output(field.boundaryFieldRef()[BC_index].data(),
+                                       field.boundaryField()[BC_index].size(), 1);
     return std::move(output);
 }
 
@@ -121,7 +122,7 @@ template Eigen::VectorXd Foam2Eigen::field2Eigen(
     surfaceScalarField& field);
 
 template <>
-Eigen::VectorXd Foam2Eigen::field2Eigen(const Field<scalar>& field)
+Eigen::VectorXd Foam2Eigen::field2Eigen(const Field<scalar> & field)
 {
     Eigen::VectorXd out;
     out.resize(label(field.size()));
@@ -135,34 +136,34 @@ Eigen::VectorXd Foam2Eigen::field2Eigen(const Field<scalar>& field)
 }
 
 template <>
-Eigen::VectorXd Foam2Eigen::field2Eigen(const Field<vector>& field)
+Eigen::VectorXd Foam2Eigen::field2Eigen(const Field<vector> & field)
 {
     Eigen::VectorXd out;
     out.resize(label(field.size() * 3));
 
     for (label l = 0; l < field.size(); l++)
     {
-      for (label j = 0; j < 3; j++)
-      {
-          out(j * field.size() + l) = field[l][j];
-      }
+        for (label j = 0; j < 3; j++)
+        {
+            out(j* field.size() + l) = field[l][j];
+        }
     }
 
     return out;
 }
 
 template <>
-Eigen::VectorXd Foam2Eigen::field2Eigen(const Field<tensor>& field)
+Eigen::VectorXd Foam2Eigen::field2Eigen(const Field<tensor> & field)
 {
     Eigen::VectorXd out;
     out.resize(label(field.size() * 9));
 
     for (label l = 0; l < field.size(); l++)
     {
-      for (label j = 0; j < 9; j++)
-      {
-          out(j * field.size() + l) = field[l][j];
-      }
+        for (label j = 0; j < 9; j++)
+        {
+            out(j* field.size() + l) = field[l][j];
+        }
     }
 
     return out;
@@ -170,7 +171,7 @@ Eigen::VectorXd Foam2Eigen::field2Eigen(const Field<tensor>& field)
 
 template <>
 Eigen::VectorXd Foam2Eigen::field2Eigen(const
-                                        DimensionedField<scalar, Foam::volMesh>& field)
+                                        DimensionedField<scalar, Foam::volMesh> & field)
 {
     Eigen::VectorXd out;
     out.resize(label(field.size()));
@@ -185,7 +186,7 @@ Eigen::VectorXd Foam2Eigen::field2Eigen(const
 
 template <template <class> class PatchField, class GeoMesh>
 List<Eigen::VectorXd> Foam2Eigen::field2EigenBC(
-    GeometricField<tensor, PatchField, GeoMesh>& field)
+    GeometricField<tensor, PatchField, GeoMesh> & field)
 {
     List<Eigen::VectorXd> Out;
     label size = field.boundaryField().size();
@@ -200,7 +201,7 @@ List<Eigen::VectorXd> Foam2Eigen::field2EigenBC(
         {
             for (label j = 0; j < 9; j++)
             {
-                Out[i](k + j * sizei) = field.boundaryField()[i][k][j];
+                Out[i](k + j* sizei) = field.boundaryField()[i][k][j];
             }
         }
     }
@@ -209,11 +210,11 @@ List<Eigen::VectorXd> Foam2Eigen::field2EigenBC(
 }
 
 template List<Eigen::VectorXd> Foam2Eigen::field2EigenBC(
-  volTensorField& field);
+    volTensorField& field);
 
 template <template <class> class PatchField, class GeoMesh>
 List<Eigen::VectorXd> Foam2Eigen::field2EigenBC(
-    GeometricField<vector, PatchField, GeoMesh>& field)
+    GeometricField<vector, PatchField, GeoMesh> & field)
 {
     List<Eigen::VectorXd> Out;
     label size = field.boundaryField().size();
@@ -228,7 +229,7 @@ List<Eigen::VectorXd> Foam2Eigen::field2EigenBC(
         {
             for (label j = 0; j < 3; j++)
             {
-                Out[i](k + j * sizei) = field.boundaryField()[i][k][j];
+                Out[i](k + j* sizei) = field.boundaryField()[i][k][j];
             }
         }
     }
@@ -242,7 +243,7 @@ template List<Eigen::VectorXd> Foam2Eigen::field2EigenBC(
 
 template <template <class> class PatchField, class GeoMesh>
 List<Eigen::VectorXd> Foam2Eigen::field2EigenBC(
-    GeometricField<scalar, PatchField, GeoMesh>& field)
+    GeometricField<scalar, PatchField, GeoMesh> & field)
 {
     List<Eigen::VectorXd> Out;
     label size = field.boundaryField().size();
@@ -261,12 +262,13 @@ List<Eigen::VectorXd> Foam2Eigen::field2EigenBC(
 
     return Out;
 }
+
 template List<Eigen::VectorXd> Foam2Eigen::field2EigenBC(
     volScalarField& field);
 
 template <template <class> class PatchField, class GeoMesh>
 List<Eigen::MatrixXd> Foam2Eigen::PtrList2EigenBC(
-    PtrList<GeometricField<scalar, PatchField, GeoMesh>>&
+    PtrList<GeometricField<scalar, PatchField, GeoMesh>> &
     fields,
     label Nfields)
 {
@@ -308,14 +310,14 @@ List<Eigen::MatrixXd> Foam2Eigen::PtrList2EigenBC(
 }
 
 template List<Eigen::MatrixXd> Foam2Eigen::PtrList2EigenBC(
-    PtrList<volScalarField>& fields, label Nfields);
+    PtrList<volScalarField> & fields, label Nfields);
 template List<Eigen::MatrixXd> Foam2Eigen::PtrList2EigenBC(
-    PtrList<surfaceScalarField>& fields, label Nfields);
+    PtrList<surfaceScalarField> & fields, label Nfields);
 
 
 template <template <class> class PatchField, class GeoMesh>
 List<Eigen::MatrixXd> Foam2Eigen::PtrList2EigenBC(
-    PtrList<GeometricField<vector, PatchField, GeoMesh>>&
+    PtrList<GeometricField<vector, PatchField, GeoMesh>> &
     fields,
     label Nfields)
 {
@@ -357,12 +359,12 @@ List<Eigen::MatrixXd> Foam2Eigen::PtrList2EigenBC(
 }
 
 template List<Eigen::MatrixXd> Foam2Eigen::PtrList2EigenBC(
-    PtrList<volVectorField>& fields, label Nfields);
+    PtrList<volVectorField> & fields, label Nfields);
 
 
 template <template <class> class PatchField, class GeoMesh>
 List<Eigen::MatrixXd> Foam2Eigen::PtrList2EigenBC(
-    PtrList<GeometricField<tensor, PatchField, GeoMesh>>&
+    PtrList<GeometricField<tensor, PatchField, GeoMesh>> &
     fields,
     label Nfields)
 {
@@ -404,21 +406,21 @@ List<Eigen::MatrixXd> Foam2Eigen::PtrList2EigenBC(
 }
 
 template List<Eigen::MatrixXd> Foam2Eigen::PtrList2EigenBC(
-    PtrList<volTensorField>& fields, label Nfields);
+    PtrList<volTensorField> & fields, label Nfields);
 
 template <template <class> class PatchField, class GeoMesh>
 GeometricField<tensor, PatchField, GeoMesh> Foam2Eigen::Eigen2field(
-    GeometricField<tensor, PatchField, GeoMesh>& field_in,
+    GeometricField<tensor, PatchField, GeoMesh> & field_in,
     Eigen::VectorXd& eigen_vector, bool correctBC)
 {
     GeometricField<tensor, PatchField, GeoMesh> field_out(field_in);
 
     for (auto i = 0; i < field_out.size(); i++)
     {
-      for (label j = 0; j < 9; j++)
-      {
-          field_out.ref()[i][j] = eigen_vector(i + field_out.size() * j);
-      }
+        for (label j = 0; j < 9; j++)
+        {
+            field_out.ref()[i][j] = eigen_vector(i + field_out.size() * j);
+        }
     }
 
     if (correctBC)
@@ -434,8 +436,8 @@ template volTensorField Foam2Eigen::Eigen2field(
 
 template <template <class> class PatchField, class GeoMesh>
 GeometricField<vector, PatchField, GeoMesh> Foam2Eigen::Eigen2field(
-    GeometricField<vector, PatchField, GeoMesh>& field_in,
-    Eigen::VectorXd& eigen_vector, List<Eigen::VectorXd>& eigen_vector_boundary)
+    GeometricField<vector, PatchField, GeoMesh> & field_in,
+    Eigen::VectorXd& eigen_vector, List<Eigen::VectorXd> & eigen_vector_boundary)
 {
     GeometricField<vector, PatchField, GeoMesh> field_out(field_in);
 
@@ -446,9 +448,10 @@ GeometricField<vector, PatchField, GeoMesh> Foam2Eigen::Eigen2field(
         field_out.ref()[i][2] = eigen_vector(i + field_out.size() * 2);
     }
 
-    for(unsigned int id = 0; id < field_out.boundaryField().size(); id++)
+    for (unsigned int id = 0; id < field_out.boundaryField().size(); id++)
     {
         unsigned int idBSize = field_out.boundaryField()[id].size();
+
         for (unsigned int ith_bcell = 0; ith_bcell < idBSize; ith_bcell++)
         {
             ITHACAutilities::assignBC(field_out, id, eigen_vector_boundary[id]);
@@ -459,12 +462,13 @@ GeometricField<vector, PatchField, GeoMesh> Foam2Eigen::Eigen2field(
 }
 
 template volVectorField Foam2Eigen::Eigen2field(
-    volVectorField& field_in, Eigen::VectorXd& eigen_vector, List<Eigen::VectorXd>& eigen_vector_boundary);
+    volVectorField& field_in, Eigen::VectorXd& eigen_vector,
+    List<Eigen::VectorXd> & eigen_vector_boundary);
 
 template<template<class> class PatchField, class GeoMesh>
 GeometricField<scalar, PatchField, GeoMesh> Foam2Eigen::Eigen2field(
-    GeometricField<scalar, PatchField, GeoMesh>& field_in,
-    Eigen::VectorXd& eigen_vector, List<Eigen::VectorXd>& eigen_vector_boundary)
+    GeometricField<scalar, PatchField, GeoMesh> & field_in,
+    Eigen::VectorXd& eigen_vector, List<Eigen::VectorXd> & eigen_vector_boundary)
 {
     GeometricField<scalar, PatchField, GeoMesh> field_out(field_in);
 
@@ -473,9 +477,10 @@ GeometricField<scalar, PatchField, GeoMesh> Foam2Eigen::Eigen2field(
         field_out.ref()[i] = eigen_vector(i);
     }
 
-    for(unsigned int id = 0; id < field_out.boundaryField().size(); id++)
+    for (unsigned int id = 0; id < field_out.boundaryField().size(); id++)
     {
-        for (unsigned int ith_bcell = 0; ith_bcell < field_out.boundaryField()[id].size(); ith_bcell++)
+        for (unsigned int ith_bcell = 0;
+                ith_bcell < field_out.boundaryField()[id].size(); ith_bcell++)
         {
             ITHACAutilities::assignBC(field_out, id, eigen_vector_boundary[id]);
         }
@@ -485,21 +490,22 @@ GeometricField<scalar, PatchField, GeoMesh> Foam2Eigen::Eigen2field(
 }
 
 template volScalarField Foam2Eigen::Eigen2field(
-    volScalarField& field_in, Eigen::VectorXd& eigen_vector, List<Eigen::VectorXd>& eigen_vector_boundary);
+    volScalarField& field_in, Eigen::VectorXd& eigen_vector,
+    List<Eigen::VectorXd> & eigen_vector_boundary);
 
 template<template<class> class PatchField, class GeoMesh>
 GeometricField<vector, PatchField, GeoMesh> Foam2Eigen::Eigen2field(
-    GeometricField<vector, PatchField, GeoMesh>& field_in,
+    GeometricField<vector, PatchField, GeoMesh> & field_in,
     Eigen::VectorXd& eigen_vector, bool correctBC)
 {
     GeometricField<vector, PatchField, GeoMesh> field_out(field_in);
 
     for (auto i = 0; i < field_out.size(); i++)
     {
-      for (label j = 0; j < 3; j++)
-      {
-          field_out.ref()[i][j] = eigen_vector(i + field_out.size() * j);
-      }
+        for (label j = 0; j < 3; j++)
+        {
+            field_out.ref()[i][j] = eigen_vector(i + field_out.size() * j);
+        }
     }
 
     if (correctBC)
@@ -515,7 +521,7 @@ template volVectorField Foam2Eigen::Eigen2field(
 
 template <template <class> class PatchField, class GeoMesh>
 GeometricField<scalar, PatchField, GeoMesh> Foam2Eigen::Eigen2field(
-    GeometricField<scalar, PatchField, GeoMesh>& field_in,
+    GeometricField<scalar, PatchField, GeoMesh> & field_in,
     Eigen::VectorXd& eigen_vector, bool correctBC)
 {
     GeometricField<scalar, PatchField, GeoMesh> field_out(field_in);
@@ -554,7 +560,7 @@ volScalarField Foam2Eigen::Eigen2field(
 
 template <>
 Field<scalar> Foam2Eigen::Eigen2field(
-    Field<scalar>& field, Eigen::MatrixXd& matrix, bool correctBC)
+    Field<scalar> & field, Eigen::MatrixXd& matrix, bool correctBC)
 {
     label sizeBC = field.size();
     M_Assert(matrix.cols() == 1,
@@ -583,7 +589,7 @@ Field<scalar> Foam2Eigen::Eigen2field(
 
 template <>
 Field<vector> Foam2Eigen::Eigen2field(
-    Field<vector>& field, Eigen::MatrixXd& matrix, bool correctBC)
+    Field<vector> & field, Eigen::MatrixXd& matrix, bool correctBC)
 {
     label sizeBC = field.size();
     M_Assert(matrix.cols() == 3,
@@ -615,7 +621,7 @@ Field<vector> Foam2Eigen::Eigen2field(
 
 template <>
 Field<tensor> Foam2Eigen::Eigen2field(
-    Field<tensor>& field, Eigen::MatrixXd& matrix, bool correctBC)
+    Field<tensor> & field, Eigen::MatrixXd& matrix, bool correctBC)
 {
     label sizeBC = field.size();
     M_Assert(matrix.cols() == 9,
@@ -647,7 +653,7 @@ Field<tensor> Foam2Eigen::Eigen2field(
 
 template <class Type, template <class> class PatchField, class GeoMesh>
 Eigen::MatrixXd Foam2Eigen::PtrList2Eigen(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& fields,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & fields,
     label Nfields)
 {
     label Nf;
@@ -676,20 +682,23 @@ Eigen::MatrixXd Foam2Eigen::PtrList2Eigen(
 }
 
 template Eigen::MatrixXd
-Foam2Eigen::PtrList2Eigen<scalar, fvPatchField, volMesh>(PtrList<volScalarField>&
-        fields,
-        label Nfields);
-template Eigen::MatrixXd Foam2Eigen::PtrList2Eigen(PtrList<surfaceScalarField>&
+Foam2Eigen::PtrList2Eigen<scalar, fvPatchField, volMesh>
+(PtrList<volScalarField> &
+ fields,
+ label Nfields);
+template Eigen::MatrixXd Foam2Eigen::PtrList2Eigen(PtrList<surfaceScalarField> &
         fields,
         label Nfields);
 template Eigen::MatrixXd
-Foam2Eigen::PtrList2Eigen<vector, fvPatchField, volMesh>(PtrList<volVectorField>&
-        fields,
-        label Nfields);
+Foam2Eigen::PtrList2Eigen<vector, fvPatchField, volMesh>
+(PtrList<volVectorField> &
+ fields,
+ label Nfields);
 template Eigen::MatrixXd
-Foam2Eigen::PtrList2Eigen<tensor, fvPatchField, volMesh>(PtrList<volTensorField>&
-        fields,
-        label Nfields);
+Foam2Eigen::PtrList2Eigen<tensor, fvPatchField, volMesh>
+(PtrList<volTensorField> &
+ fields,
+ label Nfields);
 
 template <>
 void Foam2Eigen::fvMatrix2Eigen(fvMatrix<scalar> foam_matrix,
@@ -714,6 +723,7 @@ void Foam2Eigen::fvMatrix2Eigen(fvMatrix<scalar> foam_matrix,
         A(lowerAddr[i], upperAddr[i]) = foam_matrix.upper()[i];
         A(upperAddr[i], lowerAddr[i]) = foam_matrix.lower()[i];
     }
+
     forAll(foam_matrix.psi().boundaryField(), I)
     {
         const fvPatch& ptch = foam_matrix.psi().boundaryField()[I].patch();
@@ -758,6 +768,7 @@ void Foam2Eigen::fvMatrix2Eigen(fvMatrix<vector> foam_matrix,
         A(upperAddr[i] + sizeA, lowerAddr[i] + sizeA) = foam_matrix.lower()[i];
         A(upperAddr[i] + sizeA * 2, lowerAddr[i] + sizeA * 2) = foam_matrix.lower()[i];
     }
+
     forAll(foam_matrix.psi().boundaryField(), I)
     {
         const fvPatch& ptch = foam_matrix.psi().boundaryField()[I].patch();
@@ -776,7 +787,7 @@ void Foam2Eigen::fvMatrix2Eigen(fvMatrix<vector> foam_matrix,
 
 template <>
 void Foam2Eigen::fvMatrix2Eigen(fvMatrix<scalar> foam_matrix,
-                                Eigen::SparseMatrix<double>& A, Eigen::VectorXd& b)
+                                Eigen::SparseMatrix<double> & A, Eigen::VectorXd& b)
 {
     label sizeA = foam_matrix.diag().size();
     label nel = foam_matrix.diag().size() + foam_matrix.upper().size() +
@@ -802,6 +813,7 @@ void Foam2Eigen::fvMatrix2Eigen(fvMatrix<scalar> foam_matrix,
         tripletList.push_back(Trip(lowerAddr[i], upperAddr[i], foam_matrix.upper()[i]));
         tripletList.push_back(Trip(upperAddr[i], lowerAddr[i], foam_matrix.lower()[i]));
     }
+
     forAll(foam_matrix.psi().boundaryField(), I)
     {
         const fvPatch& ptch = foam_matrix.psi().boundaryField()[I].patch();
@@ -812,12 +824,13 @@ void Foam2Eigen::fvMatrix2Eigen(fvMatrix<scalar> foam_matrix,
             b(w, 0) += foam_matrix.boundaryCoeffs()[I][J];
         }
     }
+
     A.setFromTriplets(tripletList.begin(), tripletList.end());
 }
 
 template <>
 void Foam2Eigen::fvMatrix2Eigen(fvMatrix<vector> foam_matrix,
-                                Eigen::SparseMatrix<double>& A, Eigen::VectorXd& b)
+                                Eigen::SparseMatrix<double> & A, Eigen::VectorXd& b)
 {
     label sizeA = foam_matrix.diag().size();
     label nel = foam_matrix.diag().size() + foam_matrix.upper().size() +
@@ -856,6 +869,7 @@ void Foam2Eigen::fvMatrix2Eigen(fvMatrix<vector> foam_matrix,
         tripletList.push_back(Trip(upperAddr[i] + sizeA * 2, lowerAddr[i] + sizeA * 2,
                                    foam_matrix.lower()[i]));
     }
+
     forAll(foam_matrix.psi().boundaryField(), I)
     {
         const fvPatch& ptch = foam_matrix.psi().boundaryField()[I].patch();
@@ -872,11 +886,12 @@ void Foam2Eigen::fvMatrix2Eigen(fvMatrix<vector> foam_matrix,
             b(w + sizeA * 2) += foam_matrix.boundaryCoeffs()[I][J][2];
         }
     }
+
     A.setFromTriplets(tripletList.begin(), tripletList.end());
 }
 
 template <>
-void Foam2Eigen::fvMatrix2EigenM(fvMatrix<scalar>& foam_matrix,
+void Foam2Eigen::fvMatrix2EigenM(fvMatrix<scalar> & foam_matrix,
                                  Eigen::MatrixXd& A)
 {
     label sizeA = foam_matrix.diag().size();
@@ -895,6 +910,7 @@ void Foam2Eigen::fvMatrix2EigenM(fvMatrix<scalar>& foam_matrix,
         A(lowerAddr[i], upperAddr[i]) = foam_matrix.upper()[i];
         A(upperAddr[i], lowerAddr[i]) = foam_matrix.lower()[i];
     }
+
     forAll(foam_matrix.psi().boundaryField(), I)
     {
         const fvPatch& ptch = foam_matrix.psi().boundaryField()[I].patch();
@@ -907,8 +923,8 @@ void Foam2Eigen::fvMatrix2EigenM(fvMatrix<scalar>& foam_matrix,
 }
 
 template <>
-void Foam2Eigen::fvMatrix2EigenM(fvMatrix<scalar>& foam_matrix,
-                                 Eigen::SparseMatrix<double>& A)
+void Foam2Eigen::fvMatrix2EigenM(fvMatrix<scalar> & foam_matrix,
+                                 Eigen::SparseMatrix<double> & A)
 {
     label sizeA = foam_matrix.diag().size();
     label nel = foam_matrix.diag().size() + foam_matrix.upper().size() +
@@ -932,6 +948,7 @@ void Foam2Eigen::fvMatrix2EigenM(fvMatrix<scalar>& foam_matrix,
         tripletList.push_back(Trip(lowerAddr[i], upperAddr[i], foam_matrix.upper()[i]));
         tripletList.push_back(Trip(upperAddr[i], lowerAddr[i], foam_matrix.lower()[i]));
     }
+
     forAll(foam_matrix.psi().boundaryField(), I)
     {
         const fvPatch& ptch = foam_matrix.psi().boundaryField()[I].patch();
@@ -941,11 +958,12 @@ void Foam2Eigen::fvMatrix2EigenM(fvMatrix<scalar>& foam_matrix,
             tripletList.push_back(Trip(w, w, foam_matrix.internalCoeffs()[I][J]));
         }
     }
+
     A.setFromTriplets(tripletList.begin(), tripletList.end());
 }
 
 template <>
-void Foam2Eigen::fvMatrix2EigenM(fvMatrix<vector>& foam_matrix,
+void Foam2Eigen::fvMatrix2EigenM(fvMatrix<vector> & foam_matrix,
                                  Eigen::MatrixXd& A)
 {
     label sizeA = foam_matrix.diag().size();
@@ -970,6 +988,7 @@ void Foam2Eigen::fvMatrix2EigenM(fvMatrix<vector>& foam_matrix,
         A(upperAddr[i] + sizeA, lowerAddr[i] + sizeA) = foam_matrix.lower()[i];
         A(upperAddr[i] + sizeA * 2, lowerAddr[i] + sizeA * 2) = foam_matrix.lower()[i];
     }
+
     forAll(foam_matrix.psi().boundaryField(), I)
     {
         const fvPatch& ptch = foam_matrix.psi().boundaryField()[I].patch();
@@ -985,8 +1004,8 @@ void Foam2Eigen::fvMatrix2EigenM(fvMatrix<vector>& foam_matrix,
 
 
 template <>
-void Foam2Eigen::fvMatrix2EigenM(fvMatrix<vector>& foam_matrix,
-                                 Eigen::SparseMatrix<double>& A)
+void Foam2Eigen::fvMatrix2EigenM(fvMatrix<vector> & foam_matrix,
+                                 Eigen::SparseMatrix<double> & A)
 {
     label sizeA = foam_matrix.diag().size();
     label nel = foam_matrix.diag().size() + foam_matrix.upper().size() +
@@ -1021,6 +1040,7 @@ void Foam2Eigen::fvMatrix2EigenM(fvMatrix<vector>& foam_matrix,
         tripletList.push_back(Trip(upperAddr[i] + sizeA * 2, lowerAddr[i] + sizeA * 2,
                                    foam_matrix.lower()[i]));
     }
+
     forAll(foam_matrix.psi().boundaryField(), I)
     {
         const fvPatch& ptch = foam_matrix.psi().boundaryField()[I].patch();
@@ -1034,11 +1054,12 @@ void Foam2Eigen::fvMatrix2EigenM(fvMatrix<vector>& foam_matrix,
                                        foam_matrix.internalCoeffs()[I][J][2]));
         }
     }
+
     A.setFromTriplets(tripletList.begin(), tripletList.end());
 }
 
 template <>
-void Foam2Eigen::fvMatrix2EigenV(fvMatrix<scalar>& foam_matrix,
+void Foam2Eigen::fvMatrix2EigenV(fvMatrix<scalar> & foam_matrix,
                                  Eigen::VectorXd& b)
 {
     label sizeA = foam_matrix.diag().size();
@@ -1061,7 +1082,7 @@ void Foam2Eigen::fvMatrix2EigenV(fvMatrix<scalar>& foam_matrix,
 }
 
 template <>
-void Foam2Eigen::fvMatrix2EigenV(fvMatrix<vector>& foam_matrix,
+void Foam2Eigen::fvMatrix2EigenV(fvMatrix<vector> & foam_matrix,
                                  Eigen::VectorXd& b)
 {
     label sizeA = foam_matrix.diag().size();
@@ -1089,8 +1110,8 @@ void Foam2Eigen::fvMatrix2EigenV(fvMatrix<vector>& foam_matrix,
 
 template <class Type, template <class> class PatchField, class GeoMesh>
 Eigen::VectorXd Foam2Eigen::projectField(
-    GeometricField<Type, PatchField, GeoMesh>& field,
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes,
+    GeometricField<Type, PatchField, GeoMesh> & field,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes,
     label Nmodes)
 {
     Eigen::VectorXd fr;
@@ -1114,8 +1135,8 @@ Eigen::VectorXd Foam2Eigen::projectField(
 
 template <class Type, template <class> class PatchField, class GeoMesh>
 std::tuple<Eigen::MatrixXd, Eigen::VectorXd> Foam2Eigen::projectFvMatrix(
-    fvMatrix<Type>& matrix,
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes, label Nmodes)
+    fvMatrix<Type> & matrix,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes, label Nmodes)
 {
     Eigen::SparseMatrix<double> A;
     Eigen::MatrixXd Ar;
@@ -1148,7 +1169,7 @@ std::tuple<Eigen::MatrixXd, Eigen::VectorXd> Foam2Eigen::projectFvMatrix(
         }
     }
 
-    Ar = Eig_Modes.transpose() * A * Eig_Modes;
+    Ar = Eig_Modes.transpose() * A* Eig_Modes;
     br = Eig_Modes.transpose() * b;
     std::tuple<Eigen::MatrixXd, Eigen::VectorXd> tupla;
     tupla = std::make_tuple(Ar, br);
@@ -1157,7 +1178,7 @@ std::tuple<Eigen::MatrixXd, Eigen::VectorXd> Foam2Eigen::projectFvMatrix(
 
 template <class Type, template <class> class PatchField, class GeoMesh>
 Eigen::MatrixXd Foam2Eigen::MassMatrix(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes, label Nmodes)
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes, label Nmodes)
 {
     Eigen::MatrixXd Mr;
     Eigen::MatrixXd Eig_Modes = PtrList2Eigen(modes, Nmodes);
@@ -1192,7 +1213,7 @@ Eigen::MatrixXd Foam2Eigen::MassMatrix(
 
 template <class Type>
 std::tuple<List<Eigen::SparseMatrix<double>>, List<Eigen::VectorXd>>
-        Foam2Eigen::LFvMatrix2LSM(PtrList<fvMatrix<Type>>& MatrixList)
+Foam2Eigen::LFvMatrix2LSM(PtrList<fvMatrix<Type>> & MatrixList)
 {
     List<Eigen::SparseMatrix<double>> SM_list;
     List<Eigen::VectorXd> V_list;
@@ -1215,9 +1236,9 @@ std::tuple<List<Eigen::SparseMatrix<double>>, List<Eigen::VectorXd>>
 }
 
 template std::tuple<List<Eigen::SparseMatrix<double>>, List<Eigen::VectorXd>>
-Foam2Eigen::LFvMatrix2LSM(PtrList<fvMatrix<scalar>>& MatrixList);
+Foam2Eigen::LFvMatrix2LSM(PtrList<fvMatrix<scalar>> & MatrixList);
 template std::tuple<List<Eigen::SparseMatrix<double>>, List<Eigen::VectorXd>>
-Foam2Eigen::LFvMatrix2LSM(PtrList<fvMatrix<vector>>& MatrixList);
+Foam2Eigen::LFvMatrix2LSM(PtrList<fvMatrix<vector>> & MatrixList);
 
 template <class type_matrix>
 Eigen::Matrix<type_matrix, Eigen::Dynamic, Eigen::Dynamic>
@@ -1268,24 +1289,24 @@ template List<double> Foam2Eigen::EigenMatrix2List(
     Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> matrix);
 
 template <>
-Eigen::MatrixXd Foam2Eigen::field2Eigen(const List<vector>& field)
+Eigen::MatrixXd Foam2Eigen::field2Eigen(const List<vector> & field)
 {
     Eigen::MatrixXd out;
     out.resize(label(field.size() * 3), 1);
 
     for (label l = 0; l < field.size(); l++)
     {
-      for (label j = 0; j < 3; j++)
-      {
-          out(j * field.size() + l, 0) = field[l][j];
-      }
+        for (label j = 0; j < 3; j++)
+        {
+            out(j* field.size() + l, 0) = field[l][j];
+        }
     }
 
     return out;
 }
 
 template <>
-Eigen::MatrixXd Foam2Eigen::field2Eigen(const List<scalar>& field)
+Eigen::MatrixXd Foam2Eigen::field2Eigen(const List<scalar> & field)
 {
     Eigen::MatrixXd out;
     out.resize(label(field.size()), 1);
diff --git a/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.H b/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.H
index 60aa07b3d..e71b8e92b 100644
--- a/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.H
+++ b/src/ITHACA_CORE/Foam2Eigen/Foam2Eigen.H
@@ -104,7 +104,8 @@ class Foam2Eigen
         ///                               List of them
         ///
         template <class type_foam_matrix, class type_A>
-        static void fvMatrix2EigenM(fvMatrix<type_foam_matrix>& foam_matrix, type_A& A);
+        static void fvMatrix2EigenM(fvMatrix<type_foam_matrix> & foam_matrix,
+                                    type_A& A);
 
         //----------------------------------------------------------------------
         /// @brief      Convert a ldu OpenFOAM matrix into a source vector b
@@ -121,7 +122,8 @@ class Foam2Eigen
         ///                               List<Eigen::VectorXd>
         ///
         template <class type_foam_matrix, class type_B>
-        static void fvMatrix2EigenV(fvMatrix<type_foam_matrix>& foam_matrix, type_B& b);
+        static void fvMatrix2EigenV(fvMatrix<type_foam_matrix> & foam_matrix,
+                                    type_B& b);
 
 
         //----------------------------------------------------------------------
@@ -140,7 +142,7 @@ class Foam2Eigen
         ///
         template<class Type, template<class> class PatchField, class GeoMesh>
         static Eigen::MatrixXd PtrList2Eigen(
-            PtrList<GeometricField<Type, PatchField, GeoMesh>>& fields,
+            PtrList<GeometricField<Type, PatchField, GeoMesh>> & fields,
             label Nfields = -1);
 
         //----------------------------------------------------------------------
@@ -154,8 +156,8 @@ class Foam2Eigen
         /// @return     Dense Eigen vector
         ///
         template<template<class> class PatchField, class GeoMesh>
-        static Eigen::VectorXd field2Eigen(GeometricField<tensor, PatchField, GeoMesh>&
-                                       field);
+        static Eigen::VectorXd field2Eigen(GeometricField<tensor, PatchField, GeoMesh> &
+                                           field);
 
         //----------------------------------------------------------------------
         /// @brief      Convert a vector OpenFOAM field into an Eigen Vector
@@ -168,7 +170,7 @@ class Foam2Eigen
         /// @return     Dense Eigen vector
         ///
         template<template<class> class PatchField, class GeoMesh>
-        static Eigen::VectorXd field2Eigen(GeometricField<vector, PatchField, GeoMesh>&
+        static Eigen::VectorXd field2Eigen(GeometricField<vector, PatchField, GeoMesh> &
                                            field);
 
         //----------------------------------------------------------------------
@@ -182,7 +184,7 @@ class Foam2Eigen
         /// @return     Dense Eigen vector
         ///
         template<template<class> class PatchField, class GeoMesh>
-        static Eigen::VectorXd field2Eigen(GeometricField<scalar, PatchField, GeoMesh>&
+        static Eigen::VectorXd field2Eigen(GeometricField<scalar, PatchField, GeoMesh> &
                                            field);
 
         //----------------------------------------------------------------------
@@ -197,9 +199,9 @@ class Foam2Eigen
         ///
         template<template<class> class PatchField, class GeoMesh>
         static Eigen::Map<Eigen::MatrixXd> field2EigenMap(
-            GeometricField<scalar, PatchField, GeoMesh>&
+            GeometricField<scalar, PatchField, GeoMesh> &
             field);
-        
+
         //----------------------------------------------------------------------
         /// @brief      Map a scalar OpenFOAM field boundary into an Eigen Matrix
         ///
@@ -213,7 +215,7 @@ class Foam2Eigen
         ///
         template<template<class> class PatchField, class GeoMesh>
         static Eigen::Map<Eigen::MatrixXd> field2EigenMapBC(
-            GeometricField<scalar, PatchField, GeoMesh>&
+            GeometricField<scalar, PatchField, GeoMesh> &
             field, int BC_index);
 
         //----------------------------------------------------------------------
@@ -228,7 +230,7 @@ class Foam2Eigen
         ///
         template<class Type, class GeoMesh>
         static Eigen::VectorXd field2Eigen(const
-                                           DimensionedField<Type, GeoMesh>& field);
+                                           DimensionedField<Type, GeoMesh> & field);
 
         //----------------------------------------------------------------------
         /// @brief      Convert an OpenFOAM field into an Eigen Vector
@@ -241,7 +243,7 @@ class Foam2Eigen
         /// @return     Dense   Eigen vector
         ///
         template<class Type>
-        static Eigen::VectorXd field2Eigen(const Field<Type>& field);
+        static Eigen::VectorXd field2Eigen(const Field<Type> & field);
 
         //----------------------------------------------------------------------
         /// @brief      Convert an OpenFOAM scalar field to a List of Eigen
@@ -256,7 +258,7 @@ class Foam2Eigen
         ///
         template<template<class> class PatchField, class GeoMesh>
         static List<Eigen::VectorXd> field2EigenBC(
-            GeometricField<scalar, PatchField, GeoMesh>& field);
+            GeometricField<scalar, PatchField, GeoMesh> & field);
 
         //----------------------------------------------------------------------
         /// @brief      Convert an OpenFOAM vector field to a List of Eigen
@@ -271,7 +273,7 @@ class Foam2Eigen
         ///
         template<template<class> class PatchField, class GeoMesh>
         static List<Eigen::VectorXd> field2EigenBC(
-            GeometricField<vector, PatchField, GeoMesh>& field);
+            GeometricField<vector, PatchField, GeoMesh> & field);
 
         //----------------------------------------------------------------------
         /// @brief      Convert an OpenFOAM tensor field to a List of Eigen
@@ -286,7 +288,7 @@ class Foam2Eigen
         ///
         template<template<class> class PatchField, class GeoMesh>
         static List<Eigen::VectorXd> field2EigenBC(
-            GeometricField<tensor, PatchField, GeoMesh>& field);
+            GeometricField<tensor, PatchField, GeoMesh> & field);
 
 
         //----------------------------------------------------------------------
@@ -303,7 +305,7 @@ class Foam2Eigen
         ///
         template<template<class> class PatchField, class GeoMesh>
         static List<Eigen::MatrixXd> PtrList2EigenBC(
-            PtrList<GeometricField<scalar, PatchField, GeoMesh>>& fields,
+            PtrList<GeometricField<scalar, PatchField, GeoMesh>> & fields,
             label Nfields = -1);
 
         //----------------------------------------------------------------------
@@ -320,7 +322,7 @@ class Foam2Eigen
         ///
         template<template<class> class PatchField, class GeoMesh>
         static List<Eigen::MatrixXd> PtrList2EigenBC(
-            PtrList<GeometricField<vector, PatchField, GeoMesh>>& fields,
+            PtrList<GeometricField<vector, PatchField, GeoMesh>> & fields,
             label Nfields = -1);
 
         //----------------------------------------------------------------------
@@ -337,7 +339,7 @@ class Foam2Eigen
         ///
         template<template<class> class PatchField, class GeoMesh>
         static List<Eigen::MatrixXd> PtrList2EigenBC(
-            PtrList<GeometricField<tensor, PatchField, GeoMesh>>& fields,
+            PtrList<GeometricField<tensor, PatchField, GeoMesh>> & fields,
             label Nfields = -1);
 
         //----------------------------------------------------------------------
@@ -354,7 +356,7 @@ class Foam2Eigen
         ///
         template<template<class> class PatchField, class GeoMesh>
         static GeometricField<scalar, PatchField, GeoMesh> Eigen2field(
-            GeometricField<scalar, PatchField, GeoMesh>& field,
+            GeometricField<scalar, PatchField, GeoMesh> & field,
             Eigen::VectorXd& eigen_vector, bool correctBC = true);
 
         //----------------------------------------------------------------------
@@ -371,9 +373,9 @@ class Foam2Eigen
         ///
         template<template<class> class PatchField, class GeoMesh>
         static GeometricField<vector, PatchField, GeoMesh> Eigen2field(
-            GeometricField<vector, PatchField, GeoMesh>& field,
+            GeometricField<vector, PatchField, GeoMesh> & field,
             Eigen::VectorXd& eigen_vector, bool correctBC = true);
-        
+
         //----------------------------------------------------------------------
         /// @brief         Convert a vector in Eigen format into an OpenFOAM
         ///                scalar GeometricField
@@ -389,8 +391,8 @@ class Foam2Eigen
         ///
         template<template<class> class PatchField, class GeoMesh>
         static GeometricField<scalar, PatchField, GeoMesh> Eigen2field(
-            GeometricField<scalar, PatchField, GeoMesh>& field,
-            Eigen::VectorXd& eigen_vector, List<Eigen::VectorXd>& eigen_vector_boundary);
+            GeometricField<scalar, PatchField, GeoMesh> & field,
+            Eigen::VectorXd& eigen_vector, List<Eigen::VectorXd> & eigen_vector_boundary);
 
         //----------------------------------------------------------------------
         /// @brief         Convert a vector in Eigen format into an OpenFOAM
@@ -407,8 +409,8 @@ class Foam2Eigen
         ///
         template<template<class> class PatchField, class GeoMesh>
         static GeometricField<vector, PatchField, GeoMesh> Eigen2field(
-            GeometricField<vector, PatchField, GeoMesh>& field,
-            Eigen::VectorXd& eigen_vector, List<Eigen::VectorXd>& eigen_vector_boundary);
+            GeometricField<vector, PatchField, GeoMesh> & field,
+            Eigen::VectorXd& eigen_vector, List<Eigen::VectorXd> & eigen_vector_boundary);
 
 
         //----------------------------------------------------------------------
@@ -425,7 +427,7 @@ class Foam2Eigen
         ///
         template<template<class> class PatchField, class GeoMesh>
         static GeometricField<tensor, PatchField, GeoMesh> Eigen2field(
-            GeometricField<tensor, PatchField, GeoMesh>& field,
+            GeometricField<tensor, PatchField, GeoMesh> & field,
             Eigen::VectorXd& eigen_vector, bool correctBC = true);
 
         //----------------------------------------------------------------------
@@ -441,7 +443,7 @@ class Foam2Eigen
         ///
         template <class Type>
         static Field<Type> Eigen2field(
-            Field<Type>& field, Eigen::MatrixXd& matrix, bool correctBC = true);
+            Field<Type> & field, Eigen::MatrixXd& matrix, bool correctBC = true);
 
         //----------------------------------------------------------------------
         /// @brief      Obtain the Mass Matrix from a list of reduced basis
@@ -458,8 +460,8 @@ class Foam2Eigen
         ///
         template<class Type, template<class> class PatchField, class GeoMesh>
         static std::tuple<Eigen::MatrixXd, Eigen::VectorXd> projectFvMatrix(
-            fvMatrix<Type>& matrix,
-            PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes, label Nmodes);
+            fvMatrix<Type> & matrix,
+            PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes, label Nmodes);
 
 
         //----------------------------------------------------------------------
@@ -490,8 +492,8 @@ class Foam2Eigen
         ///
         template<class Type, template<class> class PatchField, class GeoMesh>
         static Eigen::VectorXd projectField(
-            GeometricField<Type, PatchField, GeoMesh>& field,
-            PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes,
+            GeometricField<Type, PatchField, GeoMesh> & field,
+            PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes,
             label Nmodes);
 
         //----------------------------------------------------------------------
@@ -508,7 +510,7 @@ class Foam2Eigen
         ///
         template<class Type, template<class> class PatchField, class GeoMesh>
         static Eigen::MatrixXd MassMatrix(
-            PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes, label Nmodes);
+            PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes, label Nmodes);
 
         //----------------------------------------------------------------------
         /// @brief      Convert a PtrList of OpenFOAM fvMatrix into a tuple of
@@ -524,7 +526,7 @@ class Foam2Eigen
         ///
         template<class Type>
         static std::tuple<List<Eigen::SparseMatrix<double>>, List<Eigen::VectorXd>>
-                LFvMatrix2LSM(PtrList<fvMatrix<Type>>& MatrixList);
+        LFvMatrix2LSM(PtrList<fvMatrix<Type>> & MatrixList);
 
         //--------------------------------------------------------------------------
         /// @brief      Convert a Foam List into an Eigen matrix with one column
@@ -562,6 +564,7 @@ class Foam2Eigen
         /// @return     An Eigen::MatrixXd Matrix containing the OpenFOAM values
         ///
         template <class type_list>
-        static Eigen::MatrixXd field2Eigen(const List<type_list>& list);
+        static Eigen::MatrixXd field2Eigen(const List<type_list> & list);
 };
+
 #endif
diff --git a/src/ITHACA_CORE/ITHACADMD/ITHACADMD.C b/src/ITHACA_CORE/ITHACADMD/ITHACADMD.C
index 922b86c67..a0e2b2526 100644
--- a/src/ITHACA_CORE/ITHACADMD/ITHACADMD.C
+++ b/src/ITHACA_CORE/ITHACADMD/ITHACADMD.C
@@ -35,7 +35,7 @@
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 ITHACADMD<Type, PatchField, GeoMesh>::ITHACADMD(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& snapshots, double dt)
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & snapshots, double dt)
     :
     snapshotsDMD(snapshots),
     NSnaps(snapshots.size()),
@@ -98,8 +98,8 @@ void ITHACADMD<Type, PatchField, GeoMesh>::getModes(label SVD_rank, bool exact,
         S = svd.singularValues().head(SVD_rank).array().cwiseInverse();
     }
 
-    Eigen::MatrixXcd A_tilde = U.transpose().conjugate() * Ym *
-                               V *
+    Eigen::MatrixXcd A_tilde = U.transpose().conjugate() * Ym*
+                               V*
                                S.asDiagonal();
     Eigen::ComplexEigenSolver<Eigen::MatrixXcd> esEg(A_tilde);
     eigenValues = esEg.eigenvalues();
@@ -119,19 +119,19 @@ void ITHACADMD<Type, PatchField, GeoMesh>::getModes(label SVD_rank, bool exact,
 
     if (exact)
     {
-        DMDEigenModes = Ym * V * S.asDiagonal() * esEg.eigenvectors();
+        DMDEigenModes = Ym* V* S.asDiagonal() * esEg.eigenvectors();
         DMDEigenModesBC.resize(YmBC.size());
 
         for (label i = 0; i < YmBC.size(); i++)
         {
-            DMDEigenModesBC[i] = YmBC[i] * V * S.asDiagonal() * esEg.eigenvectors();
+            DMDEigenModesBC[i] = YmBC[i] * V* S.asDiagonal() * esEg.eigenvectors();
         }
     }
     else
     {
         Eigen::VectorXd eigenValueseigLam =
             S.array().sqrt();
-        PODm = (Xm * V) * eigenValueseigLam.asDiagonal();
+        PODm = (Xm* V) * eigenValueseigLam.asDiagonal();
         PODmBC.resize(XmBC.size());
 
         for (label i = 0; i < XmBC.size(); i++)
@@ -139,7 +139,7 @@ void ITHACADMD<Type, PatchField, GeoMesh>::getModes(label SVD_rank, bool exact,
             PODmBC[i] = (XmBC[i] * V) * eigenValueseigLam.asDiagonal();
         }
 
-        DMDEigenModes = PODm * esEg.eigenvectors();
+        DMDEigenModes = PODm* esEg.eigenvectors();
         DMDEigenModesBC.resize(PODmBC.size());
 
         for (label i = 0; i < PODmBC.size(); i++)
@@ -172,7 +172,7 @@ void ITHACADMD<Type, PatchField, GeoMesh>::getDynamics(double tStart,
 
     for (double t = tStart; t <= tFinal; t += dt)
     {
-        Eigen::VectorXcd coli = (omega * t).array().exp() * Amplitudes.array();
+        Eigen::VectorXcd coli = (omega* t).array().exp() * Amplitudes.array();
         dynamics.col(i) = coli;
         i++;
     }
@@ -198,7 +198,7 @@ void ITHACADMD<Type, PatchField, GeoMesh>::reconstruct(word exportFolder,
 
     for (label i = 0; i < dynamics.cols(); i++)
     {
-        Eigen::MatrixXcd col = DMDEigenModes * dynamics.col(i);
+        Eigen::MatrixXcd col = DMDEigenModes* dynamics.col(i);
         Eigen::VectorXd vec = col.real();
         GeometricField<Type, PatchField, GeoMesh> tmp2("TMP",
                 snapshotsDMD[0] * 0);
@@ -215,6 +215,7 @@ void ITHACADMD<Type, PatchField, GeoMesh>::reconstruct(word exportFolder,
 
     ITHACAstream::exportFields(snapshotsrec, exportFolder, fieldName);
 }
+
 template<class Type, template<class> class PatchField, class GeoMesh>
 void ITHACADMD<Type, PatchField, GeoMesh>::convert2Foam()
 {
@@ -243,5 +244,6 @@ void ITHACADMD<Type, PatchField, GeoMesh>::convert2Foam()
         DMDmodesImag.set(i, tmp2Imag.clone());
     }
 }
+
 template class ITHACADMD<scalar, fvPatchField, volMesh>;
 template class ITHACADMD<vector, fvPatchField, volMesh>;
diff --git a/src/ITHACA_CORE/ITHACADMD/ITHACADMD.H b/src/ITHACA_CORE/ITHACADMD/ITHACADMD.H
old mode 100755
new mode 100644
index c30874fc5..09b0b94e9
--- a/src/ITHACA_CORE/ITHACADMD/ITHACADMD.H
+++ b/src/ITHACA_CORE/ITHACADMD/ITHACADMD.H
@@ -76,7 +76,7 @@ class ITHACADMD
         /// @param[in]  snapshots  The snapshots on which you want to perform DMD
         /// @param[in]  dt         The Time Step used to acquire the snapshots
         ///
-        ITHACADMD(PtrList<GeometricField<Type, PatchField, GeoMesh>>& snapshots,
+        ITHACADMD(PtrList<GeometricField<Type, PatchField, GeoMesh>> & snapshots,
                   double dt);
 
         /// PtrList of OpenFOAM GeoometricFields where the snapshots are stored
diff --git a/src/ITHACA_CORE/ITHACAPOD/ITHACAPOD.C b/src/ITHACA_CORE/ITHACAPOD/ITHACAPOD.C
index 63cce9cd2..409ccddaa 100644
--- a/src/ITHACA_CORE/ITHACAPOD/ITHACAPOD.C
+++ b/src/ITHACA_CORE/ITHACAPOD/ITHACAPOD.C
@@ -39,8 +39,8 @@ namespace ITHACAPOD
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 void getNestedSnapshotMatrix(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& snapshots,
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& ModesGlobal,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & snapshots,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & ModesGlobal,
     word fieldName,
     label Npar, label NnestedOut)
 {
@@ -56,7 +56,7 @@ void getNestedSnapshotMatrix(
 
         for (label j = 0; j < Nt; j++)
         {
-            SnapMatrixNested[i].set(j, snapshots[j + Nt * i].clone());
+            SnapMatrixNested[i].set(j, snapshots[j + Nt* i].clone());
         }
     }
 
@@ -82,17 +82,17 @@ void getNestedSnapshotMatrix(
 }
 
 template void getNestedSnapshotMatrix(
-    PtrList<volScalarField>& snapshots, PtrList<volScalarField>& ModesGlobal,
+    PtrList<volScalarField> & snapshots, PtrList<volScalarField> & ModesGlobal,
     word fieldName, label Npar, label NnestedOut);
 
 template void getNestedSnapshotMatrix(
-    PtrList<volVectorField>& snapshots, PtrList<volVectorField>& ModesGlobal,
+    PtrList<volVectorField> & snapshots, PtrList<volVectorField> & ModesGlobal,
     word fieldName, label Npar, label NnestedOut);
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 void getModes(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& snapshots,
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & snapshots,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes,
     word fieldName, bool podex, bool supex, bool sup, label nmodes,
     bool correctBC)
 {
@@ -158,7 +158,7 @@ void getModes(
         if (para->eigensolver == "spectra")
         {
             Spectra::SymEigsSolver<double, Spectra::LARGEST_ALGE, Spectra::DenseSymMatProd<double>>
-                    es(&op, nmodes, ncv);
+            es( & op, nmodes, ncv);
             std::cout << "Using Spectra EigenSolver " << std::endl;
             es.init();
             es.compute(1000, 1e-10, Spectra::LARGEST_ALGE);
@@ -190,7 +190,7 @@ void getModes(
         //    eigenValueseig.real().array().abs().cwiseInverse().sqrt() ;
         //Eigen::MatrixXd modesEig = (SnapMatrix * eigenVectoreig) *
         //                           eigenValueseigLam.head(nmodes).asDiagonal();
-        Eigen::MatrixXd modesEig = (SnapMatrix * eigenVectoreig);
+        Eigen::MatrixXd modesEig = (SnapMatrix* eigenVectoreig);
         // Computing Normalization factors of the POD Modes
         Eigen::VectorXd V = ITHACAutilities::getMassMatrixFV(snapshots[0]);
         Eigen::MatrixXd normFact(nmodes, 1);
@@ -253,7 +253,7 @@ void getModes(
         for (label i = 0; i < modes.size(); i++)
         {
             GeometricField<Type, PatchField, GeoMesh>  tmp2(snapshots[0].name(),
-                    snapshots[0]);
+                snapshots[0]);
             Eigen::VectorXd vec = modesEig.col(i);
             tmp2 = Foam2Eigen::Eigen2field(tmp2, vec, correctBC);
 
@@ -310,24 +310,24 @@ void getModes(
 }
 
 template void getModes(
-    PtrList<volVectorField>& snapshots, PtrList<volVectorField>& modes,
+    PtrList<volVectorField> & snapshots, PtrList<volVectorField> & modes,
     word fieldName, bool podex, bool supex, bool sup, label nmodes,
     bool correctBC);
 
 template void getModes(
-    PtrList<volScalarField>& snapshots, PtrList<volScalarField>& modes,
+    PtrList<volScalarField> & snapshots, PtrList<volScalarField> & modes,
     word fieldName, bool podex, bool supex, bool sup, label nmodes,
     bool correctBC);
 
 template void getModes(
-    PtrList<surfaceScalarField>& snapshots, PtrList<surfaceScalarField>& modes,
+    PtrList<surfaceScalarField> & snapshots, PtrList<surfaceScalarField> & modes,
     word fieldName, bool podex, bool supex, bool sup, label nmodes,
     bool correctBC);
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 void getWeightedModes(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& snapshots,
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & snapshots,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes,
     word fieldName, bool podex, bool supex, bool sup, label nmodes,
     bool correctBC)
 {
@@ -356,7 +356,7 @@ void getWeightedModes(
         Spectra::DenseSymMatProd<double> op(_corMatrix);
         Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> esEg;
         Spectra::SymEigsSolver<double, Spectra::LARGEST_ALGE, Spectra::DenseSymMatProd<double>>
-                es(&op, nmodes, ncv);
+        es( & op, nmodes, ncv);
 
         if (para->eigensolver == "spectra")
         {
@@ -385,7 +385,7 @@ void getWeightedModes(
             eigenValueseig.real().array().cwiseInverse().sqrt() ;
         Eigen::VectorXd eigenValueseigWeigted = eigenValueseig.head(
                 nmodes).real().array() ;
-        Eigen::MatrixXd modesEig = (SnapMatrix * eigenVectoreig) *
+        Eigen::MatrixXd modesEig = (SnapMatrix* eigenVectoreig) *
                                    eigenValueseigLam.head(nmodes).asDiagonal() *
                                    eigenValueseigWeigted.asDiagonal();
         List<Eigen::MatrixXd> modesEigBC;
@@ -400,7 +400,7 @@ void getWeightedModes(
         for (label i = 0; i < modes.size(); i++)
         {
             GeometricField<Type, PatchField, GeoMesh> tmp2(snapshots[0].name(),
-                    snapshots[0]);
+                snapshots[0]);
             Eigen::VectorXd vec = modesEig.col(i);
             tmp2 = Foam2Eigen::Eigen2field(tmp2, vec, correctBC);
 
@@ -458,19 +458,19 @@ void getWeightedModes(
 }
 
 template void getWeightedModes(
-    PtrList<volScalarField>& snapshots, PtrList<volScalarField>& modes,
+    PtrList<volScalarField> & snapshots, PtrList<volScalarField> & modes,
     word fieldName, bool podex, bool supex, bool sup, label nmodes,
     bool correctBC);
 
 template void getWeightedModes(
-    PtrList<volVectorField>& snapshots, PtrList<volVectorField>& modes,
+    PtrList<volVectorField> & snapshots, PtrList<volVectorField> & modes,
     word fieldName, bool podex, bool supex, bool sup, label nmodes,
     bool correctBC);
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 void getModesSVD(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& snapshots,
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & snapshots,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes,
     word fieldName, bool podex, bool supex, bool sup, label nmodes,
     bool correctBC)
 {
@@ -488,7 +488,7 @@ void getModesSVD(
         Eigen::VectorXd V3dInv = V3dSqrt.array().cwiseInverse();
         auto VMsqr = V3dSqrt.asDiagonal();
         auto VMsqrInv = V3dInv.asDiagonal();
-        Eigen::MatrixXd SnapMatrix2 = VMsqr * SnapMatrix;
+        Eigen::MatrixXd SnapMatrix2 = VMsqr* SnapMatrix;
         Eigen::JacobiSVD<Eigen::MatrixXd> svd(SnapMatrix2,
                                               Eigen::ComputeThinU | Eigen::ComputeThinV);
         Info << "####### End of the POD for " << snapshots[0].name() << " #######" <<
@@ -497,7 +497,7 @@ void getModesSVD(
         Eigen::MatrixXd eigenVectoreig;
         eigenValueseig = svd.singularValues().real();
         eigenVectoreig = svd.matrixU().real();
-        Eigen::MatrixXd modesEig = VMsqrInv * eigenVectoreig;
+        Eigen::MatrixXd modesEig = VMsqrInv* eigenVectoreig;
         GeometricField<Type, PatchField, GeoMesh> tmb_bu(snapshots[0].name(),
                 snapshots[0] * 0);
 
@@ -554,18 +554,18 @@ void getModesSVD(
 }
 
 template void getModesSVD(
-    PtrList<volScalarField>& snapshots, PtrList<volScalarField>& modes,
+    PtrList<volScalarField> & snapshots, PtrList<volScalarField> & modes,
     word fieldName, bool podex, bool supex, bool sup, label nmodes,
     bool correctBC);
 
 template void getModesSVD(
-    PtrList<volVectorField>& snapshots, PtrList<volVectorField>& modes,
+    PtrList<volVectorField> & snapshots, PtrList<volVectorField> & modes,
     word fieldName, bool podex, bool supex, bool sup, label nmodes,
     bool correctBC);
 
 /// Construct the Correlation Matrix for Scalar Field
 template<>
-Eigen::MatrixXd corMatrix(PtrList<volScalarField>& snapshots)
+Eigen::MatrixXd corMatrix(PtrList<volScalarField> & snapshots)
 {
     Info << "########## Filling the correlation matrix for " << snapshots[0].name()
          << "##########" << endl;
@@ -593,7 +593,7 @@ Eigen::MatrixXd corMatrix(PtrList<volScalarField>& snapshots)
 
 /// Construct the Correlation Matrix for Vector Field
 template<>
-Eigen::MatrixXd corMatrix(PtrList<volVectorField>& snapshots)
+Eigen::MatrixXd corMatrix(PtrList<volVectorField> & snapshots)
 {
     Info << "########## Filling the correlation matrix for " << snapshots[0].name()
          << "##########" << endl;
@@ -620,7 +620,7 @@ Eigen::MatrixXd corMatrix(PtrList<volVectorField>& snapshots)
 
 /// Construct the Correlation Matrix for Vector Field
 template<>
-Eigen::MatrixXd corMatrix(List<Eigen::SparseMatrix<double>>&
+Eigen::MatrixXd corMatrix(List<Eigen::SparseMatrix<double>> &
                           snapshots)
 {
     Info << "########## Filling the correlation matrix for the matrix list ##########"
@@ -655,7 +655,7 @@ Eigen::MatrixXd corMatrix(List<Eigen::SparseMatrix<double>>&
 
 /// Construct the Correlation Matrix for Vector Field
 template<>
-Eigen::MatrixXd corMatrix(List<Eigen::VectorXd>& snapshots)
+Eigen::MatrixXd corMatrix(List<Eigen::VectorXd> & snapshots)
 {
     Info << "########## Filling the correlation matrix for the matrix list ##########"
          << endl;
@@ -684,8 +684,8 @@ Eigen::MatrixXd corMatrix(List<Eigen::VectorXd>& snapshots)
 
 /// Export the Bases
 template<class Type, template<class> class PatchField, class GeoMesh>
-void exportBases(PtrList<GeometricField<Type, PatchField, GeoMesh>>& s,
-                 PtrList<GeometricField<Type, PatchField, GeoMesh>>& bases,
+void exportBases(PtrList<GeometricField<Type, PatchField, GeoMesh>> & s,
+                 PtrList<GeometricField<Type, PatchField, GeoMesh>> & bases,
                  word fieldName, bool sup)
 {
     if (sup)
@@ -716,10 +716,11 @@ void exportBases(PtrList<GeometricField<Type, PatchField, GeoMesh>>& s,
         }
     }
 }
-template void exportBases(PtrList<volVectorField>& s,
-                          PtrList<volVectorField>& bases, word fieldName, bool sup);
-template void exportBases(PtrList<volScalarField>& s,
-                          PtrList<volScalarField>& bases, word fieldName, bool sup);
+
+template void exportBases(PtrList<volVectorField> & s,
+                          PtrList<volVectorField> & bases, word fieldName, bool sup);
+template void exportBases(PtrList<volScalarField> & s,
+                          PtrList<volScalarField> & bases, word fieldName, bool sup);
 
 void exportEigenvalues(scalarField Eigenvalues, fileName name,
                        bool sup)
@@ -781,8 +782,8 @@ void exportcumEigenvalues(scalarField cumEigenvalues, fileName name,
 
 
 std::tuple<List<Eigen::SparseMatrix<double>>, List<Eigen::VectorXd>>
-        DEIMmodes(List<Eigen::SparseMatrix<double>>& A,
-                  List<Eigen::VectorXd>& b, label nmodesA, label nmodesB, word MatrixName)
+DEIMmodes(List<Eigen::SparseMatrix<double>> & A,
+          List<Eigen::VectorXd> & b, label nmodesA, label nmodesB, word MatrixName)
 {
     ITHACAparameters* para(ITHACAparameters::getInstance());
     List<Eigen::SparseMatrix<double>> ModesA(nmodesA);
@@ -821,9 +822,9 @@ std::tuple<List<Eigen::SparseMatrix<double>>, List<Eigen::VectorXd>>
         Spectra::DenseSymMatProd<double> opA(corMatrixA);
         Spectra::DenseSymMatProd<double> opB(corMatrixB);
         Spectra::SymEigsSolver<double, Spectra::LARGEST_ALGE, Spectra:: DenseSymMatProd<double>>
-                esA(&opA, nmodesA, nmodesA + 10);
+        esA( & opA, nmodesA, nmodesA + 10);
         Spectra::SymEigsSolver<double, Spectra::LARGEST_ALGE, Spectra:: DenseSymMatProd<double>>
-                esB(&opB, nmodesB, nmodesB + 10);
+        esB( & opB, nmodesB, nmodesB + 10);
         esA.init();
         esB.init();
         esA.compute();
@@ -990,7 +991,7 @@ void GrammSchmidt(Eigen::MatrixXd& Matrix)
             double num = Ortho.col(k).transpose() * Matrix.col(i);
             double den = (Ortho.col(k).transpose() * Ortho.col(k));
             double fact = num / den;
-            Ortho.col(i) -= fact * Ortho.col(k) ;
+            Ortho.col(i) -= fact* Ortho.col(k) ;
         }
 
         Ortho.col(i).normalize();
@@ -998,11 +999,12 @@ void GrammSchmidt(Eigen::MatrixXd& Matrix)
 
     Matrix = Ortho;
 }
+
 template<class Type, template<class> class PatchField, class GeoMesh>
 void getModes(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& snapshots,
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes,
-    PtrList<volScalarField>& Volumes, word fieldName, bool podex, bool supex,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & snapshots,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes,
+    PtrList<volScalarField> & Volumes, word fieldName, bool podex, bool supex,
     bool sup, label nmodes, bool correctBC)
 {
     ITHACAparameters* para(ITHACAparameters::getInstance());
@@ -1066,7 +1068,7 @@ void getModes(
         if (para->eigensolver == "spectra")
         {
             Spectra::SymEigsSolver<double, Spectra::LARGEST_ALGE, Spectra::DenseSymMatProd<double>>
-                    es(&op, nmodes, ncv);
+            es( & op, nmodes, ncv);
             std::cout << "Using Spectra EigenSolver " << std::endl;
             es.init();
             es.compute(1000, 1e-10, Spectra::LARGEST_ALGE);
@@ -1090,7 +1092,7 @@ void getModes(
              endl;
         Eigen::VectorXd eigenValueseigLam =
             eigenValueseig.real().array().cwiseInverse().sqrt() ;
-        Eigen::MatrixXd modesEig = (SnapMatrix * eigenVectoreig) *
+        Eigen::MatrixXd modesEig = (SnapMatrix* eigenVectoreig) *
                                    eigenValueseigLam.asDiagonal();
         List<Eigen::MatrixXd> modesEigBC;
         modesEigBC.resize(NBC);
@@ -1104,7 +1106,7 @@ void getModes(
         for (label i = 0; i < modes.size(); i++)
         {
             GeometricField<Type, PatchField, GeoMesh> tmp2(snapshots[0].name(),
-                    snapshots[0] * 0);
+                snapshots[0] * 0);
             Eigen::VectorXd vec = modesEig.col(i);
             tmp2 = Foam2Eigen::Eigen2field(tmp2, vec, correctBC);
 
@@ -1149,20 +1151,21 @@ void getModes(
         }
     }
 }
+
 template void getModes(
-    PtrList<volScalarField>& snapshots, PtrList<volScalarField>& modes,
-    PtrList<volScalarField>& Volumes, word fieldName, bool podex, bool supex,
+    PtrList<volScalarField> & snapshots, PtrList<volScalarField> & modes,
+    PtrList<volScalarField> & Volumes, word fieldName, bool podex, bool supex,
     bool sup, label nmodes, bool correctBC);
 
 template void getModes(
-    PtrList<volVectorField>& snapshots, PtrList<volVectorField>& modes,
-    PtrList<volScalarField>& Volumes, word fieldName, bool podex, bool supex,
+    PtrList<volVectorField> & snapshots, PtrList<volVectorField> & modes,
+    PtrList<volScalarField> & Volumes, word fieldName, bool podex, bool supex,
     bool sup, label nmodes, bool correctBC);
 
 template<typename type_matrix>
 std::tuple<List<Eigen::SparseMatrix<double>>, List<Eigen::VectorXd>>
-        DEIMmodes(PtrList<type_matrix>& MatrixList, label nmodesA, label nmodesB,
-                  word MatrixName)
+DEIMmodes(PtrList<type_matrix> & MatrixList, label nmodesA, label nmodesB,
+          word MatrixName)
 {
     ITHACAparameters* para(ITHACAparameters::getInstance());
     List<Eigen::SparseMatrix<double>> ModesA(nmodesA);
@@ -1174,7 +1177,7 @@ std::tuple<List<Eigen::SparseMatrix<double>>, List<Eigen::VectorXd>>
                  && nmodesB <= MatrixList.size() - 2,
                  "The number of requested modes cannot be bigger than the number of Snapshots - 2");
         std::tuple<List<Eigen::SparseMatrix<double>>, List<Eigen::VectorXd>> snapshots =
-                    Foam2Eigen::LFvMatrix2LSM(MatrixList);
+            Foam2Eigen::LFvMatrix2LSM(MatrixList);
         Eigen::MatrixXd corMatrixA = corMatrix(std::get<0>(snapshots));
         Eigen::MatrixXd corMatrixB = corMatrix(std::get<1>(snapshots));
         Eigen::VectorXd eigenValueseigA;
@@ -1191,9 +1194,9 @@ std::tuple<List<Eigen::SparseMatrix<double>>, List<Eigen::VectorXd>>
             label ncvA = MatrixList.size();
             label ncvB = MatrixList.size();
             Spectra::SymEigsSolver<double, Spectra::LARGEST_ALGE, Spectra:: DenseSymMatProd<double>>
-                    esA(&opA, nmodesA, ncvA);
+            esA( & opA, nmodesA, ncvA);
             Spectra::SymEigsSolver<double, Spectra::LARGEST_ALGE, Spectra:: DenseSymMatProd<double>>
-                    esB(&opB, nmodesB, ncvB);
+            esB( & opB, nmodesB, ncvB);
             esA.init();
             esB.init();
             esA.compute(1000, 1e-10, Spectra::LARGEST_ALGE);
@@ -1334,19 +1337,19 @@ std::tuple<List<Eigen::SparseMatrix<double>>, List<Eigen::VectorXd>>
 }
 
 template std::tuple<List<Eigen::SparseMatrix<double>>, List<Eigen::VectorXd>>
-DEIMmodes(PtrList<fvScalarMatrix>& MatrixList, label nmodesA,
+DEIMmodes(PtrList<fvScalarMatrix> & MatrixList, label nmodesA,
           label nmodesB,
           word MatrixName);
 
 template std::tuple<List<Eigen::SparseMatrix<double>>, List<Eigen::VectorXd>>
-DEIMmodes(PtrList<fvVectorMatrix>& MatrixList, label nmodesA,
+DEIMmodes(PtrList<fvVectorMatrix> & MatrixList, label nmodesA,
           label nmodesB,
           word MatrixName);
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 PtrList<GeometricField<Type, PatchField, GeoMesh>>DEIMmodes(
-            PtrList<GeometricField<Type, PatchField, GeoMesh>>& snapshots, label nmodes,
-            word FunctionName, word fieldName)
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & snapshots, label nmodes,
+    word FunctionName, word fieldName)
 {
     ITHACAparameters* para(ITHACAparameters::getInstance());
     word PODkey = "POD_" + fieldName;
@@ -1407,7 +1410,7 @@ PtrList<GeometricField<Type, PatchField, GeoMesh>>DEIMmodes(
         if (para->eigensolver == "spectra")
         {
             Spectra::SymEigsSolver<double, Spectra::LARGEST_ALGE, Spectra::DenseSymMatProd<double>>
-                    es(&op, nmodes, ncv);
+            es( & op, nmodes, ncv);
             std::cout << "Using Spectra EigenSolver " << std::endl;
             es.init();
             es.compute(1000, 1e-10, Spectra::LARGEST_ALGE);
@@ -1435,7 +1438,7 @@ PtrList<GeometricField<Type, PatchField, GeoMesh>>DEIMmodes(
 
         Info << "####### End of the POD for " << snapshots[0].name() << " #######" <<
              endl;
-        Eigen::MatrixXd modesEig = (SnapMatrix * eigenVectoreig);
+        Eigen::MatrixXd modesEig = (SnapMatrix* eigenVectoreig);
         Eigen::VectorXd V = ITHACAutilities::getMassMatrixFV(snapshots[0]);
         Eigen::MatrixXd normFact(nmodes, 1);
 
@@ -1497,7 +1500,7 @@ PtrList<GeometricField<Type, PatchField, GeoMesh>>DEIMmodes(
         for (label i = 0; i < modes.size(); i++)
         {
             GeometricField<Type, PatchField, GeoMesh>  tmp2(snapshots[0].name(),
-                    snapshots[0]);
+                snapshots[0]);
             Eigen::VectorXd vec = modesEig.col(i);
             tmp2 = Foam2Eigen::Eigen2field(tmp2, vec, correctBC);
 
@@ -1545,8 +1548,8 @@ PtrList<GeometricField<Type, PatchField, GeoMesh>>DEIMmodes(
 
 template<class Field_type, class Field_type_2>
 void getModes(
-    PtrList<Field_type>& snapshots, PtrList<Field_type>& modes,
-    PtrList<Field_type_2>& fields2, word fieldName, bool podex, bool supex,
+    PtrList<Field_type> & snapshots, PtrList<Field_type> & modes,
+    PtrList<Field_type_2> & fields2, word fieldName, bool podex, bool supex,
     bool sup, label nmodes, bool correctBC)
 {
     ITHACAparameters* para(ITHACAparameters::getInstance());
@@ -1598,7 +1601,7 @@ void getModes(
         if (para->eigensolver == "spectra")
         {
             Spectra::SymEigsSolver<double, Spectra::LARGEST_ALGE, Spectra::DenseSymMatProd<double>>
-                    es(&op, nmodes, ncv);
+            es( & op, nmodes, ncv);
             std::cout << "Using Spectra EigenSolver " << std::endl;
             es.init();
             es.compute(1000, 1e-10, Spectra::LARGEST_ALGE);
@@ -1622,7 +1625,7 @@ void getModes(
              endl;
         Eigen::VectorXd eigenValueseigLam =
             eigenValueseig.real().array().cwiseInverse().abs().sqrt() ;
-        Eigen::MatrixXd modesEig = (SnapMatrix * eigenVectoreig) *
+        Eigen::MatrixXd modesEig = (SnapMatrix* eigenVectoreig) *
                                    eigenValueseigLam.asDiagonal();
         List<Eigen::MatrixXd> modesEigBC;
         modesEigBC.resize(NBC);
@@ -1683,24 +1686,24 @@ void getModes(
 }
 
 template void getModes(
-    PtrList<surfaceScalarField>& snapshots, PtrList<surfaceScalarField>& modes,
-    PtrList<volVectorField>& fields2, word fieldName, bool podex, bool supex,
+    PtrList<surfaceScalarField> & snapshots, PtrList<surfaceScalarField> & modes,
+    PtrList<volVectorField> & fields2, word fieldName, bool podex, bool supex,
     bool sup, label nmodes, bool correctBC);
 
 template void getModes(
-    PtrList<volScalarField>& snapshots, PtrList<volScalarField>& modes,
-    PtrList<volVectorField>& fields2, word fieldName, bool podex, bool supex,
+    PtrList<volScalarField> & snapshots, PtrList<volScalarField> & modes,
+    PtrList<volVectorField> & fields2, word fieldName, bool podex, bool supex,
     bool sup, label nmodes, bool correctBC);
 
 template PtrList<volScalarField>
 DEIMmodes(
-    PtrList<volScalarField>& SnapShotsMatrix,
+    PtrList<volScalarField> & SnapShotsMatrix,
     label nmodes,
     word FunctionName, word FieldName);
 
 template PtrList<volVectorField>
 DEIMmodes(
-    PtrList<volVectorField>& SnapShotsMatrix,
+    PtrList<volVectorField> & SnapShotsMatrix,
     label nmodes,
     word FunctionName, word FieldName);
 
diff --git a/src/ITHACA_CORE/ITHACAPOD/ITHACAPOD.H b/src/ITHACA_CORE/ITHACAPOD/ITHACAPOD.H
old mode 100755
new mode 100644
index 081f6e00b..5187aa642
--- a/src/ITHACA_CORE/ITHACAPOD/ITHACAPOD.H
+++ b/src/ITHACA_CORE/ITHACAPOD/ITHACAPOD.H
@@ -83,8 +83,8 @@ namespace ITHACAPOD
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
 void getModes(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& snapshots,
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & snapshots,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes,
     word fieldName, bool podex, bool supex = 0, bool sup = 0,
     label nmodes = 0, bool correctBC = true);
 
@@ -110,8 +110,8 @@ void getModes(
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
 void getModesSVD(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>&
-    snapshots, PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> &
+    snapshots, PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes,
     word fieldName, bool podex, bool supex = 0, bool sup = 0,
     label nmodes = 0, bool correctBC = true);
 
@@ -135,8 +135,8 @@ void getModesSVD(
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
 void getNestedSnapshotMatrix(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& snapshots,
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & snapshots,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes,
     word fieldName, label Npar,
     label NnestedOut);
 
@@ -163,8 +163,8 @@ void getNestedSnapshotMatrix(
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
 void getWeightedModes(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& snapshots,
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & snapshots,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes,
     word fieldName, bool podex, bool supex = 0, bool sup = 0,
     label nmodes = 0, bool correctBC = true);
 
@@ -212,8 +212,8 @@ Eigen::MatrixXd corMatrix(Field_type& snapshots);
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
 void exportBases(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& snapshots,
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& bases,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & snapshots,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & bases,
     word fieldName,
     bool sup = 0);
 
@@ -254,8 +254,8 @@ void exportcumEigenvalues(scalarField cumEigenvalues,  fileName name,
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
 PtrList<GeometricField<Type, PatchField, GeoMesh>> DEIMmodes(
-            PtrList<GeometricField<Type, PatchField, GeoMesh>>& SnapShotsMatrix,
-            label nmodes, word FunctionName, word FieldName);
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & SnapShotsMatrix,
+    label nmodes, word FunctionName, word FieldName);
 
 //------------------------------------------------------------------------------
 /// @brief      Get the DEIM modes for a generic non-parametrized matrix coming
@@ -274,8 +274,8 @@ PtrList<GeometricField<Type, PatchField, GeoMesh>> DEIMmodes(
 ///
 template<typename type_matrix>
 std::tuple<List<Eigen::SparseMatrix<double>>, List<Eigen::VectorXd>>
-        DEIMmodes(PtrList<type_matrix>& MatrixList, label nmodesA, label nmodesB,
-                  word MatrixName = "Matrix");
+DEIMmodes(PtrList<type_matrix> & MatrixList, label nmodesA, label nmodesB,
+          word MatrixName = "Matrix");
 
 //------------------------------------------------------------------------------
 /// @brief      Get the DEIM modes for a generic non a parametrized matrix
@@ -294,8 +294,8 @@ std::tuple<List<Eigen::SparseMatrix<double>>, List<Eigen::VectorXd>>
 ///             and the list of modes for the source term
 ///
 std::tuple<List<Eigen::SparseMatrix<double>>, List<Eigen::VectorXd>>
-        DEIMmodes(List<Eigen::SparseMatrix<double>>& A, List<Eigen::VectorXd>& b,
-                  label nmodesA, label nmodesB, word MatrixName = "Matrix");
+DEIMmodes(List<Eigen::SparseMatrix<double>> & A, List<Eigen::VectorXd> & b,
+          label nmodesA, label nmodesB, word MatrixName = "Matrix");
 
 
 //------------------------------------------------------------------------------
@@ -319,9 +319,9 @@ std::tuple<List<Eigen::SparseMatrix<double>>, List<Eigen::VectorXd>>
 /// @tparam     GeoMesh     volMesh or surfaceMesh.
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
-void getModes(PtrList<GeometricField<Type, PatchField, GeoMesh>>& snapshots,
-              PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes,
-              PtrList<volScalarField>& Volumes, word fieldName, bool podex, bool supex = 0,
+void getModes(PtrList<GeometricField<Type, PatchField, GeoMesh>> & snapshots,
+              PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes,
+              PtrList<volScalarField> & Volumes, word fieldName, bool podex, bool supex = 0,
               bool sup = 0,
               label nmodes = 0);
 
@@ -349,8 +349,8 @@ void getModes(PtrList<GeometricField<Type, PatchField, GeoMesh>>& snapshots,
 /// @tparam     Field_type_2  Type of the other fields
 ///
 template<class Field_type, class Field_type_2>
-void getModes(PtrList<Field_type>& snapshots, PtrList<Field_type>& modes,
-              PtrList<Field_type_2>& fields2, word fieldName, bool podex, bool supex = 0,
+void getModes(PtrList<Field_type> & snapshots, PtrList<Field_type> & modes,
+              PtrList<Field_type_2> & fields2, word fieldName, bool podex, bool supex = 0,
               bool sup = 0,
               label nmodes = 0);
 
diff --git a/src/ITHACA_CORE/ITHACAPOD/incrementalPOD.C b/src/ITHACA_CORE/ITHACAPOD/incrementalPOD.C
old mode 100755
new mode 100644
index 43b3bbc85..91162fcd1
--- a/src/ITHACA_CORE/ITHACAPOD/incrementalPOD.C
+++ b/src/ITHACA_CORE/ITHACAPOD/incrementalPOD.C
@@ -36,7 +36,7 @@
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 incrementalPOD<Type, PatchField, GeoMesh>::incrementalPOD(
-    GeometricField<Type, PatchField, GeoMesh>& snapshot,
+    GeometricField<Type, PatchField, GeoMesh> & snapshot,
     double _tol, word _PODnorm)
 {
     Info << "WARNING: the projection of the BC has not been implemented yet!" <<
@@ -50,7 +50,7 @@ incrementalPOD<Type, PatchField, GeoMesh>::incrementalPOD(
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 void incrementalPOD<Type, PatchField, GeoMesh>::initialize(
-    GeometricField<Type, PatchField, GeoMesh>& snapshot)
+    GeometricField<Type, PatchField, GeoMesh> & snapshot)
 {
     Info << "Initializing the incremental POD" << endl;
     M_Assert(tolleranceSVD > 0, "Set up the tollerance before initialization");
@@ -94,7 +94,7 @@ void incrementalPOD<Type, PatchField, GeoMesh>::initialize(
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 void incrementalPOD<Type, PatchField, GeoMesh>::addSnapshot(
-    GeometricField<Type, PatchField, GeoMesh>& snapshot)
+    GeometricField<Type, PatchField, GeoMesh> & snapshot)
 {
     Info << "********************************************************************"
          << endl;
@@ -111,7 +111,7 @@ void incrementalPOD<Type, PatchField, GeoMesh>::addSnapshot(
 
     Eigen::VectorXd redCoeff = project(snapshot);
     GeometricField<Type, PatchField, GeoMesh> projectSnap = projectSnapshot(
-                snapshot);
+            snapshot);
     GeometricField<Type, PatchField, GeoMesh> orthoSnap(snapshot - projectSnap);
     Eigen::VectorXd orthogonalSnap = Foam2Eigen::field2Eigen(orthoSnap);
 
@@ -160,7 +160,7 @@ void incrementalPOD<Type, PatchField, GeoMesh>::addSnapshot(
         Eigen::MatrixXd temp(this->EigenModes[0].rows(),
                              this->EigenModes[0].cols() + 1);
         temp << this->EigenModes[0], orthogonalSnap;
-        this->EigenModes[0] = temp * newModes;
+        this->EigenModes[0] = temp* newModes;
         singularValues = newSingVal;
         rank++;
     }
@@ -183,7 +183,7 @@ void incrementalPOD<Type, PatchField, GeoMesh>::addSnapshot(
     double EPS = 2.2204e-16;
     Info << "Orthogonality = " << orthogonalPar << endl;
 
-    if (orthogonalPar > std::min(tolleranceSVD, EPS * this->EigenModes[0].rows()))
+    if (orthogonalPar > std::min(tolleranceSVD, EPS* this->EigenModes[0].rows()))
     {
         Info << "Orthogonalization required" << endl;
 
@@ -213,15 +213,16 @@ void incrementalPOD<Type, PatchField, GeoMesh>::fillPtrList()
     for (label i = 0; i < rank; i++)
     {
         GeometricField<Type, PatchField, GeoMesh>  tmp(this->first().name(),
-                this->first());
+            this->first());
         Eigen::VectorXd vec = this->EigenModes[0].col(i);
         tmp = Foam2Eigen::Eigen2field(tmp, vec);
         this->set(i, tmp.clone());
     }
 }
+
 template<class Type, template<class> class PatchField, class GeoMesh>
 Eigen::VectorXd incrementalPOD<Type, PatchField, GeoMesh>::project(
-    GeometricField<Type, PatchField, GeoMesh>& inputField,
+    GeometricField<Type, PatchField, GeoMesh> & inputField,
     label numberOfModes)
 {
     Eigen::VectorXd fieldEig = Foam2Eigen::field2Eigen(inputField);
@@ -261,7 +262,7 @@ Eigen::VectorXd incrementalPOD<Type, PatchField, GeoMesh>::project(
 template<class Type, template<class> class PatchField, class GeoMesh>
 GeometricField<Type, PatchField, GeoMesh>
 incrementalPOD<Type, PatchField, GeoMesh>::reconstruct(
-    GeometricField<Type, PatchField, GeoMesh>& inputField,
+    GeometricField<Type, PatchField, GeoMesh> & inputField,
     Eigen::MatrixXd Coeff,
     word Name)
 {
@@ -282,7 +283,7 @@ incrementalPOD<Type, PatchField, GeoMesh>::reconstruct(
 template<class Type, template<class> class PatchField, class GeoMesh>
 GeometricField<Type, PatchField, GeoMesh>
 incrementalPOD<Type, PatchField, GeoMesh>::projectSnapshot(
-    GeometricField<Type, PatchField, GeoMesh>& snapshot,
+    GeometricField<Type, PatchField, GeoMesh> & snapshot,
     label numberOfModes)
 {
     Eigen::MatrixXd Modes;
@@ -327,7 +328,7 @@ incrementalPOD<Type, PatchField, GeoMesh>::projectSnapshot(
 template<class Type, template<class> class PatchField, class GeoMesh>
 void incrementalPOD<Type, PatchField, GeoMesh>::projectSnapshots(
     PtrList<GeometricField<Type, PatchField, GeoMesh>> snapshots,
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& projSnapshots,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & projSnapshots,
     label numberOfModes)
 {
     M_Assert(numberOfModes <= this->size(),
diff --git a/src/ITHACA_CORE/ITHACAPOD/incrementalPOD.H b/src/ITHACA_CORE/ITHACAPOD/incrementalPOD.H
old mode 100755
new mode 100644
index c28ff6cd1..d51e48dc2
--- a/src/ITHACA_CORE/ITHACAPOD/incrementalPOD.H
+++ b/src/ITHACA_CORE/ITHACAPOD/incrementalPOD.H
@@ -96,7 +96,7 @@ class incrementalPOD : public Modes<Type, PatchField, GeoMesh>
         /// @param[in]  _tol        Incremental SVD tollerance
         /// @param[in]  _maxRank   i Maximum POD rank
         ///
-        incrementalPOD(GeometricField<Type, PatchField, GeoMesh>& snapshot,
+        incrementalPOD(GeometricField<Type, PatchField, GeoMesh> & snapshot,
                        double _tol, word _PODnorm);
 
         /// Destructor
@@ -107,14 +107,14 @@ class incrementalPOD : public Modes<Type, PatchField, GeoMesh>
         ///
         /// @param[in]  snapshot    A first snapshot
         ///
-        void initialize(GeometricField<Type, PatchField, GeoMesh>& snapshot);
+        void initialize(GeometricField<Type, PatchField, GeoMesh> & snapshot);
 
         //--------------------------------------------------------------------------
         /// @brief      Add a snapshot to the POD space
         ///
         /// @param[in]  snapshot    Snapshot to add
         ///
-        void addSnapshot(GeometricField<Type, PatchField, GeoMesh>& snapshot);
+        void addSnapshot(GeometricField<Type, PatchField, GeoMesh> & snapshot);
 
         //--------------------------------------------------------------------------
         /// @brief      Fill the POD modes prtList from the Eigen matrix
@@ -129,7 +129,7 @@ class incrementalPOD : public Modes<Type, PatchField, GeoMesh>
         /// @return     The coefficient of the projected field into the reduced space
         ///
         Eigen::VectorXd project(
-            GeometricField<Type, PatchField, GeoMesh>& inputField,
+            GeometricField<Type, PatchField, GeoMesh> & inputField,
             label numberOfModes = 0);
 
         //--------------------------------------------------------------------------
@@ -142,7 +142,7 @@ class incrementalPOD : public Modes<Type, PatchField, GeoMesh>
         /// @return     Reconstructed field
         ///
         GeometricField<Type, PatchField, GeoMesh> reconstruct(
-            GeometricField<Type, PatchField, GeoMesh>& inputField,
+            GeometricField<Type, PatchField, GeoMesh> & inputField,
             Eigen::MatrixXd Coeff,
             word Name);
 
@@ -155,7 +155,7 @@ class incrementalPOD : public Modes<Type, PatchField, GeoMesh>
         /// @return     The projected snapshot
         ///
         GeometricField<Type, PatchField, GeoMesh> projectSnapshot(
-            GeometricField<Type, PatchField, GeoMesh>& snapshot,
+            GeometricField<Type, PatchField, GeoMesh> & snapshot,
             label numberOfModes = 0);
 
         //--------------------------------------------------------------------------
@@ -167,7 +167,7 @@ class incrementalPOD : public Modes<Type, PatchField, GeoMesh>
         ///
         void projectSnapshots(
             PtrList<GeometricField<Type, PatchField, GeoMesh>> snapshots,
-            PtrList<GeometricField<Type, PatchField, GeoMesh>>& projSnapshots,
+            PtrList<GeometricField<Type, PatchField, GeoMesh>> & projSnapshots,
             label numberOfModes = 0);
 
         //--------------------------------------------------------------------------
@@ -205,7 +205,7 @@ void weightedGramSchmidt(
             double den = (Ortho.col(k).transpose() * weights.asDiagonal()
                           * Ortho.col(k));
             double fact = num / den;
-            Ortho.col(i) -= fact * Ortho.col(k) ;
+            Ortho.col(i) -= fact* Ortho.col(k) ;
         }
 
         Ortho.col(i).normalize();
@@ -214,6 +214,7 @@ void weightedGramSchmidt(
     matrix = Ortho;
 };
 }
+
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
 #endif
diff --git a/src/ITHACA_CORE/ITHACAparallel/ITHACAparallel.C b/src/ITHACA_CORE/ITHACAparallel/ITHACAparallel.C
index c3e51deb6..d28b43672 100644
--- a/src/ITHACA_CORE/ITHACAparallel/ITHACAparallel.C
+++ b/src/ITHACA_CORE/ITHACAparallel/ITHACAparallel.C
@@ -131,7 +131,7 @@ void ITHACAparallel::resumeMPI()
 
 template<>
 List<List <scalar>> ITHACAparallel::combineFields(
-                     GeometricField<scalar, fvPatchField, volMesh>& field)
+    GeometricField<scalar, fvPatchField, volMesh> & field)
 {
     List<List< scalar>> GlobField(field.boundaryFieldRef().size() + 1);
     GlobField[0].resize(N_IF_glob);
@@ -173,7 +173,7 @@ List<List <scalar>> ITHACAparallel::combineFields(
 
 template<>
 List<List <vector>> ITHACAparallel::combineFields(
-                     GeometricField<vector, fvPatchField, volMesh>& field)
+    GeometricField<vector, fvPatchField, volMesh> & field)
 {
     List<List< vector>> GlobField(field.boundaryFieldRef().size() + 1);
     GlobField[0].resize(N_IF_glob);
diff --git a/src/ITHACA_CORE/ITHACAparallel/ITHACAparallel.H b/src/ITHACA_CORE/ITHACAparallel/ITHACAparallel.H
index 4f0c1a504..4364e32b4 100644
--- a/src/ITHACA_CORE/ITHACAparallel/ITHACAparallel.H
+++ b/src/ITHACA_CORE/ITHACAparallel/ITHACAparallel.H
@@ -77,7 +77,7 @@ class ITHACAparallel
 
         /// Function to get a global field from a parallel one
         template<class Type>
-        List<List <Type>> combineFields(GeometricField<Type, fvPatchField, volMesh>&
+        List<List <Type>> combineFields(GeometricField<Type, fvPatchField, volMesh> &
                                         field);
 
         template<class type>
@@ -124,7 +124,7 @@ class ITHACAparallel
 
 template<>
 List<List<scalar>> ITHACAparallel::combineFields(
-                    GeometricField<scalar, fvPatchField, volMesh>& field);
+    GeometricField<scalar, fvPatchField, volMesh> & field);
 
 template<class type>
 GeometricField<type, fvPatchField, volMesh>
@@ -175,6 +175,7 @@ ITHACAparallel::constructGlobalField(GeometricField<type, fvPatchField, volMesh>
     );
     return F_glob;
 }
+
 #endif
 
 
diff --git a/src/ITHACA_CORE/ITHACAregularization/ITHACAregularization.C b/src/ITHACA_CORE/ITHACAregularization/ITHACAregularization.C
old mode 100755
new mode 100644
index 5bd2a2c85..df8b45325
--- a/src/ITHACA_CORE/ITHACAregularization/ITHACAregularization.C
+++ b/src/ITHACA_CORE/ITHACAregularization/ITHACAregularization.C
@@ -75,7 +75,7 @@ Eigen::VectorXd  TSVD(Eigen::MatrixXd A,
                 f += tempU.col(i).dot(bVect) * tempU.col(i).dot(bVect);
             }
 
-            f += 2 * noiseVariance * col;
+            f += 2 * noiseVariance* col;
 
             if (col == 0)
             {
@@ -111,7 +111,7 @@ Eigen::VectorXd  Tikhonov(Eigen::MatrixXd A,
                           Eigen::MatrixXd b, double regularizationParameter)
 {
     M_Assert(b.cols() == 1, "The b input in TSVD must have only one column");
-    Eigen::MatrixXd Anew = A.transpose() * A + regularizationParameter *
+    Eigen::MatrixXd Anew = A.transpose() * A + regularizationParameter*
                            Eigen::MatrixXd::Identity(A.rows(), A.cols());
     Eigen::MatrixXd bNew = A.transpose() * b;
     Eigen::VectorXd x = A.inverse() * b;
diff --git a/src/ITHACA_CORE/ITHACAsensitivity/FiguresOfMerit/Tm_time.H b/src/ITHACA_CORE/ITHACAsensitivity/FiguresOfMerit/Tm_time.H
old mode 100755
new mode 100644
index 93f198245..0ca3dc52e
--- a/src/ITHACA_CORE/ITHACAsensitivity/FiguresOfMerit/Tm_time.H
+++ b/src/ITHACA_CORE/ITHACAsensitivity/FiguresOfMerit/Tm_time.H
@@ -45,6 +45,7 @@ class Tm_time : public FofM
         Tm_time();
         Tm_time(int argc, char* argv[], label Nsampled);
         ~Tm_time() {};
+
         //Members
         /// List of pointers to temperature field
         autoPtr<volScalarField> _T;
diff --git a/src/ITHACA_CORE/ITHACAsensitivity/LRSensitivity.C b/src/ITHACA_CORE/ITHACAsensitivity/LRSensitivity.C
old mode 100755
new mode 100644
index 3bd940026..226bc44bd
--- a/src/ITHACA_CORE/ITHACAsensitivity/LRSensitivity.C
+++ b/src/ITHACA_CORE/ITHACAsensitivity/LRSensitivity.C
@@ -15,7 +15,7 @@ LRSensitivity::LRSensitivity(label Npara, label Np)
 }
 
 
-void LRSensitivity::buildSamplingSet(std::vector<std::string>& pdflist,
+void LRSensitivity::buildSamplingSet(std::vector<std::string> & pdflist,
                                      Eigen::MatrixXd plist)
 {
     for (label i = 0; i < No_parameters; i++)
diff --git a/src/ITHACA_CORE/ITHACAsensitivity/LRSensitivity.H b/src/ITHACA_CORE/ITHACAsensitivity/LRSensitivity.H
old mode 100755
new mode 100644
index 0351cca40..f549d86f7
--- a/src/ITHACA_CORE/ITHACAsensitivity/LRSensitivity.H
+++ b/src/ITHACA_CORE/ITHACAsensitivity/LRSensitivity.H
@@ -92,7 +92,8 @@ class LRSensitivity
         /// Method to build MatX, it internally calls ITHACAsampling::samplingMC
         /// pdflist is the list with the names of the distributions of the parameters
         /// plist contains the parameters of the distributions, therefore its size must be (No_parameters,2)
-        void buildSamplingSet(std::vector<std::string>& pdflist, Eigen::MatrixXd plist);
+        void buildSamplingSet(std::vector<std::string> & pdflist,
+                              Eigen::MatrixXd plist);
         ///----------------------------------------------------------------------------------------
 
         /// Method to load the output of FOM/ROM inside member LRsensitivity member y
diff --git a/src/ITHACA_CORE/ITHACAstream/ITHACAparameters.C b/src/ITHACA_CORE/ITHACAstream/ITHACAparameters.C
index 668e15df4..e7c2ba4d9 100755
--- a/src/ITHACA_CORE/ITHACAstream/ITHACAparameters.C
+++ b/src/ITHACA_CORE/ITHACAstream/ITHACAparameters.C
@@ -36,6 +36,7 @@ ITHACAparameters::ITHACAparameters(fvMesh& mesh, Time& localTime)
     exportPython = ITHACAdict->lookupOrDefault<bool>("exportPython", 0);
     exportMatlab = ITHACAdict->lookupOrDefault<bool>("exportMatlab", 0);
     exportTxt = ITHACAdict->lookupOrDefault<bool>("exportTxt", 0);
+    exportNpy = ITHACAdict->lookupOrDefault<bool>("exportnpy", 0);
     debug = ITHACAdict->lookupOrDefault<bool>("debug", 0);
     warnings = ITHACAdict->lookupOrDefault<bool>("warnings", 0);
     correctBC = ITHACAdict->lookupOrDefault<bool>("correctBC", 1);
diff --git a/src/ITHACA_CORE/ITHACAstream/ITHACAparameters.H b/src/ITHACA_CORE/ITHACAstream/ITHACAparameters.H
index 5de67119d..24dc382d4 100755
--- a/src/ITHACA_CORE/ITHACAstream/ITHACAparameters.H
+++ b/src/ITHACA_CORE/ITHACAstream/ITHACAparameters.H
@@ -53,6 +53,7 @@ class ITHACAparameters
         bool exportPython;
         bool exportMatlab;
         bool exportTxt;
+        bool exportNpy;
         bool debug;
         bool warnings;
         bool correctBC;
diff --git a/src/ITHACA_CORE/ITHACAstream/ITHACAstream.C b/src/ITHACA_CORE/ITHACAstream/ITHACAstream.C
index fc7d3863c..de8cb9eaf 100644
--- a/src/ITHACA_CORE/ITHACAstream/ITHACAstream.C
+++ b/src/ITHACA_CORE/ITHACAstream/ITHACAstream.C
@@ -41,7 +41,7 @@ namespace ITHACAstream
 {
 
 template<typename Type>
-void exportFvMatrix(fvMatrix<Type>& Matrix, word folder,
+void exportFvMatrix(fvMatrix<Type> & Matrix, word folder,
                     word MatrixName)
 {
     Eigen::SparseMatrix<double> A;
@@ -170,7 +170,7 @@ template void exportMatrix(Eigen::Matrix < float, -1,
                            1 > & matrix, word Name, word type,
                            word folder);
 
-void exportMatrix(List <Eigen::MatrixXd>& matrix, word Name,
+void exportMatrix(List <Eigen::MatrixXd> & matrix, word Name,
                   word type, word folder)
 {
     std::string message = "The extension \"" +  type +
@@ -295,7 +295,7 @@ void exportTensor(Eigen::Tensor<T, 3> tensor, word Name,
                     if ( k == 0)
                     {
                         str << "[" << setprecision(10) << Eigen::SliceFromTensor(tensor, 0,
-                                i)(j, k);
+                            i)(j, k);
                     }
                     else
                     {
@@ -331,7 +331,7 @@ void exportTensor(Eigen::Tensor<T, 3> tensor, word Name,
                         0).cols(); k++)
                 {
                     str << " " << setprecision(10) << Eigen::SliceFromTensor(tensor, 0,
-                            i)(j, k);
+                        i)(j, k);
                 }
 
                 if (j != (Eigen::SliceFromTensor(tensor, 0,
@@ -418,7 +418,7 @@ Eigen::MatrixXd readMatrix(word filename)
 
         while (! stream.eof())
         {
-            stream >> buff[cols * rows + temp_cols++];
+            stream >> buff[cols* rows + temp_cols++];
         }
 
         if (temp_cols == 0)
@@ -443,7 +443,7 @@ Eigen::MatrixXd readMatrix(word filename)
     {
         for (int j = 0; j < cols; j++)
         {
-            result(i, j) = buff[ cols * i + j ];
+            result(i, j) = buff[ cols* i + j ];
         }
     }
 
@@ -452,7 +452,7 @@ Eigen::MatrixXd readMatrix(word filename)
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 void read_fields(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& Lfield, word Name,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & Lfield, word Name,
     fileName casename, int first_snap, int n_snap)
 {
     ITHACAparameters* para(ITHACAparameters::getInstance());
@@ -547,8 +547,8 @@ void read_fields(
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 void read_fields(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& Lfield,
-    GeometricField<Type, PatchField, GeoMesh>& field,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & Lfield,
+    GeometricField<Type, PatchField, GeoMesh> & field,
     fileName casename, int first_snap, int n_snap)
 {
     if (!Pstream::parRun())
@@ -641,8 +641,8 @@ void read_fields(
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 void readMiddleFields(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& Lfield,
-    GeometricField<Type, PatchField, GeoMesh>& field, fileName casename)
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & Lfield,
+    GeometricField<Type, PatchField, GeoMesh> & field, fileName casename)
 {
     int par = 1;
     M_Assert(ITHACAutilities::check_folder(casename + name(par)) != 0,
@@ -657,8 +657,8 @@ void readMiddleFields(
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 void readConvergedFields(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& Lfield,
-    GeometricField<Type, PatchField, GeoMesh>& field,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & Lfield,
+    GeometricField<Type, PatchField, GeoMesh> & field,
     fileName casename)
 {
     int par = 1;
@@ -693,8 +693,8 @@ void readConvergedFields(
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 void read_last_fields(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& Lfield,
-    const GeometricField<Type, PatchField, GeoMesh>& field,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & Lfield,
+    const GeometricField<Type, PatchField, GeoMesh> & field,
     const fileName casename)
 {
     if (!Pstream::parRun())
@@ -704,35 +704,33 @@ void read_last_fields(
         fileName rootpath(".");
         Foam::Time runTime2(Foam::Time::controlDictName, rootpath, casename);
         int last_s (runTime2.times().size());
-
-        #if defined(OFVER) && (OFVER >= 2212)
+#if defined(OFVER) && (OFVER >= 2212)
         Lfield.emplace_back
         (
             IOobject
             (
                 field.name(),
-                casename + runTime2.times()[last_s-1].name(),
+                casename + runTime2.times()[last_s - 1].name(),
                 field.mesh(),
                 IOobject::MUST_READ
             ),
             field.mesh()
         );
-        #else 
+#else
         auto tfld =
             autoPtr<GeometricField<Type, PatchField, GeoMesh>>::New
             (
                 IOobject
                 (
                     field.name(),
-                    casename + runTime2.times()[last_s-1].name(),
+                    casename + runTime2.times()[last_s - 1].name(),
                     field.mesh(),
                     IOobject::MUST_READ
                 ),
                 field.mesh()
             );
         Lfield.append(std::move(tfld));
-        #endif
-
+#endif
         std::cout << std::endl;
     }
     else
@@ -745,43 +743,42 @@ void read_last_fields(
         timename = timename + "/" + casename + "processor" + name(Pstream::myProcNo());
         int last_s = numberOfFiles(casename,
                                    "processor" + name(Pstream::myProcNo()) + "/");
-
-        #if defined(OFVER) && (OFVER >= 2212)
+#if defined(OFVER) && (OFVER >= 2212)
         Lfield.emplace_back
         (
             IOobject
             (
                 field.name(),
-                timename + "/" + name(last_s-1),
+                timename + "/" + name(last_s - 1),
                 field.mesh(),
                 IOobject::MUST_READ
             ),
             field.mesh()
         );
-        #else
+#else
         auto tfld =
             autoPtr<GeometricField<Type, PatchField, GeoMesh>>::New
             (
                 IOobject
                 (
                     field.name(),
-                    timename + "/" + name(last_s-1),
+                    timename + "/" + name(last_s - 1),
                     field.mesh(),
                     IOobject::MUST_READ
                 ),
                 field.mesh()
             );
         Lfield.append(std::move(tfld));
-        #endif
-
+#endif
         Info << endl;
     }
 }
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 void readLastFields(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& Lfield,
-    const GeometricField<Type, PatchField, GeoMesh>& field, const fileName casename)
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & Lfield,
+    const GeometricField<Type, PatchField, GeoMesh> & field,
+    const fileName casename)
 {
     int par = 1;
     M_Assert(ITHACAutilities::check_folder(casename + name(par)) != 0,
@@ -791,7 +788,7 @@ void readLastFields(
     {
         read_last_fields(Lfield, field, casename + name(par) + "/");
         par++;
-    } 
+    }
 }
 
 int numberOfFiles(word folder, word MatrixName, word ext)
@@ -816,7 +813,7 @@ int numberOfFiles(word folder, word MatrixName, word ext)
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 void exportFields(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& field,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & field,
     word folder, word fieldname)
 {
     ITHACAutilities::createSymLink(folder);
@@ -833,20 +830,20 @@ void exportFields(
 }
 
 template void exportFields(
-    PtrList<GeometricField<scalar, fvPatchField, volMesh>>& field,
+    PtrList<GeometricField<scalar, fvPatchField, volMesh>> & field,
     word folder, word fieldname);
 template void exportFields(
-    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>>& field,
+    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>> & field,
     word folder, word fieldname);
 template void exportFields(
-    PtrList<GeometricField<vector, fvPatchField, volMesh>>& field,
+    PtrList<GeometricField<vector, fvPatchField, volMesh>> & field,
     word folder, word fieldname);
 template void exportFields(
-    PtrList<GeometricField<tensor, fvPatchField, volMesh>>& field,
+    PtrList<GeometricField<tensor, fvPatchField, volMesh>> & field,
     word folder, word fieldname);
 
 template<class Type, template<class> class PatchField, class GeoMesh>
-void exportSolution(GeometricField<Type, PatchField, GeoMesh>& s,
+void exportSolution(GeometricField<Type, PatchField, GeoMesh> & s,
                     fileName subfolder, fileName folder,
                     word fieldName)
 {
@@ -875,24 +872,24 @@ void exportSolution(GeometricField<Type, PatchField, GeoMesh>& s,
 }
 
 template void exportSolution(
-    GeometricField<scalar, fvPatchField, volMesh>& s,
+    GeometricField<scalar, fvPatchField, volMesh> & s,
     fileName subfolder, fileName folder,
     word fieldName);
 template void exportSolution(
-    GeometricField<vector, fvPatchField, volMesh>& s,
+    GeometricField<vector, fvPatchField, volMesh> & s,
     fileName subfolder, fileName folder,
     word fieldName);
 template void exportSolution(
-    GeometricField<tensor, fvPatchField, volMesh>& s,
+    GeometricField<tensor, fvPatchField, volMesh> & s,
     fileName subfolder, fileName folder,
     word fieldName);
 template void exportSolution(
-    GeometricField<scalar, fvsPatchField, surfaceMesh>& s,
+    GeometricField<scalar, fvsPatchField, surfaceMesh> & s,
     fileName subfolder, fileName folder,
     word fieldName);
 
 template<class Type, template<class> class PatchField, class GeoMesh>
-void exportSolution(GeometricField<Type, PatchField, GeoMesh>& s,
+void exportSolution(GeometricField<Type, PatchField, GeoMesh> & s,
                     fileName subfolder, fileName folder)
 {
     if (!Pstream::parRun())
@@ -917,26 +914,26 @@ void exportSolution(GeometricField<Type, PatchField, GeoMesh>& s,
 }
 
 template void exportSolution(
-    GeometricField<scalar, fvPatchField, volMesh>& s,
+    GeometricField<scalar, fvPatchField, volMesh> & s,
     fileName subfolder, fileName folder);
 template void exportSolution(
-    GeometricField<vector, fvPatchField, volMesh>& s,
+    GeometricField<vector, fvPatchField, volMesh> & s,
     fileName subfolder, fileName folder);
 template void exportSolution(
-    GeometricField<tensor, fvPatchField, volMesh>& s,
+    GeometricField<tensor, fvPatchField, volMesh> & s,
     fileName subfolder, fileName folder);
 template void exportSolution(
-    GeometricField<scalar, fvsPatchField, surfaceMesh>& s,
+    GeometricField<scalar, fvsPatchField, surfaceMesh> & s,
     fileName subfolder, fileName folder);
 
 template void exportSolution(
-    GeometricField<scalar, pointPatchField, pointMesh>& s,
+    GeometricField<scalar, pointPatchField, pointMesh> & s,
     fileName subfolder, fileName folder);
 template void exportSolution(
-    GeometricField<vector, pointPatchField, pointMesh>& s,
+    GeometricField<vector, pointPatchField, pointMesh> & s,
     fileName subfolder, fileName folder);
 template void exportSolution(
-    GeometricField<tensor, pointPatchField, pointMesh>& s,
+    GeometricField<tensor, pointPatchField, pointMesh> & s,
     fileName subfolder, fileName folder);
 
 void writePoints(pointField points, fileName folder,
@@ -968,7 +965,7 @@ void writePoints(pointField points, fileName folder,
 void printProgress(double percentage)
 {
     int val = static_cast<int>(percentage * 100);
-    int lpad = static_cast<int> (percentage * PBWIDTH);
+    int lpad = static_cast<int> (percentage* PBWIDTH);
     int rpad = PBWIDTH - lpad;
 
     if (Pstream::master())
@@ -979,7 +976,7 @@ void printProgress(double percentage)
 }
 
 template<typename T>
-void save(const List<Eigen::SparseMatrix<T>>& MatrixList, word folder,
+void save(const List<Eigen::SparseMatrix<T>> & MatrixList, word folder,
           word MatrixName)
 {
     mkDir(folder);
@@ -992,7 +989,7 @@ void save(const List<Eigen::SparseMatrix<T>>& MatrixList, word folder,
 }
 
 template<typename T>
-void load(List<Eigen::SparseMatrix<T>>& MatrixList, word folder,
+void load(List<Eigen::SparseMatrix<T>> & MatrixList, word folder,
           word MatrixName)
 {
     int number_of_files = numberOfFiles(folder, MatrixName, ".npz");
@@ -1009,72 +1006,72 @@ void load(List<Eigen::SparseMatrix<T>>& MatrixList, word folder,
     }
 }
 
