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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Daniel Gomez Ferro <dgomezferro@gmail.com>
//
// 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"
template<typename Scalar> void
initSPD(double density,
Matrix<Scalar,Dynamic,Dynamic>& refMat,
SparseMatrix<Scalar>& sparseMat)
{
Matrix<Scalar,Dynamic,Dynamic> aux(refMat.rows(),refMat.cols());
initSparse(density,refMat,sparseMat);
refMat = refMat * refMat.adjoint();
for (int k=0; k<2; ++k)
{
initSparse(density,aux,sparseMat,ForceNonZeroDiag);
refMat += aux * aux.adjoint();
}
sparseMat.startFill();
for (int j=0 ; j<sparseMat.cols(); ++j)
for (int i=j ; i<sparseMat.rows(); ++i)
if (refMat(i,j)!=Scalar(0))
sparseMat.fill(i,j) = refMat(i,j);
sparseMat.endFill();
}
template<typename Scalar> void sparse_solvers(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;
// Scalar eps = 1e-6;
DenseVector vec1 = DenseVector::Random(rows);
std::vector<Vector2i> zeroCoords;
std::vector<Vector2i> nonzeroCoords;
// test triangular solver
{
DenseVector vec2 = vec1, vec3 = vec1;
SparseMatrix<Scalar> m2(rows, cols);
DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
// lower
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
VERIFY_IS_APPROX(refMat2.template marked<LowerTriangular>().solveTriangular(vec2),
m2.template marked<LowerTriangular>().solveTriangular(vec3));
// lower - transpose
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
VERIFY_IS_APPROX(refMat2.template marked<LowerTriangular>().transpose().solveTriangular(vec2),
m2.template marked<LowerTriangular>().transpose().solveTriangular(vec3));
// upper
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
VERIFY_IS_APPROX(refMat2.template marked<UpperTriangular>().solveTriangular(vec2),
m2.template marked<UpperTriangular>().solveTriangular(vec3));
// upper - transpose
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
VERIFY_IS_APPROX(refMat2.template marked<UpperTriangular>().transpose().solveTriangular(vec2),
m2.template marked<UpperTriangular>().transpose().solveTriangular(vec3));
}
// test LLT
{
// TODO fix the issue with complex (see SparseLLT::solveInPlace)
SparseMatrix<Scalar> m2(rows, cols);
DenseMatrix refMat2(rows, cols);
DenseVector b = DenseVector::Random(cols);
DenseVector refX(cols), x(cols);
initSPD(density, refMat2, m2);
refMat2.llt().solve(b, &refX);
typedef SparseMatrix<Scalar,LowerTriangular|SelfAdjoint> SparseSelfAdjointMatrix;
if (!NumTraits<Scalar>::IsComplex)
{
x = b;
SparseLLT<SparseSelfAdjointMatrix> (m2).solveInPlace(x);
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: default");
}
#ifdef EIGEN_CHOLMOD_SUPPORT
x = b;
SparseLLT<SparseSelfAdjointMatrix,Cholmod>(m2).solveInPlace(x);
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: cholmod");
#endif
if (!NumTraits<Scalar>::IsComplex)
{
#ifdef EIGEN_TAUCS_SUPPORT
x = b;
SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,IncompleteFactorization).solveInPlace(x);
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (IncompleteFactorization)");
x = b;
SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,SupernodalMultifrontal).solveInPlace(x);
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (SupernodalMultifrontal)");
x = b;
SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,SupernodalLeftLooking).solveInPlace(x);
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (SupernodalLeftLooking)");
#endif
}
}
// test LDLT
if (!NumTraits<Scalar>::IsComplex)
{
// TODO fix the issue with complex (see SparseLDLT::solveInPlace)
SparseMatrix<Scalar> m2(rows, cols);
DenseMatrix refMat2(rows, cols);
DenseVector b = DenseVector::Random(cols);
DenseVector refX(cols), x(cols);
//initSPD(density, refMat2, m2);
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, 0, 0);
refMat2 += refMat2.adjoint();
refMat2.diagonal() *= 0.5;
refMat2.ldlt().solve(b, &refX);
typedef SparseMatrix<Scalar,UpperTriangular|SelfAdjoint> SparseSelfAdjointMatrix;
x = b;
SparseLDLT<SparseSelfAdjointMatrix> ldlt(m2);
if (ldlt.succeeded())
ldlt.solveInPlace(x);
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LDLT: default");
}
// test LU
{
static int count = 0;
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);
LU<DenseMatrix> refLu(refMat2);
refLu.solve(b, &refX);
#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_SUPERLU_SUPPORT
{
x.setZero();
SparseLU<SparseMatrix<Scalar>,SuperLU> slu(m2);
if (slu.succeeded())
{
if (slu.solve(b,&x)) {
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: SuperLU");
}
// std::cerr << refDet << " == " << slu.determinant() << "\n";
if (count==0) {
VERIFY_IS_APPROX(refDet,slu.determinant()); // FIXME det is not very stable for complex
}
}
}
#endif
#ifdef EIGEN_UMFPACK_SUPPORT
{
// check solve
x.setZero();
SparseLU<SparseMatrix<Scalar>,UmfPack> slu(m2);
if (slu.succeeded()) {
if (slu.solve(b,&x)) {
if (count==0) {
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: umfpack"); // FIXME solve is not very stable for complex
}
}
VERIFY_IS_APPROX(refDet,slu.determinant());
// TODO check the extracted data
//std::cerr << slu.matrixL() << "\n";
}
}
#endif
count++;
}
}
void test_eigen2_sparse_solvers()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( sparse_solvers<double>(8, 8) );
CALL_SUBTEST_2( sparse_solvers<std::complex<double> >(16, 16) );
CALL_SUBTEST_1( sparse_solvers<double>(101, 101) );
}
}
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