Add shift_with_mirror, and add shift_distance argument to rotation()

fdfd_tools/operators.py

@@ -215,12 +215,13 @@ def m2j(omega: complex,
     return op
 
 
-def rotation(axis: int, shape: List[int]) -> sparse.spmatrix:
+def rotation(axis: int, shape: List[int], shift_distance: int=1) -> sparse.spmatrix:
     """
     Utility operator for performing a circular shift along a specified axis by 1 element.
 
     :param axis: Axis to shift along. x=0, y=1, z=2
     :param shape: Shape of the grid being shifted
+    :param shift_distance: Number of cells to shift by. May be negative. Default 1.
     :return: Sparse matrix for performing the circular shift
     """
     if len(shape) not in (2, 3):
@@ -228,12 +229,11 @@ def rotation(axis: int, shape: List[int]) -> sparse.spmatrix:
     if axis not in range(len(shape)):
         raise Exception('Invalid direction: {}, shape is {}'.format(axis, shape))
 
-    n = numpy.prod(shape)
-
-    shifts = [1 if k == axis else 0 for k in range(3)]
+    shifts = [abs(shift_distance) if a == axis else 0 for a in range(3)]
     shifted_diags = [(numpy.arange(n) + s) % n for n, s in zip(shape, shifts)]
     ijk = numpy.meshgrid(*shifted_diags, indexing='ij')
 
+    n = numpy.prod(shape)
     i_ind = numpy.arange(n)
     j_ind = ijk[0] + ijk[1] * shape[0]
     if len(shape) == 3:
@@ -241,8 +241,52 @@ def rotation(axis: int, shape: List[int]) -> sparse.spmatrix:
 
     vij = (numpy.ones(n), (i_ind, j_ind.flatten(order='F')))
 
-    D = sparse.csr_matrix(vij, shape=(n, n))
-    return D
+    d = sparse.csr_matrix(vij, shape=(n, n))
+
+    if shift_distance < 0:
+        d = d.T
+
+    return d
+
+
+def shift_with_mirror(axis: int, shape: List[int], shift_distance: int=1) -> sparse.spmatrix:
+    """
+    Utility operator for performing an n-element shift along a specified axis, with mirror
+    boundary conditions applied to the cells beyond the receding edge.
+
+    :param axis: Axis to shift along. x=0, y=1, z=2
+    :param shape: Shape of the grid being shifted
+    :param shift_distance: Number of cells to shift by. May be negative. Default 1.
+    :return: Sparse matrix for performing the circular shift
+    """
+    if len(shape) not in (2, 3):
+        raise Exception('Invalid shape: {}'.format(shape))
+    if axis not in range(len(shape)):
+        raise Exception('Invalid direction: {}, shape is {}'.format(axis, shape))
+    if shift_distance >= shape[axis]:
+        raise Exception('Shift ({}) is too large for axis {} of size {}'.format(
+                        shift_distance, axis, shape[axis]))
+
+    def mirrored_range(n, s):
+        v = numpy.arange(n) + s
+        v = numpy.where(v >= n, 2 * n - v - 1, v)
+        v = numpy.where(v < 0, - 1 - v, v)
+        return v
+
+    shifts = [shift_distance if a == axis else 0 for a in range(3)]
+    shifted_diags = [mirrored_range(n, s) for n, s in zip(shape, shifts)]
+    ijk = numpy.meshgrid(*shifted_diags, indexing='ij')
+
+    n = numpy.prod(shape)
+    i_ind = numpy.arange(n)
+    j_ind = ijk[0] + ijk[1] * shape[0]
+    if len(shape) == 3:
+        j_ind += ijk[2] * shape[0] * shape[1]
+
+    vij = (numpy.ones(n), (i_ind, j_ind.flatten(order='F')))
+
+    d = sparse.csr_matrix(vij, shape=(n, n))
+    return d
 
 
 def deriv_forward(dx_e: List[numpy.ndarray]) -> List[sparse.spmatrix]:
@@ -258,7 +302,7 @@ def deriv_forward(dx_e: List[numpy.ndarray]) -> List[sparse.spmatrix]:
     dx_e_expanded = numpy.meshgrid(*dx_e, indexing='ij')
 
     def deriv(axis):
-        return rotation(axis, shape) - sparse.eye(n)
+        return rotation(axis, shape, 1) - sparse.eye(n)
 
     Ds = [sparse.diags(+1 / dx.flatten(order='F')) @ deriv(a)
           for a, dx in enumerate(dx_e_expanded)]
@@ -279,9 +323,9 @@ def deriv_back(dx_h: List[numpy.ndarray]) -> List[sparse.spmatrix]:
     dx_h_expanded = numpy.meshgrid(*dx_h, indexing='ij')
 
     def deriv(axis):
-        return rotation(axis, shape) - sparse.eye(n)
+        return rotation(axis, shape, -1) - sparse.eye(n)
 
-    Ds = [sparse.diags(-1 / dx.flatten(order='F')) @ deriv(a).T
+    Ds = [sparse.diags(-1 / dx.flatten(order='F')) @ deriv(a)
           for a, dx in enumerate(dx_h_expanded)]
 
     return Ds