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.hh,v 1.4 2006/06/29 18:59:52 gunter Exp $ |
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28 | // GEANT4 tag $Name: HEAD $ |
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29 | // |
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30 | // class G4PolynomialSolver |
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31 | // |
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32 | // Class description: |
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33 | // |
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34 | // G4PolynomialSolver allows the user to solve a polynomial equation |
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35 | // with a great precision. This is used by Implicit Equation solver. |
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36 | // |
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37 | // The Bezier clipping method is used to solve the polynomial. |
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38 | // |
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39 | // How to use it: |
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40 | // Create a class that is the function to be solved. |
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41 | // This class could have internal parameters to allow to change |
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42 | // the equation to be solved without recreating a new one. |
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43 | // |
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44 | // Define a Polynomial solver, example: |
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45 | // G4PolynomialSolver<MyFunctionClass,G4double(MyFunctionClass::*)(G4double)> |
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46 | // PolySolver (&MyFunction, |
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47 | // &MyFunctionClass::Function, |
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48 | // &MyFunctionClass::Derivative, |
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49 | // precision); |
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50 | // |
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51 | // The precision is relative to the function to solve. |
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52 | // |
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53 | // In MyFunctionClass, provide the function to solve and its derivative: |
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54 | // Example of function to provide : |
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55 | // |
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56 | // x,y,z,dx,dy,dz,Rmin,Rmax are internal variables of MyFunctionClass |
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57 | // |
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58 | // G4double MyFunctionClass::Function(G4double value) |
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59 | // { |
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60 | // G4double Lx,Ly,Lz; |
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61 | // G4double result; |
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62 | // |
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63 | // Lx = x + value*dx; |
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64 | // Ly = y + value*dy; |
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65 | // Lz = z + value*dz; |
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66 | // |
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67 | // result = TorusEquation(Lx,Ly,Lz,Rmax,Rmin); |
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68 | // |
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69 | // return result ; |
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70 | // } |
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71 | // |
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72 | // G4double MyFunctionClass::Derivative(G4double value) |
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73 | // { |
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74 | // G4double Lx,Ly,Lz; |
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75 | // G4double result; |
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76 | // |
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77 | // Lx = x + value*dx; |
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78 | // Ly = y + value*dy; |
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79 | // Lz = z + value*dz; |
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80 | // |
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81 | // result = dx*TorusDerivativeX(Lx,Ly,Lz,Rmax,Rmin); |
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82 | // result += dy*TorusDerivativeY(Lx,Ly,Lz,Rmax,Rmin); |
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83 | // result += dz*TorusDerivativeZ(Lx,Ly,Lz,Rmax,Rmin); |
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84 | // |
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85 | // return result; |
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86 | // } |
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87 | // |
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88 | // Then to have a root inside an interval [IntervalMin,IntervalMax] do the |
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89 | // following: |
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90 | // |
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91 | // MyRoot = PolySolver.solve(IntervalMin,IntervalMax); |
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92 | // |
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93 | |
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94 | // History: |
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95 | // |
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96 | // - 19.12.00 E.Medernach, First implementation |
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97 | // |
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98 | |
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99 | #ifndef G4POL_SOLVER_HH |
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100 | #define G4POL_SOLVER_HH |
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101 | |
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102 | #include "globals.hh" |
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103 | |
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104 | template <class T, class F> |
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105 | class G4PolynomialSolver |
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106 | { |
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107 | public: // with description |
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108 | |
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109 | G4PolynomialSolver(T* typeF, F func, F deriv, G4double precision); |
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110 | ~G4PolynomialSolver(); |
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111 | |
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112 | |
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113 | G4double solve (G4double IntervalMin, G4double IntervalMax); |
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114 | |
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115 | private: |
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116 | |
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117 | G4double Newton (G4double IntervalMin, G4double IntervalMax); |
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118 | //General Newton method with Bezier Clipping |
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119 | |
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120 | // Works for polynomial of order less or equal than 4. |
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121 | // But could be changed to work for polynomial of any order providing |
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122 | // that we find the bezier control points. |
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123 | |
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124 | G4int BezierClipping(G4double *IntervalMin, G4double *IntervalMax); |
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125 | // This is just one iteration of Bezier Clipping |
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126 | |
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127 | |
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128 | T* FunctionClass ; |
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129 | F Function ; |
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130 | F Derivative ; |
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131 | |
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132 | G4double Precision; |
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133 | }; |
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134 | |
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135 | #include "G4PolynomialSolver.icc" |
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136 | |
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137 | #endif |
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