"""Classical AMG (Ruge-Stuben AMG)"""
__docformat__ = "restructuredtext en"
from warnings import warn
import scipy
from scipy.sparse import csr_matrix, isspmatrix_csr
from pyamg.multilevel import multilevel_solver
from pyamg.relaxation.smoothing import change_smoothers
from pyamg.strength import classical_strength_of_connection, \
symmetric_strength_of_connection, evolution_strength_of_connection,\
distance_strength_of_connection, energy_based_strength_of_connection,\
algebraic_distance
from interpolate import direct_interpolation
import split
__all__ = ['ruge_stuben_solver']
[docs]def ruge_stuben_solver(A,
strength=('classical', {'theta': 0.25}),
CF='RS',
presmoother=('gauss_seidel', {'sweep': 'symmetric'}),
postsmoother=('gauss_seidel', {'sweep': 'symmetric'}),
max_levels=10, max_coarse=500, keep=False, **kwargs):
"""Create a multilevel solver using Classical AMG (Ruge-Stuben AMG)
Parameters
----------
A : csr_matrix
Square matrix in CSR format
strength : ['symmetric', 'classical', 'evolution', None]
Method used to determine the strength of connection between unknowns
of the linear system. Method-specific parameters may be passed in
using a tuple, e.g. strength=('symmetric',{'theta' : 0.25 }). If
strength=None, all nonzero entries of the matrix are considered strong.
CF : {string} : default 'RS'
Method used for coarse grid selection (C/F splitting)
Supported methods are RS, PMIS, PMISc, CLJP, and CLJPc
presmoother : {string or dict}
Method used for presmoothing at each level. Method-specific parameters
may be passed in using a tuple, e.g.
presmoother=('gauss_seidel',{'sweep':'symmetric}), the default.
postsmoother : {string or dict}
Postsmoothing method with the same usage as presmoother
max_levels: {integer} : default 10
Maximum number of levels to be used in the multilevel solver.
max_coarse: {integer} : default 500
Maximum number of variables permitted on the coarse grid.
keep: {bool} : default False
Flag to indicate keeping extra operators in the hierarchy for
diagnostics. For example, if True, then strength of connection (C) and
tentative prolongation (T) are kept.
Returns
-------
ml : multilevel_solver
Multigrid hierarchy of matrices and prolongation operators
Examples
--------
>>> from pyamg.gallery import poisson
>>> from pyamg import ruge_stuben_solver
>>> A = poisson((10,),format='csr')
>>> ml = ruge_stuben_solver(A,max_coarse=3)
Notes
-----
"coarse_solver" is an optional argument and is the solver used at the
coarsest grid. The default is a pseudo-inverse. Most simply,
coarse_solver can be one of ['splu', 'lu', 'cholesky, 'pinv',
'gauss_seidel', ... ]. Additionally, coarse_solver may be a tuple
(fn, args), where fn is a string such as ['splu', 'lu', ...] or a callable
function, and args is a dictionary of arguments to be passed to fn.
References
----------
.. [1] Trottenberg, U., Oosterlee, C. W., and Schuller, A.,
"Multigrid" San Diego: Academic Press, 2001. Appendix A
See Also
--------
aggregation.smoothed_aggregation_solver, multilevel_solver,
aggregation.rootnode_solver
"""
levels = [multilevel_solver.level()]
# convert A to csr
if not isspmatrix_csr(A):
try:
A = csr_matrix(A)
warn("Implicit conversion of A to CSR",
scipy.sparse.SparseEfficiencyWarning)
except:
raise TypeError('Argument A must have type csr_matrix, \
or be convertible to csr_matrix')
# preprocess A
A = A.asfptype()
if A.shape[0] != A.shape[1]:
raise ValueError('expected square matrix')
levels[-1].A = A
while len(levels) < max_levels and levels[-1].A.shape[0] > max_coarse:
extend_hierarchy(levels, strength, CF, keep)
ml = multilevel_solver(levels, **kwargs)
change_smoothers(ml, presmoother, postsmoother)
return ml
# internal function
def extend_hierarchy(levels, strength, CF, keep):
""" helper function for local methods """
def unpack_arg(v):
if isinstance(v, tuple):
return v[0], v[1]
else:
return v, {}
A = levels[-1].A
# Compute the strength-of-connection matrix C, where larger
# C[i,j] denote stronger couplings between i and j.
fn, kwargs = unpack_arg(strength)
if fn == 'symmetric':
C = symmetric_strength_of_connection(A, **kwargs)
elif fn == 'classical':
C = classical_strength_of_connection(A, **kwargs)
elif fn == 'distance':
C = distance_strength_of_connection(A, **kwargs)
elif (fn == 'ode') or (fn == 'evolution'):
C = evolution_strength_of_connection(A, **kwargs)
elif fn == 'energy_based':
C = energy_based_strength_of_connection(A, **kwargs)
elif fn == 'algebraic_distance':
C = algebraic_distance(A, **kwargs)
elif fn is None:
C = A
else:
raise ValueError('unrecognized strength of connection method: %s' %
str(fn))
# Generate the C/F splitting
fn, kwargs = unpack_arg(CF)
if fn == 'RS':
splitting = split.RS(C)
elif fn == 'PMIS':
splitting = split.PMIS(C)
elif fn == 'PMISc':
splitting = split.PMISc(C)
elif fn == 'CLJP':
splitting = split.CLJP(C)
elif fn == 'CLJPc':
splitting = split.CLJPc(C)
else:
raise ValueError('unknown C/F splitting method (%s)' % CF)
# Generate the interpolation matrix that maps from the coarse-grid to the
# fine-grid
P = direct_interpolation(A, C, splitting)
# Generate the restriction matrix that maps from the fine-grid to the
# coarse-grid
R = P.T.tocsr()
# Store relevant information for this level
if keep:
levels[-1].C = C # strength of connection matrix
levels[-1].splitting = splitting # C/F splitting
levels[-1].P = P # prolongation operator
levels[-1].R = R # restriction operator
levels.append(multilevel_solver.level())
# Form next level through Galerkin product
A = R * A * P
levels[-1].A = A