1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2012 Desire Nuentsa Wakam <desire.nuentsa_wakam@inria.fr>
5 // Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
6 //
7 // This Source Code Form is subject to the terms of the Mozilla
8 // Public License v. 2.0. If a copy of the MPL was not distributed
9 #include "sparse.h"
10 #include <Eigen/SparseQR>
11
12 template<typename MatrixType,typename DenseMat>
generate_sparse_rectangular_problem(MatrixType & A,DenseMat & dA,int maxRows=300)13 int generate_sparse_rectangular_problem(MatrixType& A, DenseMat& dA, int maxRows = 300)
14 {
15 typedef typename MatrixType::Scalar Scalar;
16 int rows = internal::random<int>(1,maxRows);
17 int cols = internal::random<int>(1,rows);
18 double density = (std::max)(8./(rows*cols), 0.01);
19
20 A.resize(rows,cols);
21 dA.resize(rows,cols);
22 initSparse<Scalar>(density, dA, A,ForceNonZeroDiag);
23 A.makeCompressed();
24 int nop = internal::random<int>(0, internal::random<double>(0,1) > 0.5 ? cols/2 : 0);
25 for(int k=0; k<nop; ++k)
26 {
27 int j0 = internal::random<int>(0,cols-1);
28 int j1 = internal::random<int>(0,cols-1);
29 Scalar s = internal::random<Scalar>();
30 A.col(j0) = s * A.col(j1);
31 dA.col(j0) = s * dA.col(j1);
32 }
33
34 // if(rows<cols) {
35 // A.conservativeResize(cols,cols);
36 // dA.conservativeResize(cols,cols);
37 // dA.bottomRows(cols-rows).setZero();
38 // }
39
40 return rows;
41 }
42
test_sparseqr_scalar()43 template<typename Scalar> void test_sparseqr_scalar()
44 {
45 typedef SparseMatrix<Scalar,ColMajor> MatrixType;
46 typedef Matrix<Scalar,Dynamic,Dynamic> DenseMat;
47 typedef Matrix<Scalar,Dynamic,1> DenseVector;
48 MatrixType A;
49 DenseMat dA;
50 DenseVector refX,x,b;
51 SparseQR<MatrixType, COLAMDOrdering<int> > solver;
52 generate_sparse_rectangular_problem(A,dA);
53
54 b = dA * DenseVector::Random(A.cols());
55 solver.compute(A);
56 if(internal::random<float>(0,1)>0.5)
57 solver.factorize(A); // this checks that calling analyzePattern is not needed if the pattern do not change.
58 if (solver.info() != Success)
59 {
60 std::cerr << "sparse QR factorization failed\n";
61 exit(0);
62 return;
63 }
64 x = solver.solve(b);
65 if (solver.info() != Success)
66 {
67 std::cerr << "sparse QR factorization failed\n";
68 exit(0);
69 return;
70 }
71
72 VERIFY_IS_APPROX(A * x, b);
73
74 //Compare with a dense QR solver
75 ColPivHouseholderQR<DenseMat> dqr(dA);
76 refX = dqr.solve(b);
77
78 VERIFY_IS_EQUAL(dqr.rank(), solver.rank());
79 if(solver.rank()==A.cols()) // full rank
80 VERIFY_IS_APPROX(x, refX);
81 // else
82 // VERIFY((dA * refX - b).norm() * 2 > (A * x - b).norm() );
83
84 // Compute explicitly the matrix Q
85 MatrixType Q, QtQ, idM;
86 Q = solver.matrixQ();
87 //Check ||Q' * Q - I ||
88 QtQ = Q * Q.adjoint();
89 idM.resize(Q.rows(), Q.rows()); idM.setIdentity();
90 VERIFY(idM.isApprox(QtQ));
91 }
test_sparseqr()92 void test_sparseqr()
93 {
94 for(int i=0; i<g_repeat; ++i)
95 {
96 CALL_SUBTEST_1(test_sparseqr_scalar<double>());
97 CALL_SUBTEST_2(test_sparseqr_scalar<std::complex<double> >());
98 }
99 }
100
101