1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2009 Jitse Niesen <jitse@maths.leeds.ac.uk>
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
binom(int n,int k)12 double binom(int n, int k)
13 {
14 double res = 1;
15 for (int i=0; i<k; i++)
16 res = res * (n-k+i+1) / (i+1);
17 return res;
18 }
19
20 template <typename T>
expfn(T x,int)21 T expfn(T x, int)
22 {
23 return std::exp(x);
24 }
25
26 template <typename T>
test2dRotation(double tol)27 void test2dRotation(double tol)
28 {
29 Matrix<T,2,2> A, B, C;
30 T angle;
31
32 A << 0, 1, -1, 0;
33 for (int i=0; i<=20; i++)
34 {
35 angle = static_cast<T>(pow(10, i / 5. - 2));
36 B << std::cos(angle), std::sin(angle), -std::sin(angle), std::cos(angle);
37
38 C = (angle*A).matrixFunction(expfn);
39 std::cout << "test2dRotation: i = " << i << " error funm = " << relerr(C, B);
40 VERIFY(C.isApprox(B, static_cast<T>(tol)));
41
42 C = (angle*A).exp();
43 std::cout << " error expm = " << relerr(C, B) << "\n";
44 VERIFY(C.isApprox(B, static_cast<T>(tol)));
45 }
46 }
47
48 template <typename T>
test2dHyperbolicRotation(double tol)49 void test2dHyperbolicRotation(double tol)
50 {
51 Matrix<std::complex<T>,2,2> A, B, C;
52 std::complex<T> imagUnit(0,1);
53 T angle, ch, sh;
54
55 for (int i=0; i<=20; i++)
56 {
57 angle = static_cast<T>((i-10) / 2.0);
58 ch = std::cosh(angle);
59 sh = std::sinh(angle);
60 A << 0, angle*imagUnit, -angle*imagUnit, 0;
61 B << ch, sh*imagUnit, -sh*imagUnit, ch;
62
63 C = A.matrixFunction(expfn);
64 std::cout << "test2dHyperbolicRotation: i = " << i << " error funm = " << relerr(C, B);
65 VERIFY(C.isApprox(B, static_cast<T>(tol)));
66
67 C = A.exp();
68 std::cout << " error expm = " << relerr(C, B) << "\n";
69 VERIFY(C.isApprox(B, static_cast<T>(tol)));
70 }
71 }
72
73 template <typename T>
testPascal(double tol)74 void testPascal(double tol)
75 {
76 for (int size=1; size<20; size++)
77 {
78 Matrix<T,Dynamic,Dynamic> A(size,size), B(size,size), C(size,size);
79 A.setZero();
80 for (int i=0; i<size-1; i++)
81 A(i+1,i) = static_cast<T>(i+1);
82 B.setZero();
83 for (int i=0; i<size; i++)
84 for (int j=0; j<=i; j++)
85 B(i,j) = static_cast<T>(binom(i,j));
86
87 C = A.matrixFunction(expfn);
88 std::cout << "testPascal: size = " << size << " error funm = " << relerr(C, B);
89 VERIFY(C.isApprox(B, static_cast<T>(tol)));
90
91 C = A.exp();
92 std::cout << " error expm = " << relerr(C, B) << "\n";
93 VERIFY(C.isApprox(B, static_cast<T>(tol)));
94 }
95 }
96
97 template<typename MatrixType>
randomTest(const MatrixType & m,double tol)98 void randomTest(const MatrixType& m, double tol)
99 {
100 /* this test covers the following files:
101 Inverse.h
102 */
103 typename MatrixType::Index rows = m.rows();
104 typename MatrixType::Index cols = m.cols();
105 MatrixType m1(rows, cols), m2(rows, cols), identity = MatrixType::Identity(rows, cols);
106
107 typedef typename NumTraits<typename internal::traits<MatrixType>::Scalar>::Real RealScalar;
108
109 for(int i = 0; i < g_repeat; i++) {
110 m1 = MatrixType::Random(rows, cols);
111
112 m2 = m1.matrixFunction(expfn) * (-m1).matrixFunction(expfn);
113 std::cout << "randomTest: error funm = " << relerr(identity, m2);
114 VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));
115
116 m2 = m1.exp() * (-m1).exp();
117 std::cout << " error expm = " << relerr(identity, m2) << "\n";
118 VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));
119 }
120 }
121
test_matrix_exponential()122 void test_matrix_exponential()
123 {
124 CALL_SUBTEST_2(test2dRotation<double>(1e-13));
125 CALL_SUBTEST_1(test2dRotation<float>(2e-5)); // was 1e-5, relaxed for clang 2.8 / linux / x86-64
126 CALL_SUBTEST_8(test2dRotation<long double>(1e-13));
127 CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14));
128 CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5));
129 CALL_SUBTEST_8(test2dHyperbolicRotation<long double>(1e-14));
130 CALL_SUBTEST_6(testPascal<float>(1e-6));
131 CALL_SUBTEST_5(testPascal<double>(1e-15));
132 CALL_SUBTEST_2(randomTest(Matrix2d(), 1e-13));
133 CALL_SUBTEST_7(randomTest(Matrix<double,3,3,RowMajor>(), 1e-13));
134 CALL_SUBTEST_3(randomTest(Matrix4cd(), 1e-13));
135 CALL_SUBTEST_4(randomTest(MatrixXd(8,8), 1e-13));
136 CALL_SUBTEST_1(randomTest(Matrix2f(), 1e-4));
137 CALL_SUBTEST_5(randomTest(Matrix3cf(), 1e-4));
138 CALL_SUBTEST_1(randomTest(Matrix4f(), 1e-4));
139 CALL_SUBTEST_6(randomTest(MatrixXf(8,8), 1e-4));
140 CALL_SUBTEST_9(randomTest(Matrix<long double,Dynamic,Dynamic>(7,7), 1e-13));
141 }
142