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) 2011 Jitse Niesen <jitse@maths.leeds.ac.uk>
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5 | // Copyright (C) 2011 Chen-Pang He <jdh8@ms63.hinet.net>
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6 | //
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7 | // This Source Code Form is subject to the terms of the Mozilla
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8 | // Public License v. 2.0. If a copy of the MPL was not distributed
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9 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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10 |
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11 | #ifndef EIGEN_MATRIX_LOGARITHM
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12 | #define EIGEN_MATRIX_LOGARITHM
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13 |
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14 | #ifndef M_PI
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15 | #define M_PI 3.141592653589793238462643383279503L
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16 | #endif
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17 |
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18 | namespace Eigen {
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19 |
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20 | /** \ingroup MatrixFunctions_Module
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21 | * \class MatrixLogarithmAtomic
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22 | * \brief Helper class for computing matrix logarithm of atomic matrices.
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23 | *
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24 | * \internal
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25 | * Here, an atomic matrix is a triangular matrix whose diagonal
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26 | * entries are close to each other.
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27 | *
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28 | * \sa class MatrixFunctionAtomic, MatrixBase::log()
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29 | */
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30 | template <typename MatrixType>
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31 | class MatrixLogarithmAtomic
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32 | {
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33 | public:
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34 |
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35 | typedef typename MatrixType::Scalar Scalar;
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36 | // typedef typename MatrixType::Index Index;
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37 | typedef typename NumTraits<Scalar>::Real RealScalar;
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38 | // typedef typename internal::stem_function<Scalar>::type StemFunction;
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39 | // typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
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40 |
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41 | /** \brief Constructor. */
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42 | MatrixLogarithmAtomic() { }
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43 |
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44 | /** \brief Compute matrix logarithm of atomic matrix
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45 | * \param[in] A argument of matrix logarithm, should be upper triangular and atomic
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46 | * \returns The logarithm of \p A.
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47 | */
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48 | MatrixType compute(const MatrixType& A);
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49 |
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50 | private:
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51 |
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52 | void compute2x2(const MatrixType& A, MatrixType& result);
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53 | void computeBig(const MatrixType& A, MatrixType& result);
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54 | int getPadeDegree(float normTminusI);
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55 | int getPadeDegree(double normTminusI);
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56 | int getPadeDegree(long double normTminusI);
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57 | void computePade(MatrixType& result, const MatrixType& T, int degree);
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58 | void computePade3(MatrixType& result, const MatrixType& T);
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59 | void computePade4(MatrixType& result, const MatrixType& T);
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60 | void computePade5(MatrixType& result, const MatrixType& T);
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61 | void computePade6(MatrixType& result, const MatrixType& T);
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62 | void computePade7(MatrixType& result, const MatrixType& T);
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63 | void computePade8(MatrixType& result, const MatrixType& T);
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64 | void computePade9(MatrixType& result, const MatrixType& T);
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65 | void computePade10(MatrixType& result, const MatrixType& T);
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66 | void computePade11(MatrixType& result, const MatrixType& T);
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67 |
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68 | static const int minPadeDegree = 3;
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69 | static const int maxPadeDegree = std::numeric_limits<RealScalar>::digits<= 24? 5: // single precision
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70 | std::numeric_limits<RealScalar>::digits<= 53? 7: // double precision
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71 | std::numeric_limits<RealScalar>::digits<= 64? 8: // extended precision
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72 | std::numeric_limits<RealScalar>::digits<=106? 10: // double-double
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73 | 11; // quadruple precision
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74 |
