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244 lines
8.8 KiB
C++
244 lines
8.8 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008 Daniel Gomez Ferro <dgomezferro@gmail.com>
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//
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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 3 of the License, or (at your option) any later version.
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//
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// Alternatively, you can redistribute it and/or
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// modify it under the terms of the GNU General Public License as
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// published by the Free Software Foundation; either version 2 of
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// the License, or (at your option) any later version.
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//
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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#include "sparse.h"
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template<typename Scalar> void
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initSPD(double density,
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Matrix<Scalar,Dynamic,Dynamic>& refMat,
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SparseMatrix<Scalar>& sparseMat)
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{
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Matrix<Scalar,Dynamic,Dynamic> aux(refMat.rows(),refMat.cols());
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initSparse(density,refMat,sparseMat);
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refMat = refMat * refMat.adjoint();
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for (int k=0; k<2; ++k)
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{
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initSparse(density,aux,sparseMat,ForceNonZeroDiag);
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refMat += aux * aux.adjoint();
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}
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sparseMat.setZero();
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for (int j=0 ; j<sparseMat.cols(); ++j)
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for (int i=j ; i<sparseMat.rows(); ++i)
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if (refMat(i,j)!=Scalar(0))
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sparseMat.insert(i,j) = refMat(i,j);
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sparseMat.finalize();
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}
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template<typename Scalar> void sparse_solvers(int rows, int cols)
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{
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double density = std::max(8./(rows*cols), 0.01);
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typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
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typedef Matrix<Scalar,Dynamic,1> DenseVector;
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// Scalar eps = 1e-6;
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DenseVector vec1 = DenseVector::Random(rows);
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std::vector<Vector2i> zeroCoords;
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std::vector<Vector2i> nonzeroCoords;
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// test triangular solver
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{
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DenseVector vec2 = vec1, vec3 = vec1;
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SparseMatrix<Scalar> m2(rows, cols);
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DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
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// lower - dense
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initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
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VERIFY_IS_APPROX(refMat2.template triangularView<Lower>().solve(vec2),
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m2.template triangularView<Lower>().solve(vec3));
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// upper - dense
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initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
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VERIFY_IS_APPROX(refMat2.template triangularView<Upper>().solve(vec2),
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m2.template triangularView<Upper>().solve(vec3));
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// lower - transpose
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initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
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VERIFY_IS_APPROX(refMat2.transpose().template triangularView<Upper>().solve(vec2),
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m2.transpose().template triangularView<Upper>().solve(vec3));
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// upper - transpose
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initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
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VERIFY_IS_APPROX(refMat2.transpose().template triangularView<Lower>().solve(vec2),
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m2.transpose().template triangularView<Lower>().solve(vec3));
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SparseMatrix<Scalar> matB(rows, rows);
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DenseMatrix refMatB = DenseMatrix::Zero(rows, rows);
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// lower - sparse
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initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular);
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initSparse<Scalar>(density, refMatB, matB);
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refMat2.template triangularView<Lower>().solveInPlace(refMatB);
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m2.template triangularView<Lower>().solveInPlace(matB);
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VERIFY_IS_APPROX(matB.toDense(), refMatB);
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// upper - sparse
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initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular);
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initSparse<Scalar>(density, refMatB, matB);
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refMat2.template triangularView<Upper>().solveInPlace(refMatB);
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m2.template triangularView<Upper>().solveInPlace(matB);
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VERIFY_IS_APPROX(matB, refMatB);
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// test deprecated API
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initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
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VERIFY_IS_APPROX(refMat2.template triangularView<Lower>().solve(vec2),
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m2.template triangularView<Lower>().solve(vec3));
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}
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// test LLT
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{
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// TODO fix the issue with complex (see SparseLLT::solveInPlace)
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SparseMatrix<Scalar> m2(rows, cols);
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DenseMatrix refMat2(rows, cols);
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DenseVector b = DenseVector::Random(cols);
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DenseVector refX(cols), x(cols);
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initSPD(density, refMat2, m2);
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refX = refMat2.llt().solve(b);
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if (!NumTraits<Scalar>::IsComplex)
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{
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x = b;
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SparseLLT<SparseMatrix<Scalar> > (m2).solveInPlace(x);
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VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: default");
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}
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#ifdef EIGEN_CHOLMOD_SUPPORT