-template void read_fields(PtrList<volScalarField>& Lfield,
+template void read_fields(PtrList<volScalarField> & Lfield,
                           word Name,
                           fileName casename, int first_snap, int n_snap);
-template void read_fields(PtrList<volVectorField>& Lfield,
+template void read_fields(PtrList<volVectorField> & Lfield,
                           word Name,
                           fileName casename, int first_snap, int n_snap);
-template void read_fields(PtrList<volTensorField>& Lfield,
+template void read_fields(PtrList<volTensorField> & Lfield,
                           word Name,
                           fileName casename, int first_snap, int n_snap);
-template void read_fields(PtrList<surfaceScalarField>& Lfield,
+template void read_fields(PtrList<surfaceScalarField> & Lfield,
                           word Name,
                           fileName casename, int first_snap, int n_snap);
-template void read_fields(PtrList<surfaceVectorField>& Lfield,
+template void read_fields(PtrList<surfaceVectorField> & Lfield,
                           word Name,
                           fileName casename, int first_snap, int n_snap);
-template void read_fields(PtrList<volScalarField>& Lfield,
+template void read_fields(PtrList<volScalarField> & Lfield,
                           volScalarField& field, fileName casename, int first_snap, int n_snap);
-template void read_fields(PtrList<volVectorField>& Lfield,
+template void read_fields(PtrList<volVectorField> & Lfield,
                           volVectorField& field, fileName casename, int first_snap, int n_snap);
-template void read_fields(PtrList<volTensorField>& Lfield,
+template void read_fields(PtrList<volTensorField> & Lfield,
                           volTensorField& field, fileName casename, int first_snap, int n_snap);
-template void read_fields(PtrList<surfaceScalarField>& Lfield,
+template void read_fields(PtrList<surfaceScalarField> & Lfield,
                           surfaceScalarField& field, fileName casename, int first_snap, int n_snap);
-template void read_fields(PtrList<surfaceVectorField>& Lfield,
+template void read_fields(PtrList<surfaceVectorField> & Lfield,
                           surfaceVectorField& field, fileName casename, int first_snap, int n_snap);
-template void readMiddleFields(PtrList<volScalarField>& Lfield,
+template void readMiddleFields(PtrList<volScalarField> & Lfield,
                                volScalarField& field, fileName casename);
-template void readMiddleFields(PtrList<volVectorField>& Lfield,
+template void readMiddleFields(PtrList<volVectorField> & Lfield,
                                volVectorField& field, fileName casename);
-template void readMiddleFields(PtrList<volTensorField>& Lfield,
+template void readMiddleFields(PtrList<volTensorField> & Lfield,
                                volTensorField& field, fileName casename);
-template void readMiddleFields(PtrList<surfaceScalarField>&
+template void readMiddleFields(PtrList<surfaceScalarField> &
                                Lfield, surfaceScalarField& field, fileName casename);
-template void readMiddleFields(PtrList<surfaceVectorField>&
+template void readMiddleFields(PtrList<surfaceVectorField> &
                                Lfield, surfaceVectorField& field, fileName casename);
-template void readConvergedFields(PtrList<volScalarField>& Lfield,
+template void readConvergedFields(PtrList<volScalarField> & Lfield,
                                   volScalarField& field, fileName casename);
-template void readConvergedFields(PtrList<volVectorField>& Lfield,
+template void readConvergedFields(PtrList<volVectorField> & Lfield,
                                   volVectorField& field, fileName casename);
-template void readConvergedFields(PtrList<volTensorField>& Lfield,
+template void readConvergedFields(PtrList<volTensorField> & Lfield,
                                   volTensorField& field, fileName casename);
-template void readConvergedFields(PtrList<surfaceScalarField>&
+template void readConvergedFields(PtrList<surfaceScalarField> &
                                   Lfield, surfaceScalarField& field, fileName casename);
-template void readConvergedFields(PtrList<surfaceVectorField>&
+template void readConvergedFields(PtrList<surfaceVectorField> &
                                   Lfield, surfaceVectorField& field, fileName casename);
 
-template void read_last_fields(PtrList<volScalarField>& Lfield,
-                         const volScalarField& field, const fileName casename);
-template void read_last_fields(PtrList<volVectorField>& Lfield,
-                         const volVectorField& field, const fileName casename);
-template void read_last_fields(PtrList<volTensorField>& Lfield,
-                         const volTensorField& field, const fileName casename);
-template void read_last_fields(PtrList<surfaceScalarField>& Lfield,
-                         const surfaceScalarField& field, const fileName casename);
-template void read_last_fields(PtrList<surfaceVectorField>& Lfield,
-                         const surfaceVectorField& field, const fileName casename);
-template void readLastFields(PtrList<volScalarField>& Lfield,
-                              const volScalarField& field, const fileName casename);
-template void readLastFields(PtrList<volVectorField>& Lfield,
-                              const volVectorField& field, const fileName casename);
-template void readLastFields(PtrList<volTensorField>& Lfield,
-                              const volTensorField& field, const fileName casename);
-template void readLastFields(PtrList<surfaceScalarField>&
-                               Lfield, const surfaceScalarField& field, const fileName casename);
-template void readLastFields(PtrList<surfaceVectorField>&
-                               Lfield, const surfaceVectorField& field, const fileName casename);
+template void read_last_fields(PtrList<volScalarField> & Lfield,
+                               const volScalarField& field, const fileName casename);
+template void read_last_fields(PtrList<volVectorField> & Lfield,
+                               const volVectorField& field, const fileName casename);
+template void read_last_fields(PtrList<volTensorField> & Lfield,
+                               const volTensorField& field, const fileName casename);
+template void read_last_fields(PtrList<surfaceScalarField> & Lfield,
+                               const surfaceScalarField& field, const fileName casename);
+template void read_last_fields(PtrList<surfaceVectorField> & Lfield,
+                               const surfaceVectorField& field, const fileName casename);
+template void readLastFields(PtrList<volScalarField> & Lfield,
+                             const volScalarField& field, const fileName casename);
+template void readLastFields(PtrList<volVectorField> & Lfield,
+                             const volVectorField& field, const fileName casename);
+template void readLastFields(PtrList<volTensorField> & Lfield,
+                             const volTensorField& field, const fileName casename);
+template void readLastFields(PtrList<surfaceScalarField> &
+                             Lfield, const surfaceScalarField& field, const fileName casename);
+template void readLastFields(PtrList<surfaceVectorField> &
+                             Lfield, const surfaceVectorField& field, const fileName casename);
 
 template<typename T>
 void exportList(T& list, word folder, word filename)
@@ -1089,17 +1086,17 @@ void exportList(T& list, word folder, word filename)
     }
 }
 
-template void exportList(Field<scalar>& list, word folder,
+template void exportList(Field<scalar> & list, word folder,
                          word filename);
-template void exportList(Field<vector>& list, word folder,
+template void exportList(Field<vector> & list, word folder,
                          word filename);
-template void exportList(Field<tensor>& list, word folder,
+template void exportList(Field<tensor> & list, word folder,
                          word filename);
 
-template void save(const List<Eigen::SparseMatrix<double>>& MatrixList,
+template void save(const List<Eigen::SparseMatrix<double>> & MatrixList,
                    word folder, word MatrixName);
 
-template void load(List<Eigen::SparseMatrix<double>>& MatrixList, word folder,
+template void load(List<Eigen::SparseMatrix<double>> & MatrixList, word folder,
                    word MatrixName);
 
 }
diff --git a/src/ITHACA_CORE/ITHACAstream/ITHACAstream.H b/src/ITHACA_CORE/ITHACAstream/ITHACAstream.H
index f3329ec99..4885a357d 100644
--- a/src/ITHACA_CORE/ITHACAstream/ITHACAstream.H
+++ b/src/ITHACA_CORE/ITHACAstream/ITHACAstream.H
@@ -98,7 +98,7 @@ namespace ITHACAstream
 /// @tparam     Type        can be scalar or vector
 ///
 template<typename Type>
-void exportFvMatrix(fvMatrix<Type>& Matrix, word folder,
+void exportFvMatrix(fvMatrix<Type> & Matrix, word folder,
                     word MatrixName);
 
 //--------------------------------------------------------------------------
@@ -127,7 +127,7 @@ void exportMatrix(Eigen::Matrix < T, -1, dim > & matrix, word Name,
 /// @param[in] type      Format of the file: numpy (type="python"), matlab (type="matlab"), txt (type="eigen").
 /// @param[in] folder    Directory in which the file is saved.
 ///
-void exportMatrix(List <Eigen::MatrixXd>& matrix, word Name,
+void exportMatrix(List <Eigen::MatrixXd> & matrix, word Name,
                   word type = "python", word folder = "./Matrices");
 
 //--------------------------------------------------------------------------
@@ -163,7 +163,7 @@ void exportTensor(Eigen::Tensor<T, 3 > tensor, word Name,
 /// @tparam     GeoMesh     volMesh or surfaceMesh.
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
-void read_fields(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
+void read_fields(PtrList<GeometricField<Type, PatchField, GeoMesh>> &
                  Lfield, word Name,
                  fileName casename, int first_snap = 0, int n_snap = 0);
 
@@ -186,9 +186,9 @@ void read_fields(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
 /// @tparam     GeoMesh     volMesh or surfaceMesh.
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
-void read_fields(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
+void read_fields(PtrList<GeometricField<Type, PatchField, GeoMesh>> &
                  Lfield,
-                 GeometricField<Type, PatchField, GeoMesh>& field,
+                 GeometricField<Type, PatchField, GeoMesh> & field,
                  fileName casename, int first_snap = 0, int n_snap = 0);
 
 //----------------------------------------------------------------------
@@ -205,9 +205,9 @@ void read_fields(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
 /// @tparam     GeoMesh     volMesh or surfaceMesh.
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
-void readMiddleFields(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
+void readMiddleFields(PtrList<GeometricField<Type, PatchField, GeoMesh>> &
                       Lfield,
-                      GeometricField<Type, PatchField, GeoMesh>& field,
+                      GeometricField<Type, PatchField, GeoMesh> & field,
                       fileName casename);
 
 //----------------------------------------------------------------------
@@ -225,8 +225,8 @@ void readMiddleFields(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
 void readConvergedFields(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& Lfield,
-    GeometricField<Type, PatchField, GeoMesh>& field,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & Lfield,
+    GeometricField<Type, PatchField, GeoMesh> & field,
     fileName casename);
 
 //----------------------------------------------------------------------
@@ -243,10 +243,10 @@ void readConvergedFields(
 /// @tparam     GeoMesh     volMesh or surfaceMesh.
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
-void read_last_fields(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
-                 Lfield,
-                 const GeometricField<Type, PatchField, GeoMesh>& field,
-                 const fileName casename); 
+void read_last_fields(PtrList<GeometricField<Type, PatchField, GeoMesh>> &
+                      Lfield,
+                      const GeometricField<Type, PatchField, GeoMesh> & field,
+                      const fileName casename);
 
 //----------------------------------------------------------------------
 /// Funtion to read a list of volVectorField from name of the field including only the last snapshots
@@ -262,10 +262,10 @@ void read_last_fields(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
 /// @tparam     GeoMesh     volMesh or surfaceMesh.
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
-void readLastFields(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
-                      Lfield,
-                      const GeometricField<Type, PatchField, GeoMesh>& field,
-                      const fileName casename);
+void readLastFields(PtrList<GeometricField<Type, PatchField, GeoMesh>> &
+                    Lfield,
+                    const GeometricField<Type, PatchField, GeoMesh> & field,
+                    const fileName casename);
 
 //--------------------------------------------------------------------------
 /// Function to export a scalar of vector field
@@ -279,7 +279,7 @@ void readLastFields(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
 /// @tparam     GeoMesh     volMesh or surfaceMesh.
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
-void exportFields(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
+void exportFields(PtrList<GeometricField<Type, PatchField, GeoMesh>> &
                   field,
                   word folder, word fieldname);
 
@@ -320,7 +320,7 @@ List <Eigen::MatrixXd> readMatrix(word folder, word mat_name);
 /// @tparam     GeoMesh     volMesh or surfaceMesh.
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
-void exportSolution(GeometricField<Type, PatchField, GeoMesh>& s,
+void exportSolution(GeometricField<Type, PatchField, GeoMesh> & s,
                     fileName subfolder, fileName folder,
                     word fieldName);
 
@@ -336,7 +336,7 @@ void exportSolution(GeometricField<Type, PatchField, GeoMesh>& s,
 /// @tparam     GeoMesh     volMesh or surfaceMesh.
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
-void exportSolution(GeometricField<Type, PatchField, GeoMesh>& s,
+void exportSolution(GeometricField<Type, PatchField, GeoMesh> & s,
                     fileName subfolder, fileName folder);
 
 //--------------------------------------------------------------------------
@@ -364,7 +364,7 @@ void exportList(T& list, word folder, word filename);
 /// @tparam     IND         number of matrix cols
 ///
 template <typename T, int Nrows, typename IND>
-void SaveSparseMatrix(Eigen::SparseMatrix<T, Nrows, IND>& m,
+void SaveSparseMatrix(Eigen::SparseMatrix<T, Nrows, IND> & m,
                       word folder, word MatrixName);
 
 //--------------------------------------------------------------------------
@@ -379,7 +379,7 @@ void SaveSparseMatrix(Eigen::SparseMatrix<T, Nrows, IND>& m,
 /// @tparam     IND         number of matrix cols
 ///
 template <typename T, int Nrows, typename IND>
-void ReadSparseMatrix(Eigen::SparseMatrix<T, Nrows, IND>& m,
+void ReadSparseMatrix(Eigen::SparseMatrix<T, Nrows, IND> & m,
                       word folder, word MatrixName);
 
 //--------------------------------------------------------------------------
@@ -442,7 +442,7 @@ void ReadDenseTensor(TensorType& Tensor, word folder, word MatrixName);
 /// @tparam     MatrixType   MatrixType  type of the matrix, i.e. double, float, ...
 ///
 template <typename MatrixType>
-void SaveSparseMatrixList(List<MatrixType>& MatrixList, word folder,
+void SaveSparseMatrixList(List<MatrixType> & MatrixList, word folder,
                           word MatrixName);
 
 //--------------------------------------------------------------------------
@@ -457,7 +457,7 @@ void SaveSparseMatrixList(List<MatrixType>& MatrixList, word folder,
 /// @tparam     IND         number of matrix cols
 ///
 template <typename T, int Nrows, typename IND>
-void ReadSparseMatrixList(List<Eigen::SparseMatrix<T, Nrows, IND>>& m,
+void ReadSparseMatrixList(List<Eigen::SparseMatrix<T, Nrows, IND>> & m,
                           word folder, word MatrixName);
 
 //--------------------------------------------------------------------------
@@ -470,7 +470,7 @@ void ReadSparseMatrixList(List<Eigen::SparseMatrix<T, Nrows, IND>>& m,
 /// @tparam     MatrixType   MatrixType  type of the matrix, i.e. double, float, ...
 ///
 template <typename MatrixType>
-void SaveDenseMatrixList(List<MatrixType>& MatrixList, word folder,
+void SaveDenseMatrixList(List<MatrixType> & MatrixList, word folder,
                          word MatrixName);
 
 
@@ -484,7 +484,7 @@ void SaveDenseMatrixList(List<MatrixType>& MatrixList, word folder,
 /// @tparam     MatrixType   MatrixType  type of the matrix, i.e. double, float, ...
 ///
 template <typename MatrixType>
-void ReadDenseMatrixList(List<MatrixType>& m, word folder,
+void ReadDenseMatrixList(List<MatrixType> & m, word folder,
                          word MatrixName);
 
 //--------------------------------------------------------------------------
@@ -514,11 +514,11 @@ void writePoints(pointField points, fileName folder, fileName subfolder);
 void printProgress(double percentage);
 
 template<typename T>
-void save(const List<Eigen::SparseMatrix<T>>& MatrixList, word folder,
+void save(const List<Eigen::SparseMatrix<T>> & MatrixList, word folder,
           word MatrixName);
 
 template<typename T>
-void load(List<Eigen::SparseMatrix<T>>& MatrixList, word folder,
+void load(List<Eigen::SparseMatrix<T>> & MatrixList, word folder,
           word MatrixName);
 
 };
@@ -539,7 +539,7 @@ Istream& operator>> (Istream& is, Eigen::Matrix < T, -1, -1 > & mat)
     int nrow, ncol;
     is >> nrow >> ncol;
     mat.resize(nrow, ncol);
-    UList<T> list(mat.data(), nrow * ncol);
+    UList<T> list(mat.data(), nrow* ncol);
     is >> list;
     return is;
 }
@@ -558,13 +558,13 @@ Istream& operator>> (Istream& is, Eigen::Matrix < T, -1, 1 > & mat)
     int nrow, ncol;
     is >> nrow >> ncol;
     mat.resize(nrow, ncol);
-    UList<T> list(mat.data(), nrow * ncol);
+    UList<T> list(mat.data(), nrow* ncol);
     is >> list;
     return is;
 }
 
 template<typename T>
-Ostream& operator<< (Ostream& os, const Eigen::Tensor<T, 3>& tens)
+Ostream& operator<< (Ostream& os, const Eigen::Tensor<T, 3> & tens)
 {
     os << tens.dimension(0) << tens.dimension(1) << tens.dimension(
            2) << UList<T>(const_cast<Eigen::Tensor<T, 3>&>(tens).data(),
@@ -573,12 +573,12 @@ Ostream& operator<< (Ostream& os, const Eigen::Tensor<T, 3>& tens)
 }
 
 template<typename T>
-Istream& operator>> (Istream& is, Eigen::Tensor<T, 3>& tens)
+Istream& operator>> (Istream& is, Eigen::Tensor<T, 3> & tens)
 {
     int d1, d2, d3;
     is >> d1 >> d2 >> d3;
     tens.resize(d1, d2, d3);
-    UList<T> list(tens.data(), d1 * d2 * d3);
+    UList<T> list(tens.data(), d1* d2* d3);
     is >> list;
     return is;
 }
@@ -586,7 +586,7 @@ Istream& operator>> (Istream& is, Eigen::Tensor<T, 3>& tens)
 }
 
 template <typename T, int whatever, typename IND>
-void ITHACAstream::SaveSparseMatrix(Eigen::SparseMatrix<T, whatever, IND>& m,
+void ITHACAstream::SaveSparseMatrix(Eigen::SparseMatrix<T, whatever, IND> & m,
                                     word folder, word MatrixName)
 {
     typedef Eigen::Triplet<int> Trip;
@@ -604,11 +604,11 @@ void ITHACAstream::SaveSparseMatrix(Eigen::SparseMatrix<T, whatever, IND>& m,
         nnzs = m.nonZeros() ;
         outS = m.outerSize();
         innS = m.innerSize();
-        writeFile.write(reinterpret_cast<const char*> (&rows), sizeof(IND));
-        writeFile.write(reinterpret_cast<const char*> (&cols), sizeof(IND));
-        writeFile.write(reinterpret_cast<const char*> (&nnzs), sizeof(IND));
-        writeFile.write(reinterpret_cast<const char*> (&outS), sizeof(IND));
-        writeFile.write(reinterpret_cast<const char*> (&innS), sizeof(IND));
+        writeFile.write(reinterpret_cast<const char*> ( & rows), sizeof(IND));
+        writeFile.write(reinterpret_cast<const char*> ( & cols), sizeof(IND));
+        writeFile.write(reinterpret_cast<const char*> ( & nnzs), sizeof(IND));
+        writeFile.write(reinterpret_cast<const char*> ( & outS), sizeof(IND));
+        writeFile.write(reinterpret_cast<const char*> ( & innS), sizeof(IND));
         writeFile.write(reinterpret_cast<const char*>(m.valuePtr()),
                         sizeof(T  ) * m.nonZeros());
         writeFile.write(reinterpret_cast<const char*>(m.outerIndexPtr()),
@@ -620,7 +620,7 @@ void ITHACAstream::SaveSparseMatrix(Eigen::SparseMatrix<T, whatever, IND>& m,
 }
 
 template <typename T, int whatever, typename IND>
-void ITHACAstream::ReadSparseMatrix(Eigen::SparseMatrix<T, whatever, IND>& m,
+void ITHACAstream::ReadSparseMatrix(Eigen::SparseMatrix<T, whatever, IND> & m,
                                     word folder, word MatrixName)
 {
     std::fstream readFile;
@@ -635,11 +635,11 @@ void ITHACAstream::ReadSparseMatrix(Eigen::SparseMatrix<T, whatever, IND>& m,
     else if (readFile.is_open())
     {
         IND rows, cols, nnz, inSz, outSz;
-        readFile.read(reinterpret_cast<char*>(&rows ), sizeof(IND));
-        readFile.read(reinterpret_cast<char*>(&cols ), sizeof(IND));
-        readFile.read(reinterpret_cast<char*>(&nnz  ), sizeof(IND));
-        readFile.read(reinterpret_cast<char*>(&inSz ), sizeof(IND));
-        readFile.read(reinterpret_cast<char*>(&outSz), sizeof(IND));
+        readFile.read(reinterpret_cast<char*>( & rows ), sizeof(IND));
+        readFile.read(reinterpret_cast<char*>( & cols ), sizeof(IND));
+        readFile.read(reinterpret_cast<char*>( & nnz  ), sizeof(IND));
+        readFile.read(reinterpret_cast<char*>( & inSz ), sizeof(IND));
+        readFile.read(reinterpret_cast<char*>( & outSz), sizeof(IND));
         m.resize(rows, cols);
         m.makeCompressed();
         m.resizeNonZeros(nnz);
@@ -659,10 +659,12 @@ void ITHACAstream::SaveDenseMatrix(MatrixType& Matrix, word folder,
     std::ofstream out(folder + MatrixName,
                       std::ios::out | std::ios::binary | std::ios::trunc);
     typename MatrixType::Index rows = Matrix.rows(), cols = Matrix.cols();
-    out.write(reinterpret_cast<char*> (&rows), sizeof(typename MatrixType::Index));
-    out.write(reinterpret_cast<char*> (&cols), sizeof(typename MatrixType::Index));
+    out.write(reinterpret_cast<char*> ( & rows),
+              sizeof(typename MatrixType::Index));
+    out.write(reinterpret_cast<char*> ( & cols),
+              sizeof(typename MatrixType::Index));
     out.write(reinterpret_cast<char*> (Matrix.data()),
-              rows * cols * sizeof(typename MatrixType::Scalar) );
+              rows* cols* sizeof(typename MatrixType::Scalar) );
     out.close();
 }
 
@@ -682,11 +684,11 @@ void ITHACAstream::ReadDenseMatrix(MatrixType& Matrix, word folder,
     else if (in.is_open())
     {
         typename MatrixType::Index rows = 0, cols = 0;
-        in.read(reinterpret_cast<char*> (&rows), sizeof(typename MatrixType::Index));
-        in.read(reinterpret_cast<char*> (&cols), sizeof(typename MatrixType::Index));
+        in.read(reinterpret_cast<char*> ( & rows), sizeof(typename MatrixType::Index));
+        in.read(reinterpret_cast<char*> ( & cols), sizeof(typename MatrixType::Index));
         Matrix.resize(rows, cols);
         in.read( reinterpret_cast<char*>(Matrix.data()),
-                 rows * cols * sizeof(typename MatrixType::Scalar) );
+                 rows* cols* sizeof(typename MatrixType::Scalar) );
         in.close();
     }
 }
@@ -706,10 +708,10 @@ void ITHACAstream::SaveDenseTensor(TensorType& Tensor, word folder,
         tot *= dim[k];
     }
 
-    out.write(reinterpret_cast<char*> (&dim),
+    out.write(reinterpret_cast<char*> ( & dim),
               sizeof(typename TensorType::Dimensions));
     out.write(reinterpret_cast<char*> (Tensor.data()),
-              tot * sizeof(typename TensorType::Scalar) );
+              tot* sizeof(typename TensorType::Scalar) );
     out.close();
 }
 
@@ -720,7 +722,7 @@ void ITHACAstream::ReadDenseTensor(TensorType& Tensor, word folder,
     std::ifstream in;
     in.open(folder + MatrixName, std::ios::in | std::ios::binary);
     typename TensorType::Dimensions dim;
-    in.read(reinterpret_cast<char*> (&dim),
+    in.read(reinterpret_cast<char*> ( & dim),
             sizeof(typename TensorType::Dimensions));
     auto dims = Tensor.dimensions();
     M_Assert(dims.size() == dim.size(),
@@ -734,12 +736,12 @@ void ITHACAstream::ReadDenseTensor(TensorType& Tensor, word folder,
 
     Tensor.resize(dim);
     in.read( reinterpret_cast<char*>(Tensor.data()),
-             tot * sizeof(typename TensorType::Scalar) );
+             tot* sizeof(typename TensorType::Scalar) );
     in.close();
 }
 
 template <typename MatrixType>
-void ITHACAstream::SaveSparseMatrixList(List<MatrixType>& MatrixList,
+void ITHACAstream::SaveSparseMatrixList(List<MatrixType> & MatrixList,
                                         word folder, word MatrixName)
 {
     for (int i = 0; i < MatrixList.size(); i++)
@@ -749,7 +751,7 @@ void ITHACAstream::SaveSparseMatrixList(List<MatrixType>& MatrixList,
 }
 
 template <typename MatrixType>
-void ITHACAstream::SaveDenseMatrixList(List<MatrixType>& MatrixList,
+void ITHACAstream::SaveDenseMatrixList(List<MatrixType> & MatrixList,
                                        word folder, word MatrixName)
 {
     for (int i = 0; i < MatrixList.size(); i++)
@@ -760,7 +762,7 @@ void ITHACAstream::SaveDenseMatrixList(List<MatrixType>& MatrixList,
 
 template <typename T, int whatever, typename IND>
 void ITHACAstream::ReadSparseMatrixList(
-    List<Eigen::SparseMatrix<T, whatever, IND>>& m, word folder, word MatrixName)
+    List<Eigen::SparseMatrix<T, whatever, IND>> & m, word folder, word MatrixName)
 {
     int number_of_files = numberOfFiles(folder, MatrixName);
     std::cout << "Reading the Matrix " + folder + MatrixName << std::endl;
@@ -777,7 +779,7 @@ void ITHACAstream::ReadSparseMatrixList(
 
 
 template <typename MatrixType>
-void ITHACAstream::ReadDenseMatrixList(List<MatrixType>& m, word folder,
+void ITHACAstream::ReadDenseMatrixList(List<MatrixType> & m, word folder,
                                        word MatrixName)
 {
     int number_of_files = numberOfFiles(folder, MatrixName);
diff --git a/src/ITHACA_CORE/ITHACAstream/cnpy.C b/src/ITHACA_CORE/ITHACAstream/cnpy.C
index 5616aa3c1..b36412f5b 100644
--- a/src/ITHACA_CORE/ITHACAstream/cnpy.C
+++ b/src/ITHACA_CORE/ITHACAstream/cnpy.C
@@ -15,7 +15,7 @@
 char cnpy::BigEndianTest()
 {
     int x = 1;
-    return (((char*)&x)[0]) ? '<' : '>';
+    return (((char*) & x)[0]) ? '<' : '>';
 }
 
 char cnpy::map_type(const std::type_info& t)
@@ -110,15 +110,15 @@ char cnpy::map_type(const std::type_info& t)
     }
 }
 
-template<> std::vector<char>& cnpy::operator+=(std::vector<char>& lhs,
-        const std::string rhs)
+template<> std::vector<char> & cnpy::operator+=(std::vector<char> & lhs,
+    const std::string rhs)
 {
     lhs.insert(lhs.end(), rhs.begin(), rhs.end());
     return lhs;
 }
 
-template<> std::vector<char>& cnpy::operator+=(std::vector<char>& lhs,
-        const char* rhs)
+template<> std::vector<char> & cnpy::operator+=(std::vector<char> & lhs,
+    const char* rhs)
 {
     //write in little endian
     size_t len = strlen(rhs);
@@ -133,12 +133,12 @@ template<> std::vector<char>& cnpy::operator+=(std::vector<char>& lhs,
 }
 
 void cnpy::parse_npy_header(unsigned char* buffer, size_t& word_size,
-                            std::vector<size_t>& shape, bool& fortran_order, std::string& number_type)
+                            std::vector<size_t> & shape, bool& fortran_order, std::string& number_type)
 {
     //std::string magic_string(buffer,6);
-    uint8_t major_version = *reinterpret_cast<uint8_t*>(buffer + 6);
-    uint8_t minor_version = *reinterpret_cast<uint8_t*>(buffer + 7);
-    uint16_t header_len = *reinterpret_cast<uint16_t*>(buffer + 8);
+    uint8_t major_version = * reinterpret_cast<uint8_t*>(buffer + 6);
+    uint8_t minor_version = * reinterpret_cast<uint8_t*>(buffer + 7);
+    uint16_t header_len = * reinterpret_cast<uint16_t*>(buffer + 8);
     std::string header(reinterpret_cast<char*>(buffer + 9), header_len);
     size_t loc1, loc2;
     //fortran order
@@ -173,7 +173,7 @@ void cnpy::parse_npy_header(unsigned char* buffer, size_t& word_size,
 }
 
 void cnpy::parse_npy_header(FILE* fp, size_t& word_size,
-                            std::vector<size_t>& shape, bool& fortran_order, std::string& number_type)
+                            std::vector<size_t> & shape, bool& fortran_order, std::string& number_type)
 {
     char buffer[256];
     size_t res = fread(buffer, sizeof(char), 11, fp);
@@ -242,7 +242,7 @@ void cnpy::parse_zip_footer(FILE* fp, uint16_t& nrecs,
 {
     std::vector<char> footer(22);
     fseek(fp, -22, SEEK_END);
-    size_t res = fread(&footer[0], sizeof(char), 22, fp);
+    size_t res = fread( & footer[0], sizeof(char), 22, fp);
 
     if (res != 22)
     {
@@ -250,13 +250,13 @@ void cnpy::parse_zip_footer(FILE* fp, uint16_t& nrecs,
     }
 
     uint16_t disk_no, disk_start, nrecs_on_disk, comment_len;
-    disk_no = *(uint16_t*) &footer[4];
-    disk_start = *(uint16_t*) &footer[6];
-    nrecs_on_disk = *(uint16_t*) &footer[8];
-    nrecs = *(uint16_t*) &footer[10];
-    global_header_size = *(uint32_t*) &footer[12];
-    global_header_offset = *(uint32_t*) &footer[16];
-    comment_len = *(uint16_t*) &footer[20];
+    disk_no = * (uint16_t*) & footer[4];
+    disk_start = * (uint16_t*) & footer[6];
+    nrecs_on_disk = * (uint16_t*) & footer[8];
+    nrecs = * (uint16_t*) & footer[10];
+    global_header_size = * (uint32_t*) & footer[12];
+    global_header_offset = * (uint32_t*) & footer[16];
+    comment_len = * (uint16_t*) & footer[20];
     assert(disk_no == 0);
     assert(disk_start == 0);
     assert(nrecs_on_disk == nrecs);
@@ -292,7 +292,7 @@ cnpy::NpyArray load_the_npz_array(FILE* fp, uint32_t compr_bytes,
 {
     std::vector<unsigned char> buffer_compr(compr_bytes);
     std::vector<unsigned char> buffer_uncompr(uncompr_bytes);
-    size_t nread = fread(&buffer_compr[0], 1, compr_bytes, fp);
+    size_t nread = fread( & buffer_compr[0], 1, compr_bytes, fp);
 
     if (nread != compr_bytes)
     {
@@ -306,22 +306,22 @@ cnpy::NpyArray load_the_npz_array(FILE* fp, uint32_t compr_bytes,
     d_stream.opaque = Z_NULL;
     d_stream.avail_in = 0;
     d_stream.next_in = Z_NULL;
-    err = inflateInit2(&d_stream, -MAX_WBITS);
+    err = inflateInit2( & d_stream, -MAX_WBITS);
     d_stream.avail_in = compr_bytes;
-    d_stream.next_in = &buffer_compr[0];
+    d_stream.next_in = & buffer_compr[0];
     d_stream.avail_out = uncompr_bytes;
-    d_stream.next_out = &buffer_uncompr[0];
-    err = inflate(&d_stream, Z_FINISH);
-    err = inflateEnd(&d_stream);
+    d_stream.next_out = & buffer_uncompr[0];
+    err = inflate( & d_stream, Z_FINISH);
+    err = inflateEnd( & d_stream);
     std::vector<size_t> shape;
     size_t word_size;
     bool fortran_order;
     std::string number_type;
-    cnpy::parse_npy_header(&buffer_uncompr[0], word_size, shape, fortran_order,
-                           number_type);
+    cnpy::parse_npy_header( & buffer_uncompr[0], word_size, shape, fortran_order,
+                            number_type);
     cnpy::NpyArray array(shape, word_size, fortran_order, number_type);
     size_t offset = uncompr_bytes - array.num_bytes();
-    memcpy(array.data<unsigned char>(), &buffer_uncompr[0] + offset,
+    memcpy(array.data<unsigned char>(), & buffer_uncompr[0] + offset,
            array.num_bytes());
     return array;
 }
@@ -340,7 +340,7 @@ cnpy::npz_t cnpy::npz_load(std::string fname)
     while (1)
     {
         std::vector<char> local_header(30);
-        size_t headerres = fread(&local_header[0], sizeof(char), 30, fp);
+        size_t headerres = fread( & local_header[0], sizeof(char), 30, fp);
 
         if (headerres != 30)
         {
@@ -354,9 +354,9 @@ cnpy::npz_t cnpy::npz_load(std::string fname)
         }
 
         //read in the variable name
-        uint16_t name_len = *(uint16_t*) &local_header[26];
+        uint16_t name_len = * (uint16_t*) & local_header[26];
         std::string varname(name_len, ' ');
-        size_t vname_res = fread(&varname[0], sizeof(char), name_len, fp);
+        size_t vname_res = fread( & varname[0], sizeof(char), name_len, fp);
 
         if (vname_res != name_len)
         {
@@ -366,12 +366,12 @@ cnpy::npz_t cnpy::npz_load(std::string fname)
         //erase the lagging .npy
         varname.erase(varname.end() - 4, varname.end());
         //read in the extra field
-        uint16_t extra_field_len = *(uint16_t*) &local_header[28];
+        uint16_t extra_field_len = * (uint16_t*) & local_header[28];
 
         if (extra_field_len > 0)
         {
             std::vector<char> buff(extra_field_len);
-            size_t efield_res = fread(&buff[0], sizeof(char), extra_field_len, fp);
+            size_t efield_res = fread( & buff[0], sizeof(char), extra_field_len, fp);
 
             if (efield_res != extra_field_len)
             {
@@ -379,9 +379,9 @@ cnpy::npz_t cnpy::npz_load(std::string fname)
             }
         }
 
-        uint16_t compr_method = *reinterpret_cast<uint16_t*>(&local_header[0] + 8);
-        uint32_t compr_bytes = *reinterpret_cast<uint32_t*>(&local_header[0] + 18);
-        uint32_t uncompr_bytes = *reinterpret_cast<uint32_t*>(&local_header[0] + 22);
+        uint16_t compr_method = * reinterpret_cast<uint16_t*>( & local_header[0] + 8);
+        uint32_t compr_bytes = * reinterpret_cast<uint32_t*>( & local_header[0] + 18);
+        uint32_t uncompr_bytes = * reinterpret_cast<uint32_t*>( & local_header[0] + 22);
 
         if (compr_method == 0)
         {
@@ -409,7 +409,7 @@ cnpy::NpyArray cnpy::npz_load(std::string fname, std::string varname)
     while (1)
     {
         std::vector<char> local_header(30);
-        size_t header_res = fread(&local_header[0], sizeof(char), 30, fp);
+        size_t header_res = fread( & local_header[0], sizeof(char), 30, fp);
 
         if (header_res != 30)
         {
@@ -423,9 +423,9 @@ cnpy::NpyArray cnpy::npz_load(std::string fname, std::string varname)
         }
 
         //read in the variable name
-        uint16_t name_len = *(uint16_t*) &local_header[26];
+        uint16_t name_len = * (uint16_t*) & local_header[26];
         std::string vname(name_len, ' ');
-        size_t vname_res = fread(&vname[0], sizeof(char), name_len, fp);
+        size_t vname_res = fread( & vname[0], sizeof(char), name_len, fp);
 
         if (vname_res != name_len)
         {
@@ -434,11 +434,11 @@ cnpy::NpyArray cnpy::npz_load(std::string fname, std::string varname)
 
         vname.erase(vname.end() - 4, vname.end()); //erase the lagging .npy
         //read in the extra field
-        uint16_t extra_field_len = *(uint16_t*) &local_header[28];
+        uint16_t extra_field_len = * (uint16_t*) & local_header[28];
         fseek(fp, extra_field_len, SEEK_CUR); //skip past the extra field
-        uint16_t compr_method = *reinterpret_cast<uint16_t*>(&local_header[0] + 8);
-        uint32_t compr_bytes = *reinterpret_cast<uint32_t*>(&local_header[0] + 18);
-        uint32_t uncompr_bytes = *reinterpret_cast<uint32_t*>(&local_header[0] + 22);
+        uint16_t compr_method = * reinterpret_cast<uint16_t*>( & local_header[0] + 8);
+        uint32_t compr_bytes = * reinterpret_cast<uint32_t*>( & local_header[0] + 18);
+        uint32_t uncompr_bytes = * reinterpret_cast<uint32_t*>( & local_header[0] + 22);
 
         if (vname == varname)
         {
@@ -450,7 +450,7 @@ cnpy::NpyArray cnpy::npz_load(std::string fname, std::string varname)
         else
         {
             //skip past the data
-            uint32_t size = *(uint32_t*) &local_header[22];
+            uint32_t size = * (uint32_t*) & local_header[22];
             fseek(fp, size, SEEK_CUR);
         }
     }
@@ -476,7 +476,7 @@ cnpy::NpyArray cnpy::npy_load(std::string fname)
 }
 
 template<class typeNumber, int dim>
-void cnpy::save(const Eigen::Matrix<typeNumber, Eigen::Dynamic, dim>&
+void cnpy::save(const Eigen::Matrix<typeNumber, Eigen::Dynamic, dim> &
                 mat, const std::string fname)
 {
     std::vector<typeNumber> matvec(mat.rows() * mat.cols());
@@ -486,7 +486,7 @@ void cnpy::save(const Eigen::Matrix<typeNumber, Eigen::Dynamic, dim>&
     {
         for (int j = 0; j < mat.cols(); ++j)
         {
-            matvec[i * mat.cols() + j] = mat(i, j);
+            matvec[i* mat.cols() + j] = mat(i, j);
         }
     }
 
@@ -494,7 +494,7 @@ void cnpy::save(const Eigen::Matrix<typeNumber, Eigen::Dynamic, dim>&
 }
 
 template<class typeNumber>
-void cnpy::save(const Eigen::Tensor<typeNumber, 3>&
+void cnpy::save(const Eigen::Tensor<typeNumber, 3> &
                 tens, const std::string fname)
 {
     typename Eigen::Tensor<typeNumber, 3>::Dimensions dim = tens.dimensions();
@@ -514,7 +514,7 @@ void cnpy::save(const Eigen::Tensor<typeNumber, 3>&
         {
             for (int k = 0; k < dim[2]; ++k)
             {
-                matvec[i * dim[2]*dim[1] + j * dim[2] + k] = tens(i, j, k);
+                matvec[i* dim[2] * dim[1] + j* dim[2] + k] = tens(i, j, k);
             }
         }
     }
@@ -524,7 +524,7 @@ void cnpy::save(const Eigen::Tensor<typeNumber, 3>&
 
 template<class typeNumber, int dim>
 Eigen::Matrix<typeNumber, Eigen::Dynamic, dim> cnpy::load(
-    Eigen::Matrix<typeNumber, Eigen::Dynamic, dim>& mat,
+    Eigen::Matrix<typeNumber, Eigen::Dynamic, dim> & mat,
     const std::string fname, std::string order)
 {
     M_Assert(order == "rowMajor" ||
@@ -560,7 +560,7 @@ Eigen::Matrix<typeNumber, Eigen::Dynamic, dim> cnpy::load(
 }
 
 template<typename typeNumber>
-Eigen::Tensor<typeNumber, 3> cnpy::load(Eigen::Tensor<typeNumber, 3>& tens,
+Eigen::Tensor<typeNumber, 3> cnpy::load(Eigen::Tensor<typeNumber, 3> & tens,
                                         const std::string fname, std::string order)
 {
     M_Assert(order == "rowMajor" ||
@@ -579,8 +579,8 @@ Eigen::Tensor<typeNumber, 3> cnpy::load(Eigen::Tensor<typeNumber, 3>& tens,
             {
                 for (size_t k = 0; k < arr.shape[2]; ++k)
                 {
-                    tens(i, j, k) = data[arr.shape[1] * arr.shape[2] * i + j *
-                                                      arr.shape[2] + k];
+                    tens(i, j, k) = data[arr.shape[1] * arr.shape[2] * i + j*
+                                         arr.shape[2] + k];
                 }
             }
         }
@@ -593,8 +593,8 @@ Eigen::Tensor<typeNumber, 3> cnpy::load(Eigen::Tensor<typeNumber, 3>& tens,
             {
                 for (size_t k = 0; k < arr.shape[2]; ++k)
                 {
-                    tens(i, j, k) = (typeNumber) data[arr.shape[0] * arr.shape[1] * k + j *
-                                                                   arr.shape[0] + i];
+                    tens(i, j, k) = (typeNumber) data[arr.shape[0] * arr.shape[1] * k + j*
+                                                      arr.shape[0] + i];
                 }
             }
         }
@@ -605,7 +605,7 @@ Eigen::Tensor<typeNumber, 3> cnpy::load(Eigen::Tensor<typeNumber, 3>& tens,
 }
 
 template<typename T>
-Eigen::SparseMatrix<T> cnpy::load(Eigen::SparseMatrix<T>& smatrix,
+Eigen::SparseMatrix<T> cnpy::load(Eigen::SparseMatrix<T> & smatrix,
                                   const std::string fname)
 {
     auto d1 = cnpy::npz_load(fname, "data");
@@ -639,7 +639,7 @@ Eigen::SparseMatrix<T> cnpy::load(Eigen::SparseMatrix<T>& smatrix,
 }
 
 template<typename T>
-void cnpy::save(const Eigen::SparseMatrix<T>& mat, const std::string fname)
+void cnpy::save(const Eigen::SparseMatrix<T> & mat, const std::string fname)
 {
     std::vector<size_t> shape1 = std::vector<size_t> {(unsigned long) (mat.nonZeros())};
     std::vector<size_t> shape2 = std::vector<size_t> {(unsigned long) (mat.outerSize() + 1)};
@@ -655,7 +655,7 @@ void cnpy::save(const Eigen::SparseMatrix<T>& mat, const std::string fname)
     shape[1] = mat.cols();
     cnpy::npz_save(fname, "shape", shape, shape3, "a");
     char myVar2 = 'abc';
-    cnpy::npz_save(fname, "format", &myVar2, shape4, "a");
+    cnpy::npz_save(fname, "format", & myVar2, shape4, "a");
 }
 
 template void cnpy::save(const Eigen::MatrixXi& mat, const std::string fname);
@@ -682,26 +682,26 @@ template Eigen::VectorXf cnpy::load(Eigen::VectorXf& mat,
 template void cnpy::save(const Eigen::VectorXcd& mat, const std::string fname);
 template Eigen::VectorXcd cnpy::load(Eigen::VectorXcd& mat,
                                      const std::string fname, std::string order);
-template void cnpy::save(const Eigen::SparseMatrix<double>& mat,
+template void cnpy::save(const Eigen::SparseMatrix<double> & mat,
                          const std::string fname);
-template Eigen::SparseMatrix<double> cnpy::load(Eigen::SparseMatrix<double>&
+template Eigen::SparseMatrix<double> cnpy::load(Eigen::SparseMatrix<double> &
         smatrix, const std::string fname);
 
-template void cnpy::save(const Eigen::Tensor<int, 3>& mat,
+template void cnpy::save(const Eigen::Tensor<int, 3> & mat,
                          const std::string fname);
-template Eigen::Tensor<int, 3> cnpy::load(Eigen::Tensor<int, 3>& tens,
+template Eigen::Tensor<int, 3> cnpy::load(Eigen::Tensor<int, 3> & tens,
         const std::string fname, std::string order);
-template void cnpy::save(const Eigen::Tensor<double, 3>& mat,
+template void cnpy::save(const Eigen::Tensor<double, 3> & mat,
                          const std::string fname);
-template Eigen::Tensor<double, 3> cnpy::load(Eigen::Tensor<double, 3>& tens,
+template Eigen::Tensor<double, 3> cnpy::load(Eigen::Tensor<double, 3> & tens,
         const std::string fname, std::string order);
-template void cnpy::save(const Eigen::Tensor<float, 3>& mat,
+template void cnpy::save(const Eigen::Tensor<float, 3> & mat,
                          const std::string fname);
-template Eigen::Tensor<float, 3> cnpy::load(Eigen::Tensor<float, 3>& tens,
+template Eigen::Tensor<float, 3> cnpy::load(Eigen::Tensor<float, 3> & tens,
         const std::string fname, std::string order);
-template void cnpy::save(const Eigen::Tensor<std::complex<double>, 3>& mat,
+template void cnpy::save(const Eigen::Tensor<std::complex<double>, 3> & mat,
                          const std::string fname);
 template Eigen::Tensor<std::complex<double>, 3> cnpy::load(
-    Eigen::Tensor<std::complex<double>, 3>& tens,
+    Eigen::Tensor<std::complex<double>, 3> & tens,
     const std::string fname, std::string order);
 #pragma GCC diagnostic pop
diff --git a/src/ITHACA_CORE/ITHACAstream/cnpy.H b/src/ITHACA_CORE/ITHACAstream/cnpy.H
index 812523af1..1db740cfe 100644
--- a/src/ITHACA_CORE/ITHACAstream/cnpy.H
+++ b/src/ITHACA_CORE/ITHACAstream/cnpy.H
@@ -30,7 +30,7 @@ namespace cnpy
 
 struct NpyArray
 {
-    NpyArray(const std::vector<size_t>& _shape, size_t _word_size,
+    NpyArray(const std::vector<size_t> & _shape, size_t _word_size,
              bool _fortran_order, std::string _number_type) :
         shape(_shape), word_size(_word_size), fortran_order(_fortran_order),
         number_type(_number_type)
@@ -43,7 +43,7 @@ struct NpyArray
         }
 
         data_holder = std::shared_ptr<std::vector<char>>(
-                          new std::vector<char>(num_vals * word_size));
+                          new std::vector<char>(num_vals* word_size));
     }
 
     NpyArray() : shape(0), word_size(0), fortran_order(0), num_vals(0) { }
@@ -51,13 +51,13 @@ struct NpyArray
     template<typename T>
     T* data()
     {
-        return reinterpret_cast<T*>(&(*data_holder)[0]);
+        return reinterpret_cast<T*>( & ( * data_holder)[0]);
     }
 
     template<typename T>
     const T* data() const
     {
-        return reinterpret_cast<T*>(&(*data_holder)[0]);
+        return reinterpret_cast<T*>( & ( * data_holder)[0]);
     }
 
     template<typename T>
@@ -165,34 +165,34 @@ using npz_t = std::map<std::string, NpyArray>;
 char BigEndianTest();
 char map_type(const std::type_info& t);
 template<typename T> std::vector<char> create_npy_header(
-    const std::vector<size_t>& shape);
-void parse_npy_header(FILE* fp, size_t& word_size, std::vector<size_t>& shape,
+    const std::vector<size_t> & shape);
+void parse_npy_header(FILE* fp, size_t& word_size, std::vector<size_t> & shape,
                       bool& fortran_order, std::string& number_type);
 void parse_npy_header(unsigned char* buffer, size_t& word_size,
-                      std::vector<size_t>& shape, bool& fortran_order, std::string& number_type);
+                      std::vector<size_t> & shape, bool& fortran_order, std::string& number_type);
 void parse_zip_footer(FILE* fp, uint16_t& nrecs, size_t& global_header_size,
                       size_t& global_header_offset);
 npz_t npz_load(std::string fname);
 NpyArray npz_load(std::string fname, std::string varname);
 NpyArray npy_load(std::string fname);
 
-template<typename T> std::vector<char>& operator+=(std::vector<char>& lhs,
-        const T rhs)
+template<typename T> std::vector<char> & operator+=(std::vector<char> & lhs,
+    const T rhs)
 {
     //write in little endian
     for (size_t byte = 0; byte < sizeof(T); byte++)
     {
-        char val = *((char*)&rhs + byte);
+        char val = * ((char*) & rhs + byte);
         lhs.push_back(val);
     }
 
     return lhs;
 }
 
-template<> std::vector<char>& operator+=(std::vector<char>& lhs,
-        const std::string rhs);
-template<> std::vector<char>& operator+=(std::vector<char>& lhs,
-        const char* rhs);
+template<> std::vector<char> & operator+=(std::vector<char> & lhs,
+    const std::string rhs);
+template<> std::vector<char> & operator+=(std::vector<char> & lhs,
+    const char* rhs);
 
 
 template<typename T> void npy_save(std::string fname, const T* data,
@@ -253,14 +253,14 @@ template<typename T> void npy_save(std::string fname, const T* data,
     size_t nels = std::accumulate(shape.begin(), shape.end(), 1,
                                   std::multiplies<size_t>());
     fseek(fp, 0, SEEK_SET);
-    fwrite(&header[0], sizeof(char), header.size(), fp);
+    fwrite( & header[0], sizeof(char), header.size(), fp);
     fseek(fp, 0, SEEK_END);
     fwrite(data, sizeof(T), nels, fp);
     fclose(fp);
 }
 
 template<typename T> void npz_save(std::string zipname, std::string fname,
-                                   const T* data, const std::vector<size_t>& shape, std::string mode = "w")
+                                   const T* data, const std::vector<size_t> & shape, std::string mode = "w")
 {
     //first, append a .npy to the fname
     fname += ".npy";
@@ -285,7 +285,7 @@ template<typename T> void npz_save(std::string zipname, std::string fname,
         parse_zip_footer(fp, nrecs, global_header_size, global_header_offset);
         fseek(fp, global_header_offset, SEEK_SET);
         global_header.resize(global_header_size);
-        size_t res = fread(&global_header[0], sizeof(char), global_header_size, fp);
+        size_t res = fread( & global_header[0], sizeof(char), global_header_size, fp);
 
         if (res != global_header_size)
         {
@@ -302,10 +302,10 @@ template<typename T> void npz_save(std::string zipname, std::string fname,
     std::vector<char> npy_header = create_npy_header<T>(shape);
     size_t nels = std::accumulate(shape.begin(), shape.end(), 1,
                                   std::multiplies<size_t>());
-    size_t nbytes = nels * sizeof(T) + npy_header.size();
+    size_t nbytes = nels* sizeof(T) + npy_header.size();
     //get the CRC of the data to be added
-    uint32_t crc = crc32(0L, (uint8_t*)&npy_header[0], npy_header.size());
-    crc = crc32(crc, (uint8_t*)data, nels * sizeof(T));
+    uint32_t crc = crc32(0L, (uint8_t*) & npy_header[0], npy_header.size());
+    crc = crc32(crc, (uint8_t*)data, nels* sizeof(T));
     //build the local header
     std::vector<char> local_header;
     local_header += "PK"; //first part of sig
@@ -347,11 +347,11 @@ template<typename T> void npz_save(std::string zipname, std::string fname,
                           local_header.size()); //offset of start of global headers, since global header now starts after newly written array
     footer += (uint16_t) 0; //zip file comment length
     //write everything
-    fwrite(&local_header[0], sizeof(char), local_header.size(), fp);
-    fwrite(&npy_header[0], sizeof(char), npy_header.size(), fp);
+    fwrite( & local_header[0], sizeof(char), local_header.size(), fp);
+    fwrite( & npy_header[0], sizeof(char), npy_header.size(), fp);
     fwrite(data, sizeof(T), nels, fp);
-    fwrite(&global_header[0], sizeof(char), global_header.size(), fp);
-    fwrite(&footer[0], sizeof(char), footer.size(), fp);
+    fwrite( & global_header[0], sizeof(char), global_header.size(), fp);
+    fwrite( & footer[0], sizeof(char), footer.size(), fp);
     fclose(fp);
 }
 
@@ -360,7 +360,7 @@ template<typename T> void npy_save(std::string fname, const std::vector<T> data,
 {
     std::vector<size_t> shape;
     shape.push_back(data.size());
-    npy_save(fname, &data[0], shape, mode);
+    npy_save(fname, & data[0], shape, mode);
 }
 
 template<typename T> void npz_save(std::string zipname, std::string fname,
@@ -368,11 +368,11 @@ template<typename T> void npz_save(std::string zipname, std::string fname,
 {
     std::vector<size_t> shape;
     shape.push_back(data.size());
-    npz_save(zipname, fname, &data[0], shape, mode);
+    npz_save(zipname, fname, & data[0], shape, mode);
 }
 
 template<typename T> std::vector<char> create_npy_header(
-    const std::vector<size_t>& shape)
+    const std::vector<size_t> & shape)
 {
     std::vector<char> dict;
     dict += "{'descr': '";
@@ -413,21 +413,21 @@ Eigen::Matrix < T, -1, dim > load(Eigen::Matrix < T, -1, dim > & mat,
                                   const std::string fname, std::string order = "rowMajor");
 
 template<typename T>
-Eigen::SparseMatrix<T> load(Eigen::SparseMatrix<T>& mat,
+Eigen::SparseMatrix<T> load(Eigen::SparseMatrix<T> & mat,
                             const std::string fname);
 
 template<typename T>
-Eigen::Tensor<T, 3> load(Eigen::Tensor<T, 3>& tens,
+Eigen::Tensor<T, 3> load(Eigen::Tensor<T, 3> & tens,
                          const std::string fname, std::string order = "rowMajor");
 
 template<typename T, int dim>
 void save(const Eigen::Matrix < T, -1, dim > & mat, const std::string fname);
 
 template<typename T>
-void save(const Eigen::Tensor<T, 3>& tensor, const std::string fname);
+void save(const Eigen::Tensor<T, 3> & tensor, const std::string fname);
 
 template<typename T>
-void save(const Eigen::SparseMatrix<T>& mat, const std::string fname);
+void save(const Eigen::SparseMatrix<T> & mat, const std::string fname);
 
 cnpy::NpyArray load_the_npy_file(FILE* fp);
 cnpy::NpyArray load_the_npy_file(std::string fname);
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAassign.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAassign.C
index 0c22bc7b8..acc0cb789 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAassign.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAassign.C
@@ -29,7 +29,7 @@ namespace ITHACAutilities
 
 template<class TypeField>
 PtrList<TypeField> averageSubtract(PtrList<TypeField>
-                                   fields, Eigen::MatrixXd ind, PtrList<TypeField>& ave)
+                                   fields, Eigen::MatrixXd ind, PtrList<TypeField> & ave)
 {
     PtrList<TypeField> aveSubtracted;
     Eigen::VectorXd newInd;
@@ -65,13 +65,13 @@ PtrList<TypeField> averageSubtract(PtrList<TypeField>
 
 template PtrList<volScalarField> averageSubtract(
     PtrList<volScalarField>
-    fields, Eigen::MatrixXd ind, PtrList<volScalarField>& ave);
+    fields, Eigen::MatrixXd ind, PtrList<volScalarField> & ave);
 template PtrList<volVectorField> averageSubtract(
     PtrList<volVectorField>
-    fields, Eigen::MatrixXd ind, PtrList<volVectorField>& ave);
+    fields, Eigen::MatrixXd ind, PtrList<volVectorField> & ave);
 
 template<class TypeField>
-TypeField computeAverage(PtrList<TypeField>& fields)
+TypeField computeAverage(PtrList<TypeField> & fields)
 {
     TypeField av(fields[0]);
 
@@ -85,13 +85,13 @@ TypeField computeAverage(PtrList<TypeField>& fields)
 }
 
 template volVectorField computeAverage(
-    PtrList<volVectorField>& fields);
+    PtrList<volVectorField> & fields);
 template volScalarField computeAverage(
-    PtrList<volScalarField>& fields);
+    PtrList<volScalarField> & fields);
 
 
 template<typename Type>
-void assignIF(GeometricField<Type, fvPatchField, volMesh>& s,
+void assignIF(GeometricField<Type, fvPatchField, volMesh> & s,
               Type value)
 {
     for (label i = 0; i < s.internalField().size(); i++)
@@ -101,13 +101,13 @@ void assignIF(GeometricField<Type, fvPatchField, volMesh>& s,
 }
 
 template void assignIF(
-    GeometricField<scalar, fvPatchField, volMesh>& field, scalar value);
+    GeometricField<scalar, fvPatchField, volMesh> & field, scalar value);
 template void assignIF(
-    GeometricField<vector, fvPatchField, volMesh>& field, vector value);
+    GeometricField<vector, fvPatchField, volMesh> & field, vector value);
 
 template<typename Type>
-void assignIF(GeometricField<Type, fvPatchField, volMesh>& s,
-              Type& value, List<label>& indices)
+void assignIF(GeometricField<Type, fvPatchField, volMesh> & s,
+              Type& value, List<label> & indices)
 {
     for (label i = 0; i < indices.size(); i++)
     {
@@ -115,24 +115,24 @@ void assignIF(GeometricField<Type, fvPatchField, volMesh>& s,
     }
 }
 
-template void assignIF(GeometricField<scalar, fvPatchField, volMesh>& s,
-                       scalar& value, List<label>& indices);
-template void assignIF(GeometricField<vector, fvPatchField, volMesh>& s,
-                       vector& value, List<label>& indices);
+template void assignIF(GeometricField<scalar, fvPatchField, volMesh> & s,
+                       scalar& value, List<label> & indices);
+template void assignIF(GeometricField<vector, fvPatchField, volMesh> & s,
+                       vector& value, List<label> & indices);
 
 template<typename Type>
-void assignIF(GeometricField<Type, fvPatchField, volMesh>& s,
+void assignIF(GeometricField<Type, fvPatchField, volMesh> & s,
               Type& value, label index)
 {
     s.ref()[index] = value;
 }
 
-template void assignIF(GeometricField<scalar, fvPatchField, volMesh>& field,
+template void assignIF(GeometricField<scalar, fvPatchField, volMesh> & field,
                        scalar& value, label index);
-template void assignIF(GeometricField<vector, fvPatchField, volMesh>& field,
+template void assignIF(GeometricField<vector, fvPatchField, volMesh> & field,
                        vector& value, label index);
 
-void assignONE(volScalarField& s, List<label>& L)
+void assignONE(volScalarField& s, List<label> & L)
 {
     for (label i = 0; i < L.size(); i++)
     {
@@ -140,7 +140,7 @@ void assignONE(volScalarField& s, List<label>& L)
     }
 }
 
-void assignBC(GeometricField<scalar, fvPatchField, volMesh>& s, label BC_ind,
+void assignBC(GeometricField<scalar, fvPatchField, volMesh> & s, label BC_ind,
               double value)
 {
     label sizeBC = s.boundaryField()[BC_ind].size();
@@ -154,7 +154,7 @@ void assignBC(GeometricField<scalar, fvPatchField, volMesh>& s, label BC_ind,
     assignBC(s, BC_ind, valueList);
 }
 
-void assignBC(GeometricField<scalar, fvPatchField, volMesh>& s, label BC_ind,
+void assignBC(GeometricField<scalar, fvPatchField, volMesh> & s, label BC_ind,
               Eigen::MatrixXd valueVec)
 {
     label sizeBC = s.boundaryField()[BC_ind].size();
@@ -171,7 +171,7 @@ void assignBC(GeometricField<scalar, fvPatchField, volMesh>& s, label BC_ind,
 }
 
 // Assign a BC for a scalar field
-void assignBC(GeometricField<scalar, fvPatchField, volMesh>& s, label BC_ind,
+void assignBC(GeometricField<scalar, fvPatchField, volMesh> & s, label BC_ind,
               List<double> valueList)
 {
     word typeBC = s.boundaryField()[BC_ind].type();
@@ -199,7 +199,7 @@ void assignBC(GeometricField<scalar, fvPatchField, volMesh>& s, label BC_ind,
             s.boundaryFieldRef()[BC_ind][i] = value;
         }
 
-        freestreamFvPatchField<scalar>& Tpatch =
+        freestreamFvPatchField<scalar> & Tpatch =
             refCast<freestreamFvPatchField<scalar>>(s.boundaryFieldRef()[BC_ind]);
         scalarField& gradTpatch = Tpatch.freestreamValue();
         forAll(gradTpatch, faceI)
@@ -240,7 +240,7 @@ void assignBC(GeometricField<scalar, fvPatchField, volMesh>& s, label BC_ind,
     }
 }
 
-void assignBC(GeometricField<vector, fvPatchField, volMesh>& s, label BC_ind,
+void assignBC(GeometricField<vector, fvPatchField, volMesh> & s, label BC_ind,
               vector value)
 {
     M_Assert(value.size() == 3,
@@ -256,7 +256,7 @@ void assignBC(GeometricField<vector, fvPatchField, volMesh>& s, label BC_ind,
     assignBC(s, BC_ind, valueList);
 }
 
-void assignBC(GeometricField<tensor, fvPatchField, volMesh>& s, label BC_ind,
+void assignBC(GeometricField<tensor, fvPatchField, volMesh> & s, label BC_ind,
               tensor value)
 {
     M_Assert(value.size() == 9,
@@ -272,25 +272,26 @@ void assignBC(GeometricField<tensor, fvPatchField, volMesh>& s, label BC_ind,
     assignBC(s, BC_ind, valueList);
 }
 
-void assignBC(GeometricField<vector, fvPatchField, volMesh>& s, label BC_ind,
+void assignBC(GeometricField<vector, fvPatchField, volMesh> & s, label BC_ind,
               Eigen::MatrixXd valueVec)
 {
     label sizeBC = s.boundaryField()[BC_ind].size();
     M_Assert(sizeBC * 3 == valueVec.size(),
              "The size of the given values matrix has to be equal to 3 times the dimension of the boundaryField");
     List<vector> valueList(sizeBC);
+
     for (label i = 0; i < sizeBC; i++)
     {
         for (label j = 0; j < 3; j++)
         {
-            valueList[i].component(j) = valueVec(i + sizeBC * j);
+            valueList[i].component(j) = valueVec(i + sizeBC* j);
         }
     }
 
     assignBC(s, BC_ind, valueList);
 }
 
-void assignBC(GeometricField<tensor, fvPatchField, volMesh>& s, label BC_ind,
+void assignBC(GeometricField<tensor, fvPatchField, volMesh> & s, label BC_ind,
               Eigen::MatrixXd valueVec)
 {
     label sizeBC = s.boundaryField()[BC_ind].size();
@@ -302,14 +303,14 @@ void assignBC(GeometricField<tensor, fvPatchField, volMesh>& s, label BC_ind,
     {
         for (label j = 0; j < 9; j++)
         {
-            valueList[i].component(j) = valueVec(i + sizeBC * j);
+            valueList[i].component(j) = valueVec(i + sizeBC* j);
         }
     }
 
     assignBC(s, BC_ind, valueList);
 }
 
-void assignBC(GeometricField<scalar, fvsPatchField, surfaceMesh>& s,
+void assignBC(GeometricField<scalar, fvsPatchField, surfaceMesh> & s,
               label BC_ind, Eigen::MatrixXd valueVec)
 {
     label sizeBC = s.boundaryField()[BC_ind].size();
@@ -325,7 +326,7 @@ void assignBC(GeometricField<scalar, fvsPatchField, surfaceMesh>& s,
     assignBC(s, BC_ind, valueList);
 }
 
-void assignBC(GeometricField<vector, fvsPatchField, surfaceMesh>& s,
+void assignBC(GeometricField<vector, fvsPatchField, surfaceMesh> & s,
               label BC_ind, Eigen::MatrixXd valueVec)
 {
     label sizeBC = s.boundaryField()[BC_ind].size();
@@ -344,7 +345,7 @@ void assignBC(GeometricField<vector, fvsPatchField, surfaceMesh>& s,
 }
 
 // Assign a BC for a vector field
-void assignBC(GeometricField<vector, fvPatchField, volMesh>& s, label BC_ind,
+void assignBC(GeometricField<vector, fvPatchField, volMesh> & s, label BC_ind,
               List<vector> valueList)
 {
     word typeBC = s.boundaryField()[BC_ind].type();
@@ -365,7 +366,7 @@ void assignBC(GeometricField<vector, fvPatchField, volMesh>& s, label BC_ind,
             s.boundaryFieldRef()[BC_ind][i] = valueList[i];
         }
 
-        freestreamFvPatchField<vector>& Tpatch =
+        freestreamFvPatchField<vector> & Tpatch =
             refCast<freestreamFvPatchField<vector>>(s.boundaryFieldRef()[BC_ind]);
         vectorField& gradTpatch = Tpatch.freestreamValue();
         forAll(gradTpatch, faceI)
@@ -406,7 +407,7 @@ void assignBC(GeometricField<vector, fvPatchField, volMesh>& s, label BC_ind,
 
 
 // Assign a BC for a tensor field
-void assignBC(GeometricField<tensor, fvPatchField, volMesh>& s, label BC_ind,
+void assignBC(GeometricField<tensor, fvPatchField, volMesh> & s, label BC_ind,
               List<tensor> valueList)
 {
     word typeBC = s.boundaryField()[BC_ind].type();
@@ -427,7 +428,7 @@ void assignBC(GeometricField<tensor, fvPatchField, volMesh>& s, label BC_ind,
             s.boundaryFieldRef()[BC_ind][i] = valueList[i];
         }
 
-        freestreamFvPatchField<tensor>& Tpatch =
+        freestreamFvPatchField<tensor> & Tpatch =
             refCast<freestreamFvPatchField<tensor>>(s.boundaryFieldRef()[BC_ind]);
         tensorField& gradTpatch = Tpatch.freestreamValue();
         forAll(gradTpatch, faceI)
@@ -468,8 +469,9 @@ void assignBC(GeometricField<tensor, fvPatchField, volMesh>& s, label BC_ind,
 
 
 template<typename Type>
-void assignBC(GeometricField<Type, fvsPatchField, surfaceMesh>& s, label BC_ind,
-              List<Type>& valueList)
+void assignBC(GeometricField<Type, fvsPatchField, surfaceMesh> & s,
+              label BC_ind,
+              List<Type> & valueList)
 {
     word typeBC = s.boundaryField()[BC_ind].type();
     label sizeBC = s.boundaryField()[BC_ind].size();
@@ -479,9 +481,9 @@ void assignBC(GeometricField<Type, fvsPatchField, surfaceMesh>& s, label BC_ind,
 
     if (s.boundaryField()[BC_ind].type() == "fixedGradient")
     {
-        fixedGradientFvPatchField<Type>& Tpatch =
+        fixedGradientFvPatchField<Type> & Tpatch =
             refCast<fixedGradientFvPatchField<Type>>(s.boundaryFieldRef()[BC_ind]);
-        Field<Type>& gradTpatch = Tpatch.gradient();
+        Field<Type> & gradTpatch = Tpatch.gradient();
         forAll(gradTpatch, faceI)
         {
             gradTpatch[faceI] = valueList[faceI];
@@ -494,9 +496,9 @@ void assignBC(GeometricField<Type, fvsPatchField, surfaceMesh>& s, label BC_ind,
             s.boundaryFieldRef()[BC_ind][i] = valueList[i];
         }
 
-        freestreamFvPatchField<Type>& Tpatch =
+        freestreamFvPatchField<Type> & Tpatch =
             refCast<freestreamFvPatchField<Type>>(s.boundaryFieldRef()[BC_ind]);
-        Field<Type>& gradTpatch = Tpatch.freestreamValue();
+        Field<Type> & gradTpatch = Tpatch.freestreamValue();
         forAll(gradTpatch, faceI)
         {
             gradTpatch[faceI] = valueList[faceI];
@@ -534,14 +536,15 @@ void assignBC(GeometricField<Type, fvsPatchField, surfaceMesh>& s, label BC_ind,
 }
 
 template void assignBC(
-    GeometricField<scalar, fvsPatchField, surfaceMesh>& s, label BC_ind,
-    List<scalar>& valueList);
+    GeometricField<scalar, fvsPatchField, surfaceMesh> & s, label BC_ind,
+    List<scalar> & valueList);
 template void assignBC(
-    GeometricField<vector, fvsPatchField, surfaceMesh>& s, label BC_ind,
-    List<vector>& valueList);
+    GeometricField<vector, fvsPatchField, surfaceMesh> & s, label BC_ind,
+    List<vector> & valueList);
 
 template<typename Type>
-void assignBC(GeometricField<Type, fvsPatchField, surfaceMesh>& s, label BC_ind,
+void assignBC(GeometricField<Type, fvsPatchField, surfaceMesh> & s,
+              label BC_ind,
               Type& value)
 {
     label sizeBC = s.boundaryField()[BC_ind].size();
@@ -556,14 +559,15 @@ void assignBC(GeometricField<Type, fvsPatchField, surfaceMesh>& s, label BC_ind,
 }
 
 template void assignBC(
-    GeometricField<scalar, fvsPatchField, surfaceMesh>& s, label BC_ind,
+    GeometricField<scalar, fvsPatchField, surfaceMesh> & s, label BC_ind,
     scalar& valueList);
 template void assignBC(
-    GeometricField<vector, fvsPatchField, surfaceMesh>& s, label BC_ind,
+    GeometricField<vector, fvsPatchField, surfaceMesh> & s, label BC_ind,
     vector& valueList);
 
 template<typename Type>
-void changeNeumann2Dirichlet(GeometricField<Type, fvPatchField, volMesh>& field,
+void changeNeumann2Dirichlet(GeometricField<Type, fvPatchField, volMesh> &
+                             field,
                              Type& value)
 {
     forAll(field.mesh().boundary(), i)
@@ -578,12 +582,12 @@ void changeNeumann2Dirichlet(GeometricField<Type, fvPatchField, volMesh>& field,
 }
 
 template void changeNeumann2Dirichlet(
-    GeometricField<scalar, fvPatchField, volMesh>& field, scalar& value);
+    GeometricField<scalar, fvPatchField, volMesh> & field, scalar& value);
 template void changeNeumann2Dirichlet(
-    GeometricField<vector, fvPatchField, volMesh>& field, vector& value);
+    GeometricField<vector, fvPatchField, volMesh> & field, vector& value);
 
 template<typename Type>
-void assignZeroDirichlet(GeometricField<Type, fvPatchField, volMesh>& field)
+void assignZeroDirichlet(GeometricField<Type, fvPatchField, volMesh> & field)
 {
     Type v;
     v = v * 0;
@@ -595,15 +599,17 @@ void assignZeroDirichlet(GeometricField<Type, fvPatchField, volMesh>& field)
             assignBC(field, i, v);
         }
     }
+
     changeNeumann2Dirichlet(field, v);
 }
+
 template void assignZeroDirichlet(
-    GeometricField<vector, fvPatchField, volMesh>& field);
+    GeometricField<vector, fvPatchField, volMesh> & field);
 template void assignZeroDirichlet(
-    GeometricField<scalar, fvPatchField, volMesh>& field);
+    GeometricField<scalar, fvPatchField, volMesh> & field);
 
 template<typename Type>
-void setBoxToValue(GeometricField<Type, fvPatchField, volMesh>& field,
+void setBoxToValue(GeometricField<Type, fvPatchField, volMesh> & field,
                    Eigen::MatrixXd Box, Type value)
 {
     M_Assert(Box.rows() == 2
@@ -644,14 +650,14 @@ void setBoxToValue(GeometricField<Type, fvPatchField, volMesh>& field,
     }
 }
 
-template void setBoxToValue(GeometricField<scalar, fvPatchField, volMesh>&
+template void setBoxToValue(GeometricField<scalar, fvPatchField, volMesh> &
                             field, Eigen::MatrixXd Box, scalar value);
-template void setBoxToValue(GeometricField<vector, fvPatchField, volMesh>&
+template void setBoxToValue(GeometricField<vector, fvPatchField, volMesh> &
                             field, Eigen::MatrixXd Box, vector value);
 
 template<typename Type>
-void setIndices2Value(labelList& ind2set, List<Type>& value2set,
-                      labelList& movingIDS, List<Type>& originalList)
+void setIndices2Value(labelList& ind2set, List<Type> & value2set,
+                      labelList& movingIDS, List<Type> & originalList)
 {
     M_Assert(ind2set.size() == value2set.size(),
              "The size of the indices must be equal to the size of the values list");
@@ -677,14 +683,14 @@ void setIndices2Value(labelList& ind2set, List<Type>& value2set,
     }
 }
 
-template void setIndices2Value(labelList& ind2set, List<scalar>& value2set,
-                               labelList& movingIDS, List<scalar>& originalList);
-template void setIndices2Value(labelList& ind2set, List<vector>& value2set,
-                               labelList& movingIDS, List<vector>& originalList);
+template void setIndices2Value(labelList& ind2set, List<scalar> & value2set,
+                               labelList& movingIDS, List<scalar> & originalList);
+template void setIndices2Value(labelList& ind2set, List<vector> & value2set,
+                               labelList& movingIDS, List<vector> & originalList);
 
 template<class Type>
 void changeBCtype(
-    GeometricField<Type, fvPatchField, volMesh>& field, word BCtype,
+    GeometricField<Type, fvPatchField, volMesh> & field, word BCtype,
     label BC_ind)
 {
     field.boundaryFieldRef().set(BC_ind, fvPatchField<Type>::New(BCtype,
@@ -692,16 +698,16 @@ void changeBCtype(
 }
 
 template void changeBCtype<scalar>
-(GeometricField<scalar, fvPatchField, volMesh>& field, word BCtype,
+(GeometricField<scalar, fvPatchField, volMesh> & field, word BCtype,
  label BC_ind);
 template void changeBCtype<vector>
-(GeometricField<vector, fvPatchField, volMesh>& field, word BCtype,
+(GeometricField<vector, fvPatchField, volMesh> & field, word BCtype,
  label BC_ind);
 
 template<typename Type>
 void assignMixedBC(
-    GeometricField<Type, fvPatchField, volMesh>& field, label BC_ind,
-    List<Type>& value, List<Type>& grad, List<scalar>& valueFrac)
+    GeometricField<Type, fvPatchField, volMesh> & field, label BC_ind,
+    List<Type> & value, List<Type> & grad, List<scalar> & valueFrac)
 {
     std::string message = "Patch is NOT mixed. It is of type: " +
                           field.boundaryField()[BC_ind].type();
@@ -709,11 +715,11 @@ void assignMixedBC(
 
     if (field.boundaryField()[BC_ind].type() == "mixed")
     {
-        mixedFvPatchField<Type>& Tpatch =
+        mixedFvPatchField<Type> & Tpatch =
             refCast<mixedFvPatchField<Type>>(field.boundaryFieldRef()[BC_ind]);
-        Field<Type>& valueTpatch = Tpatch.refValue();
-        Field<Type>& gradTpatch = Tpatch.refGrad();
-        Field<scalar>& valueFracTpatch = Tpatch.valueFraction();
+        Field<Type> & valueTpatch = Tpatch.refValue();
+        Field<Type> & gradTpatch = Tpatch.refGrad();
+        Field<scalar> & valueFracTpatch = Tpatch.valueFraction();
         valueTpatch = value;
         gradTpatch = grad;
         valueFracTpatch = valueFrac;
@@ -721,16 +727,16 @@ void assignMixedBC(
 }
 
 template void assignMixedBC<scalar>(
-    GeometricField<scalar, fvPatchField, volMesh>& field, label BC_ind,
-    List<scalar>& value, List<scalar>& grad, List<scalar>& valueFrac);
+    GeometricField<scalar, fvPatchField, volMesh> & field, label BC_ind,
+    List<scalar> & value, List<scalar> & grad, List<scalar> & valueFrac);
 
 template void assignMixedBC<vector>(
-    GeometricField<vector, fvPatchField, volMesh>& field, label BC_ind,
-    List<vector>& value, List<vector>& grad, List<scalar>& valueFrac);
+    GeometricField<vector, fvPatchField, volMesh> & field, label BC_ind,
+    List<vector> & value, List<vector> & grad, List<scalar> & valueFrac);
 
 template<typename Type>
 void normalizeFields(
-    PtrList<GeometricField<Type, fvPatchField, volMesh>>& fields)
+    PtrList<GeometricField<Type, fvPatchField, volMesh>> & fields)
 {
     ITHACAparameters* para(ITHACAparameters::getInstance());
     word normType = para->ITHACAdict->lookupOrDefault<word>("normalizationNorm",
@@ -770,14 +776,14 @@ void normalizeFields(
 }
 
 template void normalizeFields(
-    PtrList<GeometricField<scalar, fvPatchField, volMesh>>& fields);
+    PtrList<GeometricField<scalar, fvPatchField, volMesh>> & fields);
 template void normalizeFields(
-    PtrList<GeometricField<vector, fvPatchField, volMesh>>& fields);
+    PtrList<GeometricField<vector, fvPatchField, volMesh>> & fields);
 
 
 template<typename Type>
 Eigen::MatrixXd getValues(GeometricField<Type, fvPatchField,
-                          volMesh>& field, labelList& indices)
+                          volMesh> & field, labelList& indices)
 {
     List<Type> list(indices.size());
     M_Assert(max(indices) < field.size(),
@@ -793,7 +799,7 @@ Eigen::MatrixXd getValues(GeometricField<Type, fvPatchField,
 
 template<>
 Eigen::MatrixXd getValues(GeometricField<vector, fvPatchField,
-                          volMesh>& field, labelList& indices, labelList* xyz)
+                          volMesh> & field, labelList& indices, labelList* xyz)
 {
     M_Assert(max(indices) < field.size(),
              "The list of indices is too large respect to field dimension. There is at least one value larger than the dimension of the list");
@@ -802,9 +808,9 @@ Eigen::MatrixXd getValues(GeometricField<vector, fvPatchField,
     {
         List<scalar> list;
         list.resize(indices.size());
-        M_Assert(max(*xyz) <= 2,
+        M_Assert(max( * xyz) <= 2,
                  "The list of xyz positions contains at list one value larger than 2");
-        labelList l = *xyz;
+        labelList l = * xyz;
 
         for (label i = 0; i < indices.size(); i++)
         {
@@ -829,7 +835,7 @@ Eigen::MatrixXd getValues(GeometricField<vector, fvPatchField,
 
 template<>
 Eigen::MatrixXd getValues(GeometricField<scalar, fvPatchField,
-                          volMesh>& field, labelList& indices, labelList* xyz)
+                          volMesh> & field, labelList& indices, labelList* xyz)
 {
     M_Assert(max(indices) < field.size(),
              "The list of indices is too large respect to field dimension. There is at least one value larger than the dimension of the list");
@@ -846,7 +852,7 @@ Eigen::MatrixXd getValues(GeometricField<scalar, fvPatchField,
 
 template<typename T>
 Eigen::MatrixXd getValues(PtrList<GeometricField<T, fvPatchField,
-                          volMesh>>& fields, labelList& indices, labelList* xyz)
+                          volMesh>> & fields, labelList& indices, labelList* xyz)
 {
     Eigen::MatrixXd out;
     Eigen::MatrixXd a = getValues(fields[0], indices, xyz);
@@ -864,10 +870,10 @@ Eigen::MatrixXd getValues(PtrList<GeometricField<T, fvPatchField,
 
 template
 Eigen::MatrixXd getValues(PtrList<GeometricField<scalar, fvPatchField,
-                                  volMesh>>& fields, labelList& indices, labelList* xyz);
+                                  volMesh>> & fields, labelList& indices, labelList* xyz);
 template
 Eigen::MatrixXd getValues(PtrList<GeometricField<vector, fvPatchField,
-                                  volMesh>>& fields, labelList& indices, labelList* xyz);
+                                  volMesh>> & fields, labelList& indices, labelList* xyz);
 
 
 }
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAassign.H b/src/ITHACA_CORE/ITHACAutilities/ITHACAassign.H
index 673790200..8ebe32b8e 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAassign.H
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAassign.H
@@ -75,7 +75,7 @@ namespace ITHACAutilities
 ///
 template<class TypeField>
 PtrList<TypeField> averageSubtract(PtrList<TypeField>
-                                   fields, Eigen::MatrixXd ind, PtrList<TypeField>& ave);
+                                   fields, Eigen::MatrixXd ind, PtrList<TypeField> & ave);
 
 //-----------------------------------------------------------------------------
 /// @brief      Calculates the average of a list of fields
@@ -87,7 +87,7 @@ PtrList<TypeField> averageSubtract(PtrList<TypeField>
 /// @return     The average.
 ///
 template<class TypeField>
-TypeField computeAverage(PtrList<TypeField>& fields);
+TypeField computeAverage(PtrList<TypeField> & fields);
 
 //--------------------------------------------------------------------------
 /// Assign internal field
@@ -98,7 +98,7 @@ TypeField computeAverage(PtrList<TypeField>& fields);
 /// @tparam         Type   Type of field vector or scalar
 ///
 template<typename Type>
-void assignIF(GeometricField<Type, fvPatchField, volMesh>& field,
+void assignIF(GeometricField<Type, fvPatchField, volMesh> & field,
               Type value);
 
 //--------------------------------------------------------------------------
@@ -111,8 +111,8 @@ void assignIF(GeometricField<Type, fvPatchField, volMesh>& field,
 /// @tparam         Type   Type of field vector or scalar
 ///
 template<typename Type>
-void assignIF(GeometricField<Type, fvPatchField, volMesh>& field,
-              Type& value, List<label>& indices);
+void assignIF(GeometricField<Type, fvPatchField, volMesh> & field,
+              Type& value, List<label> & indices);
 
 //--------------------------------------------------------------------------
 /// Assign internal field
@@ -124,7 +124,7 @@ void assignIF(GeometricField<Type, fvPatchField, volMesh>& field,
 /// @tparam         Type   Type of field vector or scalar
 ///
 template<typename Type>
-void assignIF(GeometricField<Type, fvPatchField, volMesh>& field,
+void assignIF(GeometricField<Type, fvPatchField, volMesh> & field,
               Type& value, label index);
 
 //--------------------------------------------------------------------------
@@ -134,7 +134,7 @@ void assignIF(GeometricField<Type, fvPatchField, volMesh>& field,
 ///                      condition
 /// @param         L     List of indices
 ///
-void assignONE(volScalarField& s, List<label>& L);
+void assignONE(volScalarField& s, List<label> & L);
 
 
 //--------------------------------------------------------------------------
@@ -144,7 +144,7 @@ void assignONE(volScalarField& s, List<label>& L);
 /// @param[in]  BC_ind  The BC index.
 /// @param[in]  value   The value you want to assign (it must be a double).
 ///
-void assignBC(GeometricField<scalar, fvPatchField, volMesh>& s, label BC_ind,
+void assignBC(GeometricField<scalar, fvPatchField, volMesh> & s, label BC_ind,
               double value);
 
 //--------------------------------------------------------------------------
@@ -154,7 +154,7 @@ void assignBC(GeometricField<scalar, fvPatchField, volMesh>& s, label BC_ind,
 /// @param[in]  BC_ind  The BC index.
 /// @param[in]  valueVec   The value you want to assign (it must be an Eigen MatrixXd).
 ///
-void assignBC(GeometricField<scalar, fvPatchField, volMesh>& s, label BC_ind,
+void assignBC(GeometricField<scalar, fvPatchField, volMesh> & s, label BC_ind,
               Eigen::MatrixXd valueVec);
 
 //--------------------------------------------------------------------------
@@ -164,7 +164,7 @@ void assignBC(GeometricField<scalar, fvPatchField, volMesh>& s, label BC_ind,
 /// @param[in]  BC_ind  The BC index.
 /// @param[in]  valueList   The value you want to assign (it must be a list of doubles).
 ///
-void assignBC(GeometricField<scalar, fvPatchField, volMesh>& s, label BC_ind,
+void assignBC(GeometricField<scalar, fvPatchField, volMesh> & s, label BC_ind,
               List<double> valueList);
 
 //--------------------------------------------------------------------------
@@ -174,7 +174,7 @@ void assignBC(GeometricField<scalar, fvPatchField, volMesh>& s, label BC_ind,
 /// @param[in]  BC_ind  The BC index.
 /// @param[in]  value   The value you want to assign (it must be an OpenFOAM vector).
 ///
-void assignBC(GeometricField<vector, fvPatchField, volMesh>& s, label BC_ind,
+void assignBC(GeometricField<vector, fvPatchField, volMesh> & s, label BC_ind,
               vector value);
 
 //--------------------------------------------------------------------------
@@ -184,7 +184,7 @@ void assignBC(GeometricField<vector, fvPatchField, volMesh>& s, label BC_ind,
 /// @param[in]  BC_ind  The BC index.
 /// @param[in]  value   The value you want to assign (it must be an OpenFOAM tensor).
 ///
-void assignBC(GeometricField<tensor, fvPatchField, volMesh>& s, label BC_ind,
+void assignBC(GeometricField<tensor, fvPatchField, volMesh> & s, label BC_ind,
               tensor value);
 
 //--------------------------------------------------------------------------
@@ -194,7 +194,7 @@ void assignBC(GeometricField<tensor, fvPatchField, volMesh>& s, label BC_ind,
 /// @param[in]  BC_ind  The BC index.
 /// @param[in]  valueVec   The value you want to assign (it must be an Eigen MatrixXd).
 ///
-void assignBC(GeometricField<vector, fvPatchField, volMesh>& s, label BC_ind,
+void assignBC(GeometricField<vector, fvPatchField, volMesh> & s, label BC_ind,
               Eigen::MatrixXd valueVec);
 
 //--------------------------------------------------------------------------
@@ -204,7 +204,7 @@ void assignBC(GeometricField<vector, fvPatchField, volMesh>& s, label BC_ind,
 /// @param[in]  BC_ind  The BC index.
 /// @param[in]  valueVec   The value you want to assign (it must be an Eigen MatrixXd).
 ///
-void assignBC(GeometricField<tensor, fvPatchField, volMesh>& s, label BC_ind,
+void assignBC(GeometricField<tensor, fvPatchField, volMesh> & s, label BC_ind,
               Eigen::MatrixXd valueVec);
 
 //--------------------------------------------------------------------------
@@ -214,7 +214,7 @@ void assignBC(GeometricField<tensor, fvPatchField, volMesh>& s, label BC_ind,
 /// @param[in]  BC_ind  The BC index.
 /// @param[in]  valueList   The value you want to assign (it must be a list of vectors).
 ///
-void assignBC(GeometricField<vector, fvPatchField, volMesh>& s, label BC_ind,
+void assignBC(GeometricField<vector, fvPatchField, volMesh> & s, label BC_ind,
               List<vector> valueList);
 
 //--------------------------------------------------------------------------
@@ -224,7 +224,7 @@ void assignBC(GeometricField<vector, fvPatchField, volMesh>& s, label BC_ind,
 /// @param[in]  BC_ind  The BC index.
 /// @param[in]  valueList   The value you want to assign (it must be a list of tensors).
 ///
-void assignBC(GeometricField<tensor, fvPatchField, volMesh>& s, label BC_ind,
+void assignBC(GeometricField<tensor, fvPatchField, volMesh> & s, label BC_ind,
               List<tensor> valueList);
 
 //------------------------------------------------------------------------------
@@ -236,10 +236,10 @@ void assignBC(GeometricField<tensor, fvPatchField, volMesh>& s, label BC_ind,
 ///
 /// @tparam     Type    Type of field (vector or scalar)
 ///
-void assignBC(GeometricField<scalar, fvsPatchField, surfaceMesh>& field,
+void assignBC(GeometricField<scalar, fvsPatchField, surfaceMesh> & field,
               label BC_ind, Eigen::MatrixXd value);
 
-void assignBC(GeometricField<vector, fvsPatchField, surfaceMesh>& field,
+void assignBC(GeometricField<vector, fvsPatchField, surfaceMesh> & field,
               label BC_ind, Eigen::MatrixXd value);
 
 //------------------------------------------------------------------------------
@@ -252,8 +252,8 @@ void assignBC(GeometricField<vector, fvsPatchField, surfaceMesh>& field,
 /// @tparam     Type    Type of field (vector or scalar)
 ///
 template<typename Type>
-void assignBC(GeometricField<Type, fvsPatchField, surfaceMesh>& field,
-              label BC_ind, List<Type>& value);
+void assignBC(GeometricField<Type, fvsPatchField, surfaceMesh> & field,
+              label BC_ind, List<Type> & value);
 
 
 
@@ -267,7 +267,7 @@ void assignBC(GeometricField<Type, fvsPatchField, surfaceMesh>& field,
 /// @tparam     Type    Type of field (vector or scalar)
 ///
 template<typename Type>
-void assignBC(GeometricField<Type, fvsPatchField, surfaceMesh>& field,
+void assignBC(GeometricField<Type, fvsPatchField, surfaceMesh> & field,
               label BC_ind, Type& value);
 
 
@@ -280,7 +280,8 @@ void assignBC(GeometricField<Type, fvsPatchField, surfaceMesh>& field,
 /// @tparam         Type   Type of field vector or scalar
 ///
 template<typename Type>
-void changeNeumann2Dirichlet(GeometricField<Type, fvPatchField, volMesh>& field,
+void changeNeumann2Dirichlet(GeometricField<Type, fvPatchField, volMesh> &
+                             field,
                              Type& value);
 
 
@@ -295,7 +296,7 @@ void changeNeumann2Dirichlet(GeometricField<Type, fvPatchField, volMesh>& field,
 ///
 template<typename Type>
 void assignZeroDirichlet(GeometricField<Type, fvPatchField,
-                         volMesh>& field);
+                         volMesh> & field);
 
 #pragma GCC diagnostic push
 #pragma GCC diagnostic ignored "-Wcomment"
@@ -321,7 +322,7 @@ void assignZeroDirichlet(GeometricField<Type, fvPatchField,
 /// @tparam     Type   Type of field can be scalar or vector
 ///
 template<typename Type>
-void setBoxToValue(GeometricField<Type, fvPatchField, volMesh>& field,
+void setBoxToValue(GeometricField<Type, fvPatchField, volMesh> & field,
                    Eigen::MatrixXd Box, Type value);
 #pragma GCC diagnostic pop
 
@@ -335,7 +336,7 @@ void setBoxToValue(GeometricField<Type, fvPatchField, volMesh>& field,
 /// @tparam     Type    The type of field it can be scalar or vector
 ///
 template<class Type>
-void changeBCtype(GeometricField<Type, fvPatchField, volMesh>&
+void changeBCtype(GeometricField<Type, fvPatchField, volMesh> &
                   field, word BCtype, label BC_ind);
 
 
@@ -350,8 +351,8 @@ void changeBCtype(GeometricField<Type, fvPatchField, volMesh>&
 /// @tparam     Type          Type of list (scalar or vector)
 ///
 template<typename Type>
-void setIndices2Value(labelList& ind2set, List<Type>& value2set,
-                      labelList& movingIDS, List<Type>& originalList);
+void setIndices2Value(labelList& ind2set, List<Type> & value2set,
+                      labelList& movingIDS, List<Type> & originalList);
 
 //--------------------------------------------------------------------------
 /// @brief      Assign value of a boundary condition of type "mixed"
@@ -365,7 +366,7 @@ void setIndices2Value(labelList& ind2set, List<Type>& value2set,
 /// @tparam          Type       Type of the field, it can be scalar or vector.
 ///
 template<typename Type>
-void assignMixedBC(GeometricField<Type, fvPatchField, volMesh>& field,
+void assignMixedBC(GeometricField<Type, fvPatchField, volMesh> & field,
                    label BC_ind, Eigen::MatrixXd& value,
                    Eigen::MatrixXd& grad, Eigen::MatrixXd& valueFrac);
 
@@ -382,9 +383,9 @@ void assignMixedBC(GeometricField<Type, fvPatchField, volMesh>& field,
 /// @tparam          Type      Type of the field, it can be scalar or vector.
 ///
 template<typename Type>
-void assignMixedBC(GeometricField<Type, fvPatchField, volMesh>& field,
-                   label BC_ind, List<Type>& value,
-                   List<Type>& grad, List<scalar>& valueFrac);
+void assignMixedBC(GeometricField<Type, fvPatchField, volMesh> & field,
+                   label BC_ind, List<Type> & value,
+                   List<Type> & grad, List<scalar> & valueFrac);
 
 
 //--------------------------------------------------------------------------
@@ -396,7 +397,7 @@ void assignMixedBC(GeometricField<Type, fvPatchField, volMesh>& field,
 ///
 template<typename Type>
 void normalizeFields(
-    PtrList<GeometricField<Type, fvPatchField, volMesh>>& fields);
+    PtrList<GeometricField<Type, fvPatchField, volMesh>> & fields);
 
 //------------------------------------------------------------------------------
 /// @brief      /// @brief      Gets the values from a list of indices
@@ -411,7 +412,7 @@ void normalizeFields(
 ///
 template<typename Type>
 Eigen::MatrixXd getValues(GeometricField<Type, fvPatchField,
-                          volMesh>& field, labelList& indices, labelList* xyz = NULL);
+                          volMesh> & field, labelList& indices, labelList* xyz = NULL);
 
 //------------------------------------------------------------------------------
 /// @brief      Gets the values from a list of indices
@@ -426,7 +427,7 @@ Eigen::MatrixXd getValues(GeometricField<Type, fvPatchField,
 ///
 template<typename Type>
 Eigen::MatrixXd getValues(PtrList<GeometricField<Type, fvPatchField,
-                          volMesh>>& field, labelList& indices, labelList* xyz = NULL);
+                          volMesh>> & field, labelList& indices, labelList* xyz = NULL);
 
 }
 
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
index cec4e3956..9d0474ccd 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.C
@@ -29,8 +29,8 @@ namespace ITHACAutilities
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 PtrList<GeometricField<Type, PatchField, GeoMesh>> reconstructFromCoeff(
-            PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes,
-            Eigen::MatrixXd& coeff_matrix, label Nmodes)
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes,
+    Eigen::MatrixXd& coeff_matrix, label Nmodes)
 {
     PtrList<GeometricField<Type, PatchField, GeoMesh>> rec_field;
     rec_field.resize(0);
@@ -40,7 +40,7 @@ PtrList<GeometricField<Type, PatchField, GeoMesh>> reconstructFromCoeff(
         for (label i = 0; i < Nmodes; i++)
             if ( i == 0)
             {
-                rec_field.append(modes[i]*coeff_matrix(i, k));
+                rec_field.append(modes[i] * coeff_matrix(i, k));
             }
             else
             {
@@ -53,20 +53,20 @@ PtrList<GeometricField<Type, PatchField, GeoMesh>> reconstructFromCoeff(
 
 template PtrList<GeometricField<scalar, fvPatchField, volMesh>>
 reconstructFromCoeff(
-    PtrList<GeometricField<scalar, fvPatchField, volMesh>>& modes,
+    PtrList<GeometricField<scalar, fvPatchField, volMesh>> & modes,
     Eigen::MatrixXd& coeff_matrix, label Nmodes);
 template PtrList<GeometricField<vector, fvPatchField, volMesh>>
 reconstructFromCoeff(
-    PtrList<GeometricField<vector, fvPatchField, volMesh>>& modes,
+    PtrList<GeometricField<vector, fvPatchField, volMesh>> & modes,
     Eigen::MatrixXd& coeff_matrix, label Nmodes);
 template PtrList<GeometricField<tensor, fvPatchField, volMesh>>
 reconstructFromCoeff(
-    PtrList<GeometricField<tensor, fvPatchField, volMesh>>& modes,
+    PtrList<GeometricField<tensor, fvPatchField, volMesh>> & modes,
     Eigen::MatrixXd& coeff_matrix, label Nmodes);
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 Eigen::MatrixXd getMassMatrix(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes, label Nmodes,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes, label Nmodes,
     bool consider_volumes)
 {
     label Msize;
@@ -83,15 +83,16 @@ Eigen::MatrixXd getMassMatrix(
     M_Assert(modes.size() >= Msize,
              "The Number of requested modes is larger then the available quantity.");
     Eigen::MatrixXd F = Foam2Eigen::PtrList2Eigen(modes);
-    Eigen::MatrixXd M = Eigen::MatrixXd::Zero(Msize,Msize);
+    Eigen::MatrixXd M = Eigen::MatrixXd::Zero(Msize, Msize);
 
     if (consider_volumes)
     {
         Eigen::VectorXd V = getMassMatrixFV(modes[0]);
+
         // If V is too big then we need a for loop to avoid RAM overload
         if (V.size() > 1e6)
         {
-            for (int i=0; i<V.size(); i++)
+            for (int i = 0; i < V.size(); i++)
             {
                 M += V(i) * F.transpose().topRows(Msize).col(i) * F.leftCols(Msize).row(i);
             }
@@ -115,29 +116,30 @@ Eigen::MatrixXd getMassMatrix(
 }
 
 template Eigen::MatrixXd getMassMatrix(
-    PtrList<GeometricField<scalar, fvPatchField, volMesh>>& modes, label Nmodes,
+    PtrList<GeometricField<scalar, fvPatchField, volMesh>> & modes, label Nmodes,
     bool consider_volumes);
 
 template Eigen::MatrixXd getMassMatrix(
-    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>>& modes,
+    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>> & modes,
     label Nmodes,
     bool consider_volumes = false);
 
 template Eigen::MatrixXd getMassMatrix(
-    PtrList<GeometricField<vector, fvPatchField, volMesh>>& modes, label Nmodes,
+    PtrList<GeometricField<vector, fvPatchField, volMesh>> & modes, label Nmodes,
     bool consider_volumes);
 
 template Eigen::MatrixXd getMassMatrix(
-    PtrList<GeometricField<tensor, fvPatchField, volMesh>>& modes, label Nmodes,
+    PtrList<GeometricField<tensor, fvPatchField, volMesh>> & modes, label Nmodes,
     bool consider_volumes);
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 Eigen::MatrixXd getMassMatrix(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes,
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes2, label Nmodes,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes,
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes2, label Nmodes,
     bool consider_volumes)
 {
-    label Msize,Msize2;
+    label Msize, Msize2;
+
     if (Nmodes == 0)
     {
         Msize =  modes.size();
@@ -148,30 +150,31 @@ Eigen::MatrixXd getMassMatrix(
         Msize = Nmodes;
         Msize2 = Nmodes;
     }
+
     M_Assert(modes.size() >= Msize,
              "The Number of requested modes is larger then the available quantity.");
     M_Assert(modes2.size() >= Msize2,
              "The Number of requested modes is larger then the available quantity.");
-
     Eigen::MatrixXd F = Foam2Eigen::PtrList2Eigen(modes);
     Eigen::MatrixXd F2 = Foam2Eigen::PtrList2Eigen(modes2);
-    Eigen::MatrixXd M = Eigen::MatrixXd::Zero(Msize,Msize2);
-    
+    Eigen::MatrixXd M = Eigen::MatrixXd::Zero(Msize, Msize2);
+
     if (consider_volumes)
     {
-       Eigen::VectorXd V = getMassMatrixFV(modes[0]);
-       // If V is too big then we need a for loop to avoid RAM overload
-       if (V.size() > 1e6)
-       {
-            for (int i=0; i<V.size(); i++)
+        Eigen::VectorXd V = getMassMatrixFV(modes[0]);
+
+        // If V is too big then we need a for loop to avoid RAM overload
+        if (V.size() > 1e6)
+        {
+            for (int i = 0; i < V.size(); i++)
             {
-             M += V(i) * F.transpose().topRows(Msize).col(i) * F2.leftCols(Msize2).row(i);
+                M += V(i) * F.transpose().topRows(Msize).col(i) * F2.leftCols(Msize2).row(i);
             }
-       }
-       else
-       {
-        // Classical M computation
-        M = F.transpose().topRows(Msize) * V.asDiagonal() * F2.leftCols(Msize2);
+        }
+        else
+        {
+            // Classical M computation
+            M = F.transpose().topRows(Msize) * V.asDiagonal() * F2.leftCols(Msize2);
         }
     }
     else
@@ -188,35 +191,37 @@ Eigen::MatrixXd getMassMatrix(
 }
 
 template Eigen::MatrixXd getMassMatrix(
-    PtrList<GeometricField<scalar, fvPatchField, volMesh>>& modes,
-    PtrList<GeometricField<scalar, fvPatchField, volMesh>>& modes2, label Nmodes,
+    PtrList<GeometricField<scalar, fvPatchField, volMesh>> & modes,
+    PtrList<GeometricField<scalar, fvPatchField, volMesh>> & modes2, label Nmodes,
     bool consider_volumes);
 
 template Eigen::MatrixXd getMassMatrix(
-    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>>& modes,
-    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>>& modes2,
+    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>> & modes,
+    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>> & modes2,
     label Nmodes,
     bool consider_volumes = false);
 
 template Eigen::MatrixXd getMassMatrix(
-    PtrList<GeometricField<vector, fvPatchField, volMesh>>& modes,
-    PtrList<GeometricField<vector, fvPatchField, volMesh>>& modes2, label Nmodes,
+    PtrList<GeometricField<vector, fvPatchField, volMesh>> & modes,
+    PtrList<GeometricField<vector, fvPatchField, volMesh>> & modes2, label Nmodes,
     bool consider_volumes);
 
 template Eigen::MatrixXd getMassMatrix(
-    PtrList<GeometricField<tensor, fvPatchField, volMesh>>& modes,
-    PtrList<GeometricField<tensor, fvPatchField, volMesh>>& modes2, label Nmodes,
+    PtrList<GeometricField<tensor, fvPatchField, volMesh>> & modes,
+    PtrList<GeometricField<tensor, fvPatchField, volMesh>> & modes2, label Nmodes,
     bool consider_volumes);
 
 
 template<class Type, template<class> class PatchField, class GeoMesh>
-Eigen::MatrixXd getMassMatrix(PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes,
-                              PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes2, 
+Eigen::MatrixXd getMassMatrix(PtrList<GeometricField<Type, PatchField, GeoMesh>>
+                              & modes,
+                              PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes2,
                               Eigen::VectorXd weights,
                               label Nmodes,
                               bool consider_volumes)
 {
-    label Msize,Msize2;
+    label Msize, Msize2;
+
     if (Nmodes == 0)
     {
         Msize =  modes.size();
@@ -227,31 +232,34 @@ Eigen::MatrixXd getMassMatrix(PtrList<GeometricField<Type, PatchField, GeoMesh>>
         Msize = Nmodes;
         Msize2 = Nmodes;
     }
+
     M_Assert(modes.size() >= Msize,
              "The Number of requested modes is larger then the available quantity.");
     M_Assert(modes2.size() >= Msize2,
              "The Number of requested modes is larger then the available quantity.");
-
     Eigen::MatrixXd F = Foam2Eigen::PtrList2Eigen(modes);
     Eigen::MatrixXd F2 = Foam2Eigen::PtrList2Eigen(modes2);
-    Eigen::MatrixXd M = Eigen::MatrixXd::Zero(Msize,Msize2);
-    
+    Eigen::MatrixXd M = Eigen::MatrixXd::Zero(Msize, Msize2);
+
     if (consider_volumes)
     {
-       Eigen::VectorXd V = getMassMatrixFV(modes[0]);
-       // If V is too big then we need a for loop to avoid RAM overload
-       if (V.size() > 1e6)
-       {
-            for (int i=0; i<V.size(); i++)
+        Eigen::VectorXd V = getMassMatrixFV(modes[0]);
+
+        // If V is too big then we need a for loop to avoid RAM overload
+        if (V.size() > 1e6)
+        {
+            for (int i = 0; i < V.size(); i++)
             {
-             M += (V(i) * weights(i)) * F.transpose().topRows(Msize).col(i) * F2.leftCols(Msize2).row(i);
+                M += (V(i) * weights(i)) * F.transpose().topRows(Msize).col(i) * F2.leftCols(
+                         Msize2).row(i);
             }
-       }
-       else
-       {
-        // Classical M computation
-        M = F.transpose().topRows(Msize) * ( V * weights ).asDiagonal() * F2.leftCols(Msize2);
-       }
+        }
+        else
+        {
+            // Classical M computation
+            M = F.transpose().topRows(Msize) * ( V* weights ).asDiagonal() * F2.leftCols(
+                    Msize2);
+        }
     }
     else
     {
@@ -267,29 +275,29 @@ Eigen::MatrixXd getMassMatrix(PtrList<GeometricField<Type, PatchField, GeoMesh>>
 }
 
 template Eigen::MatrixXd getMassMatrix(
-    PtrList<GeometricField<scalar, fvPatchField, volMesh>>& modes,
-    PtrList<GeometricField<scalar, fvPatchField, volMesh>>& modes2, 
+    PtrList<GeometricField<scalar, fvPatchField, volMesh>> & modes,
+    PtrList<GeometricField<scalar, fvPatchField, volMesh>> & modes2,
     Eigen::VectorXd weights,
     label Nmodes = 0,
     bool consider_volumes);
 
 template Eigen::MatrixXd getMassMatrix(
-    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>>& modes,
-    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>>& modes2,
+    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>> & modes,
+    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>> & modes2,
     Eigen::VectorXd weights,
     label Nmodes = 0,
     bool consider_volumes);
 
 template Eigen::MatrixXd getMassMatrix(
-    PtrList<GeometricField<vector, fvPatchField, volMesh>>& modes,
-    PtrList<GeometricField<vector, fvPatchField, volMesh>>& modes2, 
+    PtrList<GeometricField<vector, fvPatchField, volMesh>> & modes,
+    PtrList<GeometricField<vector, fvPatchField, volMesh>> & modes2,
     Eigen::VectorXd weights,
     label Nmodes = 0,
     bool consider_volumes);
 
 template Eigen::MatrixXd getMassMatrix(
-    PtrList<GeometricField<tensor, fvPatchField, volMesh>>& modes,
-    PtrList<GeometricField<tensor, fvPatchField, volMesh>>& modes2, 
+    PtrList<GeometricField<tensor, fvPatchField, volMesh>> & modes,
+    PtrList<GeometricField<tensor, fvPatchField, volMesh>> & modes2,
     Eigen::VectorXd weights,
     label Nmodes = 0,
     bool consider_volumes);
@@ -297,7 +305,7 @@ template Eigen::MatrixXd getMassMatrix(
 
 template<class Type, template<class> class PatchField, class GeoMesh>
 Eigen::VectorXd getMassMatrixFV(
-    GeometricField<Type, PatchField, GeoMesh>& snapshot)
+    GeometricField<Type, PatchField, GeoMesh> & snapshot)
 {
     Eigen::MatrixXd snapEigen = Foam2Eigen::field2Eigen(snapshot);
     label dim = std::nearbyint(snapEigen.rows() / (snapshot.mesh().V()).size());
@@ -307,16 +315,16 @@ Eigen::VectorXd getMassMatrixFV(
 }
 
 template Eigen::VectorXd getMassMatrixFV(
-    GeometricField<scalar, fvPatchField, volMesh>& snapshot);
+    GeometricField<scalar, fvPatchField, volMesh> & snapshot);
 template Eigen::VectorXd getMassMatrixFV(
-    GeometricField<vector, fvPatchField, volMesh>& snapshot);
+    GeometricField<vector, fvPatchField, volMesh> & snapshot);
 template Eigen::VectorXd getMassMatrixFV(
-    GeometricField<tensor, fvPatchField, volMesh>& snapshot);
+    GeometricField<tensor, fvPatchField, volMesh> & snapshot);
 
 template<class Type, template<class> class PatchField, class GeoMesh>
-Eigen::VectorXd getCoeffs(GeometricField<Type, PatchField, GeoMesh>&
+Eigen::VectorXd getCoeffs(GeometricField<Type, PatchField, GeoMesh> &
                           snapshot,
-                          PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes, label Nmodes,
+                          PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes, label Nmodes,
                           bool consider_volumes)
 {
     label Msize;
@@ -358,27 +366,27 @@ Eigen::VectorXd getCoeffs(GeometricField<Type, PatchField, GeoMesh>&
 }
 
 template Eigen::VectorXd getCoeffs(
-    GeometricField<scalar, fvPatchField, volMesh>&
-    snapshot, PtrList<GeometricField<scalar, fvPatchField, volMesh>>& modes,
+    GeometricField<scalar, fvPatchField, volMesh> &
+    snapshot, PtrList<GeometricField<scalar, fvPatchField, volMesh>> & modes,
     label Nmodes,
     bool consider_volumes);
 
 template Eigen::VectorXd getCoeffs(
-    GeometricField<scalar, fvsPatchField, surfaceMesh>&
-    snapshot, PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>>& modes,
+    GeometricField<scalar, fvsPatchField, surfaceMesh> &
+    snapshot, PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>> & modes,
     label Nmodes,
     bool consider_volumes = false);
 
 template Eigen::VectorXd getCoeffs(
-    GeometricField<vector, fvPatchField, volMesh>&
-    snapshot, PtrList<GeometricField<vector, fvPatchField, volMesh>>& modes,
+    GeometricField<vector, fvPatchField, volMesh> &
+    snapshot, PtrList<GeometricField<vector, fvPatchField, volMesh>> & modes,
     label Nmodes,
     bool consider_volumes);
 
 template<class Type, template<class> class PatchField, class GeoMesh>
-Eigen::MatrixXd getCoeffs(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
+Eigen::MatrixXd getCoeffs(PtrList<GeometricField<Type, PatchField, GeoMesh>> &
                           snapshots,
-                          PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes, label Nmodes,
+                          PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes, label Nmodes,
                           bool consider_volumes)
 {
     label Msize;
@@ -405,20 +413,20 @@ Eigen::MatrixXd getCoeffs(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
 }
 
 template Eigen::MatrixXd getCoeffs(
-    PtrList<GeometricField<scalar, fvPatchField, volMesh>>&
-    snapshot, PtrList<GeometricField<scalar, fvPatchField, volMesh>>& modes,
+    PtrList<GeometricField<scalar, fvPatchField, volMesh>> &
+    snapshot, PtrList<GeometricField<scalar, fvPatchField, volMesh>> & modes,
     label Nmodes,
     bool consider_volumes);
 
 template Eigen::MatrixXd getCoeffs(
-    PtrList<GeometricField<vector, fvPatchField, volMesh>>&
-    snapshot, PtrList<GeometricField<vector, fvPatchField, volMesh>>& modes,
+    PtrList<GeometricField<vector, fvPatchField, volMesh>> &
+    snapshot, PtrList<GeometricField<vector, fvPatchField, volMesh>> & modes,
     label Nmodes,
     bool consider_volumes);
 
 template Eigen::MatrixXd getCoeffs(
-    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>>&
-    snapshot, PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>>& modes,
+    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>> &
+    snapshot, PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>> & modes,
     label Nmodes,
     bool consider_volumes);
 
