| [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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| [1228] | 28 | // GEANT4 tag $Name: geant4-09-03 $
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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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