1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008 Gael Guennebaud <[email protected]>
5 // Copyright (C) 2008 Benoit Jacob <[email protected]>
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>
inverse_for_fixed_size(const MatrixType &,typename internal::enable_if<MatrixType::SizeAtCompileTime==Dynamic>::type * =0)15 void inverse_for_fixed_size(const MatrixType&, typename internal::enable_if<MatrixType::SizeAtCompileTime==Dynamic>::type* = 0)
16 {
17 }
18
19 template<typename MatrixType>
inverse_for_fixed_size(const MatrixType & m1,typename internal::enable_if<MatrixType::SizeAtCompileTime!=Dynamic>::type * =0)20 void inverse_for_fixed_size(const MatrixType& m1, typename internal::enable_if<MatrixType::SizeAtCompileTime!=Dynamic>::type* = 0)
21 {
22 using std::abs;
23
24 MatrixType m2, identity = MatrixType::Identity();
25
26 typedef typename MatrixType::Scalar Scalar;
27 typedef typename NumTraits<Scalar>::Real RealScalar;
28 typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
29
30 //computeInverseAndDetWithCheck tests
31 //First: an invertible matrix
32 bool invertible;
33 Scalar det;
34
35 m2.setZero();
36 m1.computeInverseAndDetWithCheck(m2, det, invertible);
37 VERIFY(invertible);
38 VERIFY_IS_APPROX(identity, m1*m2);
39 VERIFY_IS_APPROX(det, m1.determinant());
40
41 m2.setZero();
42 m1.computeInverseWithCheck(m2, invertible);
43 VERIFY(invertible);
44 VERIFY_IS_APPROX(identity, m1*m2);
45
46 //Second: a rank one matrix (not invertible, except for 1x1 matrices)
47 VectorType v3 = VectorType::Random();
48 MatrixType m3 = v3*v3.transpose(), m4;
49 m3.computeInverseAndDetWithCheck(m4, det, invertible);
50 VERIFY( m1.rows()==1 ? invertible : !invertible );
51 VERIFY_IS_MUCH_SMALLER_THAN(abs(det-m3.determinant()), RealScalar(1));
52 m3.computeInverseWithCheck(m4, invertible);
53 VERIFY( m1.rows()==1 ? invertible : !invertible );
54
55 // check with submatrices
56 {
57 Matrix<Scalar, MatrixType::RowsAtCompileTime+1, MatrixType::RowsAtCompileTime+1, MatrixType::Options> m5;
58 m5.setRandom();
59 m5.topLeftCorner(m1.rows(),m1.rows()) = m1;
60 m2 = m5.template topLeftCorner<MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime>().inverse();
61 VERIFY_IS_APPROX( (m5.template topLeftCorner<MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime>()), m2.inverse() );
62 }
63 }
64
inverse(const MatrixType & m)65 template<typename MatrixType> void inverse(const MatrixType& m)
66 {
67 /* this test covers the following files:
68 Inverse.h
69 */
70 Index rows = m.rows();
71 Index cols = m.cols();
72
73 typedef typename MatrixType::Scalar Scalar;
74
75 MatrixType m1(rows, cols),
76 m2(rows, cols),
77 identity = MatrixType::Identity(rows, rows);
78 createRandomPIMatrixOfRank(rows,rows,rows,m1);
79 m2 = m1.inverse();
80 VERIFY_IS_APPROX(m1, m2.inverse() );
81
82 VERIFY_IS_APPROX((Scalar(2)*m2).inverse(), m2.inverse()*Scalar(0.5));
83
84 VERIFY_IS_APPROX(identity, m1.inverse() * m1 );
85 VERIFY_IS_APPROX(identity, m1 * m1.inverse() );
86
87 VERIFY_IS_APPROX(m1, m1.inverse().inverse() );
88
89 // since for the general case we implement separately row-major and col-major, test that
90 VERIFY_IS_APPROX(MatrixType(m1.transpose().inverse()), MatrixType(m1.inverse().transpose()));
91
92 inverse_for_fixed_size(m1);
93
94 // check in-place inversion
95 if(MatrixType::RowsAtCompileTime>=2 && MatrixType::RowsAtCompileTime<=4)
96 {
97 // in-place is forbidden
98 VERIFY_RAISES_ASSERT(m1 = m1.inverse());
99 }
100 else
101 {
102 m2 = m1.inverse();
103 m1 = m1.inverse();
104 VERIFY_IS_APPROX(m1,m2);
105 }
106 }
107
108 template<typename Scalar>
inverse_zerosized()109 void inverse_zerosized()
110 {
111 Matrix<Scalar,Dynamic,Dynamic> A(0,0);
112 {
113 Matrix<Scalar,0,1> b, x;
114 x = A.inverse() * b;
115 }
116 {
117 Matrix<Scalar,Dynamic,Dynamic> b(0,1), x;
118 x = A.inverse() * b;
119 VERIFY_IS_EQUAL(x.rows(), 0);
120 VERIFY_IS_EQUAL(x.cols(), 1);
121 }
122 }
123
EIGEN_DECLARE_TEST(inverse)124 EIGEN_DECLARE_TEST(inverse)
125 {
126 int s = 0;
127 for(int i = 0; i < g_repeat; i++) {
128 CALL_SUBTEST_1( inverse(Matrix<double,1,1>()) );
129 CALL_SUBTEST_2( inverse(Matrix2d()) );
130 CALL_SUBTEST_3( inverse(Matrix3f()) );
131 CALL_SUBTEST_4( inverse(Matrix4f()) );
132 CALL_SUBTEST_4( inverse(Matrix<float,4,4,DontAlign>()) );
133
134 s = internal::random<int>(50,320);
135 CALL_SUBTEST_5( inverse(MatrixXf(s,s)) );
136 TEST_SET_BUT_UNUSED_VARIABLE(s)
137 CALL_SUBTEST_5( inverse_zerosized<float>() );
138 CALL_SUBTEST_5( inverse(MatrixXf(0, 0)) );
139 CALL_SUBTEST_5( inverse(MatrixXf(1, 1)) );
140
141 s = internal::random<int>(25,100);
142 CALL_SUBTEST_6( inverse(MatrixXcd(s,s)) );
143 TEST_SET_BUT_UNUSED_VARIABLE(s)
144
145 CALL_SUBTEST_7( inverse(Matrix4d()) );
146 CALL_SUBTEST_7( inverse(Matrix<double,4,4,DontAlign>()) );
147
148 CALL_SUBTEST_8( inverse(Matrix4cd()) );
149 }
150 }
151