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
inverse(const MatrixType & m)14 template<typename MatrixType> void inverse(const MatrixType& m)
15 {
16 typedef typename MatrixType::Index Index;
17 /* this test covers the following files:
18 Inverse.h
19 */
20 Index rows = m.rows();
21 Index cols = m.cols();
22
23 typedef typename MatrixType::Scalar Scalar;
24 typedef typename NumTraits<Scalar>::Real RealScalar;
25 typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
26
27 MatrixType m1(rows, cols),
28 m2(rows, cols),
29 identity = MatrixType::Identity(rows, rows);
30 createRandomPIMatrixOfRank(rows,rows,rows,m1);
31 m2 = m1.inverse();
32 VERIFY_IS_APPROX(m1, m2.inverse() );
33
34 VERIFY_IS_APPROX((Scalar(2)*m2).inverse(), m2.inverse()*Scalar(0.5));
35
36 VERIFY_IS_APPROX(identity, m1.inverse() * m1 );
37 VERIFY_IS_APPROX(identity, m1 * m1.inverse() );
38
39 VERIFY_IS_APPROX(m1, m1.inverse().inverse() );
40
41 // since for the general case we implement separately row-major and col-major, test that
42 VERIFY_IS_APPROX(MatrixType(m1.transpose().inverse()), MatrixType(m1.inverse().transpose()));
43
44 #if !defined(EIGEN_TEST_PART_5) && !defined(EIGEN_TEST_PART_6)
45 //computeInverseAndDetWithCheck tests
46 //First: an invertible matrix
47 bool invertible;
48 RealScalar det;
49
50 m2.setZero();
51 m1.computeInverseAndDetWithCheck(m2, det, invertible);
52 VERIFY(invertible);
53 VERIFY_IS_APPROX(identity, m1*m2);
54 VERIFY_IS_APPROX(det, m1.determinant());
55
56 m2.setZero();
57 m1.computeInverseWithCheck(m2, invertible);
58 VERIFY(invertible);
59 VERIFY_IS_APPROX(identity, m1*m2);
60
61 //Second: a rank one matrix (not invertible, except for 1x1 matrices)
62 VectorType v3 = VectorType::Random(rows);
63 MatrixType m3 = v3*v3.transpose(), m4(rows,cols);
64 m3.computeInverseAndDetWithCheck(m4, det, invertible);
65 VERIFY( rows==1 ? invertible : !invertible );
66 VERIFY_IS_MUCH_SMALLER_THAN(internal::abs(det-m3.determinant()), RealScalar(1));
67 m3.computeInverseWithCheck(m4, invertible);
68 VERIFY( rows==1 ? invertible : !invertible );
69 #endif
70
71 // check in-place inversion
72 if(MatrixType::RowsAtCompileTime>=2 && MatrixType::RowsAtCompileTime<=4)
73 {
74 // in-place is forbidden
75 VERIFY_RAISES_ASSERT(m1 = m1.inverse());
76 }
77 else
78 {
79 m2 = m1.inverse();
80 m1 = m1.inverse();
81 VERIFY_IS_APPROX(m1,m2);
82 }
83 }
84
test_inverse()85 void test_inverse()
86 {
87 int s;
88 for(int i = 0; i < g_repeat; i++) {
89 CALL_SUBTEST_1( inverse(Matrix<double,1,1>()) );
90 CALL_SUBTEST_2( inverse(Matrix2d()) );
91 CALL_SUBTEST_3( inverse(Matrix3f()) );
92 CALL_SUBTEST_4( inverse(Matrix4f()) );
93 CALL_SUBTEST_4( inverse(Matrix<float,4,4,DontAlign>()) );
94 s = internal::random<int>(50,320);
95 CALL_SUBTEST_5( inverse(MatrixXf(s,s)) );
96 s = internal::random<int>(25,100);
97 CALL_SUBTEST_6( inverse(MatrixXcd(s,s)) );
98 CALL_SUBTEST_7( inverse(Matrix4d()) );
99 CALL_SUBTEST_7( inverse(Matrix<double,4,4,DontAlign>()) );
100 }
101 EIGEN_UNUSED_VARIABLE(s)
102 }
103