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.H b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.H
index 26bf78639..f8154632c 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.H
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAcoeffsMass.H
@@ -76,8 +76,8 @@ namespace ITHACAutilities
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
 PtrList<GeometricField<Type, PatchField, GeoMesh>> reconstructFromCoeff(
-            PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes,
-            Eigen::MatrixXd& coeff_matrix, label Nmodes);
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes,
+    Eigen::MatrixXd& coeff_matrix, label Nmodes);
 
 //-----------------------------------------------------------------------------
 /// Gets the mass matrix using the eigen routine
@@ -92,7 +92,8 @@ PtrList<GeometricField<Type, PatchField, GeoMesh>> reconstructFromCoeff(
 /// @return     The mass matrix eigen.
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
-Eigen::MatrixXd getMassMatrix(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
+Eigen::MatrixXd getMassMatrix(PtrList<GeometricField<Type, PatchField, GeoMesh>>
+                              &
                               fields, label nModes = 0,
                               bool consider_volumes = true);
 
@@ -109,9 +110,10 @@ Eigen::MatrixXd getMassMatrix(PtrList<GeometricField<Type, PatchField, GeoMesh>>
 /// @return     The cross mass matrix eigen.
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
-Eigen::MatrixXd getMassMatrix(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
+Eigen::MatrixXd getMassMatrix(PtrList<GeometricField<Type, PatchField, GeoMesh>>
+                              &
                               fields,
-                              PtrList<GeometricField<Type, PatchField, GeoMesh>>&
+                              PtrList<GeometricField<Type, PatchField, GeoMesh>> &
                               fields2, label nModes = 0,
                               bool consider_volumes = true);
 
@@ -120,7 +122,7 @@ Eigen::MatrixXd getMassMatrix(PtrList<GeometricField<Type, PatchField, GeoMesh>>
 ///
 /// @param[in]  fields            The openFoam fields
 /// @param[in]  fields2           The second openFoam fields
-/// @param[in]  weights           Weights 
+/// @param[in]  weights           Weights
 /// @param[in]  consider_volumes  True if you want to consider the volumes
 ///
 /// @tparam     Type        vector or scalar.
@@ -130,8 +132,9 @@ Eigen::MatrixXd getMassMatrix(PtrList<GeometricField<Type, PatchField, GeoMesh>>
 /// @return     The cross mass matrix eigen.
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
-Eigen::MatrixXd getMassMatrix(PtrList<GeometricField<Type, PatchField, GeoMesh>>& fields,
-                              PtrList<GeometricField<Type, PatchField, GeoMesh>>& fields2, 
+Eigen::MatrixXd getMassMatrix(PtrList<GeometricField<Type, PatchField, GeoMesh>>
+                              & fields,
+                              PtrList<GeometricField<Type, PatchField, GeoMesh>> & fields2,
                               Eigen::VectorXd weights,
                               label Nmodes = 0,
                               bool consider_volumes = true);
@@ -150,7 +153,7 @@ Eigen::MatrixXd getMassMatrix(PtrList<GeometricField<Type, PatchField, GeoMesh>>
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
 Eigen::VectorXd getMassMatrixFV(
-    GeometricField<Type, PatchField, GeoMesh>& snapshot);
+    GeometricField<Type, PatchField, GeoMesh> & snapshot);
 
 //------------------------------------------------------------------------------
 /// Projects a snapshot on a basis function and gets
@@ -168,9 +171,9 @@ Eigen::VectorXd getMassMatrixFV(
 /// @return     The coefficients of the projection.
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
-Eigen::VectorXd getCoeffs(GeometricField<Type, PatchField, GeoMesh>&
+Eigen::VectorXd getCoeffs(GeometricField<Type, PatchField, GeoMesh> &
                           snapshot,
-                          PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes, label Nmodes = 0,
+                          PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes, label Nmodes = 0,
                           bool consider_volumes = true);
 
 //------------------------------------------------------------------------------
@@ -189,9 +192,9 @@ Eigen::VectorXd getCoeffs(GeometricField<Type, PatchField, GeoMesh>&
 /// @return     The coefficients of the projection.
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
-Eigen::MatrixXd getCoeffs(PtrList<GeometricField<Type, PatchField, GeoMesh>>&
+Eigen::MatrixXd getCoeffs(PtrList<GeometricField<Type, PatchField, GeoMesh>> &
                           snapshot,
-                          PtrList<GeometricField<Type, PatchField, GeoMesh>>& modes, label Nmodes = 0,
+                          PtrList<GeometricField<Type, PatchField, GeoMesh>> & modes, label Nmodes = 0,
                           bool consider_volumes = true);
 
 //--------------------------------------------------------------------------
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAerror.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAerror.C
index 42a6b5de2..290ebee20 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAerror.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAerror.C
@@ -38,23 +38,23 @@ namespace ITHACAutilities
 {
 
 template<>
-double L2Norm(GeometricField<scalar, fvPatchField, volMesh>& field)
+double L2Norm(GeometricField<scalar, fvPatchField, volMesh> & field)
 {
     double a;
-    a = Foam::sqrt(fvc::domainIntegrate(field * field).value());
+    a = Foam::sqrt(fvc::domainIntegrate(field* field).value());
     return a;
 }
 
 template<>
-double L2Norm(GeometricField<vector, fvPatchField, volMesh>& field)
+double L2Norm(GeometricField<vector, fvPatchField, volMesh> & field)
 {
     double a;
-    a = Foam::sqrt(fvc::domainIntegrate(field & field).value());
+    a = Foam::sqrt(fvc::domainIntegrate(field& field).value());
     return a;
 }
 
 template<>
-double LinfNorm(GeometricField<scalar, fvPatchField, volMesh>& field)
+double LinfNorm(GeometricField<scalar, fvPatchField, volMesh> & field)
 {
     double a;
     a = Foam::max(Foam::sqrt(field.internalField() *
@@ -63,7 +63,7 @@ double LinfNorm(GeometricField<scalar, fvPatchField, volMesh>& field)
 }
 
 template<>
-double LinfNorm(GeometricField<vector, fvPatchField, volMesh>& field)
+double LinfNorm(GeometricField<vector, fvPatchField, volMesh> & field)
 {
     double a;
     Info << "LinfNorm(GeometricField<vector, fvPatchField, volMesh>& field) is still to be implemented"
@@ -75,8 +75,8 @@ double LinfNorm(GeometricField<vector, fvPatchField, volMesh>& field)
 
 
 template<class Type, template<class> class PatchField, class GeoMesh>
-double errorFrobRel(GeometricField<Type, PatchField, GeoMesh>& field1,
-                    GeometricField<Type, PatchField, GeoMesh>& field2, List<label>* labels)
+double errorFrobRel(GeometricField<Type, PatchField, GeoMesh> & field1,
+                    GeometricField<Type, PatchField, GeoMesh> & field2, List<label>* labels)
 {
     double err;
     autoPtr<GeometricField<Type, PatchField, GeoMesh>> errField;
@@ -88,9 +88,9 @@ double errorFrobRel(GeometricField<Type, PatchField, GeoMesh>& field1,
     {
         submesh = autoPtr<fvMeshSubset>(new fvMeshSubset(field1.mesh()));
 #if OPENFOAM >= 1812
-        submesh->setCellSubset(*labels);
+        submesh->setCellSubset( * labels);
 #else
-        submesh->setLargeCellSubset(*labels);
+        submesh->setLargeCellSubset( * labels);
 #endif
         GeometricField<Type, PatchField, GeoMesh> field1tmp(submesh->interpolate(
                     field1));
@@ -125,22 +125,23 @@ double errorFrobRel(GeometricField<Type, PatchField, GeoMesh>& field1,
 }
 
 
-template double errorFrobRel(GeometricField<scalar, fvPatchField, volMesh>&
+template double errorFrobRel(GeometricField<scalar, fvPatchField, volMesh> &
                              field1,
-                             GeometricField<scalar, fvPatchField, volMesh>& field2, List<label>* labels);
-template double errorFrobRel(GeometricField<vector, fvPatchField, volMesh>&
+                             GeometricField<scalar, fvPatchField, volMesh> & field2, List<label>* labels);
+template double errorFrobRel(GeometricField<vector, fvPatchField, volMesh> &
                              field1,
-                             GeometricField<vector, fvPatchField, volMesh>& field2, List<label>* labels);
+                             GeometricField<vector, fvPatchField, volMesh> & field2, List<label>* labels);
 
-template double errorFrobRel(GeometricField<scalar, fvsPatchField, surfaceMesh>&
+template double errorFrobRel(GeometricField<scalar, fvsPatchField, surfaceMesh>
+                             &
                              field1,
-                             GeometricField<scalar, fvsPatchField, surfaceMesh>& field2,
+                             GeometricField<scalar, fvsPatchField, surfaceMesh> & field2,
                              List<label>* labels);
 
 
 template<typename T>
-double errorLinfRel(GeometricField<T, fvPatchField, volMesh>& field1,
-                    GeometricField<T, fvPatchField, volMesh>& field2, List<label>* labels)
+double errorLinfRel(GeometricField<T, fvPatchField, volMesh> & field1,
+                    GeometricField<T, fvPatchField, volMesh> & field2, List<label>* labels)
 {
     double err;
     autoPtr<GeometricField<T, fvPatchField, volMesh>> errField;
@@ -152,9 +153,9 @@ double errorLinfRel(GeometricField<T, fvPatchField, volMesh>& field1,
     {
         submesh = autoPtr<fvMeshSubset>(new fvMeshSubset(field1.mesh()));
 #if OPENFOAM >= 1812
-        submesh->setCellSubset(*labels);
+        submesh->setCellSubset( * labels);
 #else
-        submesh->setLargeCellSubset(*labels);
+        submesh->setLargeCellSubset( * labels);
 #endif
         GeometricField<T, fvPatchField, volMesh> field1tmp(submesh->interpolate(
                     field1));
@@ -189,16 +190,16 @@ double errorLinfRel(GeometricField<T, fvPatchField, volMesh>& field1,
 }
 
 
-template double errorLinfRel(GeometricField<scalar, fvPatchField, volMesh>&
+template double errorLinfRel(GeometricField<scalar, fvPatchField, volMesh> &
                              field1,
-                             GeometricField<scalar, fvPatchField, volMesh>& field2, List<label>* labels);
-template double errorLinfRel(GeometricField<vector, fvPatchField, volMesh>&
+                             GeometricField<scalar, fvPatchField, volMesh> & field2, List<label>* labels);
+template double errorLinfRel(GeometricField<vector, fvPatchField, volMesh> &
                              field1,
-                             GeometricField<vector, fvPatchField, volMesh>& field2, List<label>* labels);
+                             GeometricField<vector, fvPatchField, volMesh> & field2, List<label>* labels);
 
 template<>
-double errorL2Abs(GeometricField<vector, fvPatchField, volMesh>& field1,
-                  GeometricField<vector, fvPatchField, volMesh>& field2, volScalarField& Volumes)
+double errorL2Abs(GeometricField<vector, fvPatchField, volMesh> & field1,
+                  GeometricField<vector, fvPatchField, volMesh> & field2, volScalarField& Volumes)
 
 {
     volScalarField diffFields2 = (((field1 - field2) & (field1 - field2)) *
@@ -208,8 +209,8 @@ double errorL2Abs(GeometricField<vector, fvPatchField, volMesh>& field1,
 }
 
 template<>
-double errorL2Abs(GeometricField<scalar, fvPatchField, volMesh>& field1,
-                  GeometricField<scalar, fvPatchField, volMesh>& field2, volScalarField& Volumes)
+double errorL2Abs(GeometricField<scalar, fvPatchField, volMesh> & field1,
+                  GeometricField<scalar, fvPatchField, volMesh> & field2, volScalarField& Volumes)
 
 {
     volScalarField diffFields2 = (((field1 - field2) * (field1 - field2)) *
@@ -219,8 +220,8 @@ double errorL2Abs(GeometricField<scalar, fvPatchField, volMesh>& field1,
 }
 
 template<typename T>
-double errorL2Abs(GeometricField<T, fvPatchField, volMesh>& field1,
-                  GeometricField<T, fvPatchField, volMesh>& field2, List<label>* labels)
+double errorL2Abs(GeometricField<T, fvPatchField, volMesh> & field1,
+                  GeometricField<T, fvPatchField, volMesh> & field2, List<label>* labels)
 {
     autoPtr<GeometricField<T, fvPatchField, volMesh>> errField;
     autoPtr<GeometricField<T, fvPatchField, volMesh>> field1_S;
@@ -231,9 +232,9 @@ double errorL2Abs(GeometricField<T, fvPatchField, volMesh>& field1,
     {
         submesh = autoPtr<fvMeshSubset>(new fvMeshSubset(field1.mesh()));
 #if OPENFOAM >= 1812
-        submesh->setCellSubset(*labels);
+        submesh->setCellSubset( * labels);
 #else
-        submesh->setLargeCellSubset(*labels);
+        submesh->setLargeCellSubset( * labels);
 #endif
         GeometricField<T, fvPatchField, volMesh> field1tmp(submesh->interpolate(
                     field1));
@@ -258,18 +259,18 @@ double errorL2Abs(GeometricField<T, fvPatchField, volMesh>& field1,
     return err;
 }
 
-template double errorL2Abs(GeometricField<scalar, fvPatchField, volMesh>&
+template double errorL2Abs(GeometricField<scalar, fvPatchField, volMesh> &
                            field1,
-                           GeometricField<scalar, fvPatchField, volMesh>& field2, List<label>* labels);
-template double errorL2Abs(GeometricField<vector, fvPatchField, volMesh>&
+                           GeometricField<scalar, fvPatchField, volMesh> & field2, List<label>* labels);
+template double errorL2Abs(GeometricField<vector, fvPatchField, volMesh> &
                            field1,
-                           GeometricField<vector, fvPatchField, volMesh>& field2, List<label>* labels);
+                           GeometricField<vector, fvPatchField, volMesh> & field2, List<label>* labels);
 
 
 template<class T, template<class> class PatchField, class GeoMesh>
-Eigen::MatrixXd errorFrobRel(PtrList<GeometricField<T, PatchField, GeoMesh>>&
+Eigen::MatrixXd errorFrobRel(PtrList<GeometricField<T, PatchField, GeoMesh>> &
                              fields1,
-                             PtrList<GeometricField<T, PatchField, GeoMesh>>& fields2, List<label>* labels)
+                             PtrList<GeometricField<T, PatchField, GeoMesh>> & fields2, List<label>* labels)
 {
     Eigen::VectorXd err;
 
@@ -291,24 +292,24 @@ Eigen::MatrixXd errorFrobRel(PtrList<GeometricField<T, PatchField, GeoMesh>>&
 }
 
 template Eigen::MatrixXd errorFrobRel(
-    PtrList<GeometricField<scalar, fvPatchField, volMesh>>& fields1,
-    PtrList<GeometricField<scalar, fvPatchField, volMesh>>& fields2,
+    PtrList<GeometricField<scalar, fvPatchField, volMesh>> & fields1,
+    PtrList<GeometricField<scalar, fvPatchField, volMesh>> & fields2,
     List<label>* labels);
 template Eigen::MatrixXd errorFrobRel(
-    PtrList<GeometricField<vector, fvPatchField, volMesh>>& fields1,
-    PtrList<GeometricField<vector, fvPatchField, volMesh>>& fields2,
+    PtrList<GeometricField<vector, fvPatchField, volMesh>> & fields1,
+    PtrList<GeometricField<vector, fvPatchField, volMesh>> & fields2,
     List<label>* labels);
 template Eigen::MatrixXd errorFrobRel(
-    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>>& fields1,
-    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>>& fields2,
+    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>> & fields1,
+    PtrList<GeometricField<scalar, fvsPatchField, surfaceMesh>> & fields2,
     List<label>* labels);
 
 
 template<typename T>
 Eigen::MatrixXd errorL2Abs(
-    PtrList<GeometricField<T, fvPatchField, volMesh>>& fields1,
-    PtrList<GeometricField<T, fvPatchField, volMesh>>& fields2,
-    PtrList<volScalarField>& Volumes)
+    PtrList<GeometricField<T, fvPatchField, volMesh>> & fields1,
+    PtrList<GeometricField<T, fvPatchField, volMesh>> & fields2,
+    PtrList<volScalarField> & Volumes)
 {
     M_Assert(fields1.size() == fields2.size(),
              "The two fields do not have the same size, code will abort");
@@ -327,18 +328,19 @@ Eigen::MatrixXd errorL2Abs(
 }
 
 template Eigen::MatrixXd errorL2Abs(
-    PtrList<GeometricField<scalar, fvPatchField, volMesh>>& fields1,
-    PtrList<GeometricField<scalar, fvPatchField, volMesh>>& fields2,
-    PtrList<volScalarField>& Volumes);
+    PtrList<GeometricField<scalar, fvPatchField, volMesh>> & fields1,
+    PtrList<GeometricField<scalar, fvPatchField, volMesh>> & fields2,
+    PtrList<volScalarField> & Volumes);
 template Eigen::MatrixXd errorL2Abs(
-    PtrList<GeometricField<vector, fvPatchField, volMesh>>& fields1,
-    PtrList<GeometricField<vector, fvPatchField, volMesh>>& fields2,
-    PtrList<volScalarField>& Volumes);
+    PtrList<GeometricField<vector, fvPatchField, volMesh>> & fields1,
+    PtrList<GeometricField<vector, fvPatchField, volMesh>> & fields2,
+    PtrList<volScalarField> & Volumes);
 
 template<typename T>
-Eigen::MatrixXd errorL2Abs(PtrList<GeometricField<T, fvPatchField, volMesh>>&
+Eigen::MatrixXd errorL2Abs(PtrList<GeometricField<T, fvPatchField, volMesh>> &
                            fields1,
-                           PtrList<GeometricField<T, fvPatchField, volMesh>>& fields2, List<label>* labels)
+                           PtrList<GeometricField<T, fvPatchField, volMesh>> & fields2,
+                           List<label>* labels)
 {
     Eigen::VectorXd err;
 
@@ -360,17 +362,17 @@ Eigen::MatrixXd errorL2Abs(PtrList<GeometricField<T, fvPatchField, volMesh>>&
 }
 
 template Eigen::MatrixXd errorL2Abs(
-    PtrList<GeometricField<scalar, fvPatchField, volMesh>>& fields1,
-    PtrList<GeometricField<scalar, fvPatchField, volMesh>>& fields2,
+    PtrList<GeometricField<scalar, fvPatchField, volMesh>> & fields1,
+    PtrList<GeometricField<scalar, fvPatchField, volMesh>> & fields2,
     List<label>* labels);
 template Eigen::MatrixXd errorL2Abs(
-    PtrList<GeometricField<vector, fvPatchField, volMesh>>& fields1,
-    PtrList<GeometricField<vector, fvPatchField, volMesh>>& fields2,
+    PtrList<GeometricField<vector, fvPatchField, volMesh>> & fields1,
+    PtrList<GeometricField<vector, fvPatchField, volMesh>> & fields2,
     List<label>* labels);
 
 template<typename T>
-double errorL2Rel(GeometricField<T, fvPatchField, volMesh>& field1,
-                  GeometricField<T, fvPatchField, volMesh>& field2, List<label>* labels)
+double errorL2Rel(GeometricField<T, fvPatchField, volMesh> & field1,
+                  GeometricField<T, fvPatchField, volMesh> & field2, List<label>* labels)
 {
     double err;
     autoPtr<GeometricField<T, fvPatchField, volMesh>> errField;
@@ -382,9 +384,9 @@ double errorL2Rel(GeometricField<T, fvPatchField, volMesh>& field1,
     {
         submesh = autoPtr<fvMeshSubset>(new fvMeshSubset(field1.mesh()));
 #if OPENFOAM >= 1812
-        submesh->setCellSubset(*labels);
+        submesh->setCellSubset( * labels);
 #else
-        submesh->setLargeCellSubset(*labels);
+        submesh->setLargeCellSubset( * labels);
 #endif
         GeometricField<T, fvPatchField, volMesh> field1tmp(submesh->interpolate(
                     field1));
@@ -419,16 +421,16 @@ double errorL2Rel(GeometricField<T, fvPatchField, volMesh>& field1,
     return err;
 }
 
-template double errorL2Rel(GeometricField<scalar, fvPatchField, volMesh>&
+template double errorL2Rel(GeometricField<scalar, fvPatchField, volMesh> &
                            field1,
-                           GeometricField<scalar, fvPatchField, volMesh>& field2, List<label>* labels);
-template double errorL2Rel(GeometricField<vector, fvPatchField, volMesh>&
+                           GeometricField<scalar, fvPatchField, volMesh> & field2, List<label>* labels);
+template double errorL2Rel(GeometricField<vector, fvPatchField, volMesh> &
                            field1,
-                           GeometricField<vector, fvPatchField, volMesh>& field2, List<label>* labels);
+                           GeometricField<vector, fvPatchField, volMesh> & field2, List<label>* labels);
 
 template<typename T>
-Eigen::MatrixXd errorL2Rel(PtrList<GeometricField<T, fvPatchField, volMesh>>&
-                           fields1, PtrList<GeometricField<T, fvPatchField, volMesh>>& fields2,
+Eigen::MatrixXd errorL2Rel(PtrList<GeometricField<T, fvPatchField, volMesh>> &
+                           fields1, PtrList<GeometricField<T, fvPatchField, volMesh>> & fields2,
                            List<label>* labels)
 {
     Eigen::VectorXd err;
@@ -451,16 +453,16 @@ Eigen::MatrixXd errorL2Rel(PtrList<GeometricField<T, fvPatchField, volMesh>>&
 }
 
 template Eigen::MatrixXd errorL2Rel(
-    PtrList<GeometricField<scalar, fvPatchField, volMesh>>& fields1,
-    PtrList<GeometricField<scalar, fvPatchField, volMesh>>& fields2,
+    PtrList<GeometricField<scalar, fvPatchField, volMesh>> & fields1,
+    PtrList<GeometricField<scalar, fvPatchField, volMesh>> & fields2,
     List<label>* labels);
 template Eigen::MatrixXd errorL2Rel(
-    PtrList<GeometricField<vector, fvPatchField, volMesh>>& fields1,
-    PtrList<GeometricField<vector, fvPatchField, volMesh>>& fields2,
+    PtrList<GeometricField<vector, fvPatchField, volMesh>> & fields1,
+    PtrList<GeometricField<vector, fvPatchField, volMesh>> & fields2,
     List<label>* labels);
 
 template<>
-double H1Seminorm(GeometricField<scalar, fvPatchField, volMesh>& field)
+double H1Seminorm(GeometricField<scalar, fvPatchField, volMesh> & field)
 {
     double a;
     a = Foam::sqrt(fvc::domainIntegrate(fvc::grad(field) & fvc::grad(
@@ -469,7 +471,7 @@ double H1Seminorm(GeometricField<scalar, fvPatchField, volMesh>& field)
 }
 
 template<>
-double H1Seminorm(GeometricField<vector, fvPatchField, volMesh>& field)
+double H1Seminorm(GeometricField<vector, fvPatchField, volMesh> & field)
 {
     double a;
     a = Foam::sqrt(fvc::domainIntegrate(fvc::grad(field)
@@ -479,7 +481,7 @@ double H1Seminorm(GeometricField<vector, fvPatchField, volMesh>& field)
 
 
 template<class Type, template<class> class PatchField, class GeoMesh>
-double frobNorm(GeometricField<Type, PatchField, GeoMesh>& field)
+double frobNorm(GeometricField<Type, PatchField, GeoMesh> & field)
 {
     double norm(0);
     Eigen::VectorXd vF = Foam2Eigen::field2Eigen(field);
@@ -487,8 +489,8 @@ double frobNorm(GeometricField<Type, PatchField, GeoMesh>& field)
     return norm;
 }
 
-template double frobNorm(GeometricField<scalar, fvPatchField, volMesh>& field);
-template double frobNorm(GeometricField<vector, fvPatchField, volMesh>& field);
+template double frobNorm(GeometricField<scalar, fvPatchField, volMesh> & field);
+template double frobNorm(GeometricField<vector, fvPatchField, volMesh> & field);
 
 double L2normOnPatch(fvMesh& mesh, volScalarField& field,
                      word patch)
@@ -504,13 +506,14 @@ double L2normOnPatch(fvMesh& mesh, volScalarField& field,
         //id of the owner cell having the face
         label faceOwner = faceCells[faceI] ;
         scalar faceArea = mesh.magSf().boundaryField()[patchID][faceI];
-        L2 += faceArea * field[faceOwner] * field[faceOwner];
+        L2 += faceArea* field[faceOwner] * field[faceOwner];
     }
+
     return Foam::sqrt(L2);
 }
 
-double L2productOnPatch(fvMesh& mesh, List<scalar>& field1,
-                        List<scalar>& field2, word patch)
+double L2productOnPatch(fvMesh& mesh, List<scalar> & field1,
+                        List<scalar> & field2, word patch)
 {
     M_Assert(field1.size() == field2.size(),
              "The two fields do not have the same size, code will abort");
@@ -523,8 +526,9 @@ double L2productOnPatch(fvMesh& mesh, List<scalar>& field1,
     forAll(cPatch, faceI)
     {
         scalar faceArea = mesh.magSf().boundaryField()[patchID][faceI];
-        L2 += faceArea * field1[faceI] * field2[faceI];
+        L2 += faceArea* field1[faceI] * field2[faceI];
     }
+
     return L2;
 }
 
@@ -550,6 +554,7 @@ double LinfNormOnPatch(fvMesh& mesh, volScalarField& field,
             Linf = std::abs(field[faceOwner]);
         }
     }
+
     return Linf;
 }
 
@@ -567,8 +572,9 @@ double integralOnPatch(fvMesh& mesh, volScalarField& field,
         //id of the owner cell having the face
         label faceOwner = faceCells[faceI] ;
         scalar faceArea = mesh.magSf().boundaryField()[patchID][faceI];
-        integral += faceArea * field[faceOwner];
+        integral += faceArea* field[faceOwner];
     }
+
     return integral;
 }
 
@@ -591,8 +597,9 @@ double integralOnPatch(fvMesh& mesh, List<scalar> field,
         //id of the owner cell having the face
         label faceOwner = faceCells[faceI] ;
         scalar faceArea = mesh.magSf().boundaryField()[patchID][faceI];
-        integral += faceArea * field[faceI];
+        integral += faceArea* field[faceI];
     }
+
     return integral;
 }
 
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAerror.H b/src/ITHACA_CORE/ITHACAutilities/ITHACAerror.H
index 002564ef4..2ab79f7be 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAerror.H
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAerror.H
@@ -69,8 +69,8 @@ namespace ITHACAutilities
 /// @return     Frobenius norm of the relative error.
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
-double errorFrobRel(GeometricField<Type, PatchField, GeoMesh>& field1,
-                    GeometricField<Type, PatchField, GeoMesh>& field2, List<label>* labels = NULL);
+double errorFrobRel(GeometricField<Type, PatchField, GeoMesh> & field1,
+                    GeometricField<Type, PatchField, GeoMesh> & field2, List<label>* labels = NULL);
 
 //--------------------------------------------------------------------------
 /// @brief      Computes the relative error between two geometric Fields in L2 norm
@@ -84,8 +84,8 @@ double errorFrobRel(GeometricField<Type, PatchField, GeoMesh>& field1,
 /// @return     L2 norm of the relative error.
 ///
 template<typename T>
-double errorL2Rel(GeometricField<T, fvPatchField, volMesh>& field1,
-                  GeometricField<T, fvPatchField, volMesh>& field2, List<label>* labels = NULL);
+double errorL2Rel(GeometricField<T, fvPatchField, volMesh> & field1,
+                  GeometricField<T, fvPatchField, volMesh> & field2, List<label>* labels = NULL);
 
 //--------------------------------------------------------------------------
 /// @brief      Computes the relative error between two geometric Fields in Linf norm
@@ -99,8 +99,8 @@ double errorL2Rel(GeometricField<T, fvPatchField, volMesh>& field1,
 /// @return     Linf norm of the relative error.
 ///
 template<typename T>
-double errorLinfRel(GeometricField<T, fvPatchField, volMesh>& field1,
-                    GeometricField<T, fvPatchField, volMesh>& field2, List<label>* labels = NULL);
+double errorLinfRel(GeometricField<T, fvPatchField, volMesh> & field1,
+                    GeometricField<T, fvPatchField, volMesh> & field2, List<label>* labels = NULL);
 
 //--------------------------------------------------------------------------
 /// @brief      Computes the absolute error between two geometric Fields in
@@ -115,8 +115,8 @@ double errorLinfRel(GeometricField<T, fvPatchField, volMesh>& field1,
 /// @return     L2 norm of the absolute error.
 ///
 template<typename T>
-double errorL2Abs(GeometricField<T, fvPatchField, volMesh>& field1,
-                  GeometricField<T, fvPatchField, volMesh>& field2, volScalarField& Volumes);
+double errorL2Abs(GeometricField<T, fvPatchField, volMesh> & field1,
+                  GeometricField<T, fvPatchField, volMesh> & field2, volScalarField& Volumes);
 
 //--------------------------------------------------------------------------
 /// @brief      Computes the absolute error between two Fields in L2 norm
@@ -130,8 +130,8 @@ double errorL2Abs(GeometricField<T, fvPatchField, volMesh>& field1,
 /// @return     L2 norm of the absolute error.
 ///
 template<typename T>
-double errorL2Abs(GeometricField<T, fvPatchField, volMesh>& field1,
-                  GeometricField<T, fvPatchField, volMesh>& field2, List<label>* labels = NULL);
+double errorL2Abs(GeometricField<T, fvPatchField, volMesh> & field1,
+                  GeometricField<T, fvPatchField, volMesh> & field2, List<label>* labels = NULL);
 
 //--------------------------------------------------------------------------
 /// @brief      Computes the relative error in L2 norm between two lists of fields
@@ -145,9 +145,9 @@ double errorL2Abs(GeometricField<T, fvPatchField, volMesh>& field1,
 /// @return     Column vector, in each row the L2 norm of the relative error.
 ///
 template<typename T>
-Eigen::MatrixXd errorL2Rel(PtrList<GeometricField<T, fvPatchField, volMesh>>&
+Eigen::MatrixXd errorL2Rel(PtrList<GeometricField<T, fvPatchField, volMesh>> &
                            fields1,
-                           PtrList<GeometricField<T, fvPatchField, volMesh>>& fields2,
+                           PtrList<GeometricField<T, fvPatchField, volMesh>> & fields2,
                            List<label>* labels = NULL);
 
 //--------------------------------------------------------------------------
@@ -162,9 +162,9 @@ Eigen::MatrixXd errorL2Rel(PtrList<GeometricField<T, fvPatchField, volMesh>>&
 /// @return     Column vector, in each row the Frobenius norm of the relative error.
 ///
 template<class T, template<class> class PatchField, class GeoMesh>
-Eigen::MatrixXd errorFrobRel(PtrList<GeometricField<T, PatchField, GeoMesh>>&
+Eigen::MatrixXd errorFrobRel(PtrList<GeometricField<T, PatchField, GeoMesh>> &
                              fields1,
-                             PtrList<GeometricField<T, PatchField, GeoMesh>>& fields2,
+                             PtrList<GeometricField<T, PatchField, GeoMesh>> & fields2,
                              List<label>* labels = NULL);
 //--------------------------------------------------------------------------
 
@@ -181,9 +181,9 @@ Eigen::MatrixXd errorFrobRel(PtrList<GeometricField<T, PatchField, GeoMesh>>&
 ///
 template<typename T>
 Eigen::MatrixXd errorL2Abs(
-    PtrList<GeometricField<T, fvPatchField, volMesh>>& fields1,
-    PtrList<GeometricField<T, fvPatchField, volMesh>>& fields2,
-    PtrList<volScalarField>& Volumes);
+    PtrList<GeometricField<T, fvPatchField, volMesh>> & fields1,
+    PtrList<GeometricField<T, fvPatchField, volMesh>> & fields2,
+    PtrList<volScalarField> & Volumes);
 
 //--------------------------------------------------------------------------
 /// @brief      Computes the absolute error in L2 norm between two lists of Fields
@@ -197,9 +197,9 @@ Eigen::MatrixXd errorL2Abs(
 /// @return     column vector, in each row the L2 norm of the absolute error.
 ///
 template<typename T>
-Eigen::MatrixXd errorL2Abs(PtrList<GeometricField<T, fvPatchField, volMesh>>&
+Eigen::MatrixXd errorL2Abs(PtrList<GeometricField<T, fvPatchField, volMesh>> &
                            fields1,
-                           PtrList<GeometricField<T, fvPatchField, volMesh>>& fields2,
+                           PtrList<GeometricField<T, fvPatchField, volMesh>> & fields2,
                            List<label>* labels = NULL);
 
 //------------------------------------------------------------------------------
@@ -212,7 +212,7 @@ Eigen::MatrixXd errorL2Abs(PtrList<GeometricField<T, fvPatchField, volMesh>>&
 /// @return     L2 norm of the volVectorField.
 ///
 template<class T>
-double L2Norm(GeometricField<T, fvPatchField, volMesh>& field);
+double L2Norm(GeometricField<T, fvPatchField, volMesh> & field);
 
 //------------------------------------------------------------------------------
 /// Evaluate the Linf norm of a geometric field
@@ -224,7 +224,7 @@ double L2Norm(GeometricField<T, fvPatchField, volMesh>& field);
 /// @return     Linf norm of the volVectorField.
 ///
 template<class T>
-double LinfNorm(GeometricField<T, fvPatchField, volMesh>& field);
+double LinfNorm(GeometricField<T, fvPatchField, volMesh> & field);
 
 //------------------------------------------------------------------------------
 /// Evaluate the H1 seminorm of a geoemtri
@@ -236,7 +236,7 @@ double LinfNorm(GeometricField<T, fvPatchField, volMesh>& field);
 /// @return     H1 seminorm of the volVectorField.
 ///
 template<class T>
-double H1Seminorm(GeometricField<T, fvPatchField, volMesh>& field);
+double H1Seminorm(GeometricField<T, fvPatchField, volMesh> & field);
 
 //------------------------------------------------------------------------------
 /// Evaluate the Frobenius norm of a field
@@ -248,7 +248,7 @@ double H1Seminorm(GeometricField<T, fvPatchField, volMesh>& field);
 /// @return     Frobenius norm of the field.
 ///
 template<class Type, template<class> class PatchField, class GeoMesh>
-double frobNorm(GeometricField<Type, PatchField, GeoMesh>& field);
+double frobNorm(GeometricField<Type, PatchField, GeoMesh> & field);
 
 //--------------------------------------------------------------------------
 /// Evaluate the L2 norm of a field on a boundary patch
@@ -271,8 +271,8 @@ double L2normOnPatch(fvMesh& mesh, volScalarField& field, word patch);
 ///
 /// @return     L2 norm of the field on the patch.
 ///
-double L2productOnPatch(fvMesh& mesh, List<scalar>& field1,
-                        List<scalar>& field2, word patch);
+double L2productOnPatch(fvMesh& mesh, List<scalar> & field1,
+                        List<scalar> & field2, word patch);
 
 //--------------------------------------------------------------------------
 /// Evaluate the Linf norm of a field on a boundary patch
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAforces.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAforces.C
old mode 100755
new mode 100644
index 51be5551f..1d81b05b2
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAforces.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAforces.C
@@ -137,18 +137,21 @@ void Foam::functionObjects::ITHACAforces::writeBinHeader
         binPoints[pointi] = (binMin_ + (pointi + 1) * binDx_) * binDir_;
         os  << tab << binPoints[pointi].x();
     }
+
     os  << nl;
     writeCommented(os, "y co-ords  :");
     forAll(binPoints, pointi)
     {
         os  << tab << binPoints[pointi].y();
     }
+
     os  << nl;
     writeCommented(os, "z co-ords  :");
     forAll(binPoints, pointi)
     {
         os  << tab << binPoints[pointi].z();
     }
+
     os  << nl;
     writeHeader(os, "");
     writeCommented(os, "Time");
@@ -239,7 +242,7 @@ void Foam::functionObjects::ITHACAforces::initialiseBins()
             const scalarField dd(mesh_.C() & binDir_);
             forAllConstIter(HashTable<const porosityModel*>, models, iter)
             {
-                const porosityModel& pm = *iter();
+                const porosityModel& pm = * iter();
                 const labelList& cellZoneIDs = pm.cellZoneIDs();
 
                 for (const label zonei : cellZoneIDs)
@@ -334,7 +337,7 @@ Foam::functionObjects::ITHACAforces::devRhoReff() const
             lookupObject<dictionary>("transportProperties");
         dimensionedScalar nu("nu", dimViscosity, transportProperties);
         const volVectorField& U = lookupObject<volVectorField>(UName_);
-        return -rho() * nu * dev(twoSymm(fvc::grad(U)));
+        return -rho() * nu* dev(twoSymm(fvc::grad(U)));
     }
     else
     {
@@ -436,13 +439,13 @@ void Foam::functionObjects::ITHACAforces::applyBins
         force_[0][0] += sum(fN);
         force_[1][0] += sum(fT);
         force_[2][0] += sum(fP);
-        moment_[0][0] += sum(Md ^ fN);
-        moment_[1][0] += sum(Md ^ fT);
-        moment_[2][0] += sum(Md ^ fP);
+        moment_[0][0] += sum(Md^ fN);
+        moment_[1][0] += sum(Md^ fT);
+        moment_[2][0] += sum(Md^ fP);
     }
     else
     {
-        scalarField dd((d & binDir_) - binMin_);
+        scalarField dd((d& binDir_) - binMin_);
         forAll(dd, i)
         {
             label bini = min(max(floor(dd[i] / binDx_), 0), force_[0].size() - 1);
@@ -515,7 +518,7 @@ void Foam::functionObjects::ITHACAforces::writeIntegratedForceMoment
     const vectorField& fm0,
     const vectorField& fm1,
     const vectorField& fm2,
-    autoPtr<OFstream>& osPtr
+    autoPtr<OFstream> & osPtr
 ) const
 {
     vector pressure = sum(fm0);
@@ -600,8 +603,8 @@ void Foam::functionObjects::ITHACAforces::writeForces()
 
 void Foam::functionObjects::ITHACAforces::writeBinnedForceMoment
 (
-    const List<Field<vector>>& fm,
-    autoPtr<OFstream>& osPtr
+    const List<Field<vector>> & fm,
+    autoPtr<OFstream> & osPtr
 ) const
 {
     if ((nBin_ == 1) || !writeToFile())
@@ -639,6 +642,7 @@ void Foam::functionObjects::ITHACAforces::writeBinnedForceMoment
             os  << tab << f[2][i];
         }
     }
+
     os  << nl;
 }
 
@@ -909,7 +913,7 @@ bool Foam::functionObjects::ITHACAforces::read(const dictionary& dict)
                     IOobject::NO_WRITE
                 ),
                 mesh_,
-                dimensionedVector(dimForce * dimLength, Zero)
+                dimensionedVector(dimForce* dimLength, Zero)
             )
         );
         mesh_.objectRegistry::store(momentPtr);
@@ -945,7 +949,7 @@ void Foam::functionObjects::ITHACAforces::calcForcesMoment()
                 )
             );
             // Tangential force (total force minus normal fN)
-            vectorField fT(sA * fD.boundaryField()[patchi] - fN);
+            vectorField fT(sA* fD.boundaryField()[patchi] - fN);
             // Porous force
             vectorField fP(Md.size(), Zero);
             addToFields(patchi, Md, fN, fT, fP);
@@ -970,7 +974,7 @@ void Foam::functionObjects::ITHACAforces::calcForcesMoment()
             );
             vectorField fN
             (
-                rho(p)*Sfb[patchi] * (p.boundaryField()[patchi] - pRef)
+                rho(p) * Sfb[patchi] * (p.boundaryField()[patchi] - pRef)
             );
             vectorField fT(Sfb[patchi] & devRhoReffb[patchi]);
             vectorField fP(Md.size(), Zero);
@@ -998,7 +1002,7 @@ void Foam::functionObjects::ITHACAforces::calcForcesMoment()
         forAllConstIters(models, iter)
         {
             // Non-const access required if mesh is changing
-            porosityModel& pm = const_cast<porosityModel&>(*iter());
+            porosityModel& pm = const_cast<porosityModel&>( * iter());
             vectorField fPTot(pm.force(U, rho, mu));
             const labelList& cellZoneIDs = pm.cellZoneIDs();
 
@@ -1174,18 +1178,21 @@ void Foam::functionObjects::ITHACAforces::writeFileHeader(const label i)
                 binPoints[pointi] = (binMin_ + (pointi + 1) * binDx_) * binDir_;
                 file(i) << tab << binPoints[pointi].x();
             }
+
             file(i) << nl;
             writeCommented(file(i), "y co-ords  :");
             forAll(binPoints, pointi)
             {
                 file(i) << tab << binPoints[pointi].y();
             }
+
             file(i) << nl;
             writeCommented(file(i), "z co-ords  :");
             forAll(binPoints, pointi)
             {
                 file(i) << tab << binPoints[pointi].z();
             }
+
             file(i) << nl;
             writeCommented(file(i), "Time");
             const word binForceTypes("[pressure,viscous,porous]");
@@ -1310,7 +1317,7 @@ Foam::functionObjects::ITHACAforces::devRhoReff() const
             obr_.lookupObject<dictionary>("transportProperties");
         dimensionedScalar nu(transportProperties.lookup("nu"));
         const volVectorField& U = obr_.lookupObject<volVectorField>(UName_);
-        return -rho() * nu * dev(twoSymm(fvc::grad(U)));
+        return -rho() * nu* dev(twoSymm(fvc::grad(U)));
     }
     else
     {
@@ -1422,13 +1429,13 @@ void Foam::functionObjects::ITHACAforces::applyBins
         force_[0][0] += sum(fN);
         force_[1][0] += sum(fT);
         force_[2][0] += sum(fP);
-        moment_[0][0] += sum(Md ^ fN);
-        moment_[1][0] += sum(Md ^ fT);
-        moment_[2][0] += sum(Md ^ fP);
+        moment_[0][0] += sum(Md^ fN);
+        moment_[1][0] += sum(Md^ fT);
+        moment_[2][0] += sum(Md^ fP);
     }
     else
     {
-        scalarField dd((d & binDir_) - binMin_);
+        scalarField dd((d& binDir_) - binMin_);
         forAll(dd, i)
         {
             label bini = min(max(floor(dd[i] / binDx_), 0), force_[0].size() - 1);
@@ -1730,6 +1737,7 @@ bool Foam::functionObjects::ITHACAforces::read(const dictionary& dict)
                 binMin_ = min(min(d), binMin_);
                 binMax = max(max(d), binMax);
             }
+
             reduce(binMin_, minOp<scalar>());
             reduce(binMax, maxOp<scalar>());
             // slightly boost binMax so that region of interest is fully
@@ -1742,6 +1750,7 @@ bool Foam::functionObjects::ITHACAforces::read(const dictionary& dict)
             {
                 binPoints_[i] = (i + 0.5) * binDir_ * binDx_;
             }
+
             binDict.lookup("cumulative") >> binCumulative_;
             // allocate storage for forces and moments
             forAll(force_, i)
@@ -1799,7 +1808,7 @@ void Foam::functionObjects::ITHACAforces::calcForcesMoment()
                 )
             );
             // Tangential force (total force minus normal fN)
-            vectorField fT(sA * fD.boundaryField()[patchi] - fN);
+            vectorField fT(sA* fD.boundaryField()[patchi] - fN);
             //- Porous force
             vectorField fP(Md.size(), Zero);
             applyBins(Md, fN, fT, fP, mesh_.C().boundaryField()[patchi]);
@@ -1824,7 +1833,7 @@ void Foam::functionObjects::ITHACAforces::calcForcesMoment()
             );
             vectorField fN
             (
-                rho(p)*Sfb[patchi] * (p.boundaryField()[patchi] - pRef)
+                rho(p) * Sfb[patchi] * (p.boundaryField()[patchi] - pRef)
             );
             vectorField fT(Sfb[patchi] & devRhoReffb[patchi]);
             vectorField fP(Md.size(), Zero);
@@ -1851,7 +1860,7 @@ void Foam::functionObjects::ITHACAforces::calcForcesMoment()
         forAllConstIter(HashTable<const porosityModel*>, models, iter)
         {
             // non-const access required if mesh is changing
-            porosityModel& pm = const_cast<porosityModel&>(*iter());
+            porosityModel& pm = const_cast<porosityModel&>( * iter());
             vectorField fPTot(pm.force(U, rho, mu));
             const labelList& cellZoneIDs = pm.cellZoneIDs();
             forAll(cellZoneIDs, i)
@@ -1921,5 +1930,6 @@ bool Foam::functionObjects::ITHACAforces::write()
 
     return true;
 }
+
 #endif
 // ************************************************************************* //
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAforces18.H b/src/ITHACA_CORE/ITHACAutilities/ITHACAforces18.H
old mode 100755
new mode 100644
index 24696a5ce..4db64b7eb
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAforces18.H
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAforces18.H
@@ -226,7 +226,7 @@ class ITHACAforces
             const vectorField& fm0,
             const vectorField& fm1,
             const vectorField& fm2,
-            autoPtr<OFstream>& osPtr
+            autoPtr<OFstream> & osPtr
         ) const;
 
         //- Write force data
@@ -235,8 +235,8 @@ class ITHACAforces
         //- Helper function to write binned forces and moments
         void writeBinnedForceMoment
         (
-            const List<Field<vector>>& fm,
-            autoPtr<OFstream>& osPtr
+            const List<Field<vector>> & fm,
+            autoPtr<OFstream> & osPtr
         ) const;
 
         //- Write binned data
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAgeometry.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAgeometry.C
index 90cbf2bc9..c4f6a8fd6 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAgeometry.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAgeometry.C
@@ -29,7 +29,7 @@ namespace ITHACAutilities
 {
 
 labelList getIndicesFromBox(const fvMesh& mesh, List<label> indices,
-                            Eigen::MatrixXd Box, List<vector>& points2Move)
+                            Eigen::MatrixXd Box, List<vector> & points2Move)
 {
     points2Move.resize(0);
     labelList boxIndices;
@@ -82,6 +82,7 @@ List<label> getIndices(const fvMesh& mesh, int index, int layers)
     {
         out2.append(out[uniqueIndex[i]]);
     }
+
     return out2;
 }
 
@@ -110,11 +111,12 @@ List<label> getIndices(const fvMesh& mesh, int index_row,
     {
         out2.append(out[uniqueIndex[i]]);
     }
+
     return out2;
 }
 
 void getPointsFromPatch(fvMesh& mesh, label ind,
-                        List<vector>& points, labelList& indices)
+                        List<vector> & points, labelList& indices)
 {
     pointField meshPoints(mesh.points());
     const polyPatch& patchFound = mesh.boundaryMesh()[ind];
@@ -210,13 +212,13 @@ vector displacePolabel(vector x0, vector x_low, vector x_up,
         t2 = t1;
     }
 
-    Info << abs((x_low + t0 * direction - x0)[0]) << endl;
-    Info << abs((x_low + t1 * direction - x0)[1]) << endl;
-    Info << abs((x_low + t2 * direction - x0)[2]) << endl;
-    M_Assert(abs(abs((x_low + t0 * direction - x0)[0]) + abs((
-                     x_low + t0 * direction - x0)[1]) + abs((x_low + t0 * direction - x0)[2])) <
+    Info << abs((x_low + t0* direction - x0)[0]) << endl;
+    Info << abs((x_low + t1* direction - x0)[1]) << endl;
+    Info << abs((x_low + t2* direction - x0)[2]) << endl;
+    M_Assert(abs(abs((x_low + t0* direction - x0)[0]) + abs((
+                     x_low + t0* direction - x0)[1]) + abs((x_low + t0* direction - x0)[2])) <
              1e-6, "The givent polabel is not on the segment");
-    vector def_polabel = x_low_def + t1 * direction_def;
+    vector def_polabel = x_low_def + t1* direction_def;
     Info << def_polabel << endl;
     return def_polabel;
 }
@@ -252,7 +254,7 @@ Field<vector> rotateMesh(fvMesh& mesh, double r1, double r2,
             }
             else if (angleVariationMethod == "Sinusoidal")
             {
-                double theta = alpha / 180 *  constant::mathematical::pi * std::sin(
+                double theta = alpha / 180 *  constant::mathematical::pi* std::sin(
                                    constant::mathematical::pi / 2 * (r2 - l) / (r2 - r1));
                 quaternion q(axis, theta);
                 pointRot[movingPointsIDs[i]] = q.transform(pointNow);
@@ -280,15 +282,15 @@ Eigen::MatrixXd rotationMatrix(vector AxisOfRotation,
     scalar ux = AxisOfRotation[0] / di;
     scalar uy = AxisOfRotation[1] / di;
     scalar uz = AxisOfRotation[2] / di;
-    R(0, 0) = Foam::cos(theta) + ux * ux * (1 - Foam::cos(theta));
-    R(1, 0) = uy * ux * (1 - Foam::cos(theta)) + uz * Foam::sin(theta);
-    R(2, 0) = uz * ux * (1 - Foam::cos(theta)) - uy * Foam::sin(theta);
-    R(0, 1) = ux * uz * (1 - Foam::cos(theta)) - uz * Foam::sin(theta);
-    R(1, 1) = Foam::cos(theta) + uy * uy * (1 - Foam::cos(theta));
-    R(2, 1) = ux * uy * (1 - Foam::cos(theta)) + ux * Foam::sin(theta);
-    R(0, 2) = ux * uz * (1 - Foam::cos(theta)) + uy * Foam::sin(theta);
-    R(1, 2) = uy * uz * (1 - Foam::cos(theta)) - ux * Foam::sin(theta);
-    R(2, 2) = Foam::cos(theta) + uz * uz * (1 - Foam::cos(theta));
+    R(0, 0) = Foam::cos(theta) + ux* ux * (1 - Foam::cos(theta));
+    R(1, 0) = uy* ux * (1 - Foam::cos(theta)) + uz* Foam::sin(theta);
+    R(2, 0) = uz* ux * (1 - Foam::cos(theta)) - uy* Foam::sin(theta);
+    R(0, 1) = ux* uz * (1 - Foam::cos(theta)) - uz* Foam::sin(theta);
+    R(1, 1) = Foam::cos(theta) + uy* uy * (1 - Foam::cos(theta));
+    R(2, 1) = ux* uy * (1 - Foam::cos(theta)) + ux* Foam::sin(theta);
+    R(0, 2) = ux* uz * (1 - Foam::cos(theta)) + uy* Foam::sin(theta);
+    R(1, 2) = uy* uz * (1 - Foam::cos(theta)) - ux* Foam::sin(theta);
+    R(2, 2) = Foam::cos(theta) + uz* uz * (1 - Foam::cos(theta));
     return R;
 }
 
@@ -310,11 +312,12 @@ Eigen::VectorXd boudaryFaceToCellDistance(
         label faceOwner = faceCells[faceI] ;
         cellFaceDistance(faceI) = mag(mesh.C()[faceOwner] - mesh.Cf()[faceID]);
     }
+
     return (cellFaceDistance);
 }
 
 List<label> getIndicesFromDisc(const fvMesh& mesh, double radius,
-                               vector origin, vector axis, List<double>& radii)
+                               vector origin, vector axis, List<double> & radii)
 {
     pointField meshPoints(mesh.points());
     List<label> indices(meshPoints.size());
@@ -325,7 +328,7 @@ List<label> getIndicesFromDisc(const fvMesh& mesh, double radius,
     {
         vector pointNow = meshPoints[i];
         vector r = pointNow - origin;
-        vector projComponent = (r & axis) / (pow(mag(axis), 2)) * axis;
+        vector projComponent = (r& axis) / (pow(mag(axis), 2)) * axis;
         vector d = r - projComponent;
         double l = Foam::sqrt(pow(d[0],
                                   2) + pow(d[1], 2) + pow(d[2], 2));
@@ -345,7 +348,7 @@ List<label> getIndicesFromDisc(const fvMesh& mesh, double radius,
 
 template<typename type_f>
 List<label> getIndicesFromBox(
-    GeometricField<type_f, fvPatchField, volMesh>& field, Eigen::MatrixXd Box)
+    GeometricField<type_f, fvPatchField, volMesh> & field, Eigen::MatrixXd Box)
 {
     M_Assert(Box.rows() == 2
              && Box.cols() == 3,
@@ -372,13 +375,13 @@ List<label> getIndicesFromBox(
 }
 
 template List<label> getIndicesFromBox(
-    GeometricField<scalar, fvPatchField, volMesh>& field, Eigen::MatrixXd Box);
+    GeometricField<scalar, fvPatchField, volMesh> & field, Eigen::MatrixXd Box);
 template List<label> getIndicesFromBox(
-    GeometricField<vector, fvPatchField, volMesh>& field, Eigen::MatrixXd Box);
+    GeometricField<vector, fvPatchField, volMesh> & field, Eigen::MatrixXd Box);
 
 template<typename type_f>
 fvMeshSubset* getSubMeshFromBox(
-    GeometricField<type_f, fvPatchField, volMesh>& field, Eigen::MatrixXd Box)
+    GeometricField<type_f, fvPatchField, volMesh> & field, Eigen::MatrixXd Box)
 {
     List<label> indices = getIndicesFromBox(field, Box);
     fvMeshSubset* sub;
@@ -393,9 +396,9 @@ fvMeshSubset* getSubMeshFromBox(
 }
 
 template fvMeshSubset* getSubMeshFromBox(
-    GeometricField<scalar, fvPatchField, volMesh>& field, Eigen::MatrixXd Box);
+    GeometricField<scalar, fvPatchField, volMesh> & field, Eigen::MatrixXd Box);
 template fvMeshSubset* getSubMeshFromBox(
-    GeometricField<vector, fvPatchField, volMesh>& field, Eigen::MatrixXd Box);
+    GeometricField<vector, fvPatchField, volMesh> & field, Eigen::MatrixXd Box);
 
 volScalarField meshNonOrtho(fvMesh& mesh,
                             volScalarField& NonOrtho)
@@ -434,7 +437,7 @@ volScalarField meshNonOrtho(fvMesh& mesh,
     return NonOrtho;
 }
 
-List<vector> rotatePoints(const List<vector>& originalPoints,
+List<vector> rotatePoints(const List<vector> & originalPoints,
                           vector AxisOfRotation, double AngleOfRotation)
 {
     double theta = AngleOfRotation / 180 *  constant::mathematical::pi;
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAgeometry.H b/src/ITHACA_CORE/ITHACAutilities/ITHACAgeometry.H
old mode 100755
new mode 100644
index 14ce5fe74..56301339b
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAgeometry.H
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAgeometry.H
@@ -71,7 +71,7 @@ namespace ITHACAutilities
 /// @return     the labels list of the points
 ///
 labelList getIndicesFromBox(const fvMesh& mesh, List<label> indices,
-                            Eigen::MatrixXd Box, List<vector>& points2Move);
+                            Eigen::MatrixXd Box, List<vector> & points2Move);
 
 //--------------------------------------------------------------------------
 /// @brief      Gets the indices of the cells around a certain cell.
@@ -105,7 +105,7 @@ List<label> getIndices(const fvMesh& mesh, int index_row, int index_col,
 /// @param[out] points   The coordinates of the points on the patch
 /// @param[out] indices  The indices of the points on the patch
 ///
-void getPointsFromPatch(fvMesh& mesh, label ind, List<vector>& points,
+void getPointsFromPatch(fvMesh& mesh, label ind, List<vector> & points,
                         labelList& indices);
 
 //--------------------------------------------------------------------------
@@ -195,7 +195,7 @@ Eigen::VectorXd boudaryFaceToCellDistance(fvMesh& mesh, label BC_ind);
 /// @return     The indices of the points lying inside the specified the disc.
 ///
 List<label> getIndicesFromDisc(const fvMesh& mesh, double radius,
-                               vector origin, vector axis, List<double>& radii);
+                               vector origin, vector axis, List<double> & radii);
 
 //--------------------------------------------------------------------------
 /// @brief      Gets the indices from coordinates of a given box.
@@ -209,7 +209,7 @@ List<label> getIndicesFromDisc(const fvMesh& mesh, double radius,
 ///
 template<typename type_f>
 List<label> getIndicesFromBox(
-    GeometricField<type_f, fvPatchField, volMesh>& field, Eigen::MatrixXd Box);
+    GeometricField<type_f, fvPatchField, volMesh> & field, Eigen::MatrixXd Box);
 
 //--------------------------------------------------------------------------
 /// @brief      Gets a subMesh from a box of coordinates and a given field (used only for the mesh).
@@ -223,7 +223,7 @@ List<label> getIndicesFromBox(
 ///
 template<typename type_f>
 fvMeshSubset* getSubMeshFromBox(
-    GeometricField<type_f, fvPatchField, volMesh>& field, Eigen::MatrixXd Box);
+    GeometricField<type_f, fvPatchField, volMesh> & field, Eigen::MatrixXd Box);
 
 //--------------------------------------------------------------------------
 /// @brief      Returns a scalarField that containes the non-orthogonality value of a given mesh
@@ -245,7 +245,7 @@ volScalarField meshNonOrtho(fvMesh& mesh, volScalarField& NonOrtho);
 ///
 /// @return     The Rotated Points
 ///
-List<vector> rotatePoints(const List<vector>& originalPoints,
+List<vector> rotatePoints(const List<vector> & originalPoints,
                           vector AxisOfRotation, double AngleOfRotation);
 
 }
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C
index bf6872d6a..f5b56cce2 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.C
@@ -36,132 +36,168 @@ namespace ITHACAutilities
 namespace ITHACAsurfacetools
 {
 
-  template<typename T>
-  List<label> surfaceIndexInt(T& field, const label patchInt, const label patchExt)
-  {
+template<typename T>
+List<label> surfaceIndexInt(T& field, const label patchInt,
+                            const label patchExt)
+{
     List<label>* result = new List<label>;
 
-    for (size_t i = 0; i < field.mesh().boundaryMesh()[patchInt].size(); i++) {
-      result->append(field.mesh().boundaryMesh()[patchInt].faceCells()[i]);
+    for (size_t i = 0; i < field.mesh().boundaryMesh()[patchInt].size(); i++)
+    {
+        result->append(field.mesh().boundaryMesh()[patchInt].faceCells()[i]);
     }
 
     return *result;
-  }
-
-  template List<label> surfaceIndexInt(volScalarField& field, const label patchInt, const label patchExt);
-  template List<label> surfaceIndexInt(volVectorField& field, const label patchInt, const label patchExt);
-  template List<label> surfaceIndexInt(volTensorField& field, const label patchInt, const label patchExt);
-
-  template<typename T>
-  List<label> surfaceIndexExt(T& field, const label patchInt, const label patchExt)
-  {
+}
+
+template List<label> surfaceIndexInt(volScalarField& field,
+                                     const label patchInt, const label patchExt);
+template List<label> surfaceIndexInt(volVectorField& field,
+                                     const label patchInt, const label patchExt);
+template List<label> surfaceIndexInt(volTensorField& field,
+                                     const label patchInt, const label patchExt);
+
+template<typename T>
+List<label> surfaceIndexExt(T& field, const label patchInt,
+                            const label patchExt)
+{
     return surfaceIndexInt(field, patchExt, patchInt);
-  }
-
-  template List<label> surfaceIndexExt(volScalarField& field, const label patchInt, const label patchExt);
-  template List<label> surfaceIndexExt(volVectorField& field, const label patchInt, const label patchExt);
-  template List<label> surfaceIndexExt(volTensorField& field, const label patchInt, const label patchExt);
-
-  template<typename T, typename V>
-  void surfaceValuesInt(T& field, const label patchInt, const label patchExt, List<V>& result)
-  {
+}
+
+template List<label> surfaceIndexExt(volScalarField& field,
+                                     const label patchInt, const label patchExt);
+template List<label> surfaceIndexExt(volVectorField& field,
+                                     const label patchInt, const label patchExt);
+template List<label> surfaceIndexExt(volTensorField& field,
+                                     const label patchInt, const label patchExt);
+
+template<typename T, typename V>
+void surfaceValuesInt(T& field, const label patchInt, const label patchExt,
+                      List<V> & result)
+{
     List<label> indexes = surfaceIndexInt(field, patchInt, patchExt);
 
-    for (size_t i = 0; i < indexes.size(); i++) {
-      result.append(field[indexes[i]]);
+    for (size_t i = 0; i < indexes.size(); i++)
+    {
+        result.append(field[indexes[i]]);
     }
-  }
-
-  template void surfaceValuesInt(volScalarField& field, const label patchInt, const label patchExt, List<scalar>& result);
-  template void surfaceValuesInt(volVectorField& field, const label patchInt, const label patchExt, List<Foam::Vector<scalar>>& result);
-  template void surfaceValuesInt(volTensorField& field, const label patchInt, const label patchExt, List<Foam::Tensor<scalar>>& result);
-
-  template<typename T, typename V>
-  void surfaceValuesExt(T& field, const label patchInt, const label patchExt, List<V>& result)
-  {
+}
+
+template void surfaceValuesInt(volScalarField& field, const label patchInt,
+                               const label patchExt, List<scalar> & result);
+template void surfaceValuesInt(volVectorField& field, const label patchInt,
+                               const label patchExt, List<Foam::Vector<scalar>> & result);
+template void surfaceValuesInt(volTensorField& field, const label patchInt,
+                               const label patchExt, List<Foam::Tensor<scalar>> & result);
+
+template<typename T, typename V>
+void surfaceValuesExt(T& field, const label patchInt, const label patchExt,
+                      List<V> & result)
+{
     surfaceValuesInt(field, patchExt, patchInt, result);
-  }
-
-  template void surfaceValuesExt(volScalarField& field, const label patchInt, const label patchExt, List<scalar>& result);
-  template void surfaceValuesExt(volVectorField& field, const label patchInt, const label patchExt, List<Foam::Vector<scalar>>& result);
-  template void surfaceValuesExt(volTensorField& field, const label patchInt, const label patchExt, List<Foam::Tensor<scalar>>& result);
-
-  template<typename T>
-  Foam::Vector<scalar> surfaceFindMirrorPoint(T& field, const label patchInt, const label patchExt, const label cellID)
-  {
-    Foam::Vector<scalar> result = *(new Foam::Vector<scalar>);
+}
+
+template void surfaceValuesExt(volScalarField& field, const label patchInt,
+                               const label patchExt, List<scalar> & result);
+template void surfaceValuesExt(volVectorField& field, const label patchInt,
+                               const label patchExt, List<Foam::Vector<scalar>> & result);
+template void surfaceValuesExt(volTensorField& field, const label patchInt,
+                               const label patchExt, List<Foam::Tensor<scalar>> & result);
+
+template<typename T>
+Foam::Vector<scalar> surfaceFindMirrorPoint(T& field, const label patchInt,
+        const label patchExt, const label cellID)
+{
+    Foam::Vector<scalar> result = * (new Foam::Vector<scalar>);
     List<label> indexesInt = surfaceIndexInt(field, patchInt, patchExt);
-
-    result = 2.0 * field.mesh().boundaryMesh()[patchInt].faceCentres()[cellID] - field.mesh().C()[indexesInt[cellID]];
-
+    result = 2.0 * field.mesh().boundaryMesh()[patchInt].faceCentres()[cellID] -
+             field.mesh().C()[indexesInt[cellID]];
     return result;
-  }
-
-  template Foam::Vector<scalar> surfaceFindMirrorPoint(volScalarField& field, const label patchInt, const label patchExt, const label cellID);
-  template Foam::Vector<scalar> surfaceFindMirrorPoint(volVectorField& field, const label patchInt, const label patchExt, const label cellID);
-  template Foam::Vector<scalar> surfaceFindMirrorPoint(volTensorField& field, const label patchInt, const label patchExt, const label cellID);
-
-  template<typename T>
-  label surfaceFindClosest(T& field, const label patchInt, const label patchExt, Foam::Vector<scalar> point)
-  {
+}
+
+template Foam::Vector<scalar> surfaceFindMirrorPoint(volScalarField& field,
+        const label patchInt, const label patchExt, const label cellID);
+template Foam::Vector<scalar> surfaceFindMirrorPoint(volVectorField& field,
+        const label patchInt, const label patchExt, const label cellID);
+template Foam::Vector<scalar> surfaceFindMirrorPoint(volTensorField& field,
+        const label patchInt, const label patchExt, const label cellID);
+
+template<typename T>
+label surfaceFindClosest(T& field, const label patchInt, const label patchExt,
+                         Foam::Vector<scalar> point)
+{
     label result = 0;
     scalar dist = 0;
     List<label> indexesExt = surfaceIndexExt(field, patchInt, patchExt);
-
     dist = mag(point - field.mesh().C()[indexesExt[0]]);
 
-    for(int i = 1; i < indexesExt.size(); i++)
+    for (int i = 1; i < indexesExt.size(); i++)
     {
-      scalar temp = mag(point - field.mesh().C()[indexesExt[i]]);
-      if(temp <= dist)
-      {
-        dist = temp;
-        result = i;
-      }
+        scalar temp = mag(point - field.mesh().C()[indexesExt[i]]);
+
+        if (temp <= dist)
+        {
+            dist = temp;
+            result = i;
+        }
     }
+
     result = indexesExt[result];
     return result;
-  }
-
-  template label surfaceFindClosest(volScalarField& field, const label patchInt, const label patchExt, Foam::Vector<scalar> point);
-  template label surfaceFindClosest(volVectorField& field, const label patchInt, const label patchExt, Foam::Vector<scalar> point);
-  template label surfaceFindClosest(volTensorField& field, const label patchInt, const label patchExt, Foam::Vector<scalar> point);
-
-  template<typename T, typename V>
-  void surfaceAverage(T& field, const label patchInt, const label patchExt, List<V>& result)
-  {
+}
+
+template label surfaceFindClosest(volScalarField& field, const label patchInt,
+                                  const label patchExt, Foam::Vector<scalar> point);
+template label surfaceFindClosest(volVectorField& field, const label patchInt,
+                                  const label patchExt, Foam::Vector<scalar> point);
+template label surfaceFindClosest(volTensorField& field, const label patchInt,
+                                  const label patchExt, Foam::Vector<scalar> point);
+
+template<typename T, typename V>
+void surfaceAverage(T& field, const label patchInt, const label patchExt,
+                    List<V> & result)
+{
     List<label> indexesInt = surfaceIndexInt(field, patchInt, patchExt);
     result.resize(0);
 
-    for(int i = 0; i < indexesInt.size(); i++)
+    for (int i = 0; i < indexesInt.size(); i++)
     {
-        Foam::Vector<scalar> mirror = surfaceFindMirrorPoint(field, patchInt, patchExt, i);
+        Foam::Vector<scalar> mirror = surfaceFindMirrorPoint(field, patchInt, patchExt,
+                                      i);
         label closest = surfaceFindClosest(field, patchInt, patchExt, mirror);
         result.append(0.5 * field[closest] + 0.5 * field[indexesInt[i]]);
     }
-  }
-
-  template void surfaceAverage(volScalarField& field, const label patchInt, const label patchExt, List<scalar>& result);
-  template void surfaceAverage(volVectorField& field, const label patchInt, const label patchExt, List<Foam::Vector<scalar>>& result);
-  template void surfaceAverage(volTensorField& field, const label patchInt, const label patchExt, List<Foam::Tensor<scalar>>& result);
-
-  template<typename T, typename V>
-  void surfaceJump(T& field, const label patchInt, const label patchExt, List<V>& result)
-  {
+}
+
+template void surfaceAverage(volScalarField& field, const label patchInt,
+                             const label patchExt, List<scalar> & result);
+template void surfaceAverage(volVectorField& field, const label patchInt,
+                             const label patchExt, List<Foam::Vector<scalar>> & result);
+template void surfaceAverage(volTensorField& field, const label patchInt,
+                             const label patchExt, List<Foam::Tensor<scalar>> & result);
+
+template<typename T, typename V>
+void surfaceJump(T& field, const label patchInt, const label patchExt,
+                 List<V> & result)
+{
     List<label> indexesInt = surfaceIndexInt(field, patchInt, patchExt);
     result.resize(0);
 
-    for(int i = 0; i < indexesInt.size(); i++)
+    for (int i = 0; i < indexesInt.size(); i++)
     {
-        Foam::Vector<scalar> mirror = surfaceFindMirrorPoint(field, patchInt, patchExt, i);
+        Foam::Vector<scalar> mirror = surfaceFindMirrorPoint(field, patchInt, patchExt,
+                                      i);
         label closest = surfaceFindClosest(field, patchInt, patchExt, mirror);
         result.append(field[closest] - field[indexesInt[i]]);
     }
-  }
-
-  template void surfaceJump(volScalarField& field, const label patchInt, const label patchExt, List<scalar>& result);
-  template void surfaceJump(volVectorField& field, const label patchInt, const label patchExt, List<Foam::Vector<scalar>>& result);
-  template void surfaceJump(volTensorField& field, const label patchInt, const label patchExt, List<Foam::Tensor<scalar>>& result);
+}
+
+template void surfaceJump(volScalarField& field, const label patchInt,
+                          const label patchExt, List<scalar> & result);
+template void surfaceJump(volVectorField& field, const label patchInt,
+                          const label patchExt, List<Foam::Vector<scalar>> & result);
+template void surfaceJump(volTensorField& field, const label patchInt,
+                          const label patchExt, List<Foam::Tensor<scalar>> & result);
 } // End namespace ITHACAsurfacetools
 } // End namespace ITHACAutilities
 
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.H b/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.H
index 1ef379bdf..4f6cac6d5 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.H
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAsurfacetools.H
@@ -39,29 +39,37 @@ namespace ITHACAutilities
 namespace ITHACAsurfacetools
 {
 
-  template<typename T>
-  List<label> surfaceIndexInt(T& field, const label patchInt, const label patchExt);
+template<typename T>
+List<label> surfaceIndexInt(T& field, const label patchInt,
+                            const label patchExt);
 
-  template<typename T>
-  List<label> surfaceIndexExt(T& field, const label patchInt, const label patchExt);
+template<typename T>
+List<label> surfaceIndexExt(T& field, const label patchInt,
+                            const label patchExt);
 
-  template<typename T, typename V>
-  void surfaceValuesInt(T& field, const label patchInt, const label patchExt, List<V>& result);
+template<typename T, typename V>
+void surfaceValuesInt(T& field, const label patchInt, const label patchExt,
+                      List<V> & result);
 
-  template<typename T, typename V>
-  void surfaceValuesExt(T& field, const label patchInt, const label patchExt, List<V>& result);
+template<typename T, typename V>
+void surfaceValuesExt(T& field, const label patchInt, const label patchExt,
+                      List<V> & result);
 
-  template<typename T>
-  Foam::Vector<scalar> surfaceFindMirrorPoint(T& field, const label patchInt, const label patchExt, const label cellID);
+template<typename T>
+Foam::Vector<scalar> surfaceFindMirrorPoint(T& field, const label patchInt,
+        const label patchExt, const label cellID);
 
-  template<typename T>
-  label surfaceFindClosest(T& field, const label patchInt, const label patchExt, Foam::Vector<scalar> point);
+template<typename T>
+label surfaceFindClosest(T& field, const label patchInt, const label patchExt,
+                         Foam::Vector<scalar> point);
 
-  template<typename T, typename V>
-  void surfaceAverage(T& field, const label patchInt, const label patchExt, List<V>& result);
+template<typename T, typename V>
+void surfaceAverage(T& field, const label patchInt, const label patchExt,
+                    List<V> & result);
 
-  template<typename T, typename V>
-  void surfaceJump(T& field, const label patchInt, const label patchExt, List<V>& result);
+template<typename T, typename V>
+void surfaceJump(T& field, const label patchInt, const label patchExt,
+                 List<V> & result);
 
 }; // End namespace ITHACAsurfacetools
 } // End namespace ITHACAutilities
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAsystem.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAsystem.C
index 61100e7d5..ead1bd785 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAsystem.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAsystem.C
@@ -91,7 +91,7 @@ bool check_folder(word folder)
     struct stat sb;
     bool exist;
 
-    if (stat(folder.c_str(), &sb) == 0 && S_ISDIR(sb.st_mode))
+    if (stat(folder.c_str(), & sb) == 0 && S_ISDIR(sb.st_mode))
     {
         exist = true;
     }
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.C b/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.C
index 84d7e0d46..a4e98ae53 100644
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.C
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.C
@@ -108,7 +108,7 @@ bool isTurbulent()
 }
 
 template<typename T>
-List<T> combineList(List<List<T>>& doubleList)
+List<T> combineList(List<List<T>> & doubleList)
 {
     List<T> a = ListListOps::combine<List<T>>(doubleList,
                 accessOp<List<T>>());
@@ -130,84 +130,107 @@ List<T> combineList(List<List<T>>& doubleList)
     return a;
 }
 
-template List<label> combineList(List<List<label>>& doubleList);
+template List<label> combineList(List<List<label>> & doubleList);
 
 
 // Using the Eigen library, using the SVD decomposition method to solve the
 // matrix pseudo-inverse, the default error er is 0
-Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er) {
-  // perform svd decomposition
-  Eigen::JacobiSVD<Eigen::MatrixXd> svd_holder(origin, Eigen::ComputeThinU | Eigen::ComputeThinV);
-  // Build SVD decomposition results
-  Eigen::MatrixXd U = svd_holder.matrixU();
-  Eigen::MatrixXd V = svd_holder.matrixV();
-  Eigen::MatrixXd D = svd_holder.singularValues();
-
-  // Build the S matrix
-  Eigen::MatrixXd S(V.cols(), U.cols());
-  S.setZero();
-
-  for (unsigned int i = 0; i < D.size(); ++i) {
-
-    if (D(i, 0) > er) {
-      S(i, i) = 1 / D(i, 0);
-    } else {
-      S(i, i) = 0;
-    }
-  }
-  return V * S * U.transpose();
+Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd& origin, const float er)
+{
+    // perform svd decomposition
+    Eigen::JacobiSVD<Eigen::MatrixXd> svd_holder(origin,
+            Eigen::ComputeThinU | Eigen::ComputeThinV);
+    // Build SVD decomposition results
+    Eigen::MatrixXd U = svd_holder.matrixU();
+    Eigen::MatrixXd V = svd_holder.matrixV();
+    Eigen::MatrixXd D = svd_holder.singularValues();
+    // Build the S matrix
+    Eigen::MatrixXd S(V.cols(), U.cols());
+    S.setZero();
+
+    for (unsigned int i = 0; i < D.size(); ++i)
+    {
+        if (D(i, 0) > er)
+        {
+            S(i, i) = 1 / D(i, 0);
+        }
+        else
+        {
+            S(i, i) = 0;
+        }
+    }
+
+    return V* S* U.transpose();
 }
 
 
-Eigen::MatrixXd invertMatrix(Eigen::MatrixXd& matrixToInvert, const word inversionMethod){
-
-  Info << "Inversion method : " << inversionMethod << endl;
-  if(inversionMethod == "pinv_eigen_based"){
-    return pinv_eigen_based(matrixToInvert);
-  }
-  else if(inversionMethod == "direct"){
-    return matrixToInvert.inverse();
-  }
-  else if(inversionMethod == "fullPivLu"){
-    return matrixToInvert.fullPivLu().inverse();
-  }
-  else if(inversionMethod == "partialPivLu"){
-    return matrixToInvert.partialPivLu().inverse();
-  }
-  else if(inversionMethod == "householderQr"){
-    return matrixToInvert.householderQr().solve(Eigen::MatrixXd::Identity(matrixToInvert.rows(), matrixToInvert.cols()));
-  }
-  else if(inversionMethod == "colPivHouseholderQr"){
-    return matrixToInvert.colPivHouseholderQr().inverse();
-  }
-  else if(inversionMethod == "fullPivHouseholderQr"){
-    return matrixToInvert.fullPivHouseholderQr().inverse();
-  }
-  else if(inversionMethod == "completeOrthogonalDecomposition"){
-    return matrixToInvert.completeOrthogonalDecomposition().pseudoInverse();
-  }
-  else if(inversionMethod == "jacobiSvd")
-  {
-    return matrixToInvert.jacobiSvd(Eigen::ComputeThinU | Eigen::ComputeThinV).solve(Eigen::MatrixXd::Identity(matrixToInvert.rows(), matrixToInvert.cols()));
-  }
-  else if(inversionMethod == "llt")
-  {
-    return matrixToInvert.llt().solve(Eigen::MatrixXd::Identity(matrixToInvert.rows(), matrixToInvert.cols()));
-  }
-  else if(inversionMethod == "ldlt")
-  {
-    Eigen::LLT<Eigen::MatrixXd> lltOfA(matrixToInvert);
-    return lltOfA.solve(Eigen::MatrixXd::Identity(matrixToInvert.rows(), matrixToInvert.cols()));
-  }
-  else if(inversionMethod == "bdcSvd")
-  {
-    return matrixToInvert.bdcSvd(Eigen::ComputeThinU | Eigen::ComputeThinV).solve(Eigen::MatrixXd::Identity(matrixToInvert.rows(), matrixToInvert.cols()));
-  } 
-  else{
-    Info << "Unkwown inversion method, solving with : completeOrthogonalDecomposition" << endl;
-    return matrixToInvert.completeOrthogonalDecomposition().pseudoInverse();
-  }
+Eigen::MatrixXd invertMatrix(Eigen::MatrixXd& matrixToInvert,
+                             const word inversionMethod)
+{
+    Info << "Inversion method : " << inversionMethod << endl;
+
+    if (inversionMethod == "pinv_eigen_based")
+    {
+        return pinv_eigen_based(matrixToInvert);
+    }
+    else if (inversionMethod == "direct")
+    {
+        return matrixToInvert.inverse();
+    }
+    else if (inversionMethod == "fullPivLu")
+    {
+        return matrixToInvert.fullPivLu().inverse();
+    }
+    else if (inversionMethod == "partialPivLu")
+    {
+        return matrixToInvert.partialPivLu().inverse();
+    }
+    else if (inversionMethod == "householderQr")
+    {
+        return matrixToInvert.householderQr().solve(Eigen::MatrixXd::Identity(
+                    matrixToInvert.rows(), matrixToInvert.cols()));
+    }
+    else if (inversionMethod == "colPivHouseholderQr")
+    {
+        return matrixToInvert.colPivHouseholderQr().inverse();
+    }
+    else if (inversionMethod == "fullPivHouseholderQr")
+    {
+        return matrixToInvert.fullPivHouseholderQr().inverse();
+    }
+    else if (inversionMethod == "completeOrthogonalDecomposition")
+    {
+        return matrixToInvert.completeOrthogonalDecomposition().pseudoInverse();
+    }
+    else if (inversionMethod == "jacobiSvd")
+    {
+        return matrixToInvert.jacobiSvd(Eigen::ComputeThinU |
+                                        Eigen::ComputeThinV).solve(Eigen::MatrixXd::Identity(matrixToInvert.rows(),
+                                                matrixToInvert.cols()));
+    }
+    else if (inversionMethod == "llt")
+    {
+        return matrixToInvert.llt().solve(Eigen::MatrixXd::Identity(
+                                              matrixToInvert.rows(), matrixToInvert.cols()));
+    }
+    else if (inversionMethod == "ldlt")
+    {
+        Eigen::LLT<Eigen::MatrixXd> lltOfA(matrixToInvert);
+        return lltOfA.solve(Eigen::MatrixXd::Identity(matrixToInvert.rows(),
+                            matrixToInvert.cols()));
+    }
+    else if (inversionMethod == "bdcSvd")
+    {
+        return matrixToInvert.bdcSvd(Eigen::ComputeThinU | Eigen::ComputeThinV).solve(
+                   Eigen::MatrixXd::Identity(matrixToInvert.rows(), matrixToInvert.cols()));
+    }
+    else
+    {
+        Info << "Unkwown inversion method, solving with : completeOrthogonalDecomposition"
+             << endl;
+        return matrixToInvert.completeOrthogonalDecomposition().pseudoInverse();
+    }
 }
 
 
-}
\ No newline at end of file
+}
diff --git a/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.H b/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.H
old mode 100755
new mode 100644
index 90041cd14..11fd47854
--- a/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.H
+++ b/src/ITHACA_CORE/ITHACAutilities/ITHACAutilities.H
@@ -123,7 +123,7 @@ bool isTurbulent();
 /// @return     list in unique order
 ///
 template<typename T>
-List<T> combineList(List<List<T>>& doubleList);
+List<T> combineList(List<List<T>> & doubleList);
 
 //------------------------------------------------------------------------------
 /// @brief      Using the Eigen library, using the SVD decomposition method to solve the
@@ -134,18 +134,20 @@ List<T> combineList(List<List<T>>& doubleList);
 ///
 /// @return     Inversed matrix
 ///
-Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd &origin, const float er = 0);
+Eigen::MatrixXd pinv_eigen_based(Eigen::MatrixXd& origin, const float er = 0);
 
 //------------------------------------------------------------------------------
 /// @brief      Invert a matrix given the method name in the ITHACAdict
 ///
 /// @param[in]      matrixToInvert  Matrix to invert
-/// @param[in]      methodName      Method 
+/// @param[in]      methodName      Method
 ///
 /// @return         Inversed matrix
 ///
-Eigen::MatrixXd invertMatrix(Eigen::MatrixXd& matrixToInvert, const word inversionMethod);
+Eigen::MatrixXd invertMatrix(Eigen::MatrixXd& matrixToInvert,
+                             const word inversionMethod);
 
 
 };
+
 #endif
diff --git a/src/ITHACA_CORE/ITHACAutilities/colormod.H b/src/ITHACA_CORE/ITHACAutilities/colormod.H
old mode 100755
new mode 100644
index ac2d7310c..c1373676b
--- a/src/ITHACA_CORE/ITHACAutilities/colormod.H
+++ b/src/ITHACA_CORE/ITHACAutilities/colormod.H
@@ -25,6 +25,7 @@ class Modifier
         Code code;
     public:
         Modifier(Code pCode) : code(pCode) {}
+
         friend std::ostream&
         operator<<(std::ostream& os, const Modifier& mod)
         {
diff --git a/src/ITHACA_DEIM/DEIM.C b/src/ITHACA_DEIM/DEIM.C
index 515cd5ba8..3611a8dcb 100644
--- a/src/ITHACA_DEIM/DEIM.C
+++ b/src/ITHACA_DEIM/DEIM.C
@@ -31,7 +31,8 @@ License
 #include "DEIM.H"
 // Template function constructor
 template<typename T>
-DEIM<T>::DEIM (PtrList<T>& s, label MaxModes, word FunctionName, word FieldName)
+DEIM<T>::DEIM (PtrList<T> & s, label MaxModes, word FunctionName,
+               word FieldName)
     :
     SnapShotsMatrix(s),
     MaxModes(MaxModes),
@@ -82,7 +83,7 @@ DEIM<T>::DEIM (PtrList<T>& s, label MaxModes, word FunctionName, word FieldName)
         MatrixModes = Foam2Eigen::PtrList2Eigen(modes);
         Ncells = modes[0].size();
         label ind_max, c1, xyz_in;
-        double max = MatrixModes.cwiseAbs().col(0).maxCoeff(&ind_max, &c1);
+        double max = MatrixModes.cwiseAbs().col(0).maxCoeff( & ind_max, & c1);
         check3DIndices(ind_max, xyz_in);
         rho(0) = max;
         magicPoints().append(ind_max);
@@ -96,8 +97,8 @@ DEIM<T>::DEIM (PtrList<T>& s, label MaxModes, word FunctionName, word FieldName)
             A = P.transpose() * U;
             b = P.transpose() * MatrixModes.col(i);
             c = A.fullPivLu().solve(b);
-            r = MatrixModes.col(i) - U * c;
-            max = r.cwiseAbs().maxCoeff(&ind_max, &c1);
+            r = MatrixModes.col(i) - U* c;
+            max = r.cwiseAbs().maxCoeff( & ind_max, & c1);
             P.conservativeResize(MatrixModes.rows(), i + 1);
             P.insert(ind_max, i) = 1;
             U.conservativeResize(MatrixModes.rows(), i + 1);
@@ -123,7 +124,8 @@ DEIM<T>::DEIM (PtrList<T>& s, label MaxModes, word FunctionName, word FieldName)
 
 // constructor for matrix DEIM
 template<typename T>
-DEIM<T>::DEIM (PtrList<T>& s, label MaxModesA, label MaxModesB, word MatrixName)
+DEIM<T>::DEIM (PtrList<T> & s, label MaxModesA, label MaxModesB,
+               word MatrixName)
     :
     SnapShotsMatrix(s),
     MaxModesA(MaxModesA),
@@ -289,8 +291,8 @@ DEIM<T>::DEIM (PtrList<T>& s, label MaxModesA, label MaxModesB, word MatrixName)
         Eigen::VectorXd rB;
         Eigen::VectorXd rhoB(1);
         label ind_rowB, xyz_rowB, c1;
-        double maxB = std::get<1>(Matrix_Modes)[0].cwiseAbs().maxCoeff(&ind_rowB,
-                      &c1);
+        double maxB = std::get<1>(Matrix_Modes)[0].cwiseAbs().maxCoeff( & ind_rowB,
+                      & c1);
         label ind_rowBOF = ind_rowB;
         check3DIndices(ind_rowBOF, xyz_rowB);
         rhoB(0) = maxB;
@@ -305,8 +307,8 @@ DEIM<T>::DEIM (PtrList<T>& s, label MaxModesA, label MaxModesB, word MatrixName)
             AB = PB.transpose() * UB;
             bB = PB.transpose() * std::get<1>(Matrix_Modes)[i];
             cB = AB.fullPivLu().solve(bB);
-            rB = std::get<1>(Matrix_Modes)[i] - UB * cB;
-            maxB = rB.cwiseAbs().maxCoeff(&ind_rowB, &c1);
+            rB = std::get<1>(Matrix_Modes)[i] - UB* cB;
+            maxB = rB.cwiseAbs().maxCoeff( & ind_rowB, & c1);
             ind_rowBOF = ind_rowB;
             check3DIndices(ind_rowBOF, xyz_rowB);
             xyz_B().append(xyz_rowB);
@@ -635,7 +637,7 @@ S DEIM<T>::generateSubmeshVector(label layers, const fvMesh& mesh, S field,
 
 
 template<typename T>
-List<label> DEIM<T>::global2local(List<label>& points,
+List<label> DEIM<T>::global2local(List<label> & points,
                                   fvMeshSubset& submesh)
 {
     List<label> localPoints;
@@ -818,15 +820,15 @@ void DEIM<T>::setMagicPoints(labelList& newMagicPoints, labelList& newxyz)
 }
 
 // Specialization of the constructor
-template DEIM<fvScalarMatrix>::DEIM (PtrList<fvScalarMatrix>& s,
+template DEIM<fvScalarMatrix>::DEIM (PtrList<fvScalarMatrix> & s,
                                      label MaxModesA,
                                      label MaxModesB, word MatrixName);
-template DEIM<fvVectorMatrix>::DEIM (PtrList<fvVectorMatrix>& s,
+template DEIM<fvVectorMatrix>::DEIM (PtrList<fvVectorMatrix> & s,
                                      label MaxModesA,
                                      label MaxModesB, word MatrixName);
-template DEIM<volScalarField>::DEIM(PtrList<volScalarField>& s, label MaxModes,
+template DEIM<volScalarField>::DEIM(PtrList<volScalarField> & s, label MaxModes,
                                     word FunctionName, word FieldName);
-template DEIM<volVectorField>::DEIM(PtrList<volVectorField>& s, label MaxModes,
+template DEIM<volVectorField>::DEIM(PtrList<volVectorField> & s, label MaxModes,
                                     word FunctionName, word FieldName);
 
 // Specialization for generateSubField
diff --git a/src/ITHACA_DEIM/DEIM.H b/src/ITHACA_DEIM/DEIM.H
index 731e41130..3cec2a964 100644
--- a/src/ITHACA_DEIM/DEIM.H
+++ b/src/ITHACA_DEIM/DEIM.H
@@ -49,7 +49,7 @@ class DEIM
         /// @param[in]  FunctionName     The function name, used to save the results
         /// @param[in]  FieldName        The field name
         ///
-        DEIM (PtrList<T>& SnapShotsMatrix, label MaxModes, word FunctionName,
+        DEIM (PtrList<T> & SnapShotsMatrix, label MaxModes, word FunctionName,
               word FieldName);
 
         //----------------------------------------------------------------------
@@ -60,7 +60,7 @@ class DEIM
         /// @param[in]  MaxModesB        The maximum number of modes for the source term b
         /// @param[in]  MatrixName       The matrix name, used to save the results
         ///
-        DEIM (PtrList<T>& SnapShotsMatrix, label MaxModesA, label MaxModesB,
+        DEIM (PtrList<T> & SnapShotsMatrix, label MaxModesA, label MaxModesB,
               word MatrixName);
 
         /// The snapshots matrix containing the nonlinear function or operator
@@ -71,7 +71,7 @@ class DEIM
 
         /// Matrix Modes
         std::tuple<List<Eigen::SparseMatrix<double>>, List<Eigen::VectorXd>>
-                Matrix_Modes;
+        Matrix_Modes;
 
         /// The maximum number of modes to be considered
         label MaxModes;
@@ -279,7 +279,7 @@ class DEIM
         ///
         /// @return     The local indices
         ///
-        List<label> global2local(List<label>& points,
+        List<label> global2local(List<label> & points,
                                  fvMeshSubset& submesh);
 
         //----------------------------------------------------------------------
diff --git a/src/ITHACA_FOMPROBLEMS/Burgers/Burgers.C b/src/ITHACA_FOMPROBLEMS/Burgers/Burgers.C
index d201dbd71..0312e4ab5 100644
--- a/src/ITHACA_FOMPROBLEMS/Burgers/Burgers.C
+++ b/src/ITHACA_FOMPROBLEMS/Burgers/Burgers.C
@@ -112,11 +112,11 @@ void Burgers::truthSolve(word folder)
         }
 
         phi = linearInterpolate(U) & mesh.Sf();
-
         auto end = std::chrono::system_clock::now();
-        auto elapsed = std::chrono::duration_cast<std::chrono::microseconds>(end - start);
+        auto elapsed = std::chrono::duration_cast<std::chrono::microseconds>
+                       (end - start);
         Info << "Elapsed: " << elapsed.count() << " microseconds\n";
-        
+
         if (checkWrite(runTime))
         {
             ITHACAstream::exportSolution(U, name(counter), folder + name(folderN));
diff --git a/src/ITHACA_FOMPROBLEMS/SteadyNSSimple/SteadyNSSimple.C b/src/ITHACA_FOMPROBLEMS/SteadyNSSimple/SteadyNSSimple.C
index 81261c481..6a296139f 100644
--- a/src/ITHACA_FOMPROBLEMS/SteadyNSSimple/SteadyNSSimple.C
+++ b/src/ITHACA_FOMPROBLEMS/SteadyNSSimple/SteadyNSSimple.C
@@ -86,10 +86,10 @@ void SteadyNSSimple::getTurbRBF(label NNutModes)
             }
 
             ITHACAstream::ReadDenseMatrix(weights, "./ITHACAoutput/weights/", weightName);
-            rbfSplines[i] = new SPLINTER::RBFSpline(*samples[i],
-                                                    SPLINTER::RadialBasisFunctionType::GAUSSIAN, weights);
+            rbfSplines[i] = new SPLINTER::RBFSpline( * samples[i],
+                SPLINTER::RadialBasisFunctionType::GAUSSIAN, weights);
             // std::cout << "Constructing RadialBasisFunction for mode " << i + 1 << std::endl;
-            Info<< "Constructing RadialBasisFunction for mode " << i + 1 << endl;
+            Info << "Constructing RadialBasisFunction for mode " << i + 1 << endl;
         }
         else
         {
@@ -101,12 +101,12 @@ void SteadyNSSimple::getTurbRBF(label NNutModes)
                 samples[i]->addSample(mu.row(j), coeffL2(i, j));
             }
 
-            rbfSplines[i] = new SPLINTER::RBFSpline(*samples[i],
-                                                    SPLINTER::RadialBasisFunctionType::GAUSSIAN);
+            rbfSplines[i] = new SPLINTER::RBFSpline( * samples[i],
+                SPLINTER::RadialBasisFunctionType::GAUSSIAN);
             ITHACAstream::SaveDenseMatrix(rbfSplines[i]->weights,
                                           "./ITHACAoutput/weights/", weightName);
             // std::cout << "Constructing RadialBasisFunction for mode " << i + 1 << std::endl;
-            Info<< "Constructing RadialBasisFunction for mode " << i + 1 << endl;
+            Info << "Constructing RadialBasisFunction for mode " << i + 1 << endl;
         }
     }
 }
@@ -155,7 +155,7 @@ void SteadyNSSimple::truthSolve2(List<scalar> mu_now, word Folder)
         (
             fvm::div(phi, U)
             - fvm::laplacian(nueff, U)
-            - fvc::div(nueff * dev2(T(fvc::grad(U))))
+            - fvc::div(nueff* dev2(T(fvc::grad(U))))
         );
         UEqn.relax();
 
diff --git a/src/ITHACA_FOMPROBLEMS/SteadyNSSimple/UEqn.H b/src/ITHACA_FOMPROBLEMS/SteadyNSSimple/UEqn.H
old mode 100755
new mode 100644
index 1d91429a0..7117de308
--- a/src/ITHACA_FOMPROBLEMS/SteadyNSSimple/UEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/SteadyNSSimple/UEqn.H
@@ -33,7 +33,7 @@ tmp<fvVectorMatrix> tUEqn
     + turbulence->divDevReff(U)
     ==
     fvOptions(U)
-    );
+);
 fvVectorMatrix& UEqn = tUEqn.ref();
 
 UEqn.relax();
diff --git a/src/ITHACA_FOMPROBLEMS/SteadyNSSimple/pEqn.H b/src/ITHACA_FOMPROBLEMS/SteadyNSSimple/pEqn.H
old mode 100755
new mode 100644
index 5c62d90b5..104e0c227
--- a/src/ITHACA_FOMPROBLEMS/SteadyNSSimple/pEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/SteadyNSSimple/pEqn.H
@@ -24,7 +24,7 @@
 \*---------------------------------------------------------------------------*/
 {
     volScalarField rAU(1.0 / UEqn.A());
-    volVectorField HbyA(constrainHbyA(rAU * UEqn.H(), U, p));
+    volVectorField HbyA(constrainHbyA(rAU* UEqn.H(), U, p));
     surfaceScalarField phiHbyA("phiHbyA", fvc::flux(HbyA));
     MRF.makeRelative(phiHbyA);
     adjustPhi(phiHbyA, U, p);
diff --git a/src/ITHACA_FOMPROBLEMS/SteadyNSTurb/NLsolveSteadyNSTurb.H b/src/ITHACA_FOMPROBLEMS/SteadyNSTurb/NLsolveSteadyNSTurb.H
index 09a7cc1d8..4adb90294 100644
--- a/src/ITHACA_FOMPROBLEMS/SteadyNSTurb/NLsolveSteadyNSTurb.H
+++ b/src/ITHACA_FOMPROBLEMS/SteadyNSTurb/NLsolveSteadyNSTurb.H
@@ -64,6 +64,7 @@ while (simple.loop() && residual > tolerance && csolve < maxIter )
         Info << "\nResidual: " << residual << endl << endl;
         //Info << "Residual U: " << solve(UEqn() == -fvc::grad(p)).initialResidual() << endl;
     }
+
     laminarTransport.correct();
     turbulence->correct();
     csolve = csolve + 1;
diff --git a/src/ITHACA_FOMPROBLEMS/SteadyNSTurb/SteadyNSTurb.C b/src/ITHACA_FOMPROBLEMS/SteadyNSTurb/SteadyNSTurb.C
index 40922e283..198b7ec0e 100644
--- a/src/ITHACA_FOMPROBLEMS/SteadyNSTurb/SteadyNSTurb.C
+++ b/src/ITHACA_FOMPROBLEMS/SteadyNSTurb/SteadyNSTurb.C
@@ -36,6 +36,7 @@ License
 
 // Constructor
 SteadyNSTurb::SteadyNSTurb() {}
+
 SteadyNSTurb::SteadyNSTurb(int argc, char* argv[])
 {
     _args = autoPtr<argList>
@@ -689,8 +690,8 @@ void SteadyNSTurb::projectPPE(fileName folder, label NU, label NP, label NSUP,
 
             ITHACAstream::ReadDenseMatrix(weights, "./ITHACAoutput/weightsPPE/",
                                           weightName);
-            rbfSplines[i] = new SPLINTER::RBFSpline(*samples[i],
-                                                    SPLINTER::RadialBasisFunctionType::GAUSSIAN, weights);
+            rbfSplines[i] = new SPLINTER::RBFSpline( * samples[i],
+                SPLINTER::RadialBasisFunctionType::GAUSSIAN, weights);
             std::cout << "Constructing RadialBasisFunction for mode " << i + 1 << std::endl;
         }
         else
@@ -702,8 +703,8 @@ void SteadyNSTurb::projectPPE(fileName folder, label NU, label NP, label NSUP,
                 samples[i]->addSample(mu.row(j), coeffL2(i, j));
             }
 
-            rbfSplines[i] = new SPLINTER::RBFSpline(*samples[i],
-                                                    SPLINTER::RadialBasisFunctionType::GAUSSIAN);
+            rbfSplines[i] = new SPLINTER::RBFSpline( * samples[i],
+                SPLINTER::RadialBasisFunctionType::GAUSSIAN);
             ITHACAstream::SaveDenseMatrix(rbfSplines[i]->weights,
                                           "./ITHACAoutput/weightsPPE/", weightName);
             std::cout << "Constructing RadialBasisFunction for mode " << i + 1 << std::endl;
@@ -975,8 +976,8 @@ void SteadyNSTurb::projectSUP(fileName folder, label NU, label NP, label NSUP,
 
             ITHACAstream::ReadDenseMatrix(weights, "./ITHACAoutput/weightsSUP/",
                                           weightName);
-            rbfSplines[i] = new SPLINTER::RBFSpline(*samples[i],
-                                                    SPLINTER::RadialBasisFunctionType::GAUSSIAN, weights);
+            rbfSplines[i] = new SPLINTER::RBFSpline( * samples[i],
+                SPLINTER::RadialBasisFunctionType::GAUSSIAN, weights);
             std::cout << "Constructing RadialBasisFunction for mode " << i + 1 << std::endl;
         }
         else
@@ -988,8 +989,8 @@ void SteadyNSTurb::projectSUP(fileName folder, label NU, label NP, label NSUP,
                 samples[i]->addSample(mu.row(j), coeffL2(i, j));
             }
 
-            rbfSplines[i] = new SPLINTER::RBFSpline(*samples[i],
-                                                    SPLINTER::RadialBasisFunctionType::GAUSSIAN);
+            rbfSplines[i] = new SPLINTER::RBFSpline( * samples[i],
+                SPLINTER::RadialBasisFunctionType::GAUSSIAN);
             ITHACAstream::SaveDenseMatrix(rbfSplines[i]->weights,
                                           "./ITHACAoutput/weightsSUP/", weightName);
             ITHACAstream::exportMatrix(rbfSplines[i]->weights,
diff --git a/src/ITHACA_FOMPROBLEMS/SteadyNSTurb/UEqn.H b/src/ITHACA_FOMPROBLEMS/SteadyNSTurb/UEqn.H
old mode 100755
new mode 100644
index 1d91429a0..7117de308
--- a/src/ITHACA_FOMPROBLEMS/SteadyNSTurb/UEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/SteadyNSTurb/UEqn.H
@@ -33,7 +33,7 @@ tmp<fvVectorMatrix> tUEqn
     + turbulence->divDevReff(U)
     ==
     fvOptions(U)
-    );
+);
 fvVectorMatrix& UEqn = tUEqn.ref();
 
