determinant.cpp revision 7faaa9f3f0df9d23790277834d426c3d992ac3ba 
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@gmail.com>
5// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@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
14template<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(numext::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
54void test_determinant()
55{
56  for(int i = 0; i < g_repeat; i++) {
57    int s = 0;
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    TEST_SET_BUT_UNUSED_VARIABLE(s)
66  }
67}
68