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75 | // Prevent copying
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76 | MatrixLogarithmAtomic(const MatrixLogarithmAtomic&);
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77 | MatrixLogarithmAtomic& operator=(const MatrixLogarithmAtomic&);
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78 | };
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79 |
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80 | /** \brief Compute logarithm of triangular matrix with clustered eigenvalues. */
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81 | template <typename MatrixType>
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82 | MatrixType MatrixLogarithmAtomic<MatrixType>::compute(const MatrixType& A)
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83 | {
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84 | using std::log;
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85 | MatrixType result(A.rows(), A.rows());
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86 | if (A.rows() == 1)
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87 | result(0,0) = log(A(0,0));
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88 | else if (A.rows() == 2)
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89 | compute2x2(A, result);
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90 | else
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91 | computeBig(A, result);
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92 | return result;
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93 | }
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94 |
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95 | /** \brief Compute logarithm of 2x2 triangular matrix. */
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96 | template <typename MatrixType>
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97 | void MatrixLogarithmAtomic<MatrixType>::compute2x2(const MatrixType& A, MatrixType& result)
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98 | {
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99 | using std::abs;
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100 | using std::ceil;
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101 | using std::imag;
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102 | using std::log;
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103 |
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104 | Scalar logA00 = log(A(0,0));
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105 | Scalar logA11 = log(A(1,1));
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106 |
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107 | result(0,0) = logA00;
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108 | result(1,0) = Scalar(0);
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109 | result(1,1) = logA11;
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110 |
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111 | if (A(0,0) == A(1,1)) {
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112 | result(0,1) = A(0,1) / A(0,0);
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113 | } else if ((abs(A(0,0)) < 0.5*abs(A(1,1))) || (abs(A(0,0)) > 2*abs(A(1,1)))) {
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114 | result(0,1) = A(0,1) * (logA11 - logA00) / (A(1,1) - A(0,0));
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115 | } else {
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116 | // computation in previous branch is inaccurate if A(1,1) \approx A(0,0)
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117 | int unwindingNumber = static_cast<int>(ceil((imag(logA11 - logA00) - M_PI) / (2*M_PI)));
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118 | Scalar y = A(1,1) - A(0,0), x = A(1,1) + A(0,0);
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119 | result(0,1) = A(0,1) * (Scalar(2) * numext::atanh2(y,x) + Scalar(0,2*M_PI*unwindingNumber)) / y;
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120 | }
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121 | }
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122 |
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123 | /** \brief Compute logarithm of triangular matrices with size > 2.
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124 | * \details This uses a inverse scale-and-square algorithm. */
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125 | template <typename MatrixType>
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126 | void MatrixLogarithmAtomic<MatrixType>::computeBig(const MatrixType& A, MatrixType& result)
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127 | {
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128 | using std::pow;
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129 | int numberOfSquareRoots = 0;
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130 | int numberOfExtraSquareRoots = 0;
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131 | int degree;
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132 | MatrixType T = A, sqrtT;
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133 | const RealScalar maxNormForPade = maxPadeDegree<= 5? 5.3149729967117310e-1: // single precision
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134 | maxPadeDegree<= 7? 2.6429608311114350e-1: // double precision
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135 | maxPadeDegree<= 8? 2.32777776523703892094e-1L: // extended precision
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136 | maxPadeDegree<=10? 1.05026503471351080481093652651105e-1L: // double-double
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137 | 1.1880960220216759245467951592883642e-1L; // quadruple precision
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138 |
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139 | while (true) {
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140 | RealScalar normTminusI = (T - MatrixType::Identity(T.rows(), T.rows())).cwiseAbs().colwise().sum().maxCoeff();
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141 | if (normTminusI < maxNormForPade) {
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142 | degree = getPadeDegree(normTminusI);
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143 | int degree2 = getPadeDegree(normTminusI / RealScalar(2));
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144 | if ((degree - degree2 <= 1) || (numberOfExtraSquareRoots == 1))
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145 | break;
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146 | ++numberOfExtraSquareRoots;
