[833] | 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: G4PolynomialSolver.icc,v 1.8 2006/06/29 18:59:54 gunter Exp $ |
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[1058] | 28 | // GEANT4 tag $Name: geant4-09-02-ref-02 $ |
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[833] | 29 | // |
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| 30 | // class G4PolynomialSolver |
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| 31 | // |
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| 32 | // 19.12.00 E.Medernach, First implementation |
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| 33 | // |
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| 34 | |
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| 35 | #define POLEPSILON 1e-12 |
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| 36 | #define POLINFINITY 9.0E99 |
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| 37 | #define ITERATION 12 // 20 But 8 is really enough for Newton with a good guess |
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| 38 | |
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| 39 | template <class T, class F> |
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| 40 | G4PolynomialSolver<T,F>::G4PolynomialSolver (T* typeF, F func, F deriv, |
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| 41 | G4double precision) |
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| 42 | { |
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| 43 | Precision = precision ; |
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| 44 | FunctionClass = typeF ; |
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| 45 | Function = func ; |
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| 46 | Derivative = deriv ; |
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| 47 | } |
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| 48 | |
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| 49 | template <class T, class F> |
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| 50 | G4PolynomialSolver<T,F>::~G4PolynomialSolver () |
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| 51 | { |
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| 52 | } |
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| 53 | |
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| 54 | template <class T, class F> |
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| 55 | G4double G4PolynomialSolver<T,F>::solve(G4double IntervalMin, |
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| 56 | G4double IntervalMax) |
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| 57 | { |
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| 58 | return Newton(IntervalMin,IntervalMax); |
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| 59 | } |
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| 60 | |
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| 61 | |
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| 62 | /* If we want to be general this could work for any |
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| 63 | polynomial of order more that 4 if we find the (ORDER + 1) |
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| 64 | control points |
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| 65 | */ |
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| 66 | #define NBBEZIER 5 |
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| 67 | |
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| 68 | template <class T, class F> |
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| 69 | G4int |
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| 70 | G4PolynomialSolver<T,F>::BezierClipping(/*T* typeF,F func,F deriv,*/ |
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| 71 | G4double *IntervalMin, |
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| 72 | G4double *IntervalMax) |
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| 73 | { |
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| 74 | /** BezierClipping is a clipping interval Newton method **/ |
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| 75 | /** It works by clipping the area where the polynomial is **/ |
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| 76 | |
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| 77 | G4double P[NBBEZIER][2],D[2]; |
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| 78 | G4double NewMin,NewMax; |
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| 79 | |
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| 80 | G4int IntervalIsVoid = 1; |
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| 81 | |
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| 82 | /*** Calculating Control Points ***/ |
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| 83 | /* We see the polynomial as a Bezier curve for some control points to find */ |
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| 84 | |
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| 85 | /* |
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| 86 | For 5 control points (polynomial of degree 4) this is: |
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| 87 | |
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| 88 | 0 p0 = F((*IntervalMin)) |
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| 89 | 1/4 p1 = F((*IntervalMin)) + ((*IntervalMax) - (*IntervalMin))/4 |
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| 90 | * F'((*IntervalMin)) |
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| 91 | 2/4 p2 = 1/6 * (16*F(((*IntervalMax) + (*IntervalMin))/2) |
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| 92 | - (p0 + 4*p1 + 4*p3 + p4)) |
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| 93 | 3/4 p3 = F((*IntervalMax)) - ((*IntervalMax) - (*IntervalMin))/4 |
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| 94 | * F'((*IntervalMax)) |
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| 95 | 1 p4 = F((*IntervalMax)) |
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| 96 | */ |
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| 97 | |
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| 98 | /* x,y,z,dx,dy,dz are constant during searching */ |
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| 99 | |
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| 100 | D[0] = (FunctionClass->*Derivative)(*IntervalMin); |
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| 101 | |
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| 102 | P[0][0] = (*IntervalMin); |
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| 103 | P[0][1] = (FunctionClass->*Function)(*IntervalMin); |
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| 104 | |
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| 105 | |
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| 106 | if (std::fabs(P[0][1]) < Precision) { |
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| 107 | return 1; |
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| 108 | } |
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| 109 | |
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| 110 | if (((*IntervalMax) - (*IntervalMin)) < POLEPSILON) { |
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| 111 | return 1; |
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| 112 | } |
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| 113 | |
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| 114 | P[1][0] = (*IntervalMin) + ((*IntervalMax) - (*IntervalMin))/4; |
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| 115 | P[1][1] = P[0][1] + (((*IntervalMax) - (*IntervalMin))/4.0) * D[0]; |
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| 116 | |
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| 117 | D[1] = (FunctionClass->*Derivative)(*IntervalMax); |
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| 118 | |
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| 119 | P[4][0] = (*IntervalMax); |
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| 120 | P[4][1] = (FunctionClass->*Function)(*IntervalMax); |
