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"""Unit tests for the KrylovSolver interface"""
# Copyright (C) 2016 Nate Sime
#
# 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/>.
import pytest
from dolfin import *
from dolfin_utils.test import skip_if_not_PETsc_or_not_slepc, fixture
# Stiffness and mass bilinear formulations
def k(u, v):
return inner(grad(u), grad(v))*dx
def m(u, v):
return dot(u, v)*dx
# Wrappers around SLEPcEigenSolver for test_slepc_eigensolver_gen_hermitian
def SLEPcEigenSolverOperatorsFromInit(K, M):
return SLEPcEigenSolver(K, M)
def SLEPcEigenSolverOperatorsFromSetOperators(K, M):
slepc_eigen_solver = SLEPcEigenSolver(K.mpi_comm())
slepc_eigen_solver.set_operators(K, M)
return slepc_eigen_solver
# Fixtures
@fixture
def mesh():
return UnitSquareMesh(32, 32)
@fixture
def V(mesh):
return FunctionSpace(mesh, "CG", 1)
@fixture
def V_vec(mesh):
return VectorFunctionSpace(mesh, "CG", 1)
@fixture
def K_M(V):
u, v = TrialFunction(V), TestFunction(V)
K_mat, M_mat = PETScMatrix(), PETScMatrix()
x0 = PETScVector()
L = Constant(0.0)*v*dx
assemble_system(k(u, v), L, bcs=[], A_tensor=K_mat, b_tensor=x0)
assemble_system(m(u, v), L, bcs=[], A_tensor=M_mat, b_tensor=x0)
return K_mat, M_mat
@fixture
def K_M_vec(V_vec):
u, v = TrialFunction(V_vec), TestFunction(V_vec)
K_mat, M_mat = PETScMatrix(), PETScMatrix()
x0 = PETScVector()
L = dot(Constant([0.0]*V_vec.mesh().geometry().dim()), v)*dx
assemble_system(k(u, v), L, bcs=[], A_tensor=K_mat, b_tensor=x0)
assemble_system(m(u, v), L, bcs=[], A_tensor=M_mat, b_tensor=x0)
return K_mat, M_mat
# Tests
@skip_if_not_PETsc_or_not_slepc
def test_set_from_options():
"Test SLEPc options prefixes"
prefix = "my_slepc_"
solver = SLEPcEigenSolver(MPI.comm_world)
solver.set_options_prefix(prefix)
solver.set_from_options()
assert solver.get_options_prefix() == prefix
@skip_if_not_PETsc_or_not_slepc
@pytest.mark.parametrize("SLEPcEigenSolverWrapper", (SLEPcEigenSolverOperatorsFromInit, SLEPcEigenSolverOperatorsFromSetOperators))
def test_slepc_eigensolver_gen_hermitian(K_M, SLEPcEigenSolverWrapper):
"Test SLEPc eigen solver"
K, M = K_M
esolver = SLEPcEigenSolverWrapper(K, M)
esolver.parameters["solver"] = "krylov-schur"
esolver.parameters["spectral_transform"] = 'shift-and-invert'
esolver.parameters['spectral_shift'] = 0.0
esolver.parameters["problem_type"] = "gen_hermitian"
nevs = 20
esolver.solve(nevs)
# Test default eigenvalue
re_0, im_0 = esolver.get_eigenvalue(0)
assert near(re_0, 0.0, eps=1e-12)
assert near(im_0, 0.0)
re_0, im_0, v_re_0, v_im_0 = esolver.get_eigenpair(0)
assert near(re_0, 0.0, eps=1e-12)
assert near(im_0, 0.0)
assert v_re_0.norm("l2") > 0.0
assert near(v_im_0.norm("l2"), 0.0)
# Test remaining eigenvalues and eigenpairs
for j in range(1, nevs):
re, im = esolver.get_eigenvalue(j)
assert re > 0.0
assert near(im, 0.0)
for j in range(1, nevs):
re, im, v_re, v_im = esolver.get_eigenpair(j)
assert re > 0.0
assert near(im, 0.0)
assert v_re.norm("l2") > 0.0
