From c08c7dce65feac67c51f3d8396045c2eaa228c27 Mon Sep 17 00:00:00 2001
From: Siu Wun Cheung <cheung26@llnl.gov>
Date: Mon, 2 Oct 2023 08:34:45 -0700
Subject: [PATCH 01/16] Add example results

---
 examples/prom/dg_advection_global_rom.cpp | 36 +++++++++--------------
 1 file changed, 14 insertions(+), 22 deletions(-)

diff --git a/examples/prom/dg_advection_global_rom.cpp b/examples/prom/dg_advection_global_rom.cpp
index 6855b8743..5a24e3c3e 100644
--- a/examples/prom/dg_advection_global_rom.cpp
+++ b/examples/prom/dg_advection_global_rom.cpp
@@ -10,14 +10,21 @@
 
 //                       libROM MFEM Example: DG Advection (adapted from ex9p.cpp)
 //
+// =================================================================================
+//
 // Compile with: make dg_advection_global_rom
 //
-// For ROM (reproductive case):
+// Sample runs and results for reproductive case:
 //    dg_advection_global_rom -offline
 //    dg_advection_global_rom -merge -ns 1
 //    dg_advection_global_rom -online
 //
-// For ROM (global rom):
+// Output:
+//  Relative l2 error of ROM solution 0.0005641839849343575
+// 
+// =================================================================================
+//
+// Sample runs and results for global ROM:
 // Offline phase: dg_advection_global_rom -offline -ff 1.0 -id 0
 //                dg_advection_global_rom -offline -ff 1.1 -id 1
 //                dg_advection_global_rom -offline -ff 1.2 -id 2
@@ -28,19 +35,10 @@
 //
 // Online phase:  dg_advection_global_rom -online -ff 1.15
 //
-// Sample runs:
-//    mpirun -np 4 dg_advection_global_rom -p 0 -dt 0.005
-//    mpirun -np 4 dg_advection_global_rom -p 0 -dt 0.01
-//    mpirun -np 4 dg_advection_global_rom -p 1 -dt 0.005 -tf 9
-//    mpirun -np 4 dg_advection_global_rom -p 1 -rp 1 -dt 0.002 -tf 9
-//    mpirun -np 4 dg_advection_global_rom -p 1 -rp 1 -dt 0.02 -s 13 -tf 9
-//    mpirun -np 4 dg_advection_global_rom -p 1 -rp 1 -dt 0.004 -tf 9
-//    mpirun -np 4 dg_advection_global_rom -p 1 -rp 1 -dt 0.005 -tf 9
-//    mpirun -np 4 dg_advection_global_rom -p 3 -rp 2 -dt 0.0025 -tf 9 -vs 20
-//    mpirun -np 4 dg_advection_global_rom -p 0 -o 2 -rp 1 -dt 0.01 -tf 8
-//    mpirun -np 4 dg_advection_global_rom -p 0 -rs 2 -dt 0.005 -tf 2
-//    mpirun -np 4 dg_advection_global_rom -p 0 -rs 1 -o 2 -tf 2
-//    mpirun -np 3 dg_advection_global_rom -p 1 -rs 1 -rp 0 -dt 0.005 -tf 0.5
+// Output:
+//   Relative l2 error of ROM solution 0.0004333183604809453
+//
+// =================================================================================
 //
 // Description:  This example code solves the time-dependent advection equation
 //               du/dt + v.grad(u) = 0, where v is a given fluid velocity, and
@@ -128,10 +126,7 @@ class AIR_prec : public Solver
         delete AIR_solver;
         AIR_solver = new HypreBoomerAMG(A_s);
         AIR_solver->SetAdvectiveOptions(1, "", "FA");
-        AIR_solver->SetPrintLevel(
-            0);    // 6. Define the parallel mesh by a partitioning of the serial mesh. Refine
-        //    this mesh further in parallel to increase the resolution. Once the
-        //    parallel mesh is defined, the serial mesh can be deleted.
+        AIR_solver->SetPrintLevel(0);
         AIR_solver->SetMaxLevels(50);
     }
 
@@ -464,9 +459,6 @@ int main(int argc, char *argv[])
         {
             cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
         }
-        delete mesh;    // 6. Define the parallel mesh by a partitioning of the serial mesh. Refine
-        //    this mesh further in parallel to increase the resolution. Once the
-        //    parallel mesh is defined, the serial mesh can be deleted.
         return 3;
     }
 

From 90393b0b53c13cc0daa11f0d9c645c503fcad8f8 Mon Sep 17 00:00:00 2001
From: Siu Wun Cheung <cheung26@llnl.gov>
Date: Mon, 4 Dec 2023 14:03:04 -0800
Subject: [PATCH 02/16] Count DMD prediction timer only at final time

---
 examples/dmd/dg_advection.cpp         |  8 +++-----
 examples/dmd/dg_euler.cpp             |  8 +++-----
 examples/dmd/heat_conduction.cpp      |  8 +++-----
 examples/dmd/heat_conduction_dmdc.cpp |  8 +++-----
 examples/dmd/nonlinear_elasticity.cpp | 28 +++++++++++++--------------
 examples/dmd/wave_equation.cpp        |  6 +++---
 6 files changed, 28 insertions(+), 38 deletions(-)

diff --git a/examples/dmd/dg_advection.cpp b/examples/dmd/dg_advection.cpp
index c75c2339f..31bf61c59 100644
--- a/examples/dmd/dg_advection.cpp
+++ b/examples/dmd/dg_advection.cpp
@@ -710,9 +710,7 @@ int main(int argc, char *argv[])
     Vector true_solution_u(U->Size());
     true_solution_u = U->GetData();
 
-    dmd_prediction_timer.Start();
-
-    // 14. Predict the state at t_final using DMD.
+    // 14. Predict using DMD.
     if (myid == 0)
     {
         std::cout << "Predicting solution using DMD" << std::endl;
@@ -755,9 +753,9 @@ int main(int argc, char *argv[])
         }
     }
 
-    dmd_prediction_timer.Stop();
-
+    dmd_prediction_timer.Start();
     result_u = dmd_U.predict(t_final);
+    dmd_prediction_timer.Stop();
 
     // 15. Calculate the relative error between the DMD final solution and the true solution.
     Vector dmd_solution_u(result_u->getData(), result_u->dim());
diff --git a/examples/dmd/dg_euler.cpp b/examples/dmd/dg_euler.cpp
index 159ef76f2..43129362e 100644
--- a/examples/dmd/dg_euler.cpp
+++ b/examples/dmd/dg_euler.cpp
@@ -574,9 +574,7 @@ int main(int argc, char *argv[])
     Vector true_solution_e(u_block.GetBlock(3).Size());
     true_solution_e = u_block.GetBlock(3).GetData();
 
-    dmd_prediction_timer.Start();
-
-    // 14. Predict the state at t_final using DMD.
+    // 14. Predict using DMD.
     if (mpi.WorldRank() == 0)
     {
         std::cout << "Predicting density, momentum, and energy using DMD" << std::endl;
@@ -639,12 +637,12 @@ int main(int argc, char *argv[])
         }
     }
 
-    dmd_prediction_timer.Stop();
-
+    dmd_prediction_timer.Start();
     result_dens = dmd_dens->predict(t_final);
     result_x_mom = dmd_x_mom->predict(t_final);
     result_y_mom = dmd_y_mom->predict(t_final);
     result_e = dmd_e->predict(t_final);
+    dmd_prediction_timer.Stop();
 
     // 15. Calculate the relative error between the DMD final solution and the true solution.
     Vector dmd_solution_dens(result_dens->getData(), result_dens->dim());
diff --git a/examples/dmd/heat_conduction.cpp b/examples/dmd/heat_conduction.cpp
index 34cb44329..5c12a9ae7 100644
--- a/examples/dmd/heat_conduction.cpp
+++ b/examples/dmd/heat_conduction.cpp
@@ -498,9 +498,7 @@ int main(int argc, char *argv[])
     Vector true_solution_u(u.Size());
     true_solution_u = u.GetData();
 
-    dmd_prediction_timer.Start();
-
-    // 14. Predict the state at t_final using DMD.
+    // 14. Predict using DMD.
     if (myid == 0)
     {
         std::cout << "Predicting temperature using DMD" << std::endl;
@@ -540,9 +538,9 @@ int main(int argc, char *argv[])
         }
     }
 
