1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. Eigen itself is part of the KDE project. 3 // 4 // Copyright (C) 2008 Daniel Gomez Ferro <dgomezferro (at) gmail.com> 5 // 6 // This Source Code Form is subject to the terms of the Mozilla 7 // Public License v. 2.0. If a copy of the MPL was not distributed 8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 9 10 #include "sparse.h" 11 12 template<typename Scalar> void 13 initSPD(double density, 14 Matrix<Scalar,Dynamic,Dynamic>& refMat, 15 SparseMatrix<Scalar>& sparseMat) 16 { 17 Matrix<Scalar,Dynamic,Dynamic> aux(refMat.rows(),refMat.cols()); 18 initSparse(density,refMat,sparseMat); 19 refMat = refMat * refMat.adjoint(); 20 for (int k=0; k<2; ++k) 21 { 22 initSparse(density,aux,sparseMat,ForceNonZeroDiag); 23 refMat += aux * aux.adjoint(); 24 } 25 sparseMat.startFill(); 26 for (int j=0 ; j<sparseMat.cols(); ++j) 27 for (int i=j ; i<sparseMat.rows(); ++i) 28 if (refMat(i,j)!=Scalar(0)) 29 sparseMat.fill(i,j) = refMat(i,j); 30 sparseMat.endFill(); 31 } 32 33 template<typename Scalar> void sparse_solvers(int rows, int cols) 34 { 35 double density = std::max(8./(rows*cols), 0.01); 36 typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix; 37 typedef Matrix<Scalar,Dynamic,1> DenseVector; 38 // Scalar eps = 1e-6; 39 40 DenseVector vec1 = DenseVector::Random(rows); 41 42 std::vector<Vector2i> zeroCoords; 43 std::vector<Vector2i> nonzeroCoords; 44 45 // test triangular solver 46 { 47 DenseVector vec2 = vec1, vec3 = vec1; 48 SparseMatrix<Scalar> m2(rows, cols); 49 DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols); 50 51 // lower 52 initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords); 53 VERIFY_IS_APPROX(refMat2.template marked<LowerTriangular>().solveTriangular(vec2), 54 m2.template marked<LowerTriangular>().solveTriangular(vec3)); 55 56 // lower - transpose 57 initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords); 58 VERIFY_IS_APPROX(refMat2.template marked<LowerTriangular>().transpose().solveTriangular(vec2), 59 m2.template marked<LowerTriangular>().transpose().solveTriangular(vec3)); 60 61 // upper 62 initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords); 63 VERIFY_IS_APPROX(refMat2.template marked<UpperTriangular>().solveTriangular(vec2), 64 m2.template marked<UpperTriangular>().solveTriangular(vec3)); 65 66 // upper - transpose 67 initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords); 68 VERIFY_IS_APPROX(refMat2.template marked<UpperTriangular>().transpose().solveTriangular(vec2), 69 m2.template marked<UpperTriangular>().transpose().solveTriangular(vec3)); 70 } 71 72 // test LLT 73 { 74 // TODO fix the issue with complex (see SparseLLT::solveInPlace) 75 SparseMatrix<Scalar> m2(rows, cols); 76 DenseMatrix refMat2(rows, cols); 77 78 DenseVector b = DenseVector::Random(cols); 79 DenseVector refX(cols), x(cols); 80 81 initSPD(density, refMat2, m2); 82 83 refMat2.llt().solve(b, &refX); 84 typedef SparseMatrix<Scalar,LowerTriangular|SelfAdjoint> SparseSelfAdjointMatrix; 85 if (!NumTraits<Scalar>::IsComplex) 86 { 87 x = b; 88 SparseLLT<SparseSelfAdjointMatrix> (m2).solveInPlace(x); 89 VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: default"); 90 } 91 #ifdef EIGEN_CHOLMOD_SUPPORT 92 x = b; 93 SparseLLT<SparseSelfAdjointMatrix,Cholmod>(m2).solveInPlace(x); 94 VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: cholmod"); 95 #endif 96 if (!NumTraits<Scalar>::IsComplex) 97 { 98 #ifdef EIGEN_TAUCS_SUPPORT 99 x = b; 100 SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,IncompleteFactorization).solveInPlace(x); 101 VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (IncompleteFactorization)"); 102 x = b; 103 SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,SupernodalMultifrontal).solveInPlace(x); 104 VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (SupernodalMultifrontal)"); 105 x = b; 106 SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,SupernodalLeftLooking).solveInPlace(x); 107 VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (SupernodalLeftLooking)"); 108 #endif 109 } 110 } 111 112 // test LDLT 113 if (!NumTraits<Scalar>::IsComplex) 114 { 115 // TODO fix the issue with complex (see SparseLDLT::solveInPlace) 116 SparseMatrix<Scalar> m2(rows, cols); 117 DenseMatrix refMat2(rows, cols); 118 119 DenseVector b = DenseVector::Random(cols); 120 DenseVector refX(cols), x(cols); 121 122 //initSPD(density, refMat2, m2); 123 initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, 0, 0); 124 refMat2 += refMat2.adjoint(); 125 refMat2.diagonal() *= 0.5; 126 127 refMat2.ldlt().solve(b, &refX); 128 typedef SparseMatrix<Scalar,UpperTriangular|SelfAdjoint> SparseSelfAdjointMatrix; 129 x = b; 130 SparseLDLT<SparseSelfAdjointMatrix> ldlt(m2); 131 if (ldlt.succeeded()) 132 ldlt.solveInPlace(x); 133 VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LDLT: default"); 134 } 135 136 // test LU 137 { 138 static int count = 0; 139 SparseMatrix<Scalar> m2(rows, cols); 140 DenseMatrix refMat2(rows, cols); 141 142 DenseVector b = DenseVector::Random(cols); 143 DenseVector refX(cols), x(cols); 144 145 initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag, &zeroCoords, &nonzeroCoords); 146 147 LU<DenseMatrix> refLu(refMat2); 148 refLu.solve(b, &refX); 149 #if defined(EIGEN_SUPERLU_SUPPORT) || defined(EIGEN_UMFPACK_SUPPORT) 150 Scalar refDet = refLu.determinant(); 151 #endif 152 x.setZero(); 153 // // SparseLU<SparseMatrix<Scalar> > (m2).solve(b,&x); 154 // // VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: default"); 155 #ifdef EIGEN_SUPERLU_SUPPORT 156 { 157 x.setZero(); 158 SparseLU<SparseMatrix<Scalar>,SuperLU> slu(m2); 159 if (slu.succeeded()) 160 { 161 if (slu.solve(b,&x)) { 162 VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: SuperLU"); 163 } 164 // std::cerr << refDet << " == " << slu.determinant() << "\n"; 165 if (count==0) { 166 VERIFY_IS_APPROX(refDet,slu.determinant()); // FIXME det is not very stable for complex 167 } 168 } 169 } 170 #endif 171 #ifdef EIGEN_UMFPACK_SUPPORT 172 { 173 // check solve 174 x.setZero(); 175 SparseLU<SparseMatrix<Scalar>,UmfPack> slu(m2); 176 if (slu.succeeded()) { 177 if (slu.solve(b,&x)) { 178 if (count==0) { 179 VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: umfpack"); // FIXME solve is not very stable for complex 180 } 181 } 182 VERIFY_IS_APPROX(refDet,slu.determinant()); 183 // TODO check the extracted data 184 //std::cerr << slu.matrixL() << "\n"; 185 } 186 } 187 #endif 188 count++; 189 } 190 191 } 192 193 void test_eigen2_sparse_solvers() 194 { 195 for(int i = 0; i < g_repeat; i++) { 196 CALL_SUBTEST_1( sparse_solvers<double>(8, 8) ); 197 CALL_SUBTEST_2( sparse_solvers<std::complex<double> >(16, 16) ); 198 CALL_SUBTEST_1( sparse_solvers<double>(101, 101) ); 199 } 200 } 201
