from __future__ import absolute_import
import numpy as nm
import scipy.sparse as sps
from sfepy.base.base import output, get_default, try_imports, Struct
from sfepy.base.timing import Timer
from sfepy.solvers.solvers import Solver, EigenvalueSolver
import six
from six.moves import range
[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):
timer = Timer(start=True)
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)
if n_eigs == 0:
result = self._ret_zero(mtx_a, eigenvectors=eigenvectors)
else:
result = call(self, mtx_a, mtx_b, n_eigs, eigenvectors, status,
conf, **kwargs)
elapsed = timer.stop()
if status is not None:
status['time'] = elapsed
return result
return _standard_call
[docs]class ScipyEigenvalueSolver(EigenvalueSolver):
"""
SciPy-based solver for both dense and sparse problems.
The problem is consirered sparse if `n_eigs` argument is not None.
"""
name = 'eig.scipy'
_parameters = [
('method', "{'eig', 'eigh', 'eigs', 'eigsh'}", 'eigs', False,
"""The method for solving general or symmetric eigenvalue problems:
for dense problems :func:`eig()` or :func:`eigh()` can be used, for
sparse problems :func:`eigs()` or :func:`eigsh()` should be
used."""),
('which', "'LM' | 'SM' | 'LR' | 'SR' | 'LI' | 'SI'", 'SM', False,
"""Which eigenvectors and eigenvalues to find,
see :func:`scipy.sparse.linalg.eigs()`
or :func:`scipy.sparse.linalg.eigsh()`. For dense problmes,
only 'LM' and 'SM' can be used"""),
('*', '*', None, False,
'Additional parameters supported by the method.'),
]
def __init__(self, conf, **kwargs):
EigenvalueSolver.__init__(self, conf, **kwargs)
import scipy.linalg as sla
self.sla = sla
aux = try_imports(['import scipy.sparse.linalg as ssla'],
'cannot import scipy sparse eigenvalue solvers!')
self.ssla = aux['ssla']
@standard_call
def __call__(self, mtx_a, mtx_b=None, n_eigs=None, eigenvectors=None,
status=None, conf=None):
kwargs = self.build_solver_kwargs(conf)
if conf.method in ('eig', 'eigh'):
mtx_a, mtx_b = self._to_array(mtx_a, mtx_b)
if conf.method == 'eig':
out = self.sla.eig(mtx_a, mtx_b, right=eigenvectors, **kwargs)
else:
out = self.sla.eigh(mtx_a, mtx_b,
eigvals_only=not eigenvectors, **kwargs)
else:
eig = self.ssla.eigs if conf.method == 'eigs' else self.ssla.eigsh
out = eig(mtx_a, M=mtx_b, k=n_eigs, which=conf.which,
return_eigenvectors=eigenvectors, **kwargs)
if eigenvectors:
eigs = out[0]
else:
eigs = out
if nm.iscomplexobj(eigs):
ii = nm.argsort(nm.linalg.norm(eigs[:, None], axis=1))
else:
ii = nm.argsort(eigs)
if n_eigs is not None and (conf.method in ('eig', 'eigh')):
if conf.which == 'SM':
ii = ii[:n_eigs]
elif conf.which == 'LM':
ii = ii[:-n_eigs-1:-1]
else:
raise ValueError("only 'LM' or 'SM' can be used with dense"
" problems! (%s)" % conf.which)
if eigenvectors:
mtx_ev = out[1][:, ii]
out = (eigs[ii], mtx_ev)
else:
out = eigs[ii]
return out
[docs]class ScipySGEigenvalueSolver(EigenvalueSolver):
"""
SciPy-based solver for dense symmetric problems.
"""
name = 'eig.sgscipy'
def __init__(self, conf, **kwargs):
EigenvalueSolver.__init__(self, conf, **kwargs)
try:
import scipy.linalg.lapack as llapack
except ImportError:
import scipy.lib.lapack as llapack
self.llapack = llapack
@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.
"""
ll = self.llapack
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)
# Fix output order of scipy.linalg.lapack functions.
if out[0].ndim == 2:
out = (out[1], out[0]) + out[2:]
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])
return out
[docs]class LOBPCGEigenvalueSolver(EigenvalueSolver):
"""
SciPy-based LOBPCG solver for sparse symmetric problems.
"""
name = 'eig.scipy_lobpcg'
_parameters = [
('i_max', 'int', 20, False,
'The maximum number of iterations.'),
('eps_a', 'float', None, False,
'The absolute tolerance for the convergence.'),
('largest', 'bool', True, False,
'If True, solve for the largest eigenvalues, otherwise the smallest.'),
('precond', '{dense matrix, sparse matrix, LinearOperator}',
None, False,
'The preconditioner.'),
]
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.verbose)
if not eigenvectors:
out = out[0]
return out
[docs]def init_slepc_args():
try:
import sys, slepc4py
except ImportError:
return
argv = [arg for arg in sys.argv if arg not in ['-h', '--help']]
slepc4py.init(argv)
[docs]class SLEPcEigenvalueSolver(EigenvalueSolver):
"""
General SLEPc eigenvalue problem solver.
