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24 | // ******************************************************************** |
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25 | // |
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26 | // |
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27 | // $Id: G4ChebyshevApproximation.cc,v 1.7 2007/11/13 17:35:06 gcosmo Exp $ |
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28 | // GEANT4 tag $Name: geant4-09-04-beta-01 $ |
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29 | // |
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30 | |
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31 | #include "G4ChebyshevApproximation.hh" |
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32 | |
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33 | // Constructor for initialisation of the class data members. |
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34 | // It creates the array fChebyshevCof[0,...,fNumber-1], fNumber = n ; |
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35 | // which consists of Chebyshev coefficients describing the function |
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36 | // pointed by pFunction. The values a and b fix the interval of validity |
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37 | // of the Chebyshev approximation. |
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38 | |
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39 | G4ChebyshevApproximation::G4ChebyshevApproximation( function pFunction, |
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40 | G4int n, |
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41 | G4double a, |
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42 | G4double b ) |
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43 | : fFunction(pFunction), fNumber(n), |
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44 | fChebyshevCof(new G4double[fNumber]), |
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45 | fMean(0.5*(b+a)), fDiff(0.5*(b-a)) |
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46 | { |
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47 | G4int i=0, j=0 ; |
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48 | G4double rootSum=0.0, cofj=0.0 ; |
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49 | G4double* tempFunction = new G4double[fNumber] ; |
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50 | G4double weight = 2.0/fNumber ; |
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51 | G4double cof = 0.5*weight*pi ; // pi/n |
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52 | |
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53 | for (i=0;i<fNumber;i++) |
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54 | { |
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55 | rootSum = std::cos(cof*(i+0.5)) ; |
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56 | tempFunction[i]= fFunction(rootSum*fDiff+fMean) ; |
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57 | } |
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58 | for (j=0;j<fNumber;j++) |
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59 | { |
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60 | cofj = cof*j ; |
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61 | rootSum = 0.0 ; |
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62 | |
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63 | for (i=0;i<fNumber;i++) |
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64 | { |
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65 | rootSum += tempFunction[i]*std::cos(cofj*(i+0.5)) ; |
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66 | } |
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67 | fChebyshevCof[j] = weight*rootSum ; |
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68 | } |
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69 | delete[] tempFunction ; |
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70 | } |
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71 | |
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72 | // -------------------------------------------------------------------- |
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73 | // |
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74 | // Constructor for creation of Chebyshev coefficients for mx-derivative |
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75 | // from pFunction. The value of mx ! MUST BE ! < nx , because the result |
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76 | // array of fChebyshevCof will be of (nx-mx) size. The values a and b |
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77 | // fix the interval of validity of the Chebyshev approximation. |
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78 | |
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79 | G4ChebyshevApproximation:: |
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80 | G4ChebyshevApproximation( function pFunction, |
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81 | G4int nx, G4int mx, |
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82 | G4double a, G4double b ) |
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83 | : fFunction(pFunction), fNumber(nx), |
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84 | fChebyshevCof(new G4double[fNumber]), |
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85 | fMean(0.5*(b+a)), fDiff(0.5*(b-a)) |
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86 | { |
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87 | if(nx <= mx) |
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88 | { |
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89 | G4Exception("G4ChebyshevApproximation::G4ChebyshevApproximation()", |
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90 | "InvalidCall", FatalException, "Invalid arguments !") ; |
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91 | } |
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92 | G4int i=0, j=0 ; |
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93 | G4double rootSum = 0.0, cofj=0.0; |
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94 | G4double* tempFunction = new G4double[fNumber] ; |
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95 | G4double weight = 2.0/fNumber ; |
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96 | G4double cof = 0.5*weight*pi ; // pi/nx |
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97 | |
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98 | for (i=0;i<fNumber;i++) |
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99 | { |
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100 | rootSum = std::cos(cof*(i+0.5)) ; |
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101 | tempFunction[i] = fFunction(rootSum*fDiff+fMean) ; |
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102 | } |
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103 | for (j=0;j<fNumber;j++) |
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104 | { |
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105 | cofj = cof*j ; |
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106 | rootSum = 0.0 ; |
