1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2012, 2013 Chen-Pang He <jdh8@ms63.hinet.net>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9
10 #include "matrix_functions.h"
11
12 template<typename T>
test2dRotation(const T & tol)13 void test2dRotation(const T& tol)
14 {
15 Matrix<T,2,2> A, B, C;
16 T angle, c, s;
17
18 A << 0, 1, -1, 0;
19 MatrixPower<Matrix<T,2,2> > Apow(A);
20
21 for (int i=0; i<=20; ++i) {
22 angle = std::pow(T(10), (i-10) / T(5.));
23 c = std::cos(angle);
24 s = std::sin(angle);
25 B << c, s, -s, c;
26
27 C = Apow(std::ldexp(angle,1) / T(EIGEN_PI));
28 std::cout << "test2dRotation: i = " << i << " error powerm = " << relerr(C,B) << '\n';
29 VERIFY(C.isApprox(B, tol));
30 }
31 }
32
33 template<typename T>
test2dHyperbolicRotation(const T & tol)34 void test2dHyperbolicRotation(const T& tol)
35 {
36 Matrix<std::complex<T>,2,2> A, B, C;
37 T angle, ch = std::cosh((T)1);
38 std::complex<T> ish(0, std::sinh((T)1));
39
40 A << ch, ish, -ish, ch;
41 MatrixPower<Matrix<std::complex<T>,2,2> > Apow(A);
42
43 for (int i=0; i<=20; ++i) {
44 angle = std::ldexp(static_cast<T>(i-10), -1);
45 ch = std::cosh(angle);
46 ish = std::complex<T>(0, std::sinh(angle));
47 B << ch, ish, -ish, ch;
48
49 C = Apow(angle);
50 std::cout << "test2dHyperbolicRotation: i = " << i << " error powerm = " << relerr(C,B) << '\n';
51 VERIFY(C.isApprox(B, tol));
52 }
53 }
54
55 template<typename T>
test3dRotation(const T & tol)56 void test3dRotation(const T& tol)
57 {
58 Matrix<T,3,1> v;
59 T angle;
60
61 for (int i=0; i<=20; ++i) {
62 v = Matrix<T,3,1>::Random();
63 v.normalize();
64 angle = std::pow(T(10), (i-10) / T(5.));
65 VERIFY(AngleAxis<T>(angle, v).matrix().isApprox(AngleAxis<T>(1,v).matrix().pow(angle), tol));
66 }
67 }
68
69 template<typename MatrixType>
testGeneral(const MatrixType & m,const typename MatrixType::RealScalar & tol)70 void testGeneral(const MatrixType& m, const typename MatrixType::RealScalar& tol)
71 {
72 typedef typename MatrixType::RealScalar RealScalar;
73 MatrixType m1, m2, m3, m4, m5;
74 RealScalar x, y;
75
76 for (int i=0; i < g_repeat; ++i) {
77 generateTestMatrix<MatrixType>::run(m1, m.rows());
78 MatrixPower<MatrixType> mpow(m1);
79
80 x = internal::random<RealScalar>();
81 y = internal::random<RealScalar>();
82 m2 = mpow(x);
83 m3 = mpow(y);
84
85 m4 = mpow(x+y);
86 m5.noalias() = m2 * m3;
87 VERIFY(m4.isApprox(m5, tol));
88
89 m4 = mpow(x*y);
90 m5 = m2.pow(y);
91 VERIFY(m4.isApprox(m5, tol));
92
93 m4 = (std::abs(x) * m1).pow(y);
94 m5 = std::pow(std::abs(x), y) * m3;
95 VERIFY(m4.isApprox(m5, tol));
96 }
97 }
98
99 template<typename MatrixType>
testSingular(const MatrixType & m_const,const typename MatrixType::RealScalar & tol)100 void testSingular(const MatrixType& m_const, const typename MatrixType::RealScalar& tol)
101 {
102 // we need to pass by reference in order to prevent errors with
103 // MSVC for aligned data types ...
104 MatrixType& m = const_cast<MatrixType&>(m_const);
105
106 const int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex;
107 typedef typename internal::conditional<IsComplex, TriangularView<MatrixType,Upper>, const MatrixType&>::type TriangularType;
108 typename internal::conditional< IsComplex, ComplexSchur<MatrixType>, RealSchur<MatrixType> >::type schur;
109 MatrixType T;
110
111 for (int i=0; i < g_repeat; ++i) {
112 m.setRandom();
113 m.col(0).fill(0);
114
115 schur.compute(m);
116 T = schur.matrixT();
117 const MatrixType& U = schur.matrixU();
118 processTriangularMatrix<MatrixType>::run(m, T, U);
119 MatrixPower<MatrixType> mpow(m);
120
121 T = T.sqrt();
122 VERIFY(mpow(0.5L).isApprox(U * (TriangularType(T) * U.adjoint()), tol));
123
124 T = T.sqrt();
125 VERIFY(mpow(0.25L).isApprox(U * (TriangularType(T) * U.adjoint()), tol));
126
127 T = T.sqrt();
128 VERIFY(mpow(0.125L).isApprox(U * (TriangularType(T) * U.adjoint()), tol));
129 }
130 }
131
132 template<typename MatrixType>
testLogThenExp(const MatrixType & m_const,const typename MatrixType::RealScalar & tol)133 void testLogThenExp(const MatrixType& m_const, const typename MatrixType::RealScalar& tol)
134 {
135 // we need to pass by reference in order to prevent errors with
136 // MSVC for aligned data types ...