"""
name = 'eig.slepc'
_parameters = [
('method', 'str', 'krylovschur', False,
'The actual solver to use.'),
('problem', 'str', 'gnhep', False,
"""The problem type: Hermitian (hep), non-Hermitian (nhep), generalized
Hermitian (ghep), generalized non-Hermitian (gnhep), generalized
non-Hermitian with positive semi-definite B (pgnhep), and generalized
Hermitian-indefinite (ghiep)."""),
('i_max', 'int', 20, False,
'The maximum number of iterations.'),
('eps', 'float', None, False,
'The convergence tolerance.'),
('conv_test', '{"abs", "rel", "norm", "user"}, ', 'abs', False,
'The type of convergence test.'),
('which', """{'largest_magnitude', 'smallest_magnitude',
'largest_real', 'smallest_real',
'largest_imaginary', 'smallest_imaginary', 'target_magnitude',
'target_real', 'target_imaginary', 'all', 'which_user'}""",
'largest_magnitude', False,
'Which eigenvectors and eigenvalues to find.'),
('*', '*', None, False,
'Additional parameters supported by the method.'),
]
def __init__(self, conf, comm=None, context=None, **kwargs):
if comm is None:
init_slepc_args()
from petsc4py import PETSc as petsc
from slepc4py import SLEPc as slepc
EigenvalueSolver.__init__(self, conf, petsc=petsc, slepc=slepc,
comm=comm, context=context, **kwargs)
[docs] def create_eps(self, options=None, comm=None):
optDB = self.petsc.Options()
if options is not None:
for key, val in six.iteritems(options):
optDB[key] = val
es = self.slepc.EPS()
es.create(comm)
return es
[docs] def create_petsc_matrix(self, mtx, comm=None):
if mtx is None or isinstance(mtx, self.petsc.Mat):
pmtx = mtx
else:
mtx = sps.csr_matrix(mtx)
pmtx = self.petsc.Mat()
pmtx.createAIJ(mtx.shape, csr=(mtx.indptr, mtx.indices, mtx.data),
comm=comm)
return pmtx
@standard_call
def __call__(self, mtx_a, mtx_b=None, n_eigs=None, eigenvectors=None,
status=None, conf=None, comm=None, context=None):
solver_kwargs = self.build_solver_kwargs(conf)
pmtx_a = self.create_petsc_matrix(mtx_a, comm=comm)
pmtx_b = self.create_petsc_matrix(mtx_b, comm=comm)
es = self.create_eps(options=solver_kwargs, comm=comm)
es.setType(conf.method)
es.setProblemType(getattr(es.ProblemType, conf.problem.upper()))
es.setDimensions(nev=n_eigs)
es.setTolerances(tol=conf.eps, max_it=conf.i_max)
es.setOperators(pmtx_a, pmtx_b)
es.setConvergenceTest(getattr(es.Conv, conf.conv_test.upper()))
es.setWhichEigenpairs(getattr(es.Which, conf.which.upper()))
es.setFromOptions()
es.solve()
n_converged = es.getConverged()
if status is not None:
status['n_iter'] = es.getIterationNumber()
status['n_converged'] = n_converged
if not eigenvectors:
out = nm.array([es.getEigenvalue(ii) for ii in range(n_converged)])
else:
vr, vi = pmtx_a.createVecs()
eigs = []
vrs, vis = [], []
is_real = True
for ii in range(n_converged):
val = es.getEigenpair(ii, vr, vi)
eigs.append(val if val.imag != 0 else val.real)
vrs.append(vr.getArray().copy())
vis.append(vi.getArray().copy())
if is_real and nm.sum(nm.abs(vis[-1])) > 0.0:
is_real = False
eigs = nm.array(eigs)
vecs = nm.array(vrs).T
if not is_real:
vecs += 1j * nm.array(vis)
out = (eigs, vecs)
return out
[docs]class MatlabEigenvalueSolver(EigenvalueSolver):
"""
Matlab eigenvalue problem solver.
"""
name = 'eig.matlab'
_parameters = [
('method', """{'eig', 'eigs', None}""", 'eigs', False,
"""The solution method. Note that eig() function cannot be used for
all inputs. If `n_eigs` is not None, eigs() is used regardless of
this parameter."""),
('balance', """{'balance', 'nobalance'}""", 'balance', False,
'The balance option for eig().'),
('algorithm', """{'chol', 'qz'}""", 'chol', False,
'The algorithm option for eig().'),
('which',
"""{'lm', 'sm', 'la', 'sa', 'be' 'lr', 'sr', 'li', 'si', sigma}""",
'lm', False,
'Which eigenvectors and eigenvalues to find with eigs().'),
('*', '*', None, False,
'Additional parameters supported by eigs().'),
]
def __init__(self, conf, comm=None, context=None, **kwargs):
import matlab.engine as me
EigenvalueSolver.__init__(self, conf, me=me, context=context,
**kwargs)
@standard_call
def __call__(self, mtx_a, mtx_b=None, n_eigs=None, eigenvectors=None,
status=None, conf=None, comm=None, context=None):
import os
import shutil
import tempfile
import scipy.io as sio
solver_kwargs = self.build_solver_kwargs(conf)
dirname = tempfile.mkdtemp()
mtx_filename = os.path.join(dirname, 'matrices.mat')
eigs_filename = os.path.join(dirname, 'eigs.mat')
sio.savemat(mtx_filename, {
'A' : mtx_a,
'B' : mtx_b if mtx_b is not None else 'None',
'n_eigs' : n_eigs if n_eigs is not None else 'None',
'eigenvectors' : eigenvectors,
'method' : conf.method,
'balance' : conf.balance,
'algorithm' : conf.algorithm,
'which' : conf.which,
'verbose' : conf.verbose,
'eigs_options' : solver_kwargs,
})
eng = self.me.start_matlab()
eng.cd(os.path.dirname(__file__))
eng.matlab_eig(mtx_filename, eigs_filename)
eng.quit()
evp = sio.loadmat(eigs_filename)
shutil.rmtree(dirname)
out = evp['vals'][:, 0]
if eigenvectors:
out = (out, evp['vecs'])
return out