def PMIS(S):
"""C/F splitting using the Parallel Modified Independent Set method
Parameters
----------
S : csr_matrix
Strength of connection matrix indicating the strength between nodes i
and j (S_ij)
Returns
-------
splitting : ndarray
Array of length of S of ones (coarse) and zeros (fine)
Examples
--------
>>> from pyamg.gallery import poisson
>>> from pyamg.classical import PMIS
>>> S = poisson((7,), format='csr') # 1D mesh with 7 vertices
>>> splitting = PMIS(S)
See Also
--------
MIS
References
----------
.. [1] Hans De Sterck, Ulrike M Yang, and Jeffrey J Heys
"Reducing complexity in parallel algebraic multigrid preconditioners"
SIAM Journal on Matrix Analysis and Applications 2006; 27:1019-1039.
"""
S = remove_diagonal(S)
weights, G, S, T = preprocess(S)
return MIS(G, weights)
def PMIS(S):
"""C/F splitting using the Parallel Modified Independent Set method
Parameters
----------
S : csr_matrix
Strength of connection matrix indicating the strength between nodes i
and j (S_ij)
Returns
-------
splitting : ndarray
Array of length of S of ones (coarse) and zeros (fine)
Examples
--------
>>> from pyamg.gallery import poisson
>>> from pyamg.classical import PMIS
>>> S = poisson((7,), format='csr') # 1D mesh with 7 vertices
>>> splitting = PMIS(S)
See Also
--------
MIS
References
----------
.. [1] Hans De Sterck, Ulrike M Yang, and Jeffrey J Heys
"Reducing complexity in parallel algebraic multigrid preconditioners"
SIAM Journal on Matrix Analysis and Applications 2006; 27:1019-1039.
"""
S = remove_diagonal(S)
weights, G, S, T = preprocess(S)
return MIS(G, weights)
def RS(S, second_pass=False):
"""Compute a C/F splitting using Ruge-Stuben coarsening
Parameters
----------
S : csr_matrix
Strength of connection matrix indicating the strength between nodes i
and j (S_ij)
second_pass : bool, default False
Perform second pass of classical AMG coarsening. Can be important for
classical AMG interpolation. Typically not done in parallel (e.g. Hypre).
Returns
-------
splitting : ndarray
Array of length of S of ones (coarse) and zeros (fine)
Examples
--------
>>> from pyamg.gallery import poisson
>>> from pyamg.classical import RS
>>> S = poisson((7,), format='csr') # 1D mesh with 7 vertices
>>> splitting = RS(S)
See Also
--------
amg_core.rs_cf_splitting
References
----------
.. [1] Ruge JW, Stuben K. "Algebraic multigrid (AMG)"
In Multigrid Methods, McCormick SF (ed.),
Frontiers in Applied Mathematics, vol. 3.
SIAM: Philadelphia, PA, 1987; 73-130.
"""
if not isspmatrix_csr(S):
raise TypeError('expected csr_matrix')
S = remove_diagonal(S)
T = S.T.tocsr() # transpose S for efficient column access
splitting = np.empty(S.shape[0], dtype='intc')
influence = np.zeros((S.shape[0],), dtype='intc')
amg_core.rs_cf_splitting(S.shape[0],
S.indptr, S.indices,
T.indptr, T.indices,
influence,
splitting)
if second_pass:
amg_core.rs_cf_splitting_pass2(S.shape[0], S.indptr,
S.indices, splitting)
return splitting
def RS(S, second_pass=False):
"""Compute a C/F splitting using Ruge-Stuben coarsening
Parameters
----------
S : csr_matrix
Strength of connection matrix indicating the strength between nodes i
and j (S_ij)
second_pass : bool, default False
Perform second pass of classical AMG coarsening. Can be important for
classical AMG interpolation. Typically not done in parallel (e.g. Hypre).
Returns
-------
splitting : ndarray
Array of length of S of ones (coarse) and zeros (fine)
Examples
--------
>>> from pyamg.gallery import poisson
>>> from pyamg.classical import RS
>>> S = poisson((7,), format='csr') # 1D mesh with 7 vertices
>>> splitting = RS(S)
See Also
--------
amg_core.rs_cf_splitting
References
----------
.. [1] Ruge JW, Stuben K. "Algebraic multigrid (AMG)"
In Multigrid Methods, McCormick SF (ed.),
Frontiers in Applied Mathematics, vol. 3.
SIAM: Philadelphia, PA, 1987; 73-130.
