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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>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#include "sparse.h"
#include <Eigen/SparseCore>
#include <sstream>
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;
typedef typename Mat::StorageIndex StorageIndex;
DenseRhs refX = dA.householderQr().solve(db);
{
Rhs x(A.cols(), b.cols());
Rhs oldb = b;
solver.compute(A);
if (solver.info() != Success)
{
std::cerr << "ERROR | sparse solver testing, factorization failed (" << typeid(Solver).name() << ")\n";
VERIFY(solver.info() == Success);
}
x = solver.solve(b);
if (solver.info() != Success)
{
std::cerr << "WARNING | sparse solver testing: solving failed (" << typeid(Solver).name() << ")\n";
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);
VERIFY(solver.info() == Success && "factorization failed when using analyzePattern/factorize API");
x = solver.solve(b);
VERIFY(solver.info() == Success && "solving failed when using analyzePattern/factorize API");
VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
VERIFY(x.isApprox(refX,test_precision<Scalar>()));
x.setZero();
// test with Map
MappedSparseMatrix<Scalar,Mat::Options,StorageIndex> Am(A.rows(), A.cols(), A.nonZeros(), const_cast<StorageIndex*>(A.outerIndexPtr()), const_cast<StorageIndex*>(A.innerIndexPtr()), const_cast<Scalar*>(A.valuePtr()));
solver.compute(Am);
VERIFY(solver.info() == Success && "factorization failed when using Map");
DenseRhs dx(refX);
dx.setZero();
Map<DenseRhs> xm(dx.data(), dx.rows(), dx.cols());
Map<const DenseRhs> bm(db.data(), db.rows(), db.cols());
xm = solver.solve(bm);
VERIFY(solver.info() == Success && "solving failed when using Map");
VERIFY(oldb.isApprox(bm) && "sparse solver testing: the rhs should not be modified!");
VERIFY(xm.isApprox(refX,test_precision<Scalar>()));
}
// if not too large, do some extra check:
if(A.rows()<2000)
{
// test initialization ctor
{
Rhs x(b.rows(), b.cols());
Solver solver2(A);
VERIFY(solver2.info() == Success);
x = solver2.solve(b);
VERIFY(x.isApprox(refX,test_precision<Scalar>()));
}
// test dense Block as the result and rhs:
{
DenseRhs x(refX.rows(), refX.cols());
DenseRhs oldb(db);
x.setZero();
x.block(0,0,x.rows(),x.cols()) = solver.solve(db.block(0,0,db.rows(),db.cols()));
VERIFY(oldb.isApprox(db) && "sparse solver testing: the rhs should not be modified!");
VERIFY(x.isApprox(refX,test_precision<Scalar>()));
}
// test uncompressed inputs
{
Mat A2 = A;
A2.reserve((ArrayXf::Random(A.outerSize())+2).template cast<typename Mat::StorageIndex>().eval());
solver.compute(A2);
Rhs x = solver.solve(b);
VERIFY(x.isApprox(refX,test_precision<Scalar>()));
}
// test expression as input
{
solver.compute(0.5*(A+A));
Rhs x = solver.solve(b);
VERIFY(x.isApprox(refX,test_precision<Scalar>()));
Solver solver2(0.5*(A+A));
Rhs x2 = solver2.solve(b);
VERIFY(x2.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 typename Solver::MatrixType& fullA, const Rhs& refX)
{
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
typedef typename Mat::RealScalar RealScalar;
Rhs x(A.cols(), b.cols());
solver.compute(A);
if (solver.info() != Success)
{
std::cerr << "ERROR | sparse solver testing, factorization failed (" << typeid(Solver).name() << ")\n";
VERIFY(solver.info() == Success);
}
x = solver.solve(b);
if (solver.info() != Success)
{
std::cerr << "WARNING | sparse solver testing, solving failed (" << typeid(Solver).name() << ")\n";
return;
}
RealScalar res_error = (fullA*x-b).norm()/b.norm();
VERIFY( (res_error <= test_precision<Scalar>() ) && "sparse solver failed without noticing it");
if(refX.size() != 0 && (refX - x).norm()/refX.norm() > test_precision<Scalar>())
{
std::cerr << "WARNING | found solution is different from the provided reference one\n";
}
}
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;
solver.compute(A);
if (solver.info() != Success)
{
std::cerr << "WARNING | sparse solver testing: factorization failed (check_sparse_determinant)\n";
return;
}
Scalar refDet = dA.determinant();
VERIFY_IS_APPROX(refDet,solver.determinant());
}
template<typename Solver, typename DenseMat>
void check_sparse_abs_determinant(Solver& solver, const typename Solver::MatrixType& A, const DenseMat& dA)
{
using std::abs;
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
