Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 1 | // This file is part of Eigen, a lightweight C++ template library |
| 2 | // for linear algebra. |
| 3 | // |
| 4 | // Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net> |
| 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 "matrix_functions.h" |
| 11 | |
| 12 | template <typename MatrixType, int IsComplex = NumTraits<typename MatrixType::Scalar>::IsComplex> |
| 13 | struct generateTriangularMatrix; |
| 14 | |
| 15 | // for real matrices, make sure none of the eigenvalues are negative |
| 16 | template <typename MatrixType> |
| 17 | struct generateTriangularMatrix<MatrixType,0> |
| 18 | { |
| 19 | static void run(MatrixType& result, typename MatrixType::Index size) |
| 20 | { |
| 21 | result.resize(size, size); |
| 22 | result.template triangularView<Upper>() = MatrixType::Random(size, size); |
| 23 | for (typename MatrixType::Index i = 0; i < size; ++i) |
| 24 | result.coeffRef(i,i) = std::abs(result.coeff(i,i)); |
| 25 | } |
| 26 | }; |
| 27 | |
| 28 | // for complex matrices, any matrix is fine |
| 29 | template <typename MatrixType> |
| 30 | struct generateTriangularMatrix<MatrixType,1> |
| 31 | { |
| 32 | static void run(MatrixType& result, typename MatrixType::Index size) |
| 33 | { |
| 34 | result.resize(size, size); |
| 35 | result.template triangularView<Upper>() = MatrixType::Random(size, size); |
| 36 | } |
| 37 | }; |
| 38 | |
| 39 | template<typename T> |
| 40 | void test2dRotation(double tol) |
| 41 | { |
| 42 | Matrix<T,2,2> A, B, C; |
| 43 | T angle, c, s; |
| 44 | |
| 45 | A << 0, 1, -1, 0; |
| 46 | MatrixPower<Matrix<T,2,2> > Apow(A); |
| 47 | |
| 48 | for (int i=0; i<=20; ++i) { |
| 49 | angle = pow(10, (i-10) / 5.); |
| 50 | c = std::cos(angle); |
| 51 | s = std::sin(angle); |
| 52 | B << c, s, -s, c; |
| 53 | |
| 54 | C = Apow(std::ldexp(angle,1) / M_PI); |
| 55 | std::cout << "test2dRotation: i = " << i << " error powerm = " << relerr(C,B) << '\n'; |
| 56 | VERIFY(C.isApprox(B, static_cast<T>(tol))); |
| 57 | } |
| 58 | } |
| 59 | |
| 60 | template<typename T> |
| 61 | void test2dHyperbolicRotation(double tol) |
| 62 | { |
| 63 | Matrix<std::complex<T>,2,2> A, B, C; |
| 64 | T angle, ch = std::cosh((T)1); |
| 65 | std::complex<T> ish(0, std::sinh((T)1)); |
| 66 | |
| 67 | A << ch, ish, -ish, ch; |
| 68 | MatrixPower<Matrix<std::complex<T>,2,2> > Apow(A); |
| 69 | |
| 70 | for (int i=0; i<=20; ++i) { |
| 71 | angle = std::ldexp(static_cast<T>(i-10), -1); |
| 72 | ch = std::cosh(angle); |
| 73 | ish = std::complex<T>(0, std::sinh(angle)); |
| 74 | B << ch, ish, -ish, ch; |
| 75 | |
| 76 | C = Apow(angle); |
| 77 | std::cout << "test2dHyperbolicRotation: i = " << i << " error powerm = " << relerr(C,B) << '\n'; |
| 78 | VERIFY(C.isApprox(B, static_cast<T>(tol))); |
| 79 | } |
| 80 | } |
| 81 | |
| 82 | template<typename MatrixType> |
| 83 | void testExponentLaws(const MatrixType& m, double tol) |
| 84 | { |
| 85 | typedef typename MatrixType::RealScalar RealScalar; |
| 86 | MatrixType m1, m2, m3, m4, m5; |
| 87 | RealScalar x, y; |
| 88 | |
| 89 | for (int i=0; i < g_repeat; ++i) { |
| 90 | generateTestMatrix<MatrixType>::run(m1, m.rows()); |
| 91 | MatrixPower<MatrixType> mpow(m1); |
| 92 | |
| 93 | x = internal::random<RealScalar>(); |
| 94 | y = internal::random<RealScalar>(); |
| 95 | m2 = mpow(x); |
| 96 | m3 = mpow(y); |
| 97 | |
| 98 | m4 = mpow(x+y); |
| 99 | m5.noalias() = m2 * m3; |
| 100 | VERIFY(m4.isApprox(m5, static_cast<RealScalar>(tol))); |
| 101 | |
| 102 | m4 = mpow(x*y); |
| 103 | m5 = m2.pow(y); |
| 104 | VERIFY(m4.isApprox(m5, static_cast<RealScalar>(tol))); |
| 105 | |
| 106 | m4 = (std::abs(x) * m1).pow(y); |
| 107 | m5 = std::pow(std::abs(x), y) * m3; |
| 108 | VERIFY(m4.isApprox(m5, static_cast<RealScalar>(tol))); |
| 109 | } |
| 110 | } |
| 111 | |
| 112 | typedef Matrix<double,3,3,RowMajor> Matrix3dRowMajor; |
| 113 | typedef Matrix<long double,Dynamic,Dynamic> MatrixXe; |
| 114 | |
| 115 | void test_matrix_power() |
| 116 | { |
| 117 | CALL_SUBTEST_2(test2dRotation<double>(1e-13)); |
| 118 | CALL_SUBTEST_1(test2dRotation<float>(2e-5)); // was 1e-5, relaxed for clang 2.8 / linux / x86-64 |
| 119 | CALL_SUBTEST_9(test2dRotation<long double>(1e-13)); |
| 120 | CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14)); |
| 121 | CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5)); |
| 122 | CALL_SUBTEST_9(test2dHyperbolicRotation<long double>(1e-14)); |
| 123 | |
| 124 | CALL_SUBTEST_2(testExponentLaws(Matrix2d(), 1e-13)); |
| 125 | CALL_SUBTEST_7(testExponentLaws(Matrix3dRowMajor(), 1e-13)); |
| 126 | CALL_SUBTEST_3(testExponentLaws(Matrix4cd(), 1e-13)); |
| 127 | CALL_SUBTEST_4(testExponentLaws(MatrixXd(8,8), 2e-12)); |
| 128 | CALL_SUBTEST_1(testExponentLaws(Matrix2f(), 1e-4)); |
| 129 | CALL_SUBTEST_5(testExponentLaws(Matrix3cf(), 1e-4)); |
| 130 | CALL_SUBTEST_8(testExponentLaws(Matrix4f(), 1e-4)); |
| 131 | CALL_SUBTEST_6(testExponentLaws(MatrixXf(2,2), 1e-3)); // see bug 614 |
| 132 | CALL_SUBTEST_9(testExponentLaws(MatrixXe(7,7), 1e-13)); |
| 133 | } |