"""
if not isspmatrix_csr(S):
raise TypeError('expected csr_matrix')
S = remove_diagonal(S)
T = S.T.tocsr() # transpose S for efficient column access
splitting = np.empty(S.shape[0], dtype='intc')
influence = np.zeros((S.shape[0],), dtype='intc')
amg_core.rs_cf_splitting(S.shape[0],
S.indptr, S.indices,
T.indptr, T.indices,
influence,
splitting)
if second_pass:
amg_core.rs_cf_splitting_pass2(S.shape[0], S.indptr,
S.indices, splitting)
return splitting
def CLJP(S, color=False):
"""Compute a C/F splitting using the parallel CLJP algorithm
Parameters
----------
S : csr_matrix
Strength of connection matrix indicating the strength between nodes i
and j (S_ij)
color : bool
use the CLJP coloring approach
Returns
-------
splitting : array
Array of length of S of ones (coarse) and zeros (fine)
Examples
--------
>>> from pyamg.gallery import poisson
>>> from pyamg.classical.split import CLJP
>>> S = poisson((7,), format='csr') # 1D mesh with 7 vertices
>>> splitting = CLJP(S)
See Also
--------
MIS, PMIS, CLJPc
References
----------
.. [1] David M. Alber and Luke N. Olson
"Parallel coarse-grid selection"
Numerical Linear Algebra with Applications 2007; 14:611-643.
"""
if not isspmatrix_csr(S):
raise TypeError('expected csr_matrix')
S = remove_diagonal(S)
colorid = 0
if color:
colorid = 1
T = S.T.tocsr() # transpose S for efficient column access
splitting = np.empty(S.shape[0], dtype='intc')
amg_core.cljp_naive_splitting(S.shape[0],
S.indptr, S.indices,
T.indptr, T.indices,
splitting,
colorid)
return splitting
def CLJP(S, color=False):
"""Compute a C/F splitting using the parallel CLJP algorithm
Parameters
----------
S : csr_matrix
Strength of connection matrix indicating the strength between nodes i
and j (S_ij)
color : bool
use the CLJP coloring approach
Returns
-------
splitting : array
Array of length of S of ones (coarse) and zeros (fine)
Examples
--------
>>> from pyamg.gallery import poisson
>>> from pyamg.classical.split import CLJP
>>> S = poisson((7,), format='csr') # 1D mesh with 7 vertices
>>> splitting = CLJP(S)
See Also
--------
MIS, PMIS, CLJPc
References
----------
.. [1] David M. Alber and Luke N. Olson
"Parallel coarse-grid selection"
Numerical Linear Algebra with Applications 2007; 14:611-643.
"""
if not isspmatrix_csr(S):
raise TypeError('expected csr_matrix')
S = remove_diagonal(S)
colorid = 0
if color:
colorid = 1
T = S.T.tocsr() # transpose S for efficient column access
splitting = numpy.empty(S.shape[0], dtype='intc')
amg_core.cljp_naive_splitting(S.shape[0],
S.indptr, S.indices,
T.indptr, T.indices,
splitting,
colorid)
return splitting
def MIS(G, weights, maxiter=None):
"""Compute a maximal independent set of a graph in parallel
Parameters
----------
G : csr_matrix
Matrix graph, G[i,j] != 0 indicates an edge
weights : ndarray
Array of weights for each vertex in the graph G
maxiter : int
Maximum number of iterations (default: None)
Returns
-------
mis : array
Array of length of G of zeros/ones indicating the independent set
Examples
--------
>>> from pyamg.gallery import poisson
>>> from pyamg.classical import MIS
>>> import numpy as np
>>> G = poisson((7,), format='csr') # 1D mesh with 7 vertices
>>> w = np.ones((G.shape[0],1)).ravel()
>>> mis = MIS(G,w)
See Also
--------
fn = amg_core.maximal_independent_set_parallel
"""
if not isspmatrix_csr(G):
raise TypeError('expected csr_matrix')
G = remove_diagonal(G)
mis = np.empty(G.shape[0], dtype='intc')
mis[:] = -1
fn = amg_core.maximal_independent_set_parallel
if maxiter is None:
fn(G.shape[0], G.indptr, G.indices, -1, 1, 0, mis, weights, -1)
else:
if maxiter < 0:
raise ValueError('maxiter must be >= 0')
fn(G.shape[0], G.indptr, G.indices, -1, 1, 0, mis, weights, maxiter)
return mis
def MIS(G, weights, maxiter=None):
"""Compute a maximal independent set of a graph in parallel
Parameters
----------
G : csr_matrix
Matrix graph, G[i,j] != 0 indicates an edge
weights : ndarray
Array of weights for each vertex in the graph G
maxiter : int
Maximum number of iterations (default: None)
Returns
-------
mis : array
Array of length of G of zeros/ones indicating the independent set
Examples
--------
>>> from pyamg.gallery import poisson
>>> from pyamg.classical import MIS
>>> import numpy as np
>>> G = poisson((7,), format='csr') # 1D mesh with 7 vertices
>>> w = np.ones((G.shape[0],1)).ravel()
>>> mis = MIS(G,w)
See Also
--------
fn = amg_core.maximal_independent_set_parallel
"""
if not isspmatrix_csr(G):
raise TypeError('expected csr_matrix')
G = remove_diagonal(G)
mis = np.empty(G.shape[0], dtype='intc')
mis[:] = -1
fn = amg_core.maximal_independent_set_parallel
if maxiter is None:
fn(G.shape[0], G.indptr, G.indices, -1, 1, 0, mis, weights)
else:
if maxiter < 0:
raise ValueError('maxiter must be >= 0')
fn(G.shape[0], G.indptr, G.indices, -1, 1, 0, mis, weights, maxiter)
return mis
def PMISc(S, method='JP'):
"""C/F splitting using Parallel Modified Independent Set (in color).
