determinant.cpp

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.

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

template<typename MatrixType> void determinant(const MatrixType& m)
{
  /* this test covers the following files:
     Determinant.h
  */
  typedef typename MatrixType::Index Index;
  Index size = m.rows();

  MatrixType m1(size, size), m2(size, size);
  m1.setRandom();
  m2.setRandom();
  typedef typename MatrixType::Scalar Scalar;
  Scalar x = internal::random<Scalar>();
  VERIFY_IS_APPROX(MatrixType::Identity(size, size).determinant(), Scalar(1));
  VERIFY_IS_APPROX((m1*m2).eval().determinant(), m1.determinant() * m2.determinant());
  if(size==1) return;
  Index i = internal::random<Index>(0, size-1);
  Index j;
  do {
    j = internal::random<Index>(0, size-1);
  } while(j==i);
  m2 = m1;
  m2.row(i).swap(m2.row(j));
  VERIFY_IS_APPROX(m2.determinant(), -m1.determinant());
  m2 = m1;
  m2.col(i).swap(m2.col(j));
  VERIFY_IS_APPROX(m2.determinant(), -m1.determinant());
  VERIFY_IS_APPROX(m2.determinant(), m2.transpose().determinant());
  VERIFY_IS_APPROX(internal::conj(m2.determinant()), m2.adjoint().determinant());
  m2 = m1;
  m2.row(i) += x*m2.row(j);
  VERIFY_IS_APPROX(m2.determinant(), m1.determinant());
  m2 = m1;
  m2.row(i) *= x;
  VERIFY_IS_APPROX(m2.determinant(), m1.determinant() * x);
  
  // check empty matrix
  VERIFY_IS_APPROX(m2.block(0,0,0,0).determinant(), Scalar(1));
}

void test_determinant()
{
  for(int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_1( determinant(Matrix<float, 1, 1>()) );
    CALL_SUBTEST_2( determinant(Matrix<double, 2, 2>()) );
    CALL_SUBTEST_3( determinant(Matrix<double, 3, 3>()) );
    CALL_SUBTEST_4( determinant(Matrix<double, 4, 4>()) );
    CALL_SUBTEST_5( determinant(Matrix<std::complex<double>, 10, 10>()) );
    CALL_SUBTEST_6( determinant(MatrixXd(20, 20)) );
  }
  CALL_SUBTEST_6( determinant(MatrixXd(200, 200)) );
}