solver.compute(A);
if (solver.info() != Success)
{
std::cerr << "WARNING | sparse solver testing: factorization failed (check_sparse_abs_determinant)\n";
return;
}
Scalar refDet = abs(dA.determinant());
VERIFY_IS_APPROX(refDet,solver.absDeterminant());
}
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);
if(Solver::UpLo==(Lower|Upper))
halfA = A;
else
halfA.template selfadjointView<Solver::UpLo>().rankUpdate(M);
return size;
}
#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<std::string>("/complex/");
else
mat_folder = mat_folder + static_cast<std::string>("/real/");
return mat_folder;
}
std::string sym_to_string(int sym)
{
if(sym==Symmetric) return "Symmetric ";
if(sym==SPD) return "SPD ";
return "";
}
template<typename Derived>
std::string solver_stats(const IterativeSolverBase<Derived> &solver)
{
std::stringstream ss;
ss << solver.iterations() << " iters, error: " << solver.error();
return ss.str();
}
template<typename Derived>
std::string solver_stats(const SparseSolverBase<Derived> &/*solver*/)
{
return "";
}
#endif
template<typename Solver> void check_sparse_spd_solving(Solver& solver, int maxSize = 300, int maxRealWorldSize = 100000)
{
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
typedef typename Mat::StorageIndex StorageIndex;
typedef SparseMatrix<Scalar,ColMajor, StorageIndex> SpMat;
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
typedef Matrix<Scalar,Dynamic,1> DenseVector;
// generate the problem
Mat A, halfA;
DenseMatrix dA;
for (int i = 0; i < g_repeat; i++) {
int size = generate_sparse_spd_problem(solver, A, halfA, dA, maxSize);
// 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);
DenseVector b = DenseVector::Random(size);
DenseMatrix dB(size,rhsCols);
initSparse<Scalar>(density, dB, B, ForceNonZeroDiag);
CALL_SUBTEST( check_sparse_solving(solver, A, b, dA, b) );
CALL_SUBTEST( check_sparse_solving(solver, halfA, b, dA, b) );
CALL_SUBTEST( check_sparse_solving(solver, A, dB, dA, dB) );
CALL_SUBTEST( check_sparse_solving(solver, halfA, dB, dA, dB) );
CALL_SUBTEST( check_sparse_solving(solver, A, B, dA, dB) );
CALL_SUBTEST( check_sparse_solving(solver, halfA, B, dA, dB) );
// check only once
if(i==0)
{
b = DenseVector::Zero(size);
check_sparse_solving(solver, A, b, dA, b);
}
}
// First, get the folder
#ifdef TEST_REAL_CASES
// Test real problems with double precision only
if (internal::is_same<typename NumTraits<Scalar>::Real, double>::value)
{
std::string mat_folder = get_matrixfolder<Scalar>();
MatrixMarketIterator<Scalar> it(mat_folder);
for (; it; ++it)
{
if (it.sym() == SPD){
A = it.matrix();
if(A.diagonal().size() <= maxRealWorldSize)
{
DenseVector b = it.rhs();
DenseVector refX = it.refX();
PermutationMatrix<Dynamic, Dynamic, StorageIndex> pnull;
halfA.resize(A.rows(), A.cols());
if(Solver::UpLo == (Lower|Upper))
halfA = A;
else
halfA.template selfadjointView<Solver::UpLo>() = A.template triangularView<Eigen::Lower>().twistedBy(pnull);
std::cout << "INFO | Testing " << sym_to_string(it.sym()) << "sparse problem " << it.matname()
<< " (" << A.rows() << "x" << A.cols() << ") using " << typeid(Solver).name() << "..." << std::endl;
CALL_SUBTEST( check_sparse_solving_real_cases(solver, A, b, A, refX) );
std::string stats = solver_stats(solver);
if(stats.size()>0)
std::cout << "INFO | " << stats << std::endl;
CALL_SUBTEST( check_sparse_solving_real_cases(solver, halfA, b, A, refX) );
}
else
{
std::cout << "INFO | Skip sparse problem \"" << it.matname() << "\" (too large)" << std::endl;
}
}
}
}
#else
EIGEN_UNUSED_VARIABLE(maxRealWorldSize);
#endif
}
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 );
}
}
template<typename Solver, typename DenseMat>
Index generate_sparse_square_problem(Solver&, typename Solver::MatrixType& A, DenseMat& dA, int maxSize = 300, int options = ForceNonZeroDiag)
{
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
Index 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, options);
return size;
}
struct prune_column {
Index m_col;
prune_column(Index col) : m_col(col) {}
template<class Scalar>
bool operator()(Index, Index col, const Scalar&) const {
return col != m_col;
}
};
template<typename Solver> void check_sparse_square_solving(Solver& solver, int maxSize = 300, int maxRealWorldSize = 100000, bool checkDeficient = false)
{
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
