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 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
72 // check with submatrices
73 {
74 Matrix<Scalar, MatrixType::RowsAtCompileTime+1, MatrixType::RowsAtCompileTime+1, MatrixType::Options> m5;
75 m5.setRandom();
76 m5.topLeftCorner(rows,rows) = m1;
77 m2 = m5.template topLeftCorner<MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime>().inverse();
78 VERIFY_IS_APPROX( (m5.template topLeftCorner<MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime>()), m2.inverse() );
79 }
80 #endif
81
82 // check in-place inversion
83 if(MatrixType::RowsAtCompileTime>=2 && MatrixType::RowsAtCompileTime<=4)
84 {
85 // in-place is forbidden
86 VERIFY_RAISES_ASSERT(m1 = m1.inverse());
87 }
88 else
89 {
90 m2 = m1.inverse();
91 m1 = m1.inverse();
92 VERIFY_IS_APPROX(m1,m2);
93 }
94 }
95
test_inverse()96 void test_inverse()
97 {
98 int s = 0;
99 for(int i = 0; i < g_repeat; i++) {
100 CALL_SUBTEST_1( inverse(Matrix<double,1,1>()) );
101 CALL_SUBTEST_2( inverse(Matrix2d()) );
102 CALL_SUBTEST_3( inverse(Matrix3f()) );
103 CALL_SUBTEST_4( inverse(Matrix4f()) );
104 CALL_SUBTEST_4( inverse(Matrix<float,4,4,DontAlign>()) );
105
106 s = internal::random<int>(50,320);
107 CALL_SUBTEST_5( inverse(MatrixXf(s,s)) );
108 TEST_SET_BUT_UNUSED_VARIABLE(s)
109
110 s = internal::random<int>(25,100);
111 CALL_SUBTEST_6( inverse(MatrixXcd(s,s)) );
112 TEST_SET_BUT_UNUSED_VARIABLE(s)
113
114 CALL_SUBTEST_7( inverse(Matrix4d()) );
115 CALL_SUBTEST_7( inverse(Matrix<double,4,4,DontAlign>()) );
116 }
117 }
118