1 | // |
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2 | // ******************************************************************** |
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3 | // * License and Disclaimer * |
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4 | // * * |
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5 | // * The Geant4 software is copyright of the Copyright Holders of * |
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6 | // * the Geant4 Collaboration. It is provided under the terms and * |
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7 | // * conditions of the Geant4 Software License, included in the file * |
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8 | // * LICENSE and available at http://cern.ch/geant4/license . These * |
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9 | // * include a list of copyright holders. * |
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10 | // * * |
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11 | // * Neither the authors of this software system, nor their employing * |
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12 | // * institutes,nor the agencies providing financial support for this * |
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13 | // * work make any representation or warranty, express or implied, * |
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14 | // * regarding this software system or assume any liability for its * |
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15 | // * use. Please see the license in the file LICENSE and URL above * |
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16 | // * for the full disclaimer and the limitation of liability. * |
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17 | // * * |
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18 | // * This code implementation is the result of the scientific and * |
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19 | // * technical work of the GEANT4 collaboration. * |
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20 | // * By using, copying, modifying or distributing the software (or * |
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21 | // * any work based on the software) you agree to acknowledge its * |
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22 | // * use in resulting scientific publications, and indicate your * |
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23 | // * acceptance of all terms of the Geant4 Software license. * |
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24 | // ******************************************************************** |
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25 | // |
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26 | // |
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27 | // $Id: G4DataInterpolation.hh,v 1.5 2006/06/29 18:59:29 gunter Exp $ |
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28 | // GEANT4 tag $Name: geant4-09-04-beta-01 $ |
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29 | // |
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30 | // Class description: |
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31 | // |
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32 | // The class consists of some methods for data interpolations and extrapolations. |
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33 | // The methods based mainly on recommendations given in the book : An introduction to |
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34 | // NUMERICAL METHODS IN C++, B.H. Flowers, Claredon Press, Oxford, 1995 |
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35 | // |
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36 | // ------------------------------ Data members: --------------------------------- |
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37 | // |
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38 | // fArgument and fFunction - pointers to data table to be interpolated |
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39 | // for y[i] and x[i] respectively |
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40 | // fNumber - the corresponding table size |
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41 | // ...... |
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42 | // G4DataInterpolation( G4double pX[], G4double pY[], G4int number ) |
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43 | // |
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44 | // Constructor for initializing of fArgument, fFunction and fNumber data members: |
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45 | // ...... |
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46 | // G4DataInterpolation( G4double pX[], G4double pY[], G4int number, |
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47 | // G4double pFirstDerStart, G4double pFirstDerFinish ) |
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48 | // |
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49 | // Constructor for cubic spline interpolation. It creates the array |
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50 | // fSecondDerivative[0,...fNumber-1] which is used in this interpolation by |
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51 | // the function: |
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52 | // .... |
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53 | // ~G4DataInterpolation() |
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54 | // |
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55 | // Destructor deletes dynamically created arrays for data members: fArgument, |
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56 | // fFunction and fSecondDerivative, all have dimension of fNumber |
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57 | // |
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58 | // ------------------------------ Methods: ---------------------------------------- |
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59 | // |
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60 | // G4double PolynomInterpolation(G4double pX, G4double& deltaY ) const |
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61 | // |
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62 | // This function returns the value P(pX), where P(x) is polynom of fNumber-1 degree |
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63 | // such that P(fArgument[i]) = fFunction[i], for i = 0, ..., fNumber-1 . |
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64 | // ........ |
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65 | // void PolIntCoefficient( G4double cof[]) const |
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66 | // |
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67 | // Given arrays fArgument[0,..,fNumber-1] and fFunction[0,..,fNumber-1] , this |
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68 | // function calculates an array of coefficients. The coefficients don't provide |
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69 | // usually (fNumber>10) better accuracy for polynom interpolation, as compared with |
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70 | // PolynomInterpolation function. They could be used instead for derivate |
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71 | // calculations and some other applications. |
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72 | // ......... |
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73 | // G4double RationalPolInterpolation(G4double pX, G4double& deltaY ) const |
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74 | // |
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75 | // The function returns diagonal rational function (Bulirsch and Stoer algorithm |
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76 | // of Neville type) Pn(x)/Qm(x) where P and Q are polynoms. |
