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)
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
43template<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}
92void 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