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107 | |
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108 | for (i=0;i<fNumber;i++) |
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109 | { |
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110 | rootSum += tempFunction[i]*std::cos(cofj*(i+0.5)) ; |
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111 | } |
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112 | fChebyshevCof[j] = weight*rootSum ; // corresponds to pFunction |
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113 | } |
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114 | // Chebyshev coefficients for (mx)-derivative of pFunction |
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115 | |
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116 | for(i=1;i<=mx;i++) |
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117 | { |
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118 | DerivativeChebyshevCof(tempFunction) ; |
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119 | fNumber-- ; |
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120 | for(j=0;j<fNumber;j++) |
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121 | { |
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122 | fChebyshevCof[j] = tempFunction[j] ; // corresponds to (i)-derivative |
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123 | } |
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124 | } |
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125 | delete[] tempFunction ; // delete of dynamically allocated tempFunction |
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126 | } |
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127 | |
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128 | // ------------------------------------------------------ |
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129 | // |
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130 | // Constructor for creation of Chebyshev coefficients for integral |
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131 | // from pFunction. |
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132 | |
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133 | G4ChebyshevApproximation::G4ChebyshevApproximation( function pFunction, |
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134 | G4double a, |
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135 | G4double b, |
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136 | G4int n ) |
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137 | : fFunction(pFunction), fNumber(n), |
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138 | fChebyshevCof(new G4double[fNumber]), |
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139 | fMean(0.5*(b+a)), fDiff(0.5*(b-a)) |
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140 | { |
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141 | G4int i=0, j=0; |
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142 | G4double rootSum=0.0, cofj=0.0; |
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143 | G4double* tempFunction = new G4double[fNumber] ; |
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144 | G4double weight = 2.0/fNumber; |
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145 | G4double cof = 0.5*weight*pi ; // pi/n |
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146 | |
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147 | for (i=0;i<fNumber;i++) |
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148 | { |
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149 | rootSum = std::cos(cof*(i+0.5)) ; |
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150 | tempFunction[i]= fFunction(rootSum*fDiff+fMean) ; |
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151 | } |
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152 | for (j=0;j<fNumber;j++) |
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153 | { |
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154 | cofj = cof*j ; |
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155 | rootSum = 0.0 ; |
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156 | |
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157 | for (i=0;i<fNumber;i++) |
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158 | { |
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159 | rootSum += tempFunction[i]*std::cos(cofj*(i+0.5)) ; |
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160 | } |
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161 | fChebyshevCof[j] = weight*rootSum ; // corresponds to pFunction |
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162 | } |
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163 | // Chebyshev coefficients for integral of pFunction |
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164 | |
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165 | IntegralChebyshevCof(tempFunction) ; |
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166 | for(j=0;j<fNumber;j++) |
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167 | { |
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168 | fChebyshevCof[j] = tempFunction[j] ; // corresponds to integral |
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169 | } |
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170 | delete[] tempFunction ; // delete of dynamically allocated tempFunction |
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171 | } |
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172 | |
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173 | |
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174 | |
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175 | // --------------------------------------------------------------- |
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176 | // |
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177 | // Destructor deletes the array of Chebyshev coefficients |
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178 | |
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179 | G4ChebyshevApproximation::~G4ChebyshevApproximation() |
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180 | { |
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181 | delete[] fChebyshevCof ; |
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182 | } |
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183 | |
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184 | // --------------------------------------------------------------- |
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185 | // |
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186 | // Access function for Chebyshev coefficients |
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187 | // |
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188 | |
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189 | |
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190 | G4double |
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191 | G4ChebyshevApproximation::GetChebyshevCof(G4int number) const |
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192 | { |
