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128 lines
3.9 KiB
C++
128 lines
3.9 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2009 Jitse Niesen <jitse@maths.leeds.ac.uk>
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//
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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 3 of the License, or (at your option) any later version.
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//
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// Alternatively, you can redistribute it and/or
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// modify it under the terms of the GNU General Public License as
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// published by the Free Software Foundation; either version 2 of
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// the License, or (at your option) any later version.
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//
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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#include "main.h"
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#include <Eigen/StdVector>
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#include <unsupported/Eigen/MatrixFunctions>
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double binom(int n, int k)
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{
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double res = 1;
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for (int i=0; i<k; i++)
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res = res * (n-k+i+1) / (i+1);
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return res;
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}
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template <typename T>
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void test2dRotation(double tol)
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{
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Matrix<T,2,2> A, B, C;
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T angle;
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A << 0, 1, -1, 0;
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for (int i=0; i<=20; i++)
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{
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angle = static_cast<T>(pow(10, i / 5. - 2));
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B << cos(angle), sin(angle), -sin(angle), cos(angle);
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ei_matrix_exponential(angle*A, &C);
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VERIFY(C.isApprox(B, static_cast<T>(tol)));
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}
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}
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template <typename T>
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void test2dHyperbolicRotation(double tol)
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{
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Matrix<std::complex<T>,2,2> A, B, C;
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std::complex<T> imagUnit(0,1);
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T angle, ch, sh;
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for (int i=0; i<=20; i++)
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{
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angle = static_cast<T>((i-10) / 2.0);
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ch = std::cosh(angle);
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sh = std::sinh(angle);
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A << 0, angle*imagUnit, -angle*imagUnit, 0;
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B << ch, sh*imagUnit, -sh*imagUnit, ch;
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ei_matrix_exponential(A, &C);
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VERIFY(C.isApprox(B, static_cast<T>(tol)));
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}
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}
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template <typename T>
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void testPascal(double tol)
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{
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for (int size=1; size<20; size++)
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{
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Matrix<T,Dynamic,Dynamic> A(size,size), B(size,size), C(size,size);
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A.setZero();
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for (int i=0; i<size-1; i++)
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A(i+1,i) = static_cast<T>(i+1);
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B.setZero();
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for (int i=0; i<size; i++)
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for (int j=0; j<=i; j++)
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B(i,j) = static_cast<T>(binom(i,j));
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ei_matrix_exponential(A, &C);
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VERIFY(C.isApprox(B, static_cast<T>(tol)));
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}
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}
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template<typename MatrixType>
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void randomTest(const MatrixType& m, double tol)
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{
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/* this test covers the following files:
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Inverse.h
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*/
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int rows = m.rows();
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int cols = m.cols();
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MatrixType m1(rows, cols), m2(rows, cols), m3(rows, cols),
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identity = MatrixType::Identity(rows, rows);
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typedef typename NumTraits<typename ei_traits<MatrixType>::Scalar>::Real RealScalar;
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for(int i = 0; i < g_repeat; i++) {
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m1 = MatrixType::Random(rows, cols);
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ei_matrix_exponential(m1, &m2);
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ei_matrix_exponential(-m1, &m3);
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VERIFY(identity.isApprox(m2 * m3, static_cast<RealScalar>(tol)));
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}
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}
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void test_matrixExponential()
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{
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CALL_SUBTEST(test2dRotation<double>(1e-14));
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CALL_SUBTEST(test2dRotation<float>(1e-5));
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CALL_SUBTEST(test2dHyperbolicRotation<double>(1e-14));
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CALL_SUBTEST(test2dHyperbolicRotation<float>(1e-5));
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CALL_SUBTEST(testPascal<float>(1e-5));
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CALL_SUBTEST(testPascal<double>(1e-14));
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CALL_SUBTEST(randomTest(Matrix2d(), 1e-13));
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CALL_SUBTEST(randomTest(Matrix<double,3,3,RowMajor>(), 1e-13));
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CALL_SUBTEST(randomTest(Matrix4cd(), 1e-13));
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CALL_SUBTEST(randomTest(MatrixXd(8,8), 1e-13));
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CALL_SUBTEST(randomTest(Matrix2f(), 1e-4));
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CALL_SUBTEST(randomTest(Matrix3cf(), 1e-4));
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CALL_SUBTEST(randomTest(Matrix4f(), 1e-4));
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CALL_SUBTEST(randomTest(MatrixXf(8,8), 1e-4));
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}
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