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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