def direct_interpolation(A, C, splitting, theta=None, norm='min', cost=[0]):
"""Create prolongator using direct interpolation
Parameters
----------
A : {csr_matrix}
NxN matrix in CSR format
C : {csr_matrix}
Strength-of-Connection matrix
Must have zero diagonal
splitting : array
C/F splitting stored in an array of length N
theta : float in [0,1), default None
theta value defining strong connections in a classical AMG sense. Provide if
different SOC used for P than for CF-splitting; otherwise, theta = None.
norm : string, default 'abs'
Norm used in redefining classical SOC. Options are 'min' and 'abs' for CSR matrices,
and 'min', 'abs', and 'fro' for BSR matrices. See strength.py for more information.
Returns
-------
P : {csr_matrix}
Prolongator using direct interpolation
Examples
--------
>>> from pyamg.gallery import poisson
>>> from pyamg.classical import direct_interpolation
>>> import numpy as np
>>> A = poisson((5,),format='csr')
>>> splitting = np.array([1,0,1,0,1], dtype='intc')
>>> P = direct_interpolation(A, A, splitting)
>>> print P.todense()
[[ 1. 0. 0. ]
[ 0.5 0.5 0. ]
[ 0. 1. 0. ]
[ 0. 0.5 0.5]
[ 0. 0. 1. ]]
"""
if not isspmatrix_csr(C):
raise TypeError('Expected csr_matrix SOC matrix, C.')
# Block BSR format. Transfer A to CSR and the splitting and SOC matrix to have
# DOFs corresponding to CSR A
if isspmatrix_bsr(A):
temp_A = A.tocsr()
temp_A.eliminate_zeros()
splitting0 = splitting * np.ones((A.blocksize[0], 1), dtype='intc')
splitting0 = np.reshape(splitting0, (np.prod(splitting0.shape), ),
order='F')
if theta is not None:
C0 = classical_strength_of_connection(A,
theta=theta,
norm=norm,
cost=cost)
C0 = UnAmal(C0, A.blocksize[0], A.blocksize[1])
else:
C0 = UnAmal(C, A.blocksize[0], A.blocksize[1])
C0 = C0.tocsr()
C0.eliminate_zeros()
# Interpolation weights are computed based on entries in A, but subject to the
# sparsity pattern of C. So, copy the entries of A into sparsity pattern of C.
C0.data[:] = 1.0
C0 = C0.multiply(temp_A)
P_indptr = np.empty_like(temp_A.indptr)
amg_core.rs_direct_interpolation_pass1(temp_A.shape[0], C0.indptr,
C0.indices, splitting0,
P_indptr)
nnz = P_indptr[-1]
P_colinds = np.empty(nnz, dtype=P_indptr.dtype)
P_data = np.empty(nnz, dtype=A.dtype)
amg_core.rs_direct_interpolation_pass2(temp_A.shape[0], temp_A.indptr,
temp_A.indices, temp_A.data,
C0.indptr, C0.indices, C0.data,
splitting0, P_indptr, P_colinds,
P_data)
nc = np.sum(splitting0)
n = A.shape[0]
P = csr_matrix((P_data, P_colinds, P_indptr), shape=[n, nc])
return P.tobsr(blocksize=A.blocksize)
# CSR format
else:
if theta is not None:
C0 = classical_strength_of_connection(A,
theta=theta,
norm=norm,
cost=cost)
else:
C0 = C.copy()
C0.eliminate_zeros()