-    dmd_prediction_timer.Stop();
-
+    dmd_prediction_timer.Start();
     result_u = dmd_u->predict(t_final);
+    dmd_prediction_timer.Stop();
 
     // 15. Calculate the relative error between the DMD final solution and the true solution.
     Vector dmd_solution_u(result_u->getData(), result_u->dim());
diff --git a/examples/dmd/heat_conduction_dmdc.cpp b/examples/dmd/heat_conduction_dmdc.cpp
index 7d76568c2..4b4672b85 100644
--- a/examples/dmd/heat_conduction_dmdc.cpp
+++ b/examples/dmd/heat_conduction_dmdc.cpp
@@ -534,9 +534,7 @@ int main(int argc, char *argv[])
     Vector true_solution_u(u.Size());
     true_solution_u = u.GetData();
 
-    dmd_prediction_timer.Start();
-
-    // 14. Predict the state at t_final using DMDc.
+    // 14. Predict using DMDc.
     if (myid == 0)
     {
         std::cout << "Predicting temperature using DMDc" << std::endl;
@@ -576,9 +574,9 @@ int main(int argc, char *argv[])
         }
     }
 
-    dmd_prediction_timer.Stop();
-
+    dmd_prediction_timer.Start();
     result_u = dmd_u->predict(t_final);
+    dmd_prediction_timer.Stop();
 
     // 15. Calculate the relative error between the DMDc final solution and the true solution.
     Vector dmd_solution_u(result_u->getData(), result_u->dim());
diff --git a/examples/dmd/nonlinear_elasticity.cpp b/examples/dmd/nonlinear_elasticity.cpp
index 5bca8b44b..5f8c43384 100644
--- a/examples/dmd/nonlinear_elasticity.cpp
+++ b/examples/dmd/nonlinear_elasticity.cpp
@@ -515,6 +515,12 @@ int main(int argc, char *argv[])
 
         if (last_step || (ti % windowNumSamples) == 0)
         {
+            // Calculate DMD modes
+            if (myid == 0 && rdim != -1 && ef != -1)
+            {
+                std::cout << "Both rdim and ef are set. ef will be ignored." << std::endl;
+            }
+
             if (rdim != -1)
             {
                 if (myid == 0)
@@ -608,10 +614,10 @@ int main(int argc, char *argv[])
         w_gf.Save(ee_ofs);
     }
 
-    // 13. Calculate the DMD modes.
-    if (myid == 0 && rdim != -1 && ef != -1)
+    // 13. Predict using DMD.
+    if (myid == 0)
     {
-        std::cout << "Both rdim and ef are set. ef will be ignored." << std::endl;
+        std::cout << "Predicting position and velocity using DMD" << std::endl;
     }
 
     Vector true_solution_x(x_gf.GetTrueVector().Size());
@@ -620,14 +626,6 @@ int main(int argc, char *argv[])
     Vector true_solution_v(v_gf.GetTrueVector().Size());
     true_solution_v = v_gf.GetTrueVector();
 
-    dmd_prediction_timer.Start();
-
-    // 14. Predict the state at t_final using DMD.
-    if (myid == 0)
-    {
-        std::cout << "Predicting position and velocity using DMD" << std::endl;
-    }
-
     curr_window = 0;
     CAROM::Vector* result_x = dmd_x[curr_window]->predict(ts[0]);
     CAROM::Vector* result_v = dmd_v[curr_window]->predict(ts[0]);
@@ -687,12 +685,12 @@ int main(int argc, char *argv[])
         }
     }
 
-    dmd_prediction_timer.Stop();
-
+    dmd_prediction_timer.Start();
     result_x = dmd_x[curr_window]->predict(t_final);
     result_v = dmd_v[curr_window]->predict(t_final);
+    dmd_prediction_timer.Stop();
 
-    // 15. Calculate the relative error between the DMD final solution and the true solution.
+    // 14. Calculate the relative error between the DMD final solution and the true solution.
     Vector dmd_solution_x(result_x->getData(), result_x->dim());
     Vector diff_x(true_solution_x.Size());
     subtract(dmd_solution_x, true_solution_x, diff_x);
@@ -722,7 +720,7 @@ int main(int argc, char *argv[])
                dmd_prediction_timer.RealTime());
     }
 
-    // 16. Free the used memory.
+    // 15. Free the used memory.
     delete ode_solver;
     delete pmesh;
     delete result_x;
diff --git a/examples/dmd/wave_equation.cpp b/examples/dmd/wave_equation.cpp
index 7bc6ae3fe..d59c06b83 100644
--- a/examples/dmd/wave_equation.cpp
+++ b/examples/dmd/wave_equation.cpp
@@ -525,8 +525,7 @@ int main(int argc, char *argv[])
         dudt_gf.Save(osol);
     }
 
-    // 10. Predict the state at t_final using DMD.
-    dmd_prediction_timer.Start();
+    // 10. Predict using DMD.
     cout << "Predicting temperature using DMD" << endl;
     CAROM::Vector* result_u = nullptr;
     VisItDataCollection dmd_visit_dc("DMD_Wave_Equation", mesh);
@@ -564,8 +563,9 @@ int main(int argc, char *argv[])
             }
         }
     }
-    dmd_prediction_timer.Stop();
+    dmd_prediction_timer.Start();
     result_u = dmd_u[curr_window]->predict(t_final);
+    dmd_prediction_timer.Stop();
 
     // 11. Calculate the relative error between the DMD final solution and the true solution.
     Vector dmd_solution_u(result_u->getData(), result_u->dim());

From ffe333ead70167b5c643ce9f446d6ca78f55652b Mon Sep 17 00:00:00 2001
From: Siu Wun Cheung <cheung26@llnl.gov>
Date: Mon, 4 Dec 2023 18:58:53 -0800
Subject: [PATCH 03/16] Move final summary for basis generator into library

---
 examples/prom/mixed_nonlinear_diffusion.cpp   | 51 +-----------------
 .../prom/nonlinear_elasticity_global_rom.cpp  | 52 +------------------
 lib/linalg/BasisGenerator.cpp                 | 51 ++++++++++++++++++
 lib/linalg/BasisGenerator.h                   | 15 ++++++
 4 files changed, 69 insertions(+), 100 deletions(-)

diff --git a/examples/prom/mixed_nonlinear_diffusion.cpp b/examples/prom/mixed_nonlinear_diffusion.cpp
index 8b6f7916f..970bef672 100644
--- a/examples/prom/mixed_nonlinear_diffusion.cpp
+++ b/examples/prom/mixed_nonlinear_diffusion.cpp
@@ -427,54 +427,6 @@ CAROM::Matrix* GetFirstColumns(const int N, const CAROM::Matrix* A)
 }
 
 // TODO: move this to the library?
-void BasisGeneratorFinalSummary(CAROM::BasisGenerator* bg,
-                                const double energyFraction, int & cutoff, const std::string cutoffOutputPath)
-{
-    const int rom_dim = bg->getSpatialBasis()->numColumns();
-    const CAROM::Vector* sing_vals = bg->getSingularValues();
-
-    MFEM_VERIFY(rom_dim <= sing_vals->dim(), "");
-
-    double sum = 0.0;
-    for (int sv = 0; sv < sing_vals->dim(); ++sv) {
-        sum += (*sing_vals)(sv);
-    }
-
-    vector<double> energy_fractions = {0.9999, 0.999, 0.99, 0.9};
-    bool reached_cutoff = false;
-
-    ofstream outfile(cutoffOutputPath);
-
-    double partialSum = 0.0;
-    for (int sv = 0; sv < sing_vals->dim(); ++sv) {
-        partialSum += (*sing_vals)(sv);
-        for (int i = energy_fractions.size() - 1; i >= 0; i--)
-        {
-            if (partialSum / sum > energy_fractions[i])
-            {
-                outfile << "For energy fraction: " << energy_fractions[i] << ", take first "
-                        << sv+1 << " of " << sing_vals->dim() << " basis vectors" << endl;
-                energy_fractions.pop_back();
-            }
-            else
-            {
-                break;
-            }
-        }
-
-        if (!reached_cutoff && partialSum / sum > energyFraction)
-        {
-            cutoff = sv+1;
-            reached_cutoff = true;
-        }
-    }
-
-    if (!reached_cutoff) cutoff = sing_vals->dim();
-    outfile << "Take first " << cutoff << " of " << sing_vals->dim() <<
-            " basis vectors" << endl;
-    outfile.close();
-}
-
 void MergeBasis(const int dimFOM, const int nparam, const int max_num_snapshots,
                 std::string name)
 {
@@ -496,9 +448,10 @@ void MergeBasis(const int dimFOM, const int nparam, const int max_num_snapshots,
     generator.endSamples(); // save the merged basis file
 
     int cutoff = 0;
-    BasisGeneratorFinalSummary(&generator, 0.9999, cutoff, "mergedSV_" + name);
+    generator.FinalSummary(0.9999, cutoff, "mergedSV_" + name);
 }
 
