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() {
  Vector4i indices(0, 1, 2, 3);
  for (int i = 0; i < 24; ++i) {
    MatrixType m = PermutationMatrix<4>(indices);
    MatrixType inv = m.inverse();
    VERIFY_IS_APPROX(m * inv, MatrixType::Identity());
    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;
  double error_sum = 0., error_max = 0.;
  for (int i = 0; i < repeat; ++i) {
    // Create a random diagonally dominant (thus invertible) matrix.
    MatrixType m = MatrixType::Random();
    m.diagonal().array() += Scalar(8);  // 2 * 4 for a 4x4 matrix.
    MatrixType inv = m.inverse();
    double error = double((m * inv - MatrixType::Identity()).norm());
    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 1.0 until the NumTraits changes on 28 April 2010.
  // 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)));
}