137 MatrixType& m = const_cast<MatrixType&>(m_const);
138
139 typedef typename MatrixType::Scalar Scalar;
140 Scalar x;
141
142 for (int i=0; i < g_repeat; ++i) {
143 generateTestMatrix<MatrixType>::run(m, m.rows());
144 x = internal::random<Scalar>();
145 VERIFY(m.pow(x).isApprox((x * m.log()).exp(), tol));
146 }
147 }
148
149 typedef Matrix<double,3,3,RowMajor> Matrix3dRowMajor;
150 typedef Matrix<long double,3,3> Matrix3e;
151 typedef Matrix<long double,Dynamic,Dynamic> MatrixXe;
152
test_matrix_power()153 void test_matrix_power()
154 {
155 CALL_SUBTEST_2(test2dRotation<double>(1e-13));
156 CALL_SUBTEST_1(test2dRotation<float>(2e-5)); // was 1e-5, relaxed for clang 2.8 / linux / x86-64
157 CALL_SUBTEST_9(test2dRotation<long double>(1e-13L));
158 CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14));
159 CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5));
160 CALL_SUBTEST_9(test2dHyperbolicRotation<long double>(1e-14L));
161
162 CALL_SUBTEST_10(test3dRotation<double>(1e-13));
163 CALL_SUBTEST_11(test3dRotation<float>(1e-5));
164 CALL_SUBTEST_12(test3dRotation<long double>(1e-13L));
165
166 CALL_SUBTEST_2(testGeneral(Matrix2d(), 1e-13));
167 CALL_SUBTEST_7(testGeneral(Matrix3dRowMajor(), 1e-13));
168 CALL_SUBTEST_3(testGeneral(Matrix4cd(), 1e-13));
169 CALL_SUBTEST_4(testGeneral(MatrixXd(8,8), 2e-12));
170 CALL_SUBTEST_1(testGeneral(Matrix2f(), 1e-4));
171 CALL_SUBTEST_5(testGeneral(Matrix3cf(), 1e-4));
172 CALL_SUBTEST_8(testGeneral(Matrix4f(), 1e-4));
173 CALL_SUBTEST_6(testGeneral(MatrixXf(2,2), 1e-3)); // see bug 614
174 CALL_SUBTEST_9(testGeneral(MatrixXe(7,7), 1e-13L));
175 CALL_SUBTEST_10(testGeneral(Matrix3d(), 1e-13));
176 CALL_SUBTEST_11(testGeneral(Matrix3f(), 1e-4));
177 CALL_SUBTEST_12(testGeneral(Matrix3e(), 1e-13L));
178
179 CALL_SUBTEST_2(testSingular(Matrix2d(), 1e-13));
180 CALL_SUBTEST_7(testSingular(Matrix3dRowMajor(), 1e-13));
181 CALL_SUBTEST_3(testSingular(Matrix4cd(), 1e-13));
182 CALL_SUBTEST_4(testSingular(MatrixXd(8,8), 2e-12));
183 CALL_SUBTEST_1(testSingular(Matrix2f(), 1e-4));
184 CALL_SUBTEST_5(testSingular(Matrix3cf(), 1e-4));
185 CALL_SUBTEST_8(testSingular(Matrix4f(), 1e-4));
186 CALL_SUBTEST_6(testSingular(MatrixXf(2,2), 1e-3));
187 CALL_SUBTEST_9(testSingular(MatrixXe(7,7), 1e-13L));
188 CALL_SUBTEST_10(testSingular(Matrix3d(), 1e-13));
189 CALL_SUBTEST_11(testSingular(Matrix3f(), 1e-4));
190 CALL_SUBTEST_12(testSingular(Matrix3e(), 1e-13L));
191
192 CALL_SUBTEST_2(testLogThenExp(Matrix2d(), 1e-13));
193 CALL_SUBTEST_7(testLogThenExp(Matrix3dRowMajor(), 1e-13));
194 CALL_SUBTEST_3(testLogThenExp(Matrix4cd(), 1e-13));
195 CALL_SUBTEST_4(testLogThenExp(MatrixXd(8,8), 2e-12));
196 CALL_SUBTEST_1(testLogThenExp(Matrix2f(), 1e-4));
197 CALL_SUBTEST_5(testLogThenExp(Matrix3cf(), 1e-4));
198 CALL_SUBTEST_8(testLogThenExp(Matrix4f(), 1e-4));
199 CALL_SUBTEST_6(testLogThenExp(MatrixXf(2,2), 1e-3));
200 CALL_SUBTEST_9(testLogThenExp(MatrixXe(7,7), 1e-13L));
201 CALL_SUBTEST_10(testLogThenExp(Matrix3d(), 1e-13));
202 CALL_SUBTEST_11(testLogThenExp(Matrix3f(), 1e-4));
203 CALL_SUBTEST_12(testLogThenExp(Matrix3e(), 1e-13L));
204 }
205