+// TODO: move this to the library?
 const CAROM::Matrix* GetSnapshotMatrix(const int dimFOM, const int nparam,
                                        const int max_num_snapshots, std::string name)
 {
diff --git a/examples/prom/nonlinear_elasticity_global_rom.cpp b/examples/prom/nonlinear_elasticity_global_rom.cpp
index 984f1624d..40018ad3f 100644
--- a/examples/prom/nonlinear_elasticity_global_rom.cpp
+++ b/examples/prom/nonlinear_elasticity_global_rom.cpp
@@ -273,55 +273,6 @@ CAROM::Matrix* GetFirstColumns(const int N, const CAROM::Matrix* A)
 }
 
 // TODO: move this to the library?
-void BasisGeneratorFinalSummary(CAROM::BasisGenerator* bg,
-                                const double energyFraction, int& cutoff,
-                                const std::string cutoffOutputPath)
-{
-    const int rom_dim = bg->getSpatialBasis()->numColumns();
-    const CAROM::Vector* sing_vals = bg->getSingularValues();
-
-    MFEM_VERIFY(rom_dim <= sing_vals->dim(), "");
-
-    double sum = 0.0;
-    for (int sv = 0; sv < sing_vals->dim(); ++sv) {
-        sum += (*sing_vals)(sv);
-    }
-
-    vector<double> energy_fractions = { 0.9999999, 0.999999, 0.99999, 0.9999, 0.999, 0.99, 0.9 };
-    bool reached_cutoff = false;
-
-    ofstream outfile(cutoffOutputPath);
-
-    double partialSum = 0.0;
-    for (int sv = 0; sv < sing_vals->dim(); ++sv) {
-        partialSum += (*sing_vals)(sv);
-        for (int i = energy_fractions.size() - 1; i >= 0; i--)
-        {
-            if (partialSum / sum > energy_fractions[i])
-            {
-                outfile << "For energy fraction: " << energy_fractions[i] << ", take first "
-                        << sv + 1 << " of " << sing_vals->dim() << " basis vectors" << endl;
-                energy_fractions.pop_back();
-            }
-            else
-            {
-                break;
-            }
-        }
-
-        if (!reached_cutoff && partialSum / sum > energyFraction)
-        {
-            cutoff = sv + 1;
-            reached_cutoff = true;
-        }
-    }
-
-    if (!reached_cutoff) cutoff = sing_vals->dim();
-    outfile << "Take first " << cutoff << " of " << sing_vals->dim() <<
-            " basis vectors" << endl;
-    outfile.close();
-}
-
 void MergeBasis(const int dimFOM, const int nparam, const int max_num_snapshots,
                 std::string name)
 {
@@ -343,8 +294,7 @@ void MergeBasis(const int dimFOM, const int nparam, const int max_num_snapshots,
     generator.endSamples(); // save the merged basis file
 
     int cutoff = 0;
-    BasisGeneratorFinalSummary(&generator, 0.9999999, cutoff,
-                               "mergedSV_" + name + ".txt");
+    generator.FinalSummary(0.9999999, cutoff, "mergedSV_" + name + ".txt");
 }
 
 // TODO: remove this by making online computation serial?
diff --git a/lib/linalg/BasisGenerator.cpp b/lib/linalg/BasisGenerator.cpp
index bfd46bbb7..166910582 100644
--- a/lib/linalg/BasisGenerator.cpp
+++ b/lib/linalg/BasisGenerator.cpp
@@ -310,6 +310,57 @@ BasisGenerator::resetDt(
     }
 }
 
+void 
+BasisGenerator::FinalSummary(
+    const double energyFraction,
+    int & cutoff,
+    const std::string cutoffOutputPath,
+    const int first_sv)
+{
+    const int rom_dim = getSpatialBasis()->numColumns();
+    const Vector* sing_vals = getSingularValues();
+
+    CAROM_VERIFY(rom_dim <= sing_vals->dim());
+
+    double sum = 0.0;
+    for (int sv = first_sv; sv < sing_vals->dim(); ++sv) {
+        sum += (*sing_vals)(sv);
+    }
+
+    std::vector<double> energy_fractions = {0.99999999, 0.9999999, 0.999999, 0.99999, 0.9999, 0.999, 0.99, 0.9};
+    cutoff = first_sv;
+    bool reached_cutoff = false;
+    double partialSum = 0.0;
+
+    std::ofstream outfile(cutoffOutputPath);
+    for (int sv = first_sv; sv < sing_vals->dim(); ++sv) {
+        partialSum += (*sing_vals)(sv);
+        for (int i = energy_fractions.size() - 1; i >= 0; i--)
+        {
+            if (partialSum / sum > energy_fractions[i])
+            {
+                outfile << "For energy fraction: " << energy_fractions[i] << ", take first "
+                        << sv+1 << " of " << sing_vals->dim() << " basis vectors" << std::endl;
+                energy_fractions.pop_back();
+            }
+            else
+            {
+                break;
+            }
+        }
+        if (!reached_cutoff && partialSum / sum > energyFraction)
+        {
+            cutoff = sv+1;
+            reached_cutoff = true;
+        }
+    }
+
+    if (!reached_cutoff) cutoff = sing_vals->dim();
+    outfile << "For energy fraction: " << energyFraction << ", take first "
+            << cutoff << " of " << sing_vals->dim() << " basis vectors" << std::endl;
+    outfile.close();
+}
+
 BasisGenerator::~BasisGenerator()
 {
     if (d_basis_writer) {
diff --git a/lib/linalg/BasisGenerator.h b/lib/linalg/BasisGenerator.h
index cbd5febcc..bc009e606 100644
--- a/lib/linalg/BasisGenerator.h
+++ b/lib/linalg/BasisGenerator.h
@@ -23,6 +23,7 @@
 #include "mpi.h"
 
 #include <cmath>
+#include <fstream>
 
 /* Use C++11 built-in shared pointers if available; else fallback to Boost. */
 #if __cplusplus >= 201103L
@@ -263,6 +264,20 @@ class BasisGenerator
         return d_svd->getNumSamples();
     }
 
+    /**
+     * @brief Prints the summary of recommended numbers of basis vectors. 
+     *
+     * @param[in] energyFraction   Energy Fraction.
+     * @param[in] cutoff           Number of basis vectors selected.
+     * @param[in] cutoffOutputPath Path of the summary file.
+     * @param[in] first_sv         First singular vector in the calculaton of energy.
+     */
+    void FinalSummary(
+        const double energyFraction,
+        int & cutoff, 
+        const std::string cutoffOutputPath, 
+        const int first_sv = 0);
+
 protected:
     /**
      * @brief Writer of basis vectors.