 UEqn.relax();
diff --git a/src/ITHACA_FOMPROBLEMS/SteadyNSTurb/pEqn.H b/src/ITHACA_FOMPROBLEMS/SteadyNSTurb/pEqn.H
old mode 100755
new mode 100644
index 5c62d90b5..104e0c227
--- a/src/ITHACA_FOMPROBLEMS/SteadyNSTurb/pEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/SteadyNSTurb/pEqn.H
@@ -24,7 +24,7 @@
 \*---------------------------------------------------------------------------*/
 {
     volScalarField rAU(1.0 / UEqn.A());
-    volVectorField HbyA(constrainHbyA(rAU * UEqn.H(), U, p));
+    volVectorField HbyA(constrainHbyA(rAU* UEqn.H(), U, p));
     surfaceScalarField phiHbyA("phiHbyA", fvc::flux(HbyA));
     MRF.makeRelative(phiHbyA);
     adjustPhi(phiHbyA, U, p);
diff --git a/src/ITHACA_FOMPROBLEMS/SteadyNSTurbIntrusive/NLsolveSteadyNSTurbIntrusive.H b/src/ITHACA_FOMPROBLEMS/SteadyNSTurbIntrusive/NLsolveSteadyNSTurbIntrusive.H
index 09a7cc1d8..4adb90294 100644
--- a/src/ITHACA_FOMPROBLEMS/SteadyNSTurbIntrusive/NLsolveSteadyNSTurbIntrusive.H
+++ b/src/ITHACA_FOMPROBLEMS/SteadyNSTurbIntrusive/NLsolveSteadyNSTurbIntrusive.H
@@ -64,6 +64,7 @@ while (simple.loop() && residual > tolerance && csolve < maxIter )
         Info << "\nResidual: " << residual << endl << endl;
         //Info << "Residual U: " << solve(UEqn() == -fvc::grad(p)).initialResidual() << endl;
     }
+
     laminarTransport.correct();
     turbulence->correct();
     csolve = csolve + 1;
diff --git a/src/ITHACA_FOMPROBLEMS/SteadyNSTurbIntrusive/SteadyNSTurbIntrusive.C b/src/ITHACA_FOMPROBLEMS/SteadyNSTurbIntrusive/SteadyNSTurbIntrusive.C
old mode 100755
new mode 100644
index e3ea31350..4cf0fc70e
--- a/src/ITHACA_FOMPROBLEMS/SteadyNSTurbIntrusive/SteadyNSTurbIntrusive.C
+++ b/src/ITHACA_FOMPROBLEMS/SteadyNSTurbIntrusive/SteadyNSTurbIntrusive.C
@@ -36,6 +36,7 @@ License
 
 // Constructor
 SteadyNSTurbIntrusive::SteadyNSTurbIntrusive() {}
+
 SteadyNSTurbIntrusive::SteadyNSTurbIntrusive(int argc, char* argv[])
 {
     _args = autoPtr<argList>
diff --git a/src/ITHACA_FOMPROBLEMS/SteadyNSTurbIntrusive/UEqn.H b/src/ITHACA_FOMPROBLEMS/SteadyNSTurbIntrusive/UEqn.H
old mode 100755
new mode 100644
index 1d91429a0..7117de308
--- a/src/ITHACA_FOMPROBLEMS/SteadyNSTurbIntrusive/UEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/SteadyNSTurbIntrusive/UEqn.H
@@ -33,7 +33,7 @@ tmp<fvVectorMatrix> tUEqn
     + turbulence->divDevReff(U)
     ==
     fvOptions(U)
-    );
+);
 fvVectorMatrix& UEqn = tUEqn.ref();
 
 UEqn.relax();
diff --git a/src/ITHACA_FOMPROBLEMS/SteadyNSTurbIntrusive/pEqn.H b/src/ITHACA_FOMPROBLEMS/SteadyNSTurbIntrusive/pEqn.H
old mode 100755
new mode 100644
index 5c62d90b5..104e0c227
--- a/src/ITHACA_FOMPROBLEMS/SteadyNSTurbIntrusive/pEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/SteadyNSTurbIntrusive/pEqn.H
@@ -24,7 +24,7 @@
 \*---------------------------------------------------------------------------*/
 {
     volScalarField rAU(1.0 / UEqn.A());
-    volVectorField HbyA(constrainHbyA(rAU * UEqn.H(), U, p));
+    volVectorField HbyA(constrainHbyA(rAU* UEqn.H(), U, p));
     surfaceScalarField phiHbyA("phiHbyA", fvc::flux(HbyA));
     MRF.makeRelative(phiHbyA);
     adjustPhi(phiHbyA, U, p);
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyBB/TEqn.H b/src/ITHACA_FOMPROBLEMS/UnsteadyBB/TEqn.H
old mode 100755
new mode 100644
index cfc926504..9a96ede16
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyBB/TEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyBB/TEqn.H
@@ -39,7 +39,7 @@
 
     TEqn.solve();
 
-    rhok = 1.0 - beta * (T - TRef);
+    rhok = 1.0 - beta* (T - TRef);
 }
 
 
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyBB/UEqn.H b/src/ITHACA_FOMPROBLEMS/UnsteadyBB/UEqn.H
old mode 100755
new mode 100644
index 026ec75cb..5062cfb1f
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyBB/UEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyBB/UEqn.H
@@ -34,7 +34,7 @@ fvVectorMatrix UEqn
     + turbulence->divDevReff(U)
     ==
     fvOptions(U)
-    );
+);
 
 UEqn.relax();
 
@@ -49,9 +49,9 @@ if (pimple.momentumPredictor())
         fvc::reconstruct
         (
             (
-                - ghf * fvc::snGrad(rhok)
+                - ghf* fvc::snGrad(rhok)
                 - fvc::snGrad(p_rgh)
-            )*mesh.magSf()
+            ) * mesh.magSf()
         )
     );
     fvOptions.correct(U);
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyBB/UnsteadyBB.C b/src/ITHACA_FOMPROBLEMS/UnsteadyBB/UnsteadyBB.C
index 7dddff8b4..b42673ff8 100644
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyBB/UnsteadyBB.C
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyBB/UnsteadyBB.C
@@ -39,6 +39,7 @@
 
 // Constructor
 UnsteadyBB::UnsteadyBB() {}
+
 UnsteadyBB::UnsteadyBB(int argc, char* argv[])
 {
     _args = autoPtr<argList>
@@ -831,6 +832,7 @@ void UnsteadyBB::projectPPE(fileName folder, label NU, label NP, label NT,
         HP_matrix = buoyant_term_poisson(NPrghmodes, NTmodes);
     }
 }
+
 // * * * * * * * * * * * * * * Momentum Eq. Methods * * * * * * * * * * * * * //
 Eigen::MatrixXd UnsteadyBB::pressure_gradient_term(label NUmodes,
         label NPrghmodes,
@@ -848,7 +850,7 @@ Eigen::MatrixXd UnsteadyBB::pressure_gradient_term(label NUmodes,
         {
             K_matrix(i, j) = fvc::domainIntegrate(L_U_SUPmodes[i] &
                                                   fvc::reconstruct(fvc::snGrad(Prghmodes[j]) *
-                                                          Prghmodes[j].mesh().magSf())).value();
+                                                      Prghmodes[j].mesh().magSf())).value();
         }
     }
 
@@ -921,7 +923,7 @@ Eigen::MatrixXd UnsteadyBB::buoyant_term(label NUmodes, label NTmodes,
         for (label j = 0; j < H2size; j++)
         {
             H_matrix(i, j) = fvc::domainIntegrate(L_U_SUPmodes[i] & fvc::reconstruct(
-                    ghf * fvc::snGrad(1.0 - (beta * (L_T_modes[j] - TRef)))
+                    ghf* fvc::snGrad(1.0 - (beta * (L_T_modes[j] - TRef)))
                     * L_T_modes[j].mesh().magSf())).value();
         }
     }
@@ -964,8 +966,8 @@ Eigen::MatrixXd UnsteadyBB::buoyant_term_poisson(label NPrghmodes,
         {
             HP_matrix(i, j) = fvc::domainIntegrate(fvc::reconstruct(fvc::snGrad(
                     Prghmodes[i]) *
-                                                   Prghmodes[i].mesh().magSf())  &fvc::reconstruct(
-                                                           ghf * fvc::snGrad( -(beta * (L_T_modes[j])))
+                                                   Prghmodes[i].mesh().magSf())  & fvc::reconstruct(
+                                                           ghf* fvc::snGrad( -(beta * (L_T_modes[j])))
                                                            * L_T_modes[j].mesh().magSf())).value();
         }
     }
@@ -1148,7 +1150,7 @@ void UnsteadyBB::liftSolve()
                 IOobject::NO_WRITE
             ),
             mesh,
-            dimensionedScalar("Phi", dimLength * dimVelocity, 0),
+            dimensionedScalar("Phi", dimLength* dimVelocity, 0),
             UliftBC.boundaryField().types()
         );
         label PhiRefCell = 0;
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyBB/pEqn.H b/src/ITHACA_FOMPROBLEMS/UnsteadyBB/pEqn.H
old mode 100755
new mode 100644
index b93639d85..ff9554d6c
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyBB/pEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyBB/pEqn.H
@@ -26,15 +26,15 @@
 {
     volScalarField rAU("rAU", 1.0 / UEqn.A());
     surfaceScalarField rAUf("rAUf", fvc::interpolate(rAU));
-    volVectorField HbyA(constrainHbyA(rAU * UEqn.H(), U, p_rgh));
+    volVectorField HbyA(constrainHbyA(rAU* UEqn.H(), U, p_rgh));
 
-    surfaceScalarField phig(-rAUf* ghf * fvc::snGrad(rhok)*mesh.magSf());
+    surfaceScalarField phig(-rAUf* ghf* fvc::snGrad(rhok) * mesh.magSf());
 
     surfaceScalarField phiHbyA
     (
         "phiHbyA",
         fvc::flux(HbyA)
-        + rAUf * fvc::ddtCorr(U, phi)
+        + rAUf* fvc::ddtCorr(U, phi)
         + phig
     );
 
@@ -59,7 +59,7 @@
             // Explicitly relax pressure for momentum corrector
             p_rgh.relax();
             // Correct the momentum source with the pressure gradient flux calculated from the relaxed pressure
-            U = HbyA + rAU * fvc::reconstruct((phig - p_rghEqn.flux()) / rAUf);
+            U = HbyA + rAU* fvc::reconstruct((phig - p_rghEqn.flux()) / rAUf);
             U.correctBoundaryConditions();
             fvOptions.correct(U);
         }
@@ -67,7 +67,7 @@
 
 #include "continuityErrs.H"
 
-    p = p_rgh + rhok * gh;
+    p = p_rgh + rhok* gh;
 
 
     if (p_rgh.needReference())
@@ -78,7 +78,7 @@
                  p.dimensions(),
                  pRefValue - getRefCellValue(p, pRefCell)
              );
-        p_rgh = p - rhok * gh;
+        p_rgh = p - rhok* gh;
     }
 }
 
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyNSExplicit/CFM.H b/src/ITHACA_FOMPROBLEMS/UnsteadyNSExplicit/CFM.H
old mode 100755
new mode 100644
index a4aae601c..fb880b1a1
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyNSExplicit/CFM.H
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyNSExplicit/CFM.H
@@ -26,11 +26,11 @@ License
 
 volVectorField U1aux(U);
 volVectorField Faux(U);
-Faux = dt * (-fvc::div(phi, U) + fvc::laplacian(nu, U));
+Faux = dt* (-fvc::div(phi, U) + fvc::laplacian(nu, U));
 U1aux = U + Faux;
 fvScalarMatrix pEqn = (fvm::laplacian(p)).ref();
 pEqn.setReference(pRefCell, pRefValue);
-solve(pEqn ==  (1 / dt)*fvc::div(U1aux));
-U = U1aux - dt * fvc::grad(p);
-phi = fvc::flux(U1aux) - dt * fvc::snGrad(p) * mag(mesh.magSf());
+solve(pEqn ==  (1 / dt) * fvc::div(U1aux));
+U = U1aux - dt* fvc::grad(p);
+phi = fvc::flux(U1aux) - dt* fvc::snGrad(p) * mag(mesh.magSf());
 
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyNSExplicit/IFM.H b/src/ITHACA_FOMPROBLEMS/UnsteadyNSExplicit/IFM.H
old mode 100755
new mode 100644
index 7281f2209..4b2d86e24
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyNSExplicit/IFM.H
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyNSExplicit/IFM.H
@@ -26,11 +26,11 @@ License
 // The inconsistent flux method (forward Euler)
 volVectorField U1aux(U);
 volVectorField Faux(U);
-Faux = dt * (fvc::laplacian(nu, U) - fvc::div(phi, U));
+Faux = dt* (fvc::laplacian(nu, U) - fvc::div(phi, U));
 U1aux = U + Faux;
 fvScalarMatrix pEqn = fvm::laplacian(p).ref();
 pEqn.setReference(pRefCell, pRefValue);
-solve(pEqn ==  (1 / dt)*fvc::div(U1aux));
-U = U1aux - dt * fvc::grad(p);
-phi = fvc::interpolate(U)& mesh.Sf();
+solve(pEqn ==  (1 / dt) * fvc::div(U1aux));
+U = U1aux - dt* fvc::grad(p);
+phi = fvc::interpolate(U) & mesh.Sf();
 
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyNSExplicit/UnsteadyNSExplicit.C b/src/ITHACA_FOMPROBLEMS/UnsteadyNSExplicit/UnsteadyNSExplicit.C
index df90b7ada..872e761bf 100644
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyNSExplicit/UnsteadyNSExplicit.C
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyNSExplicit/UnsteadyNSExplicit.C
@@ -96,7 +96,7 @@ void UnsteadyNSExplicit::truthSolve(List<scalar> mu_now, fileName folder)
 
 #include "initContinuityErrs.H"
     dimensionedScalar nu = _nu() * mu_now[0];
-    dimensionedScalar dt = timeStep * _dt();
+    dimensionedScalar dt = timeStep* _dt();
     IOMRFZoneList& MRF = _MRF();
     singlePhaseTransportModel& laminarTransport = _laminarTransport();
     instantList Times = runTime.times();
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyNSExplicit/UnsteadyNSExplicit.H b/src/ITHACA_FOMPROBLEMS/UnsteadyNSExplicit/UnsteadyNSExplicit.H
old mode 100755
new mode 100644
index a521c3349..d7dfab8b5
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyNSExplicit/UnsteadyNSExplicit.H
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyNSExplicit/UnsteadyNSExplicit.H
@@ -92,6 +92,7 @@ class UnsteadyNSExplicit: public unsteadyNS
 
 
 };
+
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
 #endif
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTTurb/UEqn.H b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTTurb/UEqn.H
old mode 100755
new mode 100644
index c2dab506b..92efe6c7c
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTTurb/UEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTTurb/UEqn.H
@@ -9,7 +9,7 @@ fvVectorMatrix UEqn
     + turbulence->divDevReff(U)
     ==
     fvOptions(U)
-    );
+);
 
 UEqn.relax();
 
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTTurb/UnsteadyNSTTurb.C b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTTurb/UnsteadyNSTTurb.C
old mode 100755
new mode 100644
index 4185f9097..f0f2b7798
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTTurb/UnsteadyNSTTurb.C
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTTurb/UnsteadyNSTTurb.C
@@ -112,10 +112,12 @@ void UnsteadyNSTTurb::truthSolve(List<scalar> mu_now)
 #include "pEqn.H"
             }
         }
+
         {
 #include "TEqn.H"
             //TEqn.solve();
         }
+
         volScalarField _nut(turbulence->nut());
         laminarTransport.correct();
         turbulence->correct();
@@ -224,8 +226,9 @@ void UnsteadyNSTTurb::liftSolveT()
         scalar dt = mesh.time().deltaTValue();
         forAll(Tlift, i)
         {
-            Tlift[i] = (totalTime * Tlift[i] + dt * Tlift[i] ) / (totalTime + dt);
+            Tlift[i] = (totalTime* Tlift[i] + dt* Tlift[i] ) / (totalTime + dt);
         }
+
         Tlift.write();
         liftfieldT.append(Tlift.clone());
     }
@@ -539,8 +542,8 @@ void UnsteadyNSTTurb::projectSUP(fileName folder, label NU, label NP,
             SAMPLES[i]->addSample(mu.row(j), Ncoeff(i, j));
         }
 
-        rbfsplines[i] = new SPLINTER::RBFSpline(*SAMPLES[i],
-                                                SPLINTER::RadialBasisFunctionType::GAUSSIAN);
+        rbfsplines[i] = new SPLINTER::RBFSpline( * SAMPLES[i],
+            SPLINTER::RadialBasisFunctionType::GAUSSIAN);
         std::cout << "Constructing RadialBasisFunction for mode " << i + 1 << std::endl;
     }
 }
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTTurb/pEqn.H b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTTurb/pEqn.H
old mode 100755
new mode 100644
index 4c6dc0ccb..ca846d518
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTTurb/pEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTTurb/pEqn.H
@@ -5,8 +5,8 @@ surfaceScalarField phiHbyA
 (
     "phiHbyA",
     fvc::flux(HbyA)
-    + fvc::interpolate(rAU)*fvc::ddtCorr(U, phi)
-    );
+    + fvc::interpolate(rAU) * fvc::ddtCorr(U, phi)
+);
 
 MRF.makeRelative(phiHbyA);
 
@@ -34,6 +34,6 @@ while (piso.correctNonOrthogonal())
 
 #include "continuityErrs.H"
 
-U = HbyA - rAU * fvc::grad(p);
+U = HbyA - rAU* fvc::grad(p);
 U.correctBoundaryConditions();
 fvOptions.correct(U);
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UEqn.H b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UEqn.H
old mode 100755
new mode 100644
index 7b7e33cff..f7ad7c80c
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UEqn.H
@@ -32,7 +32,7 @@ tmp<fvVectorMatrix> tUEqn
     + turbulence->divDevReff(U)
     ==
     fvOptions(U)
-    );
+);
 fvVectorMatrix& UEqn = tUEqn.ref();
 
 UEqn.relax();
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UnsteadyNSTurb.C b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UnsteadyNSTurb.C
index 6f8ff894e..f39ca42ec 100644
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UnsteadyNSTurb.C
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/UnsteadyNSTurb.C
@@ -123,35 +123,31 @@ void UnsteadyNSTurb::truthSolve(List<scalar> mu_now, std::string& offlinepath)
     instantList Times = runTime.times();
     label& pRefCell = _pRefCell;
     scalar& pRefValue = _pRefValue;
-
     mesh.setFluxRequired(p.name());
-
     runTime.setEndTime(finalTime);
     runTime.setTime(Times[1], 1);
     runTime.setDeltaT(timeStep);
     nextWrite = startTime + writeEvery;
-
     label nsnapshots = 0;
 
     // Start the time loop
     while (runTime.run())
     {
-        #include "readTimeControls.H"
-        #include "CourantNo.H"
-        #include "setDeltaT.H"
-
+#include "readTimeControls.H"
+#include "CourantNo.H"
+#include "setDeltaT.H"
         ++runTime;
-
         Info << "Time = " << runTime.timeName() << nl << endl;
 
         // --- Pressure-velocity PIMPLE corrector loop
         while (pimple.loop())
         {
-            #include "UEqn.H"
+#include "UEqn.H"
+
             // --- Pressure corrector loop
             while (pimple.correct())
             {
-                #include "pEqn.H"
+#include "pEqn.H"
             }
 
             if (pimple.turbCorr())
@@ -159,7 +155,6 @@ void UnsteadyNSTurb::truthSolve(List<scalar> mu_now, std::string& offlinepath)
                 laminarTransport.correct();
                 turbulence->correct();
             }
-
         }
 
         Info << "ExecutionTime = " << runTime.elapsedCpuTime() << " s"
@@ -172,7 +167,6 @@ void UnsteadyNSTurb::truthSolve(List<scalar> mu_now, std::string& offlinepath)
             // Produces error when uncommented
             // volScalarField nut = turbulence->nut().ref();
             nut = turbulence->nut();
-
             ITHACAstream::exportSolution(U, name(counter), offlinepath);
             ITHACAstream::exportSolution(p, name(counter), offlinepath);
             ITHACAstream::exportSolution(nut, name(counter), offlinepath);
@@ -201,7 +195,7 @@ void UnsteadyNSTurb::truthSolve(List<scalar> mu_now, std::string& offlinepath)
         mu.resize(1, 1);
     }
 
-    if (mu_samples.rows() == nsnapshots * mu.cols())
+    if (mu_samples.rows() == nsnapshots* mu.cols())
     {
         ITHACAstream::exportMatrix(mu_samples, "mu_samples", "eigen",
                                    offlinepath);
@@ -783,8 +777,8 @@ void UnsteadyNSTurb::projectSUP(fileName folder, label NU, label NP, label NSUP,
 
                 ITHACAstream::ReadDenseMatrix(weights, "./ITHACAoutput/weightsSUP/",
                                               weightName);
-                rbfSplines[i] = new SPLINTER::RBFSpline(*samples[i],
-                                                        SPLINTER::RadialBasisFunctionType::GAUSSIAN, weights, radii(i));
+                rbfSplines[i] = new SPLINTER::RBFSpline( * samples[i],
+                    SPLINTER::RadialBasisFunctionType::GAUSSIAN, weights, radii(i));
                 std::cout << "Constructing RadialBasisFunction for mode " << i + 1 << std::endl;
             }
             else
@@ -796,8 +790,8 @@ void UnsteadyNSTurb::projectSUP(fileName folder, label NU, label NP, label NSUP,
                     samples[i]->addSample(velRBF.row(j), coeffL2(i, j));
                 }
 
-                rbfSplines[i] = new SPLINTER::RBFSpline(*samples[i],
-                                                        SPLINTER::RadialBasisFunctionType::GAUSSIAN, false, radii(i));
+                rbfSplines[i] = new SPLINTER::RBFSpline( * samples[i],
+                    SPLINTER::RadialBasisFunctionType::GAUSSIAN, false, radii(i));
                 ITHACAstream::SaveDenseMatrix(rbfSplines[i]->weights,
                                               "./ITHACAoutput/weightsSUP/", weightName);
                 std::cout << "Constructing RadialBasisFunction for mode " << i + 1 << std::endl;
@@ -1270,8 +1264,8 @@ void UnsteadyNSTurb::projectPPE(fileName folder, label NU, label NP, label NSUP,
 
                 ITHACAstream::ReadDenseMatrix(weights, "./ITHACAoutput/weightsPPE/",
                                               weightName);
-                rbfSplines[i] = new SPLINTER::RBFSpline(*samples[i],
-                                                        SPLINTER::RadialBasisFunctionType::GAUSSIAN, weights, radii(i));
+                rbfSplines[i] = new SPLINTER::RBFSpline( * samples[i],
+                    SPLINTER::RadialBasisFunctionType::GAUSSIAN, weights, radii(i));
                 std::cout << "Constructing RadialBasisFunction for mode " << i + 1 << std::endl;
             }
             else
@@ -1283,8 +1277,8 @@ void UnsteadyNSTurb::projectPPE(fileName folder, label NU, label NP, label NSUP,
                     samples[i]->addSample(velRBF.row(j), coeffL2(i, j));
                 }
 
-                rbfSplines[i] = new SPLINTER::RBFSpline(*samples[i],
-                                                        SPLINTER::RadialBasisFunctionType::GAUSSIAN, false, radii(i));
+                rbfSplines[i] = new SPLINTER::RBFSpline( * samples[i],
+                    SPLINTER::RadialBasisFunctionType::GAUSSIAN, false, radii(i));
                 ITHACAstream::SaveDenseMatrix(rbfSplines[i]->weights,
                                               "./ITHACAoutput/weightsPPE/", weightName);
                 std::cout << "Constructing RadialBasisFunction for mode " << i + 1 << std::endl;
@@ -1311,17 +1305,17 @@ List < Eigen::MatrixXd > UnsteadyNSTurb::velDerivativeCoeff(Eigen::MatrixXd A,
 
     for (label j = 0; j < parsSamplesNum; j++)
     {
-        Eigen::MatrixXd b0 = A.middleRows(j * timeSnapshotsPerSample,
+        Eigen::MatrixXd b0 = A.middleRows(j* timeSnapshotsPerSample,
                                           timeSnapshotsPerSample - 1);
-        Eigen::MatrixXd b2 = A.middleRows(j * timeSnapshotsPerSample + 1,
+        Eigen::MatrixXd b2 = A.middleRows(j* timeSnapshotsPerSample + 1,
                                           timeSnapshotsPerSample - 1);
         Eigen::MatrixXd bNew(b0.rows(), b0.cols() + b2.cols());
         bNew << b2, (b2 - b0) / (timeSnap(j, 0));
-        newCoeffs[0].block(j * timeSnapshotsPerSample - j, 0,
+        newCoeffs[0].block(j* timeSnapshotsPerSample - j, 0,
                            timeSnapshotsPerSample - 1, newColsNum) = bNew;
-        newCoeffs[1].middleRows(j * timeSnapshotsPerSample - j,
-                                timeSnapshotsPerSample - 1) = G.middleRows(j * timeSnapshotsPerSample + 1,
-                                        timeSnapshotsPerSample - 1);
+        newCoeffs[1].middleRows(j* timeSnapshotsPerSample - j,
+                                timeSnapshotsPerSample - 1) = G.middleRows(j* timeSnapshotsPerSample + 1,
+                                    timeSnapshotsPerSample - 1);
     }
 
     interChoice = 3;
@@ -1362,21 +1356,21 @@ List < Eigen::MatrixXd > UnsteadyNSTurb::velParDerivativeCoeff(
 
     for (label j = 0; j < parsSamplesNum; j++)
     {
-        Eigen::MatrixXd b0 = A.middleRows(j * timeSnapshotsPerSample,
+        Eigen::MatrixXd b0 = A.middleRows(j* timeSnapshotsPerSample,
                                           timeSnapshotsPerSample - 1);
-        Eigen::MatrixXd b2 = A.middleRows(j * timeSnapshotsPerSample + 1,
+        Eigen::MatrixXd b2 = A.middleRows(j* timeSnapshotsPerSample + 1,
                                           timeSnapshotsPerSample - 1);
         Eigen::MatrixXd bNew(b0.rows(), b0.cols() + b2.cols());
         bNew << b2, (b2 - b0) / (timeSnap(j, 0));
-        newCoeffs[0].block(j * timeSnapshotsPerSample - j, 0,
+        newCoeffs[0].block(j* timeSnapshotsPerSample - j, 0,
                            timeSnapshotsPerSample - 1, z.cols() - 1) = pars.middleRows(
-                                       j * timeSnapshotsPerSample + 1,
-                                       timeSnapshotsPerSample - 1);
-        newCoeffs[0].block(j * timeSnapshotsPerSample - j, z.cols() - 1,
+                                   j* timeSnapshotsPerSample + 1,
+                                   timeSnapshotsPerSample - 1);
+        newCoeffs[0].block(j* timeSnapshotsPerSample - j, z.cols() - 1,
                            timeSnapshotsPerSample - 1, newColsNum) = bNew;
-        newCoeffs[1].middleRows(j * timeSnapshotsPerSample - j,
-                                timeSnapshotsPerSample - 1) = G.middleRows(j * timeSnapshotsPerSample + 1,
-                                        timeSnapshotsPerSample - 1);
+        newCoeffs[1].middleRows(j* timeSnapshotsPerSample - j,
+                                timeSnapshotsPerSample - 1) = G.middleRows(j* timeSnapshotsPerSample + 1,
+                                    timeSnapshotsPerSample - 1);
     }
 
     interChoice = 4;
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/createUfIfPresent.H b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/createUfIfPresent.H
index a4b819fe3..f0840bd64 100644
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/createUfIfPresent.H
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/createUfIfPresent.H
@@ -1,7 +1,7 @@
+
 if (mesh.dynamic())
 {
-    Info<< "Constructing face velocity Uf\n" << endl;
-
+    Info << "Constructing face velocity Uf\n" << endl;
     _Uf.reset
     (
         new surfaceVectorField
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/pEqn.H b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/pEqn.H
old mode 100755
new mode 100644
index b374b900e..652831c97
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/pEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurb/pEqn.H
@@ -25,12 +25,12 @@
 // Solve pressure equation
 volScalarField rAU(1.0 / UEqn.A());
 
-volVectorField HbyA(constrainHbyA(rAU * UEqn.H(), U, p));
+volVectorField HbyA(constrainHbyA(rAU* UEqn.H(), U, p));
 surfaceScalarField phiHbyA
 (
     "phiHbyA",
     fvc::flux(HbyA)
-  + MRF.zeroFilter(fvc::interpolate(rAU)*fvc::ddtCorr(U, phi, _Uf))
+    + MRF.zeroFilter(fvc::interpolate(rAU) * fvc::ddtCorr(U, phi, _Uf))
 );
 
 MRF.makeRelative(phiHbyA);
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurbIntrusive/UEqn.H b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurbIntrusive/UEqn.H
old mode 100755
new mode 100644
index 7b7e33cff..f7ad7c80c
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurbIntrusive/UEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurbIntrusive/UEqn.H
@@ -32,7 +32,7 @@ tmp<fvVectorMatrix> tUEqn
     + turbulence->divDevReff(U)
     ==
     fvOptions(U)
-    );
+);
 fvVectorMatrix& UEqn = tUEqn.ref();
 
 UEqn.relax();
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurbIntrusive/UnsteadyNSTurbIntrusive.C b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurbIntrusive/UnsteadyNSTurbIntrusive.C
old mode 100755
new mode 100644
index 5e24dc05f..62d86573f
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurbIntrusive/UnsteadyNSTurbIntrusive.C
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurbIntrusive/UnsteadyNSTurbIntrusive.C
@@ -179,7 +179,7 @@ void UnsteadyNSTurbIntrusive::truthSolve(List<scalar> mu_now)
         mu.resize(1, 1);
     }
 
-    if (mu_samples.rows() == nsnapshots * mu.cols())
+    if (mu_samples.rows() == nsnapshots* mu.cols())
     {
         ITHACAstream::exportMatrix(mu_samples, "mu_samples", "eigen",
                                    "./ITHACAoutput/Offline");
@@ -805,7 +805,7 @@ Eigen::MatrixXd UnsteadyNSTurbIntrusive::laplacianPressure(label nPModes)
     {
         for (label j = 0; j < nPModes; j++)
         {
-            dMatrix(i, j) = fvc::domainIntegrate(fvc::grad(Pmodes[i])&fvc::grad(
+            dMatrix(i, j) = fvc::domainIntegrate(fvc::grad(Pmodes[i]) & fvc::grad(
                     Pmodes[j])).value();
         }
     }
@@ -866,7 +866,7 @@ Eigen::MatrixXd UnsteadyNSTurbIntrusive::pressureBC1(label nUModes,
         for (label j = 0; j < P_BC2size; j++)
         {
             surfaceScalarField lpl((fvc::interpolate(fvc::laplacian(
-                                        Umodes[j]))&mesh.Sf())*fvc::interpolate(Pmodes[i]));
+                                        Umodes[j])) & mesh.Sf()) * fvc::interpolate(Pmodes[i]));
             double s = 0;
 
             for (label k = 0; k < lpl.boundaryField().size(); k++)
@@ -905,7 +905,7 @@ Eigen::Tensor<double, 3 > UnsteadyNSTurbIntrusive::pressureBC2(label nUModes,
             {
                 surfaceScalarField div_m(fvc::interpolate(fvc::div(fvc::interpolate(
                                              Umodes[j]) & mesh.Sf(),
-                                         Umodes[k]))&mesh.Sf()*fvc::interpolate(Pmodes[i]));
+                                         Umodes[k])) & mesh.Sf() * fvc::interpolate(Pmodes[i]));
                 double s = 0;
 
                 for (label k = 0; k < div_m.boundaryField().size(); k++)
@@ -943,8 +943,8 @@ Eigen::MatrixXd UnsteadyNSTurbIntrusive::pressureBC3(label nUModes,
         for (label j = 0; j < P3_BC2size; j++)
         {
             surfaceVectorField BC3 = fvc::interpolate(fvc::curl(Umodes[j])).ref();
-            surfaceVectorField BC4 = (n ^ fvc::interpolate(fvc::grad(Pmodes[i]))).ref();
-            surfaceScalarField BC5 = ((BC3 & BC4) * mesh.magSf()).ref();
+            surfaceVectorField BC4 = (n^ fvc::interpolate(fvc::grad(Pmodes[i]))).ref();
+            surfaceScalarField BC5 = ((BC3& BC4) * mesh.magSf()).ref();
             double s = 0;
 
             for (label k = 0; k < BC5.boundaryField().size(); k++)
@@ -980,8 +980,8 @@ Eigen::MatrixXd UnsteadyNSTurbIntrusive::pressureBC4(label nUModes,
         for (label j = 0; j < P4_BC2size; j++)
         {
             surfaceScalarField BC3 = fvc::interpolate(Pmodes[i]).ref();
-            surfaceScalarField BC4 = (n & fvc::interpolate(Umodes[j])).ref();
-            surfaceScalarField BC5 = ((BC3 * BC4) * mesh.magSf()).ref();
+            surfaceScalarField BC4 = (n& fvc::interpolate(Umodes[j])).ref();
+            surfaceScalarField BC5 = ((BC3* BC4) * mesh.magSf()).ref();
             double s = 0;
 
             for (label k = 0; k < BC5.boundaryField().size(); k++)
diff --git a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurbIntrusive/pEqn.H b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurbIntrusive/pEqn.H
old mode 100755
new mode 100644
index 443200815..7a39f15c7
--- a/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurbIntrusive/pEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/UnsteadyNSTurbIntrusive/pEqn.H
@@ -29,8 +29,8 @@ surfaceScalarField phiHbyA
 (
     "phiHbyA",
     fvc::flux(HbyA)
-    + fvc::interpolate(rAU)*fvc::ddtCorr(U, phi)
-    );
+    + fvc::interpolate(rAU) * fvc::ddtCorr(U, phi)
+);
 
 MRF.makeRelative(phiHbyA);
 
diff --git a/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblem/inverseLaplacianProblem.C b/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblem/inverseLaplacianProblem.C
index 3cd7fb07c..6700037f9 100644
--- a/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblem/inverseLaplacianProblem.C
+++ b/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblem/inverseLaplacianProblem.C
@@ -115,6 +115,7 @@ volScalarField inverseLaplacianProblem::list2Field(List<scalar> list,
         label faceOwner = faceCells[faceI] ;
         field[faceOwner] = list[faceI];
     }
+
     return field;
 }
 
@@ -132,6 +133,7 @@ void inverseLaplacianProblem::set_valueFraction()
         valueFraction[faceI] =  1.0 / (1.0 + (k / H / faceDist));
         homogeneousBCcoldSide[faceI] =  0;
     }
+
     refGrad = homogeneousBCcoldSide;
 }
 
@@ -225,16 +227,18 @@ void inverseLaplacianProblem::readThermocouples()
             {
                 thermocouplesCellID[tcI] = mesh.findCell(thermocouplesPos[tcI]);
             }
+
             volScalarField thermocouplesField(T);
             ITHACAutilities::assignIF(thermocouplesField, homogeneousBC);
             forAll(thermocouplesCellID, tcI)
             {
                 thermocouplesField.ref()[thermocouplesCellID[tcI]] = 1;
             }
+
             ITHACAstream::exportSolution(thermocouplesField, "1", "./ITHACAoutput/debug/",
                                          "thermocouplesField,");
             Eigen::MatrixXi thermocouplesCellID_eigen = Foam2Eigen::List2EigenMatrix(
-                        thermocouplesCellID);
+                    thermocouplesCellID);
             ITHACAstream::exportMatrix(thermocouplesCellID_eigen, fileName,
                                        "eigen", "./");
         }
@@ -261,7 +265,7 @@ Eigen::VectorXd inverseLaplacianProblem::fieldValueAtThermocouples(
     dictionary interpolationDict =
         mesh.solutionDict().subDict("interpolationSchemes");
     autoPtr<Foam::interpolation<scalar>> fieldInterp =
-                                          Foam::interpolation<scalar>::New(interpolationDict, field);
+        Foam::interpolation<scalar>::New(interpolationDict, field);
     Eigen::VectorXd fieldInt;
     fieldInt.resize(thermocouplesPos.size());
     forAll(thermocouplesPos, tcI)
@@ -269,6 +273,7 @@ Eigen::VectorXd inverseLaplacianProblem::fieldValueAtThermocouples(
         fieldInt(tcI) = fieldInterp->interpolate(thermocouplesPos[tcI],
                         thermocouplesCellID[tcI]);
     }
+
     return fieldInt;
 }
 
@@ -286,12 +291,12 @@ Foam::vector inverseLaplacianProblem::cellDim(const faceList& ff,
 {
     forAll (pLabels, pointi)
     pLocal[pointi] = pp[pLabels[pointi]];
-    double  xDim = Foam::max(pLocal & Foam::vector(1, 0, 0))
-                   - Foam::min(pLocal & Foam::vector(1, 0, 0));
-    double  yDim = Foam::max(pLocal & Foam::vector(0, 1, 0))
-                   - Foam::min(pLocal & Foam::vector(0, 1, 0));
-    double  zDim = Foam::max(pLocal & Foam::vector(0, 0, 1))
-                   - Foam::min(pLocal & Foam::vector(0, 0, 1));
+    double  xDim = Foam::max(pLocal& Foam::vector(1, 0, 0))
+                   - Foam::min(pLocal& Foam::vector(1, 0, 0));
+    double  yDim = Foam::max(pLocal& Foam::vector(0, 1, 0))
+                   - Foam::min(pLocal& Foam::vector(0, 1, 0));
+    double  zDim = Foam::max(pLocal& Foam::vector(0, 0, 1))
+                   - Foam::min(pLocal& Foam::vector(0, 0, 1));
     Foam::vector dim (xDim, yDim, zDim);
     return dim;
 }
diff --git a/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblemTotalHeatMeasure_CG/inverseLaplacianProblemTotalHeatMeasure_CG.C b/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblemTotalHeatMeasure_CG/inverseLaplacianProblemTotalHeatMeasure_CG.C
old mode 100755
new mode 100644
index ea23cfa11..a2e75315c
--- a/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblemTotalHeatMeasure_CG/inverseLaplacianProblemTotalHeatMeasure_CG.C
+++ b/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblemTotalHeatMeasure_CG/inverseLaplacianProblemTotalHeatMeasure_CG.C
@@ -139,6 +139,7 @@ void inverseLaplacianProblemTotalHeatMeasure_CG::computeGradJ()
         gradJ_L2norm += gradJ[faceI] * gradJ[faceI]  *
                         mesh.magSf().boundaryField()[hotSide_ind][faceI];
     }
+
     gradJ_L2norm = Foam::sqrt(gradJ_L2norm);
     Info << "gradJ L2norm = " << gradJ_L2norm << endl;
 }
@@ -147,9 +148,9 @@ void inverseLaplacianProblemTotalHeatMeasure_CG::computeSearchStep()
 {
     fvMesh& mesh = _mesh();
     double Pintegral = ITHACAutilities::integralOnPatch(mesh, P, "hotSide");
-    beta = Tdiff.dot(Tsens) - gIntegralWeight * Pintegral *
+    beta = Tdiff.dot(Tsens) - gIntegralWeight* Pintegral *
            (gIntegral - gIntegral_meas);
-    double betaDiv = Tsens.dot(Tsens) - gIntegralWeight * Pintegral * Pintegral;
+    double betaDiv = Tsens.dot(Tsens) - gIntegralWeight* Pintegral* Pintegral;
     beta = beta / betaDiv;
     Info << "beta = " << beta << endl;
 }
@@ -158,7 +159,7 @@ int inverseLaplacianProblemTotalHeatMeasure_CG::conjugateGradientConvergenceChec
 {
     double Jold = J;
     J = 0.5 * Tdiff.dot(Tdiff) + 0.5 * gIntegralWeight * (gIntegral -
-            gIntegral_meas) * (gIntegral - gIntegral_meas);
+        gIntegral_meas) * (gIntegral - gIntegral_meas);
     //reduce(J, sumOp<double>());
     Info << "J = " << J << endl;
 
diff --git a/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblemTotalHeatMeasure_paramBC/inverseLaplacianProblemTotalHeatMeasure_paramBC.C b/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblemTotalHeatMeasure_paramBC/inverseLaplacianProblemTotalHeatMeasure_paramBC.C
old mode 100755
new mode 100644
index 89b2a1ced..c2bff518e
--- a/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblemTotalHeatMeasure_paramBC/inverseLaplacianProblemTotalHeatMeasure_paramBC.C
+++ b/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblemTotalHeatMeasure_paramBC/inverseLaplacianProblemTotalHeatMeasure_paramBC.C
@@ -154,7 +154,7 @@ void inverseLaplacianProblemTotalHeatMeasure_paramBC::parameterizedBCoffline(
         Info << "\nOffline part ENDED\n" << endl;
     }
 
-    Eigen::MatrixXd A = Theta.transpose() * Theta + gIntegralWeight * Phi;
+    Eigen::MatrixXd A = Theta.transpose() * Theta + gIntegralWeight* Phi;
     Eigen::JacobiSVD<Eigen::MatrixXd> svd(A,
                                           Eigen::ComputeThinU | Eigen::ComputeThinV);
     Eigen::MatrixXd singularValues = svd.singularValues();
@@ -178,8 +178,8 @@ inverseLaplacianProblemTotalHeatMeasure_paramBC::parameterizedBC(
     List<Eigen::MatrixXd> linSys;
     linSys.resize(2);
     Info << "debug: Theta size = " << Theta.rows() << ", " << Theta.cols() << endl;
-    linSys[0] = Theta.transpose() * Theta + gIntegralWeight * Phi;
-    linSys[1] = gIntegralWeight * gIntegral_meas * phi + Theta.transpose() *
+    linSys[0] = Theta.transpose() * Theta + gIntegralWeight* Phi;
+    linSys[1] = gIntegralWeight* gIntegral_meas* phi + Theta.transpose() *
                 (Tmeas + addSol);
     Eigen::VectorXd weigths;
     M_Assert(std::abs(gIntegral_meas) > 1e-16, "First set up gIntegral_meas");
diff --git a/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblem_CG/inverseLaplacianProblem_CG.C b/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblem_CG/inverseLaplacianProblem_CG.C
index 71309fe36..048c2c54c 100644
--- a/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblem_CG/inverseLaplacianProblem_CG.C
+++ b/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblem_CG/inverseLaplacianProblem_CG.C
@@ -65,6 +65,7 @@ void inverseLaplacianProblem_CG::set_valueFraction()
         valueFractionAdj[faceI] =  1 / (1 + (1 / k / H / faceDist));
         homogeneousBCcoldSide[faceI] =  0;
     }
+
     refGrad = homogeneousBCcoldSide;
 }
 
@@ -89,6 +90,7 @@ void inverseLaplacianProblem_CG::assignAdjointBC()
             ITHACAutilities::assignBC(lambda, patchI, homogeneousBC);
         }
     }
+
     ITHACAutilities::assignIF(lambda, homogeneousBC);
 }
 
@@ -110,7 +112,7 @@ volScalarField inverseLaplacianProblem_CG::assignAdjointBCandSource()
         forAll(interpolationPlane.cellID, cellI)
         {
             f.ref()[interpolationPlane.cellID [cellI]] =
-                interpolationPlane.Tdiff[cellI] * k;
+                 interpolationPlane.Tdiff[cellI] * k;
         }
     }
     else
@@ -122,7 +124,7 @@ volScalarField inverseLaplacianProblem_CG::assignAdjointBCandSource()
         }
     }
 
-    return (f * sourceDim).ref();
+    return (f* sourceDim).ref();
 }
 
 void inverseLaplacianProblem_CG::assignSensitivityBC()
@@ -385,6 +387,7 @@ void inverseLaplacianProblem_CG::computeGradJ()
         gradJ_L2norm += gradJ[faceI] * gradJ[faceI]  *
                         mesh.magSf().boundaryField()[hotSide_ind][faceI];
     }
+
     gradJ_L2norm = Foam::sqrt(gradJ_L2norm);
     Info << "gradJ L2norm = " << gradJ_L2norm << endl;
 }
@@ -403,7 +406,7 @@ void inverseLaplacianProblem_CG::searchDirection()
         Info << "gamma = " << gamma << endl;
     }
 
-    P = gradJ + gamma * P; //Updating P
+    P = gradJ + gamma* P;  //Updating P
     gamma_den = gammaNum;
     //reduce(gamma_den, sumOp<double>());
 }
@@ -412,20 +415,22 @@ void inverseLaplacianProblem_CG::computeSearchStep()
 {
     if (interpolation)
     {
-        List<scalar> temp = interpolationPlane.Tdiff *
+        List<scalar> temp = interpolationPlane.Tdiff*
                             interpolationPlane.Tsens;
         beta = 0.0;
         forAll(interpolationPlane.cellVol, cellI)
         {
             beta += interpolationPlane.cellVol [cellI] * temp [cellI];
         }
+
         //reduce(beta, sumOp<double>());
-        temp = interpolationPlane.Tsens * interpolationPlane.Tsens;
+        temp = interpolationPlane.Tsens* interpolationPlane.Tsens;
         scalar betaDiv = 0.0;
         forAll(interpolationPlane.cellVol, cellI)
         {
             betaDiv += interpolationPlane.cellVol [cellI] * temp [cellI];
         }
+
         //reduce(betaDiv, sumOp<double>());
         beta = beta / betaDiv;
         temp.clear();
@@ -444,7 +449,7 @@ void inverseLaplacianProblem_CG::computeSearchStep()
 
 void inverseLaplacianProblem_CG::updateHeatFlux()
 {
-    g = g - beta * P;
+    g = g - beta* P;
 }
 
 
@@ -455,12 +460,13 @@ int inverseLaplacianProblem_CG::conjugateGradientConvergenceCheck()
     if (interpolation)
     {
         List<scalar> sqTdiff;
-        sqTdiff = interpolationPlane.Tdiff * interpolationPlane.Tdiff;
+        sqTdiff = interpolationPlane.Tdiff* interpolationPlane.Tdiff;
         J = 0.0;
         forAll(sqTdiff, cellI)
         {
             J += 0.5 * sqTdiff[cellI] * interpolationPlane.cellVol[cellI];
         }
+
         sqTdiff.clear();
     }
     else
@@ -526,6 +532,7 @@ void inverseLaplacianProblem_CG::writeFields(label folderNumber,
         label faceOwner = faceCells[faceI] ;
         gVolField[faceOwner] = g[faceI];
     }
+
     ITHACAstream::exportSolution(T, std::to_string(folderNumber + 1), folder,
                                  "T");
     ITHACAstream::exportSolution(lambda, std::to_string(folderNumber + 1), folder,
@@ -564,10 +571,10 @@ void inverseLaplacianProblem_CG::thermocouplesInterpolation()
                     labelList pLabels(mesh.cells()[thermocouplesCellID [i]].labels(mesh.faces()));
                     pointField pLocal(pLabels.size(), Foam::vector::zero);
                     interpolationPlane.thermocoupleCellDim = cellDim (mesh.faces(),
-                            mesh.points(),
-                            mesh.cells()[thermocouplesCellID [i]],
-                            pLabels,
-                            pLocal);
+                        mesh.points(),
+                        mesh.cells()[thermocouplesCellID [i]],
+                        pLabels,
+                        pLocal);
                     flag = 0;
                 }
 
@@ -591,6 +598,7 @@ void inverseLaplacianProblem_CG::thermocouplesInterpolation()
                 interpolationPlane.thermocoupleZ [thermocoupleI] = 0;
             }
         }
+
         //reduce(interpolationPlane.thermocoupleX, sumOp<List<scalar>>());
         //reduce(interpolationPlane.thermocoupleZ, sumOp<List<scalar>>());
     }
@@ -601,6 +609,7 @@ void inverseLaplacianProblem_CG::thermocouplesInterpolation()
         x(1) = interpolationPlane.thermocoupleZ[thermocoupleI];
         thermocouplesSamples.addSample(x, Tmeas(thermocoupleI));
     }
+
     std::cout << Tmeas << std::endl;
     RBFSpline rbfspline(thermocouplesSamples, RadialBasisFunctionType::GAUSSIAN);
     auto inPlaneCellID = 0;
@@ -642,6 +651,7 @@ void inverseLaplacianProblem_CG::thermocouplesInterpolation()
             }
         }
     }
+
     interpolationPlaneDefined = 1;
 }
 
@@ -674,10 +684,10 @@ void inverseLaplacianProblem_CG::thermocouplesInterpolation(
                     labelList pLabels(mesh.cells()[thermocouplesCellID [i]].labels(mesh.faces()));
                     pointField pLocal(pLabels.size(), Foam::vector::zero);
                     interpolationPlane.thermocoupleCellDim = cellDim (mesh.faces(),
-                            mesh.points(),
-                            mesh.cells()[thermocouplesCellID [i]],
-                            pLabels,
-                            pLocal);
+                        mesh.points(),
+                        mesh.cells()[thermocouplesCellID [i]],
+                        pLabels,
+                        pLocal);
                     flag = 0;
                 }
 
@@ -701,6 +711,7 @@ void inverseLaplacianProblem_CG::thermocouplesInterpolation(
                 interpolationPlane.thermocoupleZ [thermocoupleI] = 0;
             }
         }
+
         //reduce(interpolationPlane.thermocoupleX, sumOp<List<scalar>>());
         //reduce(interpolationPlane.thermocoupleZ, sumOp<List<scalar>>());
     }
@@ -711,6 +722,7 @@ void inverseLaplacianProblem_CG::thermocouplesInterpolation(
         x(1) = interpolationPlane.thermocoupleZ[thermocoupleI];
         thermocouplesSamples.addSample(x, Tmeas(thermocoupleI));
     }
+
     std::cout << Tmeas << std::endl;
     RBFSpline rbfspline(thermocouplesSamples, RadialBasisFunctionType::GAUSSIAN);
     auto inPlaneCellID = 0;
@@ -752,6 +764,7 @@ void inverseLaplacianProblem_CG::thermocouplesInterpolation(
             }
         }
     }
+
     interpolationPlaneDefined = 1;
 }
 
@@ -766,6 +779,7 @@ void inverseLaplacianProblem_CG::differenceBetweenDirectAndMeasure()
             interpolationPlane.Tdirect[cellI] =
                 T.internalField()[interpolationPlane.cellID [cellI]];
         }
+
         interpolationPlane.Tdiff = interpolationPlane.Tdirect -
                                    interpolationPlane.Tmeas;
     }
diff --git a/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblem_CG/thermocouplesPlane.H b/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblem_CG/thermocouplesPlane.H
old mode 100755
new mode 100644
index 6da611104..04ae0f1c7
--- a/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblem_CG/thermocouplesPlane.H
+++ b/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblem_CG/thermocouplesPlane.H
@@ -23,4 +23,5 @@ class thermocouplesPlane
         List<scalar> thermocoupleZ;
         Foam::vector thermocoupleCellDim;
 };
+
 #endif
diff --git a/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblem_paramBC/inverseLaplacianProblem_paramBC.C b/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblem_paramBC/inverseLaplacianProblem_paramBC.C
index bf692a0b1..823b4bf97 100644
--- a/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblem_paramBC/inverseLaplacianProblem_paramBC.C
+++ b/src/ITHACA_FOMPROBLEMS/inverseLaplacianProblem_paramBC/inverseLaplacianProblem_paramBC.C
@@ -76,9 +76,9 @@ void inverseLaplacianProblem_paramBC::set_gBaseFunctions()
                 scalar faceZ = mesh.boundaryMesh()[hotSide_ind].faceCentres()[faceI].z();
                 scalar radius = Foam::sqrt((faceX - thermocoupleX) * (faceX - thermocoupleX) +
                                            (faceZ - thermocoupleZ) * (faceZ - thermocoupleZ));
-                gBaseFunctions[funcI][faceI] = Foam::exp(- (shapeParameter *
+                gBaseFunctions[funcI][faceI] = Foam::exp(- (shapeParameter*
                                                shapeParameter
-                                               * radius * radius));
+                                               * radius* radius));
             }
         }
     }
@@ -138,12 +138,13 @@ void inverseLaplacianProblem_paramBC::set_gBaseFunctionsPOD(label Nmodes)
             gBaseFuncEigen(faceI, funcI) = gBaseFunctions[funcI][faceI];
         }
     }
+
     Eigen::MatrixXd correlationMatrix = gBaseFuncEigen.transpose() *
                                         faceAreaVect.asDiagonal() * gBaseFuncEigen;
     Eigen::JacobiSVD<Eigen::MatrixXd> svd(correlationMatrix,
                                           Eigen::ComputeThinU | Eigen::ComputeThinV);
     gPODmodes = svd.matrixU().leftCols(Nmodes);
-    Eigen::MatrixXd gBaseFuncEigen_new = gBaseFuncEigen * gPODmodes;
+    Eigen::MatrixXd gBaseFuncEigen_new = gBaseFuncEigen* gPODmodes;
     Info << "gBaseFuncEigen_new size = " << gBaseFuncEigen_new.cols() << ", " <<
          gBaseFuncEigen_new.rows() << endl;
     gBaseFunctions.resize(Nmodes);
@@ -169,6 +170,7 @@ void inverseLaplacianProblem_paramBC::set_gParametrized(word _baseFuncType,
     {
         gWeights[weigthI] = 0; //-10000;
     }
+
     Info << "gWeights = " << gWeights << endl;
     forAll (T.boundaryField()[hotSide_ind], faceI)
     {
@@ -386,6 +388,7 @@ void inverseLaplacianProblem_paramBC::parameterizedBCpostProcess(
     {
         gWeights[weightI] = weigths(weightI);
     }
+
     update_gParametrized(gWeights);
     reconstructT();
     volScalarField& T = _T();
@@ -421,6 +424,7 @@ void inverseLaplacianProblem_paramBC::solveAdditional()
             ITHACAutilities::assignBC(Tad, patchI, homogeneousBC);
         }
     }
+
 #if defined(OFVER) && (OFVER == 6)
 
     while (simple.loop(runTime))
@@ -456,6 +460,7 @@ void inverseLaplacianProblem_paramBC::reconstructT()
     {
         Trec += gWeights[baseI] * (Tbasis[baseI] + Tad_base[0]);
     }
+
     Trec += - Tad_base[0];
     volScalarField& T = _T();
     T = Trec;
diff --git a/src/ITHACA_FOMPROBLEMS/laplacianProblem/laplacianProblem.C b/src/ITHACA_FOMPROBLEMS/laplacianProblem/laplacianProblem.C
old mode 100755
new mode 100644
index 092122cce..c9c830b2f
--- a/src/ITHACA_FOMPROBLEMS/laplacianProblem/laplacianProblem.C
+++ b/src/ITHACA_FOMPROBLEMS/laplacianProblem/laplacianProblem.C
@@ -38,6 +38,7 @@
 
 // Constructors
 laplacianProblem::laplacianProblem() {}
+
 laplacianProblem::laplacianProblem(int argc, char* argv[])
 {
     _args = autoPtr<argList>
@@ -65,7 +66,7 @@ void laplacianProblem::truthSolve(List<scalar> mu_now, word folder)
 {
     volScalarField& T = _T();
     volScalarField& S = _S();
-    fvScalarMatrix lhs(theta[0]*operator_list[0]);
+    fvScalarMatrix lhs(theta[0] * operator_list[0]);
 
     for (label i = 1; i < operator_list.size(); i++)
     {
@@ -97,6 +98,7 @@ void laplacianProblem::truthSolve(List<scalar> mu_now, word folder)
                                    folder);
     }
 }
+
 // Perform the projection onto the POD modes
 void laplacianProblem::project(label Nmodes)
 {
diff --git a/src/ITHACA_FOMPROBLEMS/msrProblem/DiffEqn.H b/src/ITHACA_FOMPROBLEMS/msrProblem/DiffEqn.H
old mode 100755
new mode 100644
index 9cc3f869d..177367501
--- a/src/ITHACA_FOMPROBLEMS/msrProblem/DiffEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/msrProblem/DiffEqn.H
@@ -15,7 +15,7 @@ tmp<fvScalarMatrix> tNEqn
     + lam7* prec7
     + lam8* prec8
 
-    );
+);
 
 fvScalarMatrix& NEqn = tNEqn.ref();
 NEqn.relax();
diff --git a/src/ITHACA_FOMPROBLEMS/msrProblem/NLmsrProblem.H b/src/ITHACA_FOMPROBLEMS/msrProblem/NLmsrProblem.H
index c7622b9c4..af499ff28 100644
--- a/src/ITHACA_FOMPROBLEMS/msrProblem/NLmsrProblem.H
+++ b/src/ITHACA_FOMPROBLEMS/msrProblem/NLmsrProblem.H
@@ -98,10 +98,11 @@ while (simple.loop() && residual > tolerance && csolve < maxIter )
         residual = max(residual, dec3residual);
         Info << "\nResidual: " << residual << endl << endl;
     }
+
     laminarTransport.correct();
     turbulence->correct();
-    powerDens = (1 - decbetaTot) * flux * SP1_0 + (decLam1 * dec1 + decLam2 * dec2 +
-                decLam3 * dec3);
+    powerDens = (1 - decbetaTot) * flux* SP1_0 + (decLam1* dec1 + decLam2* dec2 +
+                decLam3* dec3);
     csolve = csolve + 1;
     Info << "ExecutionTime = " << runTime.elapsedCpuTime() << " s"
          << "  ClockTime = " << runTime.elapsedClockTime() << " s"
diff --git a/src/ITHACA_FOMPROBLEMS/msrProblem/TEqn.H b/src/ITHACA_FOMPROBLEMS/msrProblem/TEqn.H
old mode 100755
new mode 100644
index abae1e1e2..c11325df9
--- a/src/ITHACA_FOMPROBLEMS/msrProblem/TEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/msrProblem/TEqn.H
@@ -8,10 +8,10 @@ tmp<fvScalarMatrix> tTEqn
     fvm::div(phi, T)
     ==
     fvm::laplacian(turbulence->nu() / Pr + alphat, T)
-    +(v / CpRef) * (decLam1 * dec1 + decLam2 * dec2 + decLam3* dec3)
-    + (SP * (1 - decbetaTot)*v / CpRef)*flux
+    +(v / CpRef) * (decLam1* dec1 + decLam2* dec2 + decLam3* dec3)
+    + (SP * (1 - decbetaTot) * v / CpRef) * flux
 
-    );
+);
 fvScalarMatrix& TEqn = tTEqn.ref();
 //TEqn.relax();
 //TEqn.solve();
diff --git a/src/ITHACA_FOMPROBLEMS/msrProblem/UEqn.H b/src/ITHACA_FOMPROBLEMS/msrProblem/UEqn.H
old mode 100755
new mode 100644
index 1d91429a0..7117de308
--- a/src/ITHACA_FOMPROBLEMS/msrProblem/UEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/msrProblem/UEqn.H
@@ -33,7 +33,7 @@ tmp<fvVectorMatrix> tUEqn
     + turbulence->divDevReff(U)
     ==
     fvOptions(U)
-    );
+);
 fvVectorMatrix& UEqn = tUEqn.ref();
 
 UEqn.relax();
diff --git a/src/ITHACA_FOMPROBLEMS/msrProblem/decEqns.H b/src/ITHACA_FOMPROBLEMS/msrProblem/decEqns.H
old mode 100755
new mode 100644
index a6185427b..ca75e792a
--- a/src/ITHACA_FOMPROBLEMS/msrProblem/decEqns.H
+++ b/src/ITHACA_FOMPROBLEMS/msrProblem/decEqns.H
@@ -8,7 +8,7 @@ tmp<fvScalarMatrix> tdecEq1
     fvm::laplacian(turbulence->nu() / Sc + difft, dec1)
     - fvm::Sp(decLam1, dec1)
     + decBeta1* SP* flux
-    );
+);
 
 fvScalarMatrix& decEq1 = tdecEq1.ref();
 decEq1.relax();
@@ -23,7 +23,7 @@ tmp<fvScalarMatrix> tdecEq2
     fvm::laplacian(turbulence->nu() / Sc + difft, dec2)
     - fvm::Sp(decLam2, dec2)
     + decBeta2* SP* flux
-    );
+);
 
 fvScalarMatrix& decEq2 = tdecEq2.ref();
 decEq2.relax();
@@ -38,7 +38,7 @@ tmp<fvScalarMatrix> tdecEq3
     fvm::laplacian(turbulence->nu() / Sc + difft, dec3)
     - fvm::Sp(decLam3, dec3)
     + decBeta3* SP* flux
-    );
+);
 
 fvScalarMatrix& decEq3 = tdecEq3.ref();
 decEq3.relax();
diff --git a/src/ITHACA_FOMPROBLEMS/msrProblem/msrProblem.C b/src/ITHACA_FOMPROBLEMS/msrProblem/msrProblem.C
index 9d059d5c4..c348b8013 100644
--- a/src/ITHACA_FOMPROBLEMS/msrProblem/msrProblem.C
+++ b/src/ITHACA_FOMPROBLEMS/msrProblem/msrProblem.C
@@ -119,8 +119,8 @@ void msrProblem::truthSolve(List<scalar> mu_now)
     volScalarField& logT = _logT();
     volScalarField& alphat = _alphat();
     volScalarField& difft = _difft();
-    volScalarField powerDens = ((1 - decbetaTot) * flux * SP +
-                                (decLam1 * dec1 + decLam2 * dec2 + decLam3 * dec3)).ref();
+    volScalarField powerDens = ((1 - decbetaTot) * flux* SP +
+                                (decLam1* dec1 + decLam2* dec2 + decLam3* dec3)).ref();
     powerDens.rename("powerDens");
 #include "NLmsrProblem.H"
     counter++;
@@ -338,7 +338,7 @@ void msrProblem::liftSolve()
                 IOobject::NO_WRITE
             ),
             mesh,
-            dimensionedScalar("Phi", dimLength * dimVelocity, 0),
+            dimensionedScalar("Phi", dimLength* dimVelocity, 0),
             p.boundaryField().types()
         );
         label PhiRefCell = 0;
@@ -767,7 +767,7 @@ Eigen::MatrixXd msrProblem::laplacian_pressure(label NPmodes)
     {
         for (label j = 0; j < Dsize; j++)
         {
-            D_matrix(i, j) = fvc::domainIntegrate(fvc::grad(Pmodes[i])&fvc::grad(
+            D_matrix(i, j) = fvc::domainIntegrate(fvc::grad(Pmodes[i]) & fvc::grad(
                     Pmodes[j])).value();
         }
     }
@@ -807,7 +807,7 @@ Eigen::MatrixXd msrProblem::pressure_BC1(label NUmodes, label NPmodes)
         for (label j = 0; j < P_BC2size; j++)
         {
             surfaceScalarField lpl((fvc::interpolate(fvc::laplacian(
-                                        Together[j]))&mesh.Sf())*fvc::interpolate(Pmodes[i]));
+                                        Together[j])) & mesh.Sf()) * fvc::interpolate(Pmodes[i]));
             double s = 0;
 
             for (label k = 0; k < lpl.boundaryField().size(); k++)
@@ -863,7 +863,8 @@ List <Eigen::MatrixXd> msrProblem::pressure_BC2(label NUmodes, label NPmodes)
             for (label k = 0; k < P2_BC2size; k++)
             {
                 surfaceScalarField div_m(fvc::interpolate(fvc::div(fvc::interpolate(
-                                             Together[j]) & mesh.Sf(), Together[k]))&mesh.Sf()*fvc::interpolate(Pmodes[i]));
+                                             Together[j]) & mesh.Sf(),
+                                         Together[k])) & mesh.Sf() * fvc::interpolate(Pmodes[i]));
                 double s = 0;
 
                 for (label k = 0; k < div_m.boundaryField().size(); k++)
@@ -913,8 +914,8 @@ Eigen::MatrixXd msrProblem::pressure_BC3(label NUmodes, label NPmodes)
         for (label j = 0; j < P3_BC2size; j++)
         {
             surfaceVectorField BC3 = fvc::interpolate(fvc::curl(Together[j])).ref();
-            surfaceVectorField BC4 = (n ^ fvc::interpolate(fvc::grad(Pmodes[i]))).ref();
-            surfaceScalarField BC5 = ((BC3 & BC4) * mesh.magSf()).ref();
+            surfaceVectorField BC4 = (n^ fvc::interpolate(fvc::grad(Pmodes[i]))).ref();
+            surfaceScalarField BC5 = ((BC3& BC4) * mesh.magSf()).ref();
             double s = 0;
 
             for (label k = 0; k < BC5.boundaryField().size(); k++)
@@ -1812,8 +1813,8 @@ void msrProblem::msrcoeff(label& NC)
             SAMPLES_v[i]->addSample(mu_samples.row(j), Ncoeff_v(i, j));
         }
 
-        rbfsplines_v[i] = new SPLINTER::RBFSpline(*SAMPLES_v[i],
-                SPLINTER::RadialBasisFunctionType::GAUSSIAN);
+        rbfsplines_v[i] = new SPLINTER::RBFSpline( * SAMPLES_v[i],
+            SPLINTER::RadialBasisFunctionType::GAUSSIAN);
     }
 
     Eigen::MatrixXd Ncoeff_D = ITHACAutilities::getCoeffs(DFields, Dmodes);
@@ -1833,8 +1834,8 @@ void msrProblem::msrcoeff(label& NC)
             SAMPLES_D[i]->addSample(mu_samples.row(j), Ncoeff_D(i, j));
         }
 
-        rbfsplines_D[i] = new SPLINTER::RBFSpline(*SAMPLES_D[i],
-                SPLINTER::RadialBasisFunctionType::GAUSSIAN);
+        rbfsplines_D[i] = new SPLINTER::RBFSpline( * SAMPLES_D[i],
+            SPLINTER::RadialBasisFunctionType::GAUSSIAN);
     }
 
     Eigen::MatrixXd Ncoeff_NSF = ITHACAutilities::getCoeffs(NSFFields,
@@ -1855,8 +1856,8 @@ void msrProblem::msrcoeff(label& NC)
             SAMPLES_NSF[i]->addSample(mu_samples.row(j), Ncoeff_NSF(i, j));
         }
 
-        rbfsplines_NSF[i] = new SPLINTER::RBFSpline(*SAMPLES_NSF[i],
-                SPLINTER::RadialBasisFunctionType::GAUSSIAN);
+        rbfsplines_NSF[i] = new SPLINTER::RBFSpline( * SAMPLES_NSF[i],
+            SPLINTER::RadialBasisFunctionType::GAUSSIAN);
     }
 
     Eigen::MatrixXd Ncoeff_A = ITHACAutilities::getCoeffs(AFields, Amodes);
@@ -1876,8 +1877,8 @@ void msrProblem::msrcoeff(label& NC)
             SAMPLES_A[i]->addSample(mu_samples.row(j), Ncoeff_A(i, j));
         }
 
-        rbfsplines_A[i] = new SPLINTER::RBFSpline(*SAMPLES_A[i],
-                SPLINTER::RadialBasisFunctionType::GAUSSIAN);
+        rbfsplines_A[i] = new SPLINTER::RBFSpline( * SAMPLES_A[i],
+            SPLINTER::RadialBasisFunctionType::GAUSSIAN);
     }
 
     Eigen::MatrixXd Ncoeff_SP = ITHACAutilities::getCoeffs(SPFields,
@@ -1898,8 +1899,8 @@ void msrProblem::msrcoeff(label& NC)
             SAMPLES_SP[i]->addSample(mu_samples.row(j), Ncoeff_SP(i, j));
         }
 
-        rbfsplines_SP[i] = new SPLINTER::RBFSpline(*SAMPLES_SP[i],
-                SPLINTER::RadialBasisFunctionType::GAUSSIAN);
+        rbfsplines_SP[i] = new SPLINTER::RBFSpline( * SAMPLES_SP[i],
+            SPLINTER::RadialBasisFunctionType::GAUSSIAN);
     }
 
     Eigen::MatrixXd Ncoeff_TXS = ITHACAutilities::getCoeffs(TXSFields,
@@ -1920,8 +1921,8 @@ void msrProblem::msrcoeff(label& NC)
             SAMPLES_TXS[i]->addSample(mu_samples.row(j), Ncoeff_TXS(i, j));
         }
 
-        rbfsplines_TXS[i] = new SPLINTER::RBFSpline(*SAMPLES_TXS[i],
-                SPLINTER::RadialBasisFunctionType::GAUSSIAN);
+        rbfsplines_TXS[i] = new SPLINTER::RBFSpline( * SAMPLES_TXS[i],
+            SPLINTER::RadialBasisFunctionType::GAUSSIAN);
     }
 }
 
@@ -1998,7 +1999,7 @@ void msrProblem::liftSolveT()
             fvScalarMatrix TEqn
             (
                 fvm::div(phi, Tlift) == fvm::laplacian(turbulence->nu() / Pr + alphat, Tlift)
-                + sp * (1 - dbtot) / (cp * rho)*source
+                + sp * (1 - dbtot) / (cp* rho) * source
             );
             TEqn.solve();
             Info << "ExecutionTime = " << runTime.elapsedCpuTime() << " s"
@@ -2065,8 +2066,8 @@ void msrProblem::restart()
     U = U0;
     phi = phi0;
     turbulence.reset(
-        (incompressible::turbulenceModel::New(U, phi, _laminarTransport())).ptr()
-    );
+                  (incompressible::turbulenceModel::New(U, phi, _laminarTransport())).ptr()
+              );
     flux = flux0;
     prec1 = prec10;
     prec2 = prec20;
diff --git a/src/ITHACA_FOMPROBLEMS/msrProblem/pEqn.H b/src/ITHACA_FOMPROBLEMS/msrProblem/pEqn.H
old mode 100755
new mode 100644
index 5c62d90b5..104e0c227
--- a/src/ITHACA_FOMPROBLEMS/msrProblem/pEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/msrProblem/pEqn.H
@@ -24,7 +24,7 @@
 \*---------------------------------------------------------------------------*/
 {
     volScalarField rAU(1.0 / UEqn.A());
-    volVectorField HbyA(constrainHbyA(rAU * UEqn.H(), U, p));
+    volVectorField HbyA(constrainHbyA(rAU* UEqn.H(), U, p));
     surfaceScalarField phiHbyA("phiHbyA", fvc::flux(HbyA));
     MRF.makeRelative(phiHbyA);
     adjustPhi(phiHbyA, U, p);
diff --git a/src/ITHACA_FOMPROBLEMS/msrProblem/precEqns.H b/src/ITHACA_FOMPROBLEMS/msrProblem/precEqns.H
old mode 100755
new mode 100644
index 471f142ea..9f0c4c49e
--- a/src/ITHACA_FOMPROBLEMS/msrProblem/precEqns.H
+++ b/src/ITHACA_FOMPROBLEMS/msrProblem/precEqns.H
@@ -8,7 +8,7 @@ tmp<fvScalarMatrix> tprecEq1
     fvm::laplacian(turbulence->nu() + difft, prec1)
     - fvm::Sp(lam1, prec1)
     + beta1* NSF* flux
-    );
+);
 
 fvScalarMatrix& precEq1 = tprecEq1.ref();
 precEq1.relax();
@@ -22,7 +22,7 @@ tmp<fvScalarMatrix> tprecEq2
     fvm::laplacian(turbulence->nu() + difft, prec2)
     - fvm::Sp(lam2, prec2)
     + beta2* NSF* flux
-    );
+);
 
 fvScalarMatrix& precEq2 = tprecEq2.ref();
 precEq2.relax();
@@ -37,7 +37,7 @@ tmp<fvScalarMatrix> tprecEq3
     fvm::laplacian(turbulence->nu() + difft, prec3)
     - fvm::Sp(lam3, prec3)
     + beta3* NSF* flux
-    );
+);
 
 fvScalarMatrix& precEq3 = tprecEq3.ref();
 precEq3.relax();
@@ -52,7 +52,7 @@ tmp<fvScalarMatrix> tprecEq4
     fvm::laplacian(turbulence->nu() + difft, prec4)
     - fvm::Sp(lam4, prec4)
     + beta4* NSF* flux
-    );
+);
 
 fvScalarMatrix& precEq4 = tprecEq4.ref();
 precEq4.relax();
@@ -68,7 +68,7 @@ tmp<fvScalarMatrix> tprecEq5
     fvm::laplacian(turbulence->nu() + difft, prec5)
     - fvm::Sp(lam5, prec5)
     + beta5* NSF* flux
-    );
+);
 
 fvScalarMatrix& precEq5 = tprecEq5.ref();
 precEq5.relax();
@@ -83,7 +83,7 @@ tmp<fvScalarMatrix> tprecEq6
     fvm::laplacian(turbulence->nu() + difft, prec6)
     - fvm::Sp(lam6, prec6)
     + beta6* NSF* flux
-    );
+);
 
 fvScalarMatrix& precEq6 = tprecEq6.ref();
 precEq6.relax();
@@ -98,7 +98,7 @@ tmp<fvScalarMatrix> tprecEq7
     fvm::laplacian(turbulence->nu() + difft, prec7)
     - fvm::Sp(lam7, prec7)
     + beta7* NSF* flux
-    );
+);
 
 fvScalarMatrix& precEq7 = tprecEq7.ref();
 precEq7.relax();
@@ -113,7 +113,7 @@ tmp<fvScalarMatrix> tprecEq8
     fvm::laplacian(turbulence->nu() + difft, prec8)
     - fvm::Sp(lam8, prec8)
     + beta8* NSF* flux
-    );
+);
 
 fvScalarMatrix& precEq8 = tprecEq8.ref();
 precEq8.relax();
diff --git a/src/ITHACA_FOMPROBLEMS/msrProblem/steadySolver.H b/src/ITHACA_FOMPROBLEMS/msrProblem/steadySolver.H
old mode 100755
new mode 100644
index 59d49f438..103acd9f5
--- a/src/ITHACA_FOMPROBLEMS/msrProblem/steadySolver.H
+++ b/src/ITHACA_FOMPROBLEMS/msrProblem/steadySolver.H
@@ -33,10 +33,10 @@ while (simple.loop(runTime))
 #include "pEqn.H"
         rho = rhoRef * (1 - betaTE * (T - Tref));
         logT = log(max(0.5, (T / TrefXS)));
-        NSF1 = (1 / Keff) * (NSF1_0 + alfa_NSF1 * logT);
-        M11 = NSF1 * (1 - betaTot) - (A1_0 + alfa_A1 * logT);
-        D1 = (D1_0 + alfa_D1 * logT);
-        SP1 = (1 / Keff) * (SP1_0 + alfa_SP1 * logT);
+        NSF1 = (1 / Keff) * (NSF1_0 + alfa_NSF1* logT);
+        M11 = NSF1 * (1 - betaTot) - (A1_0 + alfa_A1* logT);
+        D1 = (D1_0 + alfa_D1* logT);
+        SP1 = (1 / Keff) * (SP1_0 + alfa_SP1* logT);
         alphaEff = turbulence->nu() / Pr + turbulence->nut() / Prt;
         diffEff = turbulence->nu() / Sc + turbulence->nut() / Sct;
 #include "DiffEqn.H"
@@ -44,14 +44,15 @@ while (simple.loop(runTime))
 #include "decEqns.H"
 #include "TEqn.H"
     }
+
     laminarTransport.correct();
     turbulence->correct();
     runTime.write();
     Info << "ExecutionTime = " << runTime.elapsedCpuTime() << " s"
          << "  ClockTime = " << runTime.elapsedClockTime() << " s"
          << nl << endl;
-    powerDens = (1 - decbetaTot) * flux * SP1 + (decLam1 * dec1 + decLam2 * dec2 +
-                decLam3 * dec3);
+    powerDens = (1 - decbetaTot) * flux* SP1 + (decLam1* dec1 + decLam2* dec2 +
+                decLam3* dec3);
     exportSolution(U, name(counter), "./ITHACAoutput/Offline/");
     exportSolution(p, name(counter), "./ITHACAoutput/Offline/");
     exportSolution(flux, name(counter), "./ITHACAoutput/Offline/");
diff --git a/src/ITHACA_FOMPROBLEMS/msrProblem/updateConsts.H b/src/ITHACA_FOMPROBLEMS/msrProblem/updateConsts.H
old mode 100755
new mode 100644
index fd18f0918..84804d1db
--- a/src/ITHACA_FOMPROBLEMS/msrProblem/updateConsts.H
+++ b/src/ITHACA_FOMPROBLEMS/msrProblem/updateConsts.H
@@ -31,4 +31,4 @@ NSF = (1 / Keff) * (NSF1_0 + alfa_NSF1* logT) * (1 - betaTE * (T - Tref));
 A = (A1_0 + alfa_A1* logT) * (1 - betaTE * (T - Tref));
 D = (D1_0 + alfa_D1* logT) / (1 - betaTE * (T - Tref));
 SP = (1 / Keff) * (SP1_0 + alfa_SP1* logT) * (1 - betaTE * (T - Tref));
-TXS = v * SP;
+TXS = v* SP;
diff --git a/src/ITHACA_FOMPROBLEMS/msrProblem/updateK.H b/src/ITHACA_FOMPROBLEMS/msrProblem/updateK.H
old mode 100755
new mode 100644
index 4dacc48d3..4ac9e8461
--- a/src/ITHACA_FOMPROBLEMS/msrProblem/updateK.H
+++ b/src/ITHACA_FOMPROBLEMS/msrProblem/updateK.H
@@ -23,5 +23,5 @@
   along with ITHACA-FV. If not, see <http://www.gnu.org/licenses/>.
 \*---------------------------------------------------------------------------*/
 Keff = (fvc::domainIntegrate(flux).value()) / (fvc::domainIntegrate(
-            flux_old).value());
+           flux_old).value());
 
diff --git a/src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblem.C b/src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblem.C
old mode 100755
new mode 100644
index 449ddccaa..7c0fe4ec4
--- a/src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblem.C
+++ b/src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblem.C
@@ -136,7 +136,7 @@ void reductionProblem::assignBC(volScalarField& s, label BC_ind, double& value)
             s.boundaryFieldRef()[BC_ind][i] = value;
         }
 
-        freestreamFvPatchField<scalar>& Tpatch =
+        freestreamFvPatchField<scalar> & Tpatch =
             refCast<freestreamFvPatchField<scalar>>(s.boundaryFieldRef()[BC_ind]);
         scalarField& gradTpatch = Tpatch.freestreamValue();
         forAll(gradTpatch, faceI)
@@ -158,7 +158,7 @@ void reductionProblem::assignBC(volScalarField& s, label BC_ind, double& value)
 
 // Assign a BC for a scalar field
 void reductionProblem::assignBC(volVectorField& s, label BC_ind,
-                                Vector<double>& value)
+                                Vector<double> & value)
 {
     if (s.boundaryField()[BC_ind].type() == "fixedValue")
     {
@@ -179,7 +179,7 @@ void reductionProblem::assignBC(volVectorField& s, label BC_ind,
             s.boundaryFieldRef()[BC_ind][i] = value;
         }
 
-        freestreamFvPatchField<vector>& Tpatch =
+        freestreamFvPatchField<vector> & Tpatch =
             refCast<freestreamFvPatchField<vector>>(s.boundaryFieldRef()[BC_ind]);
         vectorField& gradTpatch = Tpatch.freestreamValue();
         forAll(gradTpatch, faceI)
@@ -190,8 +190,8 @@ void reductionProblem::assignBC(volVectorField& s, label BC_ind,
 }
 
 // Reconstruct using a Matrix of coefficients (vector field)
-void reductionProblem::reconstructFromMatrix(PtrList<volVectorField>&
-        rec_field2, PtrList<volVectorField>& modes, label Nmodes,
+void reductionProblem::reconstructFromMatrix(PtrList<volVectorField> &
+        rec_field2, PtrList<volVectorField> & modes, label Nmodes,
         Eigen::MatrixXd coeff_matrix)
 {
     for (label k = 0; k < coeff_matrix.cols(); k++)
@@ -200,7 +200,7 @@ void reductionProblem::reconstructFromMatrix(PtrList<volVectorField>&
         {
             if ( i == 0)
             {
-                rec_field2.append(coeff_matrix(i, k)*modes[i]);
+                rec_field2.append(coeff_matrix(i, k) * modes[i]);
             }
             else
             {
@@ -212,8 +212,8 @@ void reductionProblem::reconstructFromMatrix(PtrList<volVectorField>&
 
 
 // Reconstruct using a Matrix of coefficients (vector field)
-void reductionProblem::reconstructFromMatrix(PtrList<volScalarField>&
-        rec_field2, PtrList<volScalarField>& modes, label Nmodes,
+void reductionProblem::reconstructFromMatrix(PtrList<volScalarField> &
+        rec_field2, PtrList<volScalarField> & modes, label Nmodes,
         Eigen::MatrixXd coeff_matrix)
 {
     for (label k = 0; k < coeff_matrix.cols(); k++)
@@ -222,7 +222,7 @@ void reductionProblem::reconstructFromMatrix(PtrList<volScalarField>&
         {
             if ( i == 0)
             {
-                rec_field2.append(coeff_matrix(i, k)*modes[i]);
+                rec_field2.append(coeff_matrix(i, k) * modes[i]);
             }
             else
             {
@@ -249,6 +249,7 @@ void reductionProblem::writeMu(List<scalar> mu_now)
     {
         ofs << mu_now[i] << ' ';
     }
+
     ofs << "\n";
     ofs.close();
 }
@@ -268,7 +269,7 @@ void reductionProblem::liftSolveT()
 }
 
 std::vector<SPLINTER::RBFSpline> reductionProblem::getCoeffManifoldRBF(
-    PtrList<volVectorField> snapshots, PtrList<volVectorField>& modes,
+    PtrList<volVectorField> snapshots, PtrList<volVectorField> & modes,
     word rbfBasis)
 {
     Eigen::MatrixXd coeff = ITHACAutilities::getCoeffs(snapshots, modes);
@@ -352,7 +353,7 @@ std::vector<SPLINTER::RBFSpline> reductionProblem::getCoeffManifoldRBF(
 
 
 std::vector<SPLINTER::RBFSpline> reductionProblem::getCoeffManifoldRBF(
-    PtrList<volScalarField> snapshots, PtrList<volScalarField>& modes,
+    PtrList<volScalarField> snapshots, PtrList<volScalarField> & modes,
     word rbfBasis)
 {
     Eigen::MatrixXd coeff = ITHACAutilities::getCoeffs(snapshots, modes);
@@ -436,7 +437,8 @@ std::vector<SPLINTER::RBFSpline> reductionProblem::getCoeffManifoldRBF(
 
 
 std::vector<SPLINTER::BSpline> reductionProblem::getCoeffManifoldSPL(
-    PtrList<volVectorField> snapshots, PtrList<volVectorField>& modes, label splDeg)
+    PtrList<volVectorField> snapshots, PtrList<volVectorField> & modes,
+    label splDeg)
 {
     Eigen::MatrixXd coeff = ITHACAutilities::getCoeffs(snapshots, modes);
     M_Assert(mu_samples.rows() == coeff.cols() * mu.rows(),
@@ -490,7 +492,8 @@ std::vector<SPLINTER::BSpline> reductionProblem::getCoeffManifoldSPL(
 
 
 std::vector<SPLINTER::BSpline> reductionProblem::getCoeffManifoldSPL(
-    PtrList<volScalarField> snapshots, PtrList<volScalarField>& modes, label splDeg)
+    PtrList<volScalarField> snapshots, PtrList<volScalarField> & modes,
+    label splDeg)
 {
     Eigen::MatrixXd coeff = ITHACAutilities::getCoeffs(snapshots, modes);
     M_Assert(mu_samples.rows() == coeff.cols() * mu.rows(),
diff --git a/src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblem.H b/src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblem.H
old mode 100755
new mode 100644
index b4d754858..38d16e021
--- a/src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblem.H
+++ b/src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblem.H
@@ -193,7 +193,7 @@ class reductionProblem
         /// @param[in]  BC_ind  The BC index.
         /// @param[in]  value   The value you want to assign (it must be an OpenFOAM vector).
         ///
-        void assignBC(volVectorField& s, label BC_ind, Vector<double>& value);
+        void assignBC(volVectorField& s, label BC_ind, Vector<double> & value);
 
         //--------------------------------------------------------------------------
         /// Assign Boundary Condition to a volScalarField
@@ -213,8 +213,8 @@ class reductionProblem
         /// @param[in]  Nmodes        The number of modes you want to use.
         /// @param[in]  coeff_matrix  The matrix of coefficients.
         ///
-        void reconstructFromMatrix(PtrList<volVectorField>& rec_field2,
-                                   PtrList<volVectorField>& modes, label Nmodes, Eigen::MatrixXd coeff_matrix);
+        void reconstructFromMatrix(PtrList<volVectorField> & rec_field2,
+                                   PtrList<volVectorField> & modes, label Nmodes, Eigen::MatrixXd coeff_matrix);
 
         //--------------------------------------------------------------------------
         /// Exact reconstruction using a certain number of modes for vector list of
@@ -226,8 +226,8 @@ class reductionProblem
         /// @param[in]  coeff_matrix  The matrix of coefficients.
         ///
         /// Exact reconstruction using a certain number of modes for scalar list of fields
-        void reconstructFromMatrix(PtrList<volScalarField>& rec_field2,
-                                   PtrList<volScalarField>& modes, label Nmodes, Eigen::MatrixXd coeff_matrix);
+        void reconstructFromMatrix(PtrList<volScalarField> & rec_field2,
+                                   PtrList<volScalarField> & modes, label Nmodes, Eigen::MatrixXd coeff_matrix);
 
         //--------------------------------------------------------------------------
         /// Assign internal field condition
@@ -286,7 +286,7 @@ class reductionProblem
         /// @return     Vector of objects to the RBF splines corresponding to each mode
         ///
         std::vector<SPLINTER::RBFSpline> getCoeffManifoldRBF(PtrList<volVectorField>
-                snapshots, PtrList<volVectorField>& modes, word rbfBasis = "GAUSSIAN");
+                snapshots, PtrList<volVectorField> & modes, word rbfBasis = "GAUSSIAN");
 
         //--------------------------------------------------------------------------
         /// @brief      Constructs the parameters-coefficients manifold for scalar fields, based on RBF-spline model
@@ -298,7 +298,7 @@ class reductionProblem
         /// @return     Vector of objects to the RBF splines corresponding to each mode
         ///
         std::vector<SPLINTER::RBFSpline> getCoeffManifoldRBF(PtrList<volScalarField>
-                snapshots, PtrList<volScalarField>& modes, word rbfBasis = "GAUSSIAN");
+                snapshots, PtrList<volScalarField> & modes, word rbfBasis = "GAUSSIAN");
 
         //--------------------------------------------------------------------------
         /// @brief      Constructs the parameters-coefficients manifold for vector fields, based on the B-spline model
@@ -310,7 +310,7 @@ class reductionProblem
         ///
         // std::vector<SPLINTER::BSpline*> getCoeffManifoldSPL(PtrList<volVectorField> snapshots, PtrList<volVectorField>& modes, label splDeg=3);
         std::vector<SPLINTER::BSpline> getCoeffManifoldSPL(PtrList<volVectorField>
-                snapshots, PtrList<volVectorField>& modes, label splDeg = 3);
+                snapshots, PtrList<volVectorField> & modes, label splDeg = 3);
 
         //--------------------------------------------------------------------------
         /// @brief      Constructs the parameters-coefficients manifold for scalar fields, based on the B-spline model
@@ -321,7 +321,7 @@ class reductionProblem
         /// @return     Vector of objects to the B-splines corresponding to each mode
         ///
         std::vector<SPLINTER::BSpline> getCoeffManifoldSPL(PtrList<volScalarField>
-                snapshots, PtrList<volScalarField>& modes, label splDeg = 3);
+                snapshots, PtrList<volScalarField> & modes, label splDeg = 3);
 
 };
 
@@ -348,7 +348,7 @@ class reductionProblem
  * ITHACA-FV (In real Time Highly Advanced Computational Applications for
 Finite Volumes) is C++ library based on the finite volume solver
 [<b> OpenFOAM </b>](https://openfoam.org/). It consists of the implementation of several reduced order
-modeling techniques for parametrized problems. ITHACA-FV is developed and maintained mainly by the group of 
+modeling techniques for parametrized problems. ITHACA-FV is developed and maintained mainly by the group of
 [<b> Prof. Giovanni Stabile </b>](https://www.giovannistabile.com/) at the [<b>Sant'Anna School of Advanced Studies](https://www.santannapisa.it/en) and partially at [<b> SISSA mathLab </b>](https://mathlab.sissa.it/) in collaboration with [<b> Prof. Gianluigi Rozza's Group </b>](http://people.sissa.it/~grozza/). Check also the GitHub [webpage](https://github.com/ITHACA-FV/ITHACA-FV) for more info.
 
  *
diff --git a/src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblemTemplates.C b/src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblemTemplates.C
old mode 100755
new mode 100644
index 3b1ac95ca..6ee2dad5c
--- a/src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblemTemplates.C
+++ b/src/ITHACA_FOMPROBLEMS/reductionProblem/reductionProblemTemplates.C
@@ -62,14 +62,14 @@ void reductionProblem::computeLift(T& Lfield, T& liftfield, T& omfield)
             {
                 u_bc = gSum(Lfield[j].mesh().magSf().boundaryField()[p] *
                             Lfield[j].boundaryField()[p]).component(l) / area;
-                volVectorField C("U", Lfield[j] - liftfield[k]*u_bc / u_lf);
+                volVectorField C("U", Lfield[j] - liftfield[k] * u_bc / u_lf);
                 omfield.append(C.clone());
             }
             else
             {
                 u_bc = gSum(omfield[j].mesh().magSf().boundaryField()[p] *
                             omfield[j].boundaryField()[p]).component(l) / area;
-                volVectorField C("U", omfield[j] - liftfield[k]*u_bc / u_lf);
+                volVectorField C("U", omfield[j] - liftfield[k] * u_bc / u_lf);
                 omfield.set(j, C.clone());
             }
         }
@@ -96,14 +96,14 @@ void reductionProblem::computeLiftT(T& Lfield, T& liftfield, T& omfield)
             {
                 t_bc = gSum(Lfield[j].mesh().magSf().boundaryField()[p] *
                             Lfield[j].boundaryField()[p]) / area;
-                volScalarField C(Lfield[0].name(), Lfield[j] - liftfield[k]*t_bc / t_lf);
+                volScalarField C(Lfield[0].name(), Lfield[j] - liftfield[k] * t_bc / t_lf);
                 omfield.append(C.clone());
             }
             else
             {
                 t_bc = gSum(omfield[j].mesh().magSf().boundaryField()[p] *
                             omfield[j].boundaryField()[p]) / area;
-                volScalarField C(Lfield[0].name(), omfield[j] - liftfield[k]*t_bc / t_lf);
+                volScalarField C(Lfield[0].name(), omfield[j] - liftfield[k] * t_bc / t_lf);
                 omfield.set(j, C.clone());
             }
         }
diff --git a/src/ITHACA_FOMPROBLEMS/steadyNS/NLsolvesteadyNS.H b/src/ITHACA_FOMPROBLEMS/steadyNS/NLsolvesteadyNS.H
index fbbe91b54..310abe805 100644
--- a/src/ITHACA_FOMPROBLEMS/steadyNS/NLsolvesteadyNS.H
+++ b/src/ITHACA_FOMPROBLEMS/steadyNS/NLsolvesteadyNS.H
@@ -60,6 +60,7 @@ while (simple.loop() && residual > tolerance && csolve < maxIter )
         residual = max(presidual, uresidual);
         Info << "\nResidual: " << residual << endl << endl;
     }
+
     laminarTransport.correct();
     turbulence->correct();
     csolve = csolve + 1;
diff --git a/src/ITHACA_FOMPROBLEMS/steadyNS/UEqn.H b/src/ITHACA_FOMPROBLEMS/steadyNS/UEqn.H
old mode 100755
new mode 100644
index 1d91429a0..7117de308
--- a/src/ITHACA_FOMPROBLEMS/steadyNS/UEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/steadyNS/UEqn.H
@@ -33,7 +33,7 @@ tmp<fvVectorMatrix> tUEqn
     + turbulence->divDevReff(U)
     ==
     fvOptions(U)
-    );
+);
 fvVectorMatrix& UEqn = tUEqn.ref();
 
 UEqn.relax();
diff --git a/src/ITHACA_FOMPROBLEMS/steadyNS/pEqn.H b/src/ITHACA_FOMPROBLEMS/steadyNS/pEqn.H
old mode 100755
new mode 100644
index 5c62d90b5..104e0c227
--- a/src/ITHACA_FOMPROBLEMS/steadyNS/pEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/steadyNS/pEqn.H
@@ -24,7 +24,7 @@
 \*---------------------------------------------------------------------------*/
 {
     volScalarField rAU(1.0 / UEqn.A());
-    volVectorField HbyA(constrainHbyA(rAU * UEqn.H(), U, p));
+    volVectorField HbyA(constrainHbyA(rAU* UEqn.H(), U, p));
     surfaceScalarField phiHbyA("phiHbyA", fvc::flux(HbyA));
     MRF.makeRelative(phiHbyA);
     adjustPhi(phiHbyA, U, p);
diff --git a/src/ITHACA_FOMPROBLEMS/steadyNS/steadyNS.C b/src/ITHACA_FOMPROBLEMS/steadyNS/steadyNS.C
index 7abab9cb6..2355dc269 100644
--- a/src/ITHACA_FOMPROBLEMS/steadyNS/steadyNS.C
+++ b/src/ITHACA_FOMPROBLEMS/steadyNS/steadyNS.C
@@ -38,6 +38,7 @@
 // * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * * * //
 // Constructor
 steadyNS::steadyNS() {}
+
 steadyNS::steadyNS(int argc, char* argv[])
 {
     _args = autoPtr<argList>
@@ -299,7 +300,7 @@ void steadyNS::liftSolve()
                 IOobject::NO_WRITE
             ),
             mesh,
-            dimensionedScalar("Phi", dimLength * dimVelocity, 0),
+            dimensionedScalar("Phi", dimLength* dimVelocity, 0),
             p.boundaryField().types()
         );
         label PhiRefCell = 0;
@@ -538,6 +539,18 @@ void steadyNS::projectPPE(fileName folder, label NU, label NP, label NSUP)
         ITHACAstream::exportTensor(gTensor, "G", "eigen",
                                    "./ITHACAoutput/Matrices/G");
     }
+
+    if (para->exportNpy)
+    {
+        cnpy::save(B_matrix, "./ITHACAoutput/Matrices/B.npy");
+        cnpy::save(K_matrix, "./ITHACAoutput/Matrices/K.npy");
+        cnpy::save(D_matrix, "./ITHACAoutput/Matrices/D.npy");
+        cnpy::save(M_matrix, "./ITHACAoutput/Matrices/M.npy");
+        cnpy::save(BC3_matrix, "./ITHACAoutput/Matrices/BC3.npy");
+        cnpy::save(BC4_matrix, "./ITHACAoutput/Matrices/BC4.npy");
+        cnpy::save(C_tensor, "./ITHACAoutput/Matrices/C.npy");
+        cnpy::save(gTensor, "./ITHACAoutput/Matrices/G.npy");
+    }
 }
 
 void steadyNS::projectSUP(fileName folder, label NU, label NP, label NSUP)
@@ -682,6 +695,15 @@ void steadyNS::projectSUP(fileName folder, label NU, label NP, label NSUP)
         ITHACAstream::exportTensor(C_tensor, "C", "python",
                                    "./ITHACAoutput/Matrices/C");
     }
+
+    if (para->exportNpy)
+    {
+        cnpy::save(B_matrix, "./ITHACAoutput/Matrices/B.npy");
+        cnpy::save(K_matrix, "./ITHACAoutput/Matrices/K.npy");
+        cnpy::save(P_matrix, "./ITHACAoutput/Matrices/P.npy");
+        cnpy::save(M_matrix, "./ITHACAoutput/Matrices/M.npy");
+        cnpy::save(C_tensor, "./ITHACAoutput/Matrices/C.npy");
+    }
 }
 
 void steadyNS::discretizeThenProject(fileName folder, label NU, label NP,
@@ -902,7 +924,7 @@ Eigen::MatrixXd steadyNS::diffusive_term_sym(label NUmodes, label NPmodes,
         for (label j = 0; j < Bsize; j++)
         {
             B_matrix(i, j) = - fvc::domainIntegrate(fvc::grad(L_U_SUPmodes[i])
-                                        && fvc::grad(L_U_SUPmodes[j])).value();
+                                                    && fvc::grad(L_U_SUPmodes[j])).value();
         }
     }
 
@@ -1190,7 +1212,7 @@ Eigen::MatrixXd steadyNS::laplacian_pressure(label NPmodes)
     {
         for (label j = 0; j < Dsize; j++)
         {
-            D_matrix(i, j) = fvc::domainIntegrate(fvc::grad(Pmodes[i])&fvc::grad(
+            D_matrix(i, j) = fvc::domainIntegrate(fvc::grad(Pmodes[i]) & fvc::grad(
                     Pmodes[j])).value();
         }
     }
@@ -1221,7 +1243,7 @@ Eigen::MatrixXd steadyNS::pressure_BC1(label NUmodes, label NPmodes)
         for (label j = 0; j < P_BC2size; j++)
         {
             surfaceScalarField lpl((fvc::interpolate(fvc::laplacian(
-                                        L_U_SUPmodes[j]))&mesh.Sf())*fvc::interpolate(Pmodes[i]));
+                                        L_U_SUPmodes[j])) & mesh.Sf()) * fvc::interpolate(Pmodes[i]));
             double s = 0;
 
             for (label k = 0; k < lpl.boundaryField().size(); k++)
@@ -1269,7 +1291,7 @@ List <Eigen::MatrixXd> steadyNS::pressure_BC2(label NUmodes, label NPmodes)
             {
                 surfaceScalarField div_m(fvc::interpolate(fvc::div(fvc::interpolate(
                                              L_U_SUPmodes[j]) & mesh.Sf(),
-                                         L_U_SUPmodes[k]))&mesh.Sf()*fvc::interpolate(Pmodes[i]));
+                                         L_U_SUPmodes[k])) & mesh.Sf() * fvc::interpolate(Pmodes[i]));
                 double s = 0;
 
                 for (label k = 0; k < div_m.boundaryField().size(); k++)
@@ -1306,7 +1328,7 @@ Eigen::Tensor<double, 3> steadyNS::pressureBC2(label NUmodes, label NPmodes)
             {
                 surfaceScalarField div_m(fvc::interpolate(fvc::div(fvc::interpolate(
                                              L_U_SUPmodes[j]) & mesh.Sf(),
-                                         L_U_SUPmodes[k]))&mesh.Sf()*fvc::interpolate(Pmodes[i]));
+                                         L_U_SUPmodes[k])) & mesh.Sf() * fvc::interpolate(Pmodes[i]));
                 double s = 0;
 
                 for (label k = 0; k < div_m.boundaryField().size(); k++)
@@ -1348,8 +1370,8 @@ Eigen::MatrixXd steadyNS::pressure_BC3(label NUmodes, label NPmodes)
         for (label j = 0; j < P3_BC2size; j++)
         {
             surfaceVectorField BC3 = fvc::interpolate(fvc::curl(L_U_SUPmodes[j])).ref();
-            surfaceVectorField BC4 = (n ^ fvc::interpolate(fvc::grad(Pmodes[i]))).ref();
-            surfaceScalarField BC5 = ((BC3 & BC4) * mesh.magSf()).ref();
+            surfaceVectorField BC4 = (n^ fvc::interpolate(fvc::grad(Pmodes[i]))).ref();
+            surfaceScalarField BC5 = ((BC3& BC4) * mesh.magSf()).ref();
             double s = 0;
 
             for (label k = 0; k < BC5.boundaryField().size(); k++)
@@ -1388,8 +1410,8 @@ Eigen::MatrixXd steadyNS::pressure_BC4(label NUmodes, label NPmodes)
         for (label j = 0; j < P4_BC2size; j++)
         {
             surfaceScalarField BC3 = fvc::interpolate(Pmodes[i]).ref();
-            surfaceScalarField BC4 = (n & fvc::interpolate(L_U_SUPmodes[j])).ref();
-            surfaceScalarField BC5 = ((BC3 * BC4) * mesh.magSf()).ref();
+            surfaceScalarField BC4 = (n& fvc::interpolate(L_U_SUPmodes[j])).ref();
+            surfaceScalarField BC5 = ((BC3* BC4) * mesh.magSf()).ref();
             double s = 0;
 
             for (label k = 0; k < BC5.boundaryField().size(); k++)
@@ -1506,7 +1528,7 @@ Eigen::MatrixXd steadyNS::diffusive_term_flux_method(label NUmodes,
     {
         for (label j = 0; j < BPsize2; j++)
         {
-            L_U_SUPmodesaux = dt_dummy * fvc::laplacian(
+            L_U_SUPmodesaux = dt_dummy* fvc::laplacian(
                                   nu_dummy(), L_U_SUPmodes[j]);
             BP_matrix(i, j) = fvc::domainIntegrate(Pmodes[i] *
                                                    fvc::div(L_U_SUPmodesaux)).value();
@@ -1684,7 +1706,7 @@ List<Eigen::MatrixXd> steadyNS::pressure_gradient_term_linsys_div(label NPmodes)
         assignBC(Upara, BCind, v);
         fvScalarMatrix pEqn
         (
-            fvm::laplacian(p) == (1.0 / dt_dummy)*fvc::div(Upara)
+            fvm::laplacian(p) == (1.0 / dt_dummy) * fvc::div(Upara)
         );
         pEqn.setReference(0, 0);
         LinSysDivDummy = Pmodes.project(pEqn, NPmodes);
@@ -1719,7 +1741,7 @@ List<Eigen::MatrixXd> steadyNS::pressure_gradient_term_linsys_conv(
         Caux = dt_dummy * (-fvc::div(fvc::flux(Upara), Upara));
         fvScalarMatrix pEqn
         (
-            fvm::laplacian(p) == (1.0 / dt_dummy)*fvc::div(Caux)
+            fvm::laplacian(p) == (1.0 / dt_dummy) * fvc::div(Caux)
         );
         pEqn.setReference(0, 0);
         LinSysConvDummy = Pmodes.project(pEqn, NPmodes);
@@ -1751,10 +1773,10 @@ List<Eigen::MatrixXd> steadyNS::pressure_gradient_term_linsys_diff(
         volVectorField Upara(Uinl());
         assignBC(Upara, BCind, v);
         volVectorField Daux(L_U_SUPmodes[0]);
-        Daux = dt_dummy * fvc::laplacian(nu_dummy(), Upara);
+        Daux = dt_dummy* fvc::laplacian(nu_dummy(), Upara);
         fvScalarMatrix pEqn
         (
-            fvm::laplacian(p) == (1.0 / dt_dummy)*fvc::div(Daux)
+            fvm::laplacian(p) == (1.0 / dt_dummy) * fvc::div(Daux)
         );
         pEqn.setReference(0, 0);
         LinSysDiffDummy = Pmodes.project(pEqn, NPmodes);
@@ -1786,7 +1808,7 @@ Eigen::MatrixXd steadyNS::mass_matrix_oldtime_consistent(label NUmodes,
         {
             surfaceScalarField B = fvc::flux(L_U_SUPmodes[j]).ref();
             volVectorField CoeffB = fvc::reconstruct(B).ref();
-            I_matrix(i, j) = fvc::domainIntegrate(CoeffA &  CoeffB).value();
+            I_matrix(i, j) = fvc::domainIntegrate(CoeffA&   CoeffB).value();
         }
     }
 
@@ -1817,12 +1839,12 @@ Eigen::MatrixXd steadyNS::diffusive_term_consistent(label NUmodes,
     {
         for (label j = 0; j < DFsize; j++)
         {
-            phi_tmp = dt_dummy * nu_dummy() * fvc::flux(fvc::laplacian(
+            phi_tmp = dt_dummy* nu_dummy() * fvc::flux(fvc::laplacian(
                           dimensionedScalar("1", dimless, 1),
                           L_U_SUPmodes[j]));
             volVectorField CoeffB = fvc::reconstruct(phi_tmp).ref();
             volVectorField CoeffA = fvc::reconstruct(L_PHImodes[i]).ref();
-            DF_matrix(i, j) = fvc::domainIntegrate(CoeffA & CoeffB).value();
+            DF_matrix(i, j) = fvc::domainIntegrate(CoeffA& CoeffB).value();
         }
     }
 
@@ -1853,10 +1875,10 @@ Eigen::MatrixXd steadyNS::pressure_gradient_term_consistent(label NUmodes,
     {
         for (label j = 0; j < KF2size; j++)
         {
-            volVectorField CoeffA = (fvc::reconstruct(dt_dummy * fvc::snGrad(
+            volVectorField CoeffA = (fvc::reconstruct(dt_dummy* fvc::snGrad(
                                          Pmodes[j]) * mag(Pmodes[j].mesh().magSf()))).ref();
             volVectorField CoeffB = fvc::reconstruct(L_PHImodes[i]).ref();
-            KF_matrix(i, j) = fvc::domainIntegrate(CoeffA &  CoeffB).value();
+            KF_matrix(i, j) = fvc::domainIntegrate(CoeffA&   CoeffB).value();
         }
     }
 
@@ -1891,10 +1913,10 @@ Eigen::Tensor<double, 3> steadyNS::convective_term_consistent_tens(
         {
             for (label k = 0; k < Csize1; k++)
             {
-                phi_tmp = dt_dummy * fvc::flux(fvc::div(L_PHImodes[i], L_U_SUPmodes[k]));
+                phi_tmp = dt_dummy* fvc::flux(fvc::div(L_PHImodes[i], L_U_SUPmodes[k]));
                 volVectorField CoeffA = fvc::reconstruct(phi_tmp).ref();
                 volVectorField CoeffB = fvc::reconstruct(L_PHImodes[j]).ref();
-                Ci_tensor(i, j, k) = fvc::domainIntegrate(CoeffB &  CoeffA).value();
+                Ci_tensor(i, j, k) = fvc::domainIntegrate(CoeffB&   CoeffA).value();
             }
         }
     }
@@ -1936,9 +1958,9 @@ List <Eigen::MatrixXd> steadyNS::boundary_vector_diffusion_consistent(
         for (label j = 0; j < SDsize; j++)
         {
             volVectorField CoeffB = fvc::reconstruct(L_PHImodes[j]).ref();
-            phi_tmp = dt_dummy * fvc::flux(fvc::laplacian(nu_dummy(), Upara));
+            phi_tmp = dt_dummy* fvc::flux(fvc::laplacian(nu_dummy(), Upara));
             volVectorField CoeffA = fvc::reconstruct(phi_tmp).ref();
-            SD_matrix[i](j, 0) = fvc::domainIntegrate(CoeffA &  CoeffB).value();
+            SD_matrix[i](j, 0) = fvc::domainIntegrate(CoeffA&   CoeffB).value();
         }
 