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193 | if(number < 0 && number >= fNumber) |
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194 | { |
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195 | G4Exception("G4ChebyshevApproximation::GetChebyshevCof()", |
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196 | "InvalidCall", FatalException, "Argument out of range !") ; |
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197 | } |
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198 | return fChebyshevCof[number] ; |
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199 | } |
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200 | |
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201 | // -------------------------------------------------------------- |
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202 | // |
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203 | // Evaluate the value of fFunction at the point x via the Chebyshev coefficients |
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204 | // fChebyshevCof[0,...,fNumber-1] |
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205 | |
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206 | G4double |
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207 | G4ChebyshevApproximation::ChebyshevEvaluation(G4double x) const |
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208 | { |
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209 | G4double evaluate = 0.0, evaluate2 = 0.0, temp = 0.0, |
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210 | xReduced = 0.0, xReduced2 = 0.0 ; |
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211 | |
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212 | if ((x-fMean+fDiff)*(x-fMean-fDiff) > 0.0) |
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213 | { |
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214 | G4Exception("G4ChebyshevApproximation::ChebyshevEvaluation()", |
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215 | "InvalidCall", FatalException, "Invalid argument !") ; |
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216 | } |
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217 | xReduced = (x-fMean)/fDiff ; |
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218 | xReduced2 = 2.0*xReduced ; |
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219 | for (G4int i=fNumber-1;i>=1;i--) |
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220 | { |
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221 | temp = evaluate ; |
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222 | evaluate = xReduced2*evaluate - evaluate2 + fChebyshevCof[i] ; |
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223 | evaluate2 = temp ; |
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224 | } |
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225 | return xReduced*evaluate - evaluate2 + 0.5*fChebyshevCof[0] ; |
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226 | } |
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227 | |
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228 | // ------------------------------------------------------------------ |
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229 | // |
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230 | // Returns the array derCof[0,...,fNumber-2], the Chebyshev coefficients of the |
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231 | // derivative of the function whose coefficients are fChebyshevCof |
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232 | |
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233 | void |
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234 | G4ChebyshevApproximation::DerivativeChebyshevCof(G4double derCof[]) const |
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235 | { |
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236 | G4double cof = 1.0/fDiff ; |
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237 | derCof[fNumber-1] = 0.0 ; |
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238 | derCof[fNumber-2] = 2*(fNumber-1)*fChebyshevCof[fNumber-1] ; |
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239 | for(G4int i=fNumber-3;i>=0;i--) |
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240 | { |
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241 | derCof[i] = derCof[i+2] + 2*(i+1)*fChebyshevCof[i+1] ; |
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242 | } |
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243 | for(G4int j=0;j<fNumber;j++) |
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244 | { |
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245 | derCof[j] *= cof ; |
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246 | } |
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247 | } |
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248 | |
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249 | // ------------------------------------------------------------------------ |
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250 | // |
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251 | // This function produces the array integralCof[0,...,fNumber-1] , the Chebyshev |
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252 | // coefficients of the integral of the function whose coefficients are |
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253 | // fChebyshevCof[]. The constant of integration is set so that the integral |
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254 | // vanishes at the point (fMean - fDiff), i.e. at the begining of the interval of |
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255 | // validity (we start the integration from this point). |
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256 | // |
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257 | |
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258 | void |
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259 | G4ChebyshevApproximation::IntegralChebyshevCof(G4double integralCof[]) const |
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260 | { |
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261 | G4double cof = 0.5*fDiff, sum = 0.0, factor = 1.0 ; |
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262 | for(G4int i=1;i<fNumber-1;i++) |
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263 | { |
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264 | integralCof[i] = cof*(fChebyshevCof[i-1] - fChebyshevCof[i+1])/i ; |
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265 | sum += factor*integralCof[i] ; |
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266 | factor = -factor ; |
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267 | } |
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268 | integralCof[fNumber-1] = cof*fChebyshevCof[fNumber-2]/(fNumber-1) ; |
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269 | sum += factor*integralCof[fNumber-1] ; |
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270 | integralCof[0] = 2.0*sum ; // set the constant of integration |
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271 | } |
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