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 
12 template<typename Scalar> void
initSPD(double density,Matrix<Scalar,Dynamic,Dynamic> & refMat,SparseMatrix<Scalar> & sparseMat)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 
sparse_solvers(int rows,int cols)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 
test_eigen2_sparse_solvers()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