         ITHACAstream::SaveDenseMatrix(SD_matrix[i], "./ITHACAoutput/Matrices/SD/",
@@ -1975,9 +1997,9 @@ List <Eigen::MatrixXd> steadyNS::boundary_vector_convection_consistent(
         for (label j = 0; j < SCsize; j++)
         {
             volVectorField CoeffB = fvc::reconstruct(L_PHImodes[j]).ref();
-            phi_tmp = dt_dummy * fvc::flux(fvc::div(fvc::flux(Upara), Upara));
+            phi_tmp = dt_dummy* fvc::flux(fvc::div(fvc::flux(Upara), Upara));
             volVectorField CoeffA = fvc::reconstruct(phi_tmp).ref();
-            SC_matrix[i](j, 0) = fvc::domainIntegrate(CoeffA &  CoeffB).value();
+            SC_matrix[i](j, 0) = fvc::domainIntegrate(CoeffA&   CoeffB).value();
         }
 
         ITHACAstream::SaveDenseMatrix(SC_matrix[i], "./ITHACAoutput/Matrices/SC/",
@@ -2001,7 +2023,7 @@ Eigen::MatrixXd steadyNS::mass_matrix_newtime_consistent(label NUmodes,
         for (label j = 0; j < NUmodes; j++)
         {
             volVectorField B = fvc::reconstruct(L_PHImodes[j]).ref();
-            W_matrix(i, j) = fvc::domainIntegrate(A & B).value();
+            W_matrix(i, j) = fvc::domainIntegrate(A& B).value();
         }
     }
 
@@ -2227,8 +2249,8 @@ void steadyNS::reconstructLiftAndDrag(const Eigen::MatrixXd& velCoeffs,
     Eigen::MatrixXd fN;
     fTau.setZero(velCoeffs.rows(), 3);
     fN.setZero(pressureCoeffs.rows(), 3);
-    fTau = velCoeffs * tauMatrix;
-    fN = pressureCoeffs * nMatrix;
+    fTau = velCoeffs* tauMatrix;
+    fN = pressureCoeffs* nMatrix;
 
     // Export the matrices
     if (para->exportPython)
diff --git a/src/ITHACA_FOMPROBLEMS/steadyNS/steadyNS.H b/src/ITHACA_FOMPROBLEMS/steadyNS/steadyNS.H
index d158c549c..10093d8ca 100644
--- a/src/ITHACA_FOMPROBLEMS/steadyNS/steadyNS.H
+++ b/src/ITHACA_FOMPROBLEMS/steadyNS/steadyNS.H
@@ -395,7 +395,8 @@ class steadyNS: public reductionProblem
         ///
         /// @return     reduced matrix in Eigen::MatrixXd format for the diffusion term.
         ///
-        Eigen::MatrixXd diffusive_term_sym(label NUmodes, label NPmodes, label NSUPmodes);
+        Eigen::MatrixXd diffusive_term_sym(label NUmodes, label NPmodes,
+                                           label NSUPmodes);
 
         //--------------------------------------------------------------------------
         /// Gradient of pressure
diff --git a/src/ITHACA_FOMPROBLEMS/unsteadyNS/UEqn.H b/src/ITHACA_FOMPROBLEMS/unsteadyNS/UEqn.H
old mode 100755
new mode 100644
index 2e08e89d3..fb5ec8c64
--- a/src/ITHACA_FOMPROBLEMS/unsteadyNS/UEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/unsteadyNS/UEqn.H
@@ -33,7 +33,7 @@ tmp<fvVectorMatrix> tUEqn
     + turbulence->divDevReff(U)
     ==
     fvOptions(U)
-    );
+);
 fvVectorMatrix& UEqn = tUEqn.ref();
 
 UEqn.relax();
diff --git a/src/ITHACA_FOMPROBLEMS/unsteadyNS/pEqn.H b/src/ITHACA_FOMPROBLEMS/unsteadyNS/pEqn.H
old mode 100755
new mode 100644
index 787aab131..0f4d22c55
--- a/src/ITHACA_FOMPROBLEMS/unsteadyNS/pEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/unsteadyNS/pEqn.H
@@ -30,8 +30,8 @@ surfaceScalarField phiHbyA
 (
     "phiHbyA",
     fvc::flux(HbyA)
-    + fvc::interpolate(rAU)*fvc::ddtCorr(U, phi)
-    );
+    + fvc::interpolate(rAU) * fvc::ddtCorr(U, phi)
+);
 
 MRF.makeRelative(phiHbyA);
 
diff --git a/src/ITHACA_FOMPROBLEMS/unsteadyNS/unsteadyNS.C b/src/ITHACA_FOMPROBLEMS/unsteadyNS/unsteadyNS.C
index 4443995f8..dbf5f90a9 100644
--- a/src/ITHACA_FOMPROBLEMS/unsteadyNS/unsteadyNS.C
+++ b/src/ITHACA_FOMPROBLEMS/unsteadyNS/unsteadyNS.C
@@ -77,14 +77,13 @@ unsteadyNS::unsteadyNS(int argc, char* argv[])
 #include "createFields.H"
 #include "createFvOptions.H"
     para = ITHACAparameters::getInstance(mesh, runTime);
-    
     method = ITHACAdict->lookupOrDefault<word>("method", "supremizer");
-    M_Assert(method == "supremizer" || method == "PPE", "The method must be set to supremizer or PPE in ITHACAdict");
-    
+    M_Assert(method == "supremizer"
+             || method == "PPE",
+             "The method must be set to supremizer or PPE in ITHACAdict");
     bcMethod = ITHACAdict->lookupOrDefault<word>("bcMethod", "lift");
     M_Assert(bcMethod == "lift" || bcMethod == "penalty",
              "The BC method must be set to lift or penalty in ITHACAdict");
-    
     timedepbcMethod = ITHACAdict->lookupOrDefault<word>("timedepbcMethod", "no");
     M_Assert(timedepbcMethod == "yes" || timedepbcMethod == "no",
              "The BC method can be set to yes or no");
@@ -128,7 +127,7 @@ void unsteadyNS::truthSolve(List<scalar> mu_now, fileName folder)
 
             for (label j = 0; j < inl.size(); j++)
             {
-                inl[j] = timeBCoff(i * inl.size() + j, 0);
+                inl[j] = timeBCoff(i* inl.size() + j, 0);
             }
 
             assignBC(U, inletPatch(i, 0), inl);
@@ -164,7 +163,7 @@ void unsteadyNS::truthSolve(List<scalar> mu_now, fileName folder)
 
                 for (label j = 0; j < inl.size(); j++)
                 {
-                    inl[j] = timeBCoff(i * inl.size() + j, counter2);
+                    inl[j] = timeBCoff(i* inl.size() + j, counter2);
                 }
 
                 assignBC(U, inletPatch(i, 0), inl);
@@ -221,7 +220,7 @@ void unsteadyNS::truthSolve(List<scalar> mu_now, fileName folder)
         mu.resize(1, 1);
     }
 
-    if (mu_samples.rows() == counter * mu.cols())
+    if (mu_samples.rows() == counter* mu.cols())
     {
         ITHACAstream::exportMatrix(mu_samples, "mu_samples", "eigen",
                                    folder);
diff --git a/src/ITHACA_FOMPROBLEMS/unsteadyNS/unsteadyNS.H b/src/ITHACA_FOMPROBLEMS/unsteadyNS/unsteadyNS.H
old mode 100755
new mode 100644
index 93024860f..097e7ed1c
--- a/src/ITHACA_FOMPROBLEMS/unsteadyNS/unsteadyNS.H
+++ b/src/ITHACA_FOMPROBLEMS/unsteadyNS/unsteadyNS.H
@@ -86,7 +86,7 @@ class unsteadyNS: public steadyNS, public UnsteadyProblem
 
         // Counter used for the time-dependent boundary conditions
         label counter2 = 1;
-        
+
         word method;
 
         /// Time-dependent Boundary Method
@@ -109,6 +109,7 @@ class unsteadyNS: public steadyNS, public UnsteadyProblem
         void truthSolve(List<scalar> mu_now,
                         fileName folder = "./ITHACAoutput/Offline/");
 };
+
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
 #endif
diff --git a/src/ITHACA_FOMPROBLEMS/unsteadyNST/TEqn.H b/src/ITHACA_FOMPROBLEMS/unsteadyNST/TEqn.H
old mode 100755
new mode 100644
index 3c8cb9c80..98c5eef6e
--- a/src/ITHACA_FOMPROBLEMS/unsteadyNST/TEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/unsteadyNST/TEqn.H
@@ -28,7 +28,7 @@ fvScalarMatrix TEqn
     fvm::ddt(T)
     + fvm::div(phi, T)
     - fvm::laplacian(DT, T)
-    );
+);
 
 
 
diff --git a/src/ITHACA_FOMPROBLEMS/unsteadyNST/UEqn.H b/src/ITHACA_FOMPROBLEMS/unsteadyNST/UEqn.H
old mode 100755
new mode 100644
index 15cbcf0db..7fef24a1b
--- a/src/ITHACA_FOMPROBLEMS/unsteadyNST/UEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/unsteadyNST/UEqn.H
@@ -29,7 +29,7 @@ fvVectorMatrix UEqn
     fvm::ddt(U)
     + fvm::div(phi, U)
     - fvm::laplacian(nu, U)
-    );
+);
 
 if (piso.momentumPredictor())
 {
diff --git a/src/ITHACA_FOMPROBLEMS/unsteadyNST/pEqn.H b/src/ITHACA_FOMPROBLEMS/unsteadyNST/pEqn.H
old mode 100755
new mode 100644
index 0d2244f93..27b75cb58
--- a/src/ITHACA_FOMPROBLEMS/unsteadyNST/pEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/unsteadyNST/pEqn.H
@@ -29,8 +29,8 @@ surfaceScalarField phiHbyA
 (
     "phiHbyA",
     fvc::flux(HbyA)
-    + fvc::interpolate(rAU)*fvc::ddtCorr(U, phi)
-    );
+    + fvc::interpolate(rAU) * fvc::ddtCorr(U, phi)
+);
 
 //MRF.makeRelative(phiHbyA);
 
@@ -58,6 +58,6 @@ while (piso.correctNonOrthogonal())
 
 #include "continuityErrs.H"
 
-U = HbyA - rAU * fvc::grad(p);
+U = HbyA - rAU* fvc::grad(p);
 U.correctBoundaryConditions();
 //fvOptions.correct(U);
diff --git a/src/ITHACA_FOMPROBLEMS/unsteadyNST/unsteadyNST.C b/src/ITHACA_FOMPROBLEMS/unsteadyNST/unsteadyNST.C
old mode 100755
new mode 100644
index 1a694f63a..4095ef0a6
--- a/src/ITHACA_FOMPROBLEMS/unsteadyNST/unsteadyNST.C
+++ b/src/ITHACA_FOMPROBLEMS/unsteadyNST/unsteadyNST.C
@@ -228,8 +228,9 @@ void unsteadyNST::liftSolveT()
         scalar dt = mesh.time().deltaTValue();
         forAll(Tlift, i)
         {
-            Tlift[i] = (totalTime * Tlift[i] + dt * Tlift[i] ) / (totalTime + dt);
+            Tlift[i] = (totalTime* Tlift[i] + dt* Tlift[i] ) / (totalTime + dt);
         }
+
         Tlift.write();
         liftfieldT.append(Tlift.clone());
     }
@@ -440,6 +441,7 @@ Eigen::MatrixXd unsteadyNST::diffusive_term_temperature(label NUmodes,
             }
         }
     }
+
     // Export the matrix
     ITHACAstream::SaveDenseMatrix(Y_matrix, "./ITHACAoutput/Matrices/",
                                   "Y_" + name(liftfieldT.size()) + "_" + name(NTmodes));
@@ -465,6 +467,7 @@ Eigen::MatrixXd unsteadyNST::mass_term_temperature(label NUmodes, label NTmodes,
                                   "MT_" + name(liftfieldT.size()) + "_" + name(NTmodes));
     return MT_matrix;
 }
+
 // Calculate lifting function for velocity
 void unsteadyNST::liftSolve()
 {
@@ -517,7 +520,7 @@ void unsteadyNST::liftSolve()
                 IOobject::NO_WRITE
             ),
             mesh,
-            dimensionedScalar("Phi", dimLength * dimVelocity, 0),
+            dimensionedScalar("Phi", dimLength* dimVelocity, 0),
             p.boundaryField().types()
         );
         label PhiRefCell = 0;
diff --git a/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/DiffEqn.H b/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/DiffEqn.H
old mode 100755
new mode 100644
index 2fefc8a33..4b09f5f29
--- a/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/DiffEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/DiffEqn.H
@@ -44,7 +44,7 @@ fvScalarMatrix NEqn
     + lam7* prec7
     + lam8* prec8
 
-    );
+);
 
 NEqn.relax();
 NEqn.solve();
diff --git a/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/TEqn.H b/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/TEqn.H
old mode 100755
new mode 100644
index 3f601f2f9..5b9509669
--- a/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/TEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/TEqn.H
@@ -36,10 +36,10 @@ fvScalarMatrix TEqn
     ==
     - fvm::div(phi, T)
     + fvm::laplacian(turbulence->nu() / Pr + alphat, T)
-    + (v / CpRef) * (decLam1 * dec1 + decLam2 * dec2 + decLam3* dec3)
-    + (1 - decbetaTot) * (TXS) / (CpRef)*flux
+    + (v / CpRef) * (decLam1* dec1 + decLam2* dec2 + decLam3* dec3)
+    + (1 - decbetaTot) * (TXS) / (CpRef) * flux
 
-    );
+);
 
 TEqn.relax();
 TEqn.solve();
diff --git a/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/UEqn.H b/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/UEqn.H
old mode 100755
new mode 100644
index 2e08e89d3..fb5ec8c64
--- a/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/UEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/UEqn.H
@@ -33,7 +33,7 @@ tmp<fvVectorMatrix> tUEqn
     + turbulence->divDevReff(U)
     ==
     fvOptions(U)
-    );
+);
 fvVectorMatrix& UEqn = tUEqn.ref();
 
 UEqn.relax();
diff --git a/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/decEqns.H b/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/decEqns.H
old mode 100755
new mode 100644
index 2e6ffed2d..331d5c7be
--- a/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/decEqns.H
+++ b/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/decEqns.H
@@ -37,7 +37,7 @@ fvScalarMatrix decEq1
     + fvm::laplacian(turbulence->nu() / Sc + difft, dec1)
     - fvm::Sp(decLam1, dec1)
     + decBeta1* SP* flux
-    );
+);
 
 decEq1.relax();
 decEq1.solve();
@@ -53,7 +53,7 @@ fvScalarMatrix decEq2
     + fvm::laplacian(turbulence->nu() / Sc + difft, dec2)
     - fvm::Sp(decLam2, dec2)
     + decBeta2* SP* flux
-    );
+);
 
 decEq2.relax();
 decEq2.solve();
@@ -69,7 +69,7 @@ fvScalarMatrix decEq3
     + fvm::laplacian(turbulence->nu() / Sc + difft, dec3)
     - fvm::Sp(decLam3, dec3)
     + decBeta3* SP* flux
-    );
+);
 
 decEq3.relax();
 decEq3.solve();
diff --git a/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/pEqn.H b/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/pEqn.H
old mode 100755
new mode 100644
index 787aab131..0f4d22c55
--- a/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/pEqn.H
+++ b/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/pEqn.H
@@ -30,8 +30,8 @@ surfaceScalarField phiHbyA
 (
     "phiHbyA",
     fvc::flux(HbyA)
-    + fvc::interpolate(rAU)*fvc::ddtCorr(U, phi)
-    );
+    + fvc::interpolate(rAU) * fvc::ddtCorr(U, phi)
+);
 
 MRF.makeRelative(phiHbyA);
 
diff --git a/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/precEqns.H b/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/precEqns.H
old mode 100755
new mode 100644
index 2b68b2bfb..9f3fa8b80
--- a/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/precEqns.H
+++ b/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/precEqns.H
@@ -37,7 +37,7 @@ fvScalarMatrix precEq1
     + fvm::laplacian(turbulence->nu() / Sc + difft, prec1)
     - fvm::Sp(lam1, prec1)
     + beta1* NSF* flux
-    );
+);
 
 precEq1.relax();
 precEq1.solve();
@@ -51,7 +51,7 @@ fvScalarMatrix precEq2
     + fvm::laplacian(turbulence->nu() / Sc + difft, prec2)
     - fvm::Sp(lam2, prec2)
     + beta2* NSF* flux
-    );
+);
 
 precEq2.relax();
 precEq2.solve();
@@ -65,7 +65,7 @@ fvScalarMatrix precEq3
     + fvm::laplacian(turbulence->nu() / Sc + difft, prec3)
     - fvm::Sp(lam3, prec3)
     + beta3* NSF* flux
-    );
+);
 
 precEq3.relax();
 precEq3.solve();
@@ -79,7 +79,7 @@ fvScalarMatrix precEq4
     + fvm::laplacian(turbulence->nu() / Sc + difft, prec4)
     - fvm::Sp(lam4, prec4)
     + beta4* NSF* flux
-    );
+);
 
 precEq4.relax();
 precEq4.solve();
@@ -93,7 +93,7 @@ fvScalarMatrix precEq5
     + fvm::laplacian(turbulence->nu() / Sc + difft, prec5)
     - fvm::Sp(lam5, prec5)
     + beta5* NSF* flux
-    );
+);
 
 precEq5.relax();
 precEq5.solve();
@@ -107,7 +107,7 @@ fvScalarMatrix precEq6
     + fvm::laplacian(turbulence->nu() / Sc + difft, prec6)
     - fvm::Sp(lam6, prec6)
     + beta6* NSF* flux
-    );
+);
 
 precEq6.relax();
 precEq6.solve();
@@ -121,7 +121,7 @@ fvScalarMatrix precEq7
     + fvm::laplacian(turbulence->nu() / Sc + difft, prec7)
     - fvm::Sp(lam7, prec7)
     + beta7* NSF* flux
-    );
+);
 
 precEq7.relax();
 precEq7.solve();
@@ -135,7 +135,7 @@ fvScalarMatrix precEq8
     + fvm::laplacian(turbulence->nu() / Sc + difft, prec8)
     - fvm::Sp(lam8, prec8)
     + beta8* NSF* flux
-    );
+);
 
 precEq8.relax();
 precEq8.solve();
diff --git a/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/updateConsts.H b/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/updateConsts.H
old mode 100755
new mode 100644
index fd18f0918..84804d1db
--- a/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/updateConsts.H
+++ b/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/updateConsts.H
@@ -31,4 +31,4 @@ NSF = (1 / Keff) * (NSF1_0 + alfa_NSF1* logT) * (1 - betaTE * (T - Tref));
 A = (A1_0 + alfa_A1* logT) * (1 - betaTE * (T - Tref));
 D = (D1_0 + alfa_D1* logT) / (1 - betaTE * (T - Tref));
 SP = (1 / Keff) * (SP1_0 + alfa_SP1* logT) * (1 - betaTE * (T - Tref));
-TXS = v * SP;
+TXS = v* SP;
diff --git a/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/updateK.H b/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/updateK.H
old mode 100755
new mode 100644
index 4dacc48d3..4ac9e8461
--- a/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/updateK.H
+++ b/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/updateK.H
@@ -23,5 +23,5 @@
   along with ITHACA-FV. If not, see <http://www.gnu.org/licenses/>.
 \*---------------------------------------------------------------------------*/
 Keff = (fvc::domainIntegrate(flux).value()) / (fvc::domainIntegrate(
-            flux_old).value());
+           flux_old).value());
 
diff --git a/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/usmsrProblem.C b/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/usmsrProblem.C
index 07055a930..cf988a4d8 100644
--- a/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/usmsrProblem.C
+++ b/src/ITHACA_FOMPROBLEMS/unsteadymsrProblem/usmsrProblem.C
@@ -142,8 +142,8 @@ void usmsrProblem::truthSolve(List<scalar> mu_now)
     volScalarField& alphat = _alphat();
     volScalarField& difft = _difft();
     dimensionedScalar& tau = _tau();
-    volScalarField powerDens = ((1 - decbetaTot) * flux * SP +
-                                (decLam1 * dec1 + decLam2 * dec2 + decLam3 * dec3)).ref();
+    volScalarField powerDens = ((1 - decbetaTot) * flux* SP +
+                                (decLam1* dec1 + decLam2* dec2 + decLam3* dec3)).ref();
     powerDens.rename("powerDens");
     para = ITHACAparameters::getInstance(mesh, runTime);
     startTime = para->ITHACAdict->lookupOrDefault("startTime", 0);
@@ -202,8 +202,8 @@ void usmsrProblem::truthSolve(List<scalar> mu_now)
         Info << "ExecutionTime = " << runTime.elapsedCpuTime() << " s"
              << "  ClockTime = " << runTime.elapsedClockTime() << " s"
              << nl << endl;
-        powerDens = (1 - decbetaTot) * flux * SP + (decLam1 * dec1 + decLam2 * dec2 +
-                    decLam3 * dec3);
+        powerDens = (1 - decbetaTot) * flux* SP + (decLam1* dec1 + decLam2* dec2 +
+                    decLam3* dec3);
 
         if (checkWrite(runTime))
         {
@@ -296,7 +296,7 @@ void usmsrProblem::truthSolve(List<scalar> mu_now)
         mu.resize(1, 1);
     }
 
-    if (mu_samples.rows() == nsnapshots * mu.cols())
+    if (mu_samples.rows() == nsnapshots* mu.cols())
     {
         ITHACAstream::exportMatrix(mu_samples, "mu_samples", "eigen",
                                    "./ITHACAoutput/Offline");
@@ -406,8 +406,8 @@ void usmsrProblem::truthSolve(List<scalar> mu_now, std::string folder)
     volScalarField& logT = _logT();
     volScalarField& alphat = _alphat();
     volScalarField& difft = _difft();
-    volScalarField powerDens = ((1 - decbetaTot) * flux * SP +
-                                (decLam1 * dec1 + decLam2 * dec2 + decLam3 * dec3)).ref();
+    volScalarField powerDens = ((1 - decbetaTot) * flux* SP +
+                                (decLam1* dec1 + decLam2* dec2 + decLam3* dec3)).ref();
     powerDens.rename("powerDens");
     dimensionedScalar& tau = _tau();
     para = ITHACAparameters::getInstance(mesh, runTime);
@@ -467,8 +467,8 @@ void usmsrProblem::truthSolve(List<scalar> mu_now, std::string folder)
         Info << "ExecutionTime = " << runTime.elapsedCpuTime() << " s"
              << "  ClockTime = " << runTime.elapsedClockTime() << " s"
              << nl << endl;
-        powerDens = (1 - decbetaTot) * flux * SP + (decLam1 * dec1 + decLam2 * dec2 +
-                    decLam3 * dec3);
+        powerDens = (1 - decbetaTot) * flux* SP + (decLam1* dec1 + decLam2* dec2 +
+                    decLam3* dec3);
 
         if (checkWrite(runTime))
         {
@@ -606,35 +606,35 @@ void usmsrProblem::computePrecsBC(label call)
     bc_prec(0, call) = gSum(prec1.boundaryField()[precoutIndex] *
                             mesh.magSf().boundaryField()[precoutIndex]) / gSum(
                            mesh.magSf().boundaryField()[precoutIndex]) * std::exp(-lam1.value() *
-                                   tau.value());
+                               tau.value());
     bc_prec(1, call) = gSum(prec2.boundaryField()[precoutIndex] *
                             mesh.magSf().boundaryField()[precoutIndex]) / gSum(
                            mesh.magSf().boundaryField()[precoutIndex]) * std::exp(-lam2.value() *
-                                   tau.value());
+                               tau.value());
     bc_prec(2, call) = gSum(prec3.boundaryField()[precoutIndex] *
                             mesh.magSf().boundaryField()[precoutIndex]) / gSum(
                            mesh.magSf().boundaryField()[precoutIndex]) * std::exp(-lam3.value() *
-                                   tau.value());
+                               tau.value());
     bc_prec(3, call) = gSum(prec4.boundaryField()[precoutIndex] *
                             mesh.magSf().boundaryField()[precoutIndex]) / gSum(
                            mesh.magSf().boundaryField()[precoutIndex]) * std::exp(-lam4.value() *
-                                   tau.value());
+                               tau.value());
     bc_prec(4, call) = gSum(prec5.boundaryField()[precoutIndex] *
                             mesh.magSf().boundaryField()[precoutIndex]) / gSum(
                            mesh.magSf().boundaryField()[precoutIndex]) * std::exp(-lam5.value() *
-                                   tau.value());
+                               tau.value());
     bc_prec(5, call) = gSum(prec6.boundaryField()[precoutIndex] *
                             mesh.magSf().boundaryField()[precoutIndex]) / gSum(
                            mesh.magSf().boundaryField()[precoutIndex]) * std::exp(-lam6.value() *
-                                   tau.value());
+                               tau.value());
     bc_prec(6, call) = gSum(prec7.boundaryField()[precoutIndex] *
                             mesh.magSf().boundaryField()[precoutIndex]) / gSum(
                            mesh.magSf().boundaryField()[precoutIndex]) * std::exp(-lam7.value() *
-                                   tau.value());
+                               tau.value());
     bc_prec(7, call) = gSum(prec8.boundaryField()[precoutIndex] *
                             mesh.magSf().boundaryField()[precoutIndex]) / gSum(
                            mesh.magSf().boundaryField()[precoutIndex]) * std::exp(-lam8.value() *
-                                   tau.value());
+                               tau.value());
 }
 
 void usmsrProblem::assignPrecsBC(label call, label Ntau)
diff --git a/src/ITHACA_HR/hyperReduction.H b/src/ITHACA_HR/hyperReduction.H
index 26ec277a3..a8b7b42cc 100644
--- a/src/ITHACA_HR/hyperReduction.H
+++ b/src/ITHACA_HR/hyperReduction.H
@@ -46,422 +46,458 @@ SourceFiles
 template <typename... SnapshotsLists>
 class HyperReduction
 {
-public:
-    word methodName;
-
-    using SnapshotsListTuple = std::tuple<std::decay_t<SnapshotsLists>...>;
-    using FieldsTuple = std::tuple<typename std::decay_t<SnapshotsLists>::value_type ...>;
-    static constexpr auto n_fields = sizeof...(SnapshotsLists);
-
-    // TODO get vectorial dim from class template parameters
-    unsigned int vectorial_dim;
-    unsigned int sumFieldsDim;
-
-    template <std::size_t N>
-    using NthFieldListType = typename std::tuple_element<N, SnapshotsListTuple>::type;
-
-    template <std::size_t N>
-    using NthFieldType = typename NthFieldListType<N>::value_type;
-
-    //----------------------------------------------------------------------
-    /// @brief      Construct HyperReduction class, interpolation-based.`SnapshotsLists` is a variadic argument of PtrLists of fields e.g. for incompressible Navier-Stokes PtrList<volVectorField>, PtrList<volScalarField> for velocity and pressure.
-    ///
-    /// @param[in]  hrMethod          the chosen HR method
-    /// @param[in]  n_modes           dimension of the HR basis
-    /// @param[in]  n_nodes           number of nodes
-    /// @param[in]  initialSeeds      initial nodes
-    /// @param[in]  problemName       name of the function to be hyper-reduced
-    /// @param[in]  snapshotsLists    lists of fields
-    ///
-    HyperReduction(label n_modes,
-                   label n_nodes,
-                   Eigen::VectorXi initialSeeds,
-                   word problemName,
-                   SnapshotsLists &&...snapshotsLists);
-    
-    //----------------------------------------------------------------------
-    /// @brief      Construct HyperReduction class
-    ///
-    /// @param[in]  n_modes           Dimension of the HR basis
-    /// @param[in]  n_nodes           Number of nodes
-    /// @param[in]  vectorial_dim     Field dimension (1 for volScalarField 3 for volVectorField)
-    /// @param[in]  n_cells           Number of cells
-    /// @param[in]  initialSeeds      Initial nodes
-    /// @param[in]  problemName       Name of the function to be hyper-reduced
-    ///
-    HyperReduction(label n_modes,
-                   label n_nodes,
-                   unsigned int vectorial_dim, 
-                   label n_cells,
-                   Eigen::VectorXi initialSeeds,
-                   word problemName);
-    
-    // ITHACA parameters dict
-    ITHACAparameters* para;
-
-    //TODO
-    label n_boundary_patches;
-
-    //TODO
-    List<label> n_boundary_cells_list;
-
-    //TODO
-    label n_boundary_cells;
-
-    /// The maximum number of modes to be considered
-    label n_modes;
-
-    /// The maximum number of modes to be considered
-    label n_nodes;
-
-    /// The length of the snapshots lists
-    label n_snapshots;
-
-    // Initial nodes
-    Eigen::VectorXi initialSeeds;
-
-    // nodes
-    Eigen::VectorXi nodes;
-
-    /// The name of the non-linear function e.g. HR_method/residual
-    word problemName;
-
-    /// The snapshots matrix containing the nonlinear function or operator
-    SnapshotsListTuple snapshotsListTuple;
-
-    /// Names of the fields
-    List<word> fieldNames;
-
-    /// Dimensions of the fields
-    List<unsigned int> fieldDims;
-
-    /// Int Number of Cells;
-    label n_cells;
-
-    /// Int Number of Cells in submeshes;
-    label n_cellsSubfields;
-
-    /// Nodes in the case of the a nonlinear function
-    autoPtr<IOList<label>> nodePoints;
-
-    /// List of label lists of the nodes and corresponding surrounding nodes
-    autoPtr<IOList<labelList>> totalNodePoints;
-
-    /// List of the unique indices of the nodes that define the submesh
-    autoPtr<IOList<label>> uniqueNodePoints;
-
-    /// Folder for the HR problem
-    word folderProblem;
-
-    /// Folder for the selected HR method
-    word folderMethod;
-
-    /// Indices of the local node points in the subMesh
-    List<label> localNodePoints;
-    
-    // Outputs
-    /// Orthonormal basis of HR
-    Eigen::MatrixXd basisMatrix;
-
-    // Normalizing weights of SVD decomposition
-    Eigen::VectorXd normalizingWeights;
-
-    /// Renormalized basis of HR
-    Eigen::MatrixXd renormalizedBasisMatrix;
-
-    // TODO
-    Eigen::MatrixXd pinvPU;
-
-    // TODO
-    Eigen::MatrixXd wPU;
-
-    // TODO
-    Eigen::VectorXd eigenValueseig;
-
-    /// The P matrix of the HyperReduction method. The nodes are ordered in the order of insertion during the greedy procedure. The components related to the same node follow immediately.
-    Eigen::SparseMatrix<double> P;
-
-    // Mask field to submesh
-    Eigen::SparseMatrix<double> field2submesh;
-
-    // Mask submesh to nodes
-    Eigen::SparseMatrix<double> submesh2nodes;
-
-    // Indices submesh to nodes
-    Eigen::VectorXi submesh2nodesMask;
-
-    /// Quadrature weights. Ordered in the same order of matrix P.
-    Eigen::VectorXd quadratureWeights;
-
-    /// Submesh of the HyperReduction method
-    autoPtr<fvMeshSubset> submesh;
-    
-    /// Submeshes
-    autoPtr<volVectorField> submesh_field;
-
-    /// Online Matrix
-    Eigen::MatrixXd MatrixOnline;
-    
-    //----------------------------------------------------------------------
-    /// @brief      Methods implemented: 'GappyDEIM'  from "DEIM, Chaturantabut, Saifon, and Danny C. Sorensen. "Nonlinear model reduction via discrete empirical interpolation." SIAM Journal on Scientific Computing 32.5 (2010): 2737-2764" and "GNAT, Carlberg, Kevin, et al. "The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows." Journal of Computational Physics 242 (2013): 623-647.". Quasi-optimal point selection algorithm 'SOPT' and optimal point selection 'SOPTE' from "Lauzon, Jessica T., Siu Wun Cheung, Yeonjong Shin, Youngsoo Choi, Dylan Matthew Copeland, and Kevin Huynh. "S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models." arXiv preprint arXiv:2203.16494 (2022).""
-    ///
-    void offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights){
-        methodName = "GappyDEIM";
-        word name = "ITHACAoutput/" + problemName + "/" + methodName;
-        offlineGappyDEIM(snapshotsModes, normalizingWeights, name);
-    }
-
-    void offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights, word folderMethodName);
-
-    //----------------------------------------------------------------------
-    /// @brief      Methods implemented: 'ECP' from "ECP, Hernandez, Joaquin Alberto, Manuel Alejandro Caicedo, and Alex Ferrer. "Dimensional hyper-reduction of nonlinear finite element models via empirical cubature." Computer methods in applied mechanics and engineering 313 (2017): 687-722.". TODO implement non-negative LS.
-    ///
-    void offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights){
-        methodName = "ECP";
-        word name = "ITHACAoutput/" + problemName + "/" + methodName;
-        offlineECP(snapshotsModes, normalizingWeights, name);
-    }
-
-    void offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& normalizingWeights, word folderMethodName);
-    
-    //----------------------------------------------------------------------
-    /// @brief      TODO
-    ///
-    void initSeeds(Eigen::VectorXd mp_not_mask, std::set<label> nodePointsSet);
-
-    //----------------------------------------------------------------------
-    /// @brief      TODO
-    ///
-    void computeLS(Eigen::MatrixXd& J, Eigen::MatrixXd& JWhole, Eigen::VectorXd& b, Eigen::VectorXd& q);
-
-    //----------------------------------------------------------------------
-    /// @brief      TODO
-    ///
-    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
-    /// @param[in]  sList  The list of snapshots
-    ///
-    void getModesSVD(SnapshotsListTuple &SnapshotsListTuple, Eigen::MatrixXd &modesSVD, Eigen::VectorXd &fieldWeights, bool saveModesFlag = false);
-
-    //----------------------------------------------------------------------
-    /// @brief      TODO
-    ///
-    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
-    /// @param[in]  sList  The list of snapshots
-    ///
-    void getModesSVD(SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights, Eigen::MatrixXd& modesSVDBoundary, Eigen::VectorXd& fieldWeightsBoundary, bool saveModesFlag);
-    
-    //----------------------------------------------------------------------
-    /// @brief      TODO
-    ///
-    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
-    /// @param[in]  sList  The list of snapshots
-    ///
-    void updateNodes(Eigen::SparseMatrix<double>& P, label& ind_max, Eigen::VectorXd& mp_not_mask);
-
-    //----------------------------------------------------------------------
-    /// @brief      TODO
-    ///
-    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
-    /// @param[in]  sList  The list of snapshots
-    ///
-    template <typename SnapshotsList>
-    void stackSnapshots(SnapshotsList sList, Eigen::MatrixXd &snapshotsMatrix, Eigen::VectorXd &fieldWeights);
-
-    //----------------------------------------------------------------------
-    /// @brief      TODO
-    ///
-    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
-    /// @param[in]  sList  The list of snapshots
-    ///
-    template <typename SnapshotsList>
-    void stackSnapshotsBoundary(SnapshotsList sList, List<Eigen::MatrixXd>& snapshotsMatrixBoundary, List<Eigen::VectorXd>& fieldWeightsBoundary);
-    
-    //----------------------------------------------------------------------
-    /// @brief      TODO
-    ///
-    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
-    /// @param[in]  sList  The list of snapshots
-    ///
-    template <typename SnapshotsList>
-    void saveModes(SnapshotsList sList, Eigen::MatrixXd& snapshotsMatrix, unsigned int &rowIndex, unsigned int &modeIndex, word folder);
-
-    //----------------------------------------------------------------------
-    /// @brief      TODO
-    ///
-    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
-    /// @param[in]  sList  The list of snapshots
-    ///
-    template <typename SnapshotsList>
-    void saveModes(SnapshotsList sList, Eigen::MatrixXd& snapshotsMatrix, Eigen::MatrixXd& snapshotsMatrixBoundary, unsigned int &rowIndex,  unsigned int& rowIndexBoundary, unsigned int &modeIndex, word folder);
-
-    //----------------------------------------------------------------------
-    /// @brief      TODO
-    ///
-    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
-    /// @param[in]  sList  The list of snapshots
-    ///
-    template <typename SnapshotsList>
-    void stackNames(SnapshotsList sList){
-        fieldNames.append(sList[0].name());
-    }
-
-    //----------------------------------------------------------------------
-    /// @brief      TODO
-    ///
-    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
-    /// @param[in]  sList  The list of snapshots
-    ///
-    template <typename SnapshotsList>
-    inline void stackDimensions(SnapshotsList sList){
-        fieldDims.append(get_field_dim<typename SnapshotsList::value_type>());}
-
-    //----------------------------------------------------------------------
-    /// @brief      TODO
-    ///
-    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
-    /// @param[in]  sList  The list of snapshots
-    ///
-    template <typename SnapshotsList>
-    inline void sumDimensions(double sum, SnapshotsList sList){
-        sum+=get_field_dim<typename SnapshotsList::value_type>();}
-
-    //----------------------------------------------------------------------
-    /// @brief      Compute the pseudo-inverse of the matrix M restricted with the projector P
-    ///
-    /// @param[in]  Projector  projector into interpolation nodes
-    /// @param[in]  Modes      matrix to restrict and invert
-    ///
-    void evaluatePinv(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd& fieldWeights);
-
-     //----------------------------------------------------------------------
-    /// @brief      Compute the pseudo-inverse of the matrix M restricted with the projector P
-    ///
-    /// @param[in]  Projector  projector into interpolation nodes
-    /// @param[in]  Modes      matrix to restrict and invert
-    ///
-    void evaluateWPU(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd& fieldWeights, Eigen::VectorXd& quadratureWeights);
-
-    //----------------------------------------------------------------------
-    /// @brief      Compute the submesh common to all fields in SnapshotsLists
-    ///
-    /// @param[in]  layers          projector into interpolation nodes
-    /// @param[in]  mesh            matrix to restrict and invert
-    ///
-    void generateSubmesh(label layers, const fvMesh &mesh);
-
-    //----------------------------------------------------------------------
-    /// @brief      Get local indices in the submesh from indices in the global ones
-    ///
-    /// @param      points       The points
-    /// @param      submesh      The submesh
-    ///
-    /// @return     The local indices
-    ///
-    List<label> global2local(List<label> &points, fvMeshSubset &submesh);
-
-    /// @brief      TODO
-    ///
-    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
-    /// @param[in]  sList  The list of snapshots
-    ///
-    template <typename FieldType>
-    inline autoPtr<FieldType> interpolateField(const FieldType &field)
-    {
-        return autoPtr<FieldType>(new FieldType(submesh->interpolate(field)));
-    }
-
-    /// @brief      TODO
-    ///
-    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
-    /// @param[in]  sList  The list of snapshots
-    ///
-    // TODO expand with sphericalTensor, symmTensor, tensor
-    template <typename Field>
-    inline constexpr unsigned int get_field_dim()
-    {
-        return std::is_same<Field, volScalarField>::value ? 1 : 3;
-    }
-
-    /// @brief      TODO
-    ///
-    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
-    /// @param[in]  sList  The list of snapshots
-    ///
-    template <typename LastList>
-    inline constexpr unsigned int compute_vectorial_dim(LastList x) { return get_field_dim<typename std::decay_t<LastList>::value_type>(); }
-
-    /// @brief      TODO
-    ///
-    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
-    /// @param[in]  sList  The list of snapshots
-    ///
-    template <typename List, typename... RemainingLists>
-    inline constexpr unsigned int compute_vectorial_dim(List &&head, RemainingLists &&...tail)
-    {
-        return get_field_dim<typename std::decay_t<List>::value_type>() + compute_vectorial_dim<RemainingLists...>(tail...);
-    }
-
-    /// @brief      TODO
-    ///
-    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
-    /// @param[in]  sList  The list of snapshots
-    ///
-    static inline double s_optimality(Eigen::MatrixXd& A)
-    {   
-        return std::pow(
-            std::sqrt((A.transpose()*A).determinant())/\
-            A.colwise().lpNorm<2>().prod(),
-            1.0/A.cols());
-    }
-
-    /// @brief      TODO
-    ///
-    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
-    /// @param[in]  sList  The list of snapshots
-    ///
-    template <typename... FieldsArgs>
-    void eigen2fields(Eigen::VectorXd& eFields, FieldsArgs&&... oFields)
-    {   
-        unsigned int cumulativeSize{0}, ith_field{0};
-        
-        ([&](auto& oFieldsArg)
+    public:
+        word methodName;
+
+        using SnapshotsListTuple = std::tuple<std::decay_t<SnapshotsLists>...>;
+        using FieldsTuple =
+            std::tuple<typename std::decay_t<SnapshotsLists>::value_type ...>;
+        static constexpr auto n_fields = sizeof...(SnapshotsLists);
+
+        // TODO get vectorial dim from class template parameters
+        unsigned int vectorial_dim;
+        unsigned int sumFieldsDim;
+
+        template <std::size_t N>
+        using NthFieldListType = typename
+                                 std::tuple_element<N, SnapshotsListTuple>::type;
+
+        template <std::size_t N>
+        using NthFieldType = typename NthFieldListType<N>::value_type;
+
+        //----------------------------------------------------------------------
+        /// @brief      Construct HyperReduction class, interpolation-based.`SnapshotsLists` is a variadic argument of PtrLists of fields e.g. for incompressible Navier-Stokes PtrList<volVectorField>, PtrList<volScalarField> for velocity and pressure.
+        ///
+        /// @param[in]  hrMethod          the chosen HR method
+        /// @param[in]  n_modes           dimension of the HR basis
+        /// @param[in]  n_nodes           number of nodes
+        /// @param[in]  initialSeeds      initial nodes
+        /// @param[in]  problemName       name of the function to be hyper-reduced
+        /// @param[in]  snapshotsLists    lists of fields
+        ///
+        HyperReduction(label n_modes,
+                       label n_nodes,
+                       Eigen::VectorXi initialSeeds,
+                       word problemName,
+                       SnapshotsLists &&...snapshotsLists);
+
+        //----------------------------------------------------------------------
+        /// @brief      Construct HyperReduction class
+        ///
+        /// @param[in]  n_modes           Dimension of the HR basis
+        /// @param[in]  n_nodes           Number of nodes
+        /// @param[in]  vectorial_dim     Field dimension (1 for volScalarField 3 for volVectorField)
+        /// @param[in]  n_cells           Number of cells
+        /// @param[in]  initialSeeds      Initial nodes
+        /// @param[in]  problemName       Name of the function to be hyper-reduced
+        ///
+        HyperReduction(label n_modes,
+                       label n_nodes,
+                       unsigned int vectorial_dim,
+                       label n_cells,
+                       Eigen::VectorXi initialSeeds,
+                       word problemName);
+
+        // ITHACA parameters dict
+        ITHACAparameters* para;
+
+        //TODO
+        label n_boundary_patches;
+
+        //TODO
+        List<label> n_boundary_cells_list;
+
+        //TODO
+        label n_boundary_cells;
+
+        /// The maximum number of modes to be considered
+        label n_modes;
+
+        /// The maximum number of modes to be considered
+        label n_nodes;
+
+        /// The length of the snapshots lists
+        label n_snapshots;
+
+        // Initial nodes
+        Eigen::VectorXi initialSeeds;
+
+        // nodes
+        Eigen::VectorXi nodes;
+
+        /// The name of the non-linear function e.g. HR_method/residual
+        word problemName;
+
+        /// The snapshots matrix containing the nonlinear function or operator
+        SnapshotsListTuple snapshotsListTuple;
+
+        /// Names of the fields
+        List<word> fieldNames;
+
+        /// Dimensions of the fields
+        List<unsigned int> fieldDims;
+
+        /// Int Number of Cells;
+        label n_cells;
+
+        /// Int Number of Cells in submeshes;
+        label n_cellsSubfields;
+
+        /// Nodes in the case of the a nonlinear function
+        autoPtr<IOList<label>> nodePoints;
+
+        /// List of label lists of the nodes and corresponding surrounding nodes
+        autoPtr<IOList<labelList>> totalNodePoints;
+
+        /// List of the unique indices of the nodes that define the submesh
+        autoPtr<IOList<label>> uniqueNodePoints;
+
+        /// Folder for the HR problem
+        word folderProblem;
+
+        /// Folder for the selected HR method
+        word folderMethod;
+
+        /// Indices of the local node points in the subMesh
+        List<label> localNodePoints;
+
+        // Outputs
+        /// Orthonormal basis of HR
+        Eigen::MatrixXd basisMatrix;
+
+        // Normalizing weights of SVD decomposition
+        Eigen::VectorXd normalizingWeights;
+
+        /// Renormalized basis of HR
+        Eigen::MatrixXd renormalizedBasisMatrix;
+
+        // TODO
+        Eigen::MatrixXd pinvPU;
+
+        // TODO
+        Eigen::MatrixXd wPU;
+
+        // TODO
+        Eigen::VectorXd eigenValueseig;
+
+        /// The P matrix of the HyperReduction method. The nodes are ordered in the order of insertion during the greedy procedure. The components related to the same node follow immediately.
+        Eigen::SparseMatrix<double> P;
+
+        // Mask field to submesh
+        Eigen::SparseMatrix<double> field2submesh;
+
+        // Mask submesh to nodes
+        Eigen::SparseMatrix<double> submesh2nodes;
+
+        // Indices submesh to nodes
+        Eigen::VectorXi submesh2nodesMask;
+
+        /// Quadrature weights. Ordered in the same order of matrix P.
+        Eigen::VectorXd quadratureWeights;
+
+        /// Submesh of the HyperReduction method
+        autoPtr<fvMeshSubset> submesh;
+
+        /// Submeshes
+        autoPtr<volVectorField> submesh_field;
+
+        /// Online Matrix
+        Eigen::MatrixXd MatrixOnline;
+
+        //----------------------------------------------------------------------
+        /// @brief      Methods implemented: 'GappyDEIM'  from "DEIM, Chaturantabut, Saifon, and Danny C. Sorensen. "Nonlinear model reduction via discrete empirical interpolation." SIAM Journal on Scientific Computing 32.5 (2010): 2737-2764" and "GNAT, Carlberg, Kevin, et al. "The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows." Journal of Computational Physics 242 (2013): 623-647.". Quasi-optimal point selection algorithm 'SOPT' and optimal point selection 'SOPTE' from "Lauzon, Jessica T., Siu Wun Cheung, Yeonjong Shin, Youngsoo Choi, Dylan Matthew Copeland, and Kevin Huynh. "S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models." arXiv preprint arXiv:2203.16494 (2022).""
+        ///
+        void offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes,
+                              Eigen::VectorXd& normalizingWeights)
+        {
+            methodName = "GappyDEIM";
+            word name = "ITHACAoutput/" + problemName + "/" + methodName;
+            offlineGappyDEIM(snapshotsModes, normalizingWeights, name);
+        }
+
+        void offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes,
+                              Eigen::VectorXd& normalizingWeights, word folderMethodName);
+
+        //----------------------------------------------------------------------
+        /// @brief      Methods implemented: 'ECP' from "ECP, Hernandez, Joaquin Alberto, Manuel Alejandro Caicedo, and Alex Ferrer. "Dimensional hyper-reduction of nonlinear finite element models via empirical cubature." Computer methods in applied mechanics and engineering 313 (2017): 687-722.". TODO implement non-negative LS.
+        ///
+        void offlineECP(Eigen::MatrixXd& snapshotsModes,
+                        Eigen::VectorXd& normalizingWeights)
+        {
+            methodName = "ECP";
+            word name = "ITHACAoutput/" + problemName + "/" + methodName;
+            offlineECP(snapshotsModes, normalizingWeights, name);
+        }
+
+        void offlineECP(Eigen::MatrixXd& snapshotsModes,
+                        Eigen::VectorXd& normalizingWeights, word folderMethodName);
+
+        //----------------------------------------------------------------------
+        /// @brief      TODO
+        ///
+        void initSeeds(Eigen::VectorXd mp_not_mask, std::set<label> nodePointsSet);
+
+        //----------------------------------------------------------------------
+        /// @brief      TODO
+        ///
+        void computeLS(Eigen::MatrixXd& J, Eigen::MatrixXd& JWhole, Eigen::VectorXd& b,
+                       Eigen::VectorXd& q);
+
+        //----------------------------------------------------------------------
+        /// @brief      TODO
+        ///
+        /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+        /// @param[in]  sList  The list of snapshots
+        ///
+        void getModesSVD(SnapshotsListTuple& SnapshotsListTuple,
+                         Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights,
+                         bool saveModesFlag = false);
+
+        //----------------------------------------------------------------------
+        /// @brief      TODO
+        ///
+        /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+        /// @param[in]  sList  The list of snapshots
+        ///
+        void getModesSVD(SnapshotsListTuple& snapshotsListTuple,
+                         Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights,
+                         Eigen::MatrixXd& modesSVDBoundary, Eigen::VectorXd& fieldWeightsBoundary,
+                         bool saveModesFlag);
+
+        //----------------------------------------------------------------------
+        /// @brief      TODO
+        ///
+        /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+        /// @param[in]  sList  The list of snapshots
+        ///
+        void updateNodes(Eigen::SparseMatrix<double> & P, label& ind_max,
+                         Eigen::VectorXd& mp_not_mask);
+
+        //----------------------------------------------------------------------
+        /// @brief      TODO
+        ///
+        /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+        /// @param[in]  sList  The list of snapshots
+        ///
+        template <typename SnapshotsList>
+        void stackSnapshots(SnapshotsList sList, Eigen::MatrixXd& snapshotsMatrix,
+                            Eigen::VectorXd& fieldWeights);
+
+        //----------------------------------------------------------------------
+        /// @brief      TODO
+        ///
+        /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+        /// @param[in]  sList  The list of snapshots
+        ///
+        template <typename SnapshotsList>
+        void stackSnapshotsBoundary(SnapshotsList sList,
+                                    List<Eigen::MatrixXd> & snapshotsMatrixBoundary,
+                                    List<Eigen::VectorXd> & fieldWeightsBoundary);
+
+        //----------------------------------------------------------------------
+        /// @brief      TODO
+        ///
+        /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+        /// @param[in]  sList  The list of snapshots
+        ///
+        template <typename SnapshotsList>
+        void saveModes(SnapshotsList sList, Eigen::MatrixXd& snapshotsMatrix,
+                       unsigned int& rowIndex, unsigned int& modeIndex, word folder);
+
+        //----------------------------------------------------------------------
+        /// @brief      TODO
+        ///
+        /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+        /// @param[in]  sList  The list of snapshots
+        ///
+        template <typename SnapshotsList>
+        void saveModes(SnapshotsList sList, Eigen::MatrixXd& snapshotsMatrix,
+                       Eigen::MatrixXd& snapshotsMatrixBoundary, unsigned int& rowIndex,
+                       unsigned int& rowIndexBoundary, unsigned int& modeIndex, word folder);
+
+        //----------------------------------------------------------------------
+        /// @brief      TODO
+        ///
+        /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+        /// @param[in]  sList  The list of snapshots
+        ///
+        template <typename SnapshotsList>
+        void stackNames(SnapshotsList sList)
+        {
+            fieldNames.append(sList[0].name());
+        }
+
+        //----------------------------------------------------------------------
+        /// @brief      TODO
+        ///
+        /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+        /// @param[in]  sList  The list of snapshots
+        ///
+        template <typename SnapshotsList>
+        inline void stackDimensions(SnapshotsList sList)
+        {
+            fieldDims.append(get_field_dim<typename SnapshotsList::value_type>());
+        }
+
+        //----------------------------------------------------------------------
+        /// @brief      TODO
+        ///
+        /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+        /// @param[in]  sList  The list of snapshots
+        ///
+        template <typename SnapshotsList>
+        inline void sumDimensions(double sum, SnapshotsList sList)
+        {
+            sum += get_field_dim<typename SnapshotsList::value_type>();
+        }
+
+        //----------------------------------------------------------------------
+        /// @brief      Compute the pseudo-inverse of the matrix M restricted with the projector P
+        ///
+        /// @param[in]  Projector  projector into interpolation nodes
+        /// @param[in]  Modes      matrix to restrict and invert
+        ///
+        void evaluatePinv(Eigen::SparseMatrix<double> & Projector,
+                          Eigen::MatrixXd& Modes, Eigen::VectorXd& fieldWeights);
+
+        //----------------------------------------------------------------------
+        /// @brief      Compute the pseudo-inverse of the matrix M restricted with the projector P
+        ///
+        /// @param[in]  Projector  projector into interpolation nodes
+        /// @param[in]  Modes      matrix to restrict and invert
+        ///
+        void evaluateWPU(Eigen::SparseMatrix<double> & Projector,
+                         Eigen::MatrixXd& Modes, Eigen::VectorXd& fieldWeights,
+                         Eigen::VectorXd& quadratureWeights);
+
+        //----------------------------------------------------------------------
+        /// @brief      Compute the submesh common to all fields in SnapshotsLists
+        ///
+        /// @param[in]  layers          projector into interpolation nodes
+        /// @param[in]  mesh            matrix to restrict and invert
+        ///
+        void generateSubmesh(label layers, const fvMesh& mesh);
+
+        //----------------------------------------------------------------------
+        /// @brief      Get local indices in the submesh from indices in the global ones
+        ///
+        /// @param      points       The points
+        /// @param      submesh      The submesh
+        ///
+        /// @return     The local indices
+        ///
+        List<label> global2local(List<label> & points, fvMeshSubset& submesh);
+
+        /// @brief      TODO
+        ///
+        /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+        /// @param[in]  sList  The list of snapshots
+        ///
+        template <typename FieldType>
+        inline autoPtr<FieldType> interpolateField(const FieldType& field)
+        {
+            return autoPtr<FieldType>(new FieldType(submesh->interpolate(field)));
+        }
+
+        /// @brief      TODO
+        ///
+        /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+        /// @param[in]  sList  The list of snapshots
+        ///
+        // TODO expand with sphericalTensor, symmTensor, tensor
+        template <typename Field>
+        inline constexpr unsigned int get_field_dim()
+        {
+            return std::is_same<Field, volScalarField>::value ? 1 : 3;
+        }
+
+        /// @brief      TODO
+        ///
+        /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+        /// @param[in]  sList  The list of snapshots
+        ///
+        template <typename LastList>
+        inline constexpr unsigned int compute_vectorial_dim(LastList x)
+        {
+            return get_field_dim<typename std::decay_t<LastList>::value_type>();
+        }
+
+        /// @brief      TODO
+        ///
+        /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+        /// @param[in]  sList  The list of snapshots
+        ///
+        template <typename List, typename... RemainingLists>
+        inline constexpr unsigned int compute_vectorial_dim(List &&head,
+                RemainingLists &&...tail)
+        {
+            return get_field_dim<typename std::decay_t<List>::value_type>() +
+                   compute_vectorial_dim<RemainingLists...>(tail...);
+        }
+
+        /// @brief      TODO
+        ///
+        /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+        /// @param[in]  sList  The list of snapshots
+        ///
+        static inline double s_optimality(Eigen::MatrixXd& A)
+        {
+            return std::pow(
+                       std::sqrt((A.transpose() * A).determinant()) / \
+                       A.colwise().lpNorm<2>().prod(),
+                       1.0 / A.cols());
+        }
+
+        /// @brief      TODO
+        ///
+        /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+        /// @param[in]  sList  The list of snapshots
+        ///
+        template <typename... FieldsArgs>
+        void eigen2fields(Eigen::VectorXd& eFields, FieldsArgs&&... oFields)
+        {
+            unsigned int cumulativeSize{0}, ith_field{0};
+            ([ & ](auto& oFieldsArg)
             {
-                double ith_fieldSize = fieldDims[ith_field]*oFieldsArg.size();
+                double ith_fieldSize = fieldDims[ith_field] * oFieldsArg.size();
                 Eigen::VectorXd vec = eFields.segment(cumulativeSize, ith_fieldSize);
                 oFieldsArg = Foam2Eigen::Eigen2field(oFieldsArg, vec);
-                cumulativeSize+=ith_fieldSize;
+                cumulativeSize += ith_fieldSize;
                 ith_field++;
-            }(oFields), ...);
-
-    }
-
-    /// @brief      TODO
-    ///
-    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
-    /// @param[in]  sList  The list of snapshots
-    ///
-    void initReshapeMat(Eigen::SparseMatrix<double> &reshapeMat);
-
-    /// @brief      TODO
-    ///
-    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
-    /// @param[in]  sList  The list of snapshots
-    ///
-    void createMasks(bool offlineStage = true);
-
-    /// @brief      TODO
-    ///
-    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
-    /// @param[in]  sList  The list of snapshots
-    ///
-    void getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights);
-
-    /// @brief      TODO
-    ///
-    /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
-    /// @param[in]  sList  The list of snapshots
-    ///
-    void getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights, List<Eigen::MatrixXd>& snapMatrixBoundary, List<Eigen::VectorXd>& fieldWeightsBoundary);
+            }
+
+            (oFields), ...);
+        }
+
+        /// @brief      TODO
+        ///
+        /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+        /// @param[in]  sList  The list of snapshots
+        ///
+        void initReshapeMat(Eigen::SparseMatrix<double> & reshapeMat);
+
+        /// @brief      TODO
+        ///
+        /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+        /// @param[in]  sList  The list of snapshots
+        ///
+        void createMasks(bool offlineStage = true);
+
+        /// @brief      TODO
+        ///
+        /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+        /// @param[in]  sList  The list of snapshots
+        ///
+        void getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights);
+
+        /// @brief      TODO
+        ///
+        /// @tparam     SnapshotsList  PtrList of volScalarField or volVectorField
+        /// @param[in]  sList  The list of snapshots
+        ///
+        void getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights,
+                           List<Eigen::MatrixXd> & snapMatrixBoundary,
+                           List<Eigen::VectorXd> & fieldWeightsBoundary);
 };
 
 #endif
diff --git a/src/ITHACA_HR/hyperReduction.templates.H b/src/ITHACA_HR/hyperReduction.templates.H
index d3f0e383d..f7bf375b7 100644
--- a/src/ITHACA_HR/hyperReduction.templates.H
+++ b/src/ITHACA_HR/hyperReduction.templates.H
@@ -38,10 +38,10 @@ License
 // Template function constructor
 template <typename... SnapshotsLists>
 HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
-                                                  label n_nodes,
-                                                  Eigen::VectorXi initialSeeds,
-                                                  word problemName,
-                                                  SnapshotsLists &&...snapshotsLists)
+        label n_nodes,
+        Eigen::VectorXi initialSeeds,
+        word problemName,
+        SnapshotsLists &&...snapshotsLists)
     : vectorial_dim{compute_vectorial_dim(snapshotsLists...)},
       n_modes{n_modes},
       n_nodes{n_nodes},
@@ -49,61 +49,71 @@ HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
       problemName{problemName},
       snapshotsListTuple{std::forward_as_tuple(snapshotsLists...)}
 {
-  Info << "Init HyperReduction class with vectorial dim: " << vectorial_dim << endl;
-  para = ITHACAparameters::getInstance();
-  folderProblem = "ITHACAoutput/" + problemName;
-  mkDir(folderProblem);
-
-  // TODO check snapshotsLists is not empty
-  // TODO check that the first snapshotsList is not empty (includes above)
-
-  // TODO initialize vectorial_dim only from SnapshotsLists type
-  // vectorial_dim = std::apply(compute_vectorial_dim<SnapshotsLists&&...>, snapshotsListTuple);
-
-  // Get fields' names
-  std::apply([this](auto& ...snapList){(..., stackNames(snapList));}, snapshotsListTuple);
-
-  // Get fields' dimensions
-  std::apply([this](auto& ...snapList){(..., stackDimensions(snapList));}, snapshotsListTuple);
-
-  sumFieldsDim = 0;
-  std::apply([this](auto& ...snapList){(..., sumDimensions(this->sumFieldsDim, snapList));}, snapshotsListTuple);
-
-  Info << "Fields names: ";
-  for (unsigned int ith_field = 0; ith_field < fieldNames.size(); ith_field++)
-  {
-    Info << fieldNames[ith_field] << " (dim=" << fieldDims[ith_field] << "); ";
-  }
-  Info << endl;
-  
-  n_snapshots = std::get<0>(snapshotsListTuple).size();
-  Info << "The number of snapshots is: " << n_snapshots << endl;
-  n_cells = std::get<0>(snapshotsListTuple)[0].size();
-  Info << "The number of cells is: " << n_cells << endl;
-  Info << "Initial seeds length: " << initialSeeds.rows() << endl;
-
-  // get boundaries info
-  n_boundary_patches = std::get<0>(snapshotsListTuple)[0].boundaryField().size();
-
-  n_boundary_cells_list.resize(n_boundary_patches);
-  n_boundary_cells = 0;
-  for (unsigned int ith_boundary_patch = 0; ith_boundary_patch < n_boundary_patches; ith_boundary_patch++)
-  {
-    n_boundary_cells_list[ith_boundary_patch] = std::get<0>(snapshotsListTuple)[0].boundaryField()[ith_boundary_patch].size();
-    n_boundary_cells = n_boundary_cells + n_boundary_cells_list[ith_boundary_patch];
-  }
-  Info << "Number of boundary cells: " << n_boundary_cells << endl;
+    Info << "Init HyperReduction class with vectorial dim: " << vectorial_dim <<
+         endl;
+    para = ITHACAparameters::getInstance();
+    folderProblem = "ITHACAoutput/" + problemName;
+    mkDir(folderProblem);
+    // TODO check snapshotsLists is not empty
+    // TODO check that the first snapshotsList is not empty (includes above)
+    // TODO initialize vectorial_dim only from SnapshotsLists type
+    // vectorial_dim = std::apply(compute_vectorial_dim<SnapshotsLists&&...>, snapshotsListTuple);
+    // Get fields' names
+    std::apply([this](auto& ...snapList)
+    {
+        (..., stackNames(snapList));
+    }, snapshotsListTuple);
+
+    // Get fields' dimensions
+    std::apply([this](auto& ...snapList)
+    {
+        (..., stackDimensions(snapList));
+    }, snapshotsListTuple);
+
+    sumFieldsDim = 0;
+    std::apply([this](auto& ...snapList)
+    {
+        (..., sumDimensions(this->sumFieldsDim, snapList));
+    }, snapshotsListTuple);
+
+    Info << "Fields names: ";
+
+    for (unsigned int ith_field = 0; ith_field < fieldNames.size(); ith_field++)
+    {
+        Info << fieldNames[ith_field] << " (dim=" << fieldDims[ith_field] << "); ";
+    }
+
+    Info << endl;
+    n_snapshots = std::get<0>(snapshotsListTuple).size();
+    Info << "The number of snapshots is: " << n_snapshots << endl;
+    n_cells = std::get<0>(snapshotsListTuple)[0].size();
+    Info << "The number of cells is: " << n_cells << endl;
+    Info << "Initial seeds length: " << initialSeeds.rows() << endl;
+    // get boundaries info
+    n_boundary_patches = std::get<0>(snapshotsListTuple)[0].boundaryField().size();
+    n_boundary_cells_list.resize(n_boundary_patches);
+    n_boundary_cells = 0;
+
+    for (unsigned int ith_boundary_patch = 0;
+            ith_boundary_patch < n_boundary_patches; ith_boundary_patch++)
+    {
+        n_boundary_cells_list[ith_boundary_patch] = std::get<0>
+            (snapshotsListTuple)[0].boundaryField()[ith_boundary_patch].size();
+        n_boundary_cells = n_boundary_cells + n_boundary_cells_list[ith_boundary_patch];
+    }
+
+    Info << "Number of boundary cells: " << n_boundary_cells << endl;
 }
 
 
 // Template function constructor
 template <typename... SnapshotsLists>
 HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
-                                                  label n_nodes,
-                                                  unsigned int vectorialDim,
-                                                  label n_cells,
-                                                  Eigen::VectorXi initialSeeds,
-                                                  word problemName)
+        label n_nodes,
+        unsigned int vectorialDim,
+        label n_cells,
+        Eigen::VectorXi initialSeeds,
+        word problemName)
     : n_modes{n_modes},
       n_nodes{n_nodes},
       vectorial_dim{vectorialDim},
@@ -111,928 +121,1013 @@ HyperReduction<SnapshotsLists...>::HyperReduction(label n_modes,
       initialSeeds{initialSeeds},
       problemName{problemName}
 {
-  Info << "Init HyperReduction class with vectorial dim: " << vectorial_dim << endl;
-  para = ITHACAparameters::getInstance();
-  folderProblem = problemName;
-  mkDir(folderProblem);
-
-  Info << "Initial seeds length: " << initialSeeds.rows() << endl;
-
+    Info << "Init HyperReduction class with vectorial dim: " << vectorial_dim <<
+         endl;
+    para = ITHACAparameters::getInstance();
+    folderProblem = problemName;
+    mkDir(folderProblem);
+    Info << "Initial seeds length: " << initialSeeds.rows() << endl;
 }
 
 template <typename... SnapshotsLists>
 void HyperReduction<SnapshotsLists...>::getModesSVD(
-    SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights, bool saveModesFlag)
+    SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD,
+    Eigen::VectorXd& fieldWeights, bool saveModesFlag)
 {
-  // TODO move inside ITHACAPOD
-  ITHACAparameters* para(ITHACAparameters::getInstance());
-  word folderSVD = "ITHACAoutput/" + problemName + "/ModesSVD/";
-  if (!ITHACAutilities::check_folder(folderSVD))
-  {
-    mkDir(folderSVD);
-    // Initialize stacked snapshotsMatrix and normalizing weights
-    Eigen::MatrixXd snapMatrix;
-    getSnapMatrix(snapMatrix, fieldWeights);
-
-    word dimensionReductionMethod = para->ITHACAdict->lookupOrDefault<word>("DimensionReductionMethod", "SVD");
+    // TODO move inside ITHACAPOD
+    ITHACAparameters* para(ITHACAparameters::getInstance());
+    word folderSVD = "ITHACAoutput/" + problemName + "/ModesSVD/";
 
-    Eigen::MatrixXd eigenVectoreig;
-
-    if (dimensionReductionMethod == "RSVD")
+    if (!ITHACAutilities::check_folder(folderSVD))
     {
-      Info << "####### Performing RSVD for " << problemName << " #######" << endl;
-
-      unsigned int r_modeSVD = para->ITHACAdict->lookupOrDefault<unsigned int>("RSVDdim", snapMatrix.cols());
-      RedSVD::RedSVD svd(fieldWeights.array().cwiseInverse().matrix().asDiagonal()*snapMatrix, r_modeSVD);
-
-      Info << "####### End of RSVD for " << problemName << " #######" <<
-            endl;
-
-      eigenValueseig = svd.singularValues().real();
-      eigenVectoreig = svd.matrixU().real();
-    }
-    else
-    {
-      Info << "####### Performing SVD for " << problemName << " #######" << endl;
-
-      Eigen::JacobiSVD<Eigen::MatrixXd> svd(fieldWeights.array().cwiseInverse().matrix().asDiagonal()*snapMatrix, Eigen::ComputeThinU | Eigen::ComputeThinV);
-
-      Info << "####### End of SVD for " << problemName << " #######" <<
-            endl;
+        mkDir(folderSVD);
+        // Initialize stacked snapshotsMatrix and normalizing weights
+        Eigen::MatrixXd snapMatrix;
+        getSnapMatrix(snapMatrix, fieldWeights);
+        word dimensionReductionMethod =
+            para->ITHACAdict->lookupOrDefault<word>("DimensionReductionMethod", "SVD");
+        Eigen::MatrixXd eigenVectoreig;
+
+        if (dimensionReductionMethod == "RSVD")
+        {
+            Info << "####### Performing RSVD for " << problemName << " #######" << endl;
+            unsigned int r_modeSVD =
+                para->ITHACAdict->lookupOrDefault<unsigned int>("RSVDdim", snapMatrix.cols());
+            RedSVD::RedSVD svd(fieldWeights.array().cwiseInverse().matrix().asDiagonal() *
+                               snapMatrix, r_modeSVD);
+            Info << "####### End of RSVD for " << problemName << " #######" <<
+                 endl;
+            eigenValueseig = svd.singularValues().real();
+            eigenVectoreig = svd.matrixU().real();
+        }
+        else
+        {
+            Info << "####### Performing SVD for " << problemName << " #######" << endl;
+            Eigen::JacobiSVD<Eigen::MatrixXd> svd(
+                fieldWeights.array().cwiseInverse().matrix().asDiagonal() * snapMatrix,
+                Eigen::ComputeThinU | Eigen::ComputeThinV);
+            Info << "####### End of SVD for " << problemName << " #######" <<
+                 endl;
+            eigenValueseig = svd.singularValues().real();
+            eigenVectoreig = svd.matrixU().real();
+        }
 
-      eigenValueseig = svd.singularValues().real();
-      eigenVectoreig = svd.matrixU().real();
-    }
+        modesSVD = eigenVectoreig;
+        // TODO correct boundary conditions
+        cnpy::save(eigenValueseig,
+                   "ITHACAoutput/" + problemName + "/ModesSVD/eigenvalues.npy");
+        eigenValueseig = eigenValueseig / eigenValueseig.sum();
+        Eigen::VectorXd cumEigenValues(eigenValueseig);
 
-    modesSVD = eigenVectoreig;
+        for (label j = 1; j < cumEigenValues.size(); ++j)
+        {
+            cumEigenValues(j) += cumEigenValues(j - 1);
+        }
 
-    // TODO correct boundary conditions
-    
-    cnpy::save(eigenValueseig, "ITHACAoutput/" + problemName + "/ModesSVD/eigenvalues.npy");
+        Eigen::saveMarketVector(eigenValueseig,
+                                "ITHACAoutput/" + problemName + "/ModesSVD/Eigenvalues_" + problemName,
+                                para->precision,
+                                para->outytpe);
+        Eigen::saveMarketVector(cumEigenValues,
+                                "ITHACAoutput/" + problemName + "/ModesSVD/CumEigenvalues_" + problemName,
+                                para->precision,
+                                para->outytpe);
+        cnpy::save(modesSVD, "ITHACAoutput/" + problemName + "/ModesSVD/modes.npy");
+        cnpy::save(fieldWeights,
+                   "ITHACAoutput/" + problemName + "/ModesSVD/normalizingWeights.npy");
+
+        if (saveModesFlag)
+        {
+            unsigned int rowIndex{0};
 
-    eigenValueseig = eigenValueseig / eigenValueseig.sum();
-    Eigen::VectorXd cumEigenValues(eigenValueseig);
+            for (unsigned int modeIndex = 0; modeIndex < modesSVD.cols(); modeIndex++)
+            {
+                std::apply([this, & modesSVD, & rowIndex, & modeIndex,
+                            & folderSVD](auto& ...snapList)
+                {
+                    (..., saveModes(snapList, modesSVD, rowIndex, modeIndex, folderSVD));
+                }, snapshotsListTuple);
 
-    for (label j = 1; j < cumEigenValues.size(); ++j)
-    {
-        cumEigenValues(j) += cumEigenValues(j - 1);
+                rowIndex = 0;
+            }
+        }
     }
-
-    Eigen::saveMarketVector(eigenValueseig,
-                            "ITHACAoutput/" + problemName + "/ModesSVD/Eigenvalues_" + problemName, para->precision,
-                            para->outytpe);
-    Eigen::saveMarketVector(cumEigenValues,
-                            "ITHACAoutput/" + problemName + "/ModesSVD/CumEigenvalues_" + problemName, para->precision,
-                            para->outytpe);
-    cnpy::save(modesSVD, "ITHACAoutput/" + problemName + "/ModesSVD/modes.npy");
-    cnpy::save(fieldWeights, "ITHACAoutput/" + problemName + "/ModesSVD/normalizingWeights.npy");
-
-
-    if (saveModesFlag)
+    else
     {
-      unsigned int rowIndex{0};
-      for (unsigned int modeIndex = 0; modeIndex < modesSVD.cols(); modeIndex++)
-      {
-        std::apply([this, &modesSVD, &rowIndex, &modeIndex, &folderSVD](auto& ...snapList){(..., saveModes(snapList, modesSVD, rowIndex, modeIndex, folderSVD));}, snapshotsListTuple);
-        rowIndex = 0;
-      }
+        Info << "Reading the existing modes" << endl;
+        cnpy::load(modesSVD, folderSVD + "/modes.npy");
+        cnpy::load(fieldWeights, folderSVD + "/normalizingWeights.npy");
     }
-  }
-  else
-  {
-    Info << "Reading the existing modes" << endl;
-    cnpy::load(modesSVD, folderSVD + "/modes.npy");
-    cnpy::load(fieldWeights, folderSVD + "/normalizingWeights.npy");
-  }
 }
 
 template <typename... SnapshotsLists>
 void HyperReduction<SnapshotsLists...>::getModesSVD(
-    SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD, Eigen::VectorXd& fieldWeights, Eigen::MatrixXd& modesSVDBoundary, Eigen::VectorXd& fieldWeightsBoundary, bool saveModesFlag)
+    SnapshotsListTuple& snapshotsListTuple, Eigen::MatrixXd& modesSVD,
+    Eigen::VectorXd& fieldWeights, Eigen::MatrixXd& modesSVDBoundary,
+    Eigen::VectorXd& fieldWeightsBoundary, bool saveModesFlag)
 {
-  // TODO move inside ITHACAPOD
-  ITHACAparameters* para(ITHACAparameters::getInstance());
-  word folderSVD = "ITHACAoutput/" + problemName + "/ModesSVD/";
-  if (!ITHACAutilities::check_folder(folderSVD))
-  {
-    mkDir(folderSVD);
-    // Initialize stacked snapshotsMatrix and normalizing weights
-    Eigen::MatrixXd snapMatrix;
-    List<Eigen::MatrixXd> snapMatrixBoundary;
-    List<Eigen::VectorXd> fieldWeightsBoundaryList;
-    getSnapMatrix(snapMatrix, fieldWeights, snapMatrixBoundary, fieldWeightsBoundaryList);
+    // TODO move inside ITHACAPOD
+    ITHACAparameters* para(ITHACAparameters::getInstance());
+    word folderSVD = "ITHACAoutput/" + problemName + "/ModesSVD/";
 
-    for (unsigned int id = 0; id < n_boundary_patches; id++)
+    if (!ITHACAutilities::check_folder(folderSVD))
     {
-      snapMatrix.conservativeResize(snapMatrix.rows()+snapMatrixBoundary[id].rows(), snapMatrix.cols());
-      snapMatrix.bottomRows(snapMatrixBoundary[id].rows()) = snapMatrixBoundary[id];
-
-      fieldWeightsBoundary.conservativeResize(fieldWeightsBoundary.rows()+snapMatrixBoundary[id].rows());
-      fieldWeightsBoundary.tail(fieldWeightsBoundaryList[id].rows()) = fieldWeightsBoundaryList[id];
-    }
-
-    cnpy::save(fieldWeights, "ITHACAoutput/" + problemName + "/ModesSVD/normalizingWeights.npy");
-    cnpy::save(fieldWeightsBoundary, "ITHACAoutput/" + problemName + "/ModesSVD/normalizingWeightsBoundary.npy");
-
-    fieldWeights.conservativeResize(fieldWeights.rows()+fieldWeightsBoundary.rows());
-    fieldWeights.tail(fieldWeightsBoundary.rows()) = fieldWeightsBoundary;
-    
-    word dimensionReductionMethod = para->ITHACAdict->lookupOrDefault<word>("DimensionReductionMethod", "SVD");
-
-    Eigen::MatrixXd eigenVectoreig;
+        mkDir(folderSVD);
+        // Initialize stacked snapshotsMatrix and normalizing weights
+        Eigen::MatrixXd snapMatrix;
+        List<Eigen::MatrixXd> snapMatrixBoundary;
+        List<Eigen::VectorXd> fieldWeightsBoundaryList;
+        getSnapMatrix(snapMatrix, fieldWeights, snapMatrixBoundary,
+                      fieldWeightsBoundaryList);
+
+        for (unsigned int id = 0; id < n_boundary_patches; id++)
+        {
+            snapMatrix.conservativeResize(snapMatrix.rows() + snapMatrixBoundary[id].rows(),
+                                          snapMatrix.cols());
+            snapMatrix.bottomRows(snapMatrixBoundary[id].rows()) = snapMatrixBoundary[id];
+            fieldWeightsBoundary.conservativeResize(fieldWeightsBoundary.rows() +
+                                                    snapMatrixBoundary[id].rows());
+            fieldWeightsBoundary.tail(fieldWeightsBoundaryList[id].rows()) =
+                                    fieldWeightsBoundaryList[id];
+        }
 
-    if (dimensionReductionMethod == "RSVD")
-    {
-      Info << "####### Performing RSVD for " << problemName << " #######" << endl;
+        cnpy::save(fieldWeights,
+                   "ITHACAoutput/" + problemName + "/ModesSVD/normalizingWeights.npy");
+        cnpy::save(fieldWeightsBoundary,
+                   "ITHACAoutput/" + problemName + "/ModesSVD/normalizingWeightsBoundary.npy");
+        fieldWeights.conservativeResize(fieldWeights.rows() +
+                                        fieldWeightsBoundary.rows());
+        fieldWeights.tail(fieldWeightsBoundary.rows()) = fieldWeightsBoundary;
+        word dimensionReductionMethod =
+            para->ITHACAdict->lookupOrDefault<word>("DimensionReductionMethod", "SVD");
+        Eigen::MatrixXd eigenVectoreig;
+
+        if (dimensionReductionMethod == "RSVD")
+        {
+            Info << "####### Performing RSVD for " << problemName << " #######" << endl;
+            unsigned int r_modeSVD =
+                para->ITHACAdict->lookupOrDefault<unsigned int>("RSVDdim", snapMatrix.cols());
+            RedSVD::RedSVD svd(fieldWeights.array().cwiseInverse().matrix().asDiagonal() *
+                               snapMatrix, r_modeSVD);
+            Info << "####### End of RSVD for " << problemName << " #######" << endl;
+            eigenValueseig = svd.singularValues().real();
+            eigenVectoreig = svd.matrixU().real();
+        }
+        else
+        {
+            Info << "####### Performing SVD for " << problemName << " #######" << endl;
+            Eigen::JacobiSVD<Eigen::MatrixXd> svd(
+                fieldWeights.array().cwiseInverse().matrix().asDiagonal() * snapMatrix,
+                Eigen::ComputeThinU | Eigen::ComputeThinV);
+            Info << "####### End of SVD for " << problemName << " #######" <<
+                 endl;
+            eigenValueseig = svd.singularValues().real();
+            eigenVectoreig = svd.matrixU().real();
+        }
 
-      unsigned int r_modeSVD = para->ITHACAdict->lookupOrDefault<unsigned int>("RSVDdim", snapMatrix.cols());
+        modesSVD = eigenVectoreig.bottomRows(vectorial_dim* n_cells);
+        modesSVDBoundary = eigenVectoreig.topRows(n_boundary_cells);
+        fieldWeights.conservativeResize(fieldWeights.rows() -
+                                        fieldWeightsBoundary.rows());
+        cnpy::save(eigenValueseig,
+                   "ITHACAoutput/" + problemName + "/ModesSVD/eigenvalues.npy");
+        eigenValueseig = eigenValueseig / eigenValueseig.sum();
+        Eigen::VectorXd cumEigenValues(eigenValueseig);
 
-      RedSVD::RedSVD svd(fieldWeights.array().cwiseInverse().matrix().asDiagonal()*snapMatrix, r_modeSVD);
+        for (label j = 1; j < cumEigenValues.size(); ++j)
+        {
+            cumEigenValues(j) += cumEigenValues(j - 1);
+        }
 
-      Info << "####### End of RSVD for " << problemName << " #######" << endl;
+        Eigen::saveMarketVector(eigenValueseig,
+                                "ITHACAoutput/" + problemName + "/ModesSVD/Eigenvalues_" + problemName,
+                                para->precision,
+                                para->outytpe);
+        Eigen::saveMarketVector(cumEigenValues,
+                                "ITHACAoutput/" + problemName + "/ModesSVD/CumEigenvalues_" + problemName,
+                                para->precision,
+                                para->outytpe);
+        cnpy::save(modesSVD, "ITHACAoutput/" + problemName + "/ModesSVD/modes.npy");
+        cnpy::save(modesSVDBoundary,
+                   "ITHACAoutput/" + problemName + "/ModesSVD/modesBoundary.npy");
+
+        if (saveModesFlag)
+        {
+            unsigned int rowIndex{0};
+            unsigned int rowIndexBoundary{0};
 
-      eigenValueseig = svd.singularValues().real();
-      eigenVectoreig = svd.matrixU().real();
+            for (unsigned int modeIndex = 0; modeIndex < modesSVD.cols(); modeIndex++)
+            {
+                std::apply([this, & modesSVD,  & modesSVDBoundary, & rowIndex, & modeIndex,
+                            & rowIndexBoundary, & folderSVD](auto& ...snapList)
+                {
+                    (..., saveModes(snapList, modesSVD, modesSVDBoundary, rowIndex,
+                                    rowIndexBoundary, modeIndex, folderSVD));
+                }, snapshotsListTuple);
+
+                rowIndex = 0;
+            }
+        }
     }
     else
     {
-      Info << "####### Performing SVD for " << problemName << " #######" << endl;
-
-      Eigen::JacobiSVD<Eigen::MatrixXd> svd(fieldWeights.array().cwiseInverse().matrix().asDiagonal()*snapMatrix, Eigen::ComputeThinU | Eigen::ComputeThinV);
-
-      Info << "####### End of SVD for " << problemName << " #######" <<
-            endl;
-
-      eigenValueseig = svd.singularValues().real();
-      eigenVectoreig = svd.matrixU().real();
-    }
-
-    modesSVD = eigenVectoreig.bottomRows(vectorial_dim*n_cells);
-    modesSVDBoundary = eigenVectoreig.topRows(n_boundary_cells);
-    fieldWeights.conservativeResize(fieldWeights.rows()-fieldWeightsBoundary.rows());
-    
-    cnpy::save(eigenValueseig, "ITHACAoutput/" + problemName + "/ModesSVD/eigenvalues.npy");
-
-    eigenValueseig = eigenValueseig / eigenValueseig.sum();
-    Eigen::VectorXd cumEigenValues(eigenValueseig);
-
-    for (label j = 1; j < cumEigenValues.size(); ++j)
-    {
-        cumEigenValues(j) += cumEigenValues(j - 1);
+        Info << "Reading the existing modes" << endl;
+        cnpy::load(modesSVD, folderSVD + "/modes.npy");
+        cnpy::load(modesSVDBoundary,
+                   "ITHACAoutput/" + problemName + "/ModesSVD/modesBoundary.npy");
+        cnpy::load(fieldWeights, folderSVD + "/normalizingWeights.npy");
+        cnpy::load(fieldWeightsBoundary,
+                   "ITHACAoutput/" + problemName + "/ModesSVD/normalizingWeightsBoundary.npy");
     }
-
-    Eigen::saveMarketVector(eigenValueseig,
-                            "ITHACAoutput/" + problemName + "/ModesSVD/Eigenvalues_" + problemName, para->precision,
-                            para->outytpe);
-    Eigen::saveMarketVector(cumEigenValues,
-                            "ITHACAoutput/" + problemName + "/ModesSVD/CumEigenvalues_" + problemName, para->precision,
-                            para->outytpe);
-    cnpy::save(modesSVD, "ITHACAoutput/" + problemName + "/ModesSVD/modes.npy");
-    cnpy::save(modesSVDBoundary, "ITHACAoutput/" + problemName + "/ModesSVD/modesBoundary.npy");
-
-    if (saveModesFlag)
-    {
-      unsigned int rowIndex{0};
-      unsigned int rowIndexBoundary{0};
-      for (unsigned int modeIndex = 0; modeIndex < modesSVD.cols(); modeIndex++)
-      {
-        std::apply([this, &modesSVD,  &modesSVDBoundary, &rowIndex, &modeIndex, &rowIndexBoundary, &folderSVD](auto& ...snapList){(..., saveModes(snapList, modesSVD, modesSVDBoundary, rowIndex, rowIndexBoundary, modeIndex, folderSVD));}, snapshotsListTuple);
-        rowIndex = 0;
-      }
-    }
-  }
-  else
-  {
-    Info << "Reading the existing modes" << endl;
-    cnpy::load(modesSVD, folderSVD + "/modes.npy");
-    cnpy::load(modesSVDBoundary, "ITHACAoutput/" + problemName + "/ModesSVD/modesBoundary.npy");
-    cnpy::load(fieldWeights, folderSVD + "/normalizingWeights.npy");
-    cnpy::load(fieldWeightsBoundary, "ITHACAoutput/" + problemName + "/ModesSVD/normalizingWeightsBoundary.npy");
-  }
 }
 
 template <typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights)
+void HyperReduction<SnapshotsLists...>::getSnapMatrix(Eigen::MatrixXd&
+        snapMatrix, Eigen::VectorXd& fieldWeights)
 {
-  std::apply([this, &fieldWeights, &snapMatrix](auto& ...snapList){(..., stackSnapshots(snapList, snapMatrix, fieldWeights));}, snapshotsListTuple);
+    std::apply([this, & fieldWeights, & snapMatrix](auto& ...snapList)
+    {
+        (..., stackSnapshots(snapList, snapMatrix, fieldWeights));
+    }, snapshotsListTuple);
 }
 
 template <typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::getSnapMatrix(Eigen::MatrixXd& snapMatrix, Eigen::VectorXd& fieldWeights, List<Eigen::MatrixXd>& snapMatrixBoundary, List<Eigen::VectorXd>& fieldWeightsBoundary)
+void HyperReduction<SnapshotsLists...>::getSnapMatrix(Eigen::MatrixXd&
+        snapMatrix, Eigen::VectorXd& fieldWeights,
+        List<Eigen::MatrixXd> & snapMatrixBoundary,
+        List<Eigen::VectorXd> & fieldWeightsBoundary)
 {
-  fieldWeightsBoundary.resize(n_boundary_patches);
-  snapMatrixBoundary.resize(n_boundary_patches);
+    fieldWeightsBoundary.resize(n_boundary_patches);
+    snapMatrixBoundary.resize(n_boundary_patches);
+    std::apply([this, & fieldWeights, & snapMatrix, & fieldWeightsBoundary,
+                & snapMatrixBoundary](auto& ...snapList)
+    {
+        (..., stackSnapshots(snapList, snapMatrix, fieldWeights));
+        (..., stackSnapshotsBoundary(snapList, snapMatrixBoundary,
+                                     fieldWeightsBoundary));
+    },
 
-  std::apply([this, &fieldWeights, &snapMatrix, &fieldWeightsBoundary, &snapMatrixBoundary](auto& ...snapList){
-    (..., stackSnapshots(snapList, snapMatrix, fieldWeights));
-    (..., stackSnapshotsBoundary(snapList, snapMatrixBoundary, fieldWeightsBoundary));},
-  snapshotsListTuple);
+    snapshotsListTuple);
 }
 
 template <typename... SnapshotsLists>
 template <typename SnapshotsList>
-void HyperReduction<SnapshotsLists...>::saveModes(SnapshotsList sList, Eigen::MatrixXd& snapshotsMatrix, unsigned int &rowIndex, unsigned int &modeIndex, word folder)
+void HyperReduction<SnapshotsLists...>::saveModes(SnapshotsList sList,
+        Eigen::MatrixXd& snapshotsMatrix, unsigned int& rowIndex,
+        unsigned int& modeIndex, word folder)
 {
-  unsigned int field_dim = get_field_dim<typename SnapshotsList::value_type>();
-  auto fieldName = sList[0].name();
-  unsigned int fieldSize = field_dim*sList[0].size();
-  Eigen::VectorXd fieldBlock = snapshotsMatrix.block(rowIndex, modeIndex, fieldSize, 1);
-  auto fieldOut = Foam2Eigen::Eigen2field(sList[0], fieldBlock , true);
-  rowIndex +=fieldSize;
-  ITHACAstream::exportSolution(fieldOut, name(modeIndex), folder);
+    unsigned int field_dim = get_field_dim<typename SnapshotsList::value_type>();
+    auto fieldName = sList[0].name();
+    unsigned int fieldSize = field_dim* sList[0].size();
+    Eigen::VectorXd fieldBlock = snapshotsMatrix.block(rowIndex, modeIndex,
+                                 fieldSize, 1);
+    auto fieldOut = Foam2Eigen::Eigen2field(sList[0], fieldBlock, true);
+    rowIndex += fieldSize;
+    ITHACAstream::exportSolution(fieldOut, name(modeIndex), folder);
 }
 
 template <typename... SnapshotsLists>
 template <typename SnapshotsList>
-void HyperReduction<SnapshotsLists...>::saveModes(SnapshotsList sList, Eigen::MatrixXd& snapshotsMatrix, Eigen::MatrixXd& snapshotsMatrixBoundary, unsigned int &rowIndex,  unsigned int& rowIndexBoundary, unsigned int &modeIndex, word folder)
+void HyperReduction<SnapshotsLists...>::saveModes(SnapshotsList sList,
+        Eigen::MatrixXd& snapshotsMatrix, Eigen::MatrixXd& snapshotsMatrixBoundary,
+        unsigned int& rowIndex,  unsigned int& rowIndexBoundary,
+        unsigned int& modeIndex, word folder)
 {
-  unsigned int field_dim = get_field_dim<typename SnapshotsList::value_type>();
-  auto fieldName = sList[0].name();
-  unsigned int fieldSize = field_dim*sList[0].size();
-
-  Eigen::VectorXd fieldBlock = snapshotsMatrix.block(rowIndex, modeIndex, fieldSize, 1);
-
-  List<Eigen::VectorXd> fieldBlockBoundary;
-  fieldBlockBoundary.resize(n_boundary_patches);
-  for (unsigned int id = 0; id < n_boundary_patches; id++)
-  {
-    unsigned int bfieldDim = field_dim*int(n_boundary_cells_list[id]);
-    fieldBlockBoundary[id] = snapshotsMatrixBoundary.block(rowIndexBoundary, modeIndex, bfieldDim, 1);
-    rowIndexBoundary+=bfieldDim;
-  }
-
-  auto fieldOut = Foam2Eigen::Eigen2field(sList[0], fieldBlock, fieldBlockBoundary);
-  rowIndex +=fieldSize;
-  
-  ITHACAstream::exportSolution(fieldOut, name(modeIndex), folder);
+    unsigned int field_dim = get_field_dim<typename SnapshotsList::value_type>();
+    auto fieldName = sList[0].name();
+    unsigned int fieldSize = field_dim* sList[0].size();
+    Eigen::VectorXd fieldBlock = snapshotsMatrix.block(rowIndex, modeIndex,
+                                 fieldSize, 1);
+    List<Eigen::VectorXd> fieldBlockBoundary;
+    fieldBlockBoundary.resize(n_boundary_patches);
+
+    for (unsigned int id = 0; id < n_boundary_patches; id++)
+    {
+        unsigned int bfieldDim = field_dim* int(n_boundary_cells_list[id]);
+        fieldBlockBoundary[id] = snapshotsMatrixBoundary.block(rowIndexBoundary,
+                                 modeIndex, bfieldDim, 1);
+        rowIndexBoundary += bfieldDim;
+    }
+
+    auto fieldOut = Foam2Eigen::Eigen2field(sList[0], fieldBlock,
+                                            fieldBlockBoundary);
+    rowIndex += fieldSize;
+    ITHACAstream::exportSolution(fieldOut, name(modeIndex), folder);
 }
 
 template <typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights, word folderMethodName)
+void HyperReduction<SnapshotsLists...>::offlineGappyDEIM(
+    Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights,
+    word folderMethodName)
 {
-  folderMethod = folderMethodName;
-  Info << "FolderMethod : " << folderMethod << endl;
-  mkDir(folderMethod);
-
-  normalizingWeights = weights;
-
-  nodePoints = autoPtr<IOList<label>>(new IOList<label>(
-      IOobject("nodePoints", para->runTime.time().constant(), "../" + folderMethod,
-                para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE))); 
-
-  auto greedyMetric = para->ITHACAdict->lookupOrDefault<word>("GreedyMetric", "L2");
-  
-  bool offlineStage = !nodePoints().headerOk();
-
-  if (offlineStage)
-  {
-    assert(n_modes > 0);
-    assert(n_nodes >= n_modes);
-
-    Eigen::VectorXd mp_not_mask = Eigen::VectorXd::Constant(n_cells * vectorial_dim, 1);
-    std::set<label> nodePointsSet;
-
-    // set initialSeeds
-    if (initialSeeds.rows() > 0)
+    folderMethod = folderMethodName;
+    Info << "FolderMethod : " << folderMethod << endl;
+    mkDir(folderMethod);
+    normalizingWeights = weights;
+    nodePoints = autoPtr<IOList<label>>(new IOList<label>(
+                                            IOobject("nodePoints", para->runTime.time().constant(), "../" + folderMethod,
+                                                para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
+    auto greedyMetric = para->ITHACAdict->lookupOrDefault<word>("GreedyMetric",
+                        "L2");
+    bool offlineStage = !nodePoints().headerOk();
+
+    if (offlineStage)
     {
-      initSeeds(mp_not_mask, nodePointsSet);
-    }
+        assert(n_modes > 0);
+        assert(n_nodes >= n_modes);
+        Eigen::VectorXd mp_not_mask = Eigen::VectorXd::Constant(n_cells* vectorial_dim,
+                                      1);
+        std::set<label> nodePointsSet;
+
+        // set initialSeeds
+        if (initialSeeds.rows() > 0)
+        {
+            initSeeds(mp_not_mask, nodePointsSet);
+        }
 
-    int na = n_nodes - initialSeeds.rows();
-    if (na > 0)
-    {
-      Eigen::SparseMatrix<double> reshapeMat;
-      initReshapeMat(reshapeMat);
-
-      if (greedyMetric=="L2")
-      {
-        Info << "####### Begin Greedy-L2 GappyDEIM #######" << endl;
-        Info << "####### Modes=" <<  n_modes
-              << ", nodePoints=" << n_nodes << " #######"
-              << endl;
-
-        int nb = 0;
-        int nit = std::min(n_modes, na);
-        int ncimin = std::floor(n_modes / nit);
-        int naimin = std::floor(na / n_modes);
-        Eigen::MatrixXd A;
-        Eigen::VectorXd b;
-        Eigen::VectorXd c;
-        Eigen::VectorXd r;
-        label ind_max, c1;
-        double max;
-
-        for (int i = 1; i <= nit; i++)
+        int na = n_nodes - initialSeeds.rows();
+
+        if (na > 0)
         {
-          int nci = ncimin;
-          // add the remaining modes in the quotient n_modes / nite
-          if (i <= n_modes % nit)
-          {
-              nci = ncimin + 1;
-          }
-          int nai = naimin;
-          // add the remaining nodePoints in the quotient na / n_modes
-          if (i <= na % n_modes)
-          {
-              nai = naimin + 1;
-          }
-
-          Eigen::MatrixXd V;
-
-          // select basis
-          if (i == 1)
-          {
-              V = snapshotsModes.leftCols(nci);
-          }
-          else
-          {
-            for (int q = 1; q <= nci; q++)
+            Eigen::SparseMatrix<double> reshapeMat;
+            initReshapeMat(reshapeMat);
+
+            if (greedyMetric == "L2")
             {
-                A = P.transpose() * basisMatrix;
-                b = P.transpose() * snapshotsModes.col(nb + q - 1);
-                c = A.fullPivLu().solve(b);
-                r = snapshotsModes.col(nb + q - 1) - basisMatrix * c;
-                V.conservativeResize(snapshotsModes.rows(), q);
-                V.col(q - 1) = r;
+                Info << "####### Begin Greedy-L2 GappyDEIM #######" << endl;
+                Info << "####### Modes=" <<  n_modes
+                     << ", nodePoints=" << n_nodes << " #######"
+                     << endl;
+                int nb = 0;
+                int nit = std::min(n_modes, na);
+                int ncimin = std::floor(n_modes / nit);
+                int naimin = std::floor(na / n_modes);
+                Eigen::MatrixXd A;
+                Eigen::VectorXd b;
+                Eigen::VectorXd c;
+                Eigen::VectorXd r;
+                label ind_max, c1;
+                double max;
+
+                for (int i = 1; i <= nit; i++)
+                {
+                    int nci = ncimin;
+
+                    // add the remaining modes in the quotient n_modes / nite
+                    if (i <= n_modes % nit)
+                    {
+                        nci = ncimin + 1;
+                    }
+
+                    int nai = naimin;
+
+                    // add the remaining nodePoints in the quotient na / n_modes
+                    if (i <= na % n_modes)
+                    {
+                        nai = naimin + 1;
+                    }
+
+                    Eigen::MatrixXd V;
+
+                    // select basis
+                    if (i == 1)
+                    {
+                        V = snapshotsModes.leftCols(nci);
+                    }
+                    else
+                    {
+                        for (int q = 1; q <= nci; q++)
+                        {
+                            A = P.transpose() * basisMatrix;
+                            b = P.transpose() * snapshotsModes.col(nb + q - 1);
+                            c = A.fullPivLu().solve(b);
+                            r = snapshotsModes.col(nb + q - 1) - basisMatrix* c;
+                            V.conservativeResize(snapshotsModes.rows(), q);
+                            V.col(q - 1) = r;
+                        }
+                    }
+
+                    for (int j = 1; j <= nai; j++)
+                    {
+                        if (P.cols() > 0)
+                        {
+                            max = (reshapeMat*(mp_not_mask.asDiagonal() * V)
+                                   .rowwise()
+                                   .lpNorm<2>().array().square().matrix())
+                                  .maxCoeff( & ind_max, & c1);
+                        }
+                        else
+                        {
+                            max = (reshapeMat* V.rowwise().lpNorm<2>().array().square().matrix()).maxCoeff(
+                                      & ind_max, & c1);
+                        }
+
+                        updateNodes(P, ind_max, mp_not_mask);
+                    }
+
+                    nb += nci;
+                    basisMatrix = snapshotsModes.leftCols(nb);
+                }
+
+                Info << "####### End of greedy GappyDEIM #######\n";
             }
-          }
-
-          for (int j = 1; j <= nai; j++)
-          {
-            if (P.cols() > 0)
+            else if (greedyMetric == "SOPT")
             {
-              max = (reshapeMat*(mp_not_mask.asDiagonal() * V)
-                      .rowwise()
-                      .lpNorm<2>().array().square().matrix())
-                      .maxCoeff(&ind_max, &c1);
+                Info << "####### Begin SOPT GappyDEIM #######" << endl;
+                Info << "####### Modes=" <<  n_modes
+                     << ", nodePoints=" << n_nodes << " #######"
+                     << endl;
+                label ind_max, c1;
+                double max;
+                Eigen::MatrixXd V = snapshotsModes.leftCols(n_modes);
+
+                for (unsigned int ith_node = 0; ith_node < na; ith_node++)
+                {
+                    if (P.cols() > 0)
+                    {
+                        // TODO make efficient
+                        Eigen::MatrixXd tmp = P.transpose() * V;
+                        Eigen::MatrixXd R = mp_not_mask.asDiagonal() * V;
+                        Eigen::MatrixXd inv = (tmp.transpose() * tmp).fullPivLu().inverse();
+                        Eigen::VectorXd num = 1 + (reshapeMat*((R* inv).array() *
+                                                               R.array()).rowwise().sum().matrix()).array();
+                        Eigen::VectorXd norma = (tmp.array().square()).colwise().sum();
+                        Eigen::MatrixXd adding = reshapeMat* R.array().square().matrix();
+                        adding.rowwise() += norma.transpose();
+                        Eigen::VectorXd denom = (adding.array().pow(1. /
+                                                 V.cols()).matrix()).rowwise().prod();
+                        max = ((mp_not_mask.head(n_cells).asDiagonal() * num).array() /
+                               denom.array()).maxCoeff( & ind_max, & c1);
+                    }
+                    else
+                    {
+                        max = (reshapeMat* V.rowwise().lpNorm<2>().array().square().matrix()).maxCoeff(
+                                  & ind_max, & c1);
+                    }
+
+                    updateNodes(P, ind_max, mp_not_mask);
+                }
+
+                basisMatrix = V;
+                Info << "####### End of SOPT GappyDEIM #######\n";
             }
-            else
+            else if (greedyMetric == "SOPTE")
             {
-              max = (reshapeMat*V.rowwise().lpNorm<2>().array().square().matrix()).maxCoeff(&ind_max, &c1);
+                Info << "####### Begin SOPT-exact GappyDEIM #######" << endl;
+                Info << "####### Modes=" <<  n_modes
+                     << ", nodePoints=" << n_nodes << " #######"
+                     << endl;
+                label ind_max, c1;
+                double max;
+                Eigen::MatrixXd A;
+                Eigen::VectorXd b;
+                Eigen::VectorXd c;
+                Eigen::VectorXd r;
+                Eigen::MatrixXd V = snapshotsModes.col(0);
+                max = (reshapeMat* (mp_not_mask.asDiagonal() * snapshotsModes.leftCols(
+                                        n_modes)).rowwise().lpNorm<2>().array().square().matrix()).maxCoeff( & ind_max,
+                                            & c1);
+                updateNodes(P, ind_max, mp_not_mask);
+
+                for (unsigned int ith_node = 1; ith_node < na; ith_node++)
+                {
+                    if (ith_node < n_modes)
+                    {
+                        A = P.transpose() * V;
+                        b = P.transpose() * snapshotsModes.col(ith_node);
+                        c = A.fullPivLu().solve(b);
+                        r = snapshotsModes.col(ith_node) - V* c;
+                        V.conservativeResize(snapshotsModes.rows(), ith_node + 1);
+                        V.col(ith_node) =  snapshotsModes.col(ith_node);
+                        max = (reshapeMat* r.rowwise().lpNorm<2>().array().square().matrix()).maxCoeff(
+                                  & ind_max, & c1);
+                    }
+                    else
+                    {
+                        // TODO optimize
+                        Eigen::MatrixXd tmp = P.transpose() * snapshotsModes.leftCols(n_modes);
+                        Info << "SOPT: " << s_optimality(tmp) << endl;
+                        tmp.conservativeResize(tmp.rows() + vectorial_dim, tmp.cols());
+                        Eigen::MatrixXd masked = mp_not_mask.asDiagonal() * snapshotsModes.leftCols(
+                                                     n_modes);
+                        Eigen::VectorXd results(n_cells);
+
+                        for (unsigned int ith_cell = 0; ith_cell < n_cells; ith_cell++)
+                        {
+                            for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+                            {
+                                tmp.row(tmp.rows() - vectorial_dim + ith_field) = masked.row(
+                                        ith_cell +  ith_field* n_cells);
+                            }
+
+                            results(ith_cell) = s_optimality(tmp);
+                        }
+
+                        max = results.maxCoeff( & ind_max, & c1);
+                    }
+
+                    updateNodes(P, ind_max, mp_not_mask);
+                }
+
+                basisMatrix = snapshotsModes.leftCols(n_modes);
+                Info << "####### End of SOPTE GappyDEIM #######\n";
             }
-            
-            updateNodes(P, ind_max, mp_not_mask);
-          }
-
-          nb += nci;
-          basisMatrix = snapshotsModes.leftCols(nb);
         }
-        Info << "####### End of greedy GappyDEIM #######\n";
-      }
-      else if (greedyMetric=="SOPT")
-      {
-        Info << "####### Begin SOPT GappyDEIM #######" << endl;
-        Info << "####### Modes=" <<  n_modes
-              << ", nodePoints=" << n_nodes << " #######"
-              << endl;
-
-        label ind_max, c1;
-        double max;
-        Eigen::MatrixXd V = snapshotsModes.leftCols(n_modes);
-
-        for (unsigned int ith_node = 0; ith_node < na; ith_node++)
+        else
         {
-          if (P.cols() > 0)
-          {
-            // TODO make efficient
-            Eigen::MatrixXd tmp = P.transpose()*V;
-            Eigen::MatrixXd R = mp_not_mask.asDiagonal() * V;
-            Eigen::MatrixXd inv = (tmp.transpose()*tmp).fullPivLu().inverse();
-            Eigen::VectorXd num = 1 + (reshapeMat*((R * inv).array()*R.array()).rowwise().sum().matrix()).array();
-            Eigen::VectorXd norma = (tmp.array().square()).colwise().sum();
-            Eigen::MatrixXd adding = reshapeMat*R.array().square().matrix();
-            adding.rowwise() += norma.transpose();
-            Eigen::VectorXd denom = (adding.array().pow(1./V.cols()).matrix()).rowwise().prod();
-
-            max = ((mp_not_mask.head(n_cells).asDiagonal()*num).array()/denom.array()).maxCoeff(&ind_max, &c1);
-          }
-          else
-          {
-            max = (reshapeMat*V.rowwise().lpNorm<2>().array().square().matrix()).maxCoeff(&ind_max, &c1);
-          }
-
-          updateNodes(P, ind_max, mp_not_mask);
+            basisMatrix = snapshotsModes.leftCols(n_modes);
+            Info << "####### InitialSeeds equal to n_nodes #######\n";
         }
-        basisMatrix = V;
-        Info << "####### End of SOPT GappyDEIM #######\n";
-      }
-      else if (greedyMetric=="SOPTE")
-      {
-        Info << "####### Begin SOPT-exact GappyDEIM #######" << endl;
-        Info << "####### Modes=" <<  n_modes
-              << ", nodePoints=" << n_nodes << " #######"
-              << endl;
-
-        label ind_max, c1;
-        double max;
-        Eigen::MatrixXd A;
-        Eigen::VectorXd b;
-        Eigen::VectorXd c;
-        Eigen::VectorXd r;
-        Eigen::MatrixXd V = snapshotsModes.col(0);
-
-        max = (reshapeMat* (mp_not_mask.asDiagonal()*snapshotsModes.leftCols(n_modes)).rowwise().lpNorm<2>().array().square().matrix()).maxCoeff(&ind_max, &c1);
-        updateNodes(P, ind_max, mp_not_mask);
-
-        for (unsigned int ith_node = 1; ith_node < na; ith_node++)
-        {
-          if (ith_node<n_modes)
-          {
-            A = P.transpose() * V;
-            b = P.transpose() * snapshotsModes.col(ith_node);
-            c = A.fullPivLu().solve(b);
-            r = snapshotsModes.col(ith_node) - V * c;
-            V.conservativeResize(snapshotsModes.rows(), ith_node + 1);
-            V.col(ith_node) =  snapshotsModes.col(ith_node);
-
-            max = (reshapeMat*r.rowwise().lpNorm<2>().array().square().matrix()).maxCoeff(&ind_max, &c1);
-          }
-          else
-          {
-            // TODO optimize
-            Eigen::MatrixXd tmp = P.transpose()*snapshotsModes.leftCols(n_modes);
-            Info << "SOPT: " << s_optimality(tmp) << endl;
-            tmp.conservativeResize(tmp.rows()+vectorial_dim, tmp.cols());
-            
-            Eigen::MatrixXd masked = mp_not_mask.asDiagonal()*snapshotsModes.leftCols(n_modes);
-
-            Eigen::VectorXd results(n_cells);
-
-            for (unsigned int ith_cell = 0; ith_cell < n_cells; ith_cell++)
-            {
-              for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-              {
-                tmp.row(tmp.rows()-vectorial_dim+ith_field) = masked.row(ith_cell +  ith_field*n_cells);
-              }
-              results(ith_cell) = s_optimality(tmp);
-            }
-            max = results.maxCoeff(&ind_max, &c1);
-          }
 
