matrix_exponential.cpp revision 7faaa9f3f0df9d23790277834d426c3d992ac3ba 
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
12double 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
20template <typename T>
21T expfn(T x, int)
22{
23  return std::exp(x);
24}
25
26template <typename T>
27void 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
48template <typename T>
49void 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
73template <typename T>
74void 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
97template<typename MatrixType>
98void 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
122void 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