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,int maxCols=150)13 int generate_sparse_rectangular_problem(MatrixType& A, DenseMat& dA, int maxRows = 300, int maxCols = 150)
14 {
15 eigen_assert(maxRows >= maxCols);
16 typedef typename MatrixType::Scalar Scalar;
17 int rows = internal::random<int>(1,maxRows);
18 int cols = internal::random<int>(1,maxCols);
19 double density = (std::max)(8./(rows*cols), 0.01);
20
21 A.resize(rows,cols);
22 dA.resize(rows,cols);
23 initSparse<Scalar>(density, dA, A,ForceNonZeroDiag);
24 A.makeCompressed();
25 int nop = internal::random<int>(0, internal::random<double>(0,1) > 0.5 ? cols/2 : 0);
26 for(int k=0; k<nop; ++k)
27 {
28 int j0 = internal::random<int>(0,cols-1);
29 int j1 = internal::random<int>(0,cols-1);
30 Scalar s = internal::random<Scalar>();
31 A.col(j0) = s * A.col(j1);
32 dA.col(j0) = s * dA.col(j1);
33 }
34
35 // if(rows<cols) {
36 // A.conservativeResize(cols,cols);
37 // dA.conservativeResize(cols,cols);
38 // dA.bottomRows(cols-rows).setZero();
39 // }
40
41 return rows;
42 }
43
test_sparseqr_scalar()44 template<typename Scalar> void test_sparseqr_scalar()
45 {
46 typedef SparseMatrix<Scalar,ColMajor> MatrixType;
47 typedef Matrix<Scalar,Dynamic,Dynamic> DenseMat;
48 typedef Matrix<Scalar,Dynamic,1> DenseVector;
49 MatrixType A;
50 DenseMat dA;
51 DenseVector refX,x,b;
52 SparseQR<MatrixType, COLAMDOrdering<int> > solver;
53 generate_sparse_rectangular_problem(A,dA);
54
55 b = dA * DenseVector::Random(A.cols());
56 solver.compute(A);
57 if (solver.info() != Success)
58 {
59 std::cerr << "sparse QR factorization failed\n";
60 exit(0);
61 return;
62 }
63 x = solver.solve(b);
64 if (solver.info() != Success)
65 {
66 std::cerr << "sparse QR factorization failed\n";
67 exit(0);
68 return;
69 }
70
71 VERIFY_IS_APPROX(A * x, b);
72
73 //Compare with a dense QR solver
74 ColPivHouseholderQR<DenseMat> dqr(dA);
75 refX = dqr.solve(b);
76
77 VERIFY_IS_EQUAL(dqr.rank(), solver.rank());
78 if(solver.rank()==A.cols()) // full rank
79 VERIFY_IS_APPROX(x, refX);
80 // else
81 // VERIFY((dA * refX - b).norm() * 2 > (A * x - b).norm() );
82
83 // Compute explicitly the matrix Q
84 MatrixType Q, QtQ, idM;
85 Q = solver.matrixQ();
86 //Check ||Q' * Q - I ||
87 QtQ = Q * Q.adjoint();
88 idM.resize(Q.rows(), Q.rows()); idM.setIdentity();
89 VERIFY(idM.isApprox(QtQ));
90 }
test_sparseqr()91 void test_sparseqr()
92 {
93 for(int i=0; i<g_repeat; ++i)
94 {
95 CALL_SUBTEST_1(test_sparseqr_scalar<double>());
96 CALL_SUBTEST_2(test_sparseqr_scalar<std::complex<double> >());
97 }
98 }
99
100