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, 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
  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(internal::random<float>(0,1)>0.5f)
  58     solver.factorize(A);  // this checks that calling analyzePattern is not needed if the pattern do not change.
  59   if (solver.info() != Success)
  60   {
  61     std::cerr << "sparse QR factorization failed\n";
  62     exit(0);
  63     return;
  64   }
  65   x = solver.solve(b);
  66   if (solver.info() != Success)
  67   {
  68     std::cerr << "sparse QR factorization failed\n";
  69     exit(0);
  70     return;
  71   }
  72
  73   VERIFY_IS_APPROX(A * x, b);
  74
  75   //Compare with a dense QR solver
  76   ColPivHouseholderQR<DenseMat> dqr(dA);
  77   refX = dqr.solve(b);
  78
  79   VERIFY_IS_EQUAL(dqr.rank(), solver.rank());
  80   if(solver.rank()==A.cols()) // full rank
  81     VERIFY_IS_APPROX(x, refX);
  82 //   else
  83 //     VERIFY((dA * refX - b).norm() * 2 > (A * x - b).norm() );
  84
  85   // Compute explicitly the matrix Q
  86   MatrixType Q, QtQ, idM;
  87   Q = solver.matrixQ();
  88   //Check  ||Q' * Q - I ||
  89   QtQ = Q * Q.adjoint();
  90   idM.resize(Q.rows(), Q.rows()); idM.setIdentity();
  91   VERIFY(idM.isApprox(QtQ));
  92
  93   // Q to dense
  94   DenseMat dQ;
  95   dQ = solver.matrixQ();
  96   VERIFY_IS_APPROX(Q, dQ);
  97 }
  98 void test_sparseqr()
  99 {
 100   for(int i=0; i<g_repeat; ++i)
 101   {
 102     CALL_SUBTEST_1(test_sparseqr_scalar<double>());
 103     CALL_SUBTEST_2(test_sparseqr_scalar<std::complex<double> >());
 104   }
 105 }
 106