From b8d115684c1e3d9b1880540507a48494cb97fedf Mon Sep 17 00:00:00 2001
From: Siu Wun Cheung <cheung26@llnl.gov>
Date: Mon, 4 Dec 2023 19:01:22 -0800
Subject: [PATCH 04/16] Stylize

---
 examples/prom/dg_advection_global_rom.cpp | 2 +-
 lib/linalg/BasisGenerator.cpp             | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/examples/prom/dg_advection_global_rom.cpp b/examples/prom/dg_advection_global_rom.cpp
index 5a24e3c3e..1fa9f8b70 100644
--- a/examples/prom/dg_advection_global_rom.cpp
+++ b/examples/prom/dg_advection_global_rom.cpp
@@ -21,7 +21,7 @@
 //
 // Output:
 //  Relative l2 error of ROM solution 0.0005641839849343575
-// 
+//
 // =================================================================================
 //
 // Sample runs and results for global ROM:
diff --git a/lib/linalg/BasisGenerator.cpp b/lib/linalg/BasisGenerator.cpp
index 166910582..697b975a6 100644
--- a/lib/linalg/BasisGenerator.cpp
+++ b/lib/linalg/BasisGenerator.cpp
@@ -310,7 +310,7 @@ BasisGenerator::resetDt(
     }
 }
 
-void 
+void
 BasisGenerator::FinalSummary(
     const double energyFraction,
     int & cutoff,

From c52cd4f2c6be567b6c92f17c8f0f1d6cd1079f1e Mon Sep 17 00:00:00 2001
From: Siu Wun Cheung <cheung26@llnl.gov>
Date: Thu, 7 Dec 2023 10:10:51 -0800
Subject: [PATCH 05/16] Add finalSummary to combine_samples

---
 examples/misc/combine_samples.cpp             |  3 +++
 examples/prom/mixed_nonlinear_diffusion.cpp   |  2 +-
 .../prom/nonlinear_elasticity_global_rom.cpp  |  2 +-
 lib/linalg/BasisGenerator.cpp                 | 27 ++++++++++++++-----
 lib/linalg/BasisGenerator.h                   |  4 +--
 5 files changed, 27 insertions(+), 11 deletions(-)

diff --git a/examples/misc/combine_samples.cpp b/examples/misc/combine_samples.cpp
index 4b083e807..9444bbd24 100644
--- a/examples/misc/combine_samples.cpp
+++ b/examples/misc/combine_samples.cpp
@@ -127,12 +127,14 @@ int main(int argc, char* argv[])
                                std::endl;
     static_basis_generator->writeSnapshot();
 
+    int rdim;
     if (!subtract_mean && !subtract_offset) {
         /*-- Compute SVD and save file --*/
         if (rank==0) std::cout << "Computing SVD" << std::endl;
         int rom_dim = static_basis_generator->getSpatialBasis()->numColumns();
         if (rank==0) std::cout << "U ROM Dimension: " << rom_dim << std::endl;
         static_basis_generator->endSamples();
+        static_basis_generator->finalSummary(0.99999999, rdim);
     }
     else {
         /*-- load data from hdf5 file to find the mean and subtract it --*/
@@ -188,6 +190,7 @@ int main(int argc, char* argv[])
         int rom_dim = static_basis_generator2->getSpatialBasis()->numColumns();
         if (rank==0) std::cout << "U ROM Dimension: " << rom_dim << std::endl;
         static_basis_generator2->endSamples();
+        static_basis_generator2->finalSummary(0.99999999, rdim);
 
         static_basis_generator2 = nullptr;
     }
diff --git a/examples/prom/mixed_nonlinear_diffusion.cpp b/examples/prom/mixed_nonlinear_diffusion.cpp
index 970bef672..e73c39b29 100644
--- a/examples/prom/mixed_nonlinear_diffusion.cpp
+++ b/examples/prom/mixed_nonlinear_diffusion.cpp
@@ -448,7 +448,7 @@ void MergeBasis(const int dimFOM, const int nparam, const int max_num_snapshots,
     generator.endSamples(); // save the merged basis file
 
     int cutoff = 0;
-    generator.FinalSummary(0.9999, cutoff, "mergedSV_" + name);
+    generator.finalSummary(0.9999, cutoff, "mergedSV_" + name);
 }
 
 // TODO: move this to the library?
diff --git a/examples/prom/nonlinear_elasticity_global_rom.cpp b/examples/prom/nonlinear_elasticity_global_rom.cpp
index 40018ad3f..9e460d6c5 100644
--- a/examples/prom/nonlinear_elasticity_global_rom.cpp
+++ b/examples/prom/nonlinear_elasticity_global_rom.cpp
@@ -294,7 +294,7 @@ void MergeBasis(const int dimFOM, const int nparam, const int max_num_snapshots,
     generator.endSamples(); // save the merged basis file
 
     int cutoff = 0;
-    generator.FinalSummary(0.9999999, cutoff, "mergedSV_" + name + ".txt");
+    generator.finalSummary(0.9999999, cutoff, "mergedSV_" + name + ".txt");
 }
 
 // TODO: remove this by making online computation serial?
diff --git a/lib/linalg/BasisGenerator.cpp b/lib/linalg/BasisGenerator.cpp
index 697b975a6..fa13c7a64 100644
--- a/lib/linalg/BasisGenerator.cpp
+++ b/lib/linalg/BasisGenerator.cpp
@@ -21,6 +21,8 @@
 #include "svd/IncrementalSVDFastUpdate.h"
 #include "svd/IncrementalSVDBrand.h"
 
+#include <iomanip>
+
 namespace CAROM {
 
 BasisGenerator::BasisGenerator(
@@ -311,7 +313,7 @@ BasisGenerator::resetDt(
 }
 
 void
-BasisGenerator::FinalSummary(
+BasisGenerator::finalSummary(
     const double energyFraction,
     int & cutoff,
     const std::string cutoffOutputPath,
@@ -327,21 +329,31 @@ BasisGenerator::FinalSummary(
         sum += (*sing_vals)(sv);
     }
 
-    std::vector<double> energy_fractions = {0.99999999, 0.9999999, 0.999999, 0.99999, 0.9999, 0.999, 0.99, 0.9};
+    int p = std::floor(-std::log10(1.0 - energyFraction));
+    std::vector<double> energy_fractions(p);
+
+    for (int i = 0; i < p; ++i) {
+        energy_fractions[i] = 1 - std::pow(10, -1 - i);
+    }
+
     cutoff = first_sv;
     bool reached_cutoff = false;
     double partialSum = 0.0;
+    int count = 0;
 
     std::ofstream outfile(cutoffOutputPath);
+
     for (int sv = first_sv; sv < sing_vals->dim(); ++sv) {
         partialSum += (*sing_vals)(sv);
-        for (int i = energy_fractions.size() - 1; i >= 0; i--)
+        for (int i = count; i < p; ++i)
         {
-            if (partialSum / sum > energy_fractions[i])
+            if (partialSum / sum > 1.0 - std::pow(10, -1 - i))
             {
-                outfile << "For energy fraction: " << energy_fractions[i] << ", take first "
-                        << sv+1 << " of " << sing_vals->dim() << " basis vectors" << std::endl;
-                energy_fractions.pop_back();
+                outfile << "For energy fraction: 0.";
+                for (int j = 0; j < i+1; ++j) outfile << "9";
+                outfile << ", take first " << sv+1 << " of " << sing_vals->dim() <<
+                        " basis vectors" << std::endl;
+                count += 1;
             }
             else
             {
@@ -356,6 +368,7 @@ BasisGenerator::FinalSummary(
     }
 
     if (!reached_cutoff) cutoff = sing_vals->dim();
+    outfile << std::fixed << std::setprecision(p+1);
     outfile << "For energy fraction: " << energyFraction << ", take first "
             << cutoff << " of " << sing_vals->dim() << " basis vectors" << std::endl;
     outfile.close();
diff --git a/lib/linalg/BasisGenerator.h b/lib/linalg/BasisGenerator.h
index bc009e606..c9281d060 100644
--- a/lib/linalg/BasisGenerator.h
+++ b/lib/linalg/BasisGenerator.h
@@ -272,10 +272,10 @@ class BasisGenerator
      * @param[in] cutoffOutputPath Path of the summary file.
      * @param[in] first_sv         First singular vector in the calculaton of energy.
      */
-    void FinalSummary(
+    void finalSummary(
         const double energyFraction,
         int & cutoff, 
-        const std::string cutoffOutputPath, 
+        const std::string cutoffOutputPath = "bg_summary.txt", 
         const int first_sv = 0);
 
 protected:

From 0505fbba815be58344f287162e8136b6ba44d512 Mon Sep 17 00:00:00 2001
From: Siu Wun Cheung <cheung26@llnl.gov>
Date: Sat, 16 Dec 2023 20:59:44 -0800
Subject: [PATCH 06/16] Enable capabilities in combine_samples.cpp

