Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 1 | // This file is part of Eigen, a lightweight C++ template library |
| 2 | // for linear algebra. |
| 3 | // |
| 4 | // Copyright (C) 2009 Jitse Niesen <jitse@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 | |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 10 | #include "matrix_functions.h" |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 11 | |
| 12 | double binom(int n, int k) |
| 13 | { |
| 14 | double res = 1; |
| 15 | for (int i=0; i<k; i++) |
| 16 | res = res * (n-k+i+1) / (i+1); |
| 17 | return res; |
| 18 | } |
| 19 | |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 20 | template <typename T> |
| 21 | T expfn(T x, int) |
| 22 | { |
| 23 | return std::exp(x); |
| 24 | } |
| 25 | |
| 26 | template <typename T> |
| 27 | void test2dRotation(double tol) |
| 28 | { |
| 29 | Matrix<T,2,2> A, B, C; |
| 30 | T angle; |
| 31 | |
| 32 | A << 0, 1, -1, 0; |
| 33 | for (int i=0; i<=20; i++) |
| 34 | { |
| 35 | angle = static_cast<T>(pow(10, i / 5. - 2)); |
| 36 | B << std::cos(angle), std::sin(angle), -std::sin(angle), std::cos(angle); |
| 37 | |
| 38 | C = (angle*A).matrixFunction(expfn); |
| 39 | std::cout << "test2dRotation: i = " << i << " error funm = " << relerr(C, B); |
| 40 | VERIFY(C.isApprox(B, static_cast<T>(tol))); |
| 41 | |
| 42 | C = (angle*A).exp(); |
| 43 | std::cout << " error expm = " << relerr(C, B) << "\n"; |
| 44 | VERIFY(C.isApprox(B, static_cast<T>(tol))); |
| 45 | } |
| 46 | } |
| 47 | |
| 48 | template <typename T> |
| 49 | void test2dHyperbolicRotation(double tol) |
| 50 | { |
| 51 | Matrix<std::complex<T>,2,2> A, B, C; |
| 52 | std::complex<T> imagUnit(0,1); |
| 53 | T angle, ch, sh; |
| 54 | |
| 55 | for (int i=0; i<=20; i++) |
| 56 | { |
| 57 | angle = static_cast<T>((i-10) / 2.0); |
| 58 | ch = std::cosh(angle); |
| 59 | sh = std::sinh(angle); |
| 60 | A << 0, angle*imagUnit, -angle*imagUnit, 0; |
| 61 | B << ch, sh*imagUnit, -sh*imagUnit, ch; |
| 62 | |
| 63 | C = A.matrixFunction(expfn); |
| 64 | std::cout << "test2dHyperbolicRotation: i = " << i << " error funm = " << relerr(C, B); |
| 65 | VERIFY(C.isApprox(B, static_cast<T>(tol))); |
| 66 | |
| 67 | C = A.exp(); |
| 68 | std::cout << " error expm = " << relerr(C, B) << "\n"; |
| 69 | VERIFY(C.isApprox(B, static_cast<T>(tol))); |
| 70 | } |
| 71 | } |
| 72 | |
| 73 | template <typename T> |
| 74 | void testPascal(double tol) |
| 75 | { |
| 76 | for (int size=1; size<20; size++) |
| 77 | { |
| 78 | Matrix<T,Dynamic,Dynamic> A(size,size), B(size,size), C(size,size); |
| 79 | A.setZero(); |
| 80 | for (int i=0; i<size-1; i++) |
| 81 | A(i+1,i) = static_cast<T>(i+1); |
| 82 | B.setZero(); |
| 83 | for (int i=0; i<size; i++) |
| 84 | for (int j=0; j<=i; j++) |
| 85 | B(i,j) = static_cast<T>(binom(i,j)); |
| 86 | |
| 87 | C = A.matrixFunction(expfn); |
| 88 | std::cout << "testPascal: size = " << size << " error funm = " << relerr(C, B); |
| 89 | VERIFY(C.isApprox(B, static_cast<T>(tol))); |
| 90 | |
| 91 | C = A.exp(); |
| 92 | std::cout << " error expm = " << relerr(C, B) << "\n"; |
| 93 | VERIFY(C.isApprox(B, static_cast<T>(tol))); |
| 94 | } |
| 95 | } |
| 96 | |
| 97 | template<typename MatrixType> |
| 98 | void randomTest(const MatrixType& m, double tol) |
| 99 | { |
| 100 | /* this test covers the following files: |
| 101 | Inverse.h |
| 102 | */ |
| 103 | typename MatrixType::Index rows = m.rows(); |
| 104 | typename MatrixType::Index cols = m.cols(); |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 105 | MatrixType m1(rows, cols), m2(rows, cols), identity = MatrixType::Identity(rows, cols); |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 106 | |
| 107 | typedef typename NumTraits<typename internal::traits<MatrixType>::Scalar>::Real RealScalar; |
| 108 | |
| 109 | for(int i = 0; i < g_repeat; i++) { |
| 110 | m1 = MatrixType::Random(rows, cols); |
| 111 | |
| 112 | m2 = m1.matrixFunction(expfn) * (-m1).matrixFunction(expfn); |
| 113 | std::cout << "randomTest: error funm = " << relerr(identity, m2); |
| 114 | VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol))); |
| 115 | |
| 116 | m2 = m1.exp() * (-m1).exp(); |
| 117 | std::cout << " error expm = " << relerr(identity, m2) << "\n"; |
| 118 | VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol))); |
| 119 | } |
| 120 | } |
| 121 | |
| 122 | void test_matrix_exponential() |
| 123 | { |
| 124 | CALL_SUBTEST_2(test2dRotation<double>(1e-13)); |
| 125 | CALL_SUBTEST_1(test2dRotation<float>(2e-5)); // was 1e-5, relaxed for clang 2.8 / linux / x86-64 |
| 126 | CALL_SUBTEST_8(test2dRotation<long double>(1e-13)); |
| 127 | CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14)); |
| 128 | CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5)); |
| 129 | CALL_SUBTEST_8(test2dHyperbolicRotation<long double>(1e-14)); |
| 130 | CALL_SUBTEST_6(testPascal<float>(1e-6)); |
| 131 | CALL_SUBTEST_5(testPascal<double>(1e-15)); |
| 132 | CALL_SUBTEST_2(randomTest(Matrix2d(), 1e-13)); |
| 133 | CALL_SUBTEST_7(randomTest(Matrix<double,3,3,RowMajor>(), 1e-13)); |
| 134 | CALL_SUBTEST_3(randomTest(Matrix4cd(), 1e-13)); |
| 135 | CALL_SUBTEST_4(randomTest(MatrixXd(8,8), 1e-13)); |
| 136 | CALL_SUBTEST_1(randomTest(Matrix2f(), 1e-4)); |
| 137 | CALL_SUBTEST_5(randomTest(Matrix3cf(), 1e-4)); |
| 138 | CALL_SUBTEST_1(randomTest(Matrix4f(), 1e-4)); |
| 139 | CALL_SUBTEST_6(randomTest(MatrixXf(8,8), 1e-4)); |
| 140 | CALL_SUBTEST_9(randomTest(Matrix<long double,Dynamic,Dynamic>(7,7), 1e-13)); |
| 141 | } |