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1 // 1 // 2 // ******************************************* 2 // ******************************************************************** 3 // * License and Disclaimer 3 // * License and Disclaimer * 4 // * 4 // * * 5 // * The Geant4 software is copyright of th 5 // * The Geant4 software is copyright of the Copyright Holders of * 6 // * the Geant4 Collaboration. It is provided 6 // * the Geant4 Collaboration. It is provided under the terms and * 7 // * conditions of the Geant4 Software License 7 // * conditions of the Geant4 Software License, included in the file * 8 // * LICENSE and available at http://cern.ch/ 8 // * LICENSE and available at http://cern.ch/geant4/license . These * 9 // * include a list of copyright holders. 9 // * include a list of copyright holders. * 10 // * 10 // * * 11 // * Neither the authors of this software syst 11 // * Neither the authors of this software system, nor their employing * 12 // * institutes,nor the agencies providing fin 12 // * institutes,nor the agencies providing financial support for this * 13 // * work make any representation or warran 13 // * work make any representation or warranty, express or implied, * 14 // * regarding this software system or assum 14 // * regarding this software system or assume any liability for its * 15 // * use. Please see the license in the file 15 // * use. Please see the license in the file LICENSE and URL above * 16 // * for the full disclaimer and the limitatio 16 // * for the full disclaimer and the limitation of liability. * 17 // * 17 // * * 18 // * This code implementation is the result 18 // * This code implementation is the result of the scientific and * 19 // * technical work of the GEANT4 collaboratio 19 // * technical work of the GEANT4 collaboration. * 20 // * By using, copying, modifying or distri 20 // * By using, copying, modifying or distributing the software (or * 21 // * any work based on the software) you ag 21 // * any work based on the software) you agree to acknowledge its * 22 // * use in resulting scientific publicati 22 // * use in resulting scientific publications, and indicate your * 23 // * acceptance of all terms of the Geant4 Sof 23 // * acceptance of all terms of the Geant4 Software license. * 24 // ******************************************* 24 // ******************************************************************** 25 // 25 // 26 // G4PolynomialSolver 26 // G4PolynomialSolver 27 // 27 // 28 // Class description: 28 // Class description: 29 // 29 // 30 // G4PolynomialSolver allows the user to sol 30 // G4PolynomialSolver allows the user to solve a polynomial equation 31 // with a great precision. This is used by I 31 // with a great precision. This is used by Implicit Equation solver. 32 // 32 // 33 // The Bezier clipping method is used to sol 33 // The Bezier clipping method is used to solve the polynomial. 34 // 34 // 35 // How to use it: 35 // How to use it: 36 // Create a class that is the function to be 36 // Create a class that is the function to be solved. 37 // This class could have internal parameters 37 // This class could have internal parameters to allow to change 38 // the equation to be solved without recreat 38 // the equation to be solved without recreating a new one. 39 // 39 // 40 // Define a Polynomial solver, example: 40 // Define a Polynomial solver, example: 41 // G4PolynomialSolver<MyFunctionClass,G4doub 41 // G4PolynomialSolver<MyFunctionClass,G4double(MyFunctionClass::*)(G4double)> 42 // PolySolver (&MyFunction, 42 // PolySolver (&MyFunction, 43 // &MyFunctionClass::Function, 43 // &MyFunctionClass::Function, 44 // &MyFunctionClass::Derivativ 44 // &MyFunctionClass::Derivative, 45 // precision); 45 // precision); 46 // 46 // 47 // The precision is relative to the function 47 // The precision is relative to the function to solve. 