# Interpolation weights are computed based on entries in A, but subject to the
# sparsity pattern of C. So, copy the entries of A into sparsity pattern of C.
C0.data[:] = 1.0
C0 = C0.multiply(A)
P_indptr = np.empty_like(A.indptr)
amg_core.rs_direct_interpolation_pass1(A.shape[0], C0.indptr,
C0.indices, splitting, P_indptr)
nnz = P_indptr[-1]
P_colinds = np.empty(nnz, dtype=P_indptr.dtype)
P_data = np.empty(nnz, dtype=A.dtype)
amg_core.rs_direct_interpolation_pass2(A.shape[0], A.indptr, A.indices,
A.data, C0.indptr, C0.indices,
C0.data, splitting, P_indptr,
P_colinds, P_data)
nc = np.sum(splitting)
n = A.shape[0]
return csr_matrix((P_data, P_colinds, P_indptr), shape=[n, nc])
def direct_interpolation(A, C, splitting):
"""Create prolongator using direct interpolation
Parameters
----------
A : {csr_matrix}
NxN matrix in CSR format
C : {csr_matrix}
Strength-of-Connection matrix
Must have zero diagonal
splitting : array
C/F splitting stored in an array of length N
Returns
-------
P : {csr_matrix}
Prolongator using direct interpolation
Examples
--------
>>> from pyamg.gallery import poisson
>>> from pyamg.classical import direct_interpolation
>>> import numpy
>>> A = poisson((5,),format='csr')
>>> splitting = numpy.array([1,0,1,0,1], dtype='intc')
>>> P = direct_interpolation(A, A, splitting)
>>> print P.todense()
[[ 1. 0. 0. ]
[ 0.5 0.5 0. ]
[ 0. 1. 0. ]
[ 0. 0.5 0.5]
[ 0. 0. 1. ]]
"""
if not isspmatrix_csr(A):
raise TypeError('expected csr_matrix for A')
if not isspmatrix_csr(C):
raise TypeError('expected csr_matrix for C')
##
# Interpolation weights are computed based on entries in A, but subject to
# the sparsity pattern of C. So, copy the entries of A into the
# sparsity pattern of C.
C = C.copy()
C.data[:] = 1.0
C = C.multiply(A)
Pp = numpy.empty_like(A.indptr)
amg_core.rs_direct_interpolation_pass1(A.shape[0], C.indptr, C.indices,
splitting, Pp)
nnz = Pp[-1]
Pj = numpy.empty(nnz, dtype=Pp.dtype)
Px = numpy.empty(nnz, dtype=A.dtype)
amg_core.rs_direct_interpolation_pass2(A.shape[0], A.indptr, A.indices,
A.data, C.indptr, C.indices, C.data,
splitting, Pp, Pj, Px)
return csr_matrix((Px, Pj, Pp))
def direct_interpolation(A, C, splitting):
"""Create prolongator using direct interpolation
Parameters
----------
A : {csr_matrix}
NxN matrix in CSR format
C : {csr_matrix}
Strength-of-Connection matrix
Must have zero diagonal
splitting : array
C/F splitting stored in an array of length N
Returns
-------
P : {csr_matrix}
Prolongator using direct interpolation
Examples
--------
>>> from pyamg.gallery import poisson
>>> from pyamg.classical import direct_interpolation
>>> import numpy as np
>>> A = poisson((5,),format='csr')
>>> splitting = np.array([1,0,1,0,1], dtype='intc')
>>> P = direct_interpolation(A, A, splitting)
>>> print P.todense()
[[ 1. 0. 0. ]
[ 0.5 0.5 0. ]
[ 0. 1. 0. ]
[ 0. 0.5 0.5]
[ 0. 0. 1. ]]
"""
if not isspmatrix_csr(A):
raise TypeError('expected csr_matrix for A')
if not isspmatrix_csr(C):
raise TypeError('expected csr_matrix for C')
# Interpolation weights are computed based on entries in A, but subject to
# the sparsity pattern of C. So, copy the entries of A into the
# sparsity pattern of C.
C = C.copy()
C.data[:] = 1.0
C = C.multiply(A)
Pp = np.empty_like(A.indptr)
amg_core.rs_direct_interpolation_pass1(A.shape[0],
C.indptr, C.indices, splitting, Pp)
nnz = Pp[-1]
Pj = np.empty(nnz, dtype=Pp.dtype)
Px = np.empty(nnz, dtype=A.dtype)
amg_core.rs_direct_interpolation_pass2(A.shape[0],
A.indptr, A.indices, A.data,
C.indptr, C.indices, C.data,
splitting,
Pp, Pj, Px)
return csr_matrix((Px, Pj, Pp))