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2 | // ******************************************************************** |
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3 | // * License and Disclaimer * |
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15 | // * use. Please see the license in the file LICENSE and URL above * |
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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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21 | // * any work based on the software) you agree to acknowledge its * |
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24 | // ******************************************************************** |
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25 | // |
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26 | // |
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27 | // $Id: G4ChebyshevApproximation.hh,v 1.6 2006/06/29 18:59:26 gunter Exp $ |
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28 | // GEANT4 tag $Name: HEAD $ |
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29 | // |
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30 | // Class description: |
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31 | // |
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32 | // Class creating the Chebyshev approximation for a function pointed by fFunction |
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33 | // data member. The Chebyshev polinom approximation provides an efficient evaluation |
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34 | // of minimax polynomial, which (among all polynomials of the same degree) has the |
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35 | // smallest maximum deviation from the true function. |
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36 | // The methods based mainly on recommendations given in the book : An introduction to |
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37 | // NUMERICAL METHODS IN C++, B.H. Flowers, Claredon Press, Oxford, 1995 |
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38 | // |
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39 | // ------------------------- MEMBER DATA ------------------------------------ |
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40 | // |
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41 | // function fFunction - pointer to a function considered |
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42 | // G4int fNumber - number of Chebyshev coefficients |
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43 | // G4double* fChebyshevCof - array of Chebyshev coefficients |
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44 | // G4double fMean = (a+b)/2 - mean point of interval |
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45 | // G4double fDiff = (b-a)/2 - half of the interval value |
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46 | // |
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47 | // ------------------------ CONSTRUCTORS ---------------------------------- |
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48 | // |
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49 | // Constructor for initialisation of the class data members. It creates the array |
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50 | // fChebyshevCof[0,...,fNumber-1], fNumber = n ; which consists of Chebyshev |
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51 | // coefficients describing the function pointed by pFunction. The values a and b |
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52 | // fixe the interval of validity of Chebyshev approximation. |
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53 | // |
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54 | // G4ChebyshevApproximation( function pFunction, |
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55 | // G4int n, |
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56 | // G4double a, |
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57 | // G4double b ) |
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58 | // |
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59 | // -------------------------------------------------------------------- |
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60 | // |
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61 | // Constructor for creation of Chebyshev coefficients for m-derivative |
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62 | // from pFunction. The value of m ! MUST BE ! < n , because the result |
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63 | // array of fChebyshevCof will be of (n-m) size. There is a definite dependence |
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64 | // between the proper selection of n, m, a and b values to get better accuracy |
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65 | // of the derivative value. |
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66 | // |
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67 | // G4ChebyshevApproximation( function pFunction, |
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68 | // G4int n, |
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69 | // G4int m, |
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70 | // G4double a, |
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71 | // G4double b ) |
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72 | // |
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73 | // ------------------------------------------------------ |
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74 | // |
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75 | // Constructor for creation of Chebyshev coefficients for integral |
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76 | // from pFunction. |
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77 | // |
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78 | // G4ChebyshevApproximation( function pFunction, |
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79 | // G4double a, |
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80 | // G4double b, |
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81 | // G4int n ) |
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82 | // |
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83 | // --------------------------------------------------------------- |
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84 | // |
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85 | // Destructor deletes the array of Chebyshev coefficients |
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86 | // |
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87 | // ~G4ChebyshevApproximation() |
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88 | // |
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89 | // ----------------------------- METHODS ---------------------------------- |
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90 | // |
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91 | // Access function for Chebyshev coefficients |
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92 | // |
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93 | // G4double GetChebyshevCof(G4int number) const |
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94 | // |
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95 | // -------------------------------------------------------------- |
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96 | // |
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97 | // Evaluate the value of fFunction at the point x via the Chebyshev coefficients |
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98 | // fChebyshevCof[0,...,fNumber-1] |
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99 | // |
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100 | // G4double ChebyshevEvaluation(G4double x) const |
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101 | // |
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102 | // ------------------------------------------------------------------ |
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103 | // |
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104 | // Returns the array derCof[0,...,fNumber-2], the Chebyshev coefficients of the |
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105 | // derivative of the function whose coefficients are fChebyshevCof |
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106 | // |
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107 | // void DerivativeChebyshevCof(G4double derCof[]) const |
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108 | // |
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109 | // ------------------------------------------------------------------------ |
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110 | // |
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111 | // This function produces the array integralCof[0,...,fNumber-1] , the Chebyshev |
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112 | // coefficients of the integral of the function whose coefficients are |
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113 | // fChebyshevCof. The constant of integration is set so that the integral vanishes |
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114 | // at the point (fMean - fDiff) |
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115 | // |
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116 | // void IntegralChebyshevCof(G4double integralCof[]) const |
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117 | |
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118 | // --------------------------- HISTORY -------------------------------------- |
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119 | // |
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120 | // 24.04.97 V.Grichine ( Vladimir.Grichine@cern.ch ) |
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121 | |
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122 | #ifndef G4CHEBYSHEVAPPROXIMATION_HH |
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123 | #define G4CHEBYSHEVAPPROXIMATION_HH |
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124 | |
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125 | #include "globals.hh" |
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126 | |
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127 | typedef G4double (*function)(G4double) ; |
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128 | |
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129 | class G4ChebyshevApproximation |
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130 | { |
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131 | public: // with description |
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132 | |
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133 | G4ChebyshevApproximation( function pFunction, |
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134 | G4int n, |
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135 | G4double a, |
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136 | G4double b ) ; |
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137 | // |
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138 | // Constructor for creation of Chebyshev coefficients for m-derivative |
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139 | // from pFunction. The value of m ! MUST BE ! < n , because the result |
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140 | // array of fChebyshevCof will be of (n-m) size. |
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141 | |
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142 | G4ChebyshevApproximation( function pFunction, |
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143 | G4int n, |
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144 | G4int m, |
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145 | G4double a, |
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146 | G4double b ) ; |
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147 | // |
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148 | // Constructor for creation of Chebyshev coefficients for integral |
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149 | // from pFunction. |
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150 | |
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151 | G4ChebyshevApproximation( function pFunction, |
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152 | G4double a, |
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153 | G4double b, |
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154 | G4int n ) ; |
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155 | |
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156 | ~G4ChebyshevApproximation() ; |
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157 | |
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158 | // Access functions |
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159 | |
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160 | G4double GetChebyshevCof(G4int number) const ; |
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161 | |
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162 | // Methods |
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163 | |
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164 | G4double ChebyshevEvaluation(G4double x) const ; |
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165 | void DerivativeChebyshevCof(G4double derCof[]) const ; |
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166 | void IntegralChebyshevCof(G4double integralCof[]) const ; |
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167 | |
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168 | private: |
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169 | |
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170 | G4ChebyshevApproximation(const G4ChebyshevApproximation&); |
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171 | G4ChebyshevApproximation& operator=(const G4ChebyshevApproximation&); |
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172 | |
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173 | private: |
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174 | |
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175 | function fFunction ; |
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176 | G4int fNumber ; |
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177 | G4double* fChebyshevCof ; |
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178 | G4double fMean ; |
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179 | G4double fDiff ; |
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180 | }; |
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181 | |
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182 | #endif |
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