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
{
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 (slu.solve(b, &x, SvTranspose)) {
VERIFY(b.isApprox(m2.transpose() * x, test_precision<Scalar>()));
}
if (slu.solve(b, &x, SvAdjoint)) {
VERIFY(b.isApprox(m2.adjoint() * x, test_precision<Scalar>()));
}
if (!NumTraits<Scalar>::IsComplex) {
VERIFY_IS_APPROX(refDet,slu.determinant()); // FIXME det is not very stable for complex
}
}
}
#endif
}
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++;
}
}
