test/prec_inverse_4x4.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "main.h"
#include <Eigen/LU>
#include <algorithm>

template<typename MatrixType> void inverse_permutation_4x4()
{
  typedef typename MatrixType::Scalar Scalar;
  Vector4i indices(0,1,2,3);
  for(int i = 0; i < 24; ++i)
  {
    MatrixType m = PermutationMatrix<4>(indices);
    MatrixType inv = m.inverse();
    double error = double( (m*inv-MatrixType::Identity()).norm() / NumTraits<Scalar>::epsilon() );
    EIGEN_DEBUG_VAR(error)
    VERIFY(error == 0.0);
    std::next_permutation(indices.data(),indices.data()+4);
  }
}

template<typename MatrixType> void inverse_general_4x4(int repeat)
{
  using std::abs;
  typedef typename MatrixType::Scalar Scalar;
  typedef typename MatrixType::RealScalar RealScalar;
  double error_sum = 0., error_max = 0.;
  for(int i = 0; i < repeat; ++i)
  {
    MatrixType m;
    RealScalar absdet;
    do {
      m = MatrixType::Random();
      absdet = abs(m.determinant());
    } while(absdet < NumTraits<Scalar>::epsilon());
    MatrixType inv = m.inverse();
    double error = double( (m*inv-MatrixType::Identity()).norm() * absdet / NumTraits<Scalar>::epsilon() );
    error_sum += error;
    error_max = (std::max)(error_max, error);
  }
  std::cerr << "inverse_general_4x4, Scalar = " << type_name<Scalar>() << std::endl;
  double error_avg = error_sum / repeat;
  EIGEN_DEBUG_VAR(error_avg);
  EIGEN_DEBUG_VAR(error_max);
   // FIXME that 1.25 used to be a 1.0 until the NumTraits changes on 28 April 2010, what's going wrong??
   // FIXME that 1.25 used to be 1.2 until we tested gcc 4.1 on 30 June 2010 and got 1.21.
  VERIFY(error_avg < (NumTraits<Scalar>::IsComplex ? 8.0 : 1.25));
  VERIFY(error_max < (NumTraits<Scalar>::IsComplex ? 64.0 : 20.0));

  {
    int s = 5;//internal::random<int>(4,10);
    int i = 0;//internal::random<int>(0,s-4);
    int j = 0;//internal::random<int>(0,s-4);
    Matrix<Scalar,5,5> mat(s,s);
    mat.setRandom();
    MatrixType submat = mat.template block<4,4>(i,j);
    MatrixType mat_inv = mat.template block<4,4>(i,j).inverse();
    VERIFY_IS_APPROX(mat_inv, submat.inverse());
    mat.template block<4,4>(i,j) = submat.inverse();
    VERIFY_IS_APPROX(mat_inv, (mat.template block<4,4>(i,j)));
  }
}

EIGEN_DECLARE_TEST(prec_inverse_4x4)
{
  CALL_SUBTEST_1((inverse_permutation_4x4<Matrix4f>()));
  CALL_SUBTEST_1(( inverse_general_4x4<Matrix4f>(200000 * g_repeat) ));
  CALL_SUBTEST_1(( inverse_general_4x4<Matrix<float,4,4,RowMajor> >(200000 * g_repeat) ));

  CALL_SUBTEST_2((inverse_permutation_4x4<Matrix<double,4,4,RowMajor> >()));
  CALL_SUBTEST_2(( inverse_general_4x4<Matrix<double,4,4,ColMajor> >(200000 * g_repeat) ));
  CALL_SUBTEST_2(( inverse_general_4x4<Matrix<double,4,4,RowMajor> >(200000 * g_repeat) ));

  CALL_SUBTEST_3((inverse_permutation_4x4<Matrix4cf>()));
  CALL_SUBTEST_3((inverse_general_4x4<Matrix4cf>(50000 * g_repeat)));
}