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147 | }
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148 | MatrixSquareRootTriangular<MatrixType>(T).compute(sqrtT);
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149 | T = sqrtT.template triangularView<Upper>();
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150 | ++numberOfSquareRoots;
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151 | }
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152 |
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153 | computePade(result, T, degree);
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154 | result *= pow(RealScalar(2), numberOfSquareRoots);
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155 | }
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156 |
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157 | /* \brief Get suitable degree for Pade approximation. (specialized for RealScalar = float) */
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158 | template <typename MatrixType>
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159 | int MatrixLogarithmAtomic<MatrixType>::getPadeDegree(float normTminusI)
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160 | {
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161 | const float maxNormForPade[] = { 2.5111573934555054e-1 /* degree = 3 */ , 4.0535837411880493e-1,
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162 | 5.3149729967117310e-1 };
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163 | int degree = 3;
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164 | for (; degree <= maxPadeDegree; ++degree)
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165 | if (normTminusI <= maxNormForPade[degree - minPadeDegree])
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166 | break;
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167 | return degree;
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168 | }
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169 |
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170 | /* \brief Get suitable degree for Pade approximation. (specialized for RealScalar = double) */
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171 | template <typename MatrixType>
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172 | int MatrixLogarithmAtomic<MatrixType>::getPadeDegree(double normTminusI)
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173 | {
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174 | const double maxNormForPade[] = { 1.6206284795015624e-2 /* degree = 3 */ , 5.3873532631381171e-2,
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175 | 1.1352802267628681e-1, 1.8662860613541288e-1, 2.642960831111435e-1 };
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176 | int degree = 3;
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177 | for (; degree <= maxPadeDegree; ++degree)
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178 | if (normTminusI <= maxNormForPade[degree - minPadeDegree])
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179 | break;
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180 | return degree;
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181 | }
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182 |
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183 | /* \brief Get suitable degree for Pade approximation. (specialized for RealScalar = long double) */
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184 | template <typename MatrixType>
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185 | int MatrixLogarithmAtomic<MatrixType>::getPadeDegree(long double normTminusI)
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186 | {
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187 | #if LDBL_MANT_DIG == 53 // double precision
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188 | const long double maxNormForPade[] = { 1.6206284795015624e-2L /* degree = 3 */ , 5.3873532631381171e-2L,
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189 | 1.1352802267628681e-1L, 1.8662860613541288e-1L, 2.642960831111435e-1L };
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190 | #elif LDBL_MANT_DIG <= 64 // extended precision
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191 | const long double maxNormForPade[] = { 5.48256690357782863103e-3L /* degree = 3 */, 2.34559162387971167321e-2L,
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192 | 5.84603923897347449857e-2L, 1.08486423756725170223e-1L, 1.68385767881294446649e-1L,
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193 | 2.32777776523703892094e-1L };
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194 | #elif LDBL_MANT_DIG <= 106 // double-double
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195 | const long double maxNormForPade[] = { 8.58970550342939562202529664318890e-5L /* degree = 3 */,
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196 | 9.34074328446359654039446552677759e-4L, 4.26117194647672175773064114582860e-3L,
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197 | 1.21546224740281848743149666560464e-2L, 2.61100544998339436713088248557444e-2L,
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198 | 4.66170074627052749243018566390567e-2L, 7.32585144444135027565872014932387e-2L,
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199 | 1.05026503471351080481093652651105e-1L };
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200 | #else // quadruple precision
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201 | const long double maxNormForPade[] = { 4.7419931187193005048501568167858103e-5L /* degree = 3 */,
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202 | 5.8853168473544560470387769480192666e-4L, 2.9216120366601315391789493628113520e-3L,
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203 | 8.8415758124319434347116734705174308e-3L, 1.9850836029449446668518049562565291e-2L,
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204 | 3.6688019729653446926585242192447447e-2L, 5.9290962294020186998954055264528393e-2L,
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205 | 8.6998436081634343903250580992127677e-2L, 1.1880960220216759245467951592883642e-1L };
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206 | #endif
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207 | int degree = 3;
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208 | for (; degree <= maxPadeDegree; ++degree)
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209 | if (normTminusI <= maxNormForPade[degree - minPadeDegree])
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210 | break;