assert near(v_im.norm("l2"), 0.0)
@skip_if_not_PETsc_or_not_slepc
def test_slepc_null_space(K_M, V):
"Test SLEPc eigen solver with nullspace as PETScVector"
K, M = K_M
esolver = SLEPcEigenSolver(K, M)
esolver.parameters["solver"] = "jacobi-davidson"
esolver.parameters["problem_type"] = "gen_hermitian"
u0 = Function(V)
nullspace_basis = as_backend_type(u0.vector().copy())
V.dofmap().set(nullspace_basis, 1.0)
esolver.set_deflation_space(VectorSpaceBasis([nullspace_basis]))
nevs = 20
esolver.solve(nevs)
for j in range(1, nevs):
re, im, v_re, v_im = esolver.get_eigenpair(j)
assert re > 0.0
assert near(im, 0.0)
assert v_re.norm("l2") > 0.0
assert near(v_im.norm("l2"), 0.0)
@skip_if_not_PETsc_or_not_slepc
def test_slepc_vector_null_space(K_M_vec, V_vec):
"Test SLEPc eigen solver with nullspace as VectorSpaceBasis"
def build_nullspace(V, x):
nullspace_basis = [x.copy() for i in range(2)]
V.sub(0).dofmap().set(nullspace_basis[0], 1.0)
V.sub(1).dofmap().set(nullspace_basis[1], 1.0)
for x in nullspace_basis:
x.apply("insert")
# Create vector space basis and orthogonalize
basis = VectorSpaceBasis(nullspace_basis)
basis.orthonormalize()
return basis
K, M = K_M_vec
esolver = SLEPcEigenSolver(K, M)
esolver.parameters["solver"] = "jacobi-davidson"
esolver.parameters["problem_type"] = "gen_hermitian"
u0 = Function(V_vec)
nullspace_basis = build_nullspace(V_vec, u0.vector())
esolver.set_deflation_space(nullspace_basis)
nevs = 20
esolver.solve(nevs)
for j in range(1, nevs):
re, im, v_re, v_im = esolver.get_eigenpair(j)
assert re > 0.0
assert near(im, 0.0)
assert v_re.norm("l2") > 0.0
assert near(v_im.norm("l2"), 0.0)
@skip_if_not_PETsc_or_not_slepc
def test_slepc_initial_space(K_M, V):
"Test SLEPc eigen solver with inital space as PETScVector"
K, M = K_M
esolver = SLEPcEigenSolver(K, M)
esolver.parameters["solver"] = "jacobi-davidson"
esolver.parameters["problem_type"] = "gen_hermitian"
u0 = as_backend_type(interpolate(Constant(2.0), V).vector())
esolver.set_initial_space(VectorSpaceBasis([u0]))
nevs = 20
esolver.solve(nevs)
for j in range(1, nevs):
re, im, v_re, v_im = esolver.get_eigenpair(j)
assert re > 0.0
assert near(im, 0.0)
assert v_re.norm("l2") > 0.0
assert near(v_im.norm("l2"), 0.0)
@skip_if_not_PETsc_or_not_slepc
def test_slepc_vector_initial_space(K_M_vec, V_vec):
"Test SLEPc eigen solver with initial space as VectorSpaceBasis"
K, M = K_M_vec
esolver = SLEPcEigenSolver(K, M)
esolver.parameters["solver"] = "jacobi-davidson"
esolver.parameters["problem_type"] = "gen_hermitian"
u0 = as_backend_type(interpolate(Constant((2.0, 1.0)), V_vec).vector())
u1 = as_backend_type(interpolate(Constant((0.0, -4.0)), V_vec).vector())
initial_space = VectorSpaceBasis([u0, u1])
esolver.set_initial_space(initial_space)
nevs = 20
esolver.solve(nevs)
for j in range(1, nevs):
re, im, v_re, v_im = esolver.get_eigenpair(j)
assert re > 0.0
assert near(im, 0.0)
assert v_re.norm("l2") > 0.0
assert near(v_im.norm("l2"), 0.0)
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