1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
5// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
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 inverse(const MatrixType& m)
15{
16  using std::abs;
17  typedef typename MatrixType::Index Index;
18  /* this test covers the following files:
19     Inverse.h
20  */
21  Index rows = m.rows();
22  Index cols = m.cols();
23
24  typedef typename MatrixType::Scalar Scalar;
25
26  MatrixType m1(rows, cols),
27             m2(rows, cols),
28             identity = MatrixType::Identity(rows, rows);
29  createRandomPIMatrixOfRank(rows,rows,rows,m1);
30  m2 = m1.inverse();
31  VERIFY_IS_APPROX(m1, m2.inverse() );
32
33  VERIFY_IS_APPROX((Scalar(2)*m2).inverse(), m2.inverse()*Scalar(0.5));
34
35  VERIFY_IS_APPROX(identity, m1.inverse() * m1 );
36  VERIFY_IS_APPROX(identity, m1 * m1.inverse() );
37
38  VERIFY_IS_APPROX(m1, m1.inverse().inverse() );
39
40  // since for the general case we implement separately row-major and col-major, test that
41  VERIFY_IS_APPROX(MatrixType(m1.transpose().inverse()), MatrixType(m1.inverse().transpose()));
42
43#if !defined(EIGEN_TEST_PART_5) && !defined(EIGEN_TEST_PART_6)
44  typedef typename NumTraits<Scalar>::Real RealScalar;
45  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
46
47  //computeInverseAndDetWithCheck tests
48  //First: an invertible matrix
49  bool invertible;
50  RealScalar det;
51
52  m2.setZero();
53  m1.computeInverseAndDetWithCheck(m2, det, invertible);
54  VERIFY(invertible);
55  VERIFY_IS_APPROX(identity, m1*m2);
56  VERIFY_IS_APPROX(det, m1.determinant());
57
58  m2.setZero();
59  m1.computeInverseWithCheck(m2, invertible);
60  VERIFY(invertible);
61  VERIFY_IS_APPROX(identity, m1*m2);
62
63  //Second: a rank one matrix (not invertible, except for 1x1 matrices)
64  VectorType v3 = VectorType::Random(rows);
65  MatrixType m3 = v3*v3.transpose(), m4(rows,cols);
66  m3.computeInverseAndDetWithCheck(m4, det, invertible);
67  VERIFY( rows==1 ? invertible : !invertible );
68  VERIFY_IS_MUCH_SMALLER_THAN(abs(det-m3.determinant()), RealScalar(1));
69  m3.computeInverseWithCheck(m4, invertible);
70  VERIFY( rows==1 ? invertible : !invertible );
71#endif
72
73  // check in-place inversion
74  if(MatrixType::RowsAtCompileTime>=2 && MatrixType::RowsAtCompileTime<=4)
75  {
76    // in-place is forbidden
77    VERIFY_RAISES_ASSERT(m1 = m1.inverse());
78  }
79  else
80  {
81    m2 = m1.inverse();
82    m1 = m1.inverse();
83    VERIFY_IS_APPROX(m1,m2);
84  }
85}
86
87void test_inverse()
88{
89  int s = 0;
90  for(int i = 0; i < g_repeat; i++) {
91    CALL_SUBTEST_1( inverse(Matrix<double,1,1>()) );
92    CALL_SUBTEST_2( inverse(Matrix2d()) );
93    CALL_SUBTEST_3( inverse(Matrix3f()) );
94    CALL_SUBTEST_4( inverse(Matrix4f()) );
95    CALL_SUBTEST_4( inverse(Matrix<float,4,4,DontAlign>()) );
96    s = internal::random<int>(50,320);
97    CALL_SUBTEST_5( inverse(MatrixXf(s,s)) );
98    s = internal::random<int>(25,100);
99    CALL_SUBTEST_6( inverse(MatrixXcd(s,s)) );
100    CALL_SUBTEST_7( inverse(Matrix4d()) );
101    CALL_SUBTEST_7( inverse(Matrix<double,4,4,DontAlign>()) );
102  }
103  TEST_SET_BUT_UNUSED_VARIABLE(s)
104}
105