---
 examples/misc/combine_samples.cpp | 29 +++++++++++++++----
 lib/linalg/BasisGenerator.cpp     | 48 ++++++++++++++++++++++---------
 lib/linalg/BasisGenerator.h       | 25 ++++++++++++++--
 3 files changed, 81 insertions(+), 21 deletions(-)

diff --git a/examples/misc/combine_samples.cpp b/examples/misc/combine_samples.cpp
index 9444bbd24..8ee32d9e5 100644
--- a/examples/misc/combine_samples.cpp
+++ b/examples/misc/combine_samples.cpp
@@ -53,15 +53,19 @@ int main(int argc, char* argv[])
     std::vector<std::string> sample_names;
     int snaps = 0;
     int dim   = 0;
+    int col_min = 1;
+    int col_max = 1e9;
     bool subtract_mean = false;
     bool subtract_offset = false;
+    std::string generator_filename = "total";
     std::string kind = "snapshot";
     std::string offset_file;
 
     bool offset_arg = false;
 
     if (argc >= 2) {
-        for (int i = 1; i < argc; i++) {
+        int i = 1;
+        while (i < argc) {
             if (!strcmp(argv[i], "basis") || !strcmp(argv[i], "-b")) {
                 if (rank==0) std::cout << "Argument " << i << " identified as basis or -b" <<
                                            std::endl;
@@ -80,9 +84,25 @@ int main(int argc, char* argv[])
                 if (rank==0) std::cout << "Will subtract mean" << std::endl;
                 subtract_mean = true;
             }
+            else if (!strcmp(argv[i], "file") || !strcmp(argv[i], "-f")) {
+                i += 1;
+                generator_filename = argv[i];
+                if (rank==0) std::cout << "Output prefix = " << generator_filename << std::endl;
+            }
+            else if (!strcmp(argv[i], "col_min") || !strcmp(argv[i], "-cmin")) {
+                i += 1;
+                col_min = std::stoi(argv[i]);
+                if (rank==0) std::cout << "First column to read = " << col_min << std::endl;
+            }
+            else if (!strcmp(argv[i], "col_max") || !strcmp(argv[i], "-cmax")) {
+                i += 1;
+                col_max = std::stoi(argv[i]);
+                if (rank==0) std::cout << "Last column to read = " << col_max << std::endl;
+            }
             else {
                 sample_names.push_back(argv[i]);
             }
+            i += 1;
         }
     }
     else {
@@ -112,7 +132,6 @@ int main(int argc, char* argv[])
     CAROM_VERIFY((snaps > 0) && (dim > 0));
 
     /*-- Load data from input files --*/
-    std::string generator_filename = "total";
     std::unique_ptr<CAROM::BasisGenerator> static_basis_generator;
     static_basis_generator.reset(new CAROM::BasisGenerator(
                                      CAROM::Options(dim, snaps).setMaxBasisDimension(snaps), false,
@@ -120,7 +139,7 @@ int main(int argc, char* argv[])
 
     if (rank==0) std::cout << "Loading data from " << kind << std::endl;
     for(const auto& sample_name: sample_names) {
-        static_basis_generator->loadSamples(sample_name, kind);
+        static_basis_generator->loadSampleRange(sample_name, kind, col_min, col_max);
     }
 
     if (rank==0) std::cout << "Saving data uploaded as a snapshot matrix" <<
@@ -134,7 +153,7 @@ int main(int argc, char* argv[])
         int rom_dim = static_basis_generator->getSpatialBasis()->numColumns();
         if (rank==0) std::cout << "U ROM Dimension: " << rom_dim << std::endl;
         static_basis_generator->endSamples();
-        static_basis_generator->finalSummary(0.99999999, rdim);
+        if (rank==0) static_basis_generator->finalSummary(0.99999999, rdim);
     }
     else {
         /*-- load data from hdf5 file to find the mean and subtract it --*/
@@ -190,7 +209,7 @@ int main(int argc, char* argv[])
         int rom_dim = static_basis_generator2->getSpatialBasis()->numColumns();
         if (rank==0) std::cout << "U ROM Dimension: " << rom_dim << std::endl;
         static_basis_generator2->endSamples();
-        static_basis_generator2->finalSummary(0.99999999, rdim);
+        if (rank==0) static_basis_generator2->finalSummary(0.99999999, rdim);
 
         static_basis_generator2 = nullptr;
     }
diff --git a/lib/linalg/BasisGenerator.cpp b/lib/linalg/BasisGenerator.cpp
index fa13c7a64..ed92363e9 100644
--- a/lib/linalg/BasisGenerator.cpp
+++ b/lib/linalg/BasisGenerator.cpp
@@ -163,9 +163,10 @@ BasisGenerator::takeSample(
 }
 
 void
-BasisGenerator::loadSamples(const std::string& base_file_name,
+BasisGenerator::loadSampleRange(const std::string& base_file_name,
                             const std::string& kind,
-                            int cut_off,
+                            int col_min,
+                            int col_max,
                             Database::formats db_format)
 {
     CAROM_ASSERT(!base_file_name.empty());
@@ -188,10 +189,12 @@ BasisGenerator::loadSamples(const std::string& base_file_name,
 
     int num_rows = mat->numRows();
     int num_cols = mat->numColumns();
-    int max_cols = num_cols;
-    if (cut_off < num_cols) max_cols = cut_off;
+    if (col_min < 1) col_min = 1;
+    if (col_max > num_cols) col_max = num_cols;
+
+    CAROM_VERIFY(col_max >= col_min);
 
-    for (int j = 0; j < max_cols; j++) {
+    for (int j = col_min-1; j < col_max; j++) {
         double* u_in = new double[num_rows];
         for (int i = 0; i < num_rows; i++) {
             if (kind == "basis") {
@@ -206,6 +209,15 @@ BasisGenerator::loadSamples(const std::string& base_file_name,
     }
 }
 
+void
+BasisGenerator::loadSamples(const std::string& base_file_name,
+                            const std::string& kind,
+                            int cutoff,
+                            Database::formats db_format)
+{
+    loadSampleRange(base_file_name, kind, 1, cutoff, db_format);
+}
+
 double
 BasisGenerator::computeNextSampleTime(
     double* u_in,
@@ -341,7 +353,13 @@ BasisGenerator::finalSummary(
     double partialSum = 0.0;
     int count = 0;
 
-    std::ofstream outfile(cutoffOutputPath);
+    std::ostream* output_stream;
+
+    if (!cutoffOutputPath.empty()) {
+        output_stream = new std::ofstream(cutoffOutputPath);
+    } else {
+        output_stream = &std::cout;
+    }
 
     for (int sv = first_sv; sv < sing_vals->dim(); ++sv) {
         partialSum += (*sing_vals)(sv);
@@ -349,10 +367,10 @@ BasisGenerator::finalSummary(
         {
             if (partialSum / sum > 1.0 - std::pow(10, -1 - i))
             {
-                outfile << "For energy fraction: 0.";
-                for (int j = 0; j < i+1; ++j) outfile << "9";
-                outfile << ", take first " << sv+1 << " of " << sing_vals->dim() <<
-                        " basis vectors" << std::endl;
+                *output_stream << "For energy fraction: 0.";
+                for (int j = 0; j < i+1; ++j) *output_stream << "9";
+                *output_stream << ", take first " << sv+1 << " of " 
+                               << sing_vals->dim() << " basis vectors" << std::endl;
                 count += 1;
             }
             else
@@ -368,10 +386,14 @@ BasisGenerator::finalSummary(
     }
 
     if (!reached_cutoff) cutoff = sing_vals->dim();
-    outfile << std::fixed << std::setprecision(p+1);
-    outfile << "For energy fraction: " << energyFraction << ", take first "
+    *output_stream << std::fixed << std::setprecision(p+1);
+    *output_stream << "For energy fraction: " << energyFraction << ", take first "
             << cutoff << " of " << sing_vals->dim() << " basis vectors" << std::endl;
-    outfile.close();
+
+    if (!cutoffOutputPath.empty()) {
+        static_cast<std::ofstream*>(output_stream)->close();
+        delete output_stream;
+    }
 }
 