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211 | return degree;
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212 | }
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213 |
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214 | /* \brief Compute Pade approximation to matrix logarithm */
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215 | template <typename MatrixType>
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216 | void MatrixLogarithmAtomic<MatrixType>::computePade(MatrixType& result, const MatrixType& T, int degree)
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217 | {
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218 | switch (degree) {
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219 | case 3: computePade3(result, T); break;
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220 | case 4: computePade4(result, T); break;
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221 | case 5: computePade5(result, T); break;
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222 | case 6: computePade6(result, T); break;
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223 | case 7: computePade7(result, T); break;
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224 | case 8: computePade8(result, T); break;
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225 | case 9: computePade9(result, T); break;
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226 | case 10: computePade10(result, T); break;
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227 | case 11: computePade11(result, T); break;
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228 | default: assert(false); // should never happen
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229 | }
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230 | }
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231 |
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232 | template <typename MatrixType>
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233 | void MatrixLogarithmAtomic<MatrixType>::computePade3(MatrixType& result, const MatrixType& T)
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234 | {
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235 | const int degree = 3;
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236 | const RealScalar nodes[] = { 0.1127016653792583114820734600217600L, 0.5000000000000000000000000000000000L,
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237 | 0.8872983346207416885179265399782400L };
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238 | const RealScalar weights[] = { 0.2777777777777777777777777777777778L, 0.4444444444444444444444444444444444L,
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239 | 0.2777777777777777777777777777777778L };
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240 | eigen_assert(degree <= maxPadeDegree);
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241 | MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows());
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242 | result.setZero(T.rows(), T.rows());
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243 | for (int k = 0; k < degree; ++k)
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244 | result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI)
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245 | .template triangularView<Upper>().solve(TminusI);
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246 | }
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247 |
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248 | template <typename MatrixType>
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249 | void MatrixLogarithmAtomic<MatrixType>::computePade4(MatrixType& result, const MatrixType& T)
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250 | {
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251 | const int degree = 4;
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252 | const RealScalar nodes[] = { 0.0694318442029737123880267555535953L, 0.3300094782075718675986671204483777L,
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253 | 0.6699905217924281324013328795516223L, 0.9305681557970262876119732444464048L };
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254 | const RealScalar weights[] = { 0.1739274225687269286865319746109997L, 0.3260725774312730713134680253890003L,
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255 | 0.3260725774312730713134680253890003L, 0.1739274225687269286865319746109997L };
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256 | eigen_assert(degree <= maxPadeDegree);
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257 | MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows());
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258 | result.setZero(T.rows(), T.rows());
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259 | for (int k = 0; k < degree; ++k)
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260 | result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI)
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261 | .template triangularView<Upper>().solve(TminusI);
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262 | }
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263 |
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264 | template <typename MatrixType>
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265 | void MatrixLogarithmAtomic<MatrixType>::computePade5(MatrixType& result, const MatrixType& T)
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266 | {
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267 | const int degree = 5;
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268 | const RealScalar nodes[] = { 0.0469100770306680036011865608503035L, 0.2307653449471584544818427896498956L,
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269 | 0.5000000000000000000000000000000000L, 0.7692346550528415455181572103501044L,
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270 | 0.9530899229693319963988134391496965L };
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271 | const RealScalar weights[] = { 0.1184634425280945437571320203599587L, 0.2393143352496832340206457574178191L,
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272 | 0.2844444444444444444444444444444444L, 0.2393143352496832340206457574178191L,
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273 | 0.1184634425280945437571320203599587L };
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274 | eigen_assert(degree <= maxPadeDegree);
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275 | MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows());
