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25 // 25 //
26 // G4PolynomialSolver << 26 //
>> 27 // $Id$
>> 28 //
>> 29 // class G4PolynomialSolver
27 // 30 //
28 // Class description: 31 // Class description:
29 // 32 //
30 // G4PolynomialSolver allows the user to sol 33 // G4PolynomialSolver allows the user to solve a polynomial equation
31 // with a great precision. This is used by I 34 // with a great precision. This is used by Implicit Equation solver.
32 // 35 //
33 // The Bezier clipping method is used to sol 36 // The Bezier clipping method is used to solve the polynomial.
34 // 37 //
35 // How to use it: 38 // How to use it:
36 // Create a class that is the function to be 39 // Create a class that is the function to be solved.
37 // This class could have internal parameters 40 // This class could have internal parameters to allow to change
38 // the equation to be solved without recreat 41 // the equation to be solved without recreating a new one.
39 // 42 //
40 // Define a Polynomial solver, example: 43 // Define a Polynomial solver, example:
41 // G4PolynomialSolver<MyFunctionClass,G4doub 44 // G4PolynomialSolver<MyFunctionClass,G4double(MyFunctionClass::*)(G4double)>
42 // PolySolver (&MyFunction, 45 // PolySolver (&MyFunction,
43 // &MyFunctionClass::Function, 46 // &MyFunctionClass::Function,
44 // &MyFunctionClass::Derivativ 47 // &MyFunctionClass::Derivative,
45 // precision); 48 // precision);
46 // 49 //
47 // The precision is relative to the function 50 // The precision is relative to the function to solve.
48 // 51 //
49 // In MyFunctionClass, provide the function 52 // In MyFunctionClass, provide the function to solve and its derivative:
50 // Example of function to provide : 53 // Example of function to provide :
51 // 54 //
52 // x,y,z,dx,dy,dz,Rmin,Rmax are internal var 55 // x,y,z,dx,dy,dz,Rmin,Rmax are internal variables of MyFunctionClass
53 // 56 //
54 // G4double MyFunctionClass::Function(G4doub 57 // G4double MyFunctionClass::Function(G4double value)
55 // { 58 // {
56 // G4double Lx,Ly,Lz; 59 // G4double Lx,Ly,Lz;
57 // G4double result; << 60 // G4double result;
58 // << 61 //
59 // Lx = x + value*dx; 62 // Lx = x + value*dx;
60 // Ly = y + value*dy; 63 // Ly = y + value*dy;
61 // Lz = z + value*dz; 64 // Lz = z + value*dz;
62 // << 65 //
63 // result = TorusEquation(Lx,Ly,Lz,Rmax,Rm 66 // result = TorusEquation(Lx,Ly,Lz,Rmax,Rmin);
64 // << 67 //
65 // return result ; << 68 // return result ;
66 // } << 69 // }
67 // << 70 //
68 // G4double MyFunctionClass::Derivative(G4do 71 // G4double MyFunctionClass::Derivative(G4double value)
69 // { 72 // {
70 // G4double Lx,Ly,Lz; 73 // G4double Lx,Ly,Lz;
71 // G4double result; << 74 // G4double result;
72 // << 75 //
73 // Lx = x + value*dx; 76 // Lx = x + value*dx;
74 // Ly = y + value*dy; 77 // Ly = y + value*dy;
75 // Lz = z + value*dz; 78 // Lz = z + value*dz;
76 // << 79 //
77 // result = dx*TorusDerivativeX(Lx,Ly,Lz,R 80 // result = dx*TorusDerivativeX(Lx,Ly,Lz,Rmax,Rmin);
78 // result += dy*TorusDerivativeY(Lx,Ly,Lz, 81 // result += dy*TorusDerivativeY(Lx,Ly,Lz,Rmax,Rmin);
79 // result += dz*TorusDerivativeZ(Lx,Ly,Lz, 82 // result += dz*TorusDerivativeZ(Lx,Ly,Lz,Rmax,Rmin);
80 // << 83 //
81 // return result; 84 // return result;
82 // } 85 // }
83 // << 86 //
84 // Then to have a root inside an interval [I 87 // Then to have a root inside an interval [IntervalMin,IntervalMax] do the
85 // following: 88 // following:
86 // 89 //
87 // MyRoot = PolySolver.solve(IntervalMin,Int 90 // MyRoot = PolySolver.solve(IntervalMin,IntervalMax);
>> 91 //
>> 92
>> 93 // History:
>> 94 //
>> 95 // - 19.12.00 E.Medernach, First implementation
>> 96 //
88 97
89 // Author: E.Medernach, 19.12.2000 - First imp <<
90 // ------------------------------------------- <<
91 #ifndef G4POL_SOLVER_HH 98 #ifndef G4POL_SOLVER_HH
92 #define G4POL_SOLVER_HH 1 << 99 #define G4POL_SOLVER_HH
93 100
94 #include "globals.hh" << 101 #include "globals.hh"
95 102
96 template <class T, class F> 103 template <class T, class F>
97 class G4PolynomialSolver << 104 class G4PolynomialSolver
98 { 105 {
99 public: << 106 public: // with description
100 G4PolynomialSolver(T* typeF, F func, F deriv << 107
>> 108 G4PolynomialSolver(T* typeF, F func, F deriv, G4double precision);
101 ~G4PolynomialSolver(); 109 ~G4PolynomialSolver();
>> 110
102 111
103 G4double solve(G4double IntervalMin, G4doubl << 112 G4double solve (G4double IntervalMin, G4double IntervalMax);
>> 113
>> 114 private:
104 115
105 private: << 116 G4double Newton (G4double IntervalMin, G4double IntervalMax);
106 G4double Newton(G4double IntervalMin, G4doub << 117 //General Newton method with Bezier Clipping
107 // General Newton method with Bezier Clippin <<
108 118
109 // Works for polynomial of order less or equ 119 // Works for polynomial of order less or equal than 4.
110 // But could be changed to work for polynomi 120 // But could be changed to work for polynomial of any order providing
111 // that we find the bezier control points. 121 // that we find the bezier control points.
112 122
113 G4int BezierClipping(G4double* IntervalMin, << 123 G4int BezierClipping(G4double *IntervalMin, G4double *IntervalMax);
114 // This is just one iteration of Bezier Clip << 124 // This is just one iteration of Bezier Clipping
115 125
116 T* FunctionClass; <<
117 F Function; <<
118 F Derivative; <<
119 126
>> 127 T* FunctionClass ;
>> 128 F Function ;
>> 129 F Derivative ;
>> 130
120 G4double Precision; 131 G4double Precision;
121 }; 132 };
122 133
123 #include "G4PolynomialSolver.icc" 134 #include "G4PolynomialSolver.icc"
124 135
125 #endif << 136 #endif
126 137