[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) 2010 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 "main.h"
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| 11 | #include <unsupported/Eigen/MatrixFunctions>
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| 12 |
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| 13 | // Variant of VERIFY_IS_APPROX which uses absolute error instead of
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| 14 | // relative error.
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| 15 | #define VERIFY_IS_APPROX_ABS(a, b) VERIFY(test_isApprox_abs(a, b))
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| 16 |
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| 17 | template<typename Type1, typename Type2>
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| 18 | inline bool test_isApprox_abs(const Type1& a, const Type2& b)
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| 19 | {
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| 20 | return ((a-b).array().abs() < test_precision<typename Type1::RealScalar>()).all();
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| 21 | }
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| 22 |
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| 23 |
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| 24 | // Returns a matrix with eigenvalues clustered around 0, 1 and 2.
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| 25 | template<typename MatrixType>
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| 26 | MatrixType randomMatrixWithRealEivals(const typename MatrixType::Index size)
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| 27 | {
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| 28 | typedef typename MatrixType::Index Index;
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| 29 | typedef typename MatrixType::Scalar Scalar;
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| 30 | typedef typename MatrixType::RealScalar RealScalar;
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| 31 | MatrixType diag = MatrixType::Zero(size, size);
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| 32 | for (Index i = 0; i < size; ++i) {
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| 33 | diag(i, i) = Scalar(RealScalar(internal::random<int>(0,2)))
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| 34 | + internal::random<Scalar>() * Scalar(RealScalar(0.01));
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| 35 | }
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| 36 | MatrixType A = MatrixType::Random(size, size);
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| 37 | HouseholderQR<MatrixType> QRofA(A);
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| 38 | return QRofA.householderQ().inverse() * diag * QRofA.householderQ();
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| 39 | }
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| 40 |
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| 41 | template <typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>
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| 42 | struct randomMatrixWithImagEivals
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| 43 | {
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| 44 | // Returns a matrix with eigenvalues clustered around 0 and +/- i.
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| 45 | static MatrixType run(const typename MatrixType::Index size);
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| 46 | };
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| 47 |
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| 48 | // Partial specialization for real matrices
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| 49 | template<typename MatrixType>
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| 50 | struct randomMatrixWithImagEivals<MatrixType, 0>
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| 51 | {
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| 52 | static MatrixType run(const typename MatrixType::Index size)
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| 53 | {
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| 54 | typedef typename MatrixType::Index Index;
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| 55 | typedef typename MatrixType::Scalar Scalar;
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| 56 | MatrixType diag = MatrixType::Zero(size, size);
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| 57 | Index i = 0;
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| 58 | while (i < size) {
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| 59 | Index randomInt = internal::random<Index>(-1, 1);
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| 60 | if (randomInt == 0 || i == size-1) {
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| 61 | diag(i, i) = internal::random<Scalar>() * Scalar(0.01);
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| 62 | ++i;
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| 63 | } else {
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| 64 | Scalar alpha = Scalar(randomInt) + internal::random<Scalar>() * Scalar(0.01);
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| 65 | diag(i, i+1) = alpha;
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| 66 | diag(i+1, i) = -alpha;
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| 67 | i += 2;
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| 68 | }
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| 69 | }
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| 70 | MatrixType A = MatrixType::Random(size, size);
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| 71 | HouseholderQR<MatrixType> QRofA(A);
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| 72 | return QRofA.householderQ().inverse() * diag * QRofA.householderQ();
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| 73 | }
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| 74 | };
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| 75 |
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| 76 | // Partial specialization for complex matrices
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| 77 | template<typename MatrixType>
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| 78 | struct randomMatrixWithImagEivals<MatrixType, 1>
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| 79 | {
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| 80 | static MatrixType run(const typename MatrixType::Index size)
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| 81 | {
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| 82 | typedef typename MatrixType::Index Index;
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| 83 | typedef typename MatrixType::Scalar Scalar;
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| 84 | typedef typename MatrixType::RealScalar RealScalar;
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| 85 | const Scalar imagUnit(0, 1);
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| 86 | MatrixType diag = MatrixType::Zero(size, size);
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| 87 | for (Index i = 0; i < size; ++i) {
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| 88 | diag(i, i) = Scalar(RealScalar(internal::random<Index>(-1, 1))) * imagUnit
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| 89 | + internal::random<Scalar>() * Scalar(RealScalar(0.01));
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| 90 | }
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| 91 | MatrixType A = MatrixType::Random(size, size);
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| 92 | HouseholderQR<MatrixType> QRofA(A);
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| 93 | return QRofA.householderQ().inverse() * diag * QRofA.householderQ();
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| 94 | }
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| 95 | };
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| 96 |
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| 97 |
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| 98 | template<typename MatrixType>
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| 99 | void testMatrixExponential(const MatrixType& A)
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| 100 | {
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| 101 | typedef typename internal::traits<MatrixType>::Scalar Scalar;
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| 102 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 103 | typedef std::complex<RealScalar> ComplexScalar;
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| 104 |
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| 105 | VERIFY_IS_APPROX(A.exp(), A.matrixFunction(StdStemFunctions<ComplexScalar>::exp));
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| 106 | }
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| 107 |
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| 108 | template<typename MatrixType>
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| 109 | void testMatrixLogarithm(const MatrixType& A)
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| 110 | {
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| 111 | typedef typename internal::traits<MatrixType>::Scalar Scalar;
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| 112 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 113 |
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| 114 | MatrixType scaledA;
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| 115 | RealScalar maxImagPartOfSpectrum = A.eigenvalues().imag().cwiseAbs().maxCoeff();
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| 116 | if (maxImagPartOfSpectrum >= 0.9 * M_PI)
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| 117 | scaledA = A * 0.9 * M_PI / maxImagPartOfSpectrum;
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| 118 | else
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| 119 | scaledA = A;
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| 120 |
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| 121 | // identity X.exp().log() = X only holds if Im(lambda) < pi for all eigenvalues of X
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| 122 | MatrixType expA = scaledA.exp();
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| 123 | MatrixType logExpA = expA.log();
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| 124 | VERIFY_IS_APPROX(logExpA, scaledA);
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| 125 | }
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| 126 |
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| 127 | template<typename MatrixType>
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| 128 | void testHyperbolicFunctions(const MatrixType& A)
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| 129 | {
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| 130 | // Need to use absolute error because of possible cancellation when
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| 131 | // adding/subtracting expA and expmA.
