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1 // 1 //
2 // ******************************************* 2 // ********************************************************************
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24 // ******************************************* 21 // ********************************************************************
25 // 22 //
26 // G4PolynomialSolver << 23 //
>> 24 // $Id: G4PolynomialSolver.hh,v 1.3 2001/07/11 10:00:40 gunter Exp $
>> 25 // GEANT4 tag $Name: geant4-05-01-patch-01 $
>> 26 //
>> 27 // class G4PolynomialSolver
27 // 28 //
28 // Class description: 29 // Class description:
29 // 30 //
30 // G4PolynomialSolver allows the user to sol 31 // G4PolynomialSolver allows the user to solve a polynomial equation
31 // with a great precision. This is used by I 32 // with a great precision. This is used by Implicit Equation solver.
32 // 33 //
33 // The Bezier clipping method is used to sol 34 // The Bezier clipping method is used to solve the polynomial.
34 // 35 //
35 // How to use it: 36 // How to use it:
36 // Create a class that is the function to be 37 // Create a class that is the function to be solved.
37 // This class could have internal parameters 38 // This class could have internal parameters to allow to change
38 // the equation to be solved without recreat 39 // the equation to be solved without recreating a new one.
39 // 40 //
40 // Define a Polynomial solver, example: 41 // Define a Polynomial solver, example:
41 // G4PolynomialSolver<MyFunctionClass,G4doub 42 // G4PolynomialSolver<MyFunctionClass,G4double(MyFunctionClass::*)(G4double)>
42 // PolySolver (&MyFunction, 43 // PolySolver (&MyFunction,
43 // &MyFunctionClass::Function, 44 // &MyFunctionClass::Function,
44 // &MyFunctionClass::Derivativ 45 // &MyFunctionClass::Derivative,
45 // precision); 46 // precision);
46 // 47 //
47 // The precision is relative to the function 48 // The precision is relative to the function to solve.
48 // 49 //
49 // In MyFunctionClass, provide the function 50 // In MyFunctionClass, provide the function to solve and its derivative:
50 // Example of function to provide : 51 // Example of function to provide :
51 // 52 //
52 // x,y,z,dx,dy,dz,Rmin,Rmax are internal var 53 // x,y,z,dx,dy,dz,Rmin,Rmax are internal variables of MyFunctionClass
53 // 54 //
54 // G4double MyFunctionClass::Function(G4doub 55 // G4double MyFunctionClass::Function(G4double value)
55 // { 56 // {
56 // G4double Lx,Ly,Lz; 57 // G4double Lx,Ly,Lz;
57 // G4double result; << 58 // G4double result;
58 // << 59 //
59 // Lx = x + value*dx; 60 // Lx = x + value*dx;
60 // Ly = y + value*dy; 61 // Ly = y + value*dy;
61 // Lz = z + value*dz; 62 // Lz = z + value*dz;
62 // << 63 //
63 // result = TorusEquation(Lx,Ly,Lz,Rmax,Rm 64 // result = TorusEquation(Lx,Ly,Lz,Rmax,Rmin);
64 // << 65 //
65 // return result ; << 66 // return result ;
66 // } << 67 // }
67 // << 68 //
68 // G4double MyFunctionClass::Derivative(G4do 69 // G4double MyFunctionClass::Derivative(G4double value)
69 // { 70 // {
70 // G4double Lx,Ly,Lz; 71 // G4double Lx,Ly,Lz;
71 // G4double result; << 72 // G4double result;
72 // << 73 //
73 // Lx = x + value*dx; 74 // Lx = x + value*dx;
74 // Ly = y + value*dy; 75 // Ly = y + value*dy;
75 // Lz = z + value*dz; 76 // Lz = z + value*dz;
76 // << 77 //
77 // result = dx*TorusDerivativeX(Lx,Ly,Lz,R 78 // result = dx*TorusDerivativeX(Lx,Ly,Lz,Rmax,Rmin);
78 // result += dy*TorusDerivativeY(Lx,Ly,Lz, 79 // result += dy*TorusDerivativeY(Lx,Ly,Lz,Rmax,Rmin);
79 // result += dz*TorusDerivativeZ(Lx,Ly,Lz, 80 // result += dz*TorusDerivativeZ(Lx,Ly,Lz,Rmax,Rmin);
80 // << 81 //
81 // return result; 82 // return result;
82 // } 83 // }
83 // << 84 //
84 // Then to have a root inside an interval [I 85 // Then to have a root inside an interval [IntervalMin,IntervalMax] do the
85 // following: 86 // following:
86 // 87 //
87 // MyRoot = PolySolver.solve(IntervalMin,Int 88 // MyRoot = PolySolver.solve(IntervalMin,IntervalMax);
>> 89 //
>> 90
>> 91 // History:
>> 92 //
>> 93 // - 19.12.00 E.Medernach, First implementation
>> 94 //
88 95
89 // Author: E.Medernach, 19.12.2000 - First imp <<
90 // ------------------------------------------- <<
91 #ifndef G4POL_SOLVER_HH 96 #ifndef G4POL_SOLVER_HH
92 #define G4POL_SOLVER_HH 1 << 97 #define G4POL_SOLVER_HH
93 98
94 #include "globals.hh" << 99 #include "globals.hh"
95 100
96 template <class T, class F> 101 template <class T, class F>
97 class G4PolynomialSolver << 102 class G4PolynomialSolver
98 { 103 {
99 public: << 104 public: // with description
100 G4PolynomialSolver(T* typeF, F func, F deriv << 105
>> 106 G4PolynomialSolver(T* typeF, F func, F deriv, G4double precision);
101 ~G4PolynomialSolver(); 107 ~G4PolynomialSolver();
>> 108
102 109
103 G4double solve(G4double IntervalMin, G4doubl << 110 G4double solve (G4double IntervalMin, G4double IntervalMax);
>> 111
>> 112 private:
104 113
105 private: << 114 G4double Newton (G4double IntervalMin, G4double IntervalMax);
106 G4double Newton(G4double IntervalMin, G4doub << 115 //General Newton method with Bezier Clipping
107 // General Newton method with Bezier Clippin <<
108 116
109 // Works for polynomial of order less or equ 117 // Works for polynomial of order less or equal than 4.
110 // But could be changed to work for polynomi 118 // But could be changed to work for polynomial of any order providing
111 // that we find the bezier control points. 119 // that we find the bezier control points.
112 120
113 G4int BezierClipping(G4double* IntervalMin, << 121 G4int BezierClipping(G4double *IntervalMin, G4double *IntervalMax);
114 // This is just one iteration of Bezier Clip << 122 // This is just one iteration of Bezier Clipping
115 123
116 T* FunctionClass; <<
117 F Function; <<
118 F Derivative; <<
119 124
>> 125 T* FunctionClass ;
>> 126 F Function ;
>> 127 F Derivative ;
>> 128
120 G4double Precision; 129 G4double Precision;
121 }; 130 };
122 131
123 #include "G4PolynomialSolver.icc" 132 #include "G4PolynomialSolver.icc"
124 133
125 #endif << 134 #endif
126 135