ground/gcs/src/libs/eigen/test/sparseqr.cpp

   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>
  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
  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 }
  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