1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2009 Jitse Niesen <jitse (at) 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 13 double 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 21 template <typename Derived, typename OtherDerived> 22 double 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 27 template <typename T> 28 T expfn(T x, int) 29 { 30 return std::exp(x); 31 } 32 33 template <typename T> 34 void 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 55 template <typename T> 56 void 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 80 template <typename T> 81 void 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 } 103 104 template<typename MatrixType> 105 void 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 } 129 130 void 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
