matrix_exponential.cpp
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00001 // This file is part of Eigen, a lightweight C++ template library
00002 // for linear algebra.
00003 //
00004 // Copyright (C) 2009 Jitse Niesen <jitse@maths.leeds.ac.uk>
00005 //
00006 // Eigen is free software; you can redistribute it and/or
00007 // modify it under the terms of the GNU Lesser General Public
00008 // License as published by the Free Software Foundation; either
00009 // version 3 of the License, or (at your option) any later version.
00010 //
00011 // Alternatively, you can redistribute it and/or
00012 // modify it under the terms of the GNU General Public License as
00013 // published by the Free Software Foundation; either version 2 of
00014 // the License, or (at your option) any later version.
00015 //
00016 // Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
00017 // WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
00018 // FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
00019 // GNU General Public License for more details.
00020 //
00021 // You should have received a copy of the GNU Lesser General Public
00022 // License and a copy of the GNU General Public License along with
00023 // Eigen. If not, see <http://www.gnu.org/licenses/>.
00024 
00025 #include "main.h"
00026 #include <unsupported/Eigen/MatrixFunctions>
00027 
00028 double binom(int n, int k)
00029 {
00030   double res = 1;
00031   for (int i=0; i<k; i++)
00032     res = res * (n-k+i+1) / (i+1);
00033   return res;
00034 }
00035 
00036 template <typename Derived, typename OtherDerived>
00037 double relerr(const MatrixBase<Derived>& A, const MatrixBase<OtherDerived>& B)
00038 {
00039   return std::sqrt((A - B).cwiseAbs2().sum() / std::min(A.cwiseAbs2().sum(), B.cwiseAbs2().sum()));
00040 }
00041 
00042 template <typename T>
00043 T expfn(T x, int)
00044 {
00045   return std::exp(x);
00046 }
00047 
00048 template <typename T>
00049 void test2dRotation(double tol)
00050 {
00051   Matrix<T,2,2> A, B, C;
00052   T angle;
00053 
00054   A << 0, 1, -1, 0;
00055   for (int i=0; i<=20; i++)
00056   {
00057     angle = static_cast<T>(pow(10, i / 5. - 2));
00058     B << cos(angle), sin(angle), -sin(angle), cos(angle);
00059 
00060     C = (angle*A).matrixFunction(expfn);
00061     std::cout << "test2dRotation: i = " << i << "   error funm = " << relerr(C, B);
00062     VERIFY(C.isApprox(B, static_cast<T>(tol)));
00063 
00064     C = (angle*A).exp();
00065     std::cout << "   error expm = " << relerr(C, B) << "\n";
00066     VERIFY(C.isApprox(B, static_cast<T>(tol)));
00067   }
00068 }
00069 
00070 template <typename T>
00071 void test2dHyperbolicRotation(double tol)
00072 {
00073   Matrix<std::complex<T>,2,2> A, B, C;
00074   std::complex<T> imagUnit(0,1);
00075   T angle, ch, sh;
00076 
00077   for (int i=0; i<=20; i++)
00078   {
00079     angle = static_cast<T>((i-10) / 2.0);
00080     ch = std::cosh(angle);
00081     sh = std::sinh(angle);
00082     A << 0, angle*imagUnit, -angle*imagUnit, 0;
00083     B << ch, sh*imagUnit, -sh*imagUnit, ch;
00084 
00085     C = A.matrixFunction(expfn);
00086     std::cout << "test2dHyperbolicRotation: i = " << i << "   error funm = " << relerr(C, B);
00087     VERIFY(C.isApprox(B, static_cast<T>(tol)));
00088 
00089     C = A.exp();
00090     std::cout << "   error expm = " << relerr(C, B) << "\n";
00091     VERIFY(C.isApprox(B, static_cast<T>(tol)));
00092   }
00093 }
00094 
00095 template <typename T>
00096 void testPascal(double tol)
00097 {
00098   for (int size=1; size<20; size++)
00099   {
00100     Matrix<T,Dynamic,Dynamic> A(size,size), B(size,size), C(size,size);
00101     A.setZero();
00102     for (int i=0; i<size-1; i++)
00103       A(i+1,i) = static_cast<T>(i+1);
00104     B.setZero();
00105     for (int i=0; i<size; i++)
00106       for (int j=0; j<=i; j++)
00107     B(i,j) = static_cast<T>(binom(i,j));
00108 
00109     C = A.matrixFunction(expfn);
00110     std::cout << "testPascal: size = " << size << "   error funm = " << relerr(C, B);
00111     VERIFY(C.isApprox(B, static_cast<T>(tol)));
00112 
00113     C = A.exp();
00114     std::cout << "   error expm = " << relerr(C, B) << "\n";
00115     VERIFY(C.isApprox(B, static_cast<T>(tol)));
00116   }
00117 }
00118 
00119 template<typename MatrixType>
00120 void randomTest(const MatrixType& m, double tol)
00121 {
00122   /* this test covers the following files:
00123      Inverse.h
00124   */
00125   typename MatrixType::Index rows = m.rows();
00126   typename MatrixType::Index cols = m.cols();
00127   MatrixType m1(rows, cols), m2(rows, cols), m3(rows, cols),
00128              identity = MatrixType::Identity(rows, rows);
00129 
00130   typedef typename NumTraits<typename internal::traits<MatrixType>::Scalar>::Real RealScalar;
00131 
00132   for(int i = 0; i < g_repeat; i++) {
00133     m1 = MatrixType::Random(rows, cols);
00134 
00135     m2 = m1.matrixFunction(expfn) * (-m1).matrixFunction(expfn);
00136     std::cout << "randomTest: error funm = " << relerr(identity, m2);
00137     VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));
00138 
00139     m2 = m1.exp() * (-m1).exp();
00140     std::cout << "   error expm = " << relerr(identity, m2) << "\n";
00141     VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));
00142   }
00143 }
00144 
00145 void test_matrix_exponential()
00146 {
00147   CALL_SUBTEST_2(test2dRotation<double>(1e-13));
00148   CALL_SUBTEST_1(test2dRotation<float>(2e-5));  // was 1e-5, relaxed for clang 2.8 / linux / x86-64
00149   CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14));
00150   CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5));
00151   CALL_SUBTEST_6(testPascal<float>(1e-6));
00152   CALL_SUBTEST_5(testPascal<double>(1e-15));
00153   CALL_SUBTEST_2(randomTest(Matrix2d(), 1e-13));
00154   CALL_SUBTEST_7(randomTest(Matrix<double,3,3,RowMajor>(), 1e-13));
00155   CALL_SUBTEST_3(randomTest(Matrix4cd(), 1e-13));
00156   CALL_SUBTEST_4(randomTest(MatrixXd(8,8), 1e-13));
00157   CALL_SUBTEST_1(randomTest(Matrix2f(), 1e-4));
00158   CALL_SUBTEST_5(randomTest(Matrix3cf(), 1e-4));
00159   CALL_SUBTEST_1(randomTest(Matrix4f(), 1e-4));
00160   CALL_SUBTEST_6(randomTest(MatrixXf(8,8), 1e-4));
00161 }


libicr
Author(s): Robert Krug
autogenerated on Mon Jan 6 2014 11:33:04