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Add shift_with_mirror, and add shift_distance argument to rotation()

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jan 2016-06-17 16:49:39 -07:00
parent 35555cf4b3
commit 8f202fd061
1 changed files with 53 additions and 9 deletions
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62
fdfd_tools/operators.py
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@ -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