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276 | result.setZero(T.rows(), T.rows());
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277 | for (int k = 0; k < degree; ++k)
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278 | result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI)
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279 | .template triangularView<Upper>().solve(TminusI);
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280 | }
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281 |
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282 | template <typename MatrixType>
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283 | void MatrixLogarithmAtomic<MatrixType>::computePade6(MatrixType& result, const MatrixType& T)
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284 | {
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285 | const int degree = 6;
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286 | const RealScalar nodes[] = { 0.0337652428984239860938492227530027L, 0.1693953067668677431693002024900473L,
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287 | 0.3806904069584015456847491391596440L, 0.6193095930415984543152508608403560L,
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288 | 0.8306046932331322568306997975099527L, 0.9662347571015760139061507772469973L };
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289 | const RealScalar weights[] = { 0.0856622461895851725201480710863665L, 0.1803807865240693037849167569188581L,
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290 | 0.2339569672863455236949351719947755L, 0.2339569672863455236949351719947755L,
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291 | 0.1803807865240693037849167569188581L, 0.0856622461895851725201480710863665L };
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292 | eigen_assert(degree <= maxPadeDegree);
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293 | MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows());
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294 | result.setZero(T.rows(), T.rows());
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295 | for (int k = 0; k < degree; ++k)
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296 | result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI)
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297 | .template triangularView<Upper>().solve(TminusI);
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298 | }
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299 |
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300 | template <typename MatrixType>
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301 | void MatrixLogarithmAtomic<MatrixType>::computePade7(MatrixType& result, const MatrixType& T)
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302 | {
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303 | const int degree = 7;
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304 | const RealScalar nodes[] = { 0.0254460438286207377369051579760744L, 0.1292344072003027800680676133596058L,
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305 | 0.2970774243113014165466967939615193L, 0.5000000000000000000000000000000000L,
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306 | 0.7029225756886985834533032060384807L, 0.8707655927996972199319323866403942L,
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307 | 0.9745539561713792622630948420239256L };
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308 | const RealScalar weights[] = { 0.0647424830844348466353057163395410L, 0.1398526957446383339507338857118898L,
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309 | 0.1909150252525594724751848877444876L, 0.2089795918367346938775510204081633L,
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310 | 0.1909150252525594724751848877444876L, 0.1398526957446383339507338857118898L,
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311 | 0.0647424830844348466353057163395410L };
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312 | eigen_assert(degree <= maxPadeDegree);
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313 | MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows());
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314 | result.setZero(T.rows(), T.rows());
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315 | for (int k = 0; k < degree; ++k)
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316 | result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI)
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317 | .template triangularView<Upper>().solve(TminusI);
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318 | }
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319 |
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320 | template <typename MatrixType>
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321 | void MatrixLogarithmAtomic<MatrixType>::computePade8(MatrixType& result, const MatrixType& T)
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322 | {
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323 | const int degree = 8;
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324 | const RealScalar nodes[] = { 0.0198550717512318841582195657152635L, 0.1016667612931866302042230317620848L,
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325 | 0.2372337950418355070911304754053768L, 0.4082826787521750975302619288199080L,
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326 | 0.5917173212478249024697380711800920L, 0.7627662049581644929088695245946232L,
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327 | 0.8983332387068133697957769682379152L, 0.9801449282487681158417804342847365L };
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328 | const RealScalar weights[] = { 0.0506142681451881295762656771549811L, 0.1111905172266872352721779972131204L,
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329 | 0.1568533229389436436689811009933007L, 0.1813418916891809914825752246385978L,
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330 | 0.1813418916891809914825752246385978L, 0.1568533229389436436689811009933007L,
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331 | 0.1111905172266872352721779972131204L, 0.0506142681451881295762656771549811L };
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332 | eigen_assert(degree <= maxPadeDegree);
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333 | MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows());
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334 | result.setZero(T.rows(), T.rows());
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335 | for (int k = 0; k < degree; ++k)