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| 132 | VERIFY_IS_APPROX_ABS(A.sinh(), (A.exp() - (-A).exp()) / 2);
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| 133 | VERIFY_IS_APPROX_ABS(A.cosh(), (A.exp() + (-A).exp()) / 2);
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| 134 | }
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| 135 |
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| 136 | template<typename MatrixType>
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| 137 | void testGonioFunctions(const MatrixType& A)
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| 138 | {
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| 139 | typedef typename MatrixType::Scalar Scalar;
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| 140 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 141 | typedef std::complex<RealScalar> ComplexScalar;
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| 142 | typedef Matrix<ComplexScalar, MatrixType::RowsAtCompileTime,
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| 143 | MatrixType::ColsAtCompileTime, MatrixType::Options> ComplexMatrix;
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| 144 |
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| 145 | ComplexScalar imagUnit(0,1);
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| 146 | ComplexScalar two(2,0);
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| 147 |
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| 148 | ComplexMatrix Ac = A.template cast<ComplexScalar>();
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| 149 |
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| 150 | ComplexMatrix exp_iA = (imagUnit * Ac).exp();
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| 151 | ComplexMatrix exp_miA = (-imagUnit * Ac).exp();
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| 152 |
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| 153 | ComplexMatrix sinAc = A.sin().template cast<ComplexScalar>();
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| 154 | VERIFY_IS_APPROX_ABS(sinAc, (exp_iA - exp_miA) / (two*imagUnit));
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| 155 |
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| 156 | ComplexMatrix cosAc = A.cos().template cast<ComplexScalar>();
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| 157 | VERIFY_IS_APPROX_ABS(cosAc, (exp_iA + exp_miA) / 2);
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| 158 | }
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| 159 |
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| 160 | template<typename MatrixType>
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| 161 | void testMatrix(const MatrixType& A)
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| 162 | {
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| 163 | testMatrixExponential(A);
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| 164 | testMatrixLogarithm(A);
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| 165 | testHyperbolicFunctions(A);
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| 166 | testGonioFunctions(A);
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| 167 | }
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| 168 |
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| 169 | template<typename MatrixType>
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| 170 | void testMatrixType(const MatrixType& m)
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| 171 | {
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| 172 | // Matrices with clustered eigenvalue lead to different code paths
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| 173 | // in MatrixFunction.h and are thus useful for testing.
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| 174 | typedef typename MatrixType::Index Index;
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| 175 |
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| 176 | const Index size = m.rows();
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| 177 | for (int i = 0; i < g_repeat; i++) {
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| 178 | testMatrix(MatrixType::Random(size, size).eval());
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| 179 | testMatrix(randomMatrixWithRealEivals<MatrixType>(size));
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| 180 | testMatrix(randomMatrixWithImagEivals<MatrixType>::run(size));
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| 181 | }
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| 182 | }
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| 183 |
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| 184 | void test_matrix_function()
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| 185 | {
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| 186 | CALL_SUBTEST_1(testMatrixType(Matrix<float,1,1>()));
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| 187 | CALL_SUBTEST_2(testMatrixType(Matrix3cf()));
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| 188 | CALL_SUBTEST_3(testMatrixType(MatrixXf(8,8)));
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| 189 | CALL_SUBTEST_4(testMatrixType(Matrix2d()));
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| 190 | CALL_SUBTEST_5(testMatrixType(Matrix<double,5,5,RowMajor>()));
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| 191 | CALL_SUBTEST_6(testMatrixType(Matrix4cd()));
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| 192 | CALL_SUBTEST_7(testMatrixType(MatrixXd(13,13)));
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| 193 | }
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