eigen2_sparse_solvers.cpp revision c981c48f5bc9aefeffc0bcb0cc3934c2fae179dd 
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@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
12template<typename Scalar> void
13initSPD(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
33template<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
193void 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