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336 | result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI)
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337 | .template triangularView<Upper>().solve(TminusI);
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338 | }
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339 |
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340 | template <typename MatrixType>
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341 | void MatrixLogarithmAtomic<MatrixType>::computePade9(MatrixType& result, const MatrixType& T)
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342 | {
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343 | const int degree = 9;
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344 | const RealScalar nodes[] = { 0.0159198802461869550822118985481636L, 0.0819844463366821028502851059651326L,
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345 | 0.1933142836497048013456489803292629L, 0.3378732882980955354807309926783317L,
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346 | 0.5000000000000000000000000000000000L, 0.6621267117019044645192690073216683L,
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347 | 0.8066857163502951986543510196707371L, 0.9180155536633178971497148940348674L,
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348 | 0.9840801197538130449177881014518364L };
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349 | const RealScalar weights[] = { 0.0406371941807872059859460790552618L, 0.0903240803474287020292360156214564L,
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350 | 0.1303053482014677311593714347093164L, 0.1561735385200014200343152032922218L,
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351 | 0.1651196775006298815822625346434870L, 0.1561735385200014200343152032922218L,
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352 | 0.1303053482014677311593714347093164L, 0.0903240803474287020292360156214564L,
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353 | 0.0406371941807872059859460790552618L };
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354 | eigen_assert(degree <= maxPadeDegree);
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355 | MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows());
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356 | result.setZero(T.rows(), T.rows());
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357 | for (int k = 0; k < degree; ++k)
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358 | result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI)
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359 | .template triangularView<Upper>().solve(TminusI);
|
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360 | }
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361 |
|
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362 | template <typename MatrixType>
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363 | void MatrixLogarithmAtomic<MatrixType>::computePade10(MatrixType& result, const MatrixType& T)
|
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364 | {
|
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365 | const int degree = 10;
|
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366 | const RealScalar nodes[] = { 0.0130467357414141399610179939577740L, 0.0674683166555077446339516557882535L,
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367 | 0.1602952158504877968828363174425632L, 0.2833023029353764046003670284171079L,
|
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368 | 0.4255628305091843945575869994351400L, 0.5744371694908156054424130005648600L,
|
---|
369 | 0.7166976970646235953996329715828921L, 0.8397047841495122031171636825574368L,
|
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370 | 0.9325316833444922553660483442117465L, 0.9869532642585858600389820060422260L };
|
---|
371 | const RealScalar weights[] = { 0.0333356721543440687967844049466659L, 0.0747256745752902965728881698288487L,
|
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372 | 0.1095431812579910219977674671140816L, 0.1346333596549981775456134607847347L,
|
---|
373 | 0.1477621123573764350869464973256692L, 0.1477621123573764350869464973256692L,
|
---|
374 | 0.1346333596549981775456134607847347L, 0.1095431812579910219977674671140816L,
|
---|
375 | 0.0747256745752902965728881698288487L, 0.0333356721543440687967844049466659L };
|
---|
376 | eigen_assert(degree <= maxPadeDegree);
|
---|
377 | MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows());
|
---|
378 | result.setZero(T.rows(), T.rows());
|
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379 | for (int k = 0; k < degree; ++k)
|
---|
380 | result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI)
|
---|
381 | .template triangularView<Upper>().solve(TminusI);
|
---|
382 | }
|
---|
383 |
|
---|
384 | template <typename MatrixType>
|
---|
385 | void MatrixLogarithmAtomic<MatrixType>::computePade11(MatrixType& result, const MatrixType& T)
|
---|
386 | {
|
---|
387 | const int degree = 11;
|
---|
388 | const RealScalar nodes[] = { 0.0108856709269715035980309994385713L, 0.0564687001159523504624211153480364L,
|
---|
389 | 0.1349239972129753379532918739844233L, 0.2404519353965940920371371652706952L,
|
---|
390 | 0.3652284220238275138342340072995692L, 0.5000000000000000000000000000000000L,
|
---|
391 | 0.6347715779761724861657659927004308L, 0.7595480646034059079628628347293048L,
|
---|
392 | 0.8650760027870246620467081260155767L, 0.9435312998840476495375788846519636L,
|
---|
393 | 0.9891143290730284964019690005614287L };
|
---|
394 | const RealScalar weights[] = { 0.0278342835580868332413768602212743L, 0.0627901847324523123173471496119701L,
|
---|
395 | 0.0931451054638671257130488207158280L, 0.1165968822959952399592618524215876L,
|
---|
396 | 0.1314022722551233310903444349452546L, 0.1364625433889503153572417641681711L,
|
---|
397 | 0.1314022722551233310903444349452546L, 0.1165968822959952399592618524215876L,
|
---|
398 | 0.0931451054638671257130488207158280L, 0.0627901847324523123173471496119701L,
|
---|
399 | 0.0278342835580868332413768602212743L };
|
---|
400 | eigen_assert(degree <= maxPadeDegree);
|
---|
401 | MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows());
|
---|
402 | result.setZero(T.rows(), T.rows());
|
---|
403 | for (int k = 0; k < degree; ++k)
|
---|
404 | result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI)
|
---|
405 | .template triangularView<Upper>().solve(TminusI);
|
---|
406 | }
|
---|
407 |
|
---|
408 | /** \ingroup MatrixFunctions_Module
|
---|
409 | *
|
---|
410 | * \brief Proxy for the matrix logarithm of some matrix (expression).
