00001 // 00002 // ******************************************************************** 00003 // * License and Disclaimer * 00004 // * * 00005 // * The Geant4 software is copyright of the Copyright Holders of * 00006 // * the Geant4 Collaboration. It is provided under the terms and * 00007 // * conditions of the Geant4 Software License, included in the file * 00008 // * LICENSE and available at http://cern.ch/geant4/license . These * 00009 // * include a list of copyright holders. * 00010 // * * 00011 // * Neither the authors of this software system, nor their employing * 00012 // * institutes,nor the agencies providing financial support for this * 00013 // * work make any representation or warranty, express or implied, * 00014 // * regarding this software system or assume any liability for its * 00015 // * use. Please see the license in the file LICENSE and URL above * 00016 // * for the full disclaimer and the limitation of liability. * 00017 // * * 00018 // * This code implementation is the result of the scientific and * 00019 // * technical work of the GEANT4 collaboration. * 00020 // * By using, copying, modifying or distributing the software (or * 00021 // * any work based on the software) you agree to acknowledge its * 00022 // * use in resulting scientific publications, and indicate your * 00023 // * acceptance of all terms of the Geant4 Software license. * 00024 // ******************************************************************** 00025 // 00026 // 00027 // $Id$ 00028 // 00029 // class G4PolynomialSolver 00030 // 00031 // Class description: 00032 // 00033 // G4PolynomialSolver allows the user to solve a polynomial equation 00034 // with a great precision. This is used by Implicit Equation solver. 00035 // 00036 // The Bezier clipping method is used to solve the polynomial. 00037 // 00038 // How to use it: 00039 // Create a class that is the function to be solved. 00040 // This class could have internal parameters to allow to change 00041 // the equation to be solved without recreating a new one. 00042 // 00043 // Define a Polynomial solver, example: 00044 // G4PolynomialSolver<MyFunctionClass,G4double(MyFunctionClass::*)(G4double)> 00045 // PolySolver (&MyFunction, 00046 // &MyFunctionClass::Function, 00047 // &MyFunctionClass::Derivative, 00048 // precision); 00049 // 00050 // The precision is relative to the function to solve. 00051 // 00052 // In MyFunctionClass, provide the function to solve and its derivative: 00053 // Example of function to provide : 00054 // 00055 // x,y,z,dx,dy,dz,Rmin,Rmax are internal variables of MyFunctionClass 00056 // 00057 // G4double MyFunctionClass::Function(G4double value) 00058 // { 00059 // G4double Lx,Ly,Lz; 00060 // G4double result; 00061 // 00062 // Lx = x + value*dx; 00063 // Ly = y + value*dy; 00064 // Lz = z + value*dz; 00065 // 00066 // result = TorusEquation(Lx,Ly,Lz,Rmax,Rmin); 00067 // 00068 // return result ; 00069 // } 00070 // 00071 // G4double MyFunctionClass::Derivative(G4double value) 00072 // { 00073 // G4double Lx,Ly,Lz; 00074 // G4double result; 00075 // 00076 // Lx = x + value*dx; 00077 // Ly = y + value*dy; 00078 // Lz = z + value*dz; 00079 // 00080 // result = dx*TorusDerivativeX(Lx,Ly,Lz,Rmax,Rmin); 00081 // result += dy*TorusDerivativeY(Lx,Ly,Lz,Rmax,Rmin); 00082 // result += dz*TorusDerivativeZ(Lx,Ly,Lz,Rmax,Rmin); 00083 // 00084 // return result; 00085 // } 00086 // 00087 // Then to have a root inside an interval [IntervalMin,IntervalMax] do the 00088 // following: 00089 // 00090 // MyRoot = PolySolver.solve(IntervalMin,IntervalMax); 00091 // 00092 00093 // History: 00094 // 00095 // - 19.12.00 E.Medernach, First implementation 00096 // 00097 00098 #ifndef G4POL_SOLVER_HH 00099 #define G4POL_SOLVER_HH 00100 00101 #include "globals.hh" 00102 00103 template <class T, class F> 00104 class G4PolynomialSolver 00105 { 00106 public: // with description 00107 00108 G4PolynomialSolver(T* typeF, F func, F deriv, G4double precision); 00109 ~G4PolynomialSolver(); 00110 00111 00112 G4double solve (G4double IntervalMin, G4double IntervalMax); 00113 00114 private: 00115 00116 G4double Newton (G4double IntervalMin, G4double IntervalMax); 00117 //General Newton method with Bezier Clipping 00118 00119 // Works for polynomial of order less or equal than 4. 00120 // But could be changed to work for polynomial of any order providing 00121 // that we find the bezier control points. 00122 00123 G4int BezierClipping(G4double *IntervalMin, G4double *IntervalMax); 00124 // This is just one iteration of Bezier Clipping 00125 00126 00127 T* FunctionClass ; 00128 F Function ; 00129 F Derivative ; 00130 00131 G4double Precision; 00132 }; 00133 00134 #include "G4PolynomialSolver.icc" 00135 00136 #endif