[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2009 Jitse Niesen <jitse@maths.leeds.ac.uk>
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| 5 | //
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| 6 | // This Source Code Form is subject to the terms of the Mozilla
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| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 9 |
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| 10 | #include "matrix_functions.h"
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| 11 |
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| 12 | double binom(int n, int k)
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| 13 | {
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| 14 | double res = 1;
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| 15 | for (int i=0; i<k; i++)
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| 16 | res = res * (n-k+i+1) / (i+1);
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| 17 | return res;
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| 18 | }
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| 19 |
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| 20 | template <typename T>
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| 21 | T expfn(T x, int)
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| 22 | {
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| 23 | return std::exp(x);
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| 24 | }
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| 25 |
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| 26 | template <typename T>
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| 27 | void test2dRotation(double tol)
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| 28 | {
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| 29 | Matrix<T,2,2> A, B, C;
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| 30 | T angle;
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| 31 |
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| 32 | A << 0, 1, -1, 0;
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| 33 | for (int i=0; i<=20; i++)
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| 34 | {
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| 35 | angle = static_cast<T>(pow(10, i / 5. - 2));
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| 36 | B << std::cos(angle), std::sin(angle), -std::sin(angle), std::cos(angle);
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| 37 |
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| 38 | C = (angle*A).matrixFunction(expfn);
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| 39 | std::cout << "test2dRotation: i = " << i << " error funm = " << relerr(C, B);
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| 40 | VERIFY(C.isApprox(B, static_cast<T>(tol)));
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| 41 |
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| 42 | C = (angle*A).exp();
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| 43 | std::cout << " error expm = " << relerr(C, B) << "\n";
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| 44 | VERIFY(C.isApprox(B, static_cast<T>(tol)));
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| 45 | }
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| 46 | }
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| 47 |
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| 48 | template <typename T>
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| 49 | void test2dHyperbolicRotation(double tol)
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| 50 | {
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| 51 | Matrix<std::complex<T>,2,2> A, B, C;
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| 52 | std::complex<T> imagUnit(0,1);
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| 53 | T angle, ch, sh;
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| 54 |
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| 55 | for (int i=0; i<=20; i++)
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| 56 | {
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| 57 | angle = static_cast<T>((i-10) / 2.0);
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| 58 | ch = std::cosh(angle);
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| 59 | sh = std::sinh(angle);
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| 60 | A << 0, angle*imagUnit, -angle*imagUnit, 0;
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| 61 | B << ch, sh*imagUnit, -sh*imagUnit, ch;
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| 62 |
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| 63 | C = A.matrixFunction(expfn);
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| 64 | std::cout << "test2dHyperbolicRotation: i = " << i << " error funm = " << relerr(C, B);
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| 65 | VERIFY(C.isApprox(B, static_cast<T>(tol)));
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| 66 |
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| 67 | C = A.exp();
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| 68 | std::cout << " error expm = " << relerr(C, B) << "\n";
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| 69 | VERIFY(C.isApprox(B, static_cast<T>(tol)));
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| 70 | }
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| 71 | }
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| 72 |
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| 73 | template <typename T>
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| 74 | void testPascal(double tol)
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| 75 | {
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| 76 | for (int size=1; size<20; size++)
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| 77 | {
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| 78 | Matrix<T,Dynamic,Dynamic> A(size,size), B(size,size), C(size,size);
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| 79 | A.setZero();
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| 80 | for (int i=0; i<size-1; i++)
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| 81 | A(i+1,i) = static_cast<T>(i+1);
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| 82 | B.setZero();
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| 83 | for (int i=0; i<size; i++)
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| 84 | for (int j=0; j<=i; j++)
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| 85 | B(i,j) = static_cast<T>(binom(i,j));
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| 86 |
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| 87 | C = A.matrixFunction(expfn);
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| 88 | std::cout << "testPascal: size = " << size << " error funm = " << relerr(C, B);
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| 89 | VERIFY(C.isApprox(B, static_cast<T>(tol)));
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| 90 |
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| 91 | C = A.exp();
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| 92 | std::cout << " error expm = " << relerr(C, B) << "\n";
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| 93 | VERIFY(C.isApprox(B, static_cast<T>(tol)));
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| 94 | }
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| 95 | }
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| 96 |
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| 97 | template<typename MatrixType>
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| 98 | void randomTest(const MatrixType& m, double tol)
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| 99 | {
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| 100 | /* this test covers the following files:
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| 101 | Inverse.h
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| 102 | */
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| 103 | typename MatrixType::Index rows = m.rows();
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| 104 | typename MatrixType::Index cols = m.cols();
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| 105 | MatrixType m1(rows, cols), m2(rows, cols), identity = MatrixType::Identity(rows, cols);
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| 106 |
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| 107 | typedef typename NumTraits<typename internal::traits<MatrixType>::Scalar>::Real RealScalar;
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| 108 |
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| 109 | for(int i = 0; i < g_repeat; i++) {
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| 110 | m1 = MatrixType::Random(rows, cols);
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| 111 |
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| 112 | m2 = m1.matrixFunction(expfn) * (-m1).matrixFunction(expfn);
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| 113 | std::cout << "randomTest: error funm = " << relerr(identity, m2);
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| 114 | VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));
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| 115 |
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| 116 | m2 = m1.exp() * (-m1).exp();
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| 117 | std::cout << " error expm = " << relerr(identity, m2) << "\n";
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| 118 | VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));
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| 119 | }
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| 120 | }
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| 121 |
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| 122 | void test_matrix_exponential()
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| 123 | {
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| 124 | CALL_SUBTEST_2(test2dRotation<double>(1e-13));
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| 125 | CALL_SUBTEST_1(test2dRotation<float>(2e-5)); // was 1e-5, relaxed for clang 2.8 / linux / x86-64
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| 126 | CALL_SUBTEST_8(test2dRotation<long double>(1e-13));
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| 127 | CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14));
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| 128 | CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5));
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| 129 | CALL_SUBTEST_8(test2dHyperbolicRotation<long double>(1e-14));
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| 130 | CALL_SUBTEST_6(testPascal<float>(1e-6));
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| 131 | CALL_SUBTEST_5(testPascal<double>(1e-15));
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| 132 | CALL_SUBTEST_2(randomTest(Matrix2d(), 1e-13));
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| 133 | CALL_SUBTEST_7(randomTest(Matrix<double,3,3,RowMajor>(), 1e-13));
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| 134 | CALL_SUBTEST_3(randomTest(Matrix4cd(), 1e-13));
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| 135 | CALL_SUBTEST_4(randomTest(MatrixXd(8,8), 1e-13));
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| 136 | CALL_SUBTEST_1(randomTest(Matrix2f(), 1e-4));
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| 137 | CALL_SUBTEST_5(randomTest(Matrix3cf(), 1e-4));
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| 138 | CALL_SUBTEST_1(randomTest(Matrix4f(), 1e-4));
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| 139 | CALL_SUBTEST_6(randomTest(MatrixXf(8,8), 1e-4));
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| 140 | CALL_SUBTEST_9(randomTest(Matrix<long double,Dynamic,Dynamic>(7,7), 1e-13));
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| 141 | }
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