typedef SparseMatrix<Scalar,ColMajor, typename Mat::StorageIndex> SpMat;
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
typedef Matrix<Scalar,Dynamic,1> DenseVector;
int rhsCols = internal::random<int>(1,16);
Mat A;
DenseMatrix dA;
for (int i = 0; i < g_repeat; i++) {
Index size = generate_sparse_square_problem(solver, A, dA, maxSize);
A.makeCompressed();
DenseVector b = DenseVector::Random(size);
DenseMatrix dB(size,rhsCols);
SpMat B(size,rhsCols);
double density = (std::max)(8./(size*rhsCols), 0.1);
initSparse<Scalar>(density, dB, B, ForceNonZeroDiag);
B.makeCompressed();
CALL_SUBTEST(check_sparse_solving(solver, A, b, dA, b));
CALL_SUBTEST(check_sparse_solving(solver, A, dB, dA, dB));
CALL_SUBTEST(check_sparse_solving(solver, A, B, dA, dB));
// check only once
if(i==0)
{
b = DenseVector::Zero(size);
check_sparse_solving(solver, A, b, dA, b);
}
// regression test for Bug 792 (structurally rank deficient matrices):
if(checkDeficient && size>1) {
Index col = internal::random<int>(0,int(size-1));
A.prune(prune_column(col));
solver.compute(A);
VERIFY_IS_EQUAL(solver.info(), NumericalIssue);
}
}
// First, get the folder
#ifdef TEST_REAL_CASES
// Test real problems with double precision only
if (internal::is_same<typename NumTraits<Scalar>::Real, double>::value)
{
std::string mat_folder = get_matrixfolder<Scalar>();
MatrixMarketIterator<Scalar> it(mat_folder);
for (; it; ++it)
{
A = it.matrix();
if(A.diagonal().size() <= maxRealWorldSize)
{
DenseVector b = it.rhs();
DenseVector refX = it.refX();
std::cout << "INFO | Testing " << sym_to_string(it.sym()) << "sparse problem " << it.matname()
<< " (" << A.rows() << "x" << A.cols() << ") using " << typeid(Solver).name() << "..." << std::endl;
CALL_SUBTEST(check_sparse_solving_real_cases(solver, A, b, A, refX));
std::string stats = solver_stats(solver);
if(stats.size()>0)
std::cout << "INFO | " << stats << std::endl;
}
else
{
std::cout << "INFO | SKIP sparse problem \"" << it.matname() << "\" (too large)" << std::endl;
}
}
}
#else
EIGEN_UNUSED_VARIABLE(maxRealWorldSize);
#endif
}
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;
for (int i = 0; i < g_repeat; i++) {
// generate the problem
Mat A;
DenseMatrix dA;
int size = internal::random<int>(1,30);
dA.setRandom(size,size);
dA = (dA.array().abs()<0.3).select(0,dA);
dA.diagonal() = (dA.diagonal().array()==0).select(1,dA.diagonal());
A = dA.sparseView();
A.makeCompressed();
check_sparse_determinant(solver, A, dA);
}
}
template<typename Solver> void check_sparse_square_abs_determinant(Solver& solver)
{
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
for (int i = 0; i < g_repeat; i++) {
// generate the problem
Mat A;
DenseMatrix dA;
generate_sparse_square_problem(solver, A, dA, 30);
A.makeCompressed();
check_sparse_abs_determinant(solver, A, dA);
}
}
template<typename Solver, typename DenseMat>
void generate_sparse_leastsquare_problem(Solver&, typename Solver::MatrixType& A, DenseMat& dA, int maxSize = 300, int options = ForceNonZeroDiag)
{
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
int rows = internal::random<int>(1,maxSize);
int cols = internal::random<int>(1,rows);
double density = (std::max)(8./(rows*cols), 0.01);
A.resize(rows,cols);
dA.resize(rows,cols);
initSparse<Scalar>(density, dA, A, options);
}
template<typename Solver> void check_sparse_leastsquare_solving(Solver& solver)
{
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
typedef SparseMatrix<Scalar,ColMajor, typename Mat::StorageIndex> SpMat;
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
typedef Matrix<Scalar,Dynamic,1> DenseVector;
int rhsCols = internal::random<int>(1,16);
Mat A;
DenseMatrix dA;
for (int i = 0; i < g_repeat; i++) {
generate_sparse_leastsquare_problem(solver, A, dA);
A.makeCompressed();
DenseVector b = DenseVector::Random(A.rows());
DenseMatrix dB(A.rows(),rhsCols);
SpMat B(A.rows(),rhsCols);
double density = (std::max)(8./(A.rows()*rhsCols), 0.1);
initSparse<Scalar>(density, dB, B, ForceNonZeroDiag);
B.makeCompressed();
check_sparse_solving(solver, A, b, dA, b);
check_sparse_solving(solver, A, dB, dA, dB);
check_sparse_solving(solver, A, B, dA, dB);
// check only once
if(i==0)
{
b = DenseVector::Zero(A.rows());
check_sparse_solving(solver, A, b, dA, b);
}
}
}
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