def schwarz_parameters(A,
subdomain=None,
subdomain_ptr=None,
inv_subblock=None,
inv_subblock_ptr=None):
'''
Helper function for setting up Schwarz relaxation. This function avoids
recomputing the subdomains and block inverses manytimes, e.g., it avoids a
costly double computation when setting up pre and post smoothing with
Schwarz.
Parameters
----------
A {csr_matrix}
Returns
-------
A.schwarz_parameters[0] is subdomain
A.schwarz_parameters[1] is subdomain_ptr
A.schwarz_parameters[2] is inv_subblock
A.schwarz_parameters[3] is inv_subblock_ptr
'''
# Check if A has a pre-existing set of Schwarz parameters
if hasattr(A, 'schwarz_parameters'):
if subdomain is not None and subdomain_ptr is not None:
# check that the existing parameters correspond to the same
# subdomains
if np.array(A.schwarz_parameters[0] == subdomain).all() and \
np.array(A.schwarz_parameters[1] == subdomain_ptr).all():
return A.schwarz_parameters
else:
return A.schwarz_parameters
# Default is to use the overlapping regions defined by A's sparsity pattern
if subdomain is None or subdomain_ptr is None:
subdomain_ptr = A.indptr.copy()
subdomain = A.indices.copy()
# Extract each subdomain's block from the matrix
if inv_subblock is None or inv_subblock_ptr is None:
inv_subblock_ptr = np.zeros(subdomain_ptr.shape, dtype=A.indices.dtype)
blocksize = (subdomain_ptr[1:] - subdomain_ptr[:-1])
inv_subblock_ptr[1:] = np.cumsum(blocksize * blocksize)
# Extract each block column from A
inv_subblock = np.zeros((inv_subblock_ptr[-1], ), dtype=A.dtype)
amg_core.extract_subblocks(A.indptr, A.indices, A.data, inv_subblock,
inv_subblock_ptr, subdomain, subdomain_ptr,
int(subdomain_ptr.shape[0] - 1), A.shape[0])
# Choose tolerance for which singular values are zero in *gelss below
t = A.dtype.char
eps = np.finfo(np.float).eps
feps = np.finfo(np.single).eps
geps = np.finfo(np.longfloat).eps
_array_precision = {'f': 0, 'd': 1, 'g': 2, 'F': 0, 'D': 1, 'G': 2}
cond = {
0: feps * 1e3,
1: eps * 1e6,
2: geps * 1e6
}[_array_precision[t]]
# Invert each block column
my_pinv, = la.get_lapack_funcs(['gelss'], (np.ones(
(1, ), dtype=A.dtype)))
for i in range(subdomain_ptr.shape[0] - 1):
m = blocksize[i]
rhs = sp.eye(m, m, dtype=A.dtype)
j0 = inv_subblock_ptr[i]
j1 = inv_subblock_ptr[i + 1]
gelssoutput = my_pinv(inv_subblock[j0:j1].reshape(m, m),
rhs,
cond=cond,
overwrite_a=True,
overwrite_b=True)
inv_subblock[j0:j1] = np.ravel(gelssoutput[1])
A.schwarz_parameters = (subdomain, subdomain_ptr, inv_subblock,
inv_subblock_ptr)
return A.schwarz_parameters
def schwarz_parameters(A, subdomain=None, subdomain_ptr=None,
inv_subblock=None, inv_subblock_ptr=None):
'''
Helper function for setting up Schwarz relaxation. This function avoids
recomputing the subdomains and block inverses manytimes, e.g., it avoids a
costly double computation when setting up pre and post smoothing with
Schwarz.
Parameters
----------
A {csr_matrix}
Returns
-------
A.schwarz_parameters[0] is subdomain
A.schwarz_parameters[1] is subdomain_ptr
A.schwarz_parameters[2] is inv_subblock
A.schwarz_parameters[3] is inv_subblock_ptr
'''
# Check if A has a pre-existing set of Schwarz parameters
if hasattr(A, 'schwarz_parameters'):
if subdomain is not None and subdomain_ptr is not None:
# check that the existing parameters correspond to the same
# subdomains
if np.array(A.schwarz_parameters[0] == subdomain).all() and \
np.array(A.schwarz_parameters[1] == subdomain_ptr).all():
return A.schwarz_parameters
else:
return A.schwarz_parameters
# Default is to use the overlapping regions defined by A's sparsity pattern
if subdomain is None or subdomain_ptr is None:
subdomain_ptr = A.indptr.copy()
subdomain = A.indices.copy()
# Extract each subdomain's block from the matrix
if inv_subblock is None or inv_subblock_ptr is None:
inv_subblock_ptr = np.zeros(subdomain_ptr.shape,
dtype=A.indices.dtype)
blocksize = (subdomain_ptr[1:] - subdomain_ptr[:-1])
inv_subblock_ptr[1:] = np.cumsum(blocksize*blocksize)
# Extract each block column from A
inv_subblock = np.zeros((inv_subblock_ptr[-1],), dtype=A.dtype)
amg_core.extract_subblocks(A.indptr, A.indices, A.data, inv_subblock,
inv_subblock_ptr, subdomain, subdomain_ptr,
int(subdomain_ptr.shape[0]-1), A.shape[0])
# Choose tolerance for which singular values are zero in *gelss below
t = A.dtype.char
eps = np.finfo(np.float).eps
feps = np.finfo(np.single).eps
geps = np.finfo(np.longfloat).eps
_array_precision = {'f': 0, 'd': 1, 'g': 2, 'F': 0, 'D': 1, 'G': 2}
cond = {0: feps*1e3, 1: eps*1e6, 2: geps*1e6}[_array_precision[t]]
# Invert each block column
my_pinv, = la.get_lapack_funcs(['gelss'],
(np.ones((1,), dtype=A.dtype)))
for i in xrange(subdomain_ptr.shape[0]-1):
m = blocksize[i]
rhs = sp.eye(m, m, dtype=A.dtype)
j0 = inv_subblock_ptr[i]
j1 = inv_subblock_ptr[i+1]
gelssoutput = my_pinv(inv_subblock[j0:j1].reshape(m, m),
rhs, cond=cond, overwrite_a=True,
overwrite_b=True)
inv_subblock[j0:j1] = np.ravel(gelssoutput[1])
A.schwarz_parameters = (subdomain, subdomain_ptr, inv_subblock,
inv_subblock_ptr)
return A.schwarz_parameters