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Diffstat (limited to 'eigen/test/eigen2/eigen2_sparse_solvers.cpp')
| -rw-r--r-- | eigen/test/eigen2/eigen2_sparse_solvers.cpp | 200 |
1 files changed, 200 insertions, 0 deletions
diff --git a/eigen/test/eigen2/eigen2_sparse_solvers.cpp b/eigen/test/eigen2/eigen2_sparse_solvers.cpp new file mode 100644 index 0000000..3aef27a --- /dev/null +++ b/eigen/test/eigen2/eigen2_sparse_solvers.cpp @@ -0,0 +1,200 @@ +// 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> +// +// 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" + +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) ); + } +} |