[833] | 1 | // |
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| 2 | // ******************************************************************** |
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| 3 | // * License and Disclaimer * |
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| 4 | // * * |
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| 6 | // * the Geant4 Collaboration. It is provided under the terms and * |
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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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| 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: G4ChebyshevApproximation.cc,v 1.7 2007/11/13 17:35:06 gcosmo Exp $ |
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[850] | 28 | // GEANT4 tag $Name: HEAD $ |
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[833] | 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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