aboutsummaryrefslogtreecommitdiffhomepage
path: root/unsupported/test/matrix_exponential.cpp
blob: 74b2634c8a80ba3d3ee80629cff8437afe03713d (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Jitse Niesen <jitse@maths.leeds.ac.uk>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.

#include "main.h"
#include <unsupported/Eigen/MatrixFunctions>

double binom(int n, int k)
{
  double res = 1;
  for (int i=0; i<k; i++)
    res = res * (n-k+i+1) / (i+1);
  return res;
}

template <typename Derived, typename OtherDerived>
double relerr(const MatrixBase<Derived>& A, const MatrixBase<OtherDerived>& B)
{
  return std::sqrt((A - B).cwiseAbs2().sum() / std::min(A.cwiseAbs2().sum(), B.cwiseAbs2().sum()));
}

template <typename T>
T expfn(T x, int)
{
  return std::exp(x);
}

template <typename T>
void test2dRotation(double tol)
{
  Matrix<T,2,2> A, B, C;
  T angle;

  A << 0, 1, -1, 0;
  for (int i=0; i<=20; i++)
  {
    angle = static_cast<T>(pow(10, i / 5. - 2));
    B << cos(angle), sin(angle), -sin(angle), cos(angle);

    C = (angle*A).matrixFunction(expfn);
    std::cout << "test2dRotation: i = " << i << "   error funm = " << relerr(C, B);
    VERIFY(C.isApprox(B, static_cast<T>(tol)));

    C = (angle*A).exp();
    std::cout << "   error expm = " << relerr(C, B) << "\n";
    VERIFY(C.isApprox(B, static_cast<T>(tol)));
  }
}

template <typename T>
void test2dHyperbolicRotation(double tol)
{
  Matrix<std::complex<T>,2,2> A, B, C;
  std::complex<T> imagUnit(0,1);
  T angle, ch, sh;

  for (int i=0; i<=20; i++)
  {
    angle = static_cast<T>((i-10) / 2.0);
    ch = std::cosh(angle);
    sh = std::sinh(angle);
    A << 0, angle*imagUnit, -angle*imagUnit, 0;
    B << ch, sh*imagUnit, -sh*imagUnit, ch;

    C = A.matrixFunction(expfn);
    std::cout << "test2dHyperbolicRotation: i = " << i << "   error funm = " << relerr(C, B);
    VERIFY(C.isApprox(B, static_cast<T>(tol)));

    C = A.exp();
    std::cout << "   error expm = " << relerr(C, B) << "\n";
    VERIFY(C.isApprox(B, static_cast<T>(tol)));
  }
}

template <typename T>
void testPascal(double tol)
{
  for (int size=1; size<20; size++)
  {
    Matrix<T,Dynamic,Dynamic> A(size,size), B(size,size), C(size,size);
    A.setZero();
    for (int i=0; i<size-1; i++)
      A(i+1,i) = static_cast<T>(i+1);
    B.setZero();
    for (int i=0; i<size; i++)
      for (int j=0; j<=i; j++)
    B(i,j) = static_cast<T>(binom(i,j));

    C = A.matrixFunction(expfn);
    std::cout << "testPascal: size = " << size << "   error funm = " << relerr(C, B);
    VERIFY(C.isApprox(B, static_cast<T>(tol)));

    C = A.exp();
    std::cout << "   error expm = " << relerr(C, B) << "\n";
    VERIFY(C.isApprox(B, static_cast<T>(tol)));
  }
}

template<typename MatrixType>
void randomTest(const MatrixType& m, double tol)
{
  /* this test covers the following files:
     Inverse.h
  */
  typename MatrixType::Index rows = m.rows();
  typename MatrixType::Index cols = m.cols();
  MatrixType m1(rows, cols), m2(rows, cols), m3(rows, cols),
             identity = MatrixType::Identity(rows, rows);

  typedef typename NumTraits<typename ei_traits<MatrixType>::Scalar>::Real RealScalar;

  for(int i = 0; i < g_repeat; i++) {
    m1 = MatrixType::Random(rows, cols);

    m2 = m1.matrixFunction(expfn) * (-m1).matrixFunction(expfn);
    std::cout << "randomTest: error funm = " << relerr(identity, m2);
    VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));

    m2 = m1.exp() * (-m1).exp();
    std::cout << "   error expm = " << relerr(identity, m2) << "\n";
    VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));
  }
}

void test_matrix_exponential()
{
  CALL_SUBTEST_2(test2dRotation<double>(1e-13));
  CALL_SUBTEST_1(test2dRotation<float>(1e-5));
  CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14));
  CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5));
  CALL_SUBTEST_6(testPascal<float>(1e-6));
  CALL_SUBTEST_5(testPascal<double>(1e-15));
  CALL_SUBTEST_2(randomTest(Matrix2d(), 1e-13));
  CALL_SUBTEST_7(randomTest(Matrix<double,3,3,RowMajor>(), 1e-13));
  CALL_SUBTEST_3(randomTest(Matrix4cd(), 1e-13));
  CALL_SUBTEST_4(randomTest(MatrixXd(8,8), 1e-13));
  CALL_SUBTEST_1(randomTest(Matrix2f(), 1e-4));
  CALL_SUBTEST_5(randomTest(Matrix3cf(), 1e-4));
  CALL_SUBTEST_1(randomTest(Matrix4f(), 1e-4));
  CALL_SUBTEST_6(randomTest(MatrixXf(8,8), 1e-4));
}