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| 121 | |
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| 122 | P[3][0] = (*IntervalMax) - ((*IntervalMax) - (*IntervalMin))/4; |
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| 123 | P[3][1] = P[4][1] - ((*IntervalMax) - (*IntervalMin))/4 * D[1]; |
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| 124 | |
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| 125 | P[2][0] = ((*IntervalMax) + (*IntervalMin))/2; |
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| 126 | P[2][1] = (16*(FunctionClass->*Function)(((*IntervalMax)+(*IntervalMin))/2) |
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| 127 | - (P[0][1] + 4*P[1][1] + 4*P[3][1] + P[4][1]))/6 ; |
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| 128 | |
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| 129 | { |
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| 130 | G4double Intersection ; |
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| 131 | G4int i,j; |
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| 132 | |
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| 133 | NewMin = (*IntervalMax) ; |
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| 134 | NewMax = (*IntervalMin) ; |
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| 135 | |
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| 136 | for (i=0;i<5;i++) |
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| 137 | for (j=i+1;j<5;j++) |
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| 138 | { |
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| 139 | /* there is an intersection only if each have different signs */ |
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| 140 | if (((P[j][1] > -Precision) && (P[i][1] < Precision)) || |
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| 141 | ((P[j][1] < Precision) && (P[i][1] > -Precision))) { |
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| 142 | IntervalIsVoid = 0; |
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| 143 | Intersection = P[j][0] - P[j][1]*((P[i][0] - P[j][0])/ |
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| 144 | (P[i][1] - P[j][1])); |
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| 145 | if (Intersection < NewMin) { |
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| 146 | NewMin = Intersection; |
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| 147 | } |
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| 148 | if (Intersection > NewMax) { |
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| 149 | NewMax = Intersection; |
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| 150 | } |
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| 151 | } |
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| 152 | } |
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| 153 | |
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| 154 | |
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| 155 | if (IntervalIsVoid != 1) { |
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| 156 | (*IntervalMax) = NewMax; |
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| 157 | (*IntervalMin) = NewMin; |
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| 158 | } |
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| 159 | } |
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| 160 | |
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| 161 | if (IntervalIsVoid == 1) { |
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| 162 | return -1; |
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| 163 | } |
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| 164 | |
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| 165 | return 0; |
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| 166 | } |
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| 167 | |
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| 168 | template <class T, class F> |
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| 169 | G4double G4PolynomialSolver<T,F>::Newton (G4double IntervalMin, |
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| 170 | G4double IntervalMax) |
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| 171 | { |
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| 172 | /* So now we have a good guess and an interval where |
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| 173 | if there are an intersection the root must be */ |
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| 174 | |
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| 175 | G4double Value = 0; |
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| 176 | G4double Gradient = 0; |
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| 177 | G4double Lambda ; |
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| 178 | |
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| 179 | G4int i=0; |
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| 180 | G4int j=0; |
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| 181 | |
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| 182 | |
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| 183 | /* Reduce interval before applying Newton Method */ |
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| 184 | { |
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| 185 | G4int NewtonIsSafe ; |
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| 186 | |
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| 187 | while ((NewtonIsSafe = BezierClipping(&IntervalMin,&IntervalMax)) == 0) ; |
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| 188 | |
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| 189 | if (NewtonIsSafe == -1) { |
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| 190 | return POLINFINITY; |
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| 191 | } |
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| 192 | } |
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| 193 | |
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| 194 | Lambda = IntervalMin; |
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| 195 | Value = (FunctionClass->*Function)(Lambda); |
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| 196 | |
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| 197 | |
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| 198 | // while ((std::fabs(Value) > Precision)) { |
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| 199 | while (j != -1) { |
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| 200 | |
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| 201 | Value = (FunctionClass->*Function)(Lambda); |
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| 202 | |
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| 203 | Gradient = (FunctionClass->*Derivative)(Lambda); |
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| 204 | |
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| 205 | Lambda = Lambda - Value/Gradient ; |
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| 206 | |
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| 207 | if (std::fabs(Value) <= Precision) { |
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| 208 | j ++; |
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| 209 | if (j == 2) { |
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| 210 | j = -1; |
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| 211 | } |
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| 212 | } else { |
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| 213 | i ++; |
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| 214 | |
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| 215 | if (i > ITERATION) |
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| 216 | return POLINFINITY; |
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| 217 | } |
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| 218 | } |
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| 219 | return Lambda ; |
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| 220 | } |
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