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++; } }