-          updateNodes(P, ind_max, mp_not_mask);
-        }
-        basisMatrix = snapshotsModes.leftCols(n_modes);
-        Info << "####### End of SOPTE GappyDEIM #######\n";
-      }
+        evaluatePinv(P, basisMatrix, normalizingWeights);
+        renormalizedBasisMatrix = normalizingWeights.asDiagonal() * basisMatrix;
+        MatrixOnline = renormalizedBasisMatrix* pinvPU;
+        P.makeCompressed();
+        cnpy::save(basisMatrix, folderMethod + "/basisMatrix.npy");
+        cnpy::save(P, folderMethod + "/projectionMatrix.npz");
+        cnpy::save(normalizingWeights, folderMethod + "/normalizingWeights.npy");
+        cnpy::save(nodes, folderMethod + "/mp.npy");
+        cnpy::save(pinvPU, folderMethod + "/pinvPU.npy");
+        cnpy::save(MatrixOnline, folderMethod + "/MatrixOnline.npy");
+        nodePoints().write();
+        Info << "Projection Matrix shape: " << P.rows() << " " << P.cols() << endl;
+        Info << "Basis Matrix shape: " << basisMatrix.rows() << " " <<
+             basisMatrix.cols() << endl;
+        Info << "Pseudo Inverse Matrix shape: " << pinvPU.rows() << " " << pinvPU.cols()
+             << endl;
     }
     else
     {
-      basisMatrix = snapshotsModes.leftCols(n_modes);
-      Info << "####### InitialSeeds equal to n_nodes #######\n";
+        Info << "Read GappyDEIM\n";
+        cnpy::load(basisMatrix, folderMethod + "/basisMatrix.npy");
+        cnpy::load(MatrixOnline, folderMethod + "/MatrixOnline.npy");
+        cnpy::load(normalizingWeights, folderMethod + "/normalizingWeights.npy");
+        cnpy::load(P, folderMethod + "/projectionMatrix.npz");
+        cnpy::load(nodes, folderMethod + "/mp.npy");
+        cnpy::load(pinvPU, folderMethod + "/pinvPU.npy");
+        renormalizedBasisMatrix = normalizingWeights.asDiagonal() * basisMatrix;
+        Info << "Projection Matrix shape: " << P.rows() << " " << P.cols() << endl;
+        Info << "Basis Matrix shape: " << basisMatrix.rows() << " " <<
+             basisMatrix.cols() << endl;
+        Info << "Pseudo Inverse Matrix shape: " << pinvPU.rows() << " " << pinvPU.cols()
+             << endl;
     }
-
-    evaluatePinv(P, basisMatrix, normalizingWeights);
-    renormalizedBasisMatrix = normalizingWeights.asDiagonal()*basisMatrix;
-
-    MatrixOnline = renormalizedBasisMatrix * pinvPU;
-
-    P.makeCompressed();
-    cnpy::save(basisMatrix, folderMethod +"/basisMatrix.npy");
-    cnpy::save(P, folderMethod +"/projectionMatrix.npz");
-    cnpy::save(normalizingWeights, folderMethod + "/normalizingWeights.npy");
-    cnpy::save(nodes, folderMethod + "/mp.npy");
-    cnpy::save(pinvPU, folderMethod + "/pinvPU.npy");
-    cnpy::save(MatrixOnline, folderMethod + "/MatrixOnline.npy");
-    nodePoints().write();
-
-    Info << "Projection Matrix shape: " << P.rows() << " " << P.cols() << endl;
-    Info << "Basis Matrix shape: " << basisMatrix.rows() << " " << basisMatrix.cols() << endl;
-    Info << "Pseudo Inverse Matrix shape: " << pinvPU.rows() << " " << pinvPU.cols() << endl;
-  }
-  else
-  {
-    Info << "Read GappyDEIM\n";
-    cnpy::load(basisMatrix, folderMethod +"/basisMatrix.npy");
-    cnpy::load(MatrixOnline, folderMethod +"/MatrixOnline.npy");
-    cnpy::load(normalizingWeights, folderMethod + "/normalizingWeights.npy");
-    cnpy::load(P, folderMethod +"/projectionMatrix.npz");
-    cnpy::load(nodes, folderMethod + "/mp.npy");
-    cnpy::load(pinvPU, folderMethod + "/pinvPU.npy");
-
-    renormalizedBasisMatrix = normalizingWeights.asDiagonal()*basisMatrix;
-    
-    Info << "Projection Matrix shape: " << P.rows() << " " << P.cols() << endl;
-    Info << "Basis Matrix shape: " << basisMatrix.rows() << " " << basisMatrix.cols() << endl;
-    Info << "Pseudo Inverse Matrix shape: " << pinvPU.rows() << " " << pinvPU.cols() << endl;
-  }
 }
 
 template <typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd& snapshotsModes, Eigen::VectorXd& weights, word folderMethodName)
+void HyperReduction<SnapshotsLists...>::offlineECP(Eigen::MatrixXd&
+        snapshotsModes, Eigen::VectorXd& weights, word folderMethodName)
 {
-  folderMethod = folderMethodName;
-  Info << "FolderMethod : " << folderMethod << endl;
-  mkDir(folderMethod);
-
-  n_nodes = n_modes + 1;
-
-  normalizingWeights = weights;
-
-  Info << "####### Begin ECP #######" << endl;
-  Info << "####### Modes=" <<  n_modes
-            << ", nodePoints=" << n_nodes << " #######"
-            << endl;
-
-  nodePoints = autoPtr<IOList<label>>(new IOList<label>(
-      IOobject("nodePoints", para->runTime.time().constant(), "../" + folderMethod,
-                para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE))); 
-  
-  bool offlineStage = !nodePoints().headerOk();
+    folderMethod = folderMethodName;
+    Info << "FolderMethod : " << folderMethod << endl;
+    mkDir(folderMethod);
+    n_nodes = n_modes + 1;
+    normalizingWeights = weights;
+    Info << "####### Begin ECP #######" << endl;
+    Info << "####### Modes=" <<  n_modes
+         << ", nodePoints=" << n_nodes << " #######"
+         << endl;
+    nodePoints = autoPtr<IOList<label>>(new IOList<label>(
+                                            IOobject("nodePoints", para->runTime.time().constant(), "../" + folderMethod,
+                                                para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
+    bool offlineStage = !nodePoints().headerOk();
+
+    if (offlineStage)
+    {
+        assert(n_modes > 0);
+        assert(n_nodes >= n_modes);
+        // matrices for quadratureWeights evaluation
+        Eigen::MatrixXd J;//shape: (vectorial_dim * (n_modes + 1), nodePoints->size())
+        Eigen::MatrixXd Jwhole(vectorial_dim * (n_modes + 1), n_cells);
+        Eigen::VectorXd q(vectorial_dim * (n_modes + 1));
+        // matrices for greedy selection of the nodes
+        Eigen::MatrixXd A(vectorial_dim* n_modes, n_cells);
+        Eigen::VectorXd b = Eigen::VectorXd::Constant(vectorial_dim* n_modes, 1);
+        Eigen::VectorXd volumes = ITHACAutilities::getMassMatrixFV(std::get<0>
+                                  (snapshotsListTuple)[0]);
+        double volume = volumes.array().sum();
 
-  if (offlineStage)
-  {
-    assert(n_modes > 0);
-    assert(n_nodes >= n_modes);
+        for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+        {
+            Eigen::MatrixXd block = snapshotsModes.block(ith_field* n_cells, 0, n_cells,
+                                    n_modes).transpose();
+            q.segment(ith_field*(n_modes + 1), n_modes) = block.rowwise().sum();
+            q(ith_field*(n_modes + 1) + n_modes) = volume;
+            Jwhole.middleRows(ith_field*(n_modes + 1), n_modes) = block;
+            Jwhole.row(ith_field*(n_modes + 1) + n_modes) = Eigen::VectorXd::Constant(
+                      n_cells, 1);
+            Eigen::VectorXd mean = block.rowwise().mean();
+            block.colwise() -= mean;
+            Eigen::VectorXd Anorm = block.colwise().lpNorm<2>();
+
+            if (Anorm.minCoeff() > 0)
+            {
+                block.array().rowwise() /= Anorm.transpose().array();
+            }
 
-    // matrices for quadratureWeights evaluation
-    Eigen::MatrixXd J;//shape: (vectorial_dim * (n_modes + 1), nodePoints->size())
-    Eigen::MatrixXd Jwhole(vectorial_dim * (n_modes + 1), n_cells);
-    Eigen::VectorXd q(vectorial_dim * (n_modes + 1));
+            A.middleRows(ith_field* n_modes, n_modes) = block;
+        }
 
-    // matrices for greedy selection of the nodes
-    Eigen::MatrixXd A(vectorial_dim*n_modes, n_cells);
-    Eigen::VectorXd b = Eigen::VectorXd::Constant(vectorial_dim*n_modes, 1);
+        Eigen::VectorXd mp_not_mask = Eigen::VectorXd::Constant(n_cells* vectorial_dim,
+                                      1);
+        std::set<label> nodePointsSet;
 
-    Eigen::VectorXd volumes = ITHACAutilities::getMassMatrixFV(std::get<0>(snapshotsListTuple)[0]);
-    double volume = volumes.array().sum();
-    for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-    {
-      Eigen::MatrixXd block = snapshotsModes.block(ith_field*n_cells, 0, n_cells, n_modes).transpose();
+        // set initialSeeds
+        if (initialSeeds.rows() > 0)
+        {
+            initialSeeds(mp_not_mask, nodePointsSet);
+            computeLS(J, Jwhole, b, q);
+        }
 
-      q.segment(ith_field*(n_modes+1), n_modes) = block.rowwise().sum();
-      q(ith_field*(n_modes+1)+n_modes) = volume;
+        int na = n_nodes - initialSeeds.rows();
+        Eigen::SparseMatrix<double> reshapeMat;
+        initReshapeMat(reshapeMat);
 
-      Jwhole.middleRows(ith_field*(n_modes+1), n_modes) = block;
-      Jwhole.row(ith_field*(n_modes+1)+n_modes) = Eigen::VectorXd::Constant(n_cells, 1);
+        if (na > 0)
+        {
+            label ind_max, r1;
+            double max;
 
-      Eigen::VectorXd mean = block.rowwise().mean();
-      block.colwise() -= mean;
-      Eigen::VectorXd Anorm = block.colwise().lpNorm<2>();
-      if (Anorm.minCoeff()> 0)
-      {
-        block.array().rowwise() /= Anorm.transpose().array();
-      }
+            for (unsigned int ith_node = 0; ith_node < na; ith_node++)
+            {
+                max = ((b.transpose() * A* mp_not_mask.head(
+                            n_cells).asDiagonal()).colwise().sum()).maxCoeff( & r1, & ind_max);
+                updateNodes(P, ind_max, mp_not_mask);
+                computeLS(J, Jwhole, b, q);
+            }
+        }
 
-      A.middleRows(ith_field*n_modes, n_modes) = block;
+        Info << "####### End ECP #######" << endl;
+        basisMatrix = snapshotsModes.leftCols(n_modes);
+        evaluateWPU(P, basisMatrix, normalizingWeights, quadratureWeights);
+        cnpy::save(basisMatrix, folderMethod + "/basisMatrix.npy");
+        cnpy::save(quadratureWeights, folderMethod + "/quadratureWeights.npy");
+        cnpy::save(normalizingWeights, folderMethod + "/normalizingWeights.npy");
+        cnpy::save(nodes, folderMethod + "/mp.npy");
+        cnpy::save(wPU, folderMethod + "/wPU.npy");
+        nodePoints().write();
     }
-    Eigen::VectorXd mp_not_mask = Eigen::VectorXd::Constant(n_cells * vectorial_dim, 1);
-    std::set<label> nodePointsSet;
-
-    // set initialSeeds
-    if (initialSeeds.rows() > 0)
+    else
     {
-      initialSeeds(mp_not_mask, nodePointsSet);
-      computeLS(J, Jwhole, b, q);
+        Info << "Read ECP\n";
+        cnpy::load(basisMatrix, folderMethod + "/basisMatrix.npy");
+        cnpy::load(quadratureWeights, folderMethod + "/quadratureWeights.npy");
+        cnpy::load(normalizingWeights, folderMethod + "/normalizingWeights.npy");
+        cnpy::load(nodes, folderMethod + "/mp.npy");
+        cnpy::load(wPU, folderMethod + "/wPU.npy");
     }
+}
 
-    int na = n_nodes - initialSeeds.rows();
-    Eigen::SparseMatrix<double> reshapeMat;
-    initReshapeMat(reshapeMat);
+template<typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::initSeeds(Eigen::VectorXd mp_not_mask,
+        std::set<label> nodePointsSet)
+{
+    P.resize(n_cells* vectorial_dim, initialSeeds.rows() * vectorial_dim);
+    P.reserve(Eigen::VectorXi::Constant(initialSeeds.rows() *
+                                        vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
+    unsigned int trueSeeds{0};
 
-    if (na > 0)
+    for (int i = 0; i < initialSeeds.rows(); i++)
     {
-      label ind_max, r1;
-      double max;
+        unsigned int index = initialSeeds(i) % n_cells;
 
-      for (unsigned int ith_node = 0; ith_node < na; ith_node++)
-      {
-        max = ((b.transpose()*A*mp_not_mask.head(n_cells).asDiagonal()).colwise().sum()).maxCoeff(&r1, &ind_max);
+        // check that there are not repeated nodes in initialSeeds
+        if (nodePointsSet.find(index) == nodePointsSet.end())
+        {
+            nodePointsSet.insert(index);
+            nodePoints->append(index);
 
-        updateNodes(P, ind_max, mp_not_mask);
-        computeLS(J, Jwhole, b, q);
-      }
+            for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+            {
+                P.insert(index + ith_field* n_cells, vectorial_dim* trueSeeds + ith_field) = 1;
+                mp_not_mask(index + ith_field* n_cells) = 0;
+            }
+
+            trueSeeds++;
+        }
     }
 
-    Info << "####### End ECP #######" << endl;
-
-    basisMatrix = snapshotsModes.leftCols(n_modes);
-    evaluateWPU(P, basisMatrix, normalizingWeights, quadratureWeights);
-
-    cnpy::save(basisMatrix, folderMethod +"/basisMatrix.npy");
-    cnpy::save(quadratureWeights, folderMethod +"/quadratureWeights.npy");
-    cnpy::save(normalizingWeights, folderMethod +"/normalizingWeights.npy");
-    cnpy::save(nodes, folderMethod + "/mp.npy");
-    cnpy::save(wPU, folderMethod + "/wPU.npy");
-    nodePoints().write();
-  }
-  else
-  {
-    Info << "Read ECP\n";
-    cnpy::load(basisMatrix, folderMethod +"/basisMatrix.npy");
-    cnpy::load(quadratureWeights, folderMethod +"/quadratureWeights.npy");
-    cnpy::load(normalizingWeights, folderMethod +"/normalizingWeights.npy");
-    cnpy::load(nodes, folderMethod + "/mp.npy");
-    cnpy::load(wPU, folderMethod + "/wPU.npy");
-  }
+    P.conservativeResize(P.rows(), nodePoints->size() * vectorial_dim);
+    P.makeCompressed();
+    M_Assert(nodePoints->size() <= n_nodes,
+             "Size of 'initialSeeds' is greater than 'n_nodes'");
 }
 
-template<typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::initSeeds(Eigen::VectorXd mp_not_mask, std::set<label> nodePointsSet)
+template <typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::updateNodes(Eigen::SparseMatrix<double>
+        & P, label& ind, Eigen::VectorXd& mp_not_mask)
 {
-  P.resize(n_cells * vectorial_dim, initialSeeds.rows() * vectorial_dim);
-  P.reserve(Eigen::VectorXi::Constant(initialSeeds.rows() * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
-
-  unsigned int trueSeeds{0};
-  for (int i = 0; i < initialSeeds.rows(); i++)
-  {
-    unsigned int index = initialSeeds(i) % n_cells;
-    // check that there are not repeated nodes in initialSeeds
-    if (nodePointsSet.find(index) == nodePointsSet.end()){
-      nodePointsSet.insert(index);
-      nodePoints->append(index);
-
-      for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-      {
-        P.insert(index+ith_field*n_cells, vectorial_dim*trueSeeds+ith_field) = 1;
-        mp_not_mask(index + ith_field * n_cells) = 0;
-      }
-      trueSeeds++;
+    nodePoints->append(ind);
+    nodes.conservativeResize(nodes.rows() + 1);
+    nodes(nodes.rows() - 1) = ind;
+    unsigned int last_col{0};
+
+    if (P.rows() == 0)
+    {
+        P.resize(n_cells* vectorial_dim, vectorial_dim);
+    }
+    else
+    {
+        last_col = P.cols();
+        P.resize(P.rows(), P.cols() + vectorial_dim);
     }
-  }
 
-  P.conservativeResize(P.rows(), nodePoints->size()*vectorial_dim);
-  P.makeCompressed();
-  M_Assert(nodePoints->size()<=n_nodes, "Size of 'initialSeeds' is greater than 'n_nodes'");
-}
+    int step = P.cols() / vectorial_dim - 1;
 
-template <typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::updateNodes(Eigen::SparseMatrix<double>& P, label& ind, Eigen::VectorXd& mp_not_mask)
-{
-  nodePoints->append(ind);
-
-  nodes.conservativeResize(nodes.rows()+1);
-  nodes(nodes.rows()-1) = ind;
-
-  unsigned int last_col{0};
-
-  if (P.rows()==0)
-  {
-    P.resize(n_cells*vectorial_dim, vectorial_dim);
-  }
-  else
-  {
-    last_col = P.cols();
-    P.resize(P.rows(), P.cols() + vectorial_dim);
-  }
-  int step = P.cols() / vectorial_dim - 1;
-  
-  for (int ith_node=0; ith_node <= step; ith_node++)
-  {
-    for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+    for (int ith_node = 0; ith_node <= step; ith_node++)
     {
-      P.insert(nodes[ith_node]+ith_field*n_cells,ith_node+ith_field*(step+1))=1;
+        for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+        {
+            P.insert(nodes[ith_node] + ith_field* n_cells,
+                     ith_node + ith_field*(step + 1)) = 1;
+        }
     }
-  }
 
-  for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-  {
-    mp_not_mask(ind + ith_field * n_cells) = 0;
-  }
+    for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+    {
+        mp_not_mask(ind + ith_field* n_cells) = 0;
+    }
 }
 
 template<typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::computeLS(Eigen::MatrixXd& J, Eigen::MatrixXd& Jwhole, Eigen::VectorXd& b, Eigen::VectorXd& q)
+void HyperReduction<SnapshotsLists...>::computeLS(Eigen::MatrixXd& J,
+        Eigen::MatrixXd& Jwhole, Eigen::VectorXd& b, Eigen::VectorXd& q)
 {
-  // TODO fix with only positive weights (NNLS)
-  J.resize(vectorial_dim * (n_modes + 1), nodePoints->size());
-  J = Jwhole(Eigen::indexing::all, nodes);
-
-  quadratureWeights.resize(nodePoints->size()*vectorial_dim);
-  for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-  {
-    quadratureWeights.segment(ith_field*nodePoints->size(), nodePoints->size()) = J.middleRows(ith_field*(n_modes+1), n_modes+1).colPivHouseholderQr().solve(q.segment(ith_field*(n_modes+1), n_modes+1));
-    b.segment(ith_field*n_modes, n_modes) = q.segment(ith_field*(n_modes+1), n_modes)-J.middleRows(ith_field*(n_modes+1), n_modes)*quadratureWeights.segment(ith_field*nodePoints->size(), nodePoints->size());
-  }
-  b = b/b.lpNorm<2>();
+    // TODO fix with only positive weights (NNLS)
+    J.resize(vectorial_dim * (n_modes + 1), nodePoints->size());
+    J = Jwhole(Eigen::indexing::all, nodes);
+    quadratureWeights.resize(nodePoints->size() * vectorial_dim);
+
+    for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+    {
+        quadratureWeights.segment(ith_field* nodePoints->size(),
+                                  nodePoints->size()) = J.middleRows(ith_field*(n_modes + 1),
+                                      n_modes + 1).colPivHouseholderQr().solve(q.segment(ith_field*(n_modes + 1),
+                                          n_modes + 1));
+        b.segment(ith_field* n_modes, n_modes) = q.segment(ith_field*(n_modes + 1),
+            n_modes) - J.middleRows(ith_field*(n_modes + 1),
+                                    n_modes) * quadratureWeights.segment(ith_field* nodePoints->size(),
+                                        nodePoints->size());
+    }
+
+    b = b / b.lpNorm<2>();
 }
 
 template<typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::initReshapeMat(Eigen::SparseMatrix<double> &reshapeMat)
+void HyperReduction<SnapshotsLists...>::initReshapeMat(
+    Eigen::SparseMatrix<double> & reshapeMat)
 {
-  reshapeMat.resize(n_cells, n_cells*vectorial_dim);
-  reshapeMat.reserve(Eigen::VectorXi::Constant(n_cells * vectorial_dim /*n_cols*/, 1 /*n_non_zero_elements*/));
+    reshapeMat.resize(n_cells, n_cells* vectorial_dim);
+    reshapeMat.reserve(Eigen::VectorXi::Constant(n_cells* vectorial_dim /*n_cols*/,
+                       1 /*n_non_zero_elements*/));
 
-  for (unsigned int i = 0; i < n_cells; i++)
-  {
-    for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+    for (unsigned int i = 0; i < n_cells; i++)
     {
-      reshapeMat.insert(i, i+n_cells*ith_field) = 1;
+        for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+        {
+            reshapeMat.insert(i, i + n_cells* ith_field) = 1;
+        }
     }
-  }
-  reshapeMat.makeCompressed();
+
+    reshapeMat.makeCompressed();
 }
 
 template <typename... SnapshotsLists>
 template <typename SnapshotsList>
-void HyperReduction<SnapshotsLists...>::stackSnapshots(SnapshotsList sList, Eigen::MatrixXd& snapshotsMatrix, Eigen::VectorXd& fieldWeights)
+void HyperReduction<SnapshotsLists...>::stackSnapshots(SnapshotsList sList,
+        Eigen::MatrixXd& snapshotsMatrix, Eigen::VectorXd& fieldWeights)
 {
-  unsigned int field_dim = get_field_dim<typename SnapshotsList::value_type>();
-
-  Eigen::MatrixXd tmpSnapshots = Foam2Eigen::PtrList2Eigen(sList);
-  // get volumes
-  Eigen::VectorXd V = ITHACAutilities::getMassMatrixFV(sList[0]);
-
-
-  double maxVal = std::sqrt(tmpSnapshots.colwise().lpNorm<2>().maxCoeff());
-
-  fieldWeights.conservativeResize(fieldWeights.rows()+field_dim*n_cells);
-  fieldWeights.tail(n_cells * field_dim) = V.array().sqrt().cwiseInverse()*maxVal;
-
-  snapshotsMatrix.conservativeResize(snapshotsMatrix.rows() + n_cells * field_dim, n_snapshots);
-  snapshotsMatrix.bottomRows(n_cells * field_dim) = tmpSnapshots;
+    unsigned int field_dim = get_field_dim<typename SnapshotsList::value_type>();
+    Eigen::MatrixXd tmpSnapshots = Foam2Eigen::PtrList2Eigen(sList);
+    // get volumes
+    Eigen::VectorXd V = ITHACAutilities::getMassMatrixFV(sList[0]);
+    double maxVal = std::sqrt(tmpSnapshots.colwise().lpNorm<2>().maxCoeff());
+    fieldWeights.conservativeResize(fieldWeights.rows() + field_dim* n_cells);
+    fieldWeights.tail(n_cells* field_dim) = V.array().sqrt().cwiseInverse() *
+                                            maxVal;
+    snapshotsMatrix.conservativeResize(snapshotsMatrix.rows() + n_cells* field_dim,
+                                       n_snapshots);
+    snapshotsMatrix.bottomRows(n_cells* field_dim) = tmpSnapshots;
 }
 
 template <typename... SnapshotsLists>
 template <typename SnapshotsList>
-void HyperReduction<SnapshotsLists...>::stackSnapshotsBoundary(SnapshotsList sList, List<Eigen::MatrixXd>& snapshotsMatrixBoundary, List<Eigen::VectorXd>& fieldWeightsBoundary)
+void HyperReduction<SnapshotsLists...>::stackSnapshotsBoundary(
+    SnapshotsList sList, List<Eigen::MatrixXd> & snapshotsMatrixBoundary,
+    List<Eigen::VectorXd> & fieldWeightsBoundary)
 {
-  unsigned int field_dim = get_field_dim<typename SnapshotsList::value_type>();
-
-  List<Eigen::MatrixXd> tmpBoundarySnapshots = Foam2Eigen::PtrList2EigenBC(sList);
-
-  List<double> maxVal;
-  maxVal.resize(n_boundary_patches);
-  
-  for (label id = 0; id < n_boundary_patches; id++)
-  {
-    maxVal[id] = std::sqrt(tmpBoundarySnapshots[id].colwise().lpNorm<2>().maxCoeff());
-
-    // get surface areas
-    Eigen::VectorXd S = Foam2Eigen::field2Eigen(sList[0].mesh().magSf().boundaryField()[id]);
-    S = S.replicate(field_dim, 1);
+    unsigned int field_dim = get_field_dim<typename SnapshotsList::value_type>();
+    List<Eigen::MatrixXd> tmpBoundarySnapshots = Foam2Eigen::PtrList2EigenBC(sList);
+    List<double> maxVal;
+    maxVal.resize(n_boundary_patches);
 
-    unsigned int bSize = field_dim*int(n_boundary_cells_list[id]);
-    fieldWeightsBoundary[id].conservativeResize(fieldWeightsBoundary[id].rows()+bSize);
-    fieldWeightsBoundary[id].tail(bSize) = S.array().pow(3/4)*maxVal[id];
-
-    snapshotsMatrixBoundary[id].conservativeResize(snapshotsMatrixBoundary[id].rows() + bSize, n_snapshots);
-    snapshotsMatrixBoundary[id].bottomRows(bSize) = tmpBoundarySnapshots[id];
-  }
+    for (label id = 0; id < n_boundary_patches; id++)
+    {
+        maxVal[id] = std::sqrt(
+                         tmpBoundarySnapshots[id].colwise().lpNorm<2>().maxCoeff());
+        // get surface areas
+        Eigen::VectorXd S = Foam2Eigen::field2Eigen(
+                                sList[0].mesh().magSf().boundaryField()[id]);
+        S = S.replicate(field_dim, 1);
+        unsigned int bSize = field_dim* int(n_boundary_cells_list[id]);
+        fieldWeightsBoundary[id].conservativeResize(fieldWeightsBoundary[id].rows() +
+                bSize);
+        fieldWeightsBoundary[id].tail(bSize) = S.array().pow(3 / 4) * maxVal[id];
+        snapshotsMatrixBoundary[id].conservativeResize(
+            snapshotsMatrixBoundary[id].rows() + bSize, n_snapshots);
+        snapshotsMatrixBoundary[id].bottomRows(bSize) = tmpBoundarySnapshots[id];
+    }
 }
 
 template<typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::evaluatePinv(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd &fieldWeights) {
-  assert(Projector.cols() > 0);
-  Eigen::MatrixXd restricted = Projector.transpose() * Modes;
-  Info << "S-Optimalty: " << s_optimality(restricted) << endl;
-  pinvPU = ITHACAutilities::invertMatrix(restricted, para->ITHACAdict->lookupOrDefault<word>("InversionMethod", "completeOrthogonalDecomposition"));
-  pinvPU = pinvPU*(Projector.transpose() * fieldWeights.array().cwiseInverse().matrix()).asDiagonal();
+void HyperReduction<SnapshotsLists...>::evaluatePinv(Eigen::SparseMatrix<double>
+        & Projector, Eigen::MatrixXd& Modes, Eigen::VectorXd& fieldWeights)
+{
+    assert(Projector.cols() > 0);
+    Eigen::MatrixXd restricted = Projector.transpose() * Modes;
+    Info << "S-Optimalty: " << s_optimality(restricted) << endl;
+    pinvPU = ITHACAutilities::invertMatrix(restricted,
+                                           para->ITHACAdict->lookupOrDefault<word>("InversionMethod",
+                                               "completeOrthogonalDecomposition"));
+    pinvPU = pinvPU*(Projector.transpose() *
+                     fieldWeights.array().cwiseInverse().matrix()).asDiagonal();
 }
 
 template<typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::evaluateWPU(Eigen::SparseMatrix<double> &Projector, Eigen::MatrixXd &Modes, Eigen::VectorXd &fieldWeights, Eigen::VectorXd& quadratureWeights) {
-  assert(Projector.cols() > 0);
-
-  Eigen::VectorXd quadratureWeightsOrderedAsProjector(quadratureWeights.rows());
-  unsigned int n_weightsPerField = quadratureWeights.rows()/vectorial_dim;
-  unsigned int reorderIndex{0};
+void HyperReduction<SnapshotsLists...>::evaluateWPU(Eigen::SparseMatrix<double>
+        & Projector, Eigen::MatrixXd& Modes, Eigen::VectorXd& fieldWeights,
+        Eigen::VectorXd& quadratureWeights)
+{
+    assert(Projector.cols() > 0);
+    Eigen::VectorXd quadratureWeightsOrderedAsProjector(quadratureWeights.rows());
+    unsigned int n_weightsPerField = quadratureWeights.rows() / vectorial_dim;
+    unsigned int reorderIndex{0};
 
-  for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-  {  
-    for (unsigned int ith_weight = 0; ith_weight < n_weightsPerField; ith_weight++)
+    for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
     {
-      quadratureWeightsOrderedAsProjector(reorderIndex) = quadratureWeights(ith_weight + ith_field * n_weightsPerField);
-      reorderIndex++;
+        for (unsigned int ith_weight = 0; ith_weight < n_weightsPerField; ith_weight++)
+        {
+            quadratureWeightsOrderedAsProjector(reorderIndex) = quadratureWeights(
+                    ith_weight + ith_field* n_weightsPerField);
+            reorderIndex++;
+        }
     }
-  }
-  wPU = quadratureWeightsOrderedAsProjector.transpose()*(Projector.transpose() * fieldWeights.array().cwiseInverse().matrix()).asDiagonal();
+
+    wPU = quadratureWeightsOrderedAsProjector.transpose() *
+          (Projector.transpose() *
+           fieldWeights.array().cwiseInverse().matrix()).asDiagonal();
 }
 
 template<typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::generateSubmesh(label layers, const fvMesh &mesh) {
-
-  Info << "####### Extract submesh #######\n";
-  ITHACAparameters *para(ITHACAparameters::getInstance());
+void HyperReduction<SnapshotsLists...>::generateSubmesh(label layers,
+        const fvMesh& mesh)
+{
+    Info << "####### Extract submesh #######\n";
+    ITHACAparameters* para(ITHACAparameters::getInstance());
+    totalNodePoints = autoPtr<IOList<labelList>>(new IOList<labelList>(IOobject(
+                          "totalNodePoints", para->runTime.time().constant(),  "../" + folderMethod,
+                          para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
+    uniqueNodePoints = autoPtr<IOList<label>>(new IOList<label>(IOobject(
+                           "uniqueNodePoints", para->runTime.time().constant(),  "../" + folderMethod,
+                           para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
+    volScalarField Indici
+    (
+        IOobject
+        (
+            problemName + "_indices",
+            mesh.time().timeName(),
+            mesh,
+            IOobject::NO_READ,
+            IOobject::NO_WRITE
+        ),
+        mesh,
+        dimensionedScalar(problemName + "_indices",
+                          dimensionSet(0, 0, 0, 0, 0, 0, 0), 0.0));
+    submesh = autoPtr<fvMeshSubset>(new fvMeshSubset(mesh));
+    bool offlineStage = !totalNodePoints().headerOk();
 
-  totalNodePoints = autoPtr<IOList<labelList>>(new IOList<labelList>(IOobject(
-      "totalNodePoints", para->runTime.time().constant(),  "../" + folderMethod,
-      para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
+    if (offlineStage)
+    {
+        List<label> indices;
 
-  uniqueNodePoints = autoPtr<IOList<label>>(new IOList<label>(IOobject(
-      "uniqueNodePoints", para->runTime.time().constant(),  "../" + folderMethod,
-      para->mesh, IOobject::READ_IF_PRESENT, IOobject::NO_WRITE)));
+        for (label i = 0; i < nodePoints().size(); i++)
+        {
+            indices = ITHACAutilities::getIndices(mesh, nodePoints()[i], layers);
+            totalNodePoints().append(indices);
+        }
 
-  volScalarField Indici
-  (
-      IOobject
-      (
-        problemName + "_indices",
-        mesh.time().timeName(),
-        mesh,
-        IOobject::NO_READ,
-        IOobject::NO_WRITE
-      ),
-      mesh,
-      dimensionedScalar(problemName + "_indices",
-                        dimensionSet(0, 0, 0, 0, 0, 0, 0), 0.0));
-
-  submesh = autoPtr<fvMeshSubset>(new fvMeshSubset(mesh));
-  bool offlineStage = !totalNodePoints().headerOk();
-
-  if (offlineStage) {
-    List<label> indices;
-    for (label i = 0; i < nodePoints().size(); i++) {
-      indices = ITHACAutilities::getIndices(mesh, nodePoints()[i], layers);
-      totalNodePoints().append(indices);
+        labelList a = ListListOps::combine<labelList>(totalNodePoints(),
+                      accessOp<labelList>());
+        inplaceUniqueSort(a);
+        uniqueNodePoints() = a;
+        scalar zerodot25 = 0.25;
+        ITHACAutilities::assignIF(Indici, zerodot25,
+                                  uniqueNodePoints().List<label>::clone()());
+        ITHACAutilities::assignONE(Indici, nodePoints());
+        totalNodePoints().write();
+        uniqueNodePoints().write();
+        ITHACAstream::exportSolution(Indici, "1", folderMethod);
     }
 
-    labelList a = ListListOps::combine<labelList>(totalNodePoints(),
-                                                  accessOp<labelList>());
-
-    inplaceUniqueSort(a);
-    uniqueNodePoints() = a;
+    submesh->setCellSubset(uniqueNodePoints());
+    submesh->subMesh().fvSchemes::readOpt() = mesh.fvSchemes::readOpt();
+    submesh->subMesh().fvSolution::readOpt() = mesh.fvSolution::readOpt();
+    submesh->subMesh().fvSchemes::read();
+    submesh->subMesh().fvSolution::read();
+    std::cout.clear();
+    localNodePoints = global2local(nodePoints(), submesh());
+    n_cellsSubfields = submesh().cellMap().size();
+    Info << "####### End extract submesh size = " << n_cellsSubfields <<
+         " #######\n";
+    createMasks(offlineStage);
+    Info << "####### End create masks #######\n";
+}
 
-    scalar zerodot25 = 0.25;
-    ITHACAutilities::assignIF(Indici, zerodot25,
-                              uniqueNodePoints().List<label>::clone()());
-    ITHACAutilities::assignONE(Indici, nodePoints());
+template<typename... SnapshotsLists>
+void HyperReduction<SnapshotsLists...>::createMasks(bool offlineStage)
+{
+    if (offlineStage)
+    {
+        field2submesh.resize(submesh().cellMap().size() * vectorial_dim,
+                             n_cells* vectorial_dim);
+        field2submesh.reserve(Eigen::VectorXi::Constant(n_cells* vectorial_dim, 1));
 
-    totalNodePoints().write();
-    uniqueNodePoints().write();
-    ITHACAstream::exportSolution(Indici, "1", folderMethod);
-  }
+        for (unsigned int ith_subCell{0} ; ith_subCell < submesh().cellMap().size();
+                ith_subCell++)
+        {
+            for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+            {
+                field2submesh.insert(ith_subCell + ith_field* submesh().cellMap().size(),
+                                     submesh().cellMap()[ith_subCell] + n_cells* ith_field) = 1;
+            }
+        }
 
-  submesh->setCellSubset(uniqueNodePoints());
-  submesh->subMesh().fvSchemes::readOpt() = mesh.fvSchemes::readOpt();
-  submesh->subMesh().fvSolution::readOpt() = mesh.fvSolution::readOpt();
-  submesh->subMesh().fvSchemes::read();
-  submesh->subMesh().fvSolution::read();
-  std::cout.clear();
+        field2submesh.makeCompressed();
+        submesh2nodes.resize(nodePoints().size() * vectorial_dim,
+                             submesh().cellMap().size() * vectorial_dim);
+        submesh2nodes.reserve(Eigen::VectorXi::Constant(submesh().cellMap().size() *
+                              vectorial_dim, 1));
+        submesh2nodesMask.resize(nodePoints().size() * vectorial_dim);
+        int index_col = 0;
 
-  localNodePoints = global2local(nodePoints(), submesh());
+        for (unsigned int ith_node{0} ; ith_node < nodePoints().size(); ith_node++)
+        {
+            for (unsigned int ith_subCell{0} ; ith_subCell < submesh().cellMap().size();
+                    ith_subCell++)
+            {
+                if (nodePoints()[ith_node] == submesh().cellMap()[ith_subCell])
+                {
+                    for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+                    {
+                        submesh2nodes.insert(ith_node + nodePoints().size() * ith_field,
+                                             index_col + ith_field* submesh().cellMap().size()) = 1;
+                        submesh2nodesMask(ith_node + nodePoints().size() * ith_field) = index_col +
+                            ith_field* submesh().cellMap().size();
+                    }
+
+                    break;
+                }
+                else
+                {
+                    index_col++;
+                }
+            }
 
-  n_cellsSubfields = submesh().cellMap().size();
-  Info << "####### End extract submesh size = " << n_cellsSubfields <<" #######\n";
+            index_col = 0;
+        }
 
-  createMasks(offlineStage);
-  Info << "####### End create masks #######\n";
+        submesh2nodes.makeCompressed();
+        cnpy::save(field2submesh, folderMethod + "/field2submesh.npz");
+        cnpy::save(submesh2nodes, folderMethod + "/submesh2nodes.npz");
+        cnpy::save(submesh2nodesMask, folderMethod + "/submesh2nodesMask.npy");
+    }
+    else
+    {
+        cnpy::load(field2submesh, folderMethod + "/field2submesh.npz");
+        cnpy::load(submesh2nodes, folderMethod + "/submesh2nodes.npz");
+        cnpy::load(submesh2nodesMask, folderMethod + "/submesh2nodesMask.npy");
+    }
 }
 
 template<typename... SnapshotsLists>
-void HyperReduction<SnapshotsLists...>::createMasks(bool offlineStage)
-{ 
-  if (offlineStage)
-  {
-    field2submesh.resize(submesh().cellMap().size() * vectorial_dim, n_cells*vectorial_dim);
-    field2submesh.reserve(Eigen::VectorXi::Constant(n_cells*vectorial_dim, 1));
+List<label> HyperReduction<SnapshotsLists...>::global2local(
+    List<label> & points, fvMeshSubset& submesh)
+{
+    List<label> localPoints;
 
-    for (unsigned int ith_subCell{0} ; ith_subCell <submesh().cellMap().size(); ith_subCell++)
+    for (label i = 0; i < points.size(); i++)
     {
-        for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
+        for (label j = 0; j < submesh.cellMap().size(); j++)
         {
-          field2submesh.insert(ith_subCell+ith_field*submesh().cellMap().size(), submesh().cellMap()[ith_subCell]+n_cells*ith_field) = 1;
-        }
-    }
-    field2submesh.makeCompressed();
-
-    submesh2nodes.resize(nodePoints().size() * vectorial_dim, submesh().cellMap().size()*vectorial_dim);
-    submesh2nodes.reserve(Eigen::VectorXi::Constant(submesh().cellMap().size()*vectorial_dim, 1));
-    submesh2nodesMask.resize(nodePoints().size() * vectorial_dim);
-
-    int index_col = 0;
-    for (unsigned int ith_node{0} ; ith_node <nodePoints().size(); ith_node++) {
-      for (unsigned int ith_subCell{0} ; ith_subCell <submesh().cellMap().size(); ith_subCell++) {
-        if (nodePoints()[ith_node] == submesh().cellMap()[ith_subCell]) {
-          for (unsigned int ith_field = 0; ith_field < vectorial_dim; ith_field++)
-          {
-            submesh2nodes.insert(ith_node + nodePoints().size()*ith_field, index_col + ith_field*submesh().cellMap().size()) = 1;
-            submesh2nodesMask(ith_node + nodePoints().size()*ith_field) = index_col + ith_field*submesh().cellMap().size();
-          }
-          break;
-        } else {
-          index_col++;
+            if (submesh.cellMap()[j] == points[i])
+            {
+                localPoints.append(j);
+                break;
+            }
         }
-      }
-      index_col = 0;
-    }
-    submesh2nodes.makeCompressed();
-
-    cnpy::save(field2submesh, folderMethod +"/field2submesh.npz");
-    cnpy::save(submesh2nodes, folderMethod +"/submesh2nodes.npz");
-    cnpy::save(submesh2nodesMask, folderMethod +"/submesh2nodesMask.npy");
-  }
-  else
-  {
-    cnpy::load(field2submesh, folderMethod +"/field2submesh.npz");
-    cnpy::load(submesh2nodes, folderMethod +"/submesh2nodes.npz");
-    cnpy::load(submesh2nodesMask, folderMethod +"/submesh2nodesMask.npy");
-  }
-}
-
-template<typename... SnapshotsLists>
-List<label> HyperReduction<SnapshotsLists...>::global2local(List<label> &points, fvMeshSubset &submesh) {
-  List<label> localPoints;
-
-  for (label i = 0; i < points.size(); i++) {
-    for (label j = 0; j < submesh.cellMap().size(); j++) {
-      if (submesh.cellMap()[j] == points[i]) {
-        localPoints.append(j);
-        break;
-      }
     }
-  }
 
-  return localPoints;
+    return localPoints;
 }
 
 #endif
diff --git a/src/ITHACA_MUQ/muq2ithaca.C b/src/ITHACA_MUQ/muq2ithaca.C
old mode 100755
new mode 100644
index 0feda2a0b..b1e47d23b
--- a/src/ITHACA_MUQ/muq2ithaca.C
+++ b/src/ITHACA_MUQ/muq2ithaca.C
@@ -36,7 +36,7 @@ Eigen::MatrixXd EnsembleKalmanFilter(Eigen::MatrixXd prior,
 
     Eigen::MatrixXd Y = D -
                         observedState; //diff measurement data and simulated data
-    Eigen::MatrixXd P = HA * HA.transpose() / (Nseeds - 1.) + measurementsCov;
+    Eigen::MatrixXd P = HA* HA.transpose() / (Nseeds - 1.) + measurementsCov;
     Eigen::FullPivLU<Eigen::MatrixXd> lu_decomp(P);
     auto P_rank = lu_decomp.rank();
 
@@ -53,10 +53,10 @@ Eigen::MatrixXd EnsembleKalmanFilter(Eigen::MatrixXd prior,
     }
 
     //KF update
-    Eigen::MatrixXd M = P * Y;
-    Eigen::MatrixXd Z = (1. / (Nseeds - 1.)) * A * HA.transpose();
+    Eigen::MatrixXd M = P* Y;
+    Eigen::MatrixXd Z = (1. / (Nseeds - 1.)) * A* HA.transpose();
     //Kalman Gain
-    Eigen::MatrixXd K = (1. / (Nseeds - 1.)) * A * HA.transpose() * P;
+    Eigen::MatrixXd K = (1. / (Nseeds - 1.)) * A* HA.transpose() * P;
 
     if ((K.array() < 0.0).any())
     {
@@ -64,10 +64,10 @@ Eigen::MatrixXd EnsembleKalmanFilter(Eigen::MatrixXd prior,
                   std::endl;
     }
 
-    return prior + Z * M;
+    return prior + Z* M;
 }
 
-Eigen::MatrixXd EnsembleKalmanFilter(PtrList<volScalarField>& prior,
+Eigen::MatrixXd EnsembleKalmanFilter(PtrList<volScalarField> & prior,
                                      Eigen::VectorXd measurements,
                                      Eigen::MatrixXd measurementsCov,
                                      Eigen::MatrixXd observedState)
@@ -100,7 +100,7 @@ Eigen::MatrixXd EnsembleKalmanFilter(PtrList<volScalarField>& prior,
 
     Eigen::MatrixXd Y = D -
                         observedState; //diff measurement data and simulated data
-    Eigen::MatrixXd P = HA * HA.transpose() / (Nseeds - 1.) + measurementsCov;
+    Eigen::MatrixXd P = HA* HA.transpose() / (Nseeds - 1.) + measurementsCov;
     Eigen::FullPivLU<Eigen::MatrixXd> lu_decomp(P);
     auto P_rank = lu_decomp.rank();
 
@@ -117,10 +117,10 @@ Eigen::MatrixXd EnsembleKalmanFilter(PtrList<volScalarField>& prior,
     }
 
     //KF update
-    Eigen::MatrixXd M = P * Y;
-    Eigen::MatrixXd Z = (1. / (Nseeds - 1.)) * A * HA.transpose();
+    Eigen::MatrixXd M = P* Y;
+    Eigen::MatrixXd Z = (1. / (Nseeds - 1.)) * A* HA.transpose();
     //Kalman Gain
-    Eigen::MatrixXd K = (1. / (Nseeds - 1.)) * A * HA.transpose() * P;
+    Eigen::MatrixXd K = (1. / (Nseeds - 1.)) * A* HA.transpose() * P;
 
     if ((K.array() < 0.0).any())
     {
@@ -128,7 +128,7 @@ Eigen::MatrixXd EnsembleKalmanFilter(PtrList<volScalarField>& prior,
                   std::endl;
     }
 
-    return priorMatrix + Z * M;
+    return priorMatrix + Z* M;
 }
 
 double quantile(Eigen::VectorXd samps, double p, int method)
@@ -142,8 +142,8 @@ double quantile(Eigen::VectorXd samps, double p, int method)
     if (method == 1)
     {
         m = 0;
-        j = std::floor(p * n + m);
-        double g = p * n + m - j * 1.0;
+        j = std::floor(p* n + m);
+        double g = p* n + m - j * 1.0;
 
         if (g > 0)
         {
@@ -154,8 +154,8 @@ double quantile(Eigen::VectorXd samps, double p, int method)
     {
         gamma = 0.5;
         m = 0;
-        j = std::floor(p * n + m);
-        double g = p * n + m - j * 1.0;
+        j = std::floor(p* n + m);
+        double g = p* n + m - j * 1.0;
 
         if (g > 0)
         {
@@ -166,8 +166,8 @@ double quantile(Eigen::VectorXd samps, double p, int method)
     {
         gamma = 1.0;
         m = -0.5;
-        j = std::floor(p * n + m);
-        double g = p * n + m - j * 1.0;
+        j = std::floor(p* n + m);
+        double g = p* n + m - j * 1.0;
 
         if (g == 0 && j % 2 == 0)
         {
@@ -185,7 +185,7 @@ double quantile(Eigen::VectorXd samps, double p, int method)
         j = samps.size() - 2;
     }
 
-    return (1 - gamma) * samps(j) + gamma * samps(j + 1);
+    return (1 - gamma) * samps(j) + gamma* samps(j + 1);
 }
 
 Eigen::VectorXd quantile(Eigen::MatrixXd samps, double p, int method)
diff --git a/src/ITHACA_MUQ/muq2ithaca.H b/src/ITHACA_MUQ/muq2ithaca.H
old mode 100755
new mode 100644
index 201e1d7b5..ca09e8538
--- a/src/ITHACA_MUQ/muq2ithaca.H
+++ b/src/ITHACA_MUQ/muq2ithaca.H
@@ -81,7 +81,7 @@ Eigen::MatrixXd EnsembleKalmanFilter(Eigen::MatrixXd prior,
 ///
 /// @return     Ensamble of the posterior
 ///
-Eigen::MatrixXd EnsembleKalmanFilter(PtrList<volScalarField>& prior,
+Eigen::MatrixXd EnsembleKalmanFilter(PtrList<volScalarField> & prior,
                                      Eigen::VectorXd measurements,
                                      Eigen::MatrixXd measurementsCov,
                                      Eigen::MatrixXd observedState);
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedLaplacian/ReducedLaplacian.C b/src/ITHACA_ROMPROBLEMS/ReducedLaplacian/ReducedLaplacian.C
old mode 100755
new mode 100644
index a8982f2fb..a42e5e10b
--- a/src/ITHACA_ROMPROBLEMS/ReducedLaplacian/ReducedLaplacian.C
+++ b/src/ITHACA_ROMPROBLEMS/ReducedLaplacian/ReducedLaplacian.C
@@ -43,7 +43,7 @@ reducedLaplacian::reducedLaplacian()
 
 reducedLaplacian::reducedLaplacian(laplacianProblem& problem)
     :
-    problem(&problem)
+    problem( & problem)
 {
 }
 
@@ -68,7 +68,7 @@ void reducedLaplacian::solveOnline(Eigen::MatrixXd mu)
     online_solution.conservativeResize(count_online_solve, problem->NTmodes + 1);
     online_solution(count_online_solve - 1, 0) = count_online_solve;
     online_solution.row(count_online_solve - 1).tail(problem->NTmodes) =
-        x.transpose();
+                       x.transpose();
     count_online_solve += 1;
 }
 
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedMSR/ReducedMSR.C b/src/ITHACA_ROMPROBLEMS/ReducedMSR/ReducedMSR.C
old mode 100755
new mode 100644
index a363a2cca..4775c2ee1
--- a/src/ITHACA_ROMPROBLEMS/ReducedMSR/ReducedMSR.C
+++ b/src/ITHACA_ROMPROBLEMS/ReducedMSR/ReducedMSR.C
@@ -30,7 +30,7 @@ reducedMSR::reducedMSR()
 
 reducedMSR::reducedMSR(msrProblem& FOMproblem)
 {
-    problem = &FOMproblem;
+    problem = & FOMproblem;
     N_BC = problem->inletIndex.rows();
     N_BCt = problem->inletIndexT.rows();
     Nphi_u = problem->B_matrix.rows();
@@ -195,15 +195,15 @@ int newton_msr_fd::operator()(const Eigen::VectorXd& x,
     Eigen::MatrixXd gg(1, 1);
     Eigen::MatrixXd bb(1, 1);
     // Mom Term
-    Eigen::VectorXd M1 = problem->B_matrix * a_tmp * nu;
+    Eigen::VectorXd M1 = problem->B_matrix* a_tmp* nu;
     // Gradient of pressure
-    Eigen::VectorXd M2 = problem->K_matrix * b_tmp;
+    Eigen::VectorXd M2 = problem->K_matrix* b_tmp;
     // Pressure Term
-    Eigen::VectorXd M3 = problem->D_matrix * b_tmp;
+    Eigen::VectorXd M3 = problem->D_matrix* b_tmp;
     // BC PPE
-    Eigen::VectorXd M6 = problem->BC1_matrix * a_tmp * nu;
+    Eigen::VectorXd M6 = problem->BC1_matrix* a_tmp* nu;
     // BC PPE
-    Eigen::VectorXd M7 = problem->BC3_matrix * a_tmp * nu;
+    Eigen::VectorXd M7 = problem->BC3_matrix* a_tmp* nu;
 
     for (int i = 0; i < Nphi_u; i++)
     {
@@ -231,7 +231,7 @@ int newton_msr_fd::operator()(const Eigen::VectorXd& x,
 
 int newton_msr_fd::df(const Eigen::VectorXd& x,  Eigen::MatrixXd& fjac) const
 {
-    Eigen::NumericalDiff<newton_msr_fd> numDiff(*this);
+    Eigen::NumericalDiff<newton_msr_fd> numDiff( * this);
     numDiff.df(x, fjac);
     return 0;
 }
@@ -273,14 +273,14 @@ int newton_msr_n::operator()(const Eigen::VectorXd& n,
     // flux absorption term
     Eigen::MatrixXd af(1, 1);
     // precursor sources
-    Eigen::VectorXd F3_1 = problem->PS1_matrix * d1_tmp * l1;
-    Eigen::VectorXd F3_2 = problem->PS2_matrix * d2_tmp * l2;
-    Eigen::VectorXd F3_3 = problem->PS3_matrix * d3_tmp * l3;
-    Eigen::VectorXd F3_4 = problem->PS4_matrix * d4_tmp * l4;
-    Eigen::VectorXd F3_5 = problem->PS5_matrix * d5_tmp * l5;
-    Eigen::VectorXd F3_6 = problem->PS6_matrix * d6_tmp * l6;
-    Eigen::VectorXd F3_7 = problem->PS7_matrix * d7_tmp * l7;
-    Eigen::VectorXd F3_8 = problem->PS8_matrix * d8_tmp * l8;
+    Eigen::VectorXd F3_1 = problem->PS1_matrix* d1_tmp* l1;
+    Eigen::VectorXd F3_2 = problem->PS2_matrix* d2_tmp* l2;
+    Eigen::VectorXd F3_3 = problem->PS3_matrix* d3_tmp* l3;
+    Eigen::VectorXd F3_4 = problem->PS4_matrix* d4_tmp* l4;
+    Eigen::VectorXd F3_5 = problem->PS5_matrix* d5_tmp* l5;
+    Eigen::VectorXd F3_6 = problem->PS6_matrix* d6_tmp* l6;
+    Eigen::VectorXd F3_7 = problem->PS7_matrix* d7_tmp* l7;
+    Eigen::VectorXd F3_8 = problem->PS8_matrix* d8_tmp* l8;
     // Convective terms in prec-eq:
     Eigen::MatrixXd pp1(1, 1);
     Eigen::MatrixXd pp2(1, 1);
@@ -291,23 +291,23 @@ int newton_msr_n::operator()(const Eigen::VectorXd& n,
     Eigen::MatrixXd pp7(1, 1);
     Eigen::MatrixXd pp8(1, 1);
     // laplacian of precursor
-    Eigen::VectorXd P1_1 = problem->LP1_matrix * d1_tmp * (nu / Sc);
-    Eigen::VectorXd P1_2 = problem->LP2_matrix * d2_tmp * (nu / Sc);
-    Eigen::VectorXd P1_3 = problem->LP3_matrix * d3_tmp * (nu / Sc);
-    Eigen::VectorXd P1_4 = problem->LP4_matrix * d4_tmp * (nu / Sc);
-    Eigen::VectorXd P1_5 = problem->LP5_matrix * d5_tmp * (nu / Sc);
-    Eigen::VectorXd P1_6 = problem->LP6_matrix * d6_tmp * (nu / Sc);
-    Eigen::VectorXd P1_7 = problem->LP7_matrix * d7_tmp * (nu / Sc);
-    Eigen::VectorXd P1_8 = problem->LP8_matrix * d8_tmp * (nu / Sc);
+    Eigen::VectorXd P1_1 = problem->LP1_matrix* d1_tmp * (nu / Sc);
+    Eigen::VectorXd P1_2 = problem->LP2_matrix* d2_tmp * (nu / Sc);
+    Eigen::VectorXd P1_3 = problem->LP3_matrix* d3_tmp * (nu / Sc);
+    Eigen::VectorXd P1_4 = problem->LP4_matrix* d4_tmp * (nu / Sc);
+    Eigen::VectorXd P1_5 = problem->LP5_matrix* d5_tmp * (nu / Sc);
+    Eigen::VectorXd P1_6 = problem->LP6_matrix* d6_tmp * (nu / Sc);
+    Eigen::VectorXd P1_7 = problem->LP7_matrix* d7_tmp * (nu / Sc);
+    Eigen::VectorXd P1_8 = problem->LP8_matrix* d8_tmp * (nu / Sc);
     // algebric term
-    Eigen::VectorXd P2_1 = problem->MP1_matrix * d1_tmp * l1;
-    Eigen::VectorXd P2_2 = problem->MP2_matrix * d2_tmp * l2;
-    Eigen::VectorXd P2_3 = problem->MP3_matrix * d3_tmp * l3;
-    Eigen::VectorXd P2_4 = problem->MP4_matrix * d4_tmp * l4;
-    Eigen::VectorXd P2_5 = problem->MP5_matrix * d5_tmp * l5;
-    Eigen::VectorXd P2_6 = problem->MP6_matrix * d6_tmp * l6;
-    Eigen::VectorXd P2_7 = problem->MP7_matrix * d7_tmp * l7;
-    Eigen::VectorXd P2_8 = problem->MP8_matrix * d8_tmp * l8;
+    Eigen::VectorXd P2_1 = problem->MP1_matrix* d1_tmp* l1;
+    Eigen::VectorXd P2_2 = problem->MP2_matrix* d2_tmp* l2;
+    Eigen::VectorXd P2_3 = problem->MP3_matrix* d3_tmp* l3;
+    Eigen::VectorXd P2_4 = problem->MP4_matrix* d4_tmp* l4;
+    Eigen::VectorXd P2_5 = problem->MP5_matrix* d5_tmp* l5;
+    Eigen::VectorXd P2_6 = problem->MP6_matrix* d6_tmp* l6;
+    Eigen::VectorXd P2_7 = problem->MP7_matrix* d7_tmp* l7;
+    Eigen::VectorXd P2_8 = problem->MP8_matrix* d8_tmp* l8;
     // flux source term
     Eigen::MatrixXd fs1(1, 1);
     Eigen::MatrixXd fs2(1, 1);
@@ -334,7 +334,7 @@ int newton_msr_n::operator()(const Eigen::VectorXd& n,
     {
         int k = i + pfvecn;
         pp1 = a_tmp.transpose() * problem->ST1_matrix[i] * d1_tmp;
-        fs1 = nsf_c.transpose() * problem->FS1_matrix[i] * c_tmp * b1;
+        fs1 = nsf_c.transpose() * problem->FS1_matrix[i] * c_tmp* b1;
         fvecn(k) = -pp1(0, 0) + P1_1(i) - P2_1(i) + fs1(0, 0);
     }
 
@@ -344,7 +344,7 @@ int newton_msr_n::operator()(const Eigen::VectorXd& n,
     {
         int k = i + pfvecn;
         pp2 = a_tmp.transpose() * problem->ST2_matrix[i] * d2_tmp;
-        fs2 = nsf_c.transpose() * problem->FS2_matrix[i] * c_tmp * b2;
+        fs2 = nsf_c.transpose() * problem->FS2_matrix[i] * c_tmp* b2;
         fvecn(k) = -pp2(0, 0) + P1_2(i) - P2_2(i) + fs2(0, 0);
     }
 
@@ -354,7 +354,7 @@ int newton_msr_n::operator()(const Eigen::VectorXd& n,
     {
         int k = i + pfvecn;
         pp3 = a_tmp.transpose() * problem->ST3_matrix[i] * d3_tmp;
-        fs3 = nsf_c.transpose() * problem->FS3_matrix[i] * c_tmp * b3;
+        fs3 = nsf_c.transpose() * problem->FS3_matrix[i] * c_tmp* b3;
         fvecn(k) = -pp3(0, 0) + P1_3(i) - P2_3(i) + fs3(0, 0);
     }
 
@@ -364,7 +364,7 @@ int newton_msr_n::operator()(const Eigen::VectorXd& n,
     {
         int k = i + pfvecn;
         pp4 = a_tmp.transpose() * problem->ST4_matrix[i] * d4_tmp;
-        fs4 = nsf_c.transpose() * problem->FS4_matrix[i] * c_tmp * b4;
+        fs4 = nsf_c.transpose() * problem->FS4_matrix[i] * c_tmp* b4;
         fvecn(k) = -pp4(0, 0) + P1_4(i) - P2_4(i) + fs4(0, 0);
     }
 
@@ -374,7 +374,7 @@ int newton_msr_n::operator()(const Eigen::VectorXd& n,
     {
         int k = i + pfvecn;
         pp5 = a_tmp.transpose() * problem->ST5_matrix[i] * d5_tmp;
-        fs5 = nsf_c.transpose() * problem->FS5_matrix[i] * c_tmp * b5;
+        fs5 = nsf_c.transpose() * problem->FS5_matrix[i] * c_tmp* b5;
         fvecn(k) = -pp5(0, 0) + P1_5(i) - P2_5(i) + fs5(0, 0);
     }
 
@@ -384,7 +384,7 @@ int newton_msr_n::operator()(const Eigen::VectorXd& n,
     {
         int k = i + pfvecn;
         pp6 = a_tmp.transpose() * problem->ST6_matrix[i] * d6_tmp;
-        fs6 = nsf_c.transpose() * problem->FS6_matrix[i] * c_tmp * b6;
+        fs6 = nsf_c.transpose() * problem->FS6_matrix[i] * c_tmp* b6;
         fvecn(k) = -pp6(0, 0) + P1_6(i) - P2_6(i) + fs6(0, 0);
     }
 
@@ -394,7 +394,7 @@ int newton_msr_n::operator()(const Eigen::VectorXd& n,
     {
         int k = i + pfvecn;
         pp7 = a_tmp.transpose() * problem->ST7_matrix[i] * d7_tmp;
-        fs7 = nsf_c.transpose() * problem->FS7_matrix[i] * c_tmp * b7;
+        fs7 = nsf_c.transpose() * problem->FS7_matrix[i] * c_tmp* b7;
         fvecn(k) = -pp7(0, 0) + P1_7(i) - P2_7(i) + fs7(0, 0);
     }
 
@@ -404,7 +404,7 @@ int newton_msr_n::operator()(const Eigen::VectorXd& n,
     {
         int k = i + pfvecn;
         pp8 = a_tmp.transpose() * problem->ST8_matrix[i] * d8_tmp;
-        fs8 = nsf_c.transpose() * problem->FS8_matrix[i] * c_tmp * b8;
+        fs8 = nsf_c.transpose() * problem->FS8_matrix[i] * c_tmp* b8;
         fvecn(k) = -pp8(0, 0) + P1_8(i) - P2_8(i) + fs8(0, 0);
     }
 
@@ -414,7 +414,7 @@ int newton_msr_n::operator()(const Eigen::VectorXd& n,
 int newton_msr_n::df(const Eigen::VectorXd& n,
                      Eigen::MatrixXd& fjacn) const
 {
-    Eigen::NumericalDiff<newton_msr_n> numDiff(*this);
+    Eigen::NumericalDiff<newton_msr_n> numDiff( * this);
     numDiff.df(n, fjacn);
     return 0;
 }
@@ -437,7 +437,7 @@ int newton_msr_t::operator()(const Eigen::VectorXd& t,
     // convective term in T_eqn
     Eigen::MatrixXd tt(1, 1);
     // laplacian of T
-    Eigen::VectorXd T1 = problem->LT_matrix * e_tmp * nu / Pr;
+    Eigen::VectorXd T1 = problem->LT_matrix* e_tmp* nu / Pr;
     // temp flux source
     Eigen::MatrixXd xsf(1, 1);
     // decay heat source term (*dli/cp)
@@ -449,13 +449,13 @@ int newton_msr_t::operator()(const Eigen::VectorXd& t,
     Eigen::MatrixXd dh2(1, 1);
     Eigen::MatrixXd dh3(1, 1);
     //laplacian of dh
-    Eigen::VectorXd DH1_1 = problem->LD1_matrix * f1_tmp * nu / Sc;
-    Eigen::VectorXd DH1_2 = problem->LD2_matrix * f2_tmp * nu / Sc;
-    Eigen::VectorXd DH1_3 = problem->LD3_matrix * f3_tmp * nu / Sc;
+    Eigen::VectorXd DH1_1 = problem->LD1_matrix* f1_tmp* nu / Sc;
+    Eigen::VectorXd DH1_2 = problem->LD2_matrix* f2_tmp* nu / Sc;
+    Eigen::VectorXd DH1_3 = problem->LD3_matrix* f3_tmp* nu / Sc;
     //algebric term in dh eq
-    Eigen::VectorXd DH2_1 = problem->MD1_matrix * f1_tmp * dl1;
-    Eigen::VectorXd DH2_2 = problem->MD2_matrix * f2_tmp * dl2;
-    Eigen::VectorXd DH2_3 = problem->MD3_matrix * f3_tmp * dl3;
+    Eigen::VectorXd DH2_1 = problem->MD1_matrix* f1_tmp* dl1;
+    Eigen::VectorXd DH2_2 = problem->MD2_matrix* f2_tmp* dl2;
+    Eigen::VectorXd DH2_3 = problem->MD3_matrix* f3_tmp* dl3;
     // flux source in term dh eq (*dbi)
     Eigen::MatrixXd dfs1(1, 1);
     Eigen::MatrixXd dfs2(1, 1);
@@ -477,7 +477,7 @@ int newton_msr_t::operator()(const Eigen::VectorXd& t,
     {
         int k = i + pfvect;
         dh1 = a_tmp.transpose() * problem->SD1_matrix[i] * f1_tmp;
-        dfs1 = sp_c.transpose() * problem->DFS1_matrix[i] * c_tmp * db1;
+        dfs1 = sp_c.transpose() * problem->DFS1_matrix[i] * c_tmp* db1;
         fvect(k) = -dh1(0, 0) + DH1_1(i) - DH2_1(i) + dfs1(0, 0);
     }
 
@@ -487,7 +487,7 @@ int newton_msr_t::operator()(const Eigen::VectorXd& t,
     {
         int k = i + pfvect;
         dh2 = a_tmp.transpose() * problem->SD2_matrix[i] * f2_tmp;
-        dfs2 = sp_c.transpose() * problem->DFS2_matrix[i] * c_tmp * db2;
+        dfs2 = sp_c.transpose() * problem->DFS2_matrix[i] * c_tmp* db2;
         fvect(k) = -dh2(0, 0) + DH1_2(i) - DH2_2(i) + dfs2(0, 0);
     }
 
@@ -497,7 +497,7 @@ int newton_msr_t::operator()(const Eigen::VectorXd& t,
     {
         int k = i + pfvect;
         dh3 = a_tmp.transpose() * problem->SD3_matrix[i] * f3_tmp;
-        dfs3 = sp_c.transpose() * problem->DFS3_matrix[i] * c_tmp * db3;
+        dfs3 = sp_c.transpose() * problem->DFS3_matrix[i] * c_tmp* db3;
         fvect(k) = -dh3(0, 0) + DH1_3(i) - DH2_3(i) + dfs3(0, 0);
     }
 
@@ -512,7 +512,7 @@ int newton_msr_t::operator()(const Eigen::VectorXd& t,
 int newton_msr_t::df(const Eigen::VectorXd& t,
                      Eigen::MatrixXd& fjact) const
 {
-    Eigen::NumericalDiff<newton_msr_t> numDiff(*this);
+    Eigen::NumericalDiff<newton_msr_t> numDiff( * this);
     numDiff.df(t, fjact);
     return 0;
 }
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedMSR/ReducedMSR.H b/src/ITHACA_ROMPROBLEMS/ReducedMSR/ReducedMSR.H
old mode 100755
new mode 100644
index 260a75405..a406519ad
--- a/src/ITHACA_ROMPROBLEMS/ReducedMSR/ReducedMSR.H
+++ b/src/ITHACA_ROMPROBLEMS/ReducedMSR/ReducedMSR.H
@@ -39,13 +39,15 @@ struct newton_msr_fd: public newton_argument<double>
 {
     public:
         newton_msr_fd() {}
+
         newton_msr_fd(int Nx, int Ny, msrProblem& problem) :
             newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_u(problem.NUmodes + problem.liftfield.size()),
             Nphi_p(problem.NPmodes),
             N_BC(problem.inletIndex.rows())
         {}
+
         int operator()(const Eigen::VectorXd& x, Eigen::VectorXd& fvec) const;
         int df(const Eigen::VectorXd& x,  Eigen::MatrixXd& fjac) const;
 
@@ -63,9 +65,10 @@ struct newton_msr_n: public newton_argument<double>
 {
     public:
         newton_msr_n() {}
+
         newton_msr_n(int Nx, int Ny, msrProblem& problem) :
             newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_flux(problem.NFluxmodes),
             Nphi_prec1(problem.NPrecmodes(0)),
             Nphi_prec2(problem.NPrecmodes(1)),
@@ -80,6 +83,7 @@ struct newton_msr_n: public newton_argument<double>
             nsf_c(problem.NCmodes),
             a_c(problem.NCmodes)
         {}
+
         int operator()(const Eigen::VectorXd& n, Eigen::VectorXd& fvecn) const;
         int df(const Eigen::VectorXd& n,  Eigen::MatrixXd& fjacn) const;
 
@@ -131,9 +135,10 @@ struct newton_msr_t: public newton_argument<double>
 {
     public:
         newton_msr_t() {}
+
         newton_msr_t(int Nx, int Ny, msrProblem& problem) :
             newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_T(problem.NTmodes),
             Nphi_dec1(problem.NDecmodes(0)),
             Nphi_dec2(problem.NDecmodes(1)),
@@ -144,6 +149,7 @@ struct newton_msr_t: public newton_argument<double>
             sp_c(problem.NCmodes),
             txs_c(problem.NCmodes)
         {}
+
         int operator()(const Eigen::VectorXd& n, Eigen::VectorXd& fvecn) const;
         int df(const Eigen::VectorXd& n,  Eigen::MatrixXd& fjacn) const;
 
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedProblem/ReducedProblem.C b/src/ITHACA_ROMPROBLEMS/ReducedProblem/ReducedProblem.C
index 47a9f6d5f..c9c8cf432 100644
--- a/src/ITHACA_ROMPROBLEMS/ReducedProblem/ReducedProblem.C
+++ b/src/ITHACA_ROMPROBLEMS/ReducedProblem/ReducedProblem.C
@@ -47,7 +47,7 @@ reducedProblem::reducedProblem()
 
 reducedProblem::reducedProblem(reductionProblem& problem)
     :
-    problem(&problem)
+    problem( & problem)
 {
 }
 
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedProblem/ReducedProblem.H b/src/ITHACA_ROMPROBLEMS/ReducedProblem/ReducedProblem.H
index 70201c073..67901126b 100644
--- a/src/ITHACA_ROMPROBLEMS/ReducedProblem/ReducedProblem.H
+++ b/src/ITHACA_ROMPROBLEMS/ReducedProblem/ReducedProblem.H
@@ -93,7 +93,7 @@ class reducedProblem
         static Eigen::MatrixXd solveLinearSys(List<Eigen::MatrixXd> LinSys,
                                               Eigen::MatrixXd x,
                                               Eigen::VectorXd& residual, const Eigen::MatrixXd& bc = Eigen::MatrixXd::Zero(0,
-                                                      0), const std::string solverType = "fullPivLu");
+                                                  0), const std::string solverType = "fullPivLu");
         ///
         /// @brief      Linear system solver for the online problem. It can be used for any kind of variable.
         /// Boundary conditions are set to 0 as default so that the system is not constrained if no conditions
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedSimpleSteadyNS/ReducedSimpleSteadyNS.C b/src/ITHACA_ROMPROBLEMS/ReducedSimpleSteadyNS/ReducedSimpleSteadyNS.C
old mode 100755
new mode 100644
index b27bc0bb8..52d755600
--- a/src/ITHACA_ROMPROBLEMS/ReducedSimpleSteadyNS/ReducedSimpleSteadyNS.C
+++ b/src/ITHACA_ROMPROBLEMS/ReducedSimpleSteadyNS/ReducedSimpleSteadyNS.C
@@ -42,7 +42,7 @@ reducedSimpleSteadyNS::reducedSimpleSteadyNS()
 
 reducedSimpleSteadyNS::reducedSimpleSteadyNS(SteadyNSSimple& FOMproblem)
     :
-    problem(&FOMproblem)
+    problem( & FOMproblem)
 {
     // Create a new Umodes set where the first ones are the lift functions
     for (int i = 0; i < problem->inletIndex.rows(); i++)
@@ -118,7 +118,7 @@ void reducedSimpleSteadyNS::solveOnline_Simple(scalar mu_now,
         problem->para->ITHACAdict->lookupOrDefault<float>("residualJumpLim", 1e-5);
     float normalizedResidualLim =
         problem->para->ITHACAdict->lookupOrDefault<float>("normalizedResidualLim",
-                1e-5);
+            1e-5);
     maxIterOn = problem->para->ITHACAdict->lookupOrDefault<int>("maxIterOn",
                 1000);
     scalar residual_jump(1 + residualJumpLim);
@@ -179,11 +179,11 @@ void reducedSimpleSteadyNS::solveOnline_Simple(scalar mu_now,
         (
             fvm::div(phi, U)
             - fvm::laplacian(nueff, U)
-            - fvc::div(nueff * dev2(T(fvc::grad(U))))
+            - fvc::div(nueff* dev2(T(fvc::grad(U))))
         );
         UEqn.relax();
         List<Eigen::MatrixXd> RedLinSysU = ULmodes.project(UEqn, UprojN);
-        RedLinSysU[1] = RedLinSysU[1] - projGradModP * b;
+        RedLinSysU[1] = RedLinSysU[1] - projGradModP* b;
         a = reducedProblem::solveLinearSys(RedLinSysU, a, uresidual, vel_now);
         ULmodes.reconstruct(U, a, "U");
         volScalarField rAU(1.0 / UEqn.A());
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedSteadyNS/ReducedSteadyNS.C b/src/ITHACA_ROMPROBLEMS/ReducedSteadyNS/ReducedSteadyNS.C
index 460941fe7..c488cf7eb 100644
--- a/src/ITHACA_ROMPROBLEMS/ReducedSteadyNS/ReducedSteadyNS.C
+++ b/src/ITHACA_ROMPROBLEMS/ReducedSteadyNS/ReducedSteadyNS.C
@@ -43,7 +43,7 @@ reducedSteadyNS::reducedSteadyNS()
 
 reducedSteadyNS::reducedSteadyNS(steadyNS& FOMproblem)
     :
-    problem(&FOMproblem)
+    problem( & FOMproblem)
 {
     N_BC = problem->inletIndex.rows();
     Nphi_u = problem->B_matrix.rows();
@@ -77,11 +77,11 @@ int newton_steadyNS::operator()(const Eigen::VectorXd& x,
     // Convective term
     Eigen::MatrixXd cc(1, 1);
     // Mom Term
-    Eigen::VectorXd M1 = problem->B_matrix * a_tmp * nu;
+    Eigen::VectorXd M1 = problem->B_matrix* a_tmp* nu;
     // Gradient of pressure
-    Eigen::VectorXd M2 = problem->K_matrix * b_tmp;
+    Eigen::VectorXd M2 = problem->K_matrix* b_tmp;
     // Pressure Term
-    Eigen::VectorXd M3 = problem->P_matrix * a_tmp;
+    Eigen::VectorXd M3 = problem->P_matrix* a_tmp;
     // Penalty term
     Eigen::MatrixXd penaltyU = Eigen::MatrixXd::Zero(Nphi_u, N_BC);
 
@@ -98,7 +98,7 @@ int newton_steadyNS::operator()(const Eigen::VectorXd& x,
     for (int i = 0; i < Nphi_u; i++)
     {
         cc = a_tmp.transpose() * Eigen::SliceFromTensor(problem->C_tensor, 0,
-                i) * a_tmp;
+             i) * a_tmp;
         fvec(i) = M1(i) - cc(0, 0) - M2(i);
 
         if (problem->bcMethod == "penalty")
@@ -128,7 +128,7 @@ int newton_steadyNS::operator()(const Eigen::VectorXd& x,
 int newton_steadyNS::df(const Eigen::VectorXd& x,
                         Eigen::MatrixXd& fjac) const
 {
-    Eigen::NumericalDiff<newton_steadyNS> numDiff(*this);
+    Eigen::NumericalDiff<newton_steadyNS> numDiff( * this);
     numDiff.df(x, fjac);
     return 0;
 }
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedSteadyNS/ReducedSteadyNS.H b/src/ITHACA_ROMPROBLEMS/ReducedSteadyNS/ReducedSteadyNS.H
old mode 100755
new mode 100644
index b602abb7d..1976f619c
--- a/src/ITHACA_ROMPROBLEMS/ReducedSteadyNS/ReducedSteadyNS.H
+++ b/src/ITHACA_ROMPROBLEMS/ReducedSteadyNS/ReducedSteadyNS.H
@@ -52,10 +52,11 @@ struct newton_steadyNS: public newton_argument<double>
 {
     public:
         newton_steadyNS() {}
+
         newton_steadyNS(int Nx, int Ny,
                         steadyNS& problem): newton_argument<double>(Nx,
                                     Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_u(problem.NUmodes + problem.liftfield.size() + problem.NSUPmodes),
             Nphi_p(problem.NPmodes),
             N_BC(problem.inletIndex.rows())
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedSteadyNSTurb/ReducedSteadyNSTurb.C b/src/ITHACA_ROMPROBLEMS/ReducedSteadyNSTurb/ReducedSteadyNSTurb.C
index 6ebbe45af..0beaa9f80 100644
--- a/src/ITHACA_ROMPROBLEMS/ReducedSteadyNSTurb/ReducedSteadyNSTurb.C
+++ b/src/ITHACA_ROMPROBLEMS/ReducedSteadyNSTurb/ReducedSteadyNSTurb.C
@@ -39,7 +39,7 @@ ReducedSteadyNSTurb::ReducedSteadyNSTurb()
 
 ReducedSteadyNSTurb::ReducedSteadyNSTurb(SteadyNSTurb& fomProblem)
     :
-    problem(&fomProblem)
+    problem( & fomProblem)
 {
     N_BC = problem->inletIndex.rows();
     Nphi_u = problem->B_matrix.rows();
@@ -77,11 +77,11 @@ int newtonSteadyNSTurbSUP::operator()(const Eigen::VectorXd& x,
     // Convective term
     Eigen::MatrixXd cc(1, 1);
     // Mom Term
-    Eigen::VectorXd m1 = problem->bTotalMatrix * aTmp * nu;
+    Eigen::VectorXd m1 = problem->bTotalMatrix* aTmp* nu;
     // Gradient of pressure
-    Eigen::VectorXd m2 = problem->K_matrix * bTmp;
+    Eigen::VectorXd m2 = problem->K_matrix* bTmp;
     // Pressure Term
-    Eigen::VectorXd m3 = problem->P_matrix * aTmp;
+    Eigen::VectorXd m3 = problem->P_matrix* aTmp;
     // Penalty term
     Eigen::MatrixXd penaltyU = Eigen::MatrixXd::Zero(Nphi_u, N_BC);
 
@@ -98,13 +98,13 @@ int newtonSteadyNSTurbSUP::operator()(const Eigen::VectorXd& x,
     for (int i = 0; i < Nphi_u; i++)
     {
         cc = aTmp.transpose() * Eigen::SliceFromTensor(problem->C_tensor, 0,
-                i) * aTmp - gNut.transpose() *
+             i) * aTmp - gNut.transpose() *
              Eigen::SliceFromTensor(problem->cTotalTensor, 0, i) * aTmp;
         fvec(i) = m1(i) - cc(0, 0) - m2(i);
 
         if (problem->bcMethod == "penalty")
         {
-            fvec(i) += ((penaltyU * tauU)(i, 0));
+            fvec(i) += ((penaltyU* tauU)(i, 0));
         }
     }
 
@@ -137,13 +137,13 @@ int newtonSteadyNSTurbPPE::operator()(const Eigen::VectorXd& x,
     Eigen::MatrixXd gg(1, 1);
     Eigen::MatrixXd bb(1, 1);
     // Mom Term
-    Eigen::VectorXd m1 = problem->bTotalMatrix * aTmp * nu;
+    Eigen::VectorXd m1 = problem->bTotalMatrix* aTmp* nu;
     // Gradient of pressure
-    Eigen::VectorXd m2 = problem->K_matrix * bTmp;
+    Eigen::VectorXd m2 = problem->K_matrix* bTmp;
     // Pressure Term
-    Eigen::VectorXd m3 = problem->D_matrix * bTmp;
+    Eigen::VectorXd m3 = problem->D_matrix* bTmp;
     // BC PPE
-    Eigen::VectorXd m7 = problem->BC3_matrix * aTmp * nu;
+    Eigen::VectorXd m7 = problem->BC3_matrix* aTmp* nu;
     // Penalty term
     Eigen::MatrixXd penaltyU = Eigen::MatrixXd::Zero(Nphi_u, N_BC);
 
@@ -160,13 +160,13 @@ int newtonSteadyNSTurbPPE::operator()(const Eigen::VectorXd& x,
     for (int i = 0; i < Nphi_u; i++)
     {
         cc = aTmp.transpose() * Eigen::SliceFromTensor(problem->C_tensor, 0,
-                i) * aTmp - gNut.transpose() *
+             i) * aTmp - gNut.transpose() *
              Eigen::SliceFromTensor(problem->cTotalTensor, 0, i) * aTmp;
         fvec(i) = m1(i) - cc(0, 0) - m2(i);
 
         if (problem->bcMethod == "penalty")
         {
-            fvec(i) += ((penaltyU * tauU)(i, 0));
+            fvec(i) += ((penaltyU* tauU)(i, 0));
         }
     }
 
@@ -174,7 +174,7 @@ int newtonSteadyNSTurbPPE::operator()(const Eigen::VectorXd& x,
     {
         int k = j + Nphi_u;
         gg = aTmp.transpose() * Eigen::SliceFromTensor(problem->gTensor, 0,
-                j) * aTmp;
+             j) * aTmp;
         //fvec(k) = m3(j, 0) - gg(0, 0) - m6(j, 0) + bb(0, 0);
         fvec(k) = m3(j, 0) + gg(0, 0) - m7(j, 0);
     }
@@ -194,7 +194,7 @@ int newtonSteadyNSTurbPPE::operator()(const Eigen::VectorXd& x,
 int newtonSteadyNSTurbSUP::df(const Eigen::VectorXd& x,
                               Eigen::MatrixXd& fjac) const
 {
-    Eigen::NumericalDiff<newtonSteadyNSTurbSUP> numDiff(*this);
+    Eigen::NumericalDiff<newtonSteadyNSTurbSUP> numDiff( * this);
     numDiff.df(x, fjac);
     return 0;
 }
@@ -202,7 +202,7 @@ int newtonSteadyNSTurbSUP::df(const Eigen::VectorXd& x,
 int newtonSteadyNSTurbPPE::df(const Eigen::VectorXd& x,
                               Eigen::MatrixXd& fjac) const
 {
-    Eigen::NumericalDiff<newtonSteadyNSTurbPPE> numDiff(*this);
+    Eigen::NumericalDiff<newtonSteadyNSTurbPPE> numDiff( * this);
     numDiff.df(x, fjac);
     return 0;
 }
@@ -441,5 +441,6 @@ Eigen::MatrixXd ReducedSteadyNSTurb::setOnlineVelocity(Eigen::MatrixXd vel)
 
     return vel_scal;
 }
+
 // ************************************************************************* //
 
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedSteadyNSTurb/ReducedSteadyNSTurb.H b/src/ITHACA_ROMPROBLEMS/ReducedSteadyNSTurb/ReducedSteadyNSTurb.H
index 03253dd7b..432a41568 100644
--- a/src/ITHACA_ROMPROBLEMS/ReducedSteadyNSTurb/ReducedSteadyNSTurb.H
+++ b/src/ITHACA_ROMPROBLEMS/ReducedSteadyNSTurb/ReducedSteadyNSTurb.H
@@ -52,9 +52,10 @@ struct newtonSteadyNSTurbSUP: public newton_argument<double>
 {
     public:
         newtonSteadyNSTurbSUP() {}
+
         newtonSteadyNSTurbSUP(int Nx, int Ny,
                               SteadyNSTurb& problem): newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_u(problem.NUmodes + problem.liftfield.size() + problem.NSUPmodes),
             nphiNut(problem.nNutModes),
             Nphi_p(problem.NPmodes),
@@ -81,9 +82,10 @@ struct newtonSteadyNSTurbPPE: public newton_argument<double>
 {
     public:
         newtonSteadyNSTurbPPE() {}
+
         newtonSteadyNSTurbPPE(int Nx, int Ny,
                               SteadyNSTurb& problem): newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_u(problem.NUmodes + problem.liftfield.size()),
             nphiNut(problem.nNutModes),
             Nphi_p(problem.NPmodes),
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedSteadyNSTurbIntrusive/ReducedSteadyNSTurbIntrusive.C b/src/ITHACA_ROMPROBLEMS/ReducedSteadyNSTurbIntrusive/ReducedSteadyNSTurbIntrusive.C
old mode 100755
new mode 100644
index 61bf41750..bb9cb10bf
--- a/src/ITHACA_ROMPROBLEMS/ReducedSteadyNSTurbIntrusive/ReducedSteadyNSTurbIntrusive.C
+++ b/src/ITHACA_ROMPROBLEMS/ReducedSteadyNSTurbIntrusive/ReducedSteadyNSTurbIntrusive.C
@@ -40,7 +40,7 @@ ReducedSteadyNSTurbIntrusive::ReducedSteadyNSTurbIntrusive()
 ReducedSteadyNSTurbIntrusive::ReducedSteadyNSTurbIntrusive(
     SteadyNSTurbIntrusive& fomProblem)
     :
-    problem(&fomProblem)
+    problem( & fomProblem)
 {
     N_BC = problem->inletIndex.rows();
     Nphi_u = problem->bMatrix.rows();
@@ -62,9 +62,9 @@ int newtonSteadyNSTurbIntrusive::operator()(const Eigen::VectorXd& x,
     // Convective term
     Eigen::MatrixXd cc(1, 1);
     // Mom Term
-    Eigen::VectorXd m1 = problem->bTotalMatrix * aTmp * nu;
+    Eigen::VectorXd m1 = problem->bTotalMatrix* aTmp* nu;
     // Gradient of pressure
-    Eigen::VectorXd m2 = problem->kMatrix * aTmp;
+    Eigen::VectorXd m2 = problem->kMatrix* aTmp;
     // Penalty term
     Eigen::MatrixXd penaltyU = Eigen::MatrixXd::Zero(Nphi_u, N_BC);
 
@@ -81,12 +81,12 @@ int newtonSteadyNSTurbIntrusive::operator()(const Eigen::VectorXd& x,
     for (int i = 0; i < Nphi_u; i++)
     {
         cc = aTmp.transpose() * Eigen::SliceFromTensor(problem->cTotalTensor, 0,
-                i) * aTmp;
+             i) * aTmp;
         fvec(i) = m1(i) - cc(0, 0) - m2(i);
 
         if (problem->bcMethod == "penalty")
         {
-            fvec(i) += ((penaltyU * tauU)(i, 0));
+            fvec(i) += ((penaltyU* tauU)(i, 0));
         }
     }
 
@@ -104,7 +104,7 @@ int newtonSteadyNSTurbIntrusive::operator()(const Eigen::VectorXd& x,
 int newtonSteadyNSTurbIntrusive::df(const Eigen::VectorXd& x,
                                     Eigen::MatrixXd& fjac) const
 {
-    Eigen::NumericalDiff<newtonSteadyNSTurbIntrusive> numDiff(*this);
+    Eigen::NumericalDiff<newtonSteadyNSTurbIntrusive> numDiff( * this);
     numDiff.df(x, fjac);
     return 0;
 }
@@ -284,6 +284,7 @@ void ReducedSteadyNSTurbIntrusive::reconstructLiftAndDrag(
         ITHACAstream::exportMatrix(fN, "fN", "eigen", folder);
     }
 }
+
 // ************************************************************************* //
 
 
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedSteadyNSTurbIntrusive/ReducedSteadyNSTurbIntrusive.H b/src/ITHACA_ROMPROBLEMS/ReducedSteadyNSTurbIntrusive/ReducedSteadyNSTurbIntrusive.H
old mode 100755
new mode 100644
index d7a6df143..ce4b33e12
--- a/src/ITHACA_ROMPROBLEMS/ReducedSteadyNSTurbIntrusive/ReducedSteadyNSTurbIntrusive.H
+++ b/src/ITHACA_ROMPROBLEMS/ReducedSteadyNSTurbIntrusive/ReducedSteadyNSTurbIntrusive.H
@@ -52,9 +52,10 @@ struct newtonSteadyNSTurbIntrusive: public newton_argument<double>
 {
     public:
         newtonSteadyNSTurbIntrusive() {}
+
         newtonSteadyNSTurbIntrusive(int Nx, int Ny,
                                     SteadyNSTurbIntrusive& problem): newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_u(problem.nModesOnline),
             N_BC(problem.inletIndex.rows())
         {}
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyBB/ReducedUnsteadyBB.C b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyBB/ReducedUnsteadyBB.C
index e795cbba9..760ab5dce 100644
--- a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyBB/ReducedUnsteadyBB.C
+++ b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyBB/ReducedUnsteadyBB.C
@@ -45,7 +45,7 @@ ReducedUnsteadyBB::ReducedUnsteadyBB()
 
 ReducedUnsteadyBB::ReducedUnsteadyBB(UnsteadyBB& FOMproblem)
     :
-    problem(&FOMproblem)
+    problem( & FOMproblem)
 {
     N_BC_t    = problem->inletIndexT.rows();
     N_BC      = problem->inletIndex.rows();
@@ -107,26 +107,26 @@ int newton_unsteadyBB_sup::operator()(const Eigen::VectorXd& x,
     // Convective term
     Eigen::MatrixXd cc(1, 1);
     // Diffusive Term
-    Eigen::VectorXd M1 = problem->B_matrix * a_tmp * nu;
+    Eigen::VectorXd M1 = problem->B_matrix* a_tmp* nu;
     // Mass Term Velocity
-    Eigen::VectorXd M5 = problem->M_matrix * a_dot;
+    Eigen::VectorXd M5 = problem->M_matrix* a_dot;
     // Gradient of pressure
-    Eigen::VectorXd M2 = problem->K_matrix * b_tmp;
+    Eigen::VectorXd M2 = problem->K_matrix* b_tmp;
     // Continuity
-    Eigen::VectorXd M3 = problem->P_matrix * a_tmp;
+    Eigen::VectorXd M3 = problem->P_matrix* a_tmp;
     // Buoyancy Term
-    Eigen::VectorXd M10 = problem->H_matrix * c_tmp;
+    Eigen::VectorXd M10 = problem->H_matrix* c_tmp;
     // Convective term temperature
     Eigen::MatrixXd qq(1, 1);
     // diffusive term temperature
-    Eigen::VectorXd M6 = problem->Y_matrix * c_tmp * (nu / Pr);
+    Eigen::VectorXd M6 = problem->Y_matrix* c_tmp * (nu / Pr);
     // Mass Term Temperature
-    Eigen::VectorXd M8 = problem->W_matrix * c_dot;
+    Eigen::VectorXd M8 = problem->W_matrix* c_dot;
 
     for (int i = 0; i < Nphi_u; i++)
     {
         cc = a_tmp.transpose() * Eigen::SliceFromTensor(problem->C_tensor, 0,
-                i) * a_tmp;
+             i) * a_tmp;
         fvec(i) = - M5(i) + M1(i) - cc(0, 0) - M10(i) - M2(i);
     }
 
@@ -161,7 +161,7 @@ int newton_unsteadyBB_sup::operator()(const Eigen::VectorXd& x,
 int newton_unsteadyBB_sup::df(const Eigen::VectorXd& x,
                               Eigen::MatrixXd& fjac) const
 {
-    Eigen::NumericalDiff<newton_unsteadyBB_sup> numDiff(*this);
+    Eigen::NumericalDiff<newton_unsteadyBB_sup> numDiff( * this);
     numDiff.df(x, fjac);
     return 0;
 }
@@ -190,29 +190,29 @@ int newton_unsteadyBB_PPE::operator()(const Eigen::VectorXd& x,
     Eigen::MatrixXd qq(1, 1);
     // Eigen::MatrixXd st(1, 1);
     // Mom Term
-    Eigen::VectorXd M1 = problem->B_matrix * a_tmp * nu;
+    Eigen::VectorXd M1 = problem->B_matrix* a_tmp* nu;
     // Gradient of pressure
-    Eigen::VectorXd M2 = problem->K_matrix * b_tmp;
+    Eigen::VectorXd M2 = problem->K_matrix* b_tmp;
     // Mass Term
-    Eigen::VectorXd M5 = problem->M_matrix * a_dot;
+    Eigen::VectorXd M5 = problem->M_matrix* a_dot;
     // Pressure Term
-    Eigen::VectorXd M3 = problem->D_matrix * b_tmp;
+    Eigen::VectorXd M3 = problem->D_matrix* b_tmp;
     // BC PPE
-    Eigen::VectorXd M6 = problem->BC1_matrix * a_tmp * nu;
+    Eigen::VectorXd M6 = problem->BC1_matrix* a_tmp* nu;
     // BC PPE
     // Buoyancy Term
-    Eigen::VectorXd M10 = problem->H_matrix * c_tmp;
-    Eigen::VectorXd M11 = problem->HP_matrix * c_tmp;
-    Eigen::VectorXd M7 = problem->BC3_matrix * a_tmp * nu;
+    Eigen::VectorXd M10 = problem->H_matrix* c_tmp;
+    Eigen::VectorXd M11 = problem->HP_matrix* c_tmp;
+    Eigen::VectorXd M7 = problem->BC3_matrix* a_tmp* nu;
     // diffusive term temperature
-    Eigen::VectorXd M9 = problem->Y_matrix * c_tmp * (nu / Pr);
+    Eigen::VectorXd M9 = problem->Y_matrix* c_tmp * (nu / Pr);
     // Mass Term Temperature
-    Eigen::VectorXd M8 = problem->W_matrix * c_dot;
+    Eigen::VectorXd M8 = problem->W_matrix* c_dot;
 
     for (int i = 0; i < Nphi_u; i++)
     {
         cc = a_tmp.transpose() * Eigen::SliceFromTensor(problem->C_tensor, 0,
-                i) * a_tmp;
+             i) * a_tmp;
         fvec(i) = - M5(i) + M1(i) - cc(0, 0) - M10(i) - M2(i);
     }
 
@@ -243,7 +243,7 @@ int newton_unsteadyBB_PPE::operator()(const Eigen::VectorXd& x,
 int newton_unsteadyBB_PPE::df(const Eigen::VectorXd& x,
                               Eigen::MatrixXd& fjac) const
 {
-    Eigen::NumericalDiff<newton_unsteadyBB_PPE> numDiff(*this);
+    Eigen::NumericalDiff<newton_unsteadyBB_PPE> numDiff( * this);
     numDiff.df(x, fjac);
     return 0;
 }
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyBB/ReducedUnsteadyBB.H b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyBB/ReducedUnsteadyBB.H
old mode 100755
new mode 100644
index 50ba23892..dc5796356
--- a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyBB/ReducedUnsteadyBB.H
+++ b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyBB/ReducedUnsteadyBB.H
@@ -50,9 +50,10 @@ struct newton_unsteadyBB_sup: public newton_argument<double>
 {
     public:
         newton_unsteadyBB_sup() {}
+
         newton_unsteadyBB_sup(int Nx, int Ny,
                               UnsteadyBB& problem): newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_u(problem.NUmodes + problem.liftfield.size() + problem.NSUPmodes),
             Nphi_t(problem.NTmodes + problem.liftfieldT.size()),
             N_BC_t(problem.inletIndexT.rows()),
@@ -82,9 +83,10 @@ struct newton_unsteadyBB_PPE: public newton_argument<double>
 {
     public:
         newton_unsteadyBB_PPE() {}
+
         newton_unsteadyBB_PPE(int Nx, int Ny,
                               UnsteadyBB& problem): newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_u(problem.NUmodes + problem.liftfield.size()),
             Nphi_t(problem.NTmodes + problem.liftfieldT.size()),
             N_BC_t(problem.inletIndexT.rows()),
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyMSR/ReducedUnsteadyMSR.C b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyMSR/ReducedUnsteadyMSR.C
old mode 100755
new mode 100644
index 3976af914..664303bb8
--- a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyMSR/ReducedUnsteadyMSR.C
+++ b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyMSR/ReducedUnsteadyMSR.C
@@ -29,7 +29,7 @@ reducedusMSR::reducedusMSR() {}
 
 reducedusMSR::reducedusMSR(usmsrProblem& FOMproblem)
 {
-    problem = &FOMproblem;
+    problem = & FOMproblem;
     N_BC = problem->inletIndex.rows();
     N_BCt = problem->inletIndexT.rows();
     Nphi_u = problem->B_matrix.rows();
@@ -197,17 +197,17 @@ int newton_usmsr_fd::operator()(const Eigen::VectorXd& x,
     Eigen::MatrixXd gg(1, 1);
     Eigen::MatrixXd bb(1, 1);
     // Mom Term
-    Eigen::VectorXd M1 = problem->B_matrix * a_tmp * nu;
+    Eigen::VectorXd M1 = problem->B_matrix* a_tmp* nu;
     // Gradient of pressure
-    Eigen::VectorXd M2 = problem->K_matrix * b_tmp;
+    Eigen::VectorXd M2 = problem->K_matrix* b_tmp;
     // Mass Term
-    Eigen::VectorXd M5 = problem->M_matrix * a_dot;
+    Eigen::VectorXd M5 = problem->M_matrix* a_dot;
     // Pressure Term
-    Eigen::VectorXd M3 = problem->D_matrix * b_tmp;
+    Eigen::VectorXd M3 = problem->D_matrix* b_tmp;
     // BC PPE
-    Eigen::VectorXd M6 = problem->BC1_matrix * a_tmp * nu;
+    Eigen::VectorXd M6 = problem->BC1_matrix* a_tmp* nu;
     // BC PPE
-    Eigen::VectorXd M7 = problem->BC3_matrix * a_tmp * nu;
+    Eigen::VectorXd M7 = problem->BC3_matrix* a_tmp* nu;
 
     for (int i = 0; i < Nphi_u; i++)
     {
@@ -234,7 +234,7 @@ int newton_usmsr_fd::operator()(const Eigen::VectorXd& x,
 int newton_usmsr_fd::df(const Eigen::VectorXd& x,
                         Eigen::MatrixXd& fjac) const
 {
-    Eigen::NumericalDiff<newton_usmsr_fd> numDiff(*this);
+    Eigen::NumericalDiff<newton_usmsr_fd> numDiff( * this);
     numDiff.df(x, fjac);
     return 0;
 }
@@ -297,7 +297,7 @@ int newton_usmsr_n::operator()(const Eigen::VectorXd& n,
     d8_dot = (n.segment(pos, Nphi_prec8) - w_old.segment(pos, Nphi_prec8)) / dt;
     /// Neutronics terms
     // ddt flux term
-    Eigen::VectorXd F_dot = problem->MF_matrix * c_dot * iv;
+    Eigen::VectorXd F_dot = problem->MF_matrix* c_dot* iv;
     // Laplacian flux term
     Eigen::MatrixXd lf(1, 1);
     // flux production term
@@ -305,23 +305,23 @@ int newton_usmsr_n::operator()(const Eigen::VectorXd& n,
     // flux absorption term
     Eigen::MatrixXd af(1, 1);
     // precursor sources
-    Eigen::VectorXd F3_1 = problem->PS1_matrix * d1_tmp * l1;
-    Eigen::VectorXd F3_2 = problem->PS2_matrix * d2_tmp * l2;
-    Eigen::VectorXd F3_3 = problem->PS3_matrix * d3_tmp * l3;
-    Eigen::VectorXd F3_4 = problem->PS4_matrix * d4_tmp * l4;
-    Eigen::VectorXd F3_5 = problem->PS5_matrix * d5_tmp * l5;
-    Eigen::VectorXd F3_6 = problem->PS6_matrix * d6_tmp * l6;
-    Eigen::VectorXd F3_7 = problem->PS7_matrix * d7_tmp * l7;
-    Eigen::VectorXd F3_8 = problem->PS8_matrix * d8_tmp * l8;
+    Eigen::VectorXd F3_1 = problem->PS1_matrix* d1_tmp* l1;
+    Eigen::VectorXd F3_2 = problem->PS2_matrix* d2_tmp* l2;
+    Eigen::VectorXd F3_3 = problem->PS3_matrix* d3_tmp* l3;
+    Eigen::VectorXd F3_4 = problem->PS4_matrix* d4_tmp* l4;
+    Eigen::VectorXd F3_5 = problem->PS5_matrix* d5_tmp* l5;
+    Eigen::VectorXd F3_6 = problem->PS6_matrix* d6_tmp* l6;
+    Eigen::VectorXd F3_7 = problem->PS7_matrix* d7_tmp* l7;
+    Eigen::VectorXd F3_8 = problem->PS8_matrix* d8_tmp* l8;
     //ddt prec term
-    Eigen::VectorXd Pdot_1 = problem->MP1_matrix * d1_dot;
-    Eigen::VectorXd Pdot_2 = problem->MP2_matrix * d2_dot;
-    Eigen::VectorXd Pdot_3 = problem->MP3_matrix * d3_dot;
-    Eigen::VectorXd Pdot_4 = problem->MP4_matrix * d4_dot;
-    Eigen::VectorXd Pdot_5 = problem->MP5_matrix * d5_dot;
-    Eigen::VectorXd Pdot_6 = problem->MP6_matrix * d6_dot;
-    Eigen::VectorXd Pdot_7 = problem->MP7_matrix * d7_dot;
-    Eigen::VectorXd Pdot_8 = problem->MP8_matrix * d8_dot;
+    Eigen::VectorXd Pdot_1 = problem->MP1_matrix* d1_dot;
+    Eigen::VectorXd Pdot_2 = problem->MP2_matrix* d2_dot;
+    Eigen::VectorXd Pdot_3 = problem->MP3_matrix* d3_dot;
+    Eigen::VectorXd Pdot_4 = problem->MP4_matrix* d4_dot;
+    Eigen::VectorXd Pdot_5 = problem->MP5_matrix* d5_dot;
+    Eigen::VectorXd Pdot_6 = problem->MP6_matrix* d6_dot;
+    Eigen::VectorXd Pdot_7 = problem->MP7_matrix* d7_dot;
+    Eigen::VectorXd Pdot_8 = problem->MP8_matrix* d8_dot;
     // Convective terms in prec-eq:
     Eigen::MatrixXd pp1(1, 1);
     Eigen::MatrixXd pp2(1, 1);
@@ -332,23 +332,23 @@ int newton_usmsr_n::operator()(const Eigen::VectorXd& n,
     Eigen::MatrixXd pp7(1, 1);
     Eigen::MatrixXd pp8(1, 1);
     // laplacian of precursor
-    Eigen::VectorXd P1_1 = problem->LP1_matrix * d1_tmp * (nu / Sc);
-    Eigen::VectorXd P1_2 = problem->LP2_matrix * d2_tmp * (nu / Sc);
-    Eigen::VectorXd P1_3 = problem->LP3_matrix * d3_tmp * (nu / Sc);
-    Eigen::VectorXd P1_4 = problem->LP4_matrix * d4_tmp * (nu / Sc);
-    Eigen::VectorXd P1_5 = problem->LP5_matrix * d5_tmp * (nu / Sc);
-    Eigen::VectorXd P1_6 = problem->LP6_matrix * d6_tmp * (nu / Sc);
-    Eigen::VectorXd P1_7 = problem->LP7_matrix * d7_tmp * (nu / Sc);
-    Eigen::VectorXd P1_8 = problem->LP8_matrix * d8_tmp * (nu / Sc);
+    Eigen::VectorXd P1_1 = problem->LP1_matrix* d1_tmp * (nu / Sc);
+    Eigen::VectorXd P1_2 = problem->LP2_matrix* d2_tmp * (nu / Sc);
+    Eigen::VectorXd P1_3 = problem->LP3_matrix* d3_tmp * (nu / Sc);
+    Eigen::VectorXd P1_4 = problem->LP4_matrix* d4_tmp * (nu / Sc);
+    Eigen::VectorXd P1_5 = problem->LP5_matrix* d5_tmp * (nu / Sc);
+    Eigen::VectorXd P1_6 = problem->LP6_matrix* d6_tmp * (nu / Sc);
+    Eigen::VectorXd P1_7 = problem->LP7_matrix* d7_tmp * (nu / Sc);
+    Eigen::VectorXd P1_8 = problem->LP8_matrix* d8_tmp * (nu / Sc);
     // algebric term
-    Eigen::VectorXd P2_1 = problem->MP1_matrix * d1_tmp * l1;
-    Eigen::VectorXd P2_2 = problem->MP2_matrix * d2_tmp * l2;
-    Eigen::VectorXd P2_3 = problem->MP3_matrix * d3_tmp * l3;
-    Eigen::VectorXd P2_4 = problem->MP4_matrix * d4_tmp * l4;
-    Eigen::VectorXd P2_5 = problem->MP5_matrix * d5_tmp * l5;
-    Eigen::VectorXd P2_6 = problem->MP6_matrix * d6_tmp * l6;
-    Eigen::VectorXd P2_7 = problem->MP7_matrix * d7_tmp * l7;
-    Eigen::VectorXd P2_8 = problem->MP8_matrix * d8_tmp * l8;
+    Eigen::VectorXd P2_1 = problem->MP1_matrix* d1_tmp* l1;
+    Eigen::VectorXd P2_2 = problem->MP2_matrix* d2_tmp* l2;
+    Eigen::VectorXd P2_3 = problem->MP3_matrix* d3_tmp* l3;
+    Eigen::VectorXd P2_4 = problem->MP4_matrix* d4_tmp* l4;
+    Eigen::VectorXd P2_5 = problem->MP5_matrix* d5_tmp* l5;
+    Eigen::VectorXd P2_6 = problem->MP6_matrix* d6_tmp* l6;
+    Eigen::VectorXd P2_7 = problem->MP7_matrix* d7_tmp* l7;
+    Eigen::VectorXd P2_8 = problem->MP8_matrix* d8_tmp* l8;
     // flux source term
     Eigen::MatrixXd fs1(1, 1);
     Eigen::MatrixXd fs2(1, 1);
@@ -375,7 +375,7 @@ int newton_usmsr_n::operator()(const Eigen::VectorXd& n,
     {
         int k = i + pfvecn;
         pp1 = a_tmp.transpose() * problem->ST1_matrix[i] * d1_tmp;
-        fs1 = nsf_c.transpose() * problem->FS1_matrix[i] * c_tmp * b1;
+        fs1 = nsf_c.transpose() * problem->FS1_matrix[i] * c_tmp* b1;
         fvecn(k) = -Pdot_1(i) - pp1(0, 0) + P1_1(i) - P2_1(i) + fs1(0, 0);
     }
 
