matrix_exponential.cpp revision c981c48f5bc9aefeffc0bcb0cc3934c2fae179dd 
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 "main.h"
11#include <unsupported/Eigen/MatrixFunctions>
12
13double binom(int n, int k)
14{
15  double res = 1;
16  for (int i=0; i<k; i++)
17    res = res * (n-k+i+1) / (i+1);
18  return res;
19}
20
21template <typename Derived, typename OtherDerived>
22double relerr(const MatrixBase<Derived>& A, const MatrixBase<OtherDerived>& B)
23{
24  return std::sqrt((A - B).cwiseAbs2().sum() / (std::min)(A.cwiseAbs2().sum(), B.cwiseAbs2().sum()));
25}
26
27template <typename T>
28T expfn(T x, int)
29{
30  return std::exp(x);
31}
32
33template <typename T>
34void test2dRotation(double tol)
35{
36  Matrix<T,2,2> A, B, C;
37  T angle;
38
39  A << 0, 1, -1, 0;
40  for (int i=0; i<=20; i++)
41  {
42    angle = static_cast<T>(pow(10, i / 5. - 2));
43    B << std::cos(angle), std::sin(angle), -std::sin(angle), std::cos(angle);
44
45    C = (angle*A).matrixFunction(expfn);
46    std::cout << "test2dRotation: i = " << i << "   error funm = " << relerr(C, B);
47    VERIFY(C.isApprox(B, static_cast<T>(tol)));
48
49    C = (angle*A).exp();
50    std::cout << "   error expm = " << relerr(C, B) << "\n";
51    VERIFY(C.isApprox(B, static_cast<T>(tol)));
52  }
53}
54
55template <typename T>
56void test2dHyperbolicRotation(double tol)
57{
58  Matrix<std::complex<T>,2,2> A, B, C;
59  std::complex<T> imagUnit(0,1);
60  T angle, ch, sh;
61
62  for (int i=0; i<=20; i++)
63  {
64    angle = static_cast<T>((i-10) / 2.0);
65    ch = std::cosh(angle);
66    sh = std::sinh(angle);
67    A << 0, angle*imagUnit, -angle*imagUnit, 0;
68    B << ch, sh*imagUnit, -sh*imagUnit, ch;
69
70    C = A.matrixFunction(expfn);
71    std::cout << "test2dHyperbolicRotation: i = " << i << "   error funm = " << relerr(C, B);
72    VERIFY(C.isApprox(B, static_cast<T>(tol)));
73
74    C = A.exp();
75    std::cout << "   error expm = " << relerr(C, B) << "\n";
76    VERIFY(C.isApprox(B, static_cast<T>(tol)));
77  }
78}
79
80template <typename T>
81void testPascal(double tol)
82{
83  for (int size=1; size<20; size++)
84  {
85    Matrix<T,Dynamic,Dynamic> A(size,size), B(size,size), C(size,size);
86    A.setZero();
87    for (int i=0; i<size-1; i++)
88      A(i+1,i) = static_cast<T>(i+1);
89    B.setZero();
90    for (int i=0; i<size; i++)
91      for (int j=0; j<=i; j++)
92    B(i,j) = static_cast<T>(binom(i,j));
93
94    C = A.matrixFunction(expfn);
95    std::cout << "testPascal: size = " << size << "   error funm = " << relerr(C, B);
96    VERIFY(C.isApprox(B, static_cast<T>(tol)));
97
98    C = A.exp();
99    std::cout << "   error expm = " << relerr(C, B) << "\n";
100    VERIFY(C.isApprox(B, static_cast<T>(tol)));
101  }
102}
103
104template<typename MatrixType>
105void randomTest(const MatrixType& m, double tol)
106{
107  /* this test covers the following files:
108     Inverse.h
109  */
110  typename MatrixType::Index rows = m.rows();
111  typename MatrixType::Index cols = m.cols();
112  MatrixType m1(rows, cols), m2(rows, cols), m3(rows, cols),
113             identity = MatrixType::Identity(rows, rows);
114
115  typedef typename NumTraits<typename internal::traits<MatrixType>::Scalar>::Real RealScalar;
116
117  for(int i = 0; i < g_repeat; i++) {
118    m1 = MatrixType::Random(rows, cols);
119
120    m2 = m1.matrixFunction(expfn) * (-m1).matrixFunction(expfn);
121    std::cout << "randomTest: error funm = " << relerr(identity, m2);
122    VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));
123
124    m2 = m1.exp() * (-m1).exp();
125    std::cout << "   error expm = " << relerr(identity, m2) << "\n";
126    VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));
127  }
128}
129
130void test_matrix_exponential()
131{
132  CALL_SUBTEST_2(test2dRotation<double>(1e-13));
133  CALL_SUBTEST_1(test2dRotation<float>(2e-5));  // was 1e-5, relaxed for clang 2.8 / linux / x86-64
134  CALL_SUBTEST_8(test2dRotation<long double>(1e-13));
135  CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14));
136  CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5));
137  CALL_SUBTEST_8(test2dHyperbolicRotation<long double>(1e-14));
138  CALL_SUBTEST_6(testPascal<float>(1e-6));
139  CALL_SUBTEST_5(testPascal<double>(1e-15));
140  CALL_SUBTEST_2(randomTest(Matrix2d(), 1e-13));
141  CALL_SUBTEST_7(randomTest(Matrix<double,3,3,RowMajor>(), 1e-13));
142  CALL_SUBTEST_3(randomTest(Matrix4cd(), 1e-13));
143  CALL_SUBTEST_4(randomTest(MatrixXd(8,8), 1e-13));
144  CALL_SUBTEST_1(randomTest(Matrix2f(), 1e-4));
145  CALL_SUBTEST_5(randomTest(Matrix3cf(), 1e-4));
146  CALL_SUBTEST_1(randomTest(Matrix4f(), 1e-4));
147  CALL_SUBTEST_6(randomTest(MatrixXf(8,8), 1e-4));
148  CALL_SUBTEST_9(randomTest(Matrix<long double,Dynamic,Dynamic>(7,7), 1e-13));
149}
150