|
---|
411 | *
|
---|
412 | * \tparam Derived Type of the argument to the matrix function.
|
---|
413 | *
|
---|
414 | * This class holds the argument to the matrix function until it is
|
---|
415 | * assigned or evaluated for some other reason (so the argument
|
---|
416 | * should not be changed in the meantime). It is the return type of
|
---|
417 | * MatrixBase::log() and most of the time this is the only way it
|
---|
418 | * is used.
|
---|
419 | */
|
---|
420 | template<typename Derived> class MatrixLogarithmReturnValue
|
---|
421 | : public ReturnByValue<MatrixLogarithmReturnValue<Derived> >
|
---|
422 | {
|
---|
423 | public:
|
---|
424 |
|
---|
425 | typedef typename Derived::Scalar Scalar;
|
---|
426 | typedef typename Derived::Index Index;
|
---|
427 |
|
---|
428 | /** \brief Constructor.
|
---|
429 | *
|
---|
430 | * \param[in] A %Matrix (expression) forming the argument of the matrix logarithm.
|
---|
431 | */
|
---|
432 | MatrixLogarithmReturnValue(const Derived& A) : m_A(A) { }
|
---|
433 |
|
---|
434 | /** \brief Compute the matrix logarithm.
|
---|
435 | *
|
---|
436 | * \param[out] result Logarithm of \p A, where \A is as specified in the constructor.
|
---|
437 | */
|
---|
438 | template <typename ResultType>
|
---|
439 | inline void evalTo(ResultType& result) const
|
---|
440 | {
|
---|
441 | typedef typename Derived::PlainObject PlainObject;
|
---|
442 | typedef internal::traits<PlainObject> Traits;
|
---|
443 | static const int RowsAtCompileTime = Traits::RowsAtCompileTime;
|
---|
444 | static const int ColsAtCompileTime = Traits::ColsAtCompileTime;
|
---|
445 | static const int Options = PlainObject::Options;
|
---|
446 | typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar;
|
---|
447 | typedef Matrix<ComplexScalar, Dynamic, Dynamic, Options, RowsAtCompileTime, ColsAtCompileTime> DynMatrixType;
|
---|
448 | typedef MatrixLogarithmAtomic<DynMatrixType> AtomicType;
|
---|
449 | AtomicType atomic;
|
---|
450 |
|
---|
451 | const PlainObject Aevaluated = m_A.eval();
|
---|
452 | MatrixFunction<PlainObject, AtomicType> mf(Aevaluated, atomic);
|
---|
453 | mf.compute(result);
|
---|
454 | }
|
---|
455 |
|
---|
456 | Index rows() const { return m_A.rows(); }
|
---|
457 | Index cols() const { return m_A.cols(); }
|
---|
458 |
|
---|
459 | private:
|
---|
460 | typename internal::nested<Derived>::type m_A;
|
---|
461 |
|
---|
462 | MatrixLogarithmReturnValue& operator=(const MatrixLogarithmReturnValue&);
|
---|
463 | };
|
---|
464 |
|
---|
465 | namespace internal {
|
---|
466 | template<typename Derived>
|
---|
467 | struct traits<MatrixLogarithmReturnValue<Derived> >
|
---|
468 | {
|
---|
469 | typedef typename Derived::PlainObject ReturnType;
|
---|
470 | };
|
---|
471 | }
|
---|
472 |
|
---|
473 |
|
---|
474 | /********** MatrixBase method **********/
|
---|
475 |
|
---|
476 |
|
---|
477 | template <typename Derived>
|
---|
478 | const MatrixLogarithmReturnValue<Derived> MatrixBase<Derived>::log() const
|
---|
479 | {
|
---|
480 | eigen_assert(rows() == cols());
|
---|
481 | return MatrixLogarithmReturnValue<Derived>(derived());
|
---|
482 | }
|
---|
483 |
|
---|
484 | } // end namespace Eigen
|
---|
485 |
|
---|
486 | #endif // EIGEN_MATRIX_LOGARITHM
|
---|