@@ -385,7 +385,7 @@ int newton_usmsr_n::operator()(const Eigen::VectorXd& n,
     {
         int k = i + pfvecn;
         pp2 = a_tmp.transpose() * problem->ST2_matrix[i] * d2_tmp;
-        fs2 = nsf_c.transpose() * problem->FS2_matrix[i] * c_tmp * b2;
+        fs2 = nsf_c.transpose() * problem->FS2_matrix[i] * c_tmp* b2;
         fvecn(k) = -Pdot_2(i) - pp2(0, 0) + P1_2(i) - P2_2(i) + fs2(0, 0);
     }
 
@@ -395,7 +395,7 @@ int newton_usmsr_n::operator()(const Eigen::VectorXd& n,
     {
         int k = i + pfvecn;
         pp3 = a_tmp.transpose() * problem->ST3_matrix[i] * d3_tmp;
-        fs3 = nsf_c.transpose() * problem->FS3_matrix[i] * c_tmp * b3;
+        fs3 = nsf_c.transpose() * problem->FS3_matrix[i] * c_tmp* b3;
         fvecn(k) = -Pdot_3(i) - pp3(0, 0) + P1_3(i) - P2_3(i) + fs3(0, 0);
     }
 
@@ -405,7 +405,7 @@ int newton_usmsr_n::operator()(const Eigen::VectorXd& n,
     {
         int k = i + pfvecn;
         pp4 = a_tmp.transpose() * problem->ST4_matrix[i] * d4_tmp;
-        fs4 = nsf_c.transpose() * problem->FS4_matrix[i] * c_tmp * b4;
+        fs4 = nsf_c.transpose() * problem->FS4_matrix[i] * c_tmp* b4;
         fvecn(k) = -Pdot_4(i) - pp4(0, 0) + P1_4(i) - P2_4(i) + fs4(0, 0);
     }
 
@@ -415,7 +415,7 @@ int newton_usmsr_n::operator()(const Eigen::VectorXd& n,
     {
         int k = i + pfvecn;
         pp5 = a_tmp.transpose() * problem->ST5_matrix[i] * d5_tmp;
-        fs5 = nsf_c.transpose() * problem->FS5_matrix[i] * c_tmp * b5;
+        fs5 = nsf_c.transpose() * problem->FS5_matrix[i] * c_tmp* b5;
         fvecn(k) = -Pdot_5(i) - pp5(0, 0) + P1_5(i) - P2_5(i) + fs5(0, 0);
     }
 
@@ -425,7 +425,7 @@ int newton_usmsr_n::operator()(const Eigen::VectorXd& n,
     {
         int k = i + pfvecn;
         pp6 = a_tmp.transpose() * problem->ST6_matrix[i] * d6_tmp;
-        fs6 = nsf_c.transpose() * problem->FS6_matrix[i] * c_tmp * b6;
+        fs6 = nsf_c.transpose() * problem->FS6_matrix[i] * c_tmp* b6;
         fvecn(k) = -Pdot_6(i) - pp6(0, 0) + P1_6(i) - P2_6(i) + fs6(0, 0);
     }
 
@@ -435,7 +435,7 @@ int newton_usmsr_n::operator()(const Eigen::VectorXd& n,
     {
         int k = i + pfvecn;
         pp7 = a_tmp.transpose() * problem->ST7_matrix[i] * d7_tmp;
-        fs7 = nsf_c.transpose() * problem->FS7_matrix[i] * c_tmp * b7;
+        fs7 = nsf_c.transpose() * problem->FS7_matrix[i] * c_tmp* b7;
         fvecn(k) = -Pdot_7(i) - pp7(0, 0) + P1_7(i) - P2_7(i) + fs7(0, 0);
     }
 
@@ -445,7 +445,7 @@ int newton_usmsr_n::operator()(const Eigen::VectorXd& n,
     {
         int k = i + pfvecn;
         pp8 = a_tmp.transpose() * problem->ST8_matrix[i] * d8_tmp;
-        fs8 = nsf_c.transpose() * problem->FS8_matrix[i] * c_tmp * b8;
+        fs8 = nsf_c.transpose() * problem->FS8_matrix[i] * c_tmp* b8;
         fvecn(k) = -Pdot_8(i) - pp8(0, 0) + P1_8(i) - P2_8(i) + fs8(0, 0);
     }
 
@@ -455,7 +455,7 @@ int newton_usmsr_n::operator()(const Eigen::VectorXd& n,
 int newton_usmsr_n::df(const Eigen::VectorXd& n,
                        Eigen::MatrixXd& fjacn) const
 {
-    Eigen::NumericalDiff<newton_usmsr_n> numDiff(*this);
+    Eigen::NumericalDiff<newton_usmsr_n> numDiff( * this);
     numDiff.df(n, fjacn);
     return 0;
 }
@@ -487,11 +487,11 @@ int newton_usmsr_t::operator()(const Eigen::VectorXd& t,
     f3_dot = (t.segment(pos, Nphi_dec3) - z_old.segment(pos, Nphi_dec3)) / dt;
     /// Thermal terms
     //ddt T term
-    Eigen::VectorXd T_dot = problem->TM_matrix * e_dot;
+    Eigen::VectorXd T_dot = problem->TM_matrix* e_dot;
     // convective term in T_eqn
     Eigen::MatrixXd tt(1, 1);
     // laplacian of T
-    Eigen::VectorXd T1 = problem->LT_matrix * e_tmp * nu / Pr;
+    Eigen::VectorXd T1 = problem->LT_matrix* e_tmp* nu / Pr;
     // temp flux source
     Eigen::MatrixXd xsf(1, 1);
     // decay heat source term (*dli/cp)
@@ -499,21 +499,21 @@ int newton_usmsr_t::operator()(const Eigen::VectorXd& t,
     Eigen::MatrixXd dhs2(1, 1);
     Eigen::MatrixXd dhs3(1, 1);
     //ddt dec term
-    Eigen::VectorXd DHdot_1 = problem->MD1_matrix * f1_dot;
-    Eigen::VectorXd DHdot_2 = problem->MD2_matrix * f2_dot;
-    Eigen::VectorXd DHdot_3 = problem->MD3_matrix * f3_dot;
+    Eigen::VectorXd DHdot_1 = problem->MD1_matrix* f1_dot;
+    Eigen::VectorXd DHdot_2 = problem->MD2_matrix* f2_dot;
+    Eigen::VectorXd DHdot_3 = problem->MD3_matrix* f3_dot;
     // convective term in decay heat eq.
     Eigen::MatrixXd dh1(1, 1);
     Eigen::MatrixXd dh2(1, 1);
     Eigen::MatrixXd dh3(1, 1);
     //laplacian of dh
-    Eigen::VectorXd DH1_1 = problem->LD1_matrix * f1_tmp * nu / Sc;
-    Eigen::VectorXd DH1_2 = problem->LD2_matrix * f2_tmp * nu / Sc;
-    Eigen::VectorXd DH1_3 = problem->LD3_matrix * f3_tmp * nu / Sc;
+    Eigen::VectorXd DH1_1 = problem->LD1_matrix* f1_tmp* nu / Sc;
+    Eigen::VectorXd DH1_2 = problem->LD2_matrix* f2_tmp* nu / Sc;
+    Eigen::VectorXd DH1_3 = problem->LD3_matrix* f3_tmp* nu / Sc;
     //algebric term in dh eq
-    Eigen::VectorXd DH2_1 = problem->MD1_matrix * f1_tmp * dl1;
-    Eigen::VectorXd DH2_2 = problem->MD2_matrix * f2_tmp * dl2;
-    Eigen::VectorXd DH2_3 = problem->MD3_matrix * f3_tmp * dl3;
+    Eigen::VectorXd DH2_1 = problem->MD1_matrix* f1_tmp* dl1;
+    Eigen::VectorXd DH2_2 = problem->MD2_matrix* f2_tmp* dl2;
+    Eigen::VectorXd DH2_3 = problem->MD3_matrix* f3_tmp* dl3;
     // flux source in term dh eq (*dbi)
     Eigen::MatrixXd dfs1(1, 1);
     Eigen::MatrixXd dfs2(1, 1);
@@ -536,7 +536,7 @@ int newton_usmsr_t::operator()(const Eigen::VectorXd& t,
     {
         int k = i + pfvect;
         dh1 = a_tmp.transpose() * problem->SD1_matrix[i] * f1_tmp;
-        dfs1 = sp_c.transpose() * problem->DFS1_matrix[i] * c_tmp * db1;
+        dfs1 = sp_c.transpose() * problem->DFS1_matrix[i] * c_tmp* db1;
         fvect(k) = -DHdot_1(i) - dh1(0, 0) + DH1_1(i) - DH2_1(i) + dfs1(0, 0);
     }
 
@@ -546,7 +546,7 @@ int newton_usmsr_t::operator()(const Eigen::VectorXd& t,
     {
         int k = i + pfvect;
         dh2 = a_tmp.transpose() * problem->SD2_matrix[i] * f2_tmp;
-        dfs2 = sp_c.transpose() * problem->DFS2_matrix[i] * c_tmp * db2;
+        dfs2 = sp_c.transpose() * problem->DFS2_matrix[i] * c_tmp* db2;
         fvect(k) = -DHdot_2(i) - dh2(0, 0) + DH1_2(i) - DH2_2(i) + dfs2(0, 0);
     }
 
@@ -556,7 +556,7 @@ int newton_usmsr_t::operator()(const Eigen::VectorXd& t,
     {
         int k = i + pfvect;
         dh3 = a_tmp.transpose() * problem->SD3_matrix[i] * f3_tmp;
-        dfs3 = sp_c.transpose() * problem->DFS3_matrix[i] * c_tmp * db3;
+        dfs3 = sp_c.transpose() * problem->DFS3_matrix[i] * c_tmp* db3;
         fvect(k) = -DHdot_3(i) - dh3(0, 0) + DH1_3(i) - DH2_3(i) + dfs3(0, 0);
     }
 
@@ -571,7 +571,7 @@ int newton_usmsr_t::operator()(const Eigen::VectorXd& t,
 int newton_usmsr_t::df(const Eigen::VectorXd& t,
                        Eigen::MatrixXd& fjact) const
 {
-    Eigen::NumericalDiff<newton_usmsr_t> numDiff(*this);
+    Eigen::NumericalDiff<newton_usmsr_t> numDiff( * this);
     numDiff.df(t, fjact);
     return 0;
 }
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyMSR/ReducedUnsteadyMSR.H b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyMSR/ReducedUnsteadyMSR.H
old mode 100755
new mode 100644
index 745308c87..a026f014e
--- a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyMSR/ReducedUnsteadyMSR.H
+++ b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyMSR/ReducedUnsteadyMSR.H
@@ -40,13 +40,15 @@ struct newton_usmsr_fd: public newton_argument<double>
 {
     public:
         newton_usmsr_fd() {}
+
         newton_usmsr_fd(int Nx, int Ny, usmsrProblem& problem):
             newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_u(problem.NUmodes + problem.liftfield.size()),
             Nphi_p(problem.NPmodes),
             N_BC(problem.inletIndex.rows())
         {}
+
         int operator()(const Eigen::VectorXd& x, Eigen::VectorXd& fvec) const;
         int df(const Eigen::VectorXd& x, Eigen::MatrixXd& fjac) const;
 
@@ -66,9 +68,10 @@ struct newton_usmsr_n: public newton_argument<double>
 {
     public:
         newton_usmsr_n() {}
+
         newton_usmsr_n(int Nx, int Ny, usmsrProblem& problem):
             newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_flux(problem.NFluxmodes),
             Nphi_prec1(problem.NPrecmodes(0)),
             Nphi_prec2(problem.NPrecmodes(1)),
@@ -83,6 +86,7 @@ struct newton_usmsr_n: public newton_argument<double>
             nsf_c(problem.NCmodes),
             a_c(problem.NCmodes)
         {}
+
         int operator()(const Eigen::VectorXd& n, Eigen::VectorXd& fvecn) const;
         int df(const Eigen::VectorXd& n, Eigen::MatrixXd& fjacn) const;
         int Nphi_flux;
@@ -138,9 +142,10 @@ struct newton_usmsr_t: public newton_argument<double>
 {
     public:
         newton_usmsr_t() {}
+
         newton_usmsr_t(int Nx, int Ny, usmsrProblem& problem):
             newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_T(problem.NTmodes + problem.liftfieldT.size()),
             Nphi_dec1(problem.NDecmodes(0)),
             Nphi_dec2(problem.NDecmodes(1)),
@@ -151,6 +156,7 @@ struct newton_usmsr_t: public newton_argument<double>
             sp_c(problem.NCmodes),
             txs_c(problem.NCmodes)
         {}
+
         int operator()(const Eigen::VectorXd& t, Eigen::VectorXd& fvect) const;
         int df(const Eigen::VectorXd& t, Eigen::MatrixXd& fjact) const;
         int Nphi_T;
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNS/ReducedUnsteadyNS.C b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNS/ReducedUnsteadyNS.C
old mode 100755
new mode 100644
index 96bbe493b..9eeeafad9
--- a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNS/ReducedUnsteadyNS.C
+++ b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNS/ReducedUnsteadyNS.C
@@ -44,7 +44,7 @@ reducedUnsteadyNS::reducedUnsteadyNS()
 
 reducedUnsteadyNS::reducedUnsteadyNS(unsteadyNS& FOMproblem)
     :
-    problem(&FOMproblem)
+    problem( & FOMproblem)
 {
     N_BC = problem->inletIndex.rows();
     Nphi_u = problem->B_matrix.rows();
@@ -104,13 +104,13 @@ int newton_unsteadyNS_sup::operator()(const Eigen::VectorXd& x,
     // Convective term
     Eigen::MatrixXd cc(1, 1);
     // Mom Term
-    Eigen::VectorXd M1 = problem->B_matrix * a_tmp * nu;
+    Eigen::VectorXd M1 = problem->B_matrix* a_tmp* nu;
     // Gradient of pressure
-    Eigen::VectorXd M2 = problem->K_matrix * b_tmp;
+    Eigen::VectorXd M2 = problem->K_matrix* b_tmp;
     // Mass Term
-    Eigen::VectorXd M5 = problem->M_matrix * a_dot;
+    Eigen::VectorXd M5 = problem->M_matrix* a_dot;
     // Pressure Term
-    Eigen::VectorXd M3 = problem->P_matrix * a_tmp;
+    Eigen::VectorXd M3 = problem->P_matrix* a_tmp;
     // Penalty term
     Eigen::MatrixXd penaltyU = Eigen::MatrixXd::Zero(Nphi_u, N_BC);
 
@@ -128,7 +128,7 @@ int newton_unsteadyNS_sup::operator()(const Eigen::VectorXd& x,
     for (int i = 0; i < Nphi_u; i++)
     {
         cc = a_tmp.transpose() * Eigen::SliceFromTensor(problem->C_tensor, 0,
-                i) * a_tmp;
+             i) * a_tmp;
         fvec(i) = - M5(i) + M1(i) - cc(0, 0) - M2(i);
 
         if (problem->bcMethod == "penalty")
@@ -161,7 +161,7 @@ int newton_unsteadyNS_sup::operator()(const Eigen::VectorXd& x,
 int newton_unsteadyNS_sup::df(const Eigen::VectorXd& x,
                               Eigen::MatrixXd& fjac) const
 {
-    Eigen::NumericalDiff<newton_unsteadyNS_sup> numDiff(*this);
+    Eigen::NumericalDiff<newton_unsteadyNS_sup> numDiff( * this);
     numDiff.df(x, fjac);
     return 0;
 }
@@ -193,17 +193,17 @@ int newton_unsteadyNS_PPE::operator()(const Eigen::VectorXd& x,
     Eigen::MatrixXd cc(1, 1);
     Eigen::MatrixXd gg(1, 1);
     // Mom Term
-    Eigen::VectorXd M1 = problem->B_matrix * a_tmp * nu;
+    Eigen::VectorXd M1 = problem->B_matrix* a_tmp* nu;
     // Gradient of pressure
-    Eigen::VectorXd M2 = problem->K_matrix * b_tmp;
+    Eigen::VectorXd M2 = problem->K_matrix* b_tmp;
     // Mass Term
-    Eigen::VectorXd M5 = problem->M_matrix * a_dot;
+    Eigen::VectorXd M5 = problem->M_matrix* a_dot;
     // Pressure Term
-    Eigen::VectorXd M3 = problem->D_matrix * b_tmp;
+    Eigen::VectorXd M3 = problem->D_matrix* b_tmp;
     // BC PPE
-    Eigen::VectorXd M7 = problem->BC3_matrix * a_tmp * nu;
+    Eigen::VectorXd M7 = problem->BC3_matrix* a_tmp* nu;
     // BC PPE time-dependents BCs
-    Eigen::VectorXd M8 = problem->BC4_matrix * a_dot;
+    Eigen::VectorXd M8 = problem->BC4_matrix* a_dot;
     // Penalty term
     Eigen::MatrixXd penaltyU = Eigen::MatrixXd::Zero(Nphi_u, N_BC);
 
@@ -221,7 +221,7 @@ int newton_unsteadyNS_PPE::operator()(const Eigen::VectorXd& x,
     for (int i = 0; i < Nphi_u; i++)
     {
         cc = a_tmp.transpose() * Eigen::SliceFromTensor(problem->C_tensor, 0,
-                i) * a_tmp;
+             i) * a_tmp;
         fvec(i) = - M5(i) + M1(i) - cc(0, 0) - M2(i);
 
         if (problem->bcMethod == "penalty")
@@ -237,7 +237,7 @@ int newton_unsteadyNS_PPE::operator()(const Eigen::VectorXd& x,
     {
         int k = j + Nphi_u;
         gg = a_tmp.transpose() * Eigen::SliceFromTensor(problem->gTensor, 0,
-                j) * a_tmp;
+             j) * a_tmp;
         fvec(k) = M3(j, 0) + gg(0, 0) - M7(j, 0);
 
         if (problem->timedepbcMethod == "yes")
@@ -261,7 +261,7 @@ int newton_unsteadyNS_PPE::operator()(const Eigen::VectorXd& x,
 int newton_unsteadyNS_PPE::df(const Eigen::VectorXd& x,
                               Eigen::MatrixXd& fjac) const
 {
-    Eigen::NumericalDiff<newton_unsteadyNS_PPE> numDiff(*this);
+    Eigen::NumericalDiff<newton_unsteadyNS_PPE> numDiff( * this);
     numDiff.df(x, fjac);
     return 0;
 }
@@ -904,4 +904,5 @@ Eigen::MatrixXd reducedUnsteadyNS::setOnlineVelocity(Eigen::MatrixXd vel)
 
     return vel_scal;
 }
+
 //************************************************************************* //
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNS/ReducedUnsteadyNS.H b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNS/ReducedUnsteadyNS.H
old mode 100755
new mode 100644
index 9b82377c1..02fac891e
--- a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNS/ReducedUnsteadyNS.H
+++ b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNS/ReducedUnsteadyNS.H
@@ -50,9 +50,10 @@ struct newton_unsteadyNS_sup: public newton_argument<double>
 {
     public:
         newton_unsteadyNS_sup() {}
+
         newton_unsteadyNS_sup(int Nx, int Ny,
                               unsteadyNS& problem): newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_u(problem.NUmodes + problem.liftfield.size() + problem.NSUPmodes),
             Nphi_p(problem.NPmodes),
             N_BC(problem.inletIndex.rows())
@@ -79,9 +80,10 @@ struct newton_unsteadyNS_PPE: public newton_argument<double>
 {
     public:
         newton_unsteadyNS_PPE() {}
+
         newton_unsteadyNS_PPE(int Nx, int Ny,
                               unsteadyNS& problem): newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_u(problem.NUmodes + problem.liftfield.size()),
             Nphi_p(problem.NPmodes),
             N_BC(problem.inletIndex.rows())
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSExplicit/ReducedUnsteadyNSExplicit.C b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSExplicit/ReducedUnsteadyNSExplicit.C
index 7cd167f4d..9de08ece9 100644
--- a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSExplicit/ReducedUnsteadyNSExplicit.C
+++ b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSExplicit/ReducedUnsteadyNSExplicit.C
@@ -45,7 +45,7 @@ ReducedUnsteadyNSExplicit::ReducedUnsteadyNSExplicit()
 ReducedUnsteadyNSExplicit::ReducedUnsteadyNSExplicit(UnsteadyNSExplicit&
         FOMproblem)
     :
-    problem(&FOMproblem)
+    problem( & FOMproblem)
 {
     N_BC = problem->inletIndex.rows();
     Nphi_u = problem->B_matrix.rows();
@@ -101,16 +101,16 @@ void ReducedUnsteadyNSExplicit::solveOnline(Eigen::MatrixXd vel,
                       " ##################" << std::endl;
             // Pressure Poisson Equation
             // Diffusion Term
-            Eigen::VectorXd M1 = problem->BP_matrix * a_o * nu ;
+            Eigen::VectorXd M1 = problem->BP_matrix* a_o* nu ;
             // Convection Term
             Eigen::MatrixXd cf(1, 1);
             // Divergence term
-            Eigen::MatrixXd M2 = problem->P_matrix * a_o;
+            Eigen::MatrixXd M2 = problem->P_matrix* a_o;
 
             for (label l = 0; l < Nphi_p; l++)
             {
                 cf = a_o.transpose() * Eigen::SliceFromTensor(problem->Cf_tensor, 0,
-                        l) * a_o;
+                     l) * a_o;
                 RHS(l) = (1 / dt) * M2(l, 0) - cf(0, 0) + M1(l, 0);
             }
 
@@ -121,7 +121,7 @@ void ReducedUnsteadyNSExplicit::solveOnline(Eigen::MatrixXd vel,
             for (label i = 0; i < N_BC; i++)
             {
                 RedLinSysP[1] += vel(i, 0) * ((1 / dt) * problem->LinSysDiv[i + 1] +
-                                              nu * problem->LinSysDiff[i + 1] +
+                                              nu* problem->LinSysDiff[i + 1] +
                                               vel(i, 0) * problem->LinSysConv[i + 1]);
             }
 
@@ -130,9 +130,9 @@ void ReducedUnsteadyNSExplicit::solveOnline(Eigen::MatrixXd vel,
             // Convective term
             Eigen::MatrixXd cc(1, 1);
             // Diffusion Term
-            Eigen::VectorXd M5 = problem->B_matrix * a_o * nu ;
+            Eigen::VectorXd M5 = problem->B_matrix* a_o* nu ;
             // Pressure Gradient Term
-            Eigen::VectorXd M3 = problem->K_matrix * b;
+            Eigen::VectorXd M3 = problem->K_matrix* b;
             // Boundary Term Diffusion + Convection
             Eigen::MatrixXd boundaryTerm = Eigen::MatrixXd::Zero(Nphi_u, N_BC);
 
@@ -145,7 +145,7 @@ void ReducedUnsteadyNSExplicit::solveOnline(Eigen::MatrixXd vel,
             for (label l = 0; l < Nphi_u; l++)
             {
                 cc = a_o.transpose() * Eigen::SliceFromTensor(problem->C_tensor, 0,
-                        l) * a_o;
+                     l) * a_o;
                 a_n(l) = a_o(l) + (M5(l) - cc(0, 0) - M3(l)) * dt;
 
                 for (label j = 0; j < N_BC; j++)
@@ -211,16 +211,16 @@ void ReducedUnsteadyNSExplicit::solveOnline(Eigen::MatrixXd vel,
             Eigen::VectorXd presidual = Eigen::VectorXd::Zero(Nphi_p);
             // Pressure Poisson Equation
             // Diffusion Term
-            Eigen::VectorXd M1 = problem->BP_matrix * a_o * nu ;
+            Eigen::VectorXd M1 = problem->BP_matrix* a_o* nu ;
             // Convection Term
             Eigen::MatrixXd cf(1, 1);
             // Divergence term
-            Eigen::MatrixXd M2 = problem->P_matrix * a_o;
+            Eigen::MatrixXd M2 = problem->P_matrix* a_o;
 
             for (label l = 0; l < Nphi_p; l++)
             {
                 cf = c_o.transpose() * Eigen::SliceFromTensor(problem->Cf_tensor, 0,
-                        l) * a_o;
+                     l) * a_o;
                 RHS(l) = (1 / dt) * M2(l, 0) - cf(0, 0) + M1(l, 0);
             }
 
@@ -231,7 +231,7 @@ void ReducedUnsteadyNSExplicit::solveOnline(Eigen::MatrixXd vel,
             for (label l = 0; l < N_BC; l++)
             {
                 RedLinSysP[1] += vel(l, 0) * ((1 / dt) * problem->LinSysDiv[l + 1] +
-                                              nu * problem->LinSysDiff[l + 1] +
+                                              nu* problem->LinSysDiff[l + 1] +
                                               vel(l, 0) * problem->LinSysConv[l + 1]);
             }
 
@@ -240,9 +240,9 @@ void ReducedUnsteadyNSExplicit::solveOnline(Eigen::MatrixXd vel,
             // Convective term
             Eigen::MatrixXd cc(1, 1);
             // Diffusion Term
-            Eigen::VectorXd M5 = problem->B_matrix * a_o * nu ;
+            Eigen::VectorXd M5 = problem->B_matrix* a_o* nu ;
             // Pressure Gradient Term
-            Eigen::VectorXd M3 = problem->K_matrix * b;
+            Eigen::VectorXd M3 = problem->K_matrix* b;
             // Boundary Term Diffusion + Convection
             Eigen::MatrixXd boundaryTerm = Eigen::MatrixXd::Zero(Nphi_u, N_BC);
 
@@ -255,7 +255,7 @@ void ReducedUnsteadyNSExplicit::solveOnline(Eigen::MatrixXd vel,
             for (label k = 0; k < Nphi_u; k++)
             {
                 cc = c_o.transpose() * Eigen::SliceFromTensor(problem->C_tensor, 0,
-                        k) * a_o;
+                     k) * a_o;
                 a_n(k) = a_o(k) + (M5(k) - cc(0, 0) - M3(k)) * dt;
 
                 for (label l = 0; l < N_BC; l++)
@@ -266,18 +266,18 @@ void ReducedUnsteadyNSExplicit::solveOnline(Eigen::MatrixXd vel,
 
             // Flux Equation
             // Mass Term
-            Eigen::MatrixXd M6 = problem->I_matrix * a_o;
+            Eigen::MatrixXd M6 = problem->I_matrix* a_o;
             // Diffusion Term
-            Eigen::MatrixXd M7 = problem->DF_matrix * a_o * nu;
+            Eigen::MatrixXd M7 = problem->DF_matrix* a_o* nu;
             // Pressure Gradient Term
-            Eigen::MatrixXd M8 = problem->KF_matrix * b.col(0);
+            Eigen::MatrixXd M8 = problem->KF_matrix* b.col(0);
             // Convective Term
             Eigen::MatrixXd M9 = Eigen::VectorXd::Zero(Nphi_u);
 
             for (label k = 0; k < Nphi_u; k++)
             {
-                M9 += dt * Eigen::SliceFromTensor(problem->Ci_tensor, 0,
-                                                  k) * a_o * c_o(k);
+                M9 += dt* Eigen::SliceFromTensor(problem->Ci_tensor, 0,
+                                                 k) * a_o* c_o(k);
             }
 
             // Boundary Term Diffusion + Convection
@@ -290,7 +290,7 @@ void ReducedUnsteadyNSExplicit::solveOnline(Eigen::MatrixXd vel,
             }
 
             c_n = problem->W_matrix.colPivHouseholderQr().solve(M6 - M9 + dt * (-M8 + M7
-                    + boundaryTermFlux));
+                  + boundaryTermFlux));
             tmp_sol(0) = time;
             tmp_sol.col(0).segment(1, Nphi_u) = a_n;
             tmp_sol.col(0).segment(Nphi_u + 1, Nphi_p) = b;
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNST/ReducedUnsteadyNST.C b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNST/ReducedUnsteadyNST.C
old mode 100755
new mode 100644
index 8449e2417..07399a95d
--- a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNST/ReducedUnsteadyNST.C
+++ b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNST/ReducedUnsteadyNST.C
@@ -46,7 +46,7 @@ reducedUnsteadyNST::reducedUnsteadyNST()
 reducedUnsteadyNST::reducedUnsteadyNST(unsteadyNST& FOMproblem)
 //problem(&FOMproblem)
 {
-    problem   = &FOMproblem;
+    problem   = & FOMproblem;
     N_BC      = problem->inletIndex.rows();
     N_BC_t    = problem->inletIndexT.rows();
     Nphi_u    = problem->B_matrix.rows();
@@ -118,13 +118,13 @@ int newton_unsteadyNST_sup::operator()(const Eigen::VectorXd& x,
     // Convective term
     Eigen::MatrixXd cc(1, 1);
     // Momentum Term
-    Eigen::VectorXd M1 = problem->B_matrix * a_tmp * nu;
+    Eigen::VectorXd M1 = problem->B_matrix* a_tmp* nu;
     // Gradient of pressure
-    Eigen::VectorXd M2 = problem->K_matrix * b_tmp;
+    Eigen::VectorXd M2 = problem->K_matrix* b_tmp;
     // Mass Term Velocity
-    Eigen::VectorXd M5 = problem->M_matrix * a_dot;
+    Eigen::VectorXd M5 = problem->M_matrix* a_dot;
     // Pressure Term
-    Eigen::VectorXd M3 = problem->P_matrix * a_tmp;
+    Eigen::VectorXd M3 = problem->P_matrix* a_tmp;
 
     for (int i = 0; i < Nphi_u; i++)
     {
@@ -150,7 +150,7 @@ int newton_unsteadyNST_sup::operator()(const Eigen::VectorXd& x,
 int newton_unsteadyNST_sup::df(const Eigen::VectorXd& x,
                                Eigen::MatrixXd& fjac) const
 {
-    Eigen::NumericalDiff<newton_unsteadyNST_sup> numDiff(*this);
+    Eigen::NumericalDiff<newton_unsteadyNST_sup> numDiff( * this);
     numDiff.df(x, fjac);
     return 0;
 }
@@ -165,9 +165,9 @@ int newton_unsteadyNST_sup_t::operator()(const Eigen::VectorXd& t,
     // Convective term temperature
     Eigen::MatrixXd qq(1, 1);
     // diffusive term temperature
-    Eigen::VectorXd M6 = problem->Y_matrix * c_tmp * DT;
+    Eigen::VectorXd M6 = problem->Y_matrix* c_tmp* DT;
     // Mass Term Temperature
-    Eigen::VectorXd M8 = problem->MT_matrix * c_dot;
+    Eigen::VectorXd M8 = problem->MT_matrix* c_dot;
 
     for (int i = 0; i < Nphi_t; i++)
     {
@@ -182,10 +182,11 @@ int newton_unsteadyNST_sup_t::operator()(const Eigen::VectorXd& t,
 
     return 0;
 }
+
 int newton_unsteadyNST_sup_t::df(const Eigen::VectorXd& t,
                                  Eigen::MatrixXd& fjact) const
 {
-    Eigen::NumericalDiff<newton_unsteadyNST_sup_t> numDiff(*this);
+    Eigen::NumericalDiff<newton_unsteadyNST_sup_t> numDiff( * this);
     numDiff.df(t, fjact);
     return 0;
 }
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNST/ReducedUnsteadyNST.H b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNST/ReducedUnsteadyNST.H
old mode 100755
new mode 100644
index fecef4849..2ef464437
--- a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNST/ReducedUnsteadyNST.H
+++ b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNST/ReducedUnsteadyNST.H
@@ -49,9 +49,10 @@ struct newton_unsteadyNST_sup: public newton_argument<double>
 {
     public:
         newton_unsteadyNST_sup() {}
+
         newton_unsteadyNST_sup(int Nx, int Ny,
                                unsteadyNST& problem): newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_u(problem.NUmodes + problem.liftfield.size() + problem.NSUPmodes),
             Nphi_p(problem.NPmodes),
             N_BC(problem.inletIndex.rows())
@@ -74,9 +75,10 @@ struct newton_unsteadyNST_sup_t: public newton_argument<double>
 {
     public:
         newton_unsteadyNST_sup_t() {}
+
         newton_unsteadyNST_sup_t(int Nx, int Ny,
                                  unsteadyNST& problem): newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_t(problem.NTmodes + problem.liftfieldT.size()),
             N_BC_t(problem.inletIndexT.rows())
         {}
@@ -238,6 +240,7 @@ class reducedUnsteadyNST: public reducedUnsteadyNS
         void reconstruct_supt(fileName folder = "./ITHACAOutput/online_rec",
                               int printevery = 1);
 };
+
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
 #endif
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTTurb/ReducedUnsteadyNSTTurb.C b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTTurb/ReducedUnsteadyNSTTurb.C
old mode 100755
new mode 100644
index 605a35eb4..a724a1085
--- a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTTurb/ReducedUnsteadyNSTTurb.C
+++ b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTTurb/ReducedUnsteadyNSTTurb.C
@@ -46,7 +46,7 @@ ReducedUnsteadyNSTTurb::ReducedUnsteadyNSTTurb(UnsteadyNSTTurb& FOMproblem)
 
 //problem(&FOMproblem)
 {
-    problem   = &FOMproblem;
+    problem   = & FOMproblem;
     N_BC      = problem->inletIndex.rows();
     N_BC_t    = problem->inletIndexT.rows();
     Nphi_u    = problem->B_matrix.rows();
@@ -119,13 +119,13 @@ int newton_unsteadyNSTTurb_sup::operator()(const Eigen::VectorXd& x,
     // Convective term
     Eigen::MatrixXd cc(1, 1);
     // Mom Term
-    Eigen::VectorXd M1 = problem ->B_total_matrix * a_tmp * nu;
+    Eigen::VectorXd M1 = problem ->B_total_matrix* a_tmp* nu;
     // Gradient of pressure
-    Eigen::VectorXd M2 = problem->K_matrix * b_tmp;
+    Eigen::VectorXd M2 = problem->K_matrix* b_tmp;
     // Mass Term
-    Eigen::VectorXd M5 = problem->M_matrix * a_dot;
+    Eigen::VectorXd M5 = problem->M_matrix* a_dot;
     // Pressure Term
-    Eigen::VectorXd M3 = problem->P_matrix * a_tmp;
+    Eigen::VectorXd M3 = problem->P_matrix* a_tmp;
 
     //std::cerr << "I am here 5" << std::endl;
     for (int i = 0; i < Nphi_u; i++)
@@ -154,7 +154,7 @@ int newton_unsteadyNSTTurb_sup::operator()(const Eigen::VectorXd& x,
 int newton_unsteadyNSTTurb_sup::df(const Eigen::VectorXd& x,
                                    Eigen::MatrixXd& fjac) const
 {
-    Eigen::NumericalDiff<newton_unsteadyNSTTurb_sup> numDiff(*this);
+    Eigen::NumericalDiff<newton_unsteadyNSTTurb_sup> numDiff( * this);
     numDiff.df(x, fjac);
     return 0;
 }
@@ -172,9 +172,9 @@ int newton_unsteadyNSTTurb_sup_t::operator()(const Eigen::VectorXd& t,
     Eigen::MatrixXd qq(1, 1);
     Eigen::MatrixXd st(1, 1);
     // diffusive term temperature
-    Eigen::VectorXd M6 = problem->Y_matrix * c_tmp * nu / Pr;
+    Eigen::VectorXd M6 = problem->Y_matrix* c_tmp* nu / Pr;
     // Mass Term Temperature
-    Eigen::VectorXd M8 = problem->MT_matrix * c_dot;
+    Eigen::VectorXd M8 = problem->MT_matrix* c_dot;
 
     for (int i = 0; i < Nphi_t; i++)
     {
@@ -190,10 +190,11 @@ int newton_unsteadyNSTTurb_sup_t::operator()(const Eigen::VectorXd& t,
 
     return 0;
 }
+
 int newton_unsteadyNSTTurb_sup_t::df(const Eigen::VectorXd& t,
                                      Eigen::MatrixXd& fjact) const
 {
-    Eigen::NumericalDiff<newton_unsteadyNSTTurb_sup_t> numDiff(*this);
+    Eigen::NumericalDiff<newton_unsteadyNSTTurb_sup_t> numDiff( * this);
     numDiff.df(t, fjact);
     return 0;
 }
@@ -468,4 +469,5 @@ void ReducedUnsteadyNSTTurb::reconstructSupt(fileName folder, int printevery)
         counter++;
     }
 }
+
 // ************************************************************************* //
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTTurb/ReducedUnsteadyNSTTurb.H b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTTurb/ReducedUnsteadyNSTTurb.H
old mode 100755
new mode 100644
index 2b6513b64..7c487aada
--- a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTTurb/ReducedUnsteadyNSTTurb.H
+++ b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTTurb/ReducedUnsteadyNSTTurb.H
@@ -58,9 +58,10 @@ struct newton_unsteadyNSTTurb_sup: public newton_argument<double>
 {
     public:
         newton_unsteadyNSTTurb_sup() {}
+
         newton_unsteadyNSTTurb_sup(int Nx, int Ny,
                                    UnsteadyNSTTurb& problem): newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_u(problem.NUmodes + problem.liftfield.size() + problem.NSUPmodes),
             Nphi_nut(problem.Nnutmodes),
             Nphi_p(problem.NPmodes),
@@ -89,9 +90,10 @@ struct newton_unsteadyNSTTurb_sup_t: public newton_argument<double>
 {
     public:
         newton_unsteadyNSTTurb_sup_t() {}
+
         newton_unsteadyNSTTurb_sup_t(int Nx, int Ny,
                                      UnsteadyNSTTurb& problem): newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_t(problem.NTmodes + problem.liftfieldT.size()),
             N_BC_t(problem.inletIndexT.rows()),
             nu_c(problem.Nnutmodes)
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTurb/ReducedUnsteadyNSTurb.C b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTurb/ReducedUnsteadyNSTurb.C
index 03d5e9493..d46230bf5 100644
--- a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTurb/ReducedUnsteadyNSTurb.C
+++ b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTurb/ReducedUnsteadyNSTurb.C
@@ -44,7 +44,7 @@ ReducedUnsteadyNSTurb::ReducedUnsteadyNSTurb()
 
 ReducedUnsteadyNSTurb::ReducedUnsteadyNSTurb(UnsteadyNSTurb& fomProblem)
 {
-    problem = &fomProblem;
+    problem = & fomProblem;
     N_BC = problem->inletIndex.rows();
     Nphi_u = problem->B_matrix.rows();
     Nphi_p = problem->K_matrix.cols();
@@ -119,13 +119,13 @@ int newtonUnsteadyNSTurbSUP::operator()(const Eigen::VectorXd& x,
     // Convective term
     Eigen::MatrixXd cc(1, 1);
     // Mom Term
-    Eigen::VectorXd m1 = problem->bTotalMatrix * aTmp * nu;
+    Eigen::VectorXd m1 = problem->bTotalMatrix* aTmp* nu;
     // Gradient of pressure
-    Eigen::VectorXd m2 = problem->K_matrix * bTmp;
+    Eigen::VectorXd m2 = problem->K_matrix* bTmp;
     // Mass Term
-    Eigen::VectorXd m5 = problem->M_matrix * a_dot;
+    Eigen::VectorXd m5 = problem->M_matrix* a_dot;
     // Pressure Term
-    Eigen::VectorXd m3 = problem->P_matrix * aTmp;
+    Eigen::VectorXd m3 = problem->P_matrix* aTmp;
     // Penalty term
     Eigen::MatrixXd penaltyU = Eigen::MatrixXd::Zero(Nphi_u, N_BC);
 
@@ -142,13 +142,13 @@ int newtonUnsteadyNSTurbSUP::operator()(const Eigen::VectorXd& x,
     for (int i = 0; i < Nphi_u; i++)
     {
         cc = aTmp.transpose() * Eigen::SliceFromTensor(problem->C_tensor, 0,
-                i) * aTmp - gNut.transpose() *
+             i) * aTmp - gNut.transpose() *
              Eigen::SliceFromTensor(problem->cTotalTensor, 0, i) * aTmp;
         fvec(i) = - m5(i) + m1(i) - cc(0, 0) - m2(i);
 
         if (problem->bcMethod == "penalty")
         {
-            fvec(i) += ((penaltyU * tauU)(i, 0));
+            fvec(i) += ((penaltyU* tauU)(i, 0));
         }
     }
 
@@ -173,7 +173,7 @@ int newtonUnsteadyNSTurbSUP::operator()(const Eigen::VectorXd& x,
 int newtonUnsteadyNSTurbSUP::df(const Eigen::VectorXd& x,
                                 Eigen::MatrixXd& fjac) const
 {
-    Eigen::NumericalDiff<newtonUnsteadyNSTurbSUP> numDiff(*this);
+    Eigen::NumericalDiff<newtonUnsteadyNSTurbSUP> numDiff( * this);
     numDiff.df(x, fjac);
     return 0;
 }
@@ -202,13 +202,13 @@ int newtonUnsteadyNSTurbSUPAve::operator()(const Eigen::VectorXd& x,
     // Convective term
     Eigen::MatrixXd cc(1, 1);
     // Mom Term
-    Eigen::VectorXd m1 = problem->bTotalMatrix * aTmp * nu;
+    Eigen::VectorXd m1 = problem->bTotalMatrix* aTmp* nu;
     // Gradient of pressure
-    Eigen::VectorXd m2 = problem->K_matrix * bTmp;
+    Eigen::VectorXd m2 = problem->K_matrix* bTmp;
     // Mass Term
-    Eigen::VectorXd m5 = problem->M_matrix * a_dot;
+    Eigen::VectorXd m5 = problem->M_matrix* a_dot;
     // Pressure Term
-    Eigen::VectorXd m3 = problem->P_matrix * aTmp;
+    Eigen::VectorXd m3 = problem->P_matrix* aTmp;
     // Penalty term
     Eigen::MatrixXd penaltyU = Eigen::MatrixXd::Zero(Nphi_u, N_BC);
 
@@ -225,7 +225,7 @@ int newtonUnsteadyNSTurbSUPAve::operator()(const Eigen::VectorXd& x,
     for (int i = 0; i < Nphi_u; i++)
     {
         cc = aTmp.transpose() * Eigen::SliceFromTensor(problem->C_tensor, 0,
-                i) * aTmp - gNut.transpose() *
+             i) * aTmp - gNut.transpose() *
              Eigen::SliceFromTensor(problem->cTotalTensor, 0,
                                     i) * aTmp - gNutAve.transpose() *
              Eigen::SliceFromTensor(problem->cTotalAveTensor, 0, i) * aTmp;
@@ -233,7 +233,7 @@ int newtonUnsteadyNSTurbSUPAve::operator()(const Eigen::VectorXd& x,
 
         if (problem->bcMethod == "penalty")
         {
-            fvec(i) += ((penaltyU * tauU)(i, 0));
+            fvec(i) += ((penaltyU* tauU)(i, 0));
         }
     }
 
@@ -258,7 +258,7 @@ int newtonUnsteadyNSTurbSUPAve::operator()(const Eigen::VectorXd& x,
 int newtonUnsteadyNSTurbSUPAve::df(const Eigen::VectorXd& x,
                                    Eigen::MatrixXd& fjac) const
 {
-    Eigen::NumericalDiff<newtonUnsteadyNSTurbSUPAve> numDiff(*this);
+    Eigen::NumericalDiff<newtonUnsteadyNSTurbSUPAve> numDiff( * this);
     numDiff.df(x, fjac);
     return 0;
 }
@@ -291,17 +291,17 @@ int newtonUnsteadyNSTurbPPE::operator()(const Eigen::VectorXd& x,
     Eigen::MatrixXd gg(1, 1);
     Eigen::MatrixXd bb(1, 1);
     // Mom Term
-    Eigen::VectorXd m1 = problem->bTotalMatrix * aTmp * nu;
+    Eigen::VectorXd m1 = problem->bTotalMatrix* aTmp* nu;
     // Gradient of pressure
-    Eigen::VectorXd m2 = problem->K_matrix * bTmp;
+    Eigen::VectorXd m2 = problem->K_matrix* bTmp;
     // Mass Term
-    Eigen::VectorXd m5 = problem->M_matrix * a_dot;
+    Eigen::VectorXd m5 = problem->M_matrix* a_dot;
     // Pressure Term
-    Eigen::VectorXd m3 = problem->D_matrix * bTmp;
+    Eigen::VectorXd m3 = problem->D_matrix* bTmp;
     // BC PPE
-    Eigen::VectorXd m6 = problem->BC1_matrix * aTmp * nu;
+    Eigen::VectorXd m6 = problem->BC1_matrix* aTmp* nu;
     // BC PPE
-    Eigen::VectorXd m7 = problem->BC3_matrix * aTmp * nu;
+    Eigen::VectorXd m7 = problem->BC3_matrix* aTmp* nu;
     // Penalty term
     Eigen::MatrixXd penaltyU = Eigen::MatrixXd::Zero(Nphi_u, N_BC);
 
@@ -318,13 +318,13 @@ int newtonUnsteadyNSTurbPPE::operator()(const Eigen::VectorXd& x,
     for (int i = 0; i < Nphi_u; i++)
     {
         cc = aTmp.transpose() * Eigen::SliceFromTensor(problem->C_tensor, 0,
-                i) * aTmp - gNut.transpose() *
+             i) * aTmp - gNut.transpose() *
              Eigen::SliceFromTensor(problem->cTotalTensor, 0, i) * aTmp;
         fvec(i) = - m5(i) + m1(i) - cc(0, 0) - m2(i);
 
         if (problem->bcMethod == "penalty")
         {
-            fvec(i) += ((penaltyU * tauU)(i, 0));
+            fvec(i) += ((penaltyU* tauU)(i, 0));
         }
     }
 
@@ -332,9 +332,9 @@ int newtonUnsteadyNSTurbPPE::operator()(const Eigen::VectorXd& x,
     {
         int k = j + Nphi_u;
         gg = aTmp.transpose() * Eigen::SliceFromTensor(problem->gTensor, 0,
-                j) * aTmp;
+             j) * aTmp;
         bb = aTmp.transpose() * Eigen::SliceFromTensor(problem->bc2Tensor, 0,
-                j) * aTmp;
+             j) * aTmp;
         //fvec(k) = m3(j, 0) - gg(0, 0) - m6(j, 0) + bb(0, 0);
         fvec(k) = m3(j, 0) + gg(0, 0) - m7(j, 0);
     }
@@ -354,7 +354,7 @@ int newtonUnsteadyNSTurbPPE::operator()(const Eigen::VectorXd& x,
 int newtonUnsteadyNSTurbPPE::df(const Eigen::VectorXd& x,
                                 Eigen::MatrixXd& fjac) const
 {
-    Eigen::NumericalDiff<newtonUnsteadyNSTurbPPE> numDiff(*this);
+    Eigen::NumericalDiff<newtonUnsteadyNSTurbPPE> numDiff( * this);
     numDiff.df(x, fjac);
     return 0;
 }
@@ -385,19 +385,19 @@ int newtonUnsteadyNSTurbPPEAve::operator()(const Eigen::VectorXd& x,
     Eigen::MatrixXd bb(1, 1);
     Eigen::MatrixXd nn(1, 1);
     // Mom Term
-    Eigen::VectorXd m1 = problem->bTotalMatrix * aTmp * nu;
+    Eigen::VectorXd m1 = problem->bTotalMatrix* aTmp* nu;
     // Gradient of pressure
-    Eigen::VectorXd m2 = problem->K_matrix * bTmp;
+    Eigen::VectorXd m2 = problem->K_matrix* bTmp;
     // Mass Term
-    Eigen::VectorXd m5 = problem->M_matrix * a_dot;
+    Eigen::VectorXd m5 = problem->M_matrix* a_dot;
     // Time-derivative of the divergence Term
     //Eigen::VectorXd m5 = problem->M_matrix * a_dot;
     // Pressure Term
-    Eigen::VectorXd m3 = problem->D_matrix * bTmp;
+    Eigen::VectorXd m3 = problem->D_matrix* bTmp;
     // BC PPE
-    Eigen::VectorXd m6 = problem->BC1_matrix * aTmp * nu;
+    Eigen::VectorXd m6 = problem->BC1_matrix* aTmp* nu;
     // BC PPE
-    Eigen::VectorXd m7 = problem->BC3_matrix * aTmp * nu;
+    Eigen::VectorXd m7 = problem->BC3_matrix* aTmp* nu;
     // Penalty term
     Eigen::MatrixXd penaltyU = Eigen::MatrixXd::Zero(Nphi_u, N_BC);
 
@@ -414,7 +414,7 @@ int newtonUnsteadyNSTurbPPEAve::operator()(const Eigen::VectorXd& x,
     for (int i = 0; i < Nphi_u; i++)
     {
         cc = aTmp.transpose() * Eigen::SliceFromTensor(problem->C_tensor, 0,
-                i) * aTmp - gNut.transpose() *
+             i) * aTmp - gNut.transpose() *
              Eigen::SliceFromTensor(problem->cTotalTensor, 0,
                                     i) * aTmp - gNutAve.transpose() *
              Eigen::SliceFromTensor(problem->cTotalAveTensor, 0, i) * aTmp;
@@ -422,7 +422,7 @@ int newtonUnsteadyNSTurbPPEAve::operator()(const Eigen::VectorXd& x,
 
         if (problem->bcMethod == "penalty")
         {
-            fvec(i) += ((penaltyU * tauU)(i, 0));
+            fvec(i) += ((penaltyU* tauU)(i, 0));
         }
     }
 
@@ -430,9 +430,9 @@ int newtonUnsteadyNSTurbPPEAve::operator()(const Eigen::VectorXd& x,
     {
         int k = j + Nphi_u;
         gg = aTmp.transpose() * Eigen::SliceFromTensor(problem->gTensor, 0,
-                j) * aTmp;
+             j) * aTmp;
         bb = aTmp.transpose() * Eigen::SliceFromTensor(problem->bc2Tensor, 0,
-                j) * aTmp;
+             j) * aTmp;
         nn = gNut.transpose() *
              Eigen::SliceFromTensor(problem->cTotalPPETensor, 0,
                                     j) * aTmp + gNutAve.transpose() *
@@ -457,7 +457,7 @@ int newtonUnsteadyNSTurbPPEAve::operator()(const Eigen::VectorXd& x,
 int newtonUnsteadyNSTurbPPEAve::df(const Eigen::VectorXd& x,
                                    Eigen::MatrixXd& fjac) const
 {
-    Eigen::NumericalDiff<newtonUnsteadyNSTurbPPEAve> numDiff(*this);
+    Eigen::NumericalDiff<newtonUnsteadyNSTurbPPEAve> numDiff( * this);
     numDiff.df(x, fjac);
     return 0;
 }
@@ -1350,5 +1350,6 @@ Eigen::MatrixXd ReducedUnsteadyNSTurb::setOnlineVelocity(Eigen::MatrixXd vel)
 
     return vel_scal;
 }
+
 // ************************************************************************* //
 
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTurb/ReducedUnsteadyNSTurb.H b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTurb/ReducedUnsteadyNSTurb.H
old mode 100755
new mode 100644
index 112767c9c..758619e56
--- a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTurb/ReducedUnsteadyNSTurb.H
+++ b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTurb/ReducedUnsteadyNSTurb.H
@@ -51,9 +51,10 @@ struct newtonUnsteadyNSTurbSUP: public newton_argument<double>
 {
     public:
         newtonUnsteadyNSTurbSUP() {}
+
         newtonUnsteadyNSTurbSUP(int Nx, int Ny,
                                 UnsteadyNSTurb& problem): newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_u(problem.NUmodes + problem.liftfield.size() + problem.NSUPmodes),
             nphiNut(problem.nNutModes),
             Nphi_p(problem.NPmodes),
@@ -85,9 +86,10 @@ struct newtonUnsteadyNSTurbPPE: public newton_argument<double>
 {
     public:
         newtonUnsteadyNSTurbPPE() {}
+
         newtonUnsteadyNSTurbPPE(int Nx, int Ny,
                                 UnsteadyNSTurb& problem): newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_u(problem.NUmodes + problem.liftfield.size()),
             nphiNut(problem.nNutModes),
             Nphi_p(problem.NPmodes),
@@ -117,9 +119,10 @@ struct newtonUnsteadyNSTurbSUPAve: public newton_argument<double>
 {
     public:
         newtonUnsteadyNSTurbSUPAve() {}
+
         newtonUnsteadyNSTurbSUPAve(int Nx, int Ny,
                                    UnsteadyNSTurb& problem): newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_u(problem.NUmodes + problem.liftfield.size() + problem.NSUPmodes),
             nphiNut(problem.nNutModes),
             Nphi_p(problem.NPmodes),
@@ -151,9 +154,10 @@ struct newtonUnsteadyNSTurbPPEAve: public newton_argument<double>
 {
     public:
         newtonUnsteadyNSTurbPPEAve() {}
+
         newtonUnsteadyNSTurbPPEAve(int Nx, int Ny,
                                    UnsteadyNSTurb& problem): newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_u(problem.NUmodes + problem.liftfield.size()),
             nphiNut(problem.nNutModes),
             Nphi_p(problem.NPmodes),
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTurbIntrusive/ReducedUnsteadyNSTurbIntrusive.C b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTurbIntrusive/ReducedUnsteadyNSTurbIntrusive.C
old mode 100755
new mode 100644
index 000d07cbe..f96be3121
--- a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTurbIntrusive/ReducedUnsteadyNSTurbIntrusive.C
+++ b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTurbIntrusive/ReducedUnsteadyNSTurbIntrusive.C
@@ -45,7 +45,7 @@ ReducedUnsteadyNSTurbIntrusive::ReducedUnsteadyNSTurbIntrusive()
 ReducedUnsteadyNSTurbIntrusive::ReducedUnsteadyNSTurbIntrusive(
     UnsteadyNSTurbIntrusive& fomProblem)
 {
-    problem = &fomProblem;
+    problem = & fomProblem;
     N_BC = problem->inletIndex.rows();
     Nphi_u = problem->bMatrix.rows();
     Nphi_p = problem->kMatrix.cols();
@@ -104,9 +104,9 @@ int newtonUnsteadyNSTurbIntrusive::operator()(const Eigen::VectorXd& x,
     // Convective term
     Eigen::MatrixXd cc(1, 1);
     // Mom Term
-    Eigen::VectorXd m1 = problem->bTotalMatrix * aTmp * nu;
+    Eigen::VectorXd m1 = problem->bTotalMatrix* aTmp* nu;
     // Gradient of pressure
-    Eigen::VectorXd m2 = problem->kMatrix * aTmp;
+    Eigen::VectorXd m2 = problem->kMatrix* aTmp;
     // Penalty term
     Eigen::MatrixXd penaltyU = Eigen::MatrixXd::Zero(Nphi_u, N_BC);
 
@@ -123,12 +123,12 @@ int newtonUnsteadyNSTurbIntrusive::operator()(const Eigen::VectorXd& x,
     for (int i = 0; i < Nphi_u; i++)
     {
         cc = aTmp.transpose() * Eigen::SliceFromTensor(problem->cTotalTensor, 0,
-                i) * aTmp;
+             i) * aTmp;
         fvec(i) = - a_dot(i) + m1(i) - cc(0, 0) - m2(i);
 
         if (problem->bcMethod == "penalty")
         {
-            fvec(i) += ((penaltyU * tauU)(i, 0));
+            fvec(i) += ((penaltyU* tauU)(i, 0));
         }
     }
 
@@ -147,7 +147,7 @@ int newtonUnsteadyNSTurbIntrusive::operator()(const Eigen::VectorXd& x,
 int newtonUnsteadyNSTurbIntrusive::df(const Eigen::VectorXd& x,
                                       Eigen::MatrixXd& fjac) const
 {
-    Eigen::NumericalDiff<newtonUnsteadyNSTurbIntrusive> numDiff(*this);
+    Eigen::NumericalDiff<newtonUnsteadyNSTurbIntrusive> numDiff( * this);
     numDiff.df(x, fjac);
     return 0;
 }
@@ -181,15 +181,15 @@ int newtonUnsteadyNSTurbIntrusivePPE::operator()(const Eigen::VectorXd& x,
     Eigen::MatrixXd bb(1, 1);
     Eigen::MatrixXd nn(1, 1);
     // Mom Term
-    Eigen::VectorXd m1 = problem->bTotalMatrix * aTmp * nu;
+    Eigen::VectorXd m1 = problem->bTotalMatrix* aTmp* nu;
     // Gradient of pressure
-    Eigen::VectorXd m2 = problem->kMatrix * bTmp;
+    Eigen::VectorXd m2 = problem->kMatrix* bTmp;
     // Pressure Term
-    Eigen::VectorXd m3 = problem->D_matrix * bTmp;
+    Eigen::VectorXd m3 = problem->D_matrix* bTmp;
     // BC PPE
-    Eigen::VectorXd m6 = problem->BC1_matrix * aTmp * nu;
+    Eigen::VectorXd m6 = problem->BC1_matrix* aTmp* nu;
     // BC PPE
-    Eigen::VectorXd m7 = problem->BC3_matrix * aTmp * nu;
+    Eigen::VectorXd m7 = problem->BC3_matrix* aTmp* nu;
     // Penalty term
     Eigen::MatrixXd penaltyU = Eigen::MatrixXd::Zero(Nphi_u, N_BC);
 
@@ -206,12 +206,12 @@ int newtonUnsteadyNSTurbIntrusivePPE::operator()(const Eigen::VectorXd& x,
     for (int i = 0; i < Nphi_u; i++)
     {
         cc = aTmp.transpose() * Eigen::SliceFromTensor(problem->cTotalTensor, 0,
-                i) * aTmp;
+             i) * aTmp;
         fvec(i) = - a_dot(i) + m1(i) - cc(0, 0) - m2(i);
 
         if (problem->bcMethod == "penalty")
         {
-            fvec(i) += ((penaltyU * tauU)(i, 0));
+            fvec(i) += ((penaltyU* tauU)(i, 0));
         }
     }
 
@@ -219,11 +219,11 @@ int newtonUnsteadyNSTurbIntrusivePPE::operator()(const Eigen::VectorXd& x,
     {
         int k = j + Nphi_u;
         gg = aTmp.transpose() * Eigen::SliceFromTensor(problem->gTensor, 0,
-                j) * aTmp;
+             j) * aTmp;
         bb = aTmp.transpose() * Eigen::SliceFromTensor(problem->bc2Tensor, 0,
-                j) * aTmp;
+             j) * aTmp;
         nn = aTmp.transpose() * Eigen::SliceFromTensor(problem->cTotalPPETensor, 0,
-                j) * aTmp;
+             j) * aTmp;
         fvec(k) = m3(j, 0) + gg(0, 0) - m7(j, 0) - nn(0, 0);
     }
 
@@ -242,7 +242,7 @@ int newtonUnsteadyNSTurbIntrusivePPE::operator()(const Eigen::VectorXd& x,
 int newtonUnsteadyNSTurbIntrusivePPE::df(const Eigen::VectorXd& x,
         Eigen::MatrixXd& fjac) const
 {
-    Eigen::NumericalDiff<newtonUnsteadyNSTurbIntrusivePPE> numDiff(*this);
+    Eigen::NumericalDiff<newtonUnsteadyNSTurbIntrusivePPE> numDiff( * this);
     numDiff.df(x, fjac);
     return 0;
 }
diff --git a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTurbIntrusive/ReducedUnsteadyNSTurbIntrusive.H b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTurbIntrusive/ReducedUnsteadyNSTurbIntrusive.H
old mode 100755
new mode 100644
index b56cd703b..19160475c
--- a/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTurbIntrusive/ReducedUnsteadyNSTurbIntrusive.H
+++ b/src/ITHACA_ROMPROBLEMS/ReducedUnsteadyNSTurbIntrusive/ReducedUnsteadyNSTurbIntrusive.H
@@ -51,9 +51,10 @@ struct newtonUnsteadyNSTurbIntrusive: public newton_argument<double>
 {
     public:
         newtonUnsteadyNSTurbIntrusive() {}
+
         newtonUnsteadyNSTurbIntrusive(int Nx, int Ny,
                                       UnsteadyNSTurbIntrusive& problem): newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_u(problem.nModesOnline),
             N_BC(problem.inletIndex.rows())
         {}
@@ -76,9 +77,10 @@ struct newtonUnsteadyNSTurbIntrusivePPE: public newton_argument<double>
 {
     public:
         newtonUnsteadyNSTurbIntrusivePPE() {}
+
         newtonUnsteadyNSTurbIntrusivePPE(int Nx, int Ny,
                                          UnsteadyNSTurbIntrusive& problem): newton_argument<double>(Nx, Ny),
-            problem(&problem),
+            problem( & problem),
             Nphi_u(problem.NUmodes),
             Nphi_p(problem.NPmodes),
             N_BC(problem.inletIndex.rows())
diff --git a/src/ITHACA_THIRD_PARTY/splinter/src/bspline.C b/src/ITHACA_THIRD_PARTY/splinter/src/bspline.C
old mode 100755
new mode 100644
index d5ec09f9f..0a678c07f
--- a/src/ITHACA_THIRD_PARTY/splinter/src/bspline.C
+++ b/src/ITHACA_THIRD_PARTY/splinter/src/bspline.C
@@ -116,7 +116,7 @@ DenseMatrix BSpline::evalHessian(DenseVector x) const
     DenseMatrix identity = DenseMatrix::Identity(numVariables, numVariables);
     DenseMatrix caug = kroneckerProduct(identity, coefficients.transpose());
     DenseMatrix DB = basis.evalBasisHessian(x);
-    H = caug * DB;
+    H = caug* DB;
 
     // Fill in upper triangular of Hessian
     for (size_t i = 0; i < numVariables; ++i)
@@ -230,8 +230,8 @@ void BSpline::updateControlPoints(const DenseMatrix& A)
         throw Exception("BSpline::updateControlPoints: Incompatible size of linear transformation matrix.");
     }
 
-    coefficients = A * coefficients;
-    knotaverages = A * knotaverages;
+    coefficients = A* coefficients;
+    knotaverages = A* knotaverages;
 }
 
 void BSpline::checkControlPoints() const
@@ -396,8 +396,8 @@ void BSpline::insertKnots(double tau, unsigned int dim,
     updateControlPoints(A);
 }
 
-void BSpline::regularizeKnotVectors(std::vector<double>& lb,
-                                    std::vector<double>& ub)
+void BSpline::regularizeKnotVectors(std::vector<double> & lb,
+                                    std::vector<double> & ub)
 {
     // Add and remove controlpoints and knots to make the b-spline p-regular with support [lb, ub]
     if (!(lb.size() == numVariables && ub.size() == numVariables))
@@ -432,8 +432,8 @@ void BSpline::regularizeKnotVectors(std::vector<double>& lb,
     }
 }
 
-bool BSpline::removeUnsupportedBasisFunctions(std::vector<double>& lb,
-        std::vector<double>& ub)
+bool BSpline::removeUnsupportedBasisFunctions(std::vector<double> & lb,
+        std::vector<double> & ub)
 {
     if (lb.size() != numVariables || ub.size() != numVariables)
     {
@@ -455,14 +455,14 @@ bool BSpline::removeUnsupportedBasisFunctions(std::vector<double>& lb,
 void BSpline::save(const std::string& fileName) const
 {
     Serializer s;
-    s.serialize(*this);
+    s.serialize( * this);
     s.saveToFile(fileName);
 }
 
 void BSpline::load(const std::string& fileName)
 {
     Serializer s(fileName);
-    s.deserialize(*this);
+    s.deserialize( * this);
 }
 
 std::string BSpline::getDescription() const
diff --git a/src/ITHACA_THIRD_PARTY/splinter/src/bsplinebasis.C b/src/ITHACA_THIRD_PARTY/splinter/src/bsplinebasis.C
old mode 100755
new mode 100644
index 13ccb2c41..475699177
--- a/src/ITHACA_THIRD_PARTY/splinter/src/bsplinebasis.C
+++ b/src/ITHACA_THIRD_PARTY/splinter/src/bsplinebasis.C
@@ -20,7 +20,7 @@ BSplineBasis::BSplineBasis()
 {
 }
 
-BSplineBasis::BSplineBasis(std::vector< std::vector<double>>& knotVectors,
+BSplineBasis::BSplineBasis(std::vector< std::vector<double>> & knotVectors,
                            std::vector<unsigned int> basisDegrees)
     : numVariables(knotVectors.size())
 {
@@ -200,7 +200,7 @@ SparseMatrix BSplineBasis::evalBasisHessian(DenseVector& x) const
      * so that basis hessian H is in R^(numBasisFunctions*numInputs x numInputs)
      * The real B-spline Hessian is calculated as (c^T x 1^(numInputs x 1))*H
      */
-    SparseMatrix H(getNumBasisFunctions()*numVariables, numVariables);
+    SparseMatrix H(getNumBasisFunctions() * numVariables, numVariables);
     //H.setZero(numBasisFunctions()*numInputs, numInputs);
 
     // Calculate partial derivatives
@@ -242,7 +242,7 @@ SparseMatrix BSplineBasis::evalBasisHessian(DenseVector& x) const
                 {
                     if (it.value() != 0)
                     {
-                        int row = i * getNumBasisFunctions() + it.row();
+                        int row = i* getNumBasisFunctions() + it.row();
                         int col = j;
                         H.insert(row, col) = it.value();
                     }
@@ -339,8 +339,8 @@ SparseMatrix BSplineBasis::decomposeToBezierForm()
     return A;
 }
 
-SparseMatrix BSplineBasis::reduceSupport(std::vector<double>& lb,
-        std::vector<double>& ub)
+SparseMatrix BSplineBasis::reduceSupport(std::vector<double> & lb,
+        std::vector<double> & ub)
 {
     if (lb.size() != ub.size() || lb.size() != numVariables)
     {
@@ -367,7 +367,7 @@ std::vector<unsigned int> BSplineBasis::getBasisDegrees() const
 {
     std::vector<unsigned int> degrees;
 
-    for (const auto& basis : bases)
+    for (const auto & basis : bases)
     {
         degrees.push_back(basis.getBasisDegree());
     }
diff --git a/src/ITHACA_THIRD_PARTY/splinter/src/bsplinebasis1d.C b/src/ITHACA_THIRD_PARTY/splinter/src/bsplinebasis1d.C
old mode 100755
new mode 100644
index d3f946ecc..9b45c6a23
--- a/src/ITHACA_THIRD_PARTY/splinter/src/bsplinebasis1d.C
+++ b/src/ITHACA_THIRD_PARTY/splinter/src/bsplinebasis1d.C
@@ -20,7 +20,7 @@ BSplineBasis1D::BSplineBasis1D()
 {
 }
 
-BSplineBasis1D::BSplineBasis1D(const std::vector<double>& knots,
+BSplineBasis1D::BSplineBasis1D(const std::vector<double> & knots,
                                unsigned int degree)
     : degree(degree),
       knots(knots),
@@ -50,11 +50,11 @@ SparseVector BSplineBasis1D::eval(double x) const
     // Evaluate nonzero basis functions
     for (auto it = indexSupported.begin(); it != indexSupported.end(); ++it)
     {
-        double val = deBoorCox(x, *it, degree);
+        double val = deBoorCox(x, * it, degree);
 
         if (fabs(val) > 1e-12)
         {
-            values.insert(*it) = val;
+            values.insert( * it) = val;
         }
     }
 
@@ -98,17 +98,17 @@ SparseVector BSplineBasis1D::evalDerivative(double x, int r) const
     for (int i = 1; i <= p - r; i++)
     {
         SparseMatrix R = buildBasisMatrix(x, knotIndex, i);
-        B = B * R;
+        B = B* R;
     }
 
     for (int i = p - r + 1; i <= p; i++)
     {
         SparseMatrix DR = buildBasisMatrix(x, knotIndex, i, true);
-        B = B * DR;
+        B = B* DR;
     }
 
     double factorial = std::tgamma(p + 1) / std::tgamma(p - r + 1);
-    B = B * factorial;
+    B = B* factorial;
 
     if (B.cols() != p + 1)
     {
@@ -237,7 +237,7 @@ double BSplineBasis1D::deBoorCox(double x, int i, int k) const
         s2 = deBoorCoxCoeff(x, knots.at(i + 1), knots.at(i + k + 1));
         r1 = deBoorCox(x, i,   k - 1);
         r2 = deBoorCox(x, i + 1, k - 1);
-        return s1 * r1 + (1 - s2) * r2;
+        return s1* r1 + (1 - s2) * r2;
     }
 }
 
@@ -346,7 +346,7 @@ SparseMatrix BSplineBasis1D::refineKnotsLocally(double x)
     auto lower = std::prev(upper);
 
     // Do not insert if upper and lower bounding knot are close
-    if (assertNear(*upper, *lower))
+    if (assertNear( * upper, * lower))
     {
         unsigned int n = getNumBasisFunctions();
         DenseMatrix A = DenseMatrix::Identity(n, n);
@@ -358,10 +358,10 @@ SparseMatrix BSplineBasis1D::refineKnotsLocally(double x)
 
     // Adjust x if it is on or close to a knot
     if (knotMultiplicity(x) > 0
-            || assertNear(*upper, x, 1e-6, 1e-6)
-            || assertNear(*lower, x, 1e-6, 1e-6))
+            || assertNear( * upper, x, 1e-6, 1e-6)
+            || assertNear( * lower, x, 1e-6, 1e-6))
     {
-        insertVal = (*upper + *lower) / 2.0;
+        insertVal = ( * upper + * lower) / 2.0;
     }
 
     // Insert new knot
@@ -394,16 +394,16 @@ SparseMatrix BSplineBasis1D::decomposeToBezierForm()
     while (knoti != refinedKnots.end())
     {
         // Insert new knots
-        int mult = degree + 1 - knotMultiplicity(*knoti);
+        int mult = degree + 1 - knotMultiplicity( * knoti);
 
         if (mult > 0)
         {
-            std::vector<double> newKnots(mult, *knoti);
+            std::vector<double> newKnots(mult, * knoti);
             refinedKnots.insert(knoti, newKnots.begin(), newKnots.end());
         }
 
         // Advance to next knot
-        knoti = std::upper_bound(refinedKnots.begin(), refinedKnots.end(), *knoti);
+        knoti = std::upper_bound(refinedKnots.begin(), refinedKnots.end(), * knoti);
     }
 
     if (!isKnotVectorRegular(refinedKnots, degree))
@@ -423,7 +423,8 @@ SparseMatrix BSplineBasis1D::decomposeToBezierForm()
     return A;
 }
 
-SparseMatrix BSplineBasis1D::buildKnotInsertionMatrix(const std::vector<double>&
+SparseMatrix BSplineBasis1D::buildKnotInsertionMatrix(const std::vector<double>
+        &
         refinedKnots) const
 {
     if (!isKnotVectorRegular(refinedKnots, degree))
@@ -454,7 +455,7 @@ SparseMatrix BSplineBasis1D::buildKnotInsertionMatrix(const std::vector<double>&
         for (unsigned int j = 1; j <= degree; j++)
         {
             SparseMatrix Ri = buildBasisMatrix(knotsAug.at(i + j), u, j);
-            R = R * Ri;
+            R = R* Ri;
         }
 
         // Size check
@@ -503,7 +504,7 @@ int BSplineBasis1D::indexHalfopenInterval(double x) const
 
     // Find first knot that is larger than x
     std::vector<double>::const_iterator it = std::upper_bound(knots.begin(),
-            knots.end(), x);
+        knots.end(), x);
     // Return index
     int index = it - knots.begin();
     return index - 1;
@@ -557,7 +558,7 @@ SparseMatrix BSplineBasis1D::reduceSupport(double lb, double ub)
 
     DenseMatrix Ad = DenseMatrix::Zero(numOld, numNew);
     Ad.block(index_lower, 0, numNew, numNew) = DenseMatrix::Identity(numNew,
-            numNew);
+        numNew);
     SparseMatrix A = Ad.sparseView();
     // Update knots
     knots = si;
@@ -626,7 +627,7 @@ unsigned int BSplineBasis1D::indexLongestInterval() const
     return indexLongestInterval(knots);
 }
 
-unsigned int BSplineBasis1D::indexLongestInterval(const std::vector<double>&
+unsigned int BSplineBasis1D::indexLongestInterval(const std::vector<double> &
         vec) const
 {
     double longest = 0;
diff --git a/src/ITHACA_THIRD_PARTY/splinter/src/bsplinebuilder.C b/src/ITHACA_THIRD_PARTY/splinter/src/bsplinebuilder.C
old mode 100755
new mode 100644
index b677b8b03..55c1a96fb
--- a/src/ITHACA_THIRD_PARTY/splinter/src/bsplinebuilder.C
+++ b/src/ITHACA_THIRD_PARTY/splinter/src/bsplinebuilder.C
@@ -79,11 +79,11 @@ DenseVector BSpline::Builder::computeCoefficients(const BSpline& bspline) const
          * NOTE2: consider changing regularization factor to (alpha/numSample)
          */
         SparseMatrix Bt = B.transpose();
-        A = Bt * B;
-        b = Bt * b;
+        A = Bt* B;
+        b = Bt* b;
         auto I = SparseMatrix(A.cols(), A.cols());
         I.setIdentity();
-        A += _alpha * I;
+        A += _alpha* I;
     }
     else if (_smoothing == Smoothing::PSPLINE)
     {
@@ -113,9 +113,9 @@ DenseVector BSpline::Builder::computeCoefficients(const BSpline& bspline) const
         // Second order finite difference matrix
         SparseMatrix D = getSecondOrderFiniteDifferenceMatrix(bspline);
         // Left-hand side matrix
-        A = Bt * W * B + _alpha * D.transpose() * D;
+        A = Bt* W* B + _alpha* D.transpose() * D;
         // Compute right-hand side matrices
-        b = Bt * W * b;
+        b = Bt* W* b;
     }
 
     DenseVector x;
@@ -282,7 +282,7 @@ SparseMatrix BSpline::Builder::getSecondOrderFiniteDifferenceMatrix(
         for (int j = 0; j < rightProd; j++)
         {
             // Start column of current subblock
-            int blkBaseCol = j * leftProd * dims[d];
+            int blkBaseCol = j* leftProd* dims[d];
 
             // Block rows [I -2I I] of subblock
             for (unsigned int l = 0; l < (dims[d] - 2); l++)
@@ -290,7 +290,7 @@ SparseMatrix BSpline::Builder::getSecondOrderFiniteDifferenceMatrix(
                 // Special case for first dimension
                 if (d == 0)
                 {
-                    int k = j * leftProd * dims[d] + l;
+                    int k = j* leftProd* dims[d] + l;
                     D.insert(i, k) = 1;
                     k += leftProd;
                     D.insert(i, k) = -2;
@@ -303,7 +303,7 @@ SparseMatrix BSpline::Builder::getSecondOrderFiniteDifferenceMatrix(
                     // Loop for identity matrix
                     for (int n = 0; n < leftProd; n++)
                     {
-                        int k = blkBaseCol + l * leftProd + n;
+                        int k = blkBaseCol + l* leftProd + n;
                         D.insert(i, k) = 1;
                         k += leftProd;
                         D.insert(i, k) = -2;
@@ -344,7 +344,7 @@ std::vector<std::vector<double>> BSpline::Builder::computeKnotVectors() const
 
 // Compute a single knot vector from sample grid and degree
 std::vector<double> BSpline::Builder::computeKnotVector(
-    const std::vector<double>& values,
+    const std::vector<double> & values,
     unsigned int degree,
     unsigned int numBasisFunctions) const
 {
@@ -395,7 +395,7 @@ std::vector<double> BSpline::Builder::computeKnotVector(
 * samples are added to buckets and the knots computed as the average of these.
 */
 std::vector<double> BSpline::Builder::knotVectorMovingAverage(
-    const std::vector<double>& values,
+    const std::vector<double> & values,
     unsigned int degree) const
 {
     // Sort and remove duplicates
@@ -450,7 +450,7 @@ std::vector<double> BSpline::Builder::knotVectorMovingAverage(
 }
 
 std::vector<double> BSpline::Builder::knotVectorEquidistant(
-    const std::vector<double>& values,
+    const std::vector<double> & values,
     unsigned int degree,
     unsigned int numBasisFunctions = 0) const
 {
@@ -502,7 +502,7 @@ std::vector<double> BSpline::Builder::knotVectorEquidistant(
 }
 
 std::vector<double> BSpline::Builder::knotVectorBuckets(
-    const std::vector<double>& values, unsigned int degree,
+    const std::vector<double> & values, unsigned int degree,
     unsigned int maxSegments) const
 {
     // Sort and remove duplicates
@@ -549,7 +549,7 @@ std::vector<double> BSpline::Builder::knotVectorBuckets(
     }
 
     // Residual
-    unsigned int res = unique.size() - w * ni;
+    unsigned int res = unique.size() - w* ni;
     // Create array with window sizes
     std::vector<unsigned int> windows(ni, w);
 
@@ -591,7 +591,7 @@ std::vector<double> BSpline::Builder::knotVectorBuckets(
 }
 
 std::vector<double> BSpline::Builder::extractUniqueSorted(
-    const std::vector<double>& values) const
+    const std::vector<double> & values) const
 {
     // Sort and remove duplicates
     std::vector<double> unique(values);
diff --git a/src/ITHACA_THIRD_PARTY/splinter/src/datapoint.C b/src/ITHACA_THIRD_PARTY/splinter/src/datapoint.C
old mode 100755
new mode 100644
index d58f5829c..1a312a132
--- a/src/ITHACA_THIRD_PARTY/splinter/src/datapoint.C
+++ b/src/ITHACA_THIRD_PARTY/splinter/src/datapoint.C
@@ -38,7 +38,7 @@ DataPoint::DataPoint(DenseVector x, double y)
     setData(newX, y);
 }
 
-void DataPoint::setData(const std::vector<double>& x, double y)
+void DataPoint::setData(const std::vector<double> & x, double y)
 {
     this->x = x;
     this->y = y;
diff --git a/src/ITHACA_THIRD_PARTY/splinter/src/datatable.C b/src/ITHACA_THIRD_PARTY/splinter/src/datatable.C
old mode 100755
new mode 100644
index 21a8e1b50..66aca848b
--- a/src/ITHACA_THIRD_PARTY/splinter/src/datatable.C
+++ b/src/ITHACA_THIRD_PARTY/splinter/src/datatable.C
@@ -97,7 +97,7 @@ void DataTable::addSample(const DataPoint& sample)
 
 void DataTable::addSample(std::initializer_list<DataPoint> samples)
 {
-    for (auto& sample : samples)
+    for (auto & sample : samples)
     {
         addSample(sample);
     }
@@ -116,7 +116,7 @@ unsigned int DataTable::getNumSamplesRequired() const
     unsigned long samplesRequired = 1;
     unsigned int i = 0;
 
-    for (auto& variable : grid)
+    for (auto & variable : grid)
     {
         samplesRequired *= (unsigned long) variable.size();
         i++;
@@ -150,14 +150,14 @@ void DataTable::gridCompleteGuard() const
 void DataTable::save(const std::string& fileName) const
 {
     Serializer s;
-    s.serialize(*this);
+    s.serialize( * this);
     s.saveToFile(fileName);
 }
 
 void DataTable::load(const std::string& fileName)
 {
     Serializer s(fileName);
-    s.deserialize(*this);
+    s.deserialize( * this);
 }
 
 /*
@@ -192,7 +192,7 @@ std::vector< std::vector<double>> DataTable::getTableX() const
     // Fill table with values
     int i = 0;
 
-    for (auto& sample : samples)
+    for (auto & sample : samples)
     {
         std::vector<double> x = sample.getX();
 
@@ -231,12 +231,12 @@ DataTable operator+(const DataTable& lhs, const DataTable& rhs)
 
     for (auto it = lhs.cbegin(); it != lhs.cend(); it++)
     {
-        result.addSample(*it);
+        result.addSample( * it);
     }
 
     for (auto it = rhs.cbegin(); it != rhs.cend(); it++)
     {
-        result.addSample(*it);
+        result.addSample( * it);
     }
 
     return result;
@@ -255,9 +255,9 @@ DataTable operator-(const DataTable& lhs, const DataTable& rhs)
     // Add all samples from lhs that are not in rhs
     for (auto it = lhs.cbegin(); it != lhs.cend(); it++)
     {
-        if (rhsSamples.count(*it) == 0)
+        if (rhsSamples.count( * it) == 0)
         {
-            result.addSample(*it);
+            result.addSample( * it);
         }
     }
 
diff --git a/src/ITHACA_THIRD_PARTY/splinter/src/function.C b/src/ITHACA_THIRD_PARTY/splinter/src/function.C
old mode 100755
new mode 100644
index e34fd6cf7..fc9d2644d
--- a/src/ITHACA_THIRD_PARTY/splinter/src/function.C
+++ b/src/ITHACA_THIRD_PARTY/splinter/src/function.C
@@ -13,26 +13,26 @@
 namespace SPLINTER
 {
 
-double Function::eval(const std::vector<double>& x) const
+double Function::eval(const std::vector<double> & x) const
 {
     auto denseX = vectorToDenseVector(x);
     return eval(denseX);
 }
 
-std::vector<double> Function::evalJacobian(const std::vector<double>& x) const
+std::vector<double> Function::evalJacobian(const std::vector<double> & x) const
 {
     auto denseX = vectorToDenseVector(x);
     return denseVectorToVector(evalJacobian(denseX));
 }
 
 std::vector<std::vector<double>> Function::evalHessian(const std::vector<double>
-                              & x) const
+        & x) const
 {
     auto denseX = vectorToDenseVector(x);
     return denseMatrixToVectorVector(secondOrderCentralDifference(denseX));
 }
 
-std::vector<double> Function::centralDifference(const std::vector<double>& x)
+std::vector<double> Function::centralDifference(const std::vector<double> & x)
 const
 {
     auto denseX = vectorToDenseVector(x);
@@ -41,7 +41,7 @@ const
 }
 
 std::vector<std::vector<double>> Function::secondOrderCentralDifference(
-                                  const std::vector<double>& x) const
+    const std::vector<double> & x) const
 {
     auto denseX = vectorToDenseVector(x);
     DenseMatrix ddx = secondOrderCentralDifference(denseX);
@@ -104,7 +104,7 @@ DenseMatrix Function::secondOrderCentralDifference(DenseVector x) const
             x2(j) = x2(j) - hBackward;
             x3(i) = x3(i) - hBackward;
             x3(j) = x3(j) - hBackward;
-            ddx(i, j) = (eval(x0) - eval(x1) - eval(x2) + eval(x3)) / (h * h);
+            ddx(i, j) = (eval(x0) - eval(x1) - eval(x2) + eval(x3)) / (h* h);
         }
     }
 
diff --git a/src/ITHACA_THIRD_PARTY/splinter/src/knots.C b/src/ITHACA_THIRD_PARTY/splinter/src/knots.C
old mode 100755
new mode 100644
index 0e296fde3..65acc260c
--- a/src/ITHACA_THIRD_PARTY/splinter/src/knots.C
+++ b/src/ITHACA_THIRD_PARTY/splinter/src/knots.C
@@ -13,7 +13,7 @@
 namespace SPLINTER
 {
 
-bool isKnotVectorRegular(const std::vector<double>& knots, unsigned int degree)
+bool isKnotVectorRegular(const std::vector<double> & knots, unsigned int degree)
 {
     // Check size
     if (knots.size() < 2 * (degree + 1))
@@ -31,7 +31,7 @@ bool isKnotVectorRegular(const std::vector<double>& knots, unsigned int degree)
     for (std::vector<double>::const_iterator it = knots.begin(); it != knots.end();
             ++it)
     {
-        if (count(knots.begin(), knots.end(), *it) > degree + 1)
+        if (count(knots.begin(), knots.end(), * it) > degree + 1)
         {
             return false;
         }
@@ -40,7 +40,7 @@ bool isKnotVectorRegular(const std::vector<double>& knots, unsigned int degree)
     return true;
 }
 
-bool isKnotVectorClamped(const std::vector<double>& knots, unsigned int degree)
+bool isKnotVectorClamped(const std::vector<double> & knots, unsigned int degree)
 {
     // Check multiplicity of first knot
     if (std::count(knots.begin(), knots.begin() + degree + 1,
@@ -59,8 +59,8 @@ bool isKnotVectorClamped(const std::vector<double>& knots, unsigned int degree)
     return true;
 }
 
-bool isKnotVectorRefinement(const std::vector<double>& knots,
-                            const std::vector<double>& refinedKnots)
+bool isKnotVectorRefinement(const std::vector<double> & knots,
+                            const std::vector<double> & refinedKnots)
 {
     // Check size
     if (refinedKnots.size() < knots.size())
@@ -72,8 +72,8 @@ bool isKnotVectorRefinement(const std::vector<double>& knots,
     for (std::vector<double>::const_iterator it = knots.begin() ; it != knots.end();
             ++it)
     {
-        int m_tau = count(knots.begin(), knots.end(), *it);
-        int m_t = count(refinedKnots.begin(), refinedKnots.end(), *it);
+        int m_tau = count(knots.begin(), knots.end(), * it);
+        int m_t = count(refinedKnots.begin(), refinedKnots.end(), * it);
 
         if (m_t < m_tau)
         {
diff --git a/src/ITHACA_THIRD_PARTY/splinter/src/mykroneckerproduct.C b/src/ITHACA_THIRD_PARTY/splinter/src/mykroneckerproduct.C
old mode 100755
new mode 100644
index a62d2c619..ba287c1c8
--- a/src/ITHACA_THIRD_PARTY/splinter/src/mykroneckerproduct.C
+++ b/src/ITHACA_THIRD_PARTY/splinter/src/mykroneckerproduct.C
@@ -22,7 +22,7 @@ namespace SPLINTER
  */
 SparseMatrix myKroneckerProduct(const SparseMatrix& A, const SparseMatrix& B)
 {
-    SparseMatrix AB(A.rows()*B.rows(), A.cols()*B.cols());
+    SparseMatrix AB(A.rows() * B.rows(), A.cols() * B.cols());
     // Reserve memory for AB
     //AB.reserve(A.nonZeros()*B.nonZeros()); // Does not reserve inner vectors (slow)
     //int innernnz = std::ceil(A.nonZeros()*B.nonZeros()/AB.outerSize());
@@ -86,7 +86,7 @@ SparseMatrix myKroneckerProduct(const SparseMatrix& A, const SparseMatrix& B)
                 {
                     for (SparseMatrix::InnerIterator itB(B, jB); itB; ++itB)
                     {
-                        if (std::abs(itA.value()*itB.value()) > tolerance)
+                        if (std::abs(itA.value() * itB.value()) > tolerance)
                         {
                             int row = jrow + itB.row();
                             int col = jcol + itB.col();
@@ -102,7 +102,7 @@ SparseMatrix myKroneckerProduct(const SparseMatrix& A, const SparseMatrix& B)
     return AB;
 }
 
-SparseVector kroneckerProductVectors(const std::vector<SparseVector>& vectors)
+SparseVector kroneckerProductVectors(const std::vector<SparseVector> & vectors)
 {
     // Create two temp matrices
     SparseMatrix temp1(1, 1);
@@ -111,7 +111,7 @@ SparseVector kroneckerProductVectors(const std::vector<SparseVector>& vectors)
     // Multiply from left
     int counter = 0;
 
-    for (const auto& vec : vectors)
+    for (const auto & vec : vectors)
     {
         // Avoid copy
         if (counter % 2 == 0)
@@ -135,7 +135,7 @@ SparseVector kroneckerProductVectors(const std::vector<SparseVector>& vectors)
     return temp1;
 }
 
-DenseVector kroneckerProductVectors(const std::vector<DenseVector>& vectors)
+DenseVector kroneckerProductVectors(const std::vector<DenseVector> & vectors)
 {
     // Create two temp matrices
     DenseVector temp1(1);
@@ -144,7 +144,7 @@ DenseVector kroneckerProductVectors(const std::vector<DenseVector>& vectors)
     // Multiply from left
     int counter = 0;
 
-    for (const auto& vec : vectors)
+    for (const auto & vec : vectors)
     {
         // Avoid copy
         if (counter % 2 == 0)
@@ -168,7 +168,8 @@ DenseVector kroneckerProductVectors(const std::vector<DenseVector>& vectors)
     return temp1;
 }
 
-SparseMatrix kroneckerProductMatrices(const std::vector<SparseMatrix>& matrices)
+SparseMatrix kroneckerProductMatrices(const std::vector<SparseMatrix> &
+                                      matrices)
 {
     // Create two temp matrices
     SparseMatrix temp1(1, 1);
@@ -177,7 +178,7 @@ SparseMatrix kroneckerProductMatrices(const std::vector<SparseMatrix>& matrices)
     // Multiply from left
     int counter = 0;
 
-    for (const auto& mat : matrices)
+    for (const auto & mat : matrices)
     {
         // Avoid copy
         if (counter % 2 == 0)
diff --git a/src/ITHACA_THIRD_PARTY/splinter/src/rbfspline.C b/src/ITHACA_THIRD_PARTY/splinter/src/rbfspline.C
old mode 100755
new mode 100644
index e55664864..30f59afdb
--- a/src/ITHACA_THIRD_PARTY/splinter/src/rbfspline.C
+++ b/src/ITHACA_THIRD_PARTY/splinter/src/rbfspline.C
@@ -115,7 +115,7 @@ RBFSpline::RBFSpline(const DataTable& samples, RadialBasisFunctionType type,
 
         for (auto it2 = samples.cbegin(); it2 != samples.cend(); ++it2, ++j)
         {
-            double val = fn->eval(dist(*it1, *it2));
+            double val = fn->eval(dist( * it1, * it2));
 
             if (val != 0)
             {
@@ -129,7 +129,7 @@ RBFSpline::RBFSpline(const DataTable& samples, RadialBasisFunctionType type,
 
         if (normalized)
         {
-            b(i) = sum * y;
+            b(i) = sum* y;
         }
         else
         {
@@ -144,8 +144,8 @@ RBFSpline::RBFSpline(const DataTable& samples, RadialBasisFunctionType type,
         // Calcualte precondition matrix P
         DenseMatrix P = computePreconditionMatrix();
         // Preconditioned A and b
-        DenseMatrix Ap = P * A;
-        DenseMatrix bp = P * b;
+        DenseMatrix Ap = P* A;
+        DenseMatrix bp = P* b;
         A = Ap;
         b = bp;
     }
@@ -171,7 +171,7 @@ RBFSpline::RBFSpline(const DataTable& samples, RadialBasisFunctionType type,
     weights = A.colPivHouseholderQr().solve(b);
 #ifndef NDEBUG
     // Compute error. If it is used later on, move this statement above the NDEBUG
-    double err = (A * weights - b).norm() / b.norm();
+    double err = (A* weights - b).norm() / b.norm();
     std::cout << "Error: " << std::setprecision(10) << err << std::endl;
 #endif // NDEBUG
     //    // Alternative solver
@@ -301,7 +301,7 @@ DenseMatrix RBFSpline::computePreconditionMatrix() const
             Point p2 = p + p1;
             p2.setIndex(p.getIndex());
             points.push_back(
-                p2); // The resulting point has a different index than that of p
+                      p2); // The resulting point has a different index than that of p
             //                cout << p.getIndex() << "/" << p1.getIndex() << "/" << p2.getIndex() << endl;
             //                assert(p.getIndex() == p2.getIndex());
         }
diff --git a/src/ITHACA_THIRD_PARTY/splinter/src/serializer.C b/src/ITHACA_THIRD_PARTY/splinter/src/serializer.C
old mode 100755
new mode 100644
index 1b2c3a2e2..9e1eb1178
--- a/src/ITHACA_THIRD_PARTY/splinter/src/serializer.C
+++ b/src/ITHACA_THIRD_PARTY/splinter/src/serializer.C
@@ -34,7 +34,7 @@ void Serializer::saveToFile(const std::string& fileName)
 {
     std::fstream fs(fileName, std::fstream::out | std::fstream::binary);
 
-    for (const auto& byte : stream)
+    for (const auto & byte : stream)
     {
         fs << byte;
     }
@@ -65,7 +65,7 @@ void Serializer::loadFromFile(const std::string& fileName)
     stream.clear();
 
     // Convert from char to uint_8 vector
-    for (const char& byte : result)
+    for (const char & byte : result)
     {
         stream.push_back((uint8_t)byte);
     }
@@ -121,7 +121,7 @@ size_t Serializer::get_size(const DenseMatrix& obj)
 
     if (numElements > 0)
     {
-        size += numElements * sizeof(obj(0, 0));
+        size += numElements* sizeof(obj(0, 0));
     }
 
     return size;
@@ -134,7 +134,7 @@ size_t Serializer::get_size(const DenseVector& obj)
 
     if (numElements > 0)
     {
-        size += numElements * sizeof(obj(0));
+        size += numElements* sizeof(obj(0));
     }
 
     return size;
diff --git a/src/ITHACA_THIRD_PARTY/splinter/src/utilities.C b/src/ITHACA_THIRD_PARTY/splinter/src/utilities.C
old mode 100755
new mode 100644
index 06bd73df9..35aa3a603
--- a/src/ITHACA_THIRD_PARTY/splinter/src/utilities.C
+++ b/src/ITHACA_THIRD_PARTY/splinter/src/utilities.C
@@ -24,7 +24,7 @@ std::vector<double> denseVectorToVector(const DenseVector& denseVec)
     return vec;
 }
 
-DenseVector vectorToDenseVector(const std::vector<double>& vec)
+DenseVector vectorToDenseVector(const std::vector<double> & vec)
 {
     DenseVector denseVec(vec.size());
 
@@ -37,7 +37,7 @@ DenseVector vectorToDenseVector(const std::vector<double>& vec)
 }
 
 std::vector<std::vector<double>> denseMatrixToVectorVector(
-                                  const DenseMatrix& mat)
+    const DenseMatrix& mat)
 {
     std::vector<std::vector<double>> vec(mat.rows());
 
@@ -52,7 +52,7 @@ std::vector<std::vector<double>> denseMatrixToVectorVector(
     return vec;
 }
 
-DenseMatrix vectorVectorToDenseMatrix(const std::vector<std::vector<double>>&
+DenseMatrix vectorVectorToDenseMatrix(const std::vector<std::vector<double>> &
                                       vec)
 {
     size_t numRows = vec.size();
@@ -82,7 +82,7 @@ std::vector<double> linspace(double start, double stop, unsigned int num)
 
     for (unsigned int i = 0; i < num; ++i)
     {
-        ret.push_back(start + i * dx);
+        ret.push_back(start + i* dx);
     }
 
     return ret;
diff --git a/src/ITHACA_TORCH/ConvLayer.C b/src/ITHACA_TORCH/ConvLayer.C
index 63c9698bb..88e6df5d5 100644
--- a/src/ITHACA_TORCH/ConvLayer.C
+++ b/src/ITHACA_TORCH/ConvLayer.C
@@ -33,7 +33,7 @@ namespace ITHACAtorch
 {
 template<class Type, template<class> class PatchField, class GeoMesh>
 ConvLayer<Type, PatchField, GeoMesh>::ConvLayer(
-    PtrList<GeometricField<Type, PatchField, GeoMesh>>& snapshots):
+    PtrList<GeometricField<Type, PatchField, GeoMesh>> & snapshots):
     _snapshots(snapshots),
     mesh(snapshots[0].mesh()),
     convDict(autoPtr<IOdictionary>
@@ -87,7 +87,7 @@ void ConvLayer<Type, PatchField, GeoMesh>::setDomainDivision(label Nx, label Ny,
         }
     }
 
-    convPoints = List<point>(Nx * Ny * Nz);
+    convPoints = List<point>(Nx* Ny* Nz);
     label index = 0;
 
     for (label i = 0; i < Nx; i++)
@@ -111,9 +111,9 @@ void ConvLayer<Type, PatchField, GeoMesh>::setDomainDivision(label Nx, label Ny,
                     k = 1;
                 }
 
-                convPoints[index] = mesh.bounds().min() + cmptMultiply((ds * i), vector(1, 0,
-                                    0)) + cmptMultiply((ds * j), vector(0, 1, 0)) + cmptMultiply((ds * k), vector(0,
-                                            0, 1));
+                convPoints[index] = mesh.bounds().min() + cmptMultiply((ds* i), vector(1, 0,
+                                    0)) + cmptMultiply((ds* j), vector(0, 1, 0)) + cmptMultiply((ds* k), vector(0,
+                                        0, 1));
                 index++;
             }
         }
diff --git a/src/ITHACA_TORCH/ConvLayer.H b/src/ITHACA_TORCH/ConvLayer.H
index 4702d9d4e..451da9a71 100644
--- a/src/ITHACA_TORCH/ConvLayer.H
+++ b/src/ITHACA_TORCH/ConvLayer.H
@@ -57,9 +57,9 @@ class ConvLayer
         ///
         /// @param[in]  db    The database
         ///
-        ConvLayer(PtrList<GeometricField<Type, PatchField, GeoMesh>>& snapshots);
+        ConvLayer(PtrList<GeometricField<Type, PatchField, GeoMesh>> & snapshots);
 
-        PtrList<GeometricField<Type, PatchField, GeoMesh>>& _snapshots;
+        PtrList<GeometricField<Type, PatchField, GeoMesh>> & _snapshots;
         const fvMesh& mesh;
 
         Vector<label> domainDivision;
@@ -90,4 +90,5 @@ typedef ConvLayer<vector, fvPatchField, volMesh> volVectorLayer;
 typedef ConvLayer<scalar, fvsPatchField, surfaceMesh> surfaceScalarLayer;
 
 }
+
 #endif
diff --git a/src/ITHACA_TORCH/Filters/Filter.H b/src/ITHACA_TORCH/Filters/Filter.H
index 5be6796d0..7fbe4e4b2 100644
--- a/src/ITHACA_TORCH/Filters/Filter.H
+++ b/src/ITHACA_TORCH/Filters/Filter.H
@@ -85,8 +85,8 @@ class Filter
         virtual ~Filter()
         {};
 
-        virtual List<scalarList> apply(const List<labelList>& cells,
-                                       const List<point>& convPoints, const fvMesh& mesh) const = 0;
+        virtual List<scalarList> apply(const List<labelList> & cells,
+                                       const List<point> & convPoints, const fvMesh& mesh) const = 0;
 
         static autoPtr<Filter> New
         (
diff --git a/src/ITHACA_TORCH/Filters/IntegralFilter.C b/src/ITHACA_TORCH/Filters/IntegralFilter.C
index ab13255f6..310b2bc03 100644
--- a/src/ITHACA_TORCH/Filters/IntegralFilter.C
+++ b/src/ITHACA_TORCH/Filters/IntegralFilter.C
@@ -15,8 +15,8 @@ Foam::IntegralFilter::IntegralFilter(const dictionary& dict)
     Info << "Is IntegralFilter" << endl;
 }
 
-List<scalarList> Foam::IntegralFilter::apply(const List<labelList>& cells,
-        const List<point>& convPoints, const fvMesh& mesh) const
+List<scalarList> Foam::IntegralFilter::apply(const List<labelList> & cells,
+        const List<point> & convPoints, const fvMesh& mesh) const
 {
     List<scalarList> weights(cells.size());
 
diff --git a/src/ITHACA_TORCH/Filters/IntegralFilter.H b/src/ITHACA_TORCH/Filters/IntegralFilter.H
index d7a920580..dae3e6236 100644
--- a/src/ITHACA_TORCH/Filters/IntegralFilter.H
+++ b/src/ITHACA_TORCH/Filters/IntegralFilter.H
@@ -35,8 +35,8 @@ class IntegralFilter
         virtual ~IntegralFilter()
         {};
 
-        virtual List<scalarList> apply(const List<labelList>& cells,
-                                       const List<point>& convPoints, const fvMesh& mesh) const;
+        virtual List<scalarList> apply(const List<labelList> & cells,
+                                       const List<point> & convPoints, const fvMesh& mesh) const;
 
 
 };
diff --git a/src/ITHACA_TORCH/torch2Eigen.C b/src/ITHACA_TORCH/torch2Eigen.C
old mode 100755
new mode 100644
index 1f2270c33..55c62f6eb
--- a/src/ITHACA_TORCH/torch2Eigen.C
+++ b/src/ITHACA_TORCH/torch2Eigen.C
@@ -86,13 +86,13 @@ Eigen::Matrix<type, Eigen::Dynamic, Eigen::Dynamic> torchTensor2eigenMatrix(
 
     for (int i = 0; i < nElem; i++)
     {
-        type d(*(data_p + i));
+        type d( * (data_p + i));
         type a = static_cast <type>(d);
         raw[i] = a;
     }
 
-    Eigen::Map<MatrixXf_rm> eigenMatrix(&raw[0], rows,
-                                        cols);
+    Eigen::Map<MatrixXf_rm> eigenMatrix( & raw[0], rows,
+                                         cols);
     return eigenMatrix;
 }
 
diff --git a/src/ITHACA_TORCH/torch2Foam.C b/src/ITHACA_TORCH/torch2Foam.C
old mode 100755
new mode 100644
index fc6ca5c88..bc603c7fd
--- a/src/ITHACA_TORCH/torch2Foam.C
+++ b/src/ITHACA_TORCH/torch2Foam.C
@@ -36,21 +36,21 @@ namespace torch2Foam
 {
 
 template<>
-torch::Tensor field2Torch(Field<vector>& field)
+torch::Tensor field2Torch(Field<vector> & field)
 {
     int rows = 1;
     int cols = field.size() * 3;
-    double* dataPtr = &field[0][0];
+    double* dataPtr = & field[0][0];
     return torch::from_blob(dataPtr, {rows, cols}, {torch::kFloat64}).clone().to(
                torch::kFloat32);
 }
 
 template<>
-torch::Tensor field2Torch(Field<scalar>& field)
+torch::Tensor field2Torch(Field<scalar> & field)
 {
     int rows = 1;
     int cols = field.size();
-    double* dataPtr = &field[0];
+    double* dataPtr = & field[0];
     return torch::from_blob(dataPtr, {rows, cols}, {torch::kFloat64}).clone().to(
                torch::kFloat32);
 }
@@ -64,8 +64,8 @@ Field<vector> torch2Field(torch::Tensor& torchTensor)
     M_Assert(torchTensor.dim() <= 2, error_message.c_str());
     M_Assert(torchTensor.dim() != 0, "The provided tensor has 0 dimension");
     Field<vector> a(torchTensor.numel() / 3);
-    std::memcpy(&a[0][0], torchTensor.to(torch::kFloat64).data_ptr(),
-                sizeof (double)*torchTensor.numel());
+    std::memcpy( & a[0][0], torchTensor.to(torch::kFloat64).data_ptr(),
+                 sizeof (double) * torchTensor.numel());
     return a;
 }
 
@@ -78,13 +78,13 @@ Field<scalar> torch2Field(torch::Tensor& torchTensor)
     M_Assert(torchTensor.dim() <= 2, error_message.c_str());
     M_Assert(torchTensor.dim() != 0, "The provided tensor has 0 dimension");
     Field<scalar> a(torchTensor.numel());
-    std::memcpy(&a[0], torchTensor.to(torch::kFloat64).data_ptr(),
-                sizeof (double)*torchTensor.numel());
+    std::memcpy( & a[0], torchTensor.to(torch::kFloat64).data_ptr(),
+                 sizeof (double) * torchTensor.numel());
     return a;
 }
 
 template<>
-torch::Tensor ptrList2Torch(PtrList<Field<vector>>& ptrList)
+torch::Tensor ptrList2Torch(PtrList<Field<vector>> & ptrList)
 {
     int Nrows = ptrList.size();
     int Ncols = ptrList[0].size() * 3;
@@ -99,7 +99,7 @@ torch::Tensor ptrList2Torch(PtrList<Field<vector>>& ptrList)
 }
 
 template<>
-torch::Tensor ptrList2Torch(PtrList<Field<scalar>>& ptrList)
+torch::Tensor ptrList2Torch(PtrList<Field<scalar>> & ptrList)
 {
     int Nrows = ptrList.size();
     int Ncols = ptrList[0].size();
diff --git a/src/ITHACA_TORCH/torch2Foam.H b/src/ITHACA_TORCH/torch2Foam.H
old mode 100755
new mode 100644
index 7dcb7a757..991ffdfff
--- a/src/ITHACA_TORCH/torch2Foam.H
+++ b/src/ITHACA_TORCH/torch2Foam.H
@@ -58,7 +58,7 @@ namespace torch2Foam
 /// @return     the torch tensor
 ///
 template <class type_f>
-torch::Tensor field2Torch(Field<type_f>& field);
+torch::Tensor field2Torch(Field<type_f> & field);
 