48 // 48 // 49 // In MyFunctionClass, provide the function 49 // In MyFunctionClass, provide the function to solve and its derivative: 50 // Example of function to provide : 50 // Example of function to provide : 51 // 51 // 52 // x,y,z,dx,dy,dz,Rmin,Rmax are internal var 52 // x,y,z,dx,dy,dz,Rmin,Rmax are internal variables of MyFunctionClass 53 // 53 // 54 // G4double MyFunctionClass::Function(G4doub 54 // G4double MyFunctionClass::Function(G4double value) 55 // { 55 // { 56 // G4double Lx,Ly,Lz; 56 // G4double Lx,Ly,Lz; 57 // G4double result; 57 // G4double result; 58 // 58 // 59 // Lx = x + value*dx; 59 // Lx = x + value*dx; 60 // Ly = y + value*dy; 60 // Ly = y + value*dy; 61 // Lz = z + value*dz; 61 // Lz = z + value*dz; 62 // 62 // 63 // result = TorusEquation(Lx,Ly,Lz,Rmax,Rm 63 // result = TorusEquation(Lx,Ly,Lz,Rmax,Rmin); 64 // 64 // 65 // return result ; 65 // return result ; 66 // } 66 // } 67 // 67 // 68 // G4double MyFunctionClass::Derivative(G4do 68 // G4double MyFunctionClass::Derivative(G4double value) 69 // { 69 // { 70 // G4double Lx,Ly,Lz; 70 // G4double Lx,Ly,Lz; 71 // G4double result; 71 // G4double result; 72 // 72 // 73 // Lx = x + value*dx; 73 // Lx = x + value*dx; 74 // Ly = y + value*dy; 74 // Ly = y + value*dy; 75 // Lz = z + value*dz; 75 // Lz = z + value*dz; 76 // 76 // 77 // result = dx*TorusDerivativeX(Lx,Ly,Lz,R 77 // result = dx*TorusDerivativeX(Lx,Ly,Lz,Rmax,Rmin); 78 // result += dy*TorusDerivativeY(Lx,Ly,Lz, 78 // result += dy*TorusDerivativeY(Lx,Ly,Lz,Rmax,Rmin); 79 // result += dz*TorusDerivativeZ(Lx,Ly,Lz, 79 // result += dz*TorusDerivativeZ(Lx,Ly,Lz,Rmax,Rmin); 80 // 80 // 81 // return result; 81 // return result; 82 // } 82 // } 83 // 83 // 84 // Then to have a root inside an interval [I 84 // Then to have a root inside an interval [IntervalMin,IntervalMax] do the 85 // following: 85 // following: 86 // 86 // 87 // MyRoot = PolySolver.solve(IntervalMin,Int 87 // MyRoot = PolySolver.solve(IntervalMin,IntervalMax); 88 88 89 // Author: E.Medernach, 19.12.2000 - First imp 89 // Author: E.Medernach, 19.12.2000 - First implementation 90 // ------------------------------------------- 90 // -------------------------------------------------------------------- 91 #ifndef G4POL_SOLVER_HH 91 #ifndef G4POL_SOLVER_HH 92 #define G4POL_SOLVER_HH 1 92 #define G4POL_SOLVER_HH 1 93 93 94 #include "globals.hh" 94 #include "globals.hh" 95 95 96 template <class T, class F> 96 template <class T, class F> 97 class G4PolynomialSolver 97 class G4PolynomialSolver 98 { 98 { 99 public: 99 public: 100 G4PolynomialSolver(T* typeF, F func, F deriv 100 G4PolynomialSolver(T* typeF, F func, F deriv, G4double precision); 101 ~G4PolynomialSolver(); 101 ~G4PolynomialSolver(); 102 102 103 G4double solve(G4double IntervalMin, G4doubl 103 G4double solve(G4double IntervalMin, G4double IntervalMax); 104 104 105 private: 105 private: 106 G4double Newton(G4double IntervalMin, G4doub 106 G4double Newton(G4double IntervalMin, G4double IntervalMax); 107 // General Newton method with Bezier Clippin 107 // General Newton method with Bezier Clipping 108 108 109 // Works for polynomial of order less or equ 109 // Works for polynomial of order less or equal than 4. 110 // But could be changed to work for polynomi 110 // But could be changed to work for polynomial of any order providing 111 // that we find the bezier control points. 111 // that we find the bezier control points. 112 112 113 G4int BezierClipping(G4double* IntervalMin, 113 G4int BezierClipping(G4double* IntervalMin, G4double* IntervalMax); 114 // This is just one iteration of Bezier Clip 114 // This is just one iteration of Bezier Clipping 115 115 116 T* FunctionClass; 116 T* FunctionClass; 117 F Function; 117 F Function; 118 F Derivative; 118 F Derivative; 119 119 120 G4double Precision; 120 G4double Precision; 121 }; 121 }; 122 122 123 #include "G4PolynomialSolver.icc" 123 #include "G4PolynomialSolver.icc" 124 124 125 #endif 125 #endif 126 126