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      1 // This file is part of Eigen, a lightweight C++ template library
      2 // for linear algebra.
      3 //
      4 // Copyright (C) 2008 Benoit Jacob <jacob.benoit.1 (at) gmail.com>
      5 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud (at) inria.fr>
      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/LU>
     13 
     14 template<typename MatrixType> void determinant(const MatrixType& m)
     15 {
     16   /* this test covers the following files:
     17      Determinant.h
     18   */
     19   typedef typename MatrixType::Index Index;
     20   Index size = m.rows();
     21 
     22   MatrixType m1(size, size), m2(size, size);
     23   m1.setRandom();
     24   m2.setRandom();
     25   typedef typename MatrixType::Scalar Scalar;
     26   Scalar x = internal::random<Scalar>();
     27   VERIFY_IS_APPROX(MatrixType::Identity(size, size).determinant(), Scalar(1));
     28   VERIFY_IS_APPROX((m1*m2).eval().determinant(), m1.determinant() * m2.determinant());
     29   if(size==1) return;
     30   Index i = internal::random<Index>(0, size-1);
     31   Index j;
     32   do {
     33     j = internal::random<Index>(0, size-1);
     34   } while(j==i);
     35   m2 = m1;
     36   m2.row(i).swap(m2.row(j));
     37   VERIFY_IS_APPROX(m2.determinant(), -m1.determinant());
     38   m2 = m1;
     39   m2.col(i).swap(m2.col(j));
     40   VERIFY_IS_APPROX(m2.determinant(), -m1.determinant());
     41   VERIFY_IS_APPROX(m2.determinant(), m2.transpose().determinant());
     42   VERIFY_IS_APPROX(internal::conj(m2.determinant()), m2.adjoint().determinant());
     43   m2 = m1;
     44   m2.row(i) += x*m2.row(j);
     45   VERIFY_IS_APPROX(m2.determinant(), m1.determinant());
     46   m2 = m1;
     47   m2.row(i) *= x;
     48   VERIFY_IS_APPROX(m2.determinant(), m1.determinant() * x);
     49 
     50   // check empty matrix
     51   VERIFY_IS_APPROX(m2.block(0,0,0,0).determinant(), Scalar(1));
     52 }
     53 
     54 void test_determinant()
     55 {
     56   int s;
     57   for(int i = 0; i < g_repeat; i++) {
     58     CALL_SUBTEST_1( determinant(Matrix<float, 1, 1>()) );
     59     CALL_SUBTEST_2( determinant(Matrix<double, 2, 2>()) );
     60     CALL_SUBTEST_3( determinant(Matrix<double, 3, 3>()) );
     61     CALL_SUBTEST_4( determinant(Matrix<double, 4, 4>()) );
     62     CALL_SUBTEST_5( determinant(Matrix<std::complex<double>, 10, 10>()) );
     63     s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
     64     CALL_SUBTEST_6( determinant(MatrixXd(s, s)) );
     65   }
     66   EIGEN_UNUSED_VARIABLE(s)
     67 }
     68