 BasisGenerator::~BasisGenerator()
diff --git a/lib/linalg/BasisGenerator.h b/lib/linalg/BasisGenerator.h
index c9281d060..c8e7af7a4 100644
--- a/lib/linalg/BasisGenerator.h
+++ b/lib/linalg/BasisGenerator.h
@@ -143,6 +143,25 @@ class BasisGenerator
         }
     }
 
+    /**
+     * @brief Load previously saved sample (basis or state) 
+     *        within a column range.
+     *
+     * @param[in] base_file_name The base part of the name of the files
+     *                           holding the basis / snapshot vectors.
+     * @param[in] kind A string equal to "basis" or "snapshot", representing
+     *                 which kind of data to load.
+     * @param[in] col_min The first basis or snapshot to read.
+     * @param[in] col_max The last basis or snapshot to read.
+     * @param[in] db_format Format of the file to read.
+     */
+    void
+    loadSampleRange(const std::string& base_file_name,
+                     const std::string& kind  = "basis",
+                     int col_min = 1,
+                     int col_max = 1e9,
+                     Database::formats db_format = Database::HDF5);
+
     /**
      * @brief Load previously saved sample (basis or state).
      *
@@ -150,13 +169,13 @@ class BasisGenerator
      *                           holding the basis / snapshot vectors.
      * @param[in] kind A string equal to "basis" or "snapshot", representing
      *                 which kind of data to load.
-     * @param[in] cut_off The maximum number of bases or snapshots to read.
+     * @param[in] cutoff The maximum number of bases or snapshots to read.
      * @param[in] db_format Format of the file to read.
      */
     void
     loadSamples(const std::string& base_file_name,
                 const std::string& kind  = "basis",
-                int cut_off = 1e9,
+                int cutoff = 1e9,
                 Database::formats db_format = Database::HDF5);
 
     /**
@@ -275,7 +294,7 @@ class BasisGenerator
     void finalSummary(
         const double energyFraction,
         int & cutoff, 
-        const std::string cutoffOutputPath = "bg_summary.txt", 
+        const std::string cutoffOutputPath = "", 
         const int first_sv = 0);
 
 protected:

From bf6150cff7e868b2e464e0b75e9da65b239037b7 Mon Sep 17 00:00:00 2001
From: Siu Wun Cheung <cheung26@llnl.gov>
Date: Mon, 18 Dec 2023 13:15:28 -0800
Subject: [PATCH 07/16] Astyle

---
 lib/linalg/BasisGenerator.cpp | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/lib/linalg/BasisGenerator.cpp b/lib/linalg/BasisGenerator.cpp
index ed92363e9..d978cbac5 100644
--- a/lib/linalg/BasisGenerator.cpp
+++ b/lib/linalg/BasisGenerator.cpp
@@ -164,10 +164,10 @@ BasisGenerator::takeSample(
 
 void
 BasisGenerator::loadSampleRange(const std::string& base_file_name,
-                            const std::string& kind,
-                            int col_min,
-                            int col_max,
-                            Database::formats db_format)
+                                const std::string& kind,
+                                int col_min,
+                                int col_max,
+                                Database::formats db_format)
 {
     CAROM_ASSERT(!base_file_name.empty());
     CAROM_VERIFY(kind == "basis" || kind == "snapshot");
@@ -369,7 +369,7 @@ BasisGenerator::finalSummary(
             {
                 *output_stream << "For energy fraction: 0.";
                 for (int j = 0; j < i+1; ++j) *output_stream << "9";
-                *output_stream << ", take first " << sv+1 << " of " 
+                *output_stream << ", take first " << sv+1 << " of "
                                << sing_vals->dim() << " basis vectors" << std::endl;
                 count += 1;
             }
@@ -388,7 +388,7 @@ BasisGenerator::finalSummary(
     if (!reached_cutoff) cutoff = sing_vals->dim();
     *output_stream << std::fixed << std::setprecision(p+1);
     *output_stream << "For energy fraction: " << energyFraction << ", take first "
-            << cutoff << " of " << sing_vals->dim() << " basis vectors" << std::endl;
+                   << cutoff << " of " << sing_vals->dim() << " basis vectors" << std::endl;
 
     if (!cutoffOutputPath.empty()) {
         static_cast<std::ofstream*>(output_stream)->close();

From e2872d82870ca6effef4384241b98a0c2a2c8943 Mon Sep 17 00:00:00 2001
From: Siu Wun Cheung <cheung26@llnl.gov>
Date: Mon, 18 Dec 2023 14:04:11 -0800
Subject: [PATCH 08/16] Remove spaces

---
 lib/linalg/BasisGenerator.h | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/lib/linalg/BasisGenerator.h b/lib/linalg/BasisGenerator.h
index c8e7af7a4..5f078471e 100644
--- a/lib/linalg/BasisGenerator.h
+++ b/lib/linalg/BasisGenerator.h
@@ -157,10 +157,10 @@ class BasisGenerator
      */
     void
     loadSampleRange(const std::string& base_file_name,
-                     const std::string& kind  = "basis",
-                     int col_min = 1,
-                     int col_max = 1e9,
-                     Database::formats db_format = Database::HDF5);
+                    const std::string& kind  = "basis",
+                    int col_min = 1,
+                    int col_max = 1e9,
+                    Database::formats db_format = Database::HDF5);
 
     /**
      * @brief Load previously saved sample (basis or state).

From b57ec2be3bcd8d61d07e437540151aa2d28d4a66 Mon Sep 17 00:00:00 2001
From: Siu Wun Cheung <cheung26@llnl.gov>
Date: Thu, 15 Feb 2024 09:23:26 -0800
Subject: [PATCH 09/16] Run astyle

---
 lib/linalg/BasisGenerator.h | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/lib/linalg/BasisGenerator.h b/lib/linalg/BasisGenerator.h
index d0179f611..6baa7ebc5 100644
--- a/lib/linalg/BasisGenerator.h
+++ b/lib/linalg/BasisGenerator.h
@@ -144,7 +144,7 @@ class BasisGenerator
     }
 
     /**
-     * @brief Load previously saved sample (basis or state) 
+     * @brief Load previously saved sample (basis or state)
      *        within a column range.
      *
      * @param[in] base_file_name The base part of the name of the files
@@ -284,7 +284,7 @@ class BasisGenerator
     }
 
     /**
-     * @brief Prints the summary of recommended numbers of basis vectors. 
+     * @brief Prints the summary of recommended numbers of basis vectors.
      *
      * @param[in] energyFraction   Energy Fraction.
      * @param[in] cutoff           Number of basis vectors selected.
@@ -293,8 +293,8 @@ class BasisGenerator
      */
     void finalSummary(
         const double energyFraction,
-        int & cutoff, 
-        const std::string cutoffOutputPath = "", 
+        int & cutoff,
+        const std::string cutoffOutputPath = "",
         const int first_sv = 0);
 
 protected:

From ff4baf0cf58187173c1f0e69a83a1e4453fe8d67 Mon Sep 17 00:00:00 2001
From: Siu Wun Cheung <cheung26@llnl.gov>
Date: Thu, 7 Mar 2024 08:34:23 -0800
Subject: [PATCH 10/16] Change to 1-base

---
 examples/misc/combine_samples.cpp | 2 +-
 lib/linalg/BasisGenerator.cpp     | 9 +++++----
 lib/linalg/BasisGenerator.h       | 3 +--
 3 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/examples/misc/combine_samples.cpp b/examples/misc/combine_samples.cpp
index dc726acee..9a2ae2f3e 100644
--- a/examples/misc/combine_samples.cpp
+++ b/examples/misc/combine_samples.cpp
@@ -139,7 +139,7 @@ int main(int argc, char* argv[])
 
     if (rank==0) std::cout << "Loading data from " << kind << std::endl;
     for(const auto& sample_name: sample_names) {
-        static_basis_generator->loadSampleRange(sample_name, kind, col_min, col_max);
+        static_basis_generator->loadSampleRange(sample_name, kind, col_min-1, col_max-1);
     }
 
     if (rank==0) std::cout << "Saving data uploaded as a snapshot matrix" <<
diff --git a/lib/linalg/BasisGenerator.cpp b/lib/linalg/BasisGenerator.cpp
index 9a5e4fa12..c005132ca 100644
--- a/lib/linalg/BasisGenerator.cpp
+++ b/lib/linalg/BasisGenerator.cpp
@@ -22,6 +22,7 @@
 #include "svd/IncrementalSVDBrand.h"
 