 //--------------------------------------------------------------------------
 /// @brief      Convert an Torch TensorOpenFOAM to an OpenFoam Field
@@ -73,7 +73,7 @@ template <class type_f>
 Field<type_f> torch2Field(torch::Tensor& tTensor);
 
 template <class type_f>
-torch::Tensor ptrList2Torch(PtrList<type_f>& ptrList);
+torch::Tensor ptrList2Torch(PtrList<type_f> & ptrList);
 
 template <class type_f>
 PtrList<Field<type_f>> torch2PtrList(torch::Tensor& tTensor);
diff --git a/src/ITHACA_TORCH/torchUTILITIES.C b/src/ITHACA_TORCH/torchUTILITIES.C
index 091de7d43..60aada404 100644
--- a/src/ITHACA_TORCH/torchUTILITIES.C
+++ b/src/ITHACA_TORCH/torchUTILITIES.C
@@ -32,8 +32,8 @@
 
 namespace ITHACAtorch
 {
-torch::Tensor removeConstValues(torch::Tensor input, std::vector<int>& indices,
-                                std::vector<double>& constValues)
+torch::Tensor removeConstValues(torch::Tensor input, std::vector<int> & indices,
+                                std::vector<double> & constValues)
 {
     torch::Tensor output;
     return output;
@@ -46,7 +46,7 @@ bool isConst(torch::Tensor& tTensor)
 
     for (std::size_t i = 1, s = tTensor.numel(); i < s && all_equal; i++)
     {
-        all_equal = *ptr == *(ptr + i);
+        all_equal = * ptr == * (ptr + i);
     }
 
     return all_equal;
diff --git a/src/ITHACA_TORCH/torchUTILITIES.H b/src/ITHACA_TORCH/torchUTILITIES.H
old mode 100755
new mode 100644
index 8e62a7d14..3f1ad1576
--- a/src/ITHACA_TORCH/torchUTILITIES.H
+++ b/src/ITHACA_TORCH/torchUTILITIES.H
@@ -43,8 +43,8 @@
 
 namespace ITHACAtorch
 {
-torch::Tensor removeConstValues(torch::Tensor input, std::vector<int>& indices,
-                                std::vector<double>& constValues);
+torch::Tensor removeConstValues(torch::Tensor input, std::vector<int> & indices,
+                                std::vector<double> & constValues);
 bool isConst(torch::Tensor& tTensor);
 
 void save(const torch::Tensor& tensor, const std::string fname);
diff --git a/src/OF_EXT/RBFFunctions/TPS/TPS.C b/src/OF_EXT/RBFFunctions/TPS/TPS.C
old mode 100755
new mode 100644
index fb6d72edf..30b124a8a
--- a/src/OF_EXT/RBFFunctions/TPS/TPS.C
+++ b/src/OF_EXT/RBFFunctions/TPS/TPS.C
@@ -78,6 +78,7 @@ Foam::scalarField Foam::TPS::weights
             RBF[i] = 0.0;
         }
     }
+
     return RBF;
 }
 
diff --git a/src/OF_EXT/RBFInterpolation.C b/src/OF_EXT/RBFInterpolation.C
old mode 100755
new mode 100644
index 1ab36937c..7aa6ff176
--- a/src/OF_EXT/RBFInterpolation.C
+++ b/src/OF_EXT/RBFInterpolation.C
@@ -42,7 +42,7 @@ const Foam::scalarSquareMatrix& Foam::RBFInterpolation::B() const
     return *BPtr_;
 }
 
-Foam::SquareMatrix<double> Foam::EigenInvert(Foam::SquareMatrix<double>& A)
+Foam::SquareMatrix<double> Foam::EigenInvert(Foam::SquareMatrix<double> & A)
 {
     Foam::SquareMatrix<double> invMatrix = A;
     Eigen::MatrixXd Aeig(A.n(), A.n());
diff --git a/src/OF_EXT/RBFInterpolation.H b/src/OF_EXT/RBFInterpolation.H
old mode 100755
new mode 100644
index 67d9d0c2f..a08a168cc
--- a/src/OF_EXT/RBFInterpolation.H
+++ b/src/OF_EXT/RBFInterpolation.H
@@ -77,7 +77,7 @@ namespace Foam
                         Class RBFInterpolation Declaration
 \*---------------------------------------------------------------------------*/
 
-SquareMatrix<double> EigenInvert(SquareMatrix<double>& A);
+SquareMatrix<double> EigenInvert(SquareMatrix<double> & A);
 
 class RBFInterpolation
 {
@@ -161,7 +161,7 @@ class RBFInterpolation
 
         //- Interpolate
         template<class Type>
-        tmp<Field<Type>> interpolate(const Field<Type>& ctrlField) const;
+        tmp<Field<Type>> interpolate(const Field<Type> & ctrlField) const;
 
         //- Move points
         void movePoints();
diff --git a/src/OF_EXT/RBFInterpolationTemplates.C b/src/OF_EXT/RBFInterpolationTemplates.C
old mode 100755
new mode 100644
index e95d64928..2e72aaac5
--- a/src/OF_EXT/RBFInterpolationTemplates.C
+++ b/src/OF_EXT/RBFInterpolationTemplates.C
@@ -36,9 +36,9 @@ Author
 
 template<class Type>
 Foam::tmp<Foam::Field<Type>> Foam::RBFInterpolation::interpolate
-                          (
-                              const Field<Type>& ctrlField
-                          ) const
+(
+    const Field<Type> & ctrlField
+) const
 {
     // HJ and FB (05 Jan 2009)
     // Collect the values from ALL control points to all CPUs
@@ -57,10 +57,10 @@ Foam::tmp<Foam::Field<Type>> Foam::RBFInterpolation::interpolate
     }
 
     tmp<Field<Type>> tresult
-                  (
-                      new Field<Type>(dataPoints_.size(), pTraits<Type>::zero)
-                  );
-    Field<Type>& result = const_cast<Field<Type>&>(tresult());
+    (
+        new Field<Type>(dataPoints_.size(), pTraits<Type>::zero)
+    );
+    Field<Type> & result = const_cast<Field<Type>&>(tresult());
     // FB 21-12-2008
     // 1) Calculate alpha and beta coefficients using the Inverse
     // 2) Calculate displacements of internal nodes using RBF values,
@@ -140,9 +140,10 @@ Foam::tmp<Foam::Field<Type>> Foam::RBFInterpolation::interpolate
                 w = 1 - sqr(t) * (3 - 2 * t);
             }
 
-            result[flPoint] = w * result[flPoint];
+            result[flPoint] = w* result[flPoint];
         }
     }
+
     return tresult;
 }
 
diff --git a/src/OF_EXT/RBFMotionSolver.C b/src/OF_EXT/RBFMotionSolver.C
old mode 100755
new mode 100644
index 2dfad5233..ad26506a5
--- a/src/OF_EXT/RBFMotionSolver.C
+++ b/src/OF_EXT/RBFMotionSolver.C
@@ -70,6 +70,7 @@ void Foam::RBFMotionSolver::makeControlIDs()
             nMovingPoints++;
         }
     }
+
     // Mark moving points and select control points from moving patches
     movingIDs_.setSize(nMovingPoints);
     Info << "Total points on moving boundaries: " << nMovingPoints << endl;
@@ -89,6 +90,7 @@ void Foam::RBFMotionSolver::makeControlIDs()
             nMovingPoints++;
         }
     }
+
     movingIDs_.setSize(nMovingPoints);
     // Actual location of moving points will be set later on request
     // HJ, 19/Dec/2008
@@ -116,6 +118,7 @@ void Foam::RBFMotionSolver::makeControlIDs()
             nStaticPoints++;
         }
     }
+
     Info << "Total points on static boundaries: " << nStaticPoints << endl;
     staticIDs_.setSize(nStaticPoints);
     // Re-use counter
@@ -129,6 +132,7 @@ void Foam::RBFMotionSolver::makeControlIDs()
             nStaticPoints++;
         }
     }
+
     staticIDs_.setSize(nStaticPoints);
     // Control IDs also potentially include points on static patches
     // HJ, 24/Mar/2011
@@ -156,6 +160,7 @@ void Foam::RBFMotionSolver::makeControlIDs()
             nControlPoints++;
         }
     }
+
     Info << "Selected " << nControlPoints
          << " control points on moving boundaries" << endl;
 
@@ -183,6 +188,7 @@ void Foam::RBFMotionSolver::makeControlIDs()
                 nControlPoints++;
             }
         }
+
         Info << "Selected " << nControlPoints
              << " total control points" << endl;
     }
@@ -196,6 +202,7 @@ void Foam::RBFMotionSolver::makeControlIDs()
     {
         controlPoints_[i] = points[controlIDs_[i]];
     }
+
     // Pick up all internal points
     internalIDs_.setSize(points.size());
     internalPoints_.setSize(points.size());
@@ -211,6 +218,7 @@ void Foam::RBFMotionSolver::makeControlIDs()
             nInternalPoints++;
         }
     }
+
     Info << "Number of internal points: " << nInternalPoints << endl;
     // Resize the lists
     internalIDs_.setSize(nInternalPoints);
@@ -298,6 +306,7 @@ void Foam::RBFMotionSolver::setMotion(const vectorField& m)
         {
             controlPoints_[i] = points[controlIDs_[i]];
         }
+
         // Re-calculate interpolation
         interpolation_.movePoints();
     }
@@ -331,11 +340,13 @@ Foam::tmp<Foam::pointField> Foam::RBFMotionSolver::curPoints() const
     {
         curPoints[movingIDs_[i]] = motion_[i];
     }
+
     // 2. Insert zero motion of static points
     forAll (staticIDs_, i)
     {
         curPoints[staticIDs_[i]] = vector::zero;
     }
+
     // Set motion of control
     vectorField motionOfControl(controlIDs_.size());
     // 2. Capture positions of control points
@@ -343,6 +354,7 @@ Foam::tmp<Foam::pointField> Foam::RBFMotionSolver::curPoints() const
     {
         motionOfControl[i] = curPoints[controlIDs_[i]];
     }
+
     // Call interpolation
     vectorField interpolatedMotion =
         interpolation_.interpolate(motionOfControl).ref();
@@ -351,6 +363,7 @@ Foam::tmp<Foam::pointField> Foam::RBFMotionSolver::curPoints() const
     {
         curPoints[internalIDs_[i]] = interpolatedMotion[i];
     }
+
     // 4. Add old point positions
     curPoints += mesh().points();
     twoDCorrectPoints(const_cast<pointField&>(tcurPoints()));
diff --git a/src/OF_EXT/fvPatchFields/basic/turbulentHeatFluxTemperature/turbulentHeatFluxTemperatureFvPatchScalarField.C b/src/OF_EXT/fvPatchFields/basic/turbulentHeatFluxTemperature/turbulentHeatFluxTemperatureFvPatchScalarField.C
old mode 100755
new mode 100644
index 32c2f60cd..6bee54473
--- a/src/OF_EXT/fvPatchFields/basic/turbulentHeatFluxTemperature/turbulentHeatFluxTemperatureFvPatchScalarField.C
+++ b/src/OF_EXT/fvPatchFields/basic/turbulentHeatFluxTemperature/turbulentHeatFluxTemperatureFvPatchScalarField.C
@@ -70,7 +70,7 @@ turbulentHeatFluxTemperatureFvPatchScalarField::
 turbulentHeatFluxTemperatureFvPatchScalarField
 (
     const fvPatch& p,
-    const DimensionedField<scalar, volMesh>& iF
+    const DimensionedField<scalar, volMesh> & iF
 )
     :
     fixedGradientFvPatchScalarField(p, iF),
@@ -85,7 +85,7 @@ turbulentHeatFluxTemperatureFvPatchScalarField
 (
     const turbulentHeatFluxTemperatureFvPatchScalarField& ptf,
     const fvPatch& p,
-    const DimensionedField<scalar, volMesh>& iF,
+    const DimensionedField<scalar, volMesh> & iF,
     const fvPatchFieldMapper& mapper
 )
     :
@@ -100,7 +100,7 @@ turbulentHeatFluxTemperatureFvPatchScalarField::
 turbulentHeatFluxTemperatureFvPatchScalarField
 (
     const fvPatch& p,
-    const DimensionedField<scalar, volMesh>& iF,
+    const DimensionedField<scalar, volMesh> & iF,
     const dictionary& dict
 )
     :
@@ -139,7 +139,7 @@ turbulentHeatFluxTemperatureFvPatchScalarField::
 turbulentHeatFluxTemperatureFvPatchScalarField
 (
     const turbulentHeatFluxTemperatureFvPatchScalarField& thftpsf,
-    const DimensionedField<scalar, volMesh>& iF
+    const DimensionedField<scalar, volMesh> & iF
 )
     :
     fixedGradientFvPatchScalarField(thftpsf, iF),
@@ -196,13 +196,13 @@ void turbulentHeatFluxTemperatureFvPatchScalarField::updateCoeffs()
         case hsPower:
         {
             const scalar Ap = gSum(patch().magSf());
-            gradient() = q_ / (Ap * rhoCp0 * alphaEffp);
+            gradient() = q_ / (Ap* rhoCp0* alphaEffp);
             break;
         }
 
         case hsFlux:
         {
-            gradient() = q_ / (rhoCp0 * alphaEffp);
+            gradient() = q_ / (rhoCp0* alphaEffp);
             break;
         }
 
@@ -229,7 +229,7 @@ void turbulentHeatFluxTemperatureFvPatchScalarField::write(Ostream& os) const
 {
     fixedGradientFvPatchScalarField::write(os);
     os.writeKeyword("heatSource") << heatSourceTypeNames_[heatSource_]
-                                  << token::END_STATEMENT << nl;
+      << token::END_STATEMENT << nl;
     q_.writeEntry("q", os);
     os.writeKeyword("alphaEff") << alphaEffName_ << token::END_STATEMENT << nl;
     writeEntry("value", os);
diff --git a/src/OF_EXT/fvPatchFields/basic/turbulentHeatFluxTemperature/turbulentHeatFluxTemperatureFvPatchScalarField.H b/src/OF_EXT/fvPatchFields/basic/turbulentHeatFluxTemperature/turbulentHeatFluxTemperatureFvPatchScalarField.H
old mode 100755
new mode 100644
index 7169cacfd..da7ba1d9a
--- a/src/OF_EXT/fvPatchFields/basic/turbulentHeatFluxTemperature/turbulentHeatFluxTemperatureFvPatchScalarField.H
+++ b/src/OF_EXT/fvPatchFields/basic/turbulentHeatFluxTemperature/turbulentHeatFluxTemperatureFvPatchScalarField.H
@@ -114,14 +114,14 @@ class turbulentHeatFluxTemperatureFvPatchScalarField
         turbulentHeatFluxTemperatureFvPatchScalarField
         (
             const fvPatch&,
-            const DimensionedField<scalar, volMesh>&
+            const DimensionedField<scalar, volMesh> &
         );
 
         //- Construct from patch, internal field and dictionary
         turbulentHeatFluxTemperatureFvPatchScalarField
         (
             const fvPatch&,
-            const DimensionedField<scalar, volMesh>&,
+            const DimensionedField<scalar, volMesh> &,
             const dictionary&
         );
 
@@ -132,7 +132,7 @@ class turbulentHeatFluxTemperatureFvPatchScalarField
         (
             const turbulentHeatFluxTemperatureFvPatchScalarField&,
             const fvPatch&,
-            const DimensionedField<scalar, volMesh>&,
+            const DimensionedField<scalar, volMesh> &,
             const fvPatchFieldMapper&
         );
 
@@ -147,7 +147,7 @@ class turbulentHeatFluxTemperatureFvPatchScalarField
         {
             return tmp<fvPatchScalarField>
                    (
-                       new turbulentHeatFluxTemperatureFvPatchScalarField(*this)
+                       new turbulentHeatFluxTemperatureFvPatchScalarField( * this)
                    );
         }
 
@@ -155,20 +155,20 @@ class turbulentHeatFluxTemperatureFvPatchScalarField
         turbulentHeatFluxTemperatureFvPatchScalarField
         (
             const turbulentHeatFluxTemperatureFvPatchScalarField&,
-            const DimensionedField<scalar, volMesh>&
+            const DimensionedField<scalar, volMesh> &
         );
 
         //- Construct and return a clone setting internal field reference
         virtual tmp<fvPatchScalarField> clone
         (
-            const DimensionedField<scalar, volMesh>& iF
+            const DimensionedField<scalar, volMesh> & iF
         ) const
         {
             return tmp<fvPatchScalarField>
                    (
                        new turbulentHeatFluxTemperatureFvPatchScalarField
                        (
-                           *this,
+                           * this,
                            iF
                        )
                    );
diff --git a/tutorials/CFD/02thermalBlock/02thermalBlock.C b/tutorials/CFD/02thermalBlock/02thermalBlock.C
index 0fc892286..0d5cb9303 100644
--- a/tutorials/CFD/02thermalBlock/02thermalBlock.C
+++ b/tutorials/CFD/02thermalBlock/02thermalBlock.C
@@ -52,6 +52,7 @@ class tutorial02: public laplacianProblem
             nu(_nu()),
             S(_S())
         {}
+
         //! [tutorial02]
         /// Temperature field
         volScalarField& T;
@@ -329,6 +330,7 @@ void online_stage(tutorial02& example, tutorial02& FOM_test)
     Eigen::MatrixXd error = ITHACAutilities::errorL2Rel(FOM_test.Tfield,
                             reduced.Trec);
 }
+
 //--------
 /// \dir 02thermalBlock Folder of the turorial 2
 /// \file
diff --git a/tutorials/CFD/04unsteadyNS/04unsteadyNS.C b/tutorials/CFD/04unsteadyNS/04unsteadyNS.C
old mode 100755
new mode 100644
index 4494743e3..f4b354588
--- a/tutorials/CFD/04unsteadyNS/04unsteadyNS.C
+++ b/tutorials/CFD/04unsteadyNS/04unsteadyNS.C
@@ -38,36 +38,36 @@ SourceFiles
 
 class tutorial04 : public unsteadyNS
 {
-public:
-    explicit tutorial04(int argc, char* argv[])
-        : unsteadyNS(argc, argv), U(_U()), p(_p()) {}
+    public:
+        explicit tutorial04(int argc, char* argv[])
+            : unsteadyNS(argc, argv), U(_U()), p(_p()) {}
 
-    // Fields To Perform
-    volVectorField& U;
-    volScalarField& p;
+        // Fields To Perform
+        volVectorField& U;
+        volScalarField& p;
 
-    void offlineSolve()
-    {
-        Vector<double> inl(1, 0, 0);
-        List<scalar> mu_now(1);
-        label BCind = 0;
-
-        if (offline)
-        {
-            ITHACAstream::read_fields(Ufield, U, "./ITHACAoutput/Offline/");
-            ITHACAstream::read_fields(Pfield, p, "./ITHACAoutput/Offline/");
-        }
-        else
+        void offlineSolve()
         {
-            for (label i = 0; i < mu.cols(); i++)
+            Vector<double> inl(1, 0, 0);
+            List<scalar> mu_now(1);
+            label BCind = 0;
+
+            if (offline)
+            {
+                ITHACAstream::read_fields(Ufield, U, "./ITHACAoutput/Offline/");
+                ITHACAstream::read_fields(Pfield, p, "./ITHACAoutput/Offline/");
+            }
+            else
             {
-                mu_now[0] = mu(0, i);
-                assignIF(U, inl);
-                change_viscosity(mu(0, i));
-                truthSolve(mu_now);
+                for (label i = 0; i < mu.cols(); i++)
+                {
+                    mu_now[0] = mu(0, i);
+                    assignIF(U, inl);
+                    change_viscosity(mu(0, i));
+                    truthSolve(mu_now);
+                }
             }
         }
-    }
 };
 
 /*---------------------------------------------------------------------------*\
@@ -77,16 +77,15 @@ int main(int argc, char* argv[])
 {
     // Construct the tutorial04 object
     tutorial04 example(argc, argv);
-
     // Read parameters from ITHACAdict file
-    ITHACAparameters* para = ITHACAparameters::getInstance(example._mesh(), example._runTime());
+    ITHACAparameters* para = ITHACAparameters::getInstance(example._mesh(),
+                             example._runTime());
     int NmodesUout = para->ITHACAdict->lookupOrDefault<int>("NmodesUout", 15);
     int NmodesPout = para->ITHACAdict->lookupOrDefault<int>("NmodesPout", 15);
     int NmodesSUPout = para->ITHACAdict->lookupOrDefault<int>("NmodesSUPout", 15);
     int NmodesUproj = para->ITHACAdict->lookupOrDefault<int>("NmodesUproj", 10);
     int NmodesPproj = para->ITHACAdict->lookupOrDefault<int>("NmodesPproj", 10);
     int NmodesSUPproj = para->ITHACAdict->lookupOrDefault<int>("NmodesSUPproj", 10);
-
     // Set the number of parameters
     example.Pnumber = 1;
     // Set samples
@@ -120,20 +119,26 @@ int main(int argc, char* argv[])
         // Create homogeneous basis functions for velocity
         example.computeLift(example.Ufield, example.liftfield, example.Uomfield);
         // Perform a POD decomposition for velocity and pressure
-        ITHACAPOD::getModes(example.Uomfield, example.Umodes, example._U().name(), example.podex, 0, 0, NmodesUout);
-        ITHACAPOD::getModes(example.Pfield, example.Pmodes, example._p().name(), example.podex, 0, 0, NmodesPout);
+        ITHACAPOD::getModes(example.Uomfield, example.Umodes, example._U().name(),
+                            example.podex, 0, 0, NmodesUout);
+        ITHACAPOD::getModes(example.Pfield, example.Pmodes, example._p().name(),
+                            example.podex, 0, 0, NmodesPout);
     }
     else
     {
         // Perform a POD decomposition for velocity and pressure without lifting function
-        ITHACAPOD::getModes(example.Ufield, example.Umodes, example._U().name(), example.podex, 0, 0, NmodesUout);
-        ITHACAPOD::getModes(example.Pfield, example.Pmodes, example._p().name(), example.podex, 0, 0, NmodesPout);
+        ITHACAPOD::getModes(example.Ufield, example.Umodes, example._U().name(),
+                            example.podex, 0, 0, NmodesUout);
+        ITHACAPOD::getModes(example.Pfield, example.Pmodes, example._p().name(),
+                            example.podex, 0, 0, NmodesPout);
     }
+
     // Check the method and perform the appropriate projection
     if (example.method == "supremizer")
     {
-        example.solvesupremizer(); 
-        ITHACAPOD::getModes(example.supfield, example.supmodes, example._U().name(), example.podex, example.supex, 1, NmodesSUPout);
+        example.solvesupremizer();
+        ITHACAPOD::getModes(example.supfield, example.supmodes, example._U().name(),
+                            example.podex, example.supex, 1, NmodesSUPout);
         example.projectSUP("./Matrices", NmodesUproj, NmodesPproj, NmodesSUPproj);
     }
     else if (example.method == "PPE")
@@ -142,7 +147,6 @@ int main(int argc, char* argv[])
     }
 
     reducedUnsteadyNS reduced(example);
-
     // Set values of the reduced stuff
     reduced.nu = 0.005;
     reduced.tstart = 60;
@@ -150,7 +154,6 @@ int main(int argc, char* argv[])
     reduced.dt = 0.005;
     reduced.storeEvery = 0.005;
     reduced.exportEvery = 0.1;
-
     // Set the online velocity
     Eigen::MatrixXd vel_now(1, 1);
     vel_now(0, 0) = 1;
@@ -173,8 +176,8 @@ int main(int argc, char* argv[])
     }
 
     // Reconstruct the solution and export it
-    reduced.reconstruct(true, "./ITHACAoutput/Reconstruction" + example.method + "/");
-
+    reduced.reconstruct(true,
+                        "./ITHACAoutput/Reconstruction" + example.method + "/");
     exit(0);
 }
 
diff --git a/tutorials/CFD/06POD_RBF/06POD_RBF.C b/tutorials/CFD/06POD_RBF/06POD_RBF.C
index 9a60eb03b..38aedfa94 100644
--- a/tutorials/CFD/06POD_RBF/06POD_RBF.C
+++ b/tutorials/CFD/06POD_RBF/06POD_RBF.C
@@ -62,6 +62,7 @@ class tutorial06 : public SteadyNSTurb
             p(_p()),
             nut(_nut())
         {}
+
         //! [tutorial06]
         // Relevant Fields
         volVectorField& U;
@@ -110,6 +111,7 @@ class tutorial06 : public SteadyNSTurb
                 }
             }
         }
+
         /// Perform an Offline solve for a special set of parameter samples called par
         void offlineSolve(Eigen::MatrixXd par, fileName folder)
         {
@@ -126,6 +128,7 @@ class tutorial06 : public SteadyNSTurb
                 truthSolve(folder);
             }
         }
+
         void truthSolve(fileName folder)
         {
             Time& runTime = _runTime();
diff --git a/tutorials/CFD/06POD_RBF/NLsolveSteadyNSTurb.H b/tutorials/CFD/06POD_RBF/NLsolveSteadyNSTurb.H
index 09a7cc1d8..4adb90294 100644
--- a/tutorials/CFD/06POD_RBF/NLsolveSteadyNSTurb.H
+++ b/tutorials/CFD/06POD_RBF/NLsolveSteadyNSTurb.H
@@ -64,6 +64,7 @@ while (simple.loop() && residual > tolerance && csolve < maxIter )
         Info << "\nResidual: " << residual << endl << endl;
         //Info << "Residual U: " << solve(UEqn() == -fvc::grad(p)).initialResidual() << endl;
     }
+
     laminarTransport.correct();
     turbulence->correct();
     csolve = csolve + 1;
diff --git a/tutorials/CFD/06POD_RBF/UEqn.H b/tutorials/CFD/06POD_RBF/UEqn.H
old mode 100755
new mode 100644
index 1d91429a0..7117de308
--- a/tutorials/CFD/06POD_RBF/UEqn.H
+++ b/tutorials/CFD/06POD_RBF/UEqn.H
@@ -33,7 +33,7 @@ tmp<fvVectorMatrix> tUEqn
     + turbulence->divDevReff(U)
     ==
     fvOptions(U)
-    );
+);
 fvVectorMatrix& UEqn = tUEqn.ref();
 
 UEqn.relax();
diff --git a/tutorials/CFD/06POD_RBF/pEqn.H b/tutorials/CFD/06POD_RBF/pEqn.H
old mode 100755
new mode 100644
index 5c62d90b5..104e0c227
--- a/tutorials/CFD/06POD_RBF/pEqn.H
+++ b/tutorials/CFD/06POD_RBF/pEqn.H
@@ -24,7 +24,7 @@
 \*---------------------------------------------------------------------------*/
 {
     volScalarField rAU(1.0 / UEqn.A());
-    volVectorField HbyA(constrainHbyA(rAU * UEqn.H(), U, p));
+    volVectorField HbyA(constrainHbyA(rAU* UEqn.H(), U, p));
     surfaceScalarField phiHbyA("phiHbyA", fvc::flux(HbyA));
     MRF.makeRelative(phiHbyA);
     adjustPhi(phiHbyA, U, p);
diff --git a/tutorials/CFD/08DEIM/08DEIM.C b/tutorials/CFD/08DEIM/08DEIM.C
index 3ea6fbd4d..791d06819 100644
--- a/tutorials/CFD/08DEIM/08DEIM.C
+++ b/tutorials/CFD/08DEIM/08DEIM.C
@@ -38,7 +38,7 @@ SourceFiles
 #include "ITHACAPOD.H"
 #include "hyperReduction.templates.H"
 #include <chrono>
-class DEIM_function : public HyperReduction<PtrList<volScalarField>&>
+class DEIM_function : public HyperReduction<PtrList<volScalarField> & >
 {
     public:
         using HyperReduction::HyperReduction;
@@ -55,6 +55,7 @@ class DEIM_function : public HyperReduction<PtrList<volScalarField>&>
 
             return S;
         }
+
         Eigen::VectorXd onlineCoeffs(Eigen::MatrixXd mu)
         {
             theta.resize(nodePoints().size());
@@ -68,8 +69,8 @@ class DEIM_function : public HyperReduction<PtrList<volScalarField>&>
 
             return theta;
         }
-        
-        Eigen::VectorXd theta; 
+
+        Eigen::VectorXd theta;
         PtrList<volScalarField> fields;
         autoPtr<volScalarField> subField;
 };
@@ -111,8 +112,8 @@ int main(int argc, char* argv[])
     );
     // Parameters used to train the non-linear function
     Eigen::MatrixXd pars = ITHACAutilities::rand(100, 2, -0.5, 0.5);
-    
-    // To compare with the same parameters, save data and then load it 
+
+    // To compare with the same parameters, save data and then load it
     // cnpy::load(pars, "./random100.npy");
     // cnpy::save(pars, "./random100.npy");
 
@@ -125,36 +126,32 @@ int main(int argc, char* argv[])
     }
 
     Eigen::MatrixXd snapshotsModes;
-
     // To use the DEIMmodes method from ITHACAPOD :
-    Eigen::VectorXd normalizingWeights = ITHACAutilities::getMassMatrixFV(Sp[0]).array();
-    PtrList<volScalarField> modes = ITHACAPOD::DEIMmodes(Sp, NDEIM, "GappyDEIM", S.name());
+    Eigen::VectorXd normalizingWeights = ITHACAutilities::getMassMatrixFV(
+            Sp[0]).array();
+    PtrList<volScalarField> modes = ITHACAPOD::DEIMmodes(Sp, NDEIM, "GappyDEIM",
+                                    S.name());
     snapshotsModes = Foam2Eigen::PtrList2Eigen(modes);
-
-    // To use the SVD modes from the HyperReduction class : 
+    // To use the SVD modes from the HyperReduction class :
     // Eigen::VectorXd normalizingWeights;
-    // c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights); 
-
+    // c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights);
     // Create DEIM object with given number of basis functions
     Eigen::VectorXi initSeeds(0);
     DEIM_function c(NDEIM, NDEIM, initSeeds, "DEIM", Sp);
-
-    // Compute the DEIM 
+    // Compute the DEIM
     c.offlineGappyDEIM(snapshotsModes, normalizingWeights);
-    // To access the same folder hierarchy as before : 
+    // To access the same folder hierarchy as before :
     // c.problemName = "Gaussian_function";
     // c.offlineGappyDEIM(snapshotsModes, normalizingWeights, "ITHACAoutput/DEIM/"+c.problemName);
-                                                           
     // Generate the submeshes with the depth of the layer
-    c.generateSubmesh(2, mesh); 
+    c.generateSubmesh(2, mesh);
     c.subField = c.interpolateField<volScalarField>(Sp[0]);
-
     // Define a new online parameter
     Eigen::MatrixXd par_new(2, 1);
     par_new(0, 0) = 0;
     par_new(1, 0) = 0;
     // Online evaluation of the non linear function
-    Eigen::VectorXd aprfield = c.MatrixOnline * c.onlineCoeffs(par_new);
+    Eigen::VectorXd aprfield = c.MatrixOnline* c.onlineCoeffs(par_new);
     // Transform to an OpenFOAM field and export
     volScalarField S2("S_online", Foam2Eigen::Eigen2field(S, aprfield));
     ITHACAstream::exportSolution(S2, name(1), "./ITHACAoutput/Online/");
@@ -226,12 +223,12 @@ int main(int argc, char* argv[])
 /// \skip for
 /// \until }
 ///
-/// Compute the "DEIM" modes using the ITHACAPOD class 
+/// Compute the "DEIM" modes using the ITHACAPOD class
 /// \skip normalizingWeights
 /// \until snapshotsModes
 ///
-/// Construction of the HyperReduction object passing the maximum number of "DEIM" modes NDEIM, the initSeeds (none in this tutorial), the name used to store the output "DEIM" and the list of snapshots Sp. The constructor is taking the number of modes and the number of point to compute, for the "DEIM" method these numbers are equal. 
-/// \skip initSeeds 
+/// Construction of the HyperReduction object passing the maximum number of "DEIM" modes NDEIM, the initSeeds (none in this tutorial), the name used to store the output "DEIM" and the list of snapshots Sp. The constructor is taking the number of modes and the number of point to compute, for the "DEIM" method these numbers are equal.
+/// \skip initSeeds
 /// \until DEIM_function
 ///
 /// Compute the "DEIM" method HyperReduction::offlineGappyDEIM passing the "DEIM" modes and the normalizingWeights
diff --git a/tutorials/CFD/09DEIM_ROM/09DEIM_ROM.C b/tutorials/CFD/09DEIM_ROM/09DEIM_ROM.C
index b45a8de18..19118de8d 100644
--- a/tutorials/CFD/09DEIM_ROM/09DEIM_ROM.C
+++ b/tutorials/CFD/09DEIM_ROM/09DEIM_ROM.C
@@ -245,7 +245,7 @@ class DEIMLaplacian: public laplacianProblem
                 Eigen::MatrixXd A = EigenFunctions::MVproduct(ReducedMatricesA, thetaonA);
                 Eigen::VectorXd B = EigenFunctions::MVproduct(ReducedVectorsB, thetaonB);
                 Eigen::VectorXd x = A.fullPivLu().solve(B);
-                Eigen::VectorXd full = ModesTEig * x;
+                Eigen::VectorXd full = ModesTEig* x;
                 t2 = std::chrono::high_resolution_clock::now();
                 time_span = std::chrono::duration_cast<std::chrono::duration<double>>(t2 - t1);
                 time_rom += time_span.count();
diff --git a/tutorials/CFD/11UnsteadyBBOpen/11UnsteadyBBOpen.C b/tutorials/CFD/11UnsteadyBBOpen/11UnsteadyBBOpen.C
index 0484db59c..cd74385cf 100644
--- a/tutorials/CFD/11UnsteadyBBOpen/11UnsteadyBBOpen.C
+++ b/tutorials/CFD/11UnsteadyBBOpen/11UnsteadyBBOpen.C
@@ -264,8 +264,8 @@ int main(int argc, char* argv[])
         example.solvesupremizer("modes");
     }
 
-        // Create a list with number of modes for which the projection needs to be performed
-        Eigen::MatrixXd List_of_modes(NmodesOut - 5, 1);
+    // Create a list with number of modes for which the projection needs to be performed
+    Eigen::MatrixXd List_of_modes(NmodesOut - 5, 1);
 
     for (int i = 0; i < List_of_modes.rows(); i++)
     {
@@ -380,8 +380,7 @@ int main(int argc, char* argv[])
         temp_now_BC(1, 0) = par_on_BC(k, 1);
         temp_now_BC(2, 0) = par_on_BC(k, 2);
 
-
-            if (stabilization == "supremizer")
+        if (stabilization == "supremizer")
         {
             reduced.solveOnline_sup(temp_now_BC, vel_now_BC, k, par_on_BC.rows());
             reduced.reconstruct_sup("./ITHACAoutput/ReconstructionSUP/", 5);
diff --git a/tutorials/CFD/15MSR_cavity/15MSR_cavity.C b/tutorials/CFD/15MSR_cavity/15MSR_cavity.C
old mode 100755
new mode 100644
index e03565025..6d997002e
--- a/tutorials/CFD/15MSR_cavity/15MSR_cavity.C
+++ b/tutorials/CFD/15MSR_cavity/15MSR_cavity.C
@@ -101,14 +101,14 @@ class msr : public usmsrProblem
                     _nu().value() = mu(0, i);
                     change_viscosity(mu(0, i));
                     _betaTot().value() = mu(1, i);
-                    _beta1().value() = r1 * mu(1, i);
-                    _beta2().value() = r2 * mu(1, i);
-                    _beta3().value() = r3 * mu(1, i);
-                    _beta4().value() = r4 * mu(1, i);
-                    _beta5().value() = r5 * mu(1, i);
-                    _beta6().value() = r6 * mu(1, i);
-                    _beta7().value() = r7 * mu(1, i);
-                    _beta8().value() = r8 * mu(1, i);
+                    _beta1().value() = r1* mu(1, i);
+                    _beta2().value() = r2* mu(1, i);
+                    _beta3().value() = r3* mu(1, i);
+                    _beta4().value() = r4* mu(1, i);
+                    _beta5().value() = r5* mu(1, i);
+                    _beta6().value() = r6* mu(1, i);
+                    _beta7().value() = r7* mu(1, i);
+                    _beta8().value() = r8* mu(1, i);
                     _decLam3().value() = mu(2, i);
                     mu_now[0] = mu(0, i);
                     mu_now[1] = mu(1, i);
@@ -148,6 +148,7 @@ class Ploct: public Ptot_time
 
         volScalarField& powerDens;
 };
+
 class Plocal: public Ptot
 {
     public:
@@ -159,6 +160,7 @@ class Plocal: public Ptot
 
         volScalarField& powerDens;
 };
+
 class Tmloct: public Tm_time
 {
     public:
@@ -289,14 +291,14 @@ int main(int argc, char* argv[])
     Eigen::VectorXd mu_on(3);
     ridotto.nu = mu_f(0, central);
     ridotto.btot = mu_f(1, central);
-    ridotto.b1 = prova.r1 * ridotto.btot;
-    ridotto.b2 = prova.r2 * ridotto.btot;
-    ridotto.b3 = prova.r3 * ridotto.btot;
-    ridotto.b4 = prova.r4 * ridotto.btot;
-    ridotto.b5 = prova.r5 * ridotto.btot;
-    ridotto.b6 = prova.r6 * ridotto.btot;
-    ridotto.b7 = prova.r7 * ridotto.btot;
-    ridotto.b8 = prova.r8 * ridotto.btot;
+    ridotto.b1 = prova.r1* ridotto.btot;
+    ridotto.b2 = prova.r2* ridotto.btot;
+    ridotto.b3 = prova.r3* ridotto.btot;
+    ridotto.b4 = prova.r4* ridotto.btot;
+    ridotto.b5 = prova.r5* ridotto.btot;
+    ridotto.b6 = prova.r6* ridotto.btot;
+    ridotto.b7 = prova.r7* ridotto.btot;
+    ridotto.b8 = prova.r8* ridotto.btot;
     ridotto.dl3 = mu_f(2, central);
     // index corresponding at central solution
     int ref_start = 465;
@@ -384,14 +386,14 @@ int main(int argc, char* argv[])
     {
         ridotto.nu = mu_f(0, i);
         ridotto.btot = mu_f(1, i);
-        ridotto.b1 = prova.r1 * ridotto.btot;
-        ridotto.b2 = prova.r2 * ridotto.btot;
-        ridotto.b3 = prova.r3 * ridotto.btot;
-        ridotto.b4 = prova.r4 * ridotto.btot;
-        ridotto.b5 = prova.r5 * ridotto.btot;
-        ridotto.b6 = prova.r6 * ridotto.btot;
-        ridotto.b7 = prova.r7 * ridotto.btot;
-        ridotto.b8 = prova.r8 * ridotto.btot;
+        ridotto.b1 = prova.r1* ridotto.btot;
+        ridotto.b2 = prova.r2* ridotto.btot;
+        ridotto.b3 = prova.r3* ridotto.btot;
+        ridotto.b4 = prova.r4* ridotto.btot;
+        ridotto.b5 = prova.r5* ridotto.btot;
+        ridotto.b6 = prova.r6* ridotto.btot;
+        ridotto.b7 = prova.r7* ridotto.btot;
+        ridotto.b8 = prova.r8* ridotto.btot;
         ridotto.dl3 = mu_f(2, i);
         mu_on(0) = ridotto.nu;
         mu_on(1) = ridotto.btot;
@@ -453,14 +455,14 @@ int main(int argc, char* argv[])
     {
         ridotto.nu = analisi.MatX(j, 0);
         ridotto.btot = analisi.MatX(j, 1);
-        ridotto.b1 = prova.r1 * ridotto.btot;
-        ridotto.b2 = prova.r2 * ridotto.btot;
-        ridotto.b3 = prova.r3 * ridotto.btot;
-        ridotto.b4 = prova.r4 * ridotto.btot;
-        ridotto.b5 = prova.r5 * ridotto.btot;
-        ridotto.b6 = prova.r6 * ridotto.btot;
-        ridotto.b7 = prova.r7 * ridotto.btot;
-        ridotto.b8 = prova.r8 * ridotto.btot;
+        ridotto.b1 = prova.r1* ridotto.btot;
+        ridotto.b2 = prova.r2* ridotto.btot;
+        ridotto.b3 = prova.r3* ridotto.btot;
+        ridotto.b4 = prova.r4* ridotto.btot;
+        ridotto.b5 = prova.r5* ridotto.btot;
+        ridotto.b6 = prova.r6* ridotto.btot;
+        ridotto.b7 = prova.r7* ridotto.btot;
+        ridotto.b8 = prova.r8* ridotto.btot;
         ridotto.dl3 = analisi.MatX(j, 2);
         mu_on(0) = ridotto.nu;
         mu_on(1) = ridotto.btot;
@@ -486,7 +488,7 @@ int main(int argc, char* argv[])
     TmediaSA.buildMO(folder);
     PtotSA.buildMO(folder);
     //assign FofM to LRSensitivity object, first figure of merit considered is the average temperature
-    analisi.M = autoPtr<FofM>(&TmediaSA);
+    analisi.M = autoPtr<FofM>( & TmediaSA);
     //load the model output in the LRSensitivity object
     analisi.load_output();
     //compute output statistics
@@ -519,7 +521,7 @@ int main(int argc, char* argv[])
     coeffsT.row(3) = analisi.betas;
     ITHACAstream::exportMatrix(coeffsT, "coeffsT", "eigen", "./ITHACAoutput");
     //assign FofM object to LRSensitivity object
-    analisi.M = autoPtr<FofM>(&PtotSA);
+    analisi.M = autoPtr<FofM>( & PtotSA);
     //load the model output in the LRSensitivity object, repeat all the previous step
     // for the total power
     analisi.load_output();
diff --git a/tutorials/CFD/16MSR_FOMSA/16MSR_FOMSA.C b/tutorials/CFD/16MSR_FOMSA/16MSR_FOMSA.C
old mode 100755
new mode 100644
index 4f3d32d90..f6bdbf1db
--- a/tutorials/CFD/16MSR_FOMSA/16MSR_FOMSA.C
+++ b/tutorials/CFD/16MSR_FOMSA/16MSR_FOMSA.C
@@ -104,14 +104,14 @@ class msr : public usmsrProblem
                     _nu().value() = mu(0, i);
                     change_viscosity(mu(0, i));
                     _betaTot().value() = mu(1, i);
-                    _beta1().value() = r1 * mu(1, i);
-                    _beta2().value() = r2 * mu(1, i);
-                    _beta3().value() = r3 * mu(1, i);
-                    _beta4().value() = r4 * mu(1, i);
-                    _beta5().value() = r5 * mu(1, i);
-                    _beta6().value() = r6 * mu(1, i);
-                    _beta7().value() = r7 * mu(1, i);
-                    _beta8().value() = r8 * mu(1, i);
+                    _beta1().value() = r1* mu(1, i);
+                    _beta2().value() = r2* mu(1, i);
+                    _beta3().value() = r3* mu(1, i);
+                    _beta4().value() = r4* mu(1, i);
+                    _beta5().value() = r5* mu(1, i);
+                    _beta6().value() = r6* mu(1, i);
+                    _beta7().value() = r7* mu(1, i);
+                    _beta8().value() = r8* mu(1, i);
                     _decLam3().value() = mu(2, i);
                     mu_now[0] = mu(0, i);
                     mu_now[1] = mu(1, i);
@@ -222,7 +222,7 @@ int main(int argc, char* argv[])
     TmediaSA.buildMO(folder);
     PtotSA.buildMO(folder);
     //assign it to VDSensitivity object
-    analisi.M = autoPtr<FofM>(&TmediaSA);
+    analisi.M = autoPtr<FofM>( & TmediaSA);
     //load the model output in the VDSensitivity object
     analisi.load_output();
     analisi.getYstat();
@@ -251,7 +251,7 @@ int main(int argc, char* argv[])
     coeffsT.row(3) = analisi.betas;
     ITHACAstream::exportMatrix(coeffsT, "coeffsT", "eigen", "./ITHACAoutput");
     //assign it to VDSensitivity object
-    analisi.M = autoPtr<FofM>(&PtotSA);
+    analisi.M = autoPtr<FofM>( & PtotSA);
     //load the model output in the VDSensitivity object
     analisi.load_output();
     analisi.getYstat();
diff --git a/tutorials/CFD/17YJunction/17YJunction.C b/tutorials/CFD/17YJunction/17YJunction.C
index 1cb6e25ca..76bfa3388 100644
--- a/tutorials/CFD/17YJunction/17YJunction.C
+++ b/tutorials/CFD/17YJunction/17YJunction.C
@@ -121,7 +121,7 @@ class tutorial17: public unsteadyNS
                         IOobject::NO_WRITE
                     ),
                     mesh,
-                    dimensionedScalar("Phi", dimLength * dimVelocity, 0),
+                    dimensionedScalar("Phi", dimLength* dimVelocity, 0),
                     p.boundaryField().types()
                 );
                 label PhiRefCell = 0;
diff --git a/tutorials/CFD/20incrementalPOD/20incrementalPOD.C b/tutorials/CFD/20incrementalPOD/20incrementalPOD.C
old mode 100755
new mode 100644
index ec9b0289b..ee16f094a
--- a/tutorials/CFD/20incrementalPOD/20incrementalPOD.C
+++ b/tutorials/CFD/20incrementalPOD/20incrementalPOD.C
@@ -53,6 +53,7 @@ class tutorialIPOD: public laplacianProblem
             nu(_nu()),
             S(_S())
         {}
+
         //! [tutorialIPOD]
         /// Temperature field
         volScalarField& T;
@@ -289,6 +290,7 @@ int main(int argc, char* argv[])
     Info << "\n\nRelative error L2 norm incrementalPOD = " <<
          ITHACAutilities::L2Norm(relativeErrorField) << endl;
 }
+
 //--------
 /// \dir 20incrementalPOD Folder of the tutorial
 /// \file
diff --git a/tutorials/CFD/22datadriven_corrections/offline.C b/tutorials/CFD/22datadriven_corrections/offline.C
index 0daa469a2..e5488e529 100644
--- a/tutorials/CFD/22datadriven_corrections/offline.C
+++ b/tutorials/CFD/22datadriven_corrections/offline.C
@@ -106,6 +106,7 @@ class tutorial22 : public UnsteadyNSTurb
                 truthSolve(mu_now, offlinepath);
             }
         }
+
         Eigen::MatrixXd vectorTensorMult(Eigen::VectorXd g, Eigen::Tensor<double, 3> c,
                                          Eigen::VectorXd a)
         {
diff --git a/tutorials/CFD/24HyperReduction/24HyperReduction.C b/tutorials/CFD/24HyperReduction/24HyperReduction.C
index d7013bda6..2c65fccae 100644
--- a/tutorials/CFD/24HyperReduction/24HyperReduction.C
+++ b/tutorials/CFD/24HyperReduction/24HyperReduction.C
@@ -39,10 +39,11 @@ SourceFiles
 #include "hyperReduction.templates.H"
 #include <chrono>
 
-class HyperReduction_function : public HyperReduction<PtrList<volScalarField>&>
+class HyperReduction_function : public
+    HyperReduction<PtrList<volScalarField> & >
 {
     public:
-    using HyperReduction::HyperReduction;
+        using HyperReduction::HyperReduction;
         static volScalarField evaluate_expression(volScalarField& S, Eigen::MatrixXd mu)
         {
             volScalarField yPos = S.mesh().C().component(vector::Y).ref();
@@ -57,7 +58,8 @@ class HyperReduction_function : public HyperReduction<PtrList<volScalarField>&>
             return S;
         }
 
-        static Eigen::VectorXd evaluate_expression(volScalarField& S, Eigen::MatrixXd mu, List<label> nodesList)
+        static Eigen::VectorXd evaluate_expression(volScalarField& S,
+                Eigen::MatrixXd mu, List<label> nodesList)
         {
             Eigen::VectorXd ret(nodesList.size());
             volScalarField yPos = S.mesh().C().component(vector::Y).ref();
@@ -66,24 +68,25 @@ class HyperReduction_function : public HyperReduction<PtrList<volScalarField>&>
             for (auto i = 0; i < nodesList.size(); i++)
             {
                 ret[i] = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
-                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
+                                                  2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
             }
 
             return ret;
         }
-        
+
         Eigen::VectorXd onlineCoeffs(volScalarField& S, Eigen::MatrixXd mu)
         {
             Eigen::VectorXd f = evaluate_expression(S, mu, localNodePoints);
-            return pinvPU*f;
+            return pinvPU* f;
         }
 
 };
 
-class HyperReduction_vectorFunction : public HyperReduction<PtrList<volVectorField>&>
+class HyperReduction_vectorFunction : public
+    HyperReduction<PtrList<volVectorField> & >
 {
     public:
-    using HyperReduction::HyperReduction;
+        using HyperReduction::HyperReduction;
         static volVectorField evaluate_expression(volVectorField& S, Eigen::MatrixXd mu)
         {
             volScalarField yPos = S.mesh().C().component(vector::Y).ref();
@@ -92,48 +95,53 @@ class HyperReduction_vectorFunction : public HyperReduction<PtrList<volVectorFie
             for (auto i = 0; i < S.size(); i++)
             {
                 S[i][0] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1,
-                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
+                                                   2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
                 S[i][1] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 0.5,
-                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
+                                                   2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
                 S[i][2] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1.5,
-                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0., 2));
+                                                   2) - 2 * std::pow(yPos[i] - mu(1) - 0., 2));
             }
 
             return S;
         }
 
-        static Eigen::VectorXd evaluate_expression(volVectorField& S, Eigen::MatrixXd mu, List<label> nodesList)
+        static Eigen::VectorXd evaluate_expression(volVectorField& S,
+                Eigen::MatrixXd mu, List<label> nodesList)
         {
-            Eigen::VectorXd ret(nodesList.size()*3);
+            Eigen::VectorXd ret(nodesList.size() * 3);
             volScalarField yPos = S.mesh().C().component(vector::Y).ref();
             volScalarField xPos = S.mesh().C().component(vector::X).ref();
 
             for (auto i = 0; i < nodesList.size(); i++)
             {
                 ret(i) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
-                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
-                ret(i + nodesList.size()) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 0.5,
-                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
-                ret(i + 2 * nodesList.size()) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1.5,
-                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0., 2));
+                                                  2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
+                ret(i + nodesList.size()) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(
+                        0) - 0.5,
+                                                      2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
+                ret(i + 2 * nodesList.size()) = std::exp( - 2 * std::pow(
+                                                    xPos[nodesList[i]] - mu(0) - 1.5,
+                                                    2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0., 2));
             }
 
             return ret;
         }
-        
+
         Eigen::VectorXd onlineCoeffs(volVectorField& S, Eigen::MatrixXd mu)
         {
             Eigen::VectorXd f = evaluate_expression(S, mu, localNodePoints);
-            return pinvPU*f;
+            return pinvPU* f;
         }
 
 };
 
-class HyperReduction_vectorScalarFunction : public HyperReduction<PtrList<volVectorField>&, PtrList<volScalarField>&>
+class HyperReduction_vectorScalarFunction : public
+    HyperReduction<PtrList<volVectorField> &, PtrList<volScalarField> & >
 {
     public:
-    using HyperReduction::HyperReduction;
-        static std::pair<volVectorField, volScalarField> evaluate_expression(volVectorField& V, volScalarField& S, Eigen::MatrixXd mu)
+        using HyperReduction::HyperReduction;
+        static std::pair<volVectorField, volScalarField> evaluate_expression(
+            volVectorField& V, volScalarField& S, Eigen::MatrixXd mu)
         {
             volScalarField yPos = S.mesh().C().component(vector::Y).ref();
             volScalarField xPos = S.mesh().C().component(vector::X).ref();
@@ -141,11 +149,11 @@ class HyperReduction_vectorScalarFunction : public HyperReduction<PtrList<volVec
             for (auto i = 0; i < S.size(); i++)
             {
                 V[i][0] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1,
-                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
+                                                   2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
                 V[i][1] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 0.5,
-                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
+                                                   2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
                 V[i][2] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1.5,
-                                                2) - 2 * std::pow(yPos[i] - mu(1) - 0., 2));
+                                                   2) - 2 * std::pow(yPos[i] - mu(1) - 0., 2));
                 S[i] = std::exp( - 2 * std::pow(xPos[i] - mu(0) - 1,
                                                 2) - 2 * std::pow(yPos[i] - mu(1) - 0.5, 2));
             }
@@ -153,42 +161,47 @@ class HyperReduction_vectorScalarFunction : public HyperReduction<PtrList<volVec
             return std::make_pair(V, S);
         }
 
-        static Eigen::VectorXd evaluate_expression(volScalarField& S, Eigen::MatrixXd mu, List<label> nodesList)
+        static Eigen::VectorXd evaluate_expression(volScalarField& S,
+                Eigen::MatrixXd mu, List<label> nodesList)
         {
-            Eigen::VectorXd ret(nodesList.size()*4);
+            Eigen::VectorXd ret(nodesList.size() * 4);
             volScalarField yPos = S.mesh().C().component(vector::Y).ref();
             volScalarField xPos = S.mesh().C().component(vector::X).ref();
 
             for (auto i = 0; i < nodesList.size(); i++)
             {
                 ret(i) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
-                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
-                ret(i + nodesList.size()) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 0.5,
-                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
-                ret(i + 2 * nodesList.size()) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1.5,
-                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0., 2));
-                ret(i + 3 * nodesList.size()) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(0) - 1,
-                                                2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
+                                                  2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
+                ret(i + nodesList.size()) = std::exp( - 2 * std::pow(xPos[nodesList[i]] - mu(
+                        0) - 0.5,
+                                                      2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
+                ret(i + 2 * nodesList.size()) = std::exp( - 2 * std::pow(
+                                                    xPos[nodesList[i]] - mu(0) - 1.5,
+                                                    2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0., 2));
+                ret(i + 3 * nodesList.size()) = std::exp( - 2 * std::pow(
+                                                    xPos[nodesList[i]] - mu(0) - 1,
+                                                    2) - 2 * std::pow(yPos[nodesList[i]] - mu(1) - 0.5, 2));
             }
 
             return ret;
         }
-        
+
         Eigen::VectorXd onlineCoeffs(volScalarField& S, Eigen::MatrixXd mu)
         {
             Eigen::VectorXd f = evaluate_expression(S, mu, localNodePoints);
-            return pinvPU*f;
+            return pinvPU* f;
         }
 
 };
 
-void test_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime){
+void test_scalar(ITHACAparameters* para, Foam::fvMesh& mesh,
+                 Foam::Time& runTime)
+{
     int n_modes = para->ITHACAdict->lookupOrDefault<int>("Modes", 15);
     int n_nodes = para->ITHACAdict->lookupOrDefault<int>("Nodes", 15);
     simpleControl simple(mesh);
-
-    word methodName = para->ITHACAdict->lookupOrDefault<word>("HyperReduction", "GappyDEIM");
-
+    word methodName = para->ITHACAdict->lookupOrDefault<word>("HyperReduction",
+                      "GappyDEIM");
 #include "createFields.H"
     // List of volScalarField where the snapshots are stored
     PtrList<volScalarField> Sp;
@@ -221,38 +234,35 @@ void test_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
     // Define new online parameters
     Eigen::MatrixXd parTest;// = ITHACAutilities::rand(100, 2, -0.5, 0.5);
     cnpy::load(parTest, "testingPars.npy");
-
     // Create HyperReduction object with given number of basis functions
     Eigen::VectorXi initSeeds;
     // initSeeds = cnpy::load(initSeeds, "./mp.npy");//load mp to test initialSeeds
 
-    if (methodName=="GappyDEIM")
+    if (methodName == "GappyDEIM")
     {
         HyperReduction_function c(n_modes, n_nodes, initSeeds, "Gaussian_function", Sp);
         Eigen::MatrixXd snapshotsModes;
         Eigen::VectorXd normalizingWeights;
-        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights); 
+        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights);
         c.offlineGappyDEIM(snapshotsModes, normalizingWeights);
-
         // Generate the submeshes with the depth of the layer
         unsigned int layers{2};
         c.generateSubmesh(layers, mesh);
         auto sfield = c.interpolateField<volScalarField>(Sp[0]);
-        
         PtrList<volScalarField> testTrueFields;
         PtrList<volScalarField> testRecFields;
+
         for (unsigned int idTest = 0; idTest < parTest.rows(); idTest++)
-        {        
+        {
             // Online evaluation of the non linear function
-            Eigen::VectorXd aprfield = c.renormalizedBasisMatrix*c.onlineCoeffs(sfield(), parTest.row(idTest));
+            Eigen::VectorXd aprfield = c.renormalizedBasisMatrix* c.onlineCoeffs(sfield(),
+                                       parTest.row(idTest));
             // Transform to an OpenFOAM field and export
             volScalarField S2("S_online", Foam2Eigen::Eigen2field(S, aprfield));
             // Evaluate the full order function and export it
             HyperReduction_function::evaluate_expression(S, parTest.row(idTest));
-            
             testRecFields.append(S2.clone());
             testTrueFields.append(S.clone());
-
             ITHACAstream::exportSolution(S2, name(idTest), "./ITHACAoutput/Online/");
             ITHACAstream::exportSolution(S, name(idTest), "./ITHACAoutput/Online/");
         }
@@ -262,46 +272,49 @@ void test_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
         Info << "GappyDEIM max relative error: " << err.maxCoeff() << endl;
         Info << "GappyDEIM mean relative error: " << err.array().mean() << endl;
     }
-    else if (methodName=="ECP")
+    else if (methodName == "ECP")
     {
         HyperReduction_function c(n_modes, n_nodes, initSeeds, "Gaussian_function", Sp);
-
         bool saveOFModes{true};
         Eigen::MatrixXd snapshotsModes;
         Eigen::VectorXd normalizingWeights;
-        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights, saveOFModes); 
+        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights,
+                      saveOFModes);
         c.offlineECP(snapshotsModes, normalizingWeights);
-
         // Generate the submeshes with the depth of the layer
         unsigned int layers{2};
         c.generateSubmesh(layers, mesh);
         auto sfield = c.interpolateField<volScalarField>(Sp[0]);
-        
         Eigen::VectorXd results(parTest.rows());
+
         for (unsigned int idTest = 0; idTest < parTest.rows(); idTest++)
         {
-            // Online evaluation of the non linear function            
-            Eigen::VectorXd f = c.evaluate_expression(sfield(), parTest.row(idTest), c.localNodePoints);
-            Eigen::VectorXd ff = Foam2Eigen::field2Eigen(c.evaluate_expression(Sp[0], parTest.row(idTest)));
-            
-            double trueIntegral = (normalizingWeights.cwiseInverse().asDiagonal()*ff).array().sum();
-            double testIntegral = (c.wPU*f).array().sum();
+            // Online evaluation of the non linear function
+            Eigen::VectorXd f = c.evaluate_expression(sfield(), parTest.row(idTest),
+                                c.localNodePoints);
+            Eigen::VectorXd ff = Foam2Eigen::field2Eigen(c.evaluate_expression(Sp[0],
+                                 parTest.row(idTest)));
+            double trueIntegral = (normalizingWeights.cwiseInverse().asDiagonal() *
+                                   ff).array().sum();
+            double testIntegral = (c.wPU* f).array().sum();
             // Info << "Integral: " << trueIntegral << endl;
             // Info << "Reconstructed Integral: " << testIntegral << endl;
-
-            results(idTest) = trueIntegral-testIntegral;
+            results(idTest) = trueIntegral - testIntegral;
         }
+
         Info << "ECP max error: " << results.cwiseAbs().maxCoeff() << endl;
         Info << "ECP mean error: " << results.cwiseAbs().mean() << endl;
     }
 }
 
-void test_vector(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime){
+void test_vector(ITHACAparameters* para, Foam::fvMesh& mesh,
+                 Foam::Time& runTime)
+{
     int n_modes = para->ITHACAdict->lookupOrDefault<int>("Modes", 15);
     int n_nodes = para->ITHACAdict->lookupOrDefault<int>("Nodes", 15);
     simpleControl simple(mesh);
-    word methodName = para->ITHACAdict->lookupOrDefault<word>("HyperReduction", "GappyDEIM");
-
+    word methodName = para->ITHACAdict->lookupOrDefault<word>("HyperReduction",
+                      "GappyDEIM");
 #include "createFields.H"
     // List of volVectorField where the snapshots are stored
     PtrList<volVectorField> Sp;
@@ -319,10 +332,10 @@ void test_vector(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
         T.mesh(),
         dimensionedVector("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), vector(0, 0, 0))
     );
-
     // Parameters used to train the non-linear function
     Eigen::MatrixXd pars;
     cnpy::load(pars, "trainingPars.npy");
+
     // Perform the offline phase
     for (int i = 0; i < 100; i++)
     {
@@ -334,38 +347,36 @@ void test_vector(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
     // Define new online parameters
     Eigen::MatrixXd parTest;// = ITHACAutilities::rand(100, 2, -0.5, 0.5);
     cnpy::load(parTest, "testingPars.npy");
-
     // Create HyperReduction object with given number of basis functions
     Eigen::VectorXi initSeeds;
     // initSeeds = cnpy::load(initSeeds, "./mp.npy");//load mp to test initialSeeds
 
-    if (methodName=="GappyDEIM")
+    if (methodName == "GappyDEIM")
     {
-        HyperReduction_vectorFunction c(n_modes, n_nodes, initSeeds, "Gaussian_function", Sp);
+        HyperReduction_vectorFunction c(n_modes, n_nodes, initSeeds,
+                                        "Gaussian_function", Sp);
         Eigen::MatrixXd snapshotsModes;
         Eigen::VectorXd normalizingWeights;
-        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights); 
+        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights);
         c.offlineGappyDEIM(snapshotsModes, normalizingWeights);
-
         // Generate the submeshes with the depth of the layer
         unsigned int layers{2};
         c.generateSubmesh(layers, mesh);
         auto sfield = c.interpolateField<volVectorField>(Sp[0]);
-        
         PtrList<volVectorField> testTrueFields;
         PtrList<volVectorField> testRecFields;
+
         for (unsigned int idTest = 0; idTest < parTest.rows(); idTest++)
-        {        
+        {
             // Online evaluation of the non linear function
-            Eigen::VectorXd aprfield = c.renormalizedBasisMatrix*c.onlineCoeffs(sfield(), parTest.row(idTest));
+            Eigen::VectorXd aprfield = c.renormalizedBasisMatrix* c.onlineCoeffs(sfield(),
+                                       parTest.row(idTest));
             // Transform to an OpenFOAM field and export
             volVectorField S2("S_online", Foam2Eigen::Eigen2field(S, aprfield));
             // Evaluate the full order function and export it
             HyperReduction_vectorFunction::evaluate_expression(S, parTest.row(idTest));
-            
             testRecFields.append(S2.clone());
             testTrueFields.append(S.clone());
-
             ITHACAstream::exportSolution(S2, name(idTest), "./ITHACAoutput/Online/");
             ITHACAstream::exportSolution(S, name(idTest), "./ITHACAoutput/Online/");
         }
@@ -375,47 +386,50 @@ void test_vector(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime
         Info << "GappyDEIM max relative error: " << err.maxCoeff() << endl;
         Info << "GappyDEIM mean relative error: " << err.array().mean() << endl;
     }
-    else if (methodName=="ECP")
+    else if (methodName == "ECP")
     {
-        HyperReduction_vectorFunction c(n_modes, n_nodes, initSeeds, "Gaussian_function", Sp);
-        
+        HyperReduction_vectorFunction c(n_modes, n_nodes, initSeeds,
+                                        "Gaussian_function", Sp);
         bool saveOFModes{true};
         Eigen::MatrixXd snapshotsModes;
         Eigen::VectorXd normalizingWeights;
-        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights, saveOFModes); 
+        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights,
+                      saveOFModes);
         c.offlineECP(snapshotsModes, normalizingWeights);
-
         // Generate the submeshes with the depth of the layer
         unsigned int layers{2};
         c.generateSubmesh(layers, mesh);
         auto sfield = c.interpolateField<volVectorField>(Sp[0]);
-        
         Eigen::VectorXd results(parTest.rows());
+
         for (unsigned int idTest = 0; idTest < parTest.rows(); idTest++)
         {
-            // Online evaluation of the non linear function            
-            Eigen::VectorXd f = c.evaluate_expression(sfield(), parTest.row(idTest), c.localNodePoints);
+            // Online evaluation of the non linear function
+            Eigen::VectorXd f = c.evaluate_expression(sfield(), parTest.row(idTest),
+                                c.localNodePoints);
             auto wholeField = c.evaluate_expression(Sp[0], parTest.row(idTest));
             Eigen::VectorXd ff = Foam2Eigen::field2Eigen(wholeField);
-            
-            double trueIntegral = (normalizingWeights.cwiseInverse().asDiagonal()*ff).array().sum();
-            double testIntegral = (c.wPU*f).array().sum();
+            double trueIntegral = (normalizingWeights.cwiseInverse().asDiagonal() *
+                                   ff).array().sum();
+            double testIntegral = (c.wPU* f).array().sum();
             // Info << "Integral: " << trueIntegral << endl;
             // Info << "Reconstructed Integral: " << testIntegral << endl;
-
-            results(idTest) = trueIntegral-testIntegral;
+            results(idTest) = trueIntegral - testIntegral;
         }
+
         Info << "ECP max error: " << results.cwiseAbs().maxCoeff() << endl;
         Info << "ECP mean error: " << results.cwiseAbs().mean() << endl;
     }
 }
 
-void test_vector_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time& runTime){
+void test_vector_scalar(ITHACAparameters* para, Foam::fvMesh& mesh,
+                        Foam::Time& runTime)
+{
     int n_modes = para->ITHACAdict->lookupOrDefault<int>("Modes", 15);
     int n_nodes = para->ITHACAdict->lookupOrDefault<int>("Nodes", 15);
     simpleControl simple(mesh);
-    word methodName = para->ITHACAdict->lookupOrDefault<word>("HyperReduction", "GappyDEIM");
-
+    word methodName = para->ITHACAdict->lookupOrDefault<word>("HyperReduction",
+                      "GappyDEIM");
 #include "createFields.H"
     // List of volVectorField where the snapshots are stored
     PtrList<volVectorField> Vp;
@@ -448,10 +462,10 @@ void test_vector_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time&
         T.mesh(),
         dimensionedScalar("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), 0)
     );
-    
     // Parameters used to train the non-linear function
     Eigen::MatrixXd pars;
     cnpy::load(pars, "trainingPars.npy");
+
     // Perform the offline phase
     for (int i = 0; i < 100; i++)
     {
@@ -465,99 +479,98 @@ void test_vector_scalar(ITHACAparameters* para, Foam::fvMesh& mesh, Foam::Time&
     // Define new online parameters
     Eigen::MatrixXd parTest;// = ITHACAutilities::rand(100, 2, -0.5, 0.5);
     cnpy::load(parTest, "testingPars.npy");
-
     // Create HyperReduction object with given number of basis functions
     Eigen::VectorXi initSeeds;
     // initSeeds = cnpy::load(initSeeds, "./mp.npy");//load mp to test initialSeeds
 
-    if (methodName=="GappyDEIM")
+    if (methodName == "GappyDEIM")
     {
-        HyperReduction_vectorScalarFunction c(n_modes, n_nodes, initSeeds, "Gaussian_function", Vp, Sp);
+        HyperReduction_vectorScalarFunction c(n_modes, n_nodes, initSeeds,
+                                              "Gaussian_function", Vp, Sp);
         Eigen::MatrixXd snapshotsModes;
         Eigen::VectorXd normalizingWeights;
-        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights); 
+        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights);
         c.offlineGappyDEIM(snapshotsModes, normalizingWeights);
-
         // Generate the submeshes with the depth of the layer
         unsigned int layers{2};
         c.generateSubmesh(layers, mesh);
         auto vfield = c.interpolateField<volVectorField>(Vp[0]);
         auto sfield = c.interpolateField<volScalarField>(Sp[0]);
-        
         PtrList<volVectorField> testTrueFieldsV;
         PtrList<volVectorField> testRecFieldsV;
         PtrList<volScalarField> testTrueFieldsS;
         PtrList<volScalarField> testRecFieldsS;
+
         for (unsigned int idTest = 0; idTest < parTest.rows(); idTest++)
-        {        
+        {
             // Online evaluation of the non linear function
             auto theta = c.onlineCoeffs(sfield(), parTest.row(idTest));
-            Eigen::VectorXd aprfield = c.renormalizedBasisMatrix*theta;
-            Eigen::VectorXd recvec = aprfield.head(3*S.size());
+            Eigen::VectorXd aprfield = c.renormalizedBasisMatrix* theta;
+            Eigen::VectorXd recvec = aprfield.head(3 * S.size());
             Eigen::VectorXd recsca = aprfield.tail(S.size());
             // Transform to an OpenFOAM field and export
             volVectorField V2("V_online", Foam2Eigen::Eigen2field(V, recvec));
             volScalarField S2("S_online", Foam2Eigen::Eigen2field(S, recsca));
             // Evaluate the full order function and export it
-            HyperReduction_vectorScalarFunction::evaluate_expression(V, S, parTest.row(idTest));
-            
+            HyperReduction_vectorScalarFunction::evaluate_expression(V, S,
+                    parTest.row(idTest));
             testRecFieldsV.append(V2.clone());
             testTrueFieldsV.append(V.clone());
-
             ITHACAstream::exportSolution(V2, name(idTest), "./ITHACAoutput/Online/");
             ITHACAstream::exportSolution(V, name(idTest), "./ITHACAoutput/Online/");
-
             testRecFieldsS.append(S2.clone());
             testTrueFieldsS.append(S.clone());
-
             ITHACAstream::exportSolution(S2, name(idTest), "./ITHACAoutput/Online/");
             ITHACAstream::exportSolution(S, name(idTest), "./ITHACAoutput/Online/");
         }
 
         // Compute the L2 error and print it
         auto errV = ITHACAutilities::errorL2Rel(testRecFieldsV, testTrueFieldsV);
-        Info << "GappyDEIM vector field max relative error: " << errV.maxCoeff() << endl;
-        Info << "GappyDEIM vector field mean relative error: " << errV.array().mean() << endl;
-
+        Info << "GappyDEIM vector field max relative error: " << errV.maxCoeff() <<
+             endl;
+        Info << "GappyDEIM vector field mean relative error: " << errV.array().mean() <<
+             endl;
         auto errS = ITHACAutilities::errorL2Rel(testRecFieldsS, testTrueFieldsS);
         Info << "GappyDEIM scalar max relative error: " << errS.maxCoeff() << endl;
         Info << "GappyDEIM scalar mean relative error: " << errS.array().mean() << endl;
     }
-    else if (methodName=="ECP")
+    else if (methodName == "ECP")
     {
-        HyperReduction_vectorScalarFunction c(n_modes, n_nodes, initSeeds, "Gaussian_function", Vp, Sp);
-        
+        HyperReduction_vectorScalarFunction c(n_modes, n_nodes, initSeeds,
+                                              "Gaussian_function", Vp, Sp);
         bool saveOFModes{true};
         Eigen::MatrixXd snapshotsModes;
         Eigen::VectorXd normalizingWeights;
-        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights, saveOFModes); 
+        c.getModesSVD(c.snapshotsListTuple, snapshotsModes, normalizingWeights,
+                      saveOFModes);
         c.offlineECP(snapshotsModes, normalizingWeights);
-
         // Generate the submeshes with the depth of the layer
         unsigned int layers{2};
         c.generateSubmesh(layers, mesh);
         auto vfield = c.interpolateField<volVectorField>(Vp[0]);
         auto sfield = c.interpolateField<volScalarField>(Sp[0]);
-        
         Eigen::VectorXd results(parTest.rows());
+
         for (unsigned int idTest = 0; idTest < parTest.rows(); idTest++)
         {
-            // Online evaluation of the non linear function            
-            Eigen::VectorXd f = c.evaluate_expression(sfield(), parTest.row(idTest), c.localNodePoints);
-            HyperReduction_vectorScalarFunction::evaluate_expression(V, S, parTest.row(idTest));
+            // Online evaluation of the non linear function
+            Eigen::VectorXd f = c.evaluate_expression(sfield(), parTest.row(idTest),
+                                c.localNodePoints);
+            HyperReduction_vectorScalarFunction::evaluate_expression(V, S,
+                    parTest.row(idTest));
             Eigen::VectorXd ffV = Foam2Eigen::field2Eigen(V);
             Eigen::VectorXd ffS = Foam2Eigen::field2Eigen(S);
             Eigen::VectorXd ff(ffV.rows() + ffS.rows());
             ff.head(ffV.rows()) = ffV;
             ff.tail(ffS.rows()) = ffS;
-            
-            double trueIntegral = (normalizingWeights.cwiseInverse().asDiagonal()*ff).array().sum();
-            double testIntegral = (c.wPU*f).array().sum();
+            double trueIntegral = (normalizingWeights.cwiseInverse().asDiagonal() *
+                                   ff).array().sum();
+            double testIntegral = (c.wPU* f).array().sum();
             // Info << "Integral: " << trueIntegral << endl;
             // Info << "Reconstructed Integral: " << testIntegral << endl;
-
-            results(idTest) = trueIntegral-testIntegral;
+            results(idTest) = trueIntegral - testIntegral;
         }
+
         Info << "ECP max error: " << results.cwiseAbs().maxCoeff() << endl;
         Info << "ECP mean error: " << results.cwiseAbs().mean() << endl;
     }
@@ -586,7 +599,6 @@ int main(int argc, char* argv[])
         "test",
         "vs"
     );
-
     // Read parameters from ITHACAdict file
 #include "setRootCase.H"
     Foam::Time runTime(Foam::Time::controlDictName, args);
@@ -603,7 +615,7 @@ int main(int argc, char* argv[])
     ITHACAparameters* para = ITHACAparameters::getInstance(mesh, runTime);
 
     if (args.get("test").match("scalar"))
-    {   
+    {
         Info << "Init scalar testcase\n";
         test_scalar(para, mesh, runTime);
     }
@@ -621,6 +633,6 @@ int main(int argc, char* argv[])
     {
         Info << "Pass '-test scalar', '-test vector', '-test vs'" << endl;
     }
-    
+
     return 0;
-}
\ No newline at end of file
+}
diff --git a/tutorials/NN/01simpleTurbGeomClosed/01simpleTurbGeomClosed.C b/tutorials/NN/01simpleTurbGeomClosed/01simpleTurbGeomClosed.C
index bb309b1d0..c3f68dbe2 100644
--- a/tutorials/NN/01simpleTurbGeomClosed/01simpleTurbGeomClosed.C
+++ b/tutorials/NN/01simpleTurbGeomClosed/01simpleTurbGeomClosed.C
@@ -205,7 +205,7 @@ class reducedSimpleSteadyNN : public reducedSimpleSteadyNS
         /// Constructor
         explicit reducedSimpleSteadyNN(SteadyNSSimpleNN& FOMproblem)
             :
-            problem(&FOMproblem)
+            problem( & FOMproblem)
         {}
 
         /// Full problem.
@@ -253,7 +253,7 @@ class reducedSimpleSteadyNN : public reducedSimpleSteadyNS
                 problem->para->ITHACAdict->lookupOrDefault<float>("residualJumpLim", 1e-5);
             float normalizedResidualLim =
                 problem->para->ITHACAdict->lookupOrDefault<float>("normalizedResidualLim",
-                        1e-5);
+                    1e-5);
             scalar residual_jump(1 + residualJumpLim);
             volScalarField& P = problem->_p();
             volVectorField& U = problem->_U();
@@ -314,7 +314,7 @@ class reducedSimpleSteadyNN : public reducedSimpleSteadyNS
                 (
                     fvm::div(phi, U)
                     - fvm::laplacian(nueff, U)
-                    - fvc::div(nueff * dev2(T(fvc::grad(U))))
+                    - fvc::div(nueff* dev2(T(fvc::grad(U))))
                 );
                 UEqn.relax();
                 //solve(UEqn == - fvc::grad(P));
@@ -500,7 +500,7 @@ class tutorial01cl : public SteadyNSSimpleNN
             }
         }
 
-        void linearMovePts(double angle, List<vector>& points2Move)
+        void linearMovePts(double angle, List<vector> & points2Move)
         {
             double sMax;
             scalarList x;
@@ -516,13 +516,13 @@ class tutorial01cl : public SteadyNSSimpleNN
             double xMax = max(x);
             double yMin = min(y);
             double yMax = max(y);
-            sMax = (yMax - yMin) * std::tan(M_PI * angle / 180);
+            sMax = (yMax - yMin) * std::tan(M_PI* angle / 180);
 
             for (label i = 0; i < points2Move.size(); i++)
             {
                 points2Move[i].component(0) = points2Move[i].component(0) +
                                               (yMax - points2Move[i].component(1)) / (yMax - yMin) * (xMax -
-                                                      points2Move[i].component(0)) / (xMax - xMin) * sMax;
+                                                  points2Move[i].component(0)) / (xMax - xMin) * sMax;
             }
         }
 };
diff --git a/tutorials/UQ/01enKF/01enKF.C b/tutorials/UQ/01enKF/01enKF.C
old mode 100755
new mode 100644
index ab9180aaa..fc6067435
--- a/tutorials/UQ/01enKF/01enKF.C
+++ b/tutorials/UQ/01enKF/01enKF.C
@@ -79,10 +79,10 @@ int main(int argc, char* argv[])
 
     for (int timeI = 0; timeI < Ntimes - 1; timeI++)
     {
-        Eigen::VectorXd xNew = (A * deltaTime + Eigen::MatrixXd::Identity(A.rows(),
+        Eigen::VectorXd xNew = (A* deltaTime + Eigen::MatrixXd::Identity(A.rows(),
                                 A.cols()))  * xOld;
         xOld = xNew;
-        Eigen::VectorXd dNew = H * xNew;
+        Eigen::VectorXd dNew = H* xNew;
         X.col(timeI + 1) = xNew;
         sampleFlag--;
 
@@ -136,7 +136,7 @@ int main(int argc, char* argv[])
         //Forecast step
         for (int i = 0; i < Nseeds; i++)
         {
-            forwardSamples.col(i) = (A * deltaTime + Eigen::MatrixXd::Identity(A.rows(),
+            forwardSamples.col(i) = (A* deltaTime + Eigen::MatrixXd::Identity(A.rows(),
                                      A.cols())) * priorSamples.col(i) + modelErrorDensity->Sample();
         }
 
@@ -148,7 +148,7 @@ int main(int argc, char* argv[])
             Eigen::VectorXd meas = obs.col(sampleI);
             //Kalman filter
             posteriorSamples = ITHACAmuq::muq2ithaca::EnsembleKalmanFilter(forwardSamples,
-                               meas, meas_cov, H * forwardSamples);
+                               meas, meas_cov, H* forwardSamples);
             sampleI++;
         }
         else
diff --git a/tutorials/UQ/02enKF_1DinverseHeatTransfer/02enKF_1DinverseHeatTransfer.C b/tutorials/UQ/02enKF_1DinverseHeatTransfer/02enKF_1DinverseHeatTransfer.C
old mode 100755
new mode 100644
index d134e0732..ca2352da5
--- a/tutorials/UQ/02enKF_1DinverseHeatTransfer/02enKF_1DinverseHeatTransfer.C
+++ b/tutorials/UQ/02enKF_1DinverseHeatTransfer/02enKF_1DinverseHeatTransfer.C
@@ -90,6 +90,7 @@ int main(int argc, char* argv[])
     example.reconstruct();
     return 0;
 }
+
 //--------
 /// \dir  02enKF_1DinverseHeatTransfer Folder of the UQ tutorial 2
 /// \file
diff --git a/tutorials/UQ/02enKF_1DinverseHeatTransfer/02enKF_1DinverseHeatTransfer.H b/tutorials/UQ/02enKF_1DinverseHeatTransfer/02enKF_1DinverseHeatTransfer.H
old mode 100755
new mode 100644
index cbd1820c8..df5ef16a4
--- a/tutorials/UQ/02enKF_1DinverseHeatTransfer/02enKF_1DinverseHeatTransfer.H
+++ b/tutorials/UQ/02enKF_1DinverseHeatTransfer/02enKF_1DinverseHeatTransfer.H
@@ -146,6 +146,7 @@ class EnKF_1DinverseHeatTransfer: public laplacianProblem
                 //add check if I put two measurements on the same cell
                 measures(pntI) = field[mesh.findCell(measurementPoints[pntI])];
             }
+
             return measures;
         }
 
@@ -159,7 +160,7 @@ class EnKF_1DinverseHeatTransfer: public laplacianProblem
             simpleControl& simple = _simple();
             fv::options& fvOptions(_fvOptions());
             dimensionedScalar diffusivity("diffusivity", dimensionSet(0, 2, -1, 0, 0, 0, 0),
-                                          k / (rho * Cp));
+                                          k / (rho* Cp));
             Info << "Thermal diffusivity = " << diffusivity << " m2/s" << endl;
             int timeI = 0;
 
@@ -271,7 +272,7 @@ class EnKF_1DinverseHeatTransfer: public laplacianProblem
 
             for (int timeI = 0; timeI < Ntimes; timeI++)
             {
-                double initialTime = timeI * deltaTime + startTime;
+                double initialTime = timeI* deltaTime + startTime;
                 Info << "\n\nTime " << initialTime + deltaTime << endl;
                 Eigen::MatrixXd forecastOutput = forecastStep(initialTime, timeI,
                                                  initialTime + deltaTime);
diff --git a/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/CGtest.H b/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/CGtest.H
index 823735b54..823fe30b2 100644
--- a/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/CGtest.H
+++ b/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/CGtest.H
@@ -26,6 +26,7 @@ if (example_CG.conjugateGradient())
                                      std::to_string(solutionI + 1), outputFolder,
                                      "g_CG");
     }
+
     example_CG.postProcess(outputFolder, "g_CG");
 }
 else
diff --git a/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/IHTP01inverseLaplacian.C b/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/IHTP01inverseLaplacian.C
index fdbdfd6a6..5d02988e2 100644
--- a/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/IHTP01inverseLaplacian.C
+++ b/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/IHTP01inverseLaplacian.C
@@ -92,7 +92,7 @@ int main(int argc, char* argv[])
                        0.000001);
     example_CG.JtolRel =
         para->ITHACAdict->lookupOrDefault<double>("JrelativeTolerance",
-                0.001);
+            0.001);
     double rbfShapePar = para->ITHACAdict->lookupOrDefault<double>("rbfShapePar",
                          0);
     M_Assert(rbfShapePar > 0, "rbfShapePar not specified");
@@ -114,7 +114,7 @@ int main(int argc, char* argv[])
         auto cx = T_true.mesh().C()[i].component(vector::X);
         auto cy = T_true.mesh().C()[i].component(vector::Y);
         auto cz = T_true.mesh().C()[i].component(vector::Z);
-        T_true.ref()[i] = a * cx * cx + b * cx * cy + c * cy - a * cz * cz + c;
+        T_true.ref()[i] = a* cx* cx + b* cx* cy + c* cy - a* cz* cz + c;
     }
 
     // Perform true solution
@@ -127,8 +127,9 @@ int main(int argc, char* argv[])
     {
         scalar faceX =
             mesh.boundaryMesh()[example_paramBC.hotSide_ind].faceCentres()[faceI].x();
-        example_paramBC.g[faceI] = example_paramBC.k * (b * faceX + c) ;
+        example_paramBC.g[faceI] = example_paramBC.k * (b* faceX + c) ;
     }
+
     example_paramBC.gTrue = example_paramBC.g;
     example_paramBC.solveTrue();
     example_CG.g = example_paramBC.g;
diff --git a/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/IHTP01inverseLaplacian.H b/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/IHTP01inverseLaplacian.H
index 2e27577ca..c0d9942da 100644
--- a/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/IHTP01inverseLaplacian.H
+++ b/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/IHTP01inverseLaplacian.H
@@ -109,6 +109,7 @@ class IHTP01inverseLaplacian_paramBC: public inverseLaplacianProblem_paramBC
                     ITHACAutilities::assignBC(Tad, patchI, -heatFlux_gammaEx4);
                 }
             }
+
 #if defined(OFVER) && (OFVER == 6)
 
             while (simple.loop(runTime))
@@ -186,9 +187,11 @@ class IHTP01inverseLaplacian_paramBC: public inverseLaplacianProblem_paramBC
                     mass(baseI, baseJ) = ITHACAutilities::L2productOnPatch(mesh,
                                          gBaseFunctions[baseI], gBaseFunctions[baseJ], "hotSide");
                 }
+
                 source(baseI) = ITHACAutilities::L2productOnPatch(mesh, gBaseFunctions[baseI],
                                 gTrue, "hotSide");
             }
+
             return mass.fullPivLu().solve(source); //Vector of coefficients
         }
 
@@ -213,12 +216,14 @@ class IHTP01inverseLaplacian_paramBC: public inverseLaplacianProblem_paramBC
                     scalar tcZ = thermocouplesPos[TCi].z();
                     double radius = Foam::sqrt((tcX - centerX) * (tcX - centerX) +
                                                (tcZ - centerZ) * (tcZ - centerZ));
-                    Phi(TCi, baseI) = Foam::exp(- (shapeParameter *
+                    Phi(TCi, baseI) = Foam::exp(- (shapeParameter*
                                                    shapeParameter
-                                                   * radius * radius));
+                                                   * radius* radius));
                 }
-                coeff(baseI) = k * (b * thermocouplesPos[baseI].x() + c);
+
+                coeff(baseI) = k * (b* thermocouplesPos[baseI].x() + c);
             }
+
             return Phi.fullPivLu().solve(coeff);
         }
 
@@ -336,4 +341,5 @@ class IHTP01inverseLaplacian_CG: public inverseLaplacianProblem_CG
 #include"solveTrue.H"
         }
 };
+
 #endif
diff --git a/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/directBC.H b/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/directBC.H
old mode 100755
new mode 100644
index beb7e6734..8cab55fba
--- a/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/directBC.H
+++ b/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/directBC.H
@@ -14,9 +14,10 @@ forAll(Tf, faceI)
         mesh.boundaryMesh()[coldSide_ind].faceCentres()[faceI].y();
     scalar faceX =
         mesh.boundaryMesh()[coldSide_ind].faceCentres()[faceI].x();
-    Tf[faceI] = k / H * (b * faceX + c) + a * faceX * faceX +
-                b * faceX * faceY + c * faceY - a * faceZ * faceZ + c;
+    Tf[faceI] = k / H * (b* faceX + c) + a* faceX* faceX +
+                b* faceX* faceY + c* faceY - a* faceZ* faceZ + c;
 }
+
 // Setting BC at gammaEx1
 gammaEx1_ind = mesh.boundaryMesh().findPatchID("gammaEx1");
 label gammaEx1Size = T.boundaryField()[gammaEx1_ind].size();
@@ -25,8 +26,9 @@ forAll(heatFlux_gammaEx1, faceI)
 {
     scalar faceZ =
         mesh.boundaryMesh()[gammaEx1_ind].faceCentres()[faceI].z();
-    heatFlux_gammaEx1[faceI] = k * 2 * a * faceZ;
+    heatFlux_gammaEx1[faceI] = k * 2 * a* faceZ;
 }
+
 // Setting BC at gammaEx2
 gammaEx2_ind = mesh.boundaryMesh().findPatchID("gammaEx2");
 label gammaEx2Size = T.boundaryField()[gammaEx2_ind].size();
@@ -37,8 +39,9 @@ forAll(heatFlux_gammaEx2, faceI)
         mesh.boundaryMesh()[gammaEx2_ind].faceCentres()[faceI].x();
     scalar faceY =
         mesh.boundaryMesh()[gammaEx2_ind].faceCentres()[faceI].y();
-    heatFlux_gammaEx2[faceI] = - k * (2 * a * faceX + b * faceY);
+    heatFlux_gammaEx2[faceI] = - k * (2 * a* faceX + b* faceY);
 }
+
 // Setting BC at gammaEx3
 gammaEx3_ind = mesh.boundaryMesh().findPatchID("gammaEx3");
 label gammaEx3Size = T.boundaryField()[gammaEx3_ind].size();
@@ -47,6 +50,7 @@ forAll(heatFlux_gammaEx3, faceI)
 {
     heatFlux_gammaEx3[faceI] = 0;
 }
+
 // Setting BC at gammaEx4
 gammaEx4_ind = mesh.boundaryMesh().findPatchID("gammaEx4");
 label gammaEx4Size = T.boundaryField()[gammaEx4_ind].size();
@@ -55,8 +59,9 @@ forAll(heatFlux_gammaEx4, faceI)
 {
     scalar faceY =
         mesh.boundaryMesh()[gammaEx4_ind].faceCentres()[faceI].y();
-    heatFlux_gammaEx4[faceI] = k * (b * faceY);
+    heatFlux_gammaEx4[faceI] = k * (b* faceY);
 }
+
 set_valueFraction();
 forAll(mesh.boundaryMesh(), patchI)
 {
diff --git a/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/parameterizedBCtest.H b/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/parameterizedBCtest.H
old mode 100755
new mode 100644
index b87e6e6cd..3a108a713
--- a/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/parameterizedBCtest.H
+++ b/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/parameterizedBCtest.H
@@ -43,6 +43,7 @@ forAll(linSys_solvers, solverI)
     residualNorms(solverI) = Foam::sqrt(
                                  example_paramBC.residual.squaredNorm());
 }
+
 Eigen::MatrixXd A = example_paramBC.Theta.transpose() * example_paramBC.Theta;
 ITHACAstream::exportMatrix(residualNorms, "residuals2norm", "eigen",
                            outputFolder);
diff --git a/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/postProcess.H b/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/postProcess.H
old mode 100755
new mode 100644
index 90ae730e3..921d1b466
--- a/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/postProcess.H
+++ b/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/postProcess.H
@@ -51,6 +51,7 @@ forAll(gField, solutionI)
                                   relativeErrorField,
                                   "hotSide");
 }
+
 ITHACAstream::exportMatrix(heatFluxL2norm, "relError_L2norm", "eigen",
                            folder);
 ITHACAstream::exportMatrix(heatFluxLinfNorm, "relError_LinfNorm", "eigen",
diff --git a/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/thermocouplesLocation_paramBC.H b/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/thermocouplesLocation_paramBC.H
old mode 100755
new mode 100644
index 414401cfd..0881e83e8
--- a/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/thermocouplesLocation_paramBC.H
+++ b/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/thermocouplesLocation_paramBC.H
@@ -42,7 +42,7 @@ for (int i = 0; i < testSize; i++)
         auto cx = Ttrue.mesh().C()[i].component(vector::X);
         auto cy = Ttrue.mesh().C()[i].component(vector::Y);
         auto cz = Ttrue.mesh().C()[i].component(vector::Z);
-        Ttrue.ref()[i] = a * cx * cx + b * cx * cy + c * cy - a * cz * cz + c;
+        Ttrue.ref()[i] = a* cx* cx + b* cx* cy + c* cy - a* cz* cz + c;
     }
 
     example_paramBC.thermocouplesRead = 0;
diff --git a/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/thermocouplesNumberTest_paramBC.H b/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/thermocouplesNumberTest_paramBC.H
old mode 100755
new mode 100644
index 6d60222db..0f4620da6
--- a/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/thermocouplesNumberTest_paramBC.H
+++ b/tutorials/inverseHeatTransfer/IHTP01inverseLaplacian/thermocouplesNumberTest_paramBC.H
@@ -63,7 +63,7 @@ for (int i = 0; i < testSize; i++)
         auto cx = Ttrue.mesh().C()[i].component(vector::X);
         auto cy = Ttrue.mesh().C()[i].component(vector::Y);
         auto cz = Ttrue.mesh().C()[i].component(vector::Z);
-        Ttrue.ref()[i] = a * cx * cx + b * cx * cy + c * cy - a * cz * cz + c;
+        Ttrue.ref()[i] = a* cx* cx + b* cx* cy + c* cy - a* cz* cz + c;
     }
 
     example_paramBC.thermocouplesRead = 0;
diff --git a/unitTests/RBF_def/defGeom.C b/unitTests/RBF_def/defGeom.C
index 712ebab76..cf66519e8 100755
--- a/unitTests/RBF_def/defGeom.C
+++ b/unitTests/RBF_def/defGeom.C
@@ -117,4 +117,4 @@ int main(int argc, char* argv[])
         ITHACAstream::writePoints(mesh.points(), "defGeoms/", name(k + 1) + "/polyMesh/");
 
     }
-}
\ No newline at end of file
+}
diff --git a/unitTests/pybind11/residual_of/lnInclude/createFields.H b/unitTests/pybind11/residual_of/lnInclude/createFields.H
deleted file mode 120000
index 28ef2aa38..000000000
--- a/unitTests/pybind11/residual_of/lnInclude/createFields.H
+++ /dev/null
@@ -1 +0,0 @@
-../createFields.H
\ No newline at end of file
diff --git a/unitTests/pybind11/residual_of/lnInclude/createFields.H b/unitTests/pybind11/residual_of/lnInclude/createFields.H
new file mode 100755
index 000000000..3d07e1986
--- /dev/null
+++ b/unitTests/pybind11/residual_of/lnInclude/createFields.H
@@ -0,0 +1,108 @@
+/*---------------------------------------------------------------------------*\
+     ██╗████████╗██╗  ██╗ █████╗  ██████╗ █████╗       ███████╗██╗   ██╗
+     ██║╚══██╔══╝██║  ██║██╔══██╗██╔════╝██╔══██╗      ██╔════╝██║   ██║
+     ██║   ██║   ███████║███████║██║     ███████║█████╗█████╗  ██║   ██║
+     ██║   ██║   ██╔══██║██╔══██║██║     ██╔══██║╚════╝██╔══╝  ╚██╗ ██╔╝
+     ██║   ██║   ██║  ██║██║  ██║╚██████╗██║  ██║      ██║      ╚████╔╝
+     ╚═╝   ╚═╝   ╚═╝  ╚═╝╚═╝  ╚═╝ ╚═════╝╚═╝  ╚═╝      ╚═╝       ╚═══╝
+
+ * In real Time Highly Advanced Computational Applications for Finite Volumes
+ * Copyright (C) 2017 by the ITHACA-FV authors
+-------------------------------------------------------------------------------
+  License
+  This file is part of ITHACA-FV
+  ITHACA-FV is free software: you can redistribute it and/or modify
+  it under the terms of the GNU Lesser General Public License as published by
+  the Free Software Foundation, either version 3 of the License, or
+  (at your option) any later version.
+  ITHACA-FV is distributed in the hope that it will be useful,
+  but WITHOUT ANY WARRANTY; without even the implied warranty of
+  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+  GNU Lesser General Public License for more details.
+  You should have received a copy of the GNU Lesser General Public License
+  along with ITHACA-FV. If not, see <http://www.gnu.org/licenses/>.
+ \*---------------------------------------------------------------------------*/
+_T = autoPtr<volScalarField>
+     (
+         new volScalarField
+         (
+             IOobject
+             (
+                 "T",
+                 runTime.timeName(),
+                 mesh,
+                 IOobject::MUST_READ,
+                 IOobject::AUTO_WRITE
+             ),
+             mesh
+         )
+     );
+
+volScalarField& T = _T();
+
+_S = autoPtr<volScalarField>
+     (
+         new volScalarField
+         (
+             IOobject
+             (
+                 "S",
+                 runTime.timeName(),
+                 mesh,
+                 IOobject::NO_READ,
+                 IOobject::AUTO_WRITE
+             ),
+             T.mesh(),
+             dimensionedScalar("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), 0)
+         )
+     );
+
+_res = autoPtr<volScalarField>
+     (
+         new volScalarField
+         (
+             IOobject
+             (
+                 "res",
+                 runTime.timeName(),
+                 mesh,
+                 IOobject::NO_READ,
+                 IOobject::AUTO_WRITE
+             ),
+             T.mesh(),
+             dimensionedScalar("zero", dimensionSet(0, 0, -1, 1, 0, 0, 0), 0)
+         )
+     );
+
+_nu = autoPtr<volScalarField>
+      (
+          new volScalarField
+          (
+              IOobject
+              (
+                  "nu",
+                  runTime.timeName(),
+                  mesh,
+                  IOobject::NO_READ,
+                  IOobject::AUTO_WRITE
+              ),
+              T.mesh(),
+              dimensionedScalar("zero", dimensionSet( 0, 2, -1, 0, 0, 0, 0), 0)
+          )
+      );
+
+    IOdictionary transportProperties
+    (
+        IOobject
+        (
+            "transportProperties",
+            runTime.constant(),
+            mesh,
+            IOobject::MUST_READ_IF_MODIFIED,
+            IOobject::NO_WRITE
+        )
+    );
+
+_nu() = dimensionedScalar("DT", dimViscosity, transportProperties);
+
+
diff --git a/unitTests/pybind11/residual_of/lnInclude/createMesh.H b/unitTests/pybind11/residual_of/lnInclude/createMesh.H
deleted file mode 120000
index 3b31580b9..000000000
--- a/unitTests/pybind11/residual_of/lnInclude/createMesh.H
+++ /dev/null
@@ -1 +0,0 @@
-../createMesh.H
\ No newline at end of file
diff --git a/unitTests/pybind11/residual_of/lnInclude/createMesh.H b/unitTests/pybind11/residual_of/lnInclude/createMesh.H
new file mode 100755
index 000000000..35cd75067
--- /dev/null
+++ b/unitTests/pybind11/residual_of/lnInclude/createMesh.H
@@ -0,0 +1,45 @@
+/*---------------------------------------------------------------------------*\
+     ██╗████████╗██╗  ██╗ █████╗  ██████╗ █████╗       ███████╗██╗   ██╗
+     ██║╚══██╔══╝██║  ██║██╔══██╗██╔════╝██╔══██╗      ██╔════╝██║   ██║
+     ██║   ██║   ███████║███████║██║     ███████║█████╗█████╗  ██║   ██║
+     ██║   ██║   ██╔══██║██╔══██║██║     ██╔══██║╚════╝██╔══╝  ╚██╗ ██╔╝
+     ██║   ██║   ██║  ██║██║  ██║╚██████╗██║  ██║      ██║      ╚████╔╝
+     ╚═╝   ╚═╝   ╚═╝  ╚═╝╚═╝  ╚═╝ ╚═════╝╚═╝  ╚═╝      ╚═╝       ╚═══╝
+
+ * In real Time Highly Advanced Computational Applications for Finite Volumes
+ * Copyright (C) 2017 by the ITHACA-FV authors
+-------------------------------------------------------------------------------
+  License
+  This file is part of ITHACA-FV
+  ITHACA-FV is free software: you can redistribute it and/or modify
+  it under the terms of the GNU Lesser General Public License as published by
+  the Free Software Foundation, either version 3 of the License, or
+  (at your option) any later version.
+  ITHACA-FV is distributed in the hope that it will be useful,
+  but WITHOUT ANY WARRANTY; without even the implied warranty of
+  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+  GNU Lesser General Public License for more details.
+  You should have received a copy of the GNU Lesser General Public License
+  along with ITHACA-FV. If not, see <http://www.gnu.org/licenses/>.
+\*---------------------------------------------------------------------------*/
+
+Info << "Reading field p\n" << endl;
+
+Info << "Create mesh for time = "
+     << runTime.timeName() << nl << endl;
+
+_mesh = autoPtr<fvMesh>
+        (
+            new fvMesh
+            (
+                IOobject
+                (
+                    fvMesh::defaultRegion,
+                    runTime.timeName(),
+                    runTime,
+                    IOobject::MUST_READ
+                )
+            )
+        );
+
+Foam::fvMesh& mesh = _mesh();
diff --git a/unitTests/pybind11/residual_of/lnInclude/createTime.H b/unitTests/pybind11/residual_of/lnInclude/createTime.H
deleted file mode 120000
index 9565282db..000000000
--- a/unitTests/pybind11/residual_of/lnInclude/createTime.H
+++ /dev/null
@@ -1 +0,0 @@
-../createTime.H
\ No newline at end of file
diff --git a/unitTests/pybind11/residual_of/lnInclude/createTime.H b/unitTests/pybind11/residual_of/lnInclude/createTime.H
new file mode 100755
index 000000000..388324cc7
--- /dev/null
+++ b/unitTests/pybind11/residual_of/lnInclude/createTime.H
@@ -0,0 +1,31 @@
+/*---------------------------------------------------------------------------*\
+     ██╗████████╗██╗  ██╗ █████╗  ██████╗ █████╗       ███████╗██╗   ██╗
+     ██║╚══██╔══╝██║  ██║██╔══██╗██╔════╝██╔══██╗      ██╔════╝██║   ██║
+     ██║   ██║   ███████║███████║██║     ███████║█████╗█████╗  ██║   ██║
+     ██║   ██║   ██╔══██║██╔══██║██║     ██╔══██║╚════╝██╔══╝  ╚██╗ ██╔╝
+     ██║   ██║   ██║  ██║██║  ██║╚██████╗██║  ██║      ██║      ╚████╔╝
+     ╚═╝   ╚═╝   ╚═╝  ╚═╝╚═╝  ╚═╝ ╚═════╝╚═╝  ╚═╝      ╚═╝       ╚═══╝
+
+ * In real Time Highly Advanced Computational Applications for Finite Volumes
+ * Copyright (C) 2017 by the ITHACA-FV authors
+-------------------------------------------------------------------------------
+  License
+  This file is part of ITHACA-FV
+  ITHACA-FV is free software: you can redistribute it and/or modify
+  it under the terms of the GNU Lesser General Public License as published by
+  the Free Software Foundation, either version 3 of the License, or
+  (at your option) any later version.
+  ITHACA-FV is distributed in the hope that it will be useful,
+  but WITHOUT ANY WARRANTY; without even the implied warranty of
+  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+  GNU Lesser General Public License for more details.
+  You should have received a copy of the GNU Lesser General Public License
+  along with ITHACA-FV. If not, see <http://www.gnu.org/licenses/>.
+\*---------------------------------------------------------------------------*/
+Info << "Reading field p\n" << endl;
+
+
+Foam::Info << "Create time\n" << Foam::endl;
+_runTime = autoPtr<Foam::Time>( new Foam::Time( Foam::Time::controlDictName,
+                                args ) );
+Foam::Time& runTime = _runTime();

From ba91799384fd1fd0515ed0b6ec8b6e0ea65b7635 Mon Sep 17 00:00:00 2001
From: Giovanni Stabile <giovanni.stabile87@gmail.com>
Date: Fri, 4 Oct 2024 17:44:46 +0200
Subject: [PATCH 57/59] FIX: fixed problem in ithacaparameters

---
 src/ITHACA_CORE/ITHACAstream/ITHACAparameters.C | 2 +-
 tutorials/CFD/03steadyNS/system/ITHACAdict      | 1 +
 2 files changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/ITHACA_CORE/ITHACAstream/ITHACAparameters.C b/src/ITHACA_CORE/ITHACAstream/ITHACAparameters.C
index e7c2ba4d9..860baffa5 100755
--- a/src/ITHACA_CORE/ITHACAstream/ITHACAparameters.C
+++ b/src/ITHACA_CORE/ITHACAstream/ITHACAparameters.C
@@ -36,7 +36,7 @@ ITHACAparameters::ITHACAparameters(fvMesh& mesh, Time& localTime)
     exportPython = ITHACAdict->lookupOrDefault<bool>("exportPython", 0);
     exportMatlab = ITHACAdict->lookupOrDefault<bool>("exportMatlab", 0);
     exportTxt = ITHACAdict->lookupOrDefault<bool>("exportTxt", 0);
-    exportNpy = ITHACAdict->lookupOrDefault<bool>("exportnpy", 0);
+    exportNpy = ITHACAdict->lookupOrDefault<bool>("exportNpy", 0);
     debug = ITHACAdict->lookupOrDefault<bool>("debug", 0);
     warnings = ITHACAdict->lookupOrDefault<bool>("warnings", 0);
     correctBC = ITHACAdict->lookupOrDefault<bool>("correctBC", 1);
diff --git a/tutorials/CFD/03steadyNS/system/ITHACAdict b/tutorials/CFD/03steadyNS/system/ITHACAdict
index de6e6b37d..610036853 100755
--- a/tutorials/CFD/03steadyNS/system/ITHACAdict
+++ b/tutorials/CFD/03steadyNS/system/ITHACAdict
@@ -36,6 +36,7 @@ tolerance 1e-5;
 exportPython 1;
 exportMatlab 1;
 exportTxt 1;
+exportNpy 1;
 
 bcMethod lift;
 

From 24862509cfa5fce2432053b614a9c81a28c5d8cc Mon Sep 17 00:00:00 2001
From: Giovanni Stabile <giovanni.stabile87@gmail.com>
Date: Wed, 23 Oct 2024 11:57:22 +0200
Subject: [PATCH 58/59] Update README.md

---
 README.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.md b/README.md
index f4e00e36f..0623180f8 100644
--- a/README.md
+++ b/README.md
@@ -207,6 +207,7 @@ A significant part of ITHACA-FV has been written either as a by-product for othe
 Beyond this, ITHACA-FV has also been supported by some dedicated projects that have allowed us to work on extensions, documentation, training and dissemination that would otherwise not have been possible. In particular, we acknowledge the following sources of support with great gratitude:
 
 * [H2020 ERC CoG 2015 AROMA-CFD project 681447](https://people.sissa.it/~grozza/aroma-cfd/), P.I. Professor [Gianluigi Rozza](https://people.sissa.it/~grozza) at [SISSA mathLab](https://mathlab.sissa.it/).
+* [Horizon Europe ERC StG 2023 DANTE project 	101115741](https://www.santannapisa.it/it/istituto/biorobotica/dante), P.I. Professor [Giovanni Stabile](https://www.giovannistabile.com) at the [Biorobotics Institute](https://www.santannapisa.it/en/institute/biorobotics) of the [Scuola Superiore Sant'Anna di Pisa](https://www.santannapisa.it/en) 
 
 ### 8. License
 **ITHACA-FV** is freely available under the GNU LGPL, version 3.

From 5107077229b9bd5f1210eca3cfbaa588bffdb124 Mon Sep 17 00:00:00 2001
From: Giovanni Stabile <giovanni.stabile87@gmail.com>
Date: Wed, 23 Oct 2024 11:58:01 +0200
Subject: [PATCH 59/59] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 0623180f8..e717dbc06 100644
--- a/README.md
+++ b/README.md
@@ -207,7 +207,7 @@ A significant part of ITHACA-FV has been written either as a by-product for othe
 Beyond this, ITHACA-FV has also been supported by some dedicated projects that have allowed us to work on extensions, documentation, training and dissemination that would otherwise not have been possible. In particular, we acknowledge the following sources of support with great gratitude:
 
 * [H2020 ERC CoG 2015 AROMA-CFD project 681447](https://people.sissa.it/~grozza/aroma-cfd/), P.I. Professor [Gianluigi Rozza](https://people.sissa.it/~grozza) at [SISSA mathLab](https://mathlab.sissa.it/).
-* [Horizon Europe ERC StG 2023 DANTE project 	101115741](https://www.santannapisa.it/it/istituto/biorobotica/dante), P.I. Professor [Giovanni Stabile](https://www.giovannistabile.com) at the [Biorobotics Institute](https://www.santannapisa.it/en/institute/biorobotics) of the [Scuola Superiore Sant'Anna di Pisa](https://www.santannapisa.it/en) 
+* [Horizon Europe ERC StG 2023 DANTE project 	101115741](https://www.santannapisa.it/it/istituto/biorobotica/dante), P.I. Professor [Giovanni Stabile](https://www.giovannistabile.com) at the [Biorobotics Institute](https://www.santannapisa.it/en/institute/biorobotics) of the [Scuola Superiore Sant'Anna di Pisa](https://www.santannapisa.it/en).
 
 ### 8. License
 **ITHACA-FV** is freely available under the GNU LGPL, version 3.