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25 // 25 //
26 // G4PolynomialSolver << 26 //
>> 27 // $Id: G4PolynomialSolver.hh,v 1.4 2006/06/29 18:59:52 gunter Exp $
>> 28 // GEANT4 tag $Name: geant4-08-01-patch-01 $
>> 29 //
>> 30 // class G4PolynomialSolver
27 // 31 //
28 // Class description: 32 // Class description:
29 // 33 //
30 // G4PolynomialSolver allows the user to sol 34 // G4PolynomialSolver allows the user to solve a polynomial equation
31 // with a great precision. This is used by I 35 // with a great precision. This is used by Implicit Equation solver.
32 // 36 //
33 // The Bezier clipping method is used to sol 37 // The Bezier clipping method is used to solve the polynomial.
34 // 38 //
35 // How to use it: 39 // How to use it:
36 // Create a class that is the function to be 40 // Create a class that is the function to be solved.
37 // This class could have internal parameters 41 // This class could have internal parameters to allow to change
38 // the equation to be solved without recreat 42 // the equation to be solved without recreating a new one.
39 // 43 //
40 // Define a Polynomial solver, example: 44 // Define a Polynomial solver, example:
41 // G4PolynomialSolver<MyFunctionClass,G4doub 45 // G4PolynomialSolver<MyFunctionClass,G4double(MyFunctionClass::*)(G4double)>
42 // PolySolver (&MyFunction, 46 // PolySolver (&MyFunction,
43 // &MyFunctionClass::Function, 47 // &MyFunctionClass::Function,
44 // &MyFunctionClass::Derivativ 48 // &MyFunctionClass::Derivative,
45 // precision); 49 // precision);
46 // 50 //
47 // The precision is relative to the function 51 // The precision is relative to the function to solve.
48 // 52 //
49 // In MyFunctionClass, provide the function 53 // In MyFunctionClass, provide the function to solve and its derivative:
50 // Example of function to provide : 54 // Example of function to provide :
51 // 55 //
52 // x,y,z,dx,dy,dz,Rmin,Rmax are internal var 56 // x,y,z,dx,dy,dz,Rmin,Rmax are internal variables of MyFunctionClass
53 // 57 //
54 // G4double MyFunctionClass::Function(G4doub 58 // G4double MyFunctionClass::Function(G4double value)
55 // { 59 // {
56 // G4double Lx,Ly,Lz; 60 // G4double Lx,Ly,Lz;
57 // G4double result; << 61 // G4double result;
58 // << 62 //
59 // Lx = x + value*dx; 63 // Lx = x + value*dx;
60 // Ly = y + value*dy; 64 // Ly = y + value*dy;
61 // Lz = z + value*dz; 65 // Lz = z + value*dz;
62 // << 66 //
63 // result = TorusEquation(Lx,Ly,Lz,Rmax,Rm 67 // result = TorusEquation(Lx,Ly,Lz,Rmax,Rmin);
64 // << 68 //
65 // return result ; << 69 // return result ;
66 // } << 70 // }
67 // << 71 //
68 // G4double MyFunctionClass::Derivative(G4do 72 // G4double MyFunctionClass::Derivative(G4double value)
69 // { 73 // {
70 // G4double Lx,Ly,Lz; 74 // G4double Lx,Ly,Lz;
71 // G4double result; << 75 // G4double result;
72 // << 76 //
73 // Lx = x + value*dx; 77 // Lx = x + value*dx;
74 // Ly = y + value*dy; 78 // Ly = y + value*dy;
75 // Lz = z + value*dz; 79 // Lz = z + value*dz;
76 // << 80 //
77 // result = dx*TorusDerivativeX(Lx,Ly,Lz,R 81 // result = dx*TorusDerivativeX(Lx,Ly,Lz,Rmax,Rmin);
78 // result += dy*TorusDerivativeY(Lx,Ly,Lz, 82 // result += dy*TorusDerivativeY(Lx,Ly,Lz,Rmax,Rmin);
79 // result += dz*TorusDerivativeZ(Lx,Ly,Lz, 83 // result += dz*TorusDerivativeZ(Lx,Ly,Lz,Rmax,Rmin);
80 // << 84 //
81 // return result; 85 // return result;
82 // } 86 // }
83 // << 87 //
84 // Then to have a root inside an interval [I 88 // Then to have a root inside an interval [IntervalMin,IntervalMax] do the
85 // following: 89 // following:
86 // 90 //
87 // MyRoot = PolySolver.solve(IntervalMin,Int 91 // MyRoot = PolySolver.solve(IntervalMin,IntervalMax);
>> 92 //
>> 93
>> 94 // History:
>> 95 //
>> 96 // - 19.12.00 E.Medernach, First implementation
>> 97 //
88 98
89 // Author: E.Medernach, 19.12.2000 - First imp <<
90 // ------------------------------------------- <<
91 #ifndef G4POL_SOLVER_HH 99 #ifndef G4POL_SOLVER_HH
92 #define G4POL_SOLVER_HH 1 << 100 #define G4POL_SOLVER_HH
93 101
94 #include "globals.hh" << 102 #include "globals.hh"
95 103
96 template <class T, class F> 104 template <class T, class F>
97 class G4PolynomialSolver << 105 class G4PolynomialSolver
98 { 106 {
99 public: << 107 public: // with description
100 G4PolynomialSolver(T* typeF, F func, F deriv << 108
>> 109 G4PolynomialSolver(T* typeF, F func, F deriv, G4double precision);
101 ~G4PolynomialSolver(); 110 ~G4PolynomialSolver();
>> 111
102 112
103 G4double solve(G4double IntervalMin, G4doubl << 113 G4double solve (G4double IntervalMin, G4double IntervalMax);
>> 114
>> 115 private:
104 116
105 private: << 117 G4double Newton (G4double IntervalMin, G4double IntervalMax);
106 G4double Newton(G4double IntervalMin, G4doub << 118 //General Newton method with Bezier Clipping
107 // General Newton method with Bezier Clippin <<
108 119
109 // Works for polynomial of order less or equ 120 // Works for polynomial of order less or equal than 4.
110 // But could be changed to work for polynomi 121 // But could be changed to work for polynomial of any order providing
111 // that we find the bezier control points. 122 // that we find the bezier control points.
112 123
113 G4int BezierClipping(G4double* IntervalMin, << 124 G4int BezierClipping(G4double *IntervalMin, G4double *IntervalMax);
114 // This is just one iteration of Bezier Clip << 125 // This is just one iteration of Bezier Clipping
115 126
116 T* FunctionClass; <<
117 F Function; <<
118 F Derivative; <<
119 127
>> 128 T* FunctionClass ;
>> 129 F Function ;
>> 130 F Derivative ;
>> 131
120 G4double Precision; 132 G4double Precision;
121 }; 133 };
122 134
123 #include "G4PolynomialSolver.icc" 135 #include "G4PolynomialSolver.icc"
124 136
125 #endif << 137 #endif
126 138