PMIS-c, or PMIS in color, improves PMIS by perturbing the initial
random weights with weights determined by a vertex coloring.
Parameters
----------
S : csr_matrix
Strength of connection matrix indicating the strength between nodes i
and j (S_ij)
method : string
Algorithm used to compute the initial vertex coloring:
* 'MIS' - Maximal Independent Set
* 'JP' - Jones-Plassmann (parallel)
* 'LDF' - Largest-Degree-First (parallel)
Returns
-------
splitting : array
Array of length of S of ones (coarse) and zeros (fine)
Examples
--------
>>> from pyamg.gallery import poisson
>>> from pyamg.classical.split import PMISc
>>> S = poisson((7,), format='csr') # 1D mesh with 7 vertices
>>> splitting = PMISc(S)
See Also
--------
MIS
References
----------
.. [7] David M. Alber and Luke N. Olson
"Parallel coarse-grid selection"
Numerical Linear Algebra with Applications 2007; 14:611-643.
"""
S = remove_diagonal(S)
weights, G, S, T = _preprocess(S, coloring_method=method)
del S, T
return MIS(G, weights)
def PMISc(S, method='JP'):
"""C/F splitting using Parallel Modified Independent Set (in color)
PMIS-c, or PMIS in color, improves PMIS by perturbing the initial
random weights with weights determined by a vertex coloring.
Parameters
----------
S : csr_matrix
Strength of connection matrix indicating the strength between nodes i
and j (S_ij)
method : string
Algorithm used to compute the initial vertex coloring:
* 'MIS' - Maximal Independent Set
* 'JP' - Jones-Plassmann (parallel)
* 'LDF' - Largest-Degree-First (parallel)
Returns
-------
splitting : array
Array of length of S of ones (coarse) and zeros (fine)
Examples
--------
>>> from pyamg.gallery import poisson
>>> from pyamg.classical import PMISc
>>> S = poisson((7,), format='csr') # 1D mesh with 7 vertices
>>> splitting = PMISc(S)
See Also
--------
MIS
References
----------
.. [1] David M. Alber and Luke N. Olson
"Parallel coarse-grid selection"
Numerical Linear Algebra with Applications 2007; 14:611-643.
"""
S = remove_diagonal(S)
weights, G, S, T = preprocess(S, coloring_method=method)
return MIS(G, weights)
def CLJPc(S):
"""Compute a C/F splitting using the parallel CLJP-c algorithm
CLJP-c, or CLJP in color, improves CLJP by perturbing the initial
random weights with weights determined by a vertex coloring.
Parameters
----------
S : csr_matrix
Strength of connection matrix indicating the strength between nodes i
and j (S_ij)
Returns
-------
splitting : array
Array of length of S of ones (coarse) and zeros (fine)
Examples
--------
>>> from pyamg.gallery import poisson
>>> from pyamg.classical.split import CLJPc
>>> S = poisson((7,), format='csr') # 1D mesh with 7 vertices
>>> splitting = CLJPc(S)
See Also
--------
MIS, PMIS, CLJP
References
----------
.. [1] David M. Alber and Luke N. Olson
"Parallel coarse-grid selection"
Numerical Linear Algebra with Applications 2007; 14:611-643.
"""
S = remove_diagonal(S)
return CLJP(S, color=True)
def CLJPc(S):
"""Compute a C/F splitting using the parallel CLJP-c algorithm
CLJP-c, or CLJP in color, improves CLJP by perturbing the initial
random weights with weights determined by a vertex coloring.
Parameters
----------
S : csr_matrix
Strength of connection matrix indicating the strength between nodes i
and j (S_ij)
Returns
-------
splitting : array
Array of length of S of ones (coarse) and zeros (fine)
Examples
--------
>>> from pyamg.gallery import poisson
>>> from pyamg.classical.split import CLJPc
>>> S = poisson((7,), format='csr') # 1D mesh with 7 vertices
>>> splitting = CLJPc(S)
See Also
--------
MIS, PMIS, CLJP
References
----------
.. [1] David M. Alber and Luke N. Olson
"Parallel coarse-grid selection"
Numerical Linear Algebra with Applications 2007; 14:611-643.
"""
S = remove_diagonal(S)
return CLJP(S, color=True)