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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2010 Gael Guennebaud <g.gael@free.fr>
//
// Eigen 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.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen 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 or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#include "sparse.h"
#include <Eigen/SparseExtra>
#ifdef EIGEN_UMFPACK_SUPPORT
#include <Eigen/UmfPackSupport>
#endif
#ifdef EIGEN_SUPERLU_SUPPORT
#include <Eigen/SuperLUSupport>
#endif
template<typename Scalar> void sparse_lu(int rows, int cols)
{
double density = std::max(8./(rows*cols), 0.01);
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
typedef Matrix<Scalar,Dynamic,1> DenseVector;
DenseVector vec1 = DenseVector::Random(rows);
std::vector<Vector2i> zeroCoords;
std::vector<Vector2i> nonzeroCoords;
SparseMatrix<Scalar> m2(rows, cols);
DenseMatrix refMat2(rows, cols);
DenseVector b = DenseVector::Random(cols);
DenseVector refX(cols), x(cols);
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag, &zeroCoords, &nonzeroCoords);
FullPivLU<DenseMatrix> refLu(refMat2);
refX = refLu.solve(b);
#if defined(EIGEN_SUPERLU_SUPPORT) || defined(EIGEN_UMFPACK_SUPPORT)
Scalar refDet = refLu.determinant();
#endif
x.setZero();
// // SparseLU<SparseMatrix<Scalar> > (m2).solve(b,&x);
// // VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: default");
#ifdef EIGEN_UMFPACK_SUPPORT
{
// check solve
x.setZero();
SparseLU<SparseMatrix<Scalar>,UmfPack> lu(m2);
VERIFY(lu.succeeded() && "umfpack LU decomposition failed");
VERIFY(lu.solve(b,&x) && "umfpack LU solving failed");
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: umfpack");
VERIFY_IS_APPROX(refDet,lu.determinant());
// TODO check the extracted data
//std::cerr << slu.matrixL() << "\n";
}
#endif
#ifdef EIGEN_SUPERLU_SUPPORT
// legacy, deprecated API
{
x.setZero();
SparseLU<SparseMatrix<Scalar>,SuperLULegacy> slu(m2);
if (slu.succeeded())
{
DenseVector oldb = b;
if (slu.solve(b,&x)) {
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: SuperLU");
}
else
std::cerr << "super lu solving failed\n";
VERIFY(oldb.isApprox(b) && "the rhs should not be modified!");
// std::cerr << refDet << " == " << slu.determinant() << "\n";
if (slu.solve(b, &x, SvTranspose)) {
VERIFY(b.isApprox(m2.transpose() * x, test_precision<Scalar>()));
}
else
std::cerr << "super lu solving failed\n";
if (slu.solve(b, &x, SvAdjoint)) {
VERIFY(b.isApprox(m2.adjoint() * x, test_precision<Scalar>()));
}
else
std::cerr << "super lu solving failed\n";
if (!NumTraits<Scalar>::IsComplex) {
VERIFY_IS_APPROX(refDet,slu.determinant()); // FIXME det is not very stable for complex
}
}
else
std::cerr << "super lu factorize failed\n";
}
// New API
{
x.setZero();
SuperLU<SparseMatrix<Scalar> > slu(m2);
if (slu.info() == Success)
{
DenseVector oldb = b;
x = slu.solve(b);
VERIFY(oldb.isApprox(b) && "the rhs should not be modified!");
if (slu.info() == Success) {
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "SuperLU");
}
else
std::cerr << "super lu solving failed\n";
if (!NumTraits<Scalar>::IsComplex) {
VERIFY_IS_APPROX(refDet,slu.determinant()); // FIXME det is not very stable for complex
}
}
else
std::cerr << "super lu factorize failed\n";
}
#endif
}
void test_sparse_lu()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1(sparse_lu<double>(8, 8) );
int s = internal::random<int>(1,300);
CALL_SUBTEST_2(sparse_lu<std::complex<double> >(s,s) );
CALL_SUBTEST_1(sparse_lu<double>(s,s) );
}
}
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