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