ground/gcs/src/libs/eigen/test/qr.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 //
   6 // This Source Code Form is subject to the terms of the Mozilla
   7 // Public License v. 2.0. If a copy of the MPL was not distributed
   8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
   9
  10 #include "main.h"
  11 #include <Eigen/QR>
  12
  13 template<typename MatrixType> void qr(const MatrixType& m)
  14 {
  15   typedef typename MatrixType::Index Index;
  16
  17   Index rows = m.rows();
  18   Index cols = m.cols();
  19
  20   typedef typename MatrixType::Scalar Scalar;
  21   typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
  22
  23   MatrixType a = MatrixType::Random(rows,cols);
  24   HouseholderQR<MatrixType> qrOfA(a);
  25
  26   MatrixQType q = qrOfA.householderQ();
  27   VERIFY_IS_UNITARY(q);
  28
  29   MatrixType r = qrOfA.matrixQR().template triangularView<Upper>();
  30   VERIFY_IS_APPROX(a, qrOfA.householderQ() * r);
  31 }
  32
  33 template<typename MatrixType, int Cols2> void qr_fixedsize()
  34 {
  35   enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
  36   typedef typename MatrixType::Scalar Scalar;
  37   Matrix<Scalar,Rows,Cols> m1 = Matrix<Scalar,Rows,Cols>::Random();
  38   HouseholderQR<Matrix<Scalar,Rows,Cols> > qr(m1);
  39
  40   Matrix<Scalar,Rows,Cols> r = qr.matrixQR();
  41   // FIXME need better way to construct trapezoid
  42   for(int i = 0; i < Rows; i++) for(int j = 0; j < Cols; j++) if(i>j) r(i,j) = Scalar(0);
  43
  44   VERIFY_IS_APPROX(m1, qr.householderQ() * r);
  45
  46   Matrix<Scalar,Cols,Cols2> m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
  47   Matrix<Scalar,Rows,Cols2> m3 = m1*m2;
  48   m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
  49   m2 = qr.solve(m3);
  50   VERIFY_IS_APPROX(m3, m1*m2);
  51 }
  52
  53 template<typename MatrixType> void qr_invertible()
  54 {
  55   using std::log;
  56   using std::abs;
  57   using std::pow;
  58   using std::max;
  59   typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
  60   typedef typename MatrixType::Scalar Scalar;
  61
  62   int size = internal::random<int>(10,50);
  63
  64   MatrixType m1(size, size), m2(size, size), m3(size, size);
  65   m1 = MatrixType::Random(size,size);
  66
  67   if (internal::is_same<RealScalar,float>::value)
  68   {
  69     // let's build a matrix more stable to inverse
  70     MatrixType a = MatrixType::Random(size,size*4);
  71     m1 += a * a.adjoint();
  72   }
  73
  74   HouseholderQR<MatrixType> qr(m1);
  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.householderQ(); // get a unitary
  84   m1 = m3 * m1 * m3;
  85   qr.compute(m1);
  86   VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
  87   // This test is tricky if the determinant becomes too small.
  88   // Since we generate random numbers with magnitude rrange [0,1], the average determinant is 0.5^size
  89   VERIFY_IS_MUCH_SMALLER_THAN( abs(absdet-qr.absDeterminant()), numext::maxi(RealScalar(pow(0.5,size)),numext::maxi<RealScalar>(abs(absdet),abs(qr.absDeterminant()))) );
  90
  91 }
  92
  93 template<typename MatrixType> void qr_verify_assert()
  94 {
  95   MatrixType tmp;
  96
  97   HouseholderQR<MatrixType> qr;
  98   VERIFY_RAISES_ASSERT(qr.matrixQR())
  99   VERIFY_RAISES_ASSERT(qr.solve(tmp))
 100   VERIFY_RAISES_ASSERT(qr.householderQ())
 101   VERIFY_RAISES_ASSERT(qr.absDeterminant())
 102   VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
 103 }
 104
 105 void test_qr()
 106 {
 107   for(int i = 0; i < g_repeat; i++) {
 108    CALL_SUBTEST_1( qr(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
 109    CALL_SUBTEST_2( qr(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2),internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
 110    CALL_SUBTEST_3(( qr_fixedsize<Matrix<float,3,4>, 2 >() ));
 111    CALL_SUBTEST_4(( qr_fixedsize<Matrix<double,6,2>, 4 >() ));
 112    CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,2,5>, 7 >() ));
 113    CALL_SUBTEST_11( qr(Matrix<float,1,1>()) );
 114   }
 115
 116   for(int i = 0; i < g_repeat; i++) {
 117     CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
 118     CALL_SUBTEST_6( qr_invertible<MatrixXd>() );
 119     CALL_SUBTEST_7( qr_invertible<MatrixXcf>() );
 120     CALL_SUBTEST_8( qr_invertible<MatrixXcd>() );
 121   }
 122
 123   CALL_SUBTEST_9(qr_verify_assert<Matrix3f>());
 124   CALL_SUBTEST_10(qr_verify_assert<Matrix3d>());
 125   CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
 126   CALL_SUBTEST_6(qr_verify_assert<MatrixXd>());
 127   CALL_SUBTEST_7(qr_verify_assert<MatrixXcf>());
 128   CALL_SUBTEST_8(qr_verify_assert<MatrixXcd>());
 129
 130   // Test problem size constructors
 131   CALL_SUBTEST_12(HouseholderQR<MatrixXf>(10, 20));
 132 }