eigen/test/sparse_solver.h

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2011 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/SparseCore>
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template<typename Solver, typename Rhs, typename DenseMat, typename DenseRhs>
void check_sparse_solving(Solver& solver, const typename Solver::MatrixType& A, const Rhs& b, const DenseMat& dA, const DenseRhs& db)
{
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
DenseRhs refX = dA.lu().solve(db);
Rhs x(b.rows(), b.cols());
Rhs oldb = b;
solver.compute(A);
if (solver.info() != Success)
{
std::cerr << "sparse solver testing: factorization failed (check_sparse_solving)\n";
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exit(0);
return;
}
x = solver.solve(b);
if (solver.info() != Success)
{
std::cerr << "sparse solver testing: solving failed\n";
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return;
}
VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
VERIFY(x.isApprox(refX,test_precision<Scalar>()));
x.setZero();
// test the analyze/factorize API
solver.analyzePattern(A);
solver.factorize(A);
if (solver.info() != Success)
{
std::cerr << "sparse solver testing: factorization failed (check_sparse_solving)\n";
exit(0);
return;
}
x = solver.solve(b);
if (solver.info() != Success)
{
std::cerr << "sparse solver testing: solving failed\n";
return;
}
VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
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VERIFY(x.isApprox(refX,test_precision<Scalar>()));
}
template<typename Solver, typename Rhs>
void check_sparse_solving_real_cases(Solver& solver, const typename Solver::MatrixType& A, const Rhs& b, const Rhs& refX)
{
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
typedef typename Mat::RealScalar RealScalar;
Rhs x(b.rows(), b.cols());
solver.compute(A);
if (solver.info() != Success)
{
std::cerr << "sparse solver testing: factorization failed (check_sparse_solving_real_cases)\n";
exit(0);
return;
}
x = solver.solve(b);
if (solver.info() != Success)
{
std::cerr << "sparse solver testing: solving failed\n";
return;
}
RealScalar res_error;
// Compute the norm of the relative error
if(refX.size() != 0)
res_error = (refX - x).norm()/refX.norm();
else
{
// Compute the relative residual norm
res_error = (b - A * x).norm()/b.norm();
}
if (res_error > test_precision<Scalar>() ){
std::cerr << "Test " << g_test_stack.back() << " failed in "EI_PP_MAKE_STRING(__FILE__)
<< " (" << EI_PP_MAKE_STRING(__LINE__) << ")" << std::endl << std::endl;
abort();
}
}
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template<typename Solver, typename DenseMat>
void check_sparse_determinant(Solver& solver, const typename Solver::MatrixType& A, const DenseMat& dA)
{
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
typedef typename Mat::RealScalar RealScalar;
solver.compute(A);
if (solver.info() != Success)
{
std::cerr << "sparse solver testing: factorization failed (check_sparse_determinant)\n";
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return;
}
Scalar refDet = dA.determinant();
VERIFY_IS_APPROX(refDet,solver.determinant());
}
template<typename Solver, typename DenseMat>
int generate_sparse_spd_problem(Solver& , typename Solver::MatrixType& A, typename Solver::MatrixType& halfA, DenseMat& dA, int maxSize = 300)
{
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
int size = internal::random<int>(1,maxSize);
double density = (std::max)(8./(size*size), 0.01);
Mat M(size, size);
DenseMatrix dM(size, size);
initSparse<Scalar>(density, dM, M, ForceNonZeroDiag);
A = M * M.adjoint();
dA = dM * dM.adjoint();
halfA.resize(size,size);
halfA.template selfadjointView<Solver::UpLo>().rankUpdate(M);
return size;
}
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#ifdef TEST_REAL_CASES
template<typename Scalar>
inline std::string get_matrixfolder()
{
std::string mat_folder = TEST_REAL_CASES;
if( internal::is_same<Scalar, std::complex<float> >::value || internal::is_same<Scalar, std::complex<double> >::value )
mat_folder = mat_folder + static_cast<string>("/complex/");
else
mat_folder = mat_folder + static_cast<string>("/real/");
return mat_folder;
}
#endif
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template<typename Solver> void check_sparse_spd_solving(Solver& solver)