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77 | // Tests showed the method is not stable and hasn't advantage if compared with |
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78 | // polynomial interpolation |
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79 | // ................ |
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80 | // G4double CubicSplineInterpolation(G4double pX) const |
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81 | // |
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82 | // Cubic spline interpolation in point pX for function given by the table: |
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83 | // fArgument, fFunction. The constructor, which creates fSecondDerivative, must be |
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84 | // called before. The function works optimal, if sequential calls are in random |
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85 | // values of pX. |
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86 | // .................. |
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87 | // G4double FastCubicSpline(G4double pX, G4int index) const |
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88 | // |
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89 | // Return cubic spline interpolation in the point pX which is located between |
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90 | // fArgument[index] and fArgument[index+1]. It is usually called in sequence of |
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91 | // known from external analysis values of index. |
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92 | // ......... |
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93 | // G4int LocateArgument(G4double pX) const |
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94 | // |
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95 | // Given argument pX, returns index k, so that pX bracketed by fArgument[k] and |
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96 | // fArgument[k+1] |
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97 | // ...................... |
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98 | // void CorrelatedSearch( G4double pX, G4int& index ) const |
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99 | // |
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100 | // Given a value pX, returns a value 'index' such that pX is between fArgument[index] |
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101 | // and fArgument[index+1]. fArgument MUST BE MONOTONIC, either increasing or |
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102 | // decreasing. If index = -1 or fNumber, this indicates that pX is out of range. |
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103 | // The value index on input is taken as the initial approximation for index on |
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104 | // output. |
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105 | |
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106 | // --------------------------------- History: -------------------------------------- |
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107 | // |
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108 | // 3.4.97 V.Grichine (Vladimir.Grichine@cern.ch) |
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109 | // |
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110 | |
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111 | |
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112 | #ifndef G4DATAINTERPOLATION_HH |
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113 | #define G4DATAINTERPOLATION_HH |
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114 | |
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115 | #include "globals.hh" |
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116 | |
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117 | class G4DataInterpolation |
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118 | { |
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119 | public: |
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120 | G4DataInterpolation( G4double pX[], |
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121 | G4double pY[], |
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122 | G4int number ); |
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123 | |
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124 | // Constructor for cubic spline interpolation. It creates fSecond Deivative array |
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125 | // as well as fArgument and fFunction |
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126 | |
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127 | G4DataInterpolation( G4double pX[], |
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128 | G4double pY[], |
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129 | G4int number, |
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130 | G4double pFirstDerStart, |
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131 | G4double pFirstDerFinish ) ; |
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132 | |
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133 | ~G4DataInterpolation() ; |
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134 | |
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135 | G4double PolynomInterpolation( G4double pX, |
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136 | G4double& deltaY ) const ; |
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137 | |
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138 | void PolIntCoefficient( G4double cof[]) const ; |
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139 | |
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140 | G4double RationalPolInterpolation( G4double pX, |
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141 | G4double& deltaY ) const ; |
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142 | |
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143 | G4double CubicSplineInterpolation( G4double pX ) const ; |
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144 | |
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145 | G4double FastCubicSpline( G4double pX, |
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146 | G4int index ) const ; |
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147 | |
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148 | G4int LocateArgument( G4double pX ) const ; |
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149 | |
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150 | void CorrelatedSearch( G4double pX, |
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151 | G4int& index ) const ; |
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152 | |
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153 | private: |
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154 | |
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155 | G4DataInterpolation(const G4DataInterpolation&); |
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156 | G4DataInterpolation& operator=(const G4DataInterpolation&); |
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157 | |
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158 | private: |
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159 | G4double* fArgument ; |
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160 | G4double* fFunction ; |
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161 | G4double* fSecondDerivative ; |
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162 | G4int fNumber ; |
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163 | } ; |
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164 | |
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165 | #endif |
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