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"Unit tests for matrix-free linear solvers (LinearOperator)"
# Copyright (C) 2012 Anders Logg
#
# This file is part of DOLFIN.
#
# DOLFIN is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# DOLFIN 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 DOLFIN. If not, see <http://www.gnu.org/licenses/>.
from dolfin import *
import pytest
from dolfin_utils.test import *
backends = ["PETSc"]
# Backends supporting the LinearOperator interface
@pytest.mark.parametrize('backend', backends)
def test_linear_operator(backend):
# Check whether backend is available
if not has_linear_algebra_backend(backend):
pytest.skip('Need %s as backend to run this test' % backend)
# Set linear algebra backend
prev_backend = parameters["linear_algebra_backend"]
parameters["linear_algebra_backend"] = backend
# Define linear operator
class MyLinearOperator(LinearOperator):
def __init__(self, a_action, u):
LinearOperator.__init__(self, u.vector(), u.vector())
self.a_action = a_action
self.u = u
def size(self, dim):
return self.u.function_space().dim()
def mult(self, x, y):
# Update coefficient vector
self.u.vector()[:] = x
# Assemble action
assemble(self.a_action, tensor=y)
# Try wrapped and backend implementation of operator
for _as_backend_type in [(lambda x: x), as_backend_type]:
# Compute reference value by solving ordinary linear system
mesh = UnitSquareMesh(8, 8)
V = FunctionSpace(mesh, "Lagrange", 1)
u = TrialFunction(V)
v = TestFunction(V)
f = Constant(1.0)
a = dot(grad(u), grad(v))*dx + u*v*dx
L = f*v*dx
A = assemble(a)
b = assemble(L)
x = Vector()
solve(A, x, b, "gmres", "none")
norm_ref = norm(x, "l2")
# Solve using linear operator defined by form action
u = Function(V)
a_action = action(a, coefficient=u)
O = MyLinearOperator(a_action, u)
Ob = _as_backend_type(O)
solve(Ob, x, b, "gmres", "none")
norm_action = norm(x, "l2")
# Check at least that petsc4py interface is available
if backend == 'PETSc' and has_petsc4py() and _as_backend_type == as_backend_type:
from petsc4py import PETSc
assert isinstance(Ob.mat(), PETSc.Mat)
# Reset backend
parameters["linear_algebra_backend"] = prev_backend
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