{
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
typedef typename Mat::Index Index;
typedef SparseMatrix<Scalar,ColMajor> SpMat;
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typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
typedef Matrix<Scalar,Dynamic,1> DenseVector;
// generate the problem
Mat A, halfA;
DenseMatrix dA;
int size = generate_sparse_spd_problem(solver, A, halfA, dA);
// generate the right hand sides
int rhsCols = internal::random<int>(1,16);
double density = (std::max)(8./(size*rhsCols), 0.1);
SpMat B(size,rhsCols);
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DenseVector b = DenseVector::Random(size);
DenseMatrix dB(size,rhsCols);
initSparse<Scalar>(density, dB, B);
for (int i = 0; i < g_repeat; i++) {
check_sparse_solving(solver, A, b, dA, b);
check_sparse_solving(solver, halfA, b, dA, b);
check_sparse_solving(solver, A, dB, dA, dB);
check_sparse_solving(solver, halfA, dB, dA, dB);
check_sparse_solving(solver, A, B, dA, dB);
check_sparse_solving(solver, halfA, B, dA, dB);
}
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// First, get the folder
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#ifdef TEST_REAL_CASES
if (internal::is_same<Scalar, float>::value
|| internal::is_same<Scalar, std::complex<float> >::value)
return ;
std::string mat_folder = get_matrixfolder<Scalar>();
MatrixMarketIterator<Scalar> it(mat_folder);
for (; it; ++it)
{
if (it.sym() == SPD){
Mat halfA;
PermutationMatrix<Dynamic, Dynamic, Index> pnull;
halfA.template selfadjointView<Solver::UpLo>() = it.matrix().template triangularView<Eigen::Lower>().twistedBy(pnull);
std::cout<< " ==== SOLVING WITH MATRIX " << it.matname() << " ==== \n";
check_sparse_solving_real_cases(solver, it.matrix(), it.rhs(), it.refX());
check_sparse_solving_real_cases(solver, halfA, it.rhs(), it.refX());
}
}
#endif
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}
template<typename Solver> void check_sparse_spd_determinant(Solver& solver)
{
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
// generate the problem
Mat A, halfA;
DenseMatrix dA;
generate_sparse_spd_problem(solver, A, halfA, dA, 30);
for (int i = 0; i < g_repeat; i++) {
check_sparse_determinant(solver, A, dA);
check_sparse_determinant(solver, halfA, dA );
}
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}
template<typename Solver, typename DenseMat>
int generate_sparse_square_problem(Solver&, typename Solver::MatrixType& A, DenseMat& dA, int maxSize = 300)
{
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
int size = internal::random<int>(1,maxSize);
double density = (std::max)(8./(size*size), 0.01);
A.resize(size,size);
dA.resize(size,size);
initSparse<Scalar>(density, dA, A, ForceNonZeroDiag);
return size;
}
template<typename Solver> void check_sparse_square_solving(Solver& solver)
{
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
typedef Matrix<Scalar,Dynamic,1> DenseVector;
int rhsCols = internal::random<int>(1,16);
Mat A;
DenseMatrix dA;
int size = generate_sparse_square_problem(solver, A, dA);
DenseVector b = DenseVector::Random(size);
DenseMatrix dB = DenseMatrix::Random(size,rhsCols);
A.makeCompressed();
for (int i = 0; i < g_repeat; i++) {
check_sparse_solving(solver, A, b, dA, b);
check_sparse_solving(solver, A, dB, dA, dB);
}
// First, get the folder
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#ifdef TEST_REAL_CASES
if (internal::is_same<Scalar, float>::value
|| internal::is_same<Scalar, std::complex<float> >::value)
return ;
std::string mat_folder = get_matrixfolder<Scalar>();
MatrixMarketIterator<Scalar> it(mat_folder);
for (; it; ++it)
{
std::cout<< " ==== SOLVING WITH MATRIX " << it.matname() << " ==== \n";
check_sparse_solving_real_cases(solver, it.matrix(), it.rhs(), it.refX());
}
#endif
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}
template<typename Solver> void check_sparse_square_determinant(Solver& solver)
{
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
// generate the problem
Mat A;
DenseMatrix dA;
generate_sparse_square_problem(solver, A, dA, 30);
A.makeCompressed();
for (int i = 0; i < g_repeat; i++) {
check_sparse_determinant(solver, A, dA);
}
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}