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
12template<typename MatrixType,typename DenseMat>
13int 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
44template<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}
91void 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