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