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

   1 // This file is part of Eigen, a lightweight C++ template library
   2 // for linear algebra.
   3 //
   4 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
   5 // Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
   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 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
  10
  11 #include "main.h"
  12 #include <Eigen/QR>
  13
  14 template<typename MatrixType> void qr()
  15 {
  16   typedef typename MatrixType::Index Index;
  17
  18   Index rows = internal::random<Index>(20,200), cols = internal::random<int>(20,200), cols2 = internal::random<int>(20,200);
  19   Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1);
  20
  21   typedef typename MatrixType::Scalar Scalar;
  22   typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
  23   MatrixType m1;
  24   createRandomPIMatrixOfRank(rank,rows,cols,m1);
  25   FullPivHouseholderQR<MatrixType> qr(m1);
  26   VERIFY(rank == qr.rank());
  27   VERIFY(cols - qr.rank() == qr.dimensionOfKernel());
  28   VERIFY(!qr.isInjective());
  29   VERIFY(!qr.isInvertible());
  30   VERIFY(!qr.isSurjective());
  31
  32   MatrixType r = qr.matrixQR();
  33
  34   MatrixQType q = qr.matrixQ();
  35   VERIFY_IS_UNITARY(q);
  36
  37   // FIXME need better way to construct trapezoid
  38   for(int i = 0; i < rows; i++) for(int j = 0; j < cols; j++) if(i>j) r(i,j) = Scalar(0);
  39
  40   MatrixType c = qr.matrixQ() * r * qr.colsPermutation().inverse();
  41
  42   VERIFY_IS_APPROX(m1, c);
  43
  44   MatrixType m2 = MatrixType::Random(cols,cols2);
  45   MatrixType m3 = m1*m2;
  46   m2 = MatrixType::Random(cols,cols2);
  47   m2 = qr.solve(m3);
  48   VERIFY_IS_APPROX(m3, m1*m2);
  49 }
  50
  51 template<typename MatrixType> void qr_invertible()
  52 {
  53   using std::log;
  54   using std::abs;
  55   typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
  56   typedef typename MatrixType::Scalar Scalar;
  57
  58   int size = internal::random<int>(10,50);
  59
  60   MatrixType m1(size, size), m2(size, size), m3(size, size);
  61   m1 = MatrixType::Random(size,size);
  62
  63   if (internal::is_same<RealScalar,float>::value)
  64   {
  65     // let's build a matrix more stable to inverse
  66     MatrixType a = MatrixType::Random(size,size*2);
  67     m1 += a * a.adjoint();
  68   }
  69
  70   FullPivHouseholderQR<MatrixType> qr(m1);
  71   VERIFY(qr.isInjective());
  72   VERIFY(qr.isInvertible());
  73   VERIFY(qr.isSurjective());
  74
  75   m3 = MatrixType::Random(size,size);
  76   m2 = qr.solve(m3);
  77   VERIFY_IS_APPROX(m3, m1*m2);
  78
  79   // now construct a matrix with prescribed determinant
  80   m1.setZero();
  81   for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
  82   RealScalar absdet = abs(m1.diagonal().prod());
  83   m3 = qr.matrixQ(); // get a unitary
  84   m1 = m3 * m1 * m3;
  85   qr.compute(m1);
  86   VERIFY_IS_APPROX(absdet, qr.absDeterminant());
  87   VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
  88 }
  89
  90 template<typename MatrixType> void qr_verify_assert()
  91 {
  92   MatrixType tmp;
  93
  94   FullPivHouseholderQR<MatrixType> qr;
  95   VERIFY_RAISES_ASSERT(qr.matrixQR())
  96   VERIFY_RAISES_ASSERT(qr.solve(tmp))
  97   VERIFY_RAISES_ASSERT(qr.matrixQ())
  98   VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())
  99   VERIFY_RAISES_ASSERT(qr.isInjective())
 100   VERIFY_RAISES_ASSERT(qr.isSurjective())
 101   VERIFY_RAISES_ASSERT(qr.isInvertible())
 102   VERIFY_RAISES_ASSERT(qr.inverse())
 103   VERIFY_RAISES_ASSERT(qr.absDeterminant())
 104   VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
 105 }
 106
 107 void test_qr_fullpivoting()
 108 {
 109  for(int i = 0; i < 1; i++) {
 110     // FIXME : very weird bug here
 111 //     CALL_SUBTEST(qr(Matrix2f()) );
 112     CALL_SUBTEST_1( qr<MatrixXf>() );
 113     CALL_SUBTEST_2( qr<MatrixXd>() );
 114     CALL_SUBTEST_3( qr<MatrixXcd>() );
 115   }
 116
 117   for(int i = 0; i < g_repeat; i++) {
 118     CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
 119     CALL_SUBTEST_2( qr_invertible<MatrixXd>() );
 120     CALL_SUBTEST_4( qr_invertible<MatrixXcf>() );
 121     CALL_SUBTEST_3( qr_invertible<MatrixXcd>() );
 122   }
 123
 124   CALL_SUBTEST_5(qr_verify_assert<Matrix3f>());
 125   CALL_SUBTEST_6(qr_verify_assert<Matrix3d>());
 126   CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
 127   CALL_SUBTEST_2(qr_verify_assert<MatrixXd>());
 128   CALL_SUBTEST_4(qr_verify_assert<MatrixXcf>());
 129   CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>());
 130
 131   // Test problem size constructors
 132   CALL_SUBTEST_7(FullPivHouseholderQR<MatrixXf>(10, 20));
 133   CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(10,20)));
 134   CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(Matrix<float,10,20>::Random())));
 135   CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(20,10)));
 136   CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(Matrix<float,20,10>::Random())));
 137 }