[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.hh,v 1.4 2006/06/29 18:59:52 gunter Exp $ |
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[850] | 28 | // GEANT4 tag $Name: HEAD $ |
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[833] | 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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