implemented derivation of gradient weights via rotation

derive gradient weights of other direction with already calculated weights of one direction via rotation and apply them to a field.

pystencils/fd/derivation.py

 from collections import defaultdict
 
 import sympy as sp
+import numpy as np
+import sys
 
 from pystencils.field import Field
 from pystencils.sympyextensions import multidimensional_sum, prod
@@ -170,13 +172,45 @@ class FiniteDifferenceStencilDerivation:
 
         def as_matrix(self):
             dim = len(self.stencil[0])
-            assert dim == 2
             max_offset = max(max(abs(e) for e in direction) for direction in self.stencil)
-            result = sp.Matrix(2 * max_offset + 1, 2 * max_offset + 1, lambda i, j: 0)
-            for direction, weight in zip(self.stencil, self.weights):
-                result[max_offset - direction[1], max_offset + direction[0]] = weight
+
+            if dim == 2:
+                result = sp.Matrix(2 * max_offset + 1, 2 * max_offset + 1, lambda i, j: 0)
+                for direction, weight in zip(self.stencil, self.weights):
+                    result[max_offset - direction[1], max_offset + direction[0]] = weight
+            elif dim == 3:
+                result = np.zeros((2 * max_offset + 1, 2 * max_offset + 1, 2 * max_offset + 1), dtype=object)
+                for direction, weight in zip(self.stencil, self.weights):
+                    result[max_offset - direction[1], max_offset + direction[0], max_offset + direction[2]] = weight
+            else:
+                print('only 2D or 3D matrix representations are available')
+                sys.exit()
+
             return result
 
+        def rotate_weights_and_apply(self, field_access: Field.Access, axis):
+            """derive gradient weights of other direction with already calculated weights of one direction
+               via rotation and apply them to a field."""
+            dim = len(self.stencil[0])
+            rotated_weights = np.rot90(self.as_matrix(), 1, axis)
+
+            result = []
+            max_offset = max(max(abs(e) for e in direction) for direction in self.stencil)
+            for direction in self.stencil:
+                if dim == 2:
+                    result.append(rotated_weights[max_offset - direction[1],
+                                                  max_offset + direction[0]])
+                elif dim == 3:
+                    result.append(rotated_weights[max_offset - direction[1],
+                                                  max_offset + direction[0],
+                                                  max_offset + direction[2]])
+                else:
+                    print('only 2D or 3D matrix representations are available')
+                    sys.exit()
+
+            f = field_access
+            return sum(f.get_shifted(*offset) * weight for offset, weight in zip(self.stencil, result))
+
         def __repr__(self):
             return "Finite difference stencil of accuracy {}, isotropic error: {}".format(self.accuracy,
                                                                                           self.is_isotropic)