# -*- coding: utf-8 -*-
# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# License version 3 as published by the Free Software Foundation.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
# Contributors:
# INITIAL AUTHORS - API and implementation and/or documentation
# :author: Francois Gallard, Charlie Vanaret
# OTHER AUTHORS - MACROSCOPIC CHANGES
"""
Linear solvers wrapper
**********************
"""
from __future__ import division, unicode_literals
import logging
import numpy as np
import scipy.sparse.linalg as scipy_linalg
from scipy.sparse.base import issparse
from scipy.sparse.linalg import bicgstab, cgs
LOGGER = logging.getLogger(__name__)
[docs]class LinearSolver(object):
"""Solve a linear system Ax=b."""
LGMRES = "lgmres"
AVAILABLE_SOLVERS = {LGMRES: scipy_linalg.lgmres}
def __init__(self):
"""Constructor."""
self.outer_v = [] # Used to store (v,Av) pairs for restart and multiple RHS
@staticmethod
def _check_linear_solver(linear_solver):
"""Check that linear solver is available.
:param linear_solver: name of linear solver used to solve linear solver
"""
solver = LinearSolver.AVAILABLE_SOLVERS.get(linear_solver, None)
if solver is None:
raise AttributeError(
"Invalid linear solver" + str(linear_solver) + " for scipy sparse: "
)
return solver
@staticmethod
def _check_b(a_mat, b_vec):
"""Check the dimensions of the vector b converts it to ndarray if sparse, for
lgmres needs.
:param a_mat: the matrix A
:param b_vec: the vector b
:returns: the vector b with consistent dimensions
"""
if len(b_vec.shape) == 2 and b_vec.shape[1] != 1:
LOGGER.error(
"Incompatible dimensions in linear system Ax=b, A "
"shape is %s and b shape is %s",
str(a_mat.shape),
str(b_vec.shape),
)
raise ValueError(
"Second member of the linear system" + " must be a column vector"
)
if issparse(b_vec):
b_vec = b_vec.toarray()
return b_vec.real
[docs] def solve(self, a_mat, b_vec, linear_solver="lgmres", **kwargs_lin):
"""Solves the linear system Ax=b using scipy sparse GMRES solver.
:param a_mat: matrix A of the system, can be a sparse matrix
:param b_vec: second member
:param linear_solver: name of linear solver (Default value = 'lgmres')
:param kwargs_lin: arguments passed to the scipy linear solver
:returns: solution x such that A.x=b
"""
scipy_linear_solver = LinearSolver._check_linear_solver(linear_solver)
# check the dimensions of b
b_vec = LinearSolver._check_b(a_mat, b_vec)
# solve the system
if "tol" not in kwargs_lin:
kwargs_lin["tol"] = 1e-8
kwargs_lin["atol"] = kwargs_lin["tol"]
if "maxiter" not in kwargs_lin:
kwargs_lin["maxiter"] = 50 * len(b_vec)
else:
kwargs_lin["maxiter"] = min(kwargs_lin["maxiter"], 50 * len(b_vec))
sol, info = scipy_linear_solver(
A=a_mat, b=b_vec, outer_v=self.outer_v, **kwargs_lin
)
base_msg = "scipy linear solver algorithm stop info: "
if info > 0:
msg = "convergence to tolerance not achieved, number of iterations"
total_msg = base_msg + msg
LOGGER.warning(total_msg)
total_msg = base_msg + "--- trying bicgstab method"
LOGGER.warning(total_msg)
sol, info = bicgstab(
a_mat, b_vec, sol, maxiter=50 * len(b_vec), atol=kwargs_lin["atol"]
)
diff = a_mat.dot(sol) - b_vec.T
res = np.sqrt(np.sum(diff))
total_msg = "{} --- --- residual = {}".format(base_msg, res)
LOGGER.warning(total_msg)
total_msg = "{} --- --- info = {}".format(base_msg, info)
LOGGER.warning(total_msg)
if info < 0:
total_msg = "{} --- trying cgs method".format(base_msg)
LOGGER.warning(total_msg)
sol, info = cgs(
a_mat, b_vec, sol, maxiter=50 * len(b_vec), atol=kwargs_lin["atol"]
)
diff = a_mat.dot(sol) - b_vec.T
res = np.sqrt(np.sum(diff))
total_msg = "{} --- --- residual = {}".format(base_msg, res)
LOGGER.warning(total_msg)
total_msg = "{} --- --- info = {}".format(base_msg, info)
LOGGER.warning(total_msg)
elif info < 0:
msg = "illegal input or breakdown"
total_msg = base_msg + msg
LOGGER.error(total_msg)
return np.atleast_2d(sol).T
