import time
import numpy as nm
import scipy.linalg as sla
from sfepy.base.base import output, get_default, try_imports, Struct
from sfepy.solvers.solvers import make_get_conf, Solver, EigenvalueSolver
[docs]def eig(mtx_a, mtx_b=None, n_eigs=None, eigenvectors=True,
return_time=None, method='eig.scipy', **ckwargs):
"""
Utility function that constructs an eigenvalue solver given by
`method`, calls it and returns solution.
"""
kwargs = {'name' : 'aux', 'kind' : method}
kwargs.update(ckwargs)
conf = Struct(**kwargs)
solver = Solver.any_from_conf(conf)
status = {}
out = solver(mtx_a, mtx_b, n_eigs, eigenvectors, status)
if return_time is not None:
return_time[0] = status['time']
return out
[docs]def standard_call(call):
"""
Decorator handling argument preparation and timing for eigensolvers.
"""
def _standard_call(self, mtx_a, mtx_b=None, n_eigs=None,
eigenvectors=None, status=None, conf=None, **kwargs):
tt = time.clock()
conf = get_default(conf, self.conf)
mtx_a = get_default(mtx_a, self.mtx_a)
mtx_b = get_default(mtx_b, self.mtx_b)
n_eigs = get_default(n_eigs, self.n_eigs)
eigenvectors = get_default(eigenvectors, self.eigenvectors)
status = get_default(status, self.status)
result = call(self, mtx_a, mtx_b, n_eigs, eigenvectors, status, conf,
**kwargs)
ttt = time.clock() - tt
if status is not None:
status['time'] = ttt
return result
return _standard_call
[docs]class ScipyEigenvalueSolver(EigenvalueSolver):
"""
SciPy-based solver for both dense and sparse problems (if `n_eigs`
is given).
"""
name = 'eig.scipy'
def __init__(self, conf, **kwargs):
EigenvalueSolver.__init__(self, conf, **kwargs)
@standard_call
def __call__(self, mtx_a, mtx_b=None, n_eigs=None, eigenvectors=None,
status=None, conf=None):
if n_eigs is None:
mtx_a, mtx_b = self._to_array(mtx_a, mtx_b)
out = sla.eig(mtx_a, mtx_b, right=eigenvectors)
if eigenvectors:
eigs = out[0]
else:
eigs = out
ii = nm.argsort(eigs)
if eigenvectors:
mtx_ev = out[1][:,ii]
out = (eigs[ii], mtx_ev)
else:
out = (eigs,)
else:
try:
from scipy.splinalg import eigen_symmetric
except ImportError:
eigen_symmetric = None
try:
from scipy.sparse.linalg.eigen.arpack import eigen_symmetric
except ImportError:
eigen_symmetric = None
if eigen_symmetric is None:
raise ImportError('cannot import eigen_symmetric!')
out = eigen_symmetric(mtx_a, k=n_eigs, M=mtx_b)
return out
[docs]class ScipySGEigenvalueSolver(ScipyEigenvalueSolver):
"""
SciPy-based solver for dense symmetric problems.
"""
name = 'eig.sgscipy'
@staticmethod
[docs] def process_conf(conf, kwargs):
"""
Missing items are set to default values.
Example configuration, all items::
solver_20 = {
'name' : 'eigen2',
'kind' : 'eig.sgscipy',
'force_n_eigs' : True,
}
"""
get = make_get_conf(conf, kwargs)
common = EigenvalueSolver.process_conf(conf)
return Struct(force_n_eigs=get('force_n_eigs', False)) + common
@standard_call
def __call__(self, mtx_a, mtx_b=None, n_eigs=None, eigenvectors=None,
status=None, conf=None):
"""
Notes
-----
Eigenvectors argument is ignored, as they are computed always.
"""
import scipy.lib.lapack as ll
if (n_eigs is None) or (conf.force_n_eigs):
mtx_a, mtx_b = self._to_array(mtx_a, mtx_b)
if nm.iscomplexobj(mtx_a):
if mtx_b is None:
fun = ll.get_lapack_funcs(['heev'], arrays=(mtx_a,))[0]
else:
fun = ll.get_lapack_funcs(['hegv'], arrays=(mtx_a,))[0]
else:
if mtx_b is None:
fun = ll.get_lapack_funcs(['syev'], arrays=(mtx_a,))[0]
else:
fun = ll.get_lapack_funcs(['sygv'], arrays=(mtx_a,))[0]
if mtx_b is None:
out = fun(mtx_a)
else:
out = fun(mtx_a, mtx_b)
if not eigenvectors:
if n_eigs is None:
out = out[0]
else:
out = out[0][:n_eigs]
else:
if n_eigs is None:
out = out[:-1]
else:
out = (out[0][:n_eigs], out[1][:, :n_eigs])
else:
out = ScipyEigenvalueSolver.call(self, mtx_a, mtx_b, n_eigs,
eigenvectors, status=status)
return out
[docs]class LOBPCGEigenvalueSolver(EigenvalueSolver):
"""
SciPy-based LOBPCG solver for sparse symmetric problems.