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x = b;
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SparseLLT<SparseMatrix<Scalar> ,Cholmod>(m2).solveInPlace(x);
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VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: cholmod");
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#endif
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#ifdef EIGEN_TAUCS_SUPPORT
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x = b;
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SparseLLT<SparseMatrix<Scalar> ,Taucs>(m2,IncompleteFactorization).solveInPlace(x);
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VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (IncompleteFactorization)");
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// TODO fix TAUCS with complexes
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x = b;
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SparseLLT<SparseMatrix<Scalar> ,Taucs>(m2,SupernodalMultifrontal).solveInPlace(x);
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VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (SupernodalMultifrontal)");
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x = b;
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SparseLLT<SparseMatrix<Scalar> ,Taucs>(m2,SupernodalLeftLooking).solveInPlace(x);
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VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (SupernodalLeftLooking)");
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#endif
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}
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// test LDLT
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if (!NumTraits<Scalar>::IsComplex)
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{
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// TODO fix the issue with complex (see SparseLDLT::solveInPlace)
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SparseMatrix<Scalar> m2(rows, cols);
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DenseMatrix refMat2(rows, cols);
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DenseVector b = DenseVector::Random(cols);
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DenseVector refX(cols), x(cols);
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//initSPD(density, refMat2, m2);
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initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, 0, 0);
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refMat2 += refMat2.adjoint();
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refMat2.diagonal() *= 0.5;
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refX = refMat2.llt().solve(b); // FIXME use LLT to compute the reference because LDLT seems to fail with large matrices
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typedef SparseMatrix<Scalar,Upper|SelfAdjoint> SparseSelfAdjointMatrix;
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x = b;
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SparseLDLT<SparseSelfAdjointMatrix> ldlt(m2);
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if (ldlt.succeeded())
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ldlt.solveInPlace(x);
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VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LDLT: default");
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}
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// test LU
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{
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static int count = 0;
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SparseMatrix<Scalar> m2(rows, cols);
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DenseMatrix refMat2(rows, cols);
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DenseVector b = DenseVector::Random(cols);
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DenseVector refX(cols), x(cols);
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initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag, &zeroCoords, &nonzeroCoords);
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FullPivLU<DenseMatrix> refLu(refMat2);
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refX = refLu.solve(b);
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#if defined(EIGEN_SUPERLU_SUPPORT) || defined(EIGEN_UMFPACK_SUPPORT)
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Scalar refDet = refLu.determinant();
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#endif
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x.setZero();
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// // SparseLU<SparseMatrix<Scalar> > (m2).solve(b,&x);
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// // VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: default");
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#ifdef EIGEN_SUPERLU_SUPPORT
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{
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x.setZero();
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SparseLU<SparseMatrix<Scalar>,SuperLU> slu(m2);
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if (slu.succeeded())
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{
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if (slu.solve(b,&x)) {
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VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: SuperLU");
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}
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// std::cerr << refDet << " == " << slu.determinant() << "\n";
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if (slu.solve(b, &x, SvTranspose)) {
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VERIFY(b.isApprox(m2.transpose() * x, test_precision<Scalar>()));
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}
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if (slu.solve(b, &x, SvAdjoint)) {
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// VERIFY(b.isApprox(m2.adjoint() * x, test_precision<Scalar>()));
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}
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if (count==0) {
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VERIFY_IS_APPROX(refDet,slu.determinant()); // FIXME det is not very stable for complex
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}
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}
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}
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#endif
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#ifdef EIGEN_UMFPACK_SUPPORT
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{
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// check solve
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x.setZero();
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SparseLU<SparseMatrix<Scalar>,UmfPack> slu(m2);
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if (slu.succeeded()) {
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if (slu.solve(b,&x)) {
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if (count==0) {
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VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: umfpack"); // FIXME solve is not very stable for complex
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}
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}
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VERIFY_IS_APPROX(refDet,slu.determinant());
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// TODO check the extracted data
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//std::cerr << slu.matrixL() << "\n";
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}
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}
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#endif
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count++;
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}
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}
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void test_sparse_solvers()
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{
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for(int i = 0; i < g_repeat; i++) {
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// CALL_SUBTEST(sparse_solvers<double>(8, 8) );
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CALL_SUBTEST(sparse_solvers<std::complex<double> >(16, 16) );
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// CALL_SUBTEST(sparse_solvers<double>(100, 100) );
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}
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}
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