Merge pull request #6 from eisenforschung/add_doc

Add doc

elaston/linear_elasticity/eshelby.py

@@ -5,8 +5,10 @@
 import numpy as np
 
 __author__ = "Sam Waseda"
-__copyright__ = "Copyright 2021, Max-Planck-Institut für Eisenforschung GmbH " \
-                "- Computational Materials Design (CM) Department"
+__copyright__ = (
+    "Copyright 2021, Max-Planck-Institut für Eisenforschung GmbH "
+    "- Computational Materials Design (CM) Department"
+)
 __version__ = "1.0"
 __maintainer__ = "Sam Waseda"
 __email__ = "[email protected]"
@@ -21,6 +23,7 @@ class Eshelby:
 
     All notations follow the original paper.
     """
+
     def __init__(self, elastic_tensor, burgers_vector):
         self.elastic_tensor = elastic_tensor
         self.burgers_vector = burgers_vector
@@ -33,17 +36,21 @@ def _get_pmat(self, x):
         return (
             self.elastic_tensor[:, 0, :, 0]
             + np.einsum(
-                '...,ij->...ij', x, self.elastic_tensor[:, 0, :, 1]+self.elastic_tensor[:, 1, :, 0]
+                "...,ij->...ij",
+                x,
+                self.elastic_tensor[:, 0, :, 1] + self.elastic_tensor[:, 1, :, 0],
             )
-            + np.einsum('...,ij->...ij', x**2, self.elastic_tensor[:, 1, :, 1])
+            + np.einsum("...,ij->...ij", x**2, self.elastic_tensor[:, 1, :, 1])
         )
 
     @property
     def p(self):
         if self._p is None:
-            coeff = np.polyfit(self.fit_range, np.linalg.det(self._get_pmat(self.fit_range)), 6)
+            coeff = np.polyfit(
+                self.fit_range, np.linalg.det(self._get_pmat(self.fit_range)), 6
+            )
             self._p = np.roots(coeff)
-            self._p = self._p[np.imag(self._p)>0]
+            self._p = self._p[np.imag(self._p) > 0]
         return self._p
 
     @property
@@ -59,13 +66,15 @@ def Ak(self):
     @property
     def D(self):
         if self._D is None:
-            F = np.einsum('n,ij->nij', self.p, self.elastic_tensor[:, 1, :, 1])
+            F = np.einsum("n,ij->nij", self.p, self.elastic_tensor[:, 1, :, 1])
             F += self.elastic_tensor[:, 1, :, 0]
-            F = np.einsum('nik,nk->ni', F, self.Ak)
+            F = np.einsum("nik,nk->ni", F, self.Ak)
             F = np.concatenate((F.T, self.Ak.T), axis=0)
             F = np.concatenate((np.real(F), -np.imag(F)), axis=-1)
-            self._D = np.linalg.solve(F, np.concatenate((np.zeros(3), self.burgers_vector)))
-            self._D = self._D[:3]+1j*self._D[3:]
+            self._D = np.linalg.solve(
+                F, np.concatenate((np.zeros(3), self.burgers_vector))
+            )
+            self._D = self._D[:3] + 1j * self._D[3:]
         return self._D
 
     @property
@@ -74,7 +83,7 @@ def dzdx(self):
 
     def _get_z(self, positions):
         z = np.stack((np.ones_like(self.p), self.p), axis=-1)
-        return np.einsum('nk,...k->...n', z, np.asarray(positions)[..., :2])
+        return np.einsum("nk,...k->...n", z, np.asarray(positions)[..., :2])
 
     def get_displacement(self, positions):
         """
@@ -87,8 +96,10 @@ def get_displacement(self, positions):
             ((n,3)-array): Displacement vectors
         """
         return np.imag(
-            np.einsum('nk,n,...n->...k', self.Ak, self.D, np.log(self._get_z(positions)))
-        )/(2*np.pi)
+            np.einsum(
+                "nk,n,...n->...k", self.Ak, self.D, np.log(self._get_z(positions))
+            )
+        ) / (2 * np.pi)
 
     def get_strain(self, positions):
         """
@@ -101,7 +112,13 @@ def get_strain(self, positions):
             ((n,3,3)-array): Strain tensors
         """
         strain = np.imag(
-            np.einsum('ni,n,...n,nj->...ij', self.Ak, self.D, 1/self._get_z(positions), self.dzdx)
+            np.einsum(
+                "ni,n,...n,nj->...ij",
+                self.Ak,
+                self.D,
+                1 / self._get_z(positions),
+                self.dzdx,
+            )
         )
-        strain = strain+np.einsum('...ij->...ji', strain)
-        return strain/4/np.pi
+        strain = strain + np.einsum("...ij->...ji", strain)
+        return strain / 4 / np.pi