"""
name = 'eig.scipy_lobpcg'
@staticmethod
[docs] def process_conf(conf, kwargs):
"""
Missing items are set to default values.
Example configuration, all items::
solver_2 = {
'name' : 'lobpcg',
'kind' : 'eig.scipy_lobpcg',
'i_max' : 20,
'n_eigs' : 5,
'eps_a' : None,
'largest' : True,
'precond' : None,
'verbosity' : 0,
}
"""
get = make_get_conf(conf, kwargs)
common = EigenvalueSolver.process_conf(conf)
return Struct(i_max=get('i_max', 20),
n_eigs=get('n_eigs', None),
eps_a=get('eps_a', None),
largest=get('largest', True),
precond=get('precond', None),
verbosity=get('verbosity', 0)) + common
def __init__(self, conf, **kwargs):
EigenvalueSolver.__init__(self, conf, **kwargs)
from scipy.sparse.linalg.eigen import lobpcg
self.lobpcg = lobpcg
@standard_call
def __call__(self, mtx_a, mtx_b=None, n_eigs=None, eigenvectors=None,
status=None, conf=None):
if n_eigs is None:
n_eigs = mtx_a.shape[0]
else:
n_eigs = min(n_eigs, mtx_a.shape[0])
x = nm.zeros((mtx_a.shape[0], n_eigs), dtype=nm.float64)
x[:n_eigs] = nm.eye(n_eigs, dtype=nm.float64)
out = self.lobpcg(mtx_a, x, mtx_b,
M=conf.precond,
tol=conf.eps_a, maxiter=conf.i_max,
largest=conf.largest,
verbosityLevel=conf.verbosity)
if not eigenvectors:
out = out[0]
return out
[docs]class PysparseEigenvalueSolver(EigenvalueSolver):
"""
Pysparse-based eigenvalue solver for sparse symmetric problems.
"""
name = 'eig.pysparse'
@staticmethod
[docs] def process_conf(conf, kwargs):
"""
Missing items are set to default values.
Example configuration, all items::
solver_2 = {
'name' : 'eigen1',
'kind' : 'eig.pysparse',
'i_max' : 150,
'eps_a' : 1e-5,
'tau' : -10.0,
'method' : 'qmrs',
'verbosity' : 0,
'strategy' : 1,
}
"""
get = make_get_conf(conf, kwargs)
common = EigenvalueSolver.process_conf(conf)
return Struct(i_max=get('i_max', 100),
n_eigs=get('n_eigs', 5),
eps_a=get('eps_a', 1e-5),
tau=get('tau', 0.0),
method=get('method', 'qmrs'),
verbosity=get('verbosity', 0),
strategy=get('strategy', 1)) + common
@staticmethod
def _convert_mat(mtx):
from pysparse import spmatrix
A = spmatrix.ll_mat(*mtx.shape)
for i in xrange(mtx.indptr.shape[0] - 1):
ii = slice(mtx.indptr[i], mtx.indptr[i+1])
n_in_row = ii.stop - ii.start
A.update_add_at(mtx.data[ii], [i] * n_in_row, mtx.indices[ii])
return A
def __init__(self, conf, **kwargs):
EigenvalueSolver.__init__(self, conf, **kwargs)
@standard_call
def __call__(self, mtx_a, mtx_b=None, n_eigs=None,
eigenvectors=None, status=None, conf=None):
imp = try_imports(['from pysparse import jdsym, itsolvers, precon',
'from pysparse.eigen import jdsym;'
' from pysparse import itsolvers, precon'],
'cannot import pysparse eigensolvers!')
jdsym = imp['jdsym']
itsolvers = imp['itsolvers']
precon = imp['precon']
output("solving...")
A = self._convert_mat(mtx_a)
Atau = A.copy()
if mtx_b is not None:
M = self._convert_mat(mtx_b)
Atau.shift(-conf.tau, M)
K = precon.jacobi(Atau)
A = A.to_sss()
if mtx_b is not None:
M = M.to_sss()
else:
M = None
method = getattr(itsolvers, conf.method)
kconv, lmbd, Q, it, it_in = jdsym.jdsym(A, M, K, n_eigs, conf.tau,
conf.eps_a, conf.i_max,
method,
clvl=conf.verbosity,
strategy=conf.strategy)
output("number of converged eigenvalues:", kconv)
output("...done")
if status is not None:
status['q'] = Q
status['it'] = it
status['it_in'] = it_in
return lmbd, Q
