142 lines
4.3 KiB
C++
142 lines
4.3 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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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include "matrix_functions.h"
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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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T expfn(T x, int)
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{
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return std::exp(x);
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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 << std::cos(angle), std::sin(angle), -std::sin(angle), std::cos(angle);
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C = (angle*A).matrixFunction(expfn);
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std::cout << "test2dRotation: i = " << i << " error funm = " << relerr(C, B);
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VERIFY(C.isApprox(B, static_cast<T>(tol)));
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C = (angle*A).exp();
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std::cout << " error expm = " << relerr(C, B) << "\n";
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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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C = A.matrixFunction(expfn);
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std::cout << "test2dHyperbolicRotation: i = " << i << " error funm = " << relerr(C, B);
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VERIFY(C.isApprox(B, static_cast<T>(tol)));
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C = A.exp();
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std::cout << " error expm = " << relerr(C, B) << "\n";
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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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C = A.matrixFunction(expfn);
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std::cout << "testPascal: size = " << size << " error funm = " << relerr(C, B);
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VERIFY(C.isApprox(B, static_cast<T>(tol)));
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C = A.exp();
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std::cout << " error expm = " << relerr(C, B) << "\n";
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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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typename MatrixType::Index rows = m.rows();
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typename MatrixType::Index cols = m.cols();
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MatrixType m1(rows, cols), m2(rows, cols), identity = MatrixType::Identity(rows, cols);
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typedef typename NumTraits<typename internal::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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m2 = m1.matrixFunction(expfn) * (-m1).matrixFunction(expfn);
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std::cout << "randomTest: error funm = " << relerr(identity, m2);
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VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));
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m2 = m1.exp() * (-m1).exp();
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std::cout << " error expm = " << relerr(identity, m2) << "\n";
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VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));
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}
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}
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void test_matrix_exponential()
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{
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CALL_SUBTEST_2(test2dRotation<double>(1e-13));
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CALL_SUBTEST_1(test2dRotation<float>(2e-5)); // was 1e-5, relaxed for clang 2.8 / linux / x86-64
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CALL_SUBTEST_8(test2dRotation<long double>(1e-13));
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CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14));
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CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5));
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CALL_SUBTEST_8(test2dHyperbolicRotation<long double>(1e-14));
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CALL_SUBTEST_6(testPascal<float>(1e-6));
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CALL_SUBTEST_5(testPascal<double>(1e-15));
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CALL_SUBTEST_2(randomTest(Matrix2d(), 1e-13));
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CALL_SUBTEST_7(randomTest(Matrix<double,3,3,RowMajor>(), 1e-13));
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CALL_SUBTEST_3(randomTest(Matrix4cd(), 1e-13));
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CALL_SUBTEST_4(randomTest(MatrixXd(8,8), 1e-13));
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CALL_SUBTEST_1(randomTest(Matrix2f(), 1e-4));
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CALL_SUBTEST_5(randomTest(Matrix3cf(), 1e-4));
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CALL_SUBTEST_1(randomTest(Matrix4f(), 1e-4));
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CALL_SUBTEST_6(randomTest(MatrixXf(8,8), 1e-4));
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CALL_SUBTEST_9(randomTest(Matrix<long double,Dynamic,Dynamic>(7,7), 1e-13));
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}
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