 #include <iomanip>
+#include <fstream>
 
 namespace CAROM {
 
@@ -189,12 +190,12 @@ BasisGenerator::loadSampleRange(const std::string& base_file_name,
 
     int num_rows = mat->numRows();
     int num_cols = mat->numColumns();
-    if (col_min < 1) col_min = 1;
-    if (col_max > num_cols) col_max = num_cols;
+    if (col_min < 0) col_min = 0;
+    if (col_max > num_cols-1) col_max = num_cols-1;
 
     CAROM_VERIFY(col_max >= col_min);
 
-    for (int j = col_min-1; j < col_max; j++) {
+    for (int j = col_min; j <= col_max; j++) {
         double* u_in = new double[num_rows];
         for (int i = 0; i < num_rows; i++) {
             if (kind == "basis") {
@@ -215,7 +216,7 @@ BasisGenerator::loadSamples(const std::string& base_file_name,
                             int cutoff,
                             Database::formats db_format)
 {
-    loadSampleRange(base_file_name, kind, 1, cutoff, db_format);
+    loadSampleRange(base_file_name, kind, 0, cutoff-1, db_format);
 }
 
 double
diff --git a/lib/linalg/BasisGenerator.h b/lib/linalg/BasisGenerator.h
index 6baa7ebc5..4fbcfb1e6 100644
--- a/lib/linalg/BasisGenerator.h
+++ b/lib/linalg/BasisGenerator.h
@@ -23,7 +23,6 @@
 #include "mpi.h"
 
 #include <cmath>
-#include <fstream>
 
 /* Use C++11 built-in shared pointers if available; else fallback to Boost. */
 #if __cplusplus >= 201103L
@@ -158,7 +157,7 @@ class BasisGenerator
     void
     loadSampleRange(const std::string& base_file_name,
                     const std::string& kind  = "basis",
-                    int col_min = 1,
+                    int col_min = 0,
                     int col_max = 1e9,
                     Database::formats db_format = Database::HDF5);
 

From 0602769cd7352545babdc70e9596d90d42c0550a Mon Sep 17 00:00:00 2001
From: Siu Wun Cheung <cheung26@llnl.gov>
Date: Thu, 7 Mar 2024 08:35:57 -0800
Subject: [PATCH 11/16] Change comments

---
 lib/linalg/BasisGenerator.h | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/lib/linalg/BasisGenerator.h b/lib/linalg/BasisGenerator.h
index 4fbcfb1e6..749ce90c1 100644
--- a/lib/linalg/BasisGenerator.h
+++ b/lib/linalg/BasisGenerator.h
@@ -147,11 +147,11 @@ class BasisGenerator
      *        within a column range.
      *
      * @param[in] base_file_name The base part of the name of the files
-     *                           holding the basis / snapshot vectors.
+     *                           holding the basis/snapshot vectors.
      * @param[in] kind A string equal to "basis" or "snapshot", representing
      *                 which kind of data to load.
-     * @param[in] col_min The first basis or snapshot to read.
-     * @param[in] col_max The last basis or snapshot to read.
+     * @param[in] col_min The first basis/snapshot vector to read.
+     * @param[in] col_max The last basis/snapshot vector to read.
      * @param[in] db_format Format of the file to read.
      */
     void
@@ -165,10 +165,10 @@ class BasisGenerator
      * @brief Load previously saved sample (basis or state).
      *
      * @param[in] base_file_name The base part of the name of the files
-     *                           holding the basis / snapshot vectors.
+     *                           holding the basis/snapshot vectors.
      * @param[in] kind A string equal to "basis" or "snapshot", representing
      *                 which kind of data to load.
-     * @param[in] cutoff The maximum number of bases or snapshots to read.
+     * @param[in] cutoff The maximum number of basis/snapshot vectors to read.
      * @param[in] db_format Format of the file to read.
      */
     void

From ba33c97e1e981a721415291bdd7c8287e4d01f48 Mon Sep 17 00:00:00 2001
From: Siu Wun Cheung <cheung26@llnl.gov>
Date: Thu, 7 Mar 2024 08:51:46 -0800
Subject: [PATCH 12/16] Change to energy fraction threshold

---
 examples/misc/combine_samples.cpp                 |  4 ++--
 examples/prom/mixed_nonlinear_diffusion.cpp       |  2 +-
 examples/prom/nonlinear_elasticity_global_rom.cpp |  2 +-
 lib/linalg/BasisGenerator.cpp                     |  8 ++++----
 lib/linalg/BasisGenerator.h                       | 11 ++++++-----
 5 files changed, 14 insertions(+), 13 deletions(-)

diff --git a/examples/misc/combine_samples.cpp b/examples/misc/combine_samples.cpp
index 9a2ae2f3e..c2e2ef427 100644
--- a/examples/misc/combine_samples.cpp
+++ b/examples/misc/combine_samples.cpp
@@ -153,7 +153,7 @@ int main(int argc, char* argv[])
         int rom_dim = static_basis_generator->getSpatialBasis()->numColumns();
         if (rank==0) std::cout << "U ROM Dimension: " << rom_dim << std::endl;
         static_basis_generator->endSamples();
-        if (rank==0) static_basis_generator->finalSummary(0.99999999, rdim);
+        if (rank==0) static_basis_generator->finalSummary(1e-8, rdim);
     }
     else {
         /*-- load data from hdf5 file to find the mean and subtract it --*/
@@ -209,7 +209,7 @@ int main(int argc, char* argv[])
         int rom_dim = static_basis_generator2->getSpatialBasis()->numColumns();
         if (rank==0) std::cout << "U ROM Dimension: " << rom_dim << std::endl;
         static_basis_generator2->endSamples();
-        if (rank==0) static_basis_generator2->finalSummary(0.99999999, rdim);
+        if (rank==0) static_basis_generator2->finalSummary(1e-8, rdim);
 
         static_basis_generator2 = nullptr;
     }
diff --git a/examples/prom/mixed_nonlinear_diffusion.cpp b/examples/prom/mixed_nonlinear_diffusion.cpp
index 2079e7899..5d1e15f59 100644
--- a/examples/prom/mixed_nonlinear_diffusion.cpp
+++ b/examples/prom/mixed_nonlinear_diffusion.cpp
@@ -448,7 +448,7 @@ void MergeBasis(const int dimFOM, const int nparam, const int max_num_snapshots,
     generator.endSamples(); // save the merged basis file
 
     int cutoff = 0;
-    generator.finalSummary(0.9999, cutoff, "mergedSV_" + name);
+    generator.finalSummary(1e-4, cutoff, "mergedSV_" + name);
 }
 
 // TODO: move this to the library?
diff --git a/examples/prom/nonlinear_elasticity_global_rom.cpp b/examples/prom/nonlinear_elasticity_global_rom.cpp
index b79316317..911596035 100644
--- a/examples/prom/nonlinear_elasticity_global_rom.cpp
+++ b/examples/prom/nonlinear_elasticity_global_rom.cpp
@@ -328,7 +328,7 @@ void MergeBasis(const int dimFOM, const int nparam, const int max_num_snapshots,
     generator.endSamples(); // save the merged basis file
 
     int cutoff = 0;
-    generator.finalSummary(0.9999999, cutoff, "mergedSV_" + name + ".txt");
+    generator.finalSummary(1e-7, cutoff, "mergedSV_" + name + ".txt");
 }
 
 const CAROM::Matrix *GetSnapshotMatrix(const int dimFOM, const int nparam,
diff --git a/lib/linalg/BasisGenerator.cpp b/lib/linalg/BasisGenerator.cpp
index c005132ca..2dd581657 100644
--- a/lib/linalg/BasisGenerator.cpp
+++ b/lib/linalg/BasisGenerator.cpp
@@ -327,7 +327,7 @@ BasisGenerator::resetDt(
 
 void
 BasisGenerator::finalSummary(
-    const double energyFraction,
+    const double energyFractionThreshold,
     int & cutoff,
     const std::string cutoffOutputPath,
     const int first_sv)
@@ -342,7 +342,7 @@ BasisGenerator::finalSummary(
         sum += (*sing_vals)(sv);
     }
 
