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