-    int p = std::floor(-std::log10(1.0 - energyFraction));
+    int p = std::floor(-std::log10(energyFractionThreshold));
     std::vector<double> energy_fractions(p);
 
     for (int i = 0; i < p; ++i) {
@@ -379,7 +379,7 @@ BasisGenerator::finalSummary(
                 break;
             }
         }
-        if (!reached_cutoff && partialSum / sum > energyFraction)
+        if (!reached_cutoff && partialSum / sum > 1.0 - energyFractionThreshold)
         {
             cutoff = sv+1;
             reached_cutoff = true;
@@ -388,7 +388,7 @@ BasisGenerator::finalSummary(
 
     if (!reached_cutoff) cutoff = sing_vals->dim();
     *output_stream << std::fixed << std::setprecision(p+1);
-    *output_stream << "For energy fraction: " << energyFraction << ", take first "
+    *output_stream << "For energy fraction: " << 1.0 - energyFractionThreshold << ", take first "
                    << cutoff << " of " << sing_vals->dim() << " basis vectors" << std::endl;
 
     if (!cutoffOutputPath.empty()) {
diff --git a/lib/linalg/BasisGenerator.h b/lib/linalg/BasisGenerator.h
index 749ce90c1..7eac2a077 100644
--- a/lib/linalg/BasisGenerator.h
+++ b/lib/linalg/BasisGenerator.h
@@ -285,13 +285,14 @@ class BasisGenerator
     /**
      * @brief Prints the summary of recommended numbers of basis vectors.
      *
-     * @param[in] energyFraction   Energy Fraction.
-     * @param[in] cutoff           Number of basis vectors selected.
-     * @param[in] cutoffOutputPath Path of the summary file.
-     * @param[in] first_sv         First singular vector in the calculaton of energy.
+     * @param[in] energyFractionThreshold   Energy Fraction threshold 
+     *                                      (difference of energy difference from 1.0).
+     * @param[in] cutoff                    Number of basis vectors selected.
+     * @param[in] cutoffOutputPath          Path of the summary file.
+     * @param[in] first_sv                  First singular vector in the calculaton of energy.
      */
     void finalSummary(
-        const double energyFraction,
+        const double energyFractionThreshold,
         int & cutoff,
         const std::string cutoffOutputPath = "",
         const int first_sv = 0);

From d774492525fe6208090a7c0c9184abcac61534f6 Mon Sep 17 00:00:00 2001
From: Siu Wun Cheung <cheung26@llnl.gov>
Date: Thu, 7 Mar 2024 08:54:35 -0800
Subject: [PATCH 13/16] Pass the string by reference

---
 lib/linalg/BasisGenerator.cpp | 2 +-
 lib/linalg/BasisGenerator.h   | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/linalg/BasisGenerator.cpp b/lib/linalg/BasisGenerator.cpp
index 2dd581657..ae8326deb 100644
--- a/lib/linalg/BasisGenerator.cpp
+++ b/lib/linalg/BasisGenerator.cpp
@@ -329,7 +329,7 @@ void
 BasisGenerator::finalSummary(
     const double energyFractionThreshold,
     int & cutoff,
-    const std::string cutoffOutputPath,
+    const std::string & cutoffOutputPath,
     const int first_sv)
 {
     const int rom_dim = getSpatialBasis()->numColumns();
diff --git a/lib/linalg/BasisGenerator.h b/lib/linalg/BasisGenerator.h
index 7eac2a077..202af25f5 100644
--- a/lib/linalg/BasisGenerator.h
+++ b/lib/linalg/BasisGenerator.h
@@ -294,7 +294,7 @@ class BasisGenerator
     void finalSummary(
         const double energyFractionThreshold,
         int & cutoff,
-        const std::string cutoffOutputPath = "",
+        const std::string & cutoffOutputPath = "",
         const int first_sv = 0);
 
 protected:

From 6d4f7e5d49121ac253f6b47204e4b1aa54e09305 Mon Sep 17 00:00:00 2001
From: Siu Wun Cheung <cheung26@llnl.gov>
Date: Thu, 7 Mar 2024 08:56:19 -0800
Subject: [PATCH 14/16] Astyle

---
 examples/misc/combine_samples.cpp | 3 ++-
 lib/linalg/BasisGenerator.cpp     | 3 ++-
 2 files changed, 4 insertions(+), 2 deletions(-)

diff --git a/examples/misc/combine_samples.cpp b/examples/misc/combine_samples.cpp
index c2e2ef427..8ab5f19e1 100644
--- a/examples/misc/combine_samples.cpp
+++ b/examples/misc/combine_samples.cpp
@@ -139,7 +139,8 @@ int main(int argc, char* argv[])
 
     if (rank==0) std::cout << "Loading data from " << kind << std::endl;
     for(const auto& sample_name: sample_names) {
-        static_basis_generator->loadSampleRange(sample_name, kind, col_min-1, col_max-1);
+        static_basis_generator->loadSampleRange(sample_name, kind, col_min-1,
+                                                col_max-1);
     }
 
     if (rank==0) std::cout << "Saving data uploaded as a snapshot matrix" <<
diff --git a/lib/linalg/BasisGenerator.cpp b/lib/linalg/BasisGenerator.cpp
index ae8326deb..c1a94a11b 100644
--- a/lib/linalg/BasisGenerator.cpp
+++ b/lib/linalg/BasisGenerator.cpp
@@ -388,7 +388,8 @@ BasisGenerator::finalSummary(
 
     if (!reached_cutoff) cutoff = sing_vals->dim();
     *output_stream << std::fixed << std::setprecision(p+1);
-    *output_stream << "For energy fraction: " << 1.0 - energyFractionThreshold << ", take first "
+    *output_stream << "For energy fraction: " << 1.0 - energyFractionThreshold <<
+                   ", take first "
                    << cutoff << " of " << sing_vals->dim() << " basis vectors" << std::endl;
 
     if (!cutoffOutputPath.empty()) {

From 7ba3a8f1851428a980a22cd57a98b47111c7ab9f Mon Sep 17 00:00:00 2001
From: Siu Wun Cheung <cheung26@llnl.gov>
Date: Sun, 10 Mar 2024 22:27:41 -0700
Subject: [PATCH 15/16] Modify brief

---
 lib/linalg/BasisGenerator.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/linalg/BasisGenerator.h b/lib/linalg/BasisGenerator.h
index 202af25f5..88a600b5f 100644
--- a/lib/linalg/BasisGenerator.h
+++ b/lib/linalg/BasisGenerator.h
@@ -286,7 +286,7 @@ class BasisGenerator
      * @brief Prints the summary of recommended numbers of basis vectors.
      *
      * @param[in] energyFractionThreshold   Energy Fraction threshold 
-     *                                      (difference of energy difference from 1.0).
+     *                                      (energy fraction = 1.0 - energyFractionThreshold).
      * @param[in] cutoff                    Number of basis vectors selected.
      * @param[in] cutoffOutputPath          Path of the summary file.
      * @param[in] first_sv                  First singular vector in the calculaton of energy.

From 751887af88769afb3c4dc3e808ef49176cd2d2cc Mon Sep 17 00:00:00 2001
From: Siu Wun Cheung <cheung26@llnl.gov>
Date: Mon, 11 Mar 2024 08:38:06 -0700
Subject: [PATCH 16/16] Run astyle

---
 lib/linalg/BasisGenerator.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/linalg/BasisGenerator.h b/lib/linalg/BasisGenerator.h
index 88a600b5f..2857db8d3 100644
--- a/lib/linalg/BasisGenerator.h
+++ b/lib/linalg/BasisGenerator.h
@@ -285,7 +285,7 @@ class BasisGenerator
     /**
      * @brief Prints the summary of recommended numbers of basis vectors.
      *
-     * @param[in] energyFractionThreshold   Energy Fraction threshold 
+     * @param[in] energyFractionThreshold   Energy Fraction threshold
      *                                      (energy fraction = 1.0 - energyFractionThreshold).
      * @param[in] cutoff                    Number of basis vectors selected.
      * @param[in] cutoffOutputPath          Path of the summary file.