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G4PolynomialSolver.hh
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27 // $Id: G4PolynomialSolver.hh 67970 2013-03-13 10:10:06Z gcosmo $
28 //
29 // class G4PolynomialSolver
30 //
31 // Class description:
32 //
33 // G4PolynomialSolver allows the user to solve a polynomial equation
34 // with a great precision. This is used by Implicit Equation solver.
35 //
36 // The Bezier clipping method is used to solve the polynomial.
37 //
38 // How to use it:
39 // Create a class that is the function to be solved.
40 // This class could have internal parameters to allow to change
41 // the equation to be solved without recreating a new one.
42 //
43 // Define a Polynomial solver, example:
44 // G4PolynomialSolver<MyFunctionClass,G4double(MyFunctionClass::*)(G4double)>
45 // PolySolver (&MyFunction,
46 // &MyFunctionClass::Function,
47 // &MyFunctionClass::Derivative,
48 // precision);
49 //
50 // The precision is relative to the function to solve.
51 //
52 // In MyFunctionClass, provide the function to solve and its derivative:
53 // Example of function to provide :
54 //
55 // x,y,z,dx,dy,dz,Rmin,Rmax are internal variables of MyFunctionClass
56 //
57 // G4double MyFunctionClass::Function(G4double value)
58 // {
59 // G4double Lx,Ly,Lz;
60 // G4double result;
61 //
62 // Lx = x + value*dx;
63 // Ly = y + value*dy;
64 // Lz = z + value*dz;
65 //
66 // result = TorusEquation(Lx,Ly,Lz,Rmax,Rmin);
67 //
68 // return result ;
69 // }
70 //
71 // G4double MyFunctionClass::Derivative(G4double value)
72 // {
73 // G4double Lx,Ly,Lz;
74 // G4double result;
75 //
76 // Lx = x + value*dx;
77 // Ly = y + value*dy;
78 // Lz = z + value*dz;
79 //
80 // result = dx*TorusDerivativeX(Lx,Ly,Lz,Rmax,Rmin);
81 // result += dy*TorusDerivativeY(Lx,Ly,Lz,Rmax,Rmin);
82 // result += dz*TorusDerivativeZ(Lx,Ly,Lz,Rmax,Rmin);
83 //
84 // return result;
85 // }
86 //
87 // Then to have a root inside an interval [IntervalMin,IntervalMax] do the
88 // following:
89 //
90 // MyRoot = PolySolver.solve(IntervalMin,IntervalMax);
91 //
92 
93 // History:
94 //
95 // - 19.12.00 E.Medernach, First implementation
96 //
97 
98 #ifndef G4POL_SOLVER_HH
99 #define G4POL_SOLVER_HH
100 
101 #include "globals.hh"
102 
103 template <class T, class F>
105 {
106 public: // with description
107 
108  G4PolynomialSolver(T* typeF, F func, F deriv, G4double precision);
110 
111 
112  G4double solve (G4double IntervalMin, G4double IntervalMax);
113 
114 private:
115 
116  G4double Newton (G4double IntervalMin, G4double IntervalMax);
117  //General Newton method with Bezier Clipping
118 
119  // Works for polynomial of order less or equal than 4.
120  // But could be changed to work for polynomial of any order providing
121  // that we find the bezier control points.
122 
123  G4int BezierClipping(G4double *IntervalMin, G4double *IntervalMax);
124  // This is just one iteration of Bezier Clipping
125 
126 
127  T* FunctionClass ;
128  F Function ;
129  F Derivative ;
130 
131  G4double Precision;
132 };
133 
134 #include "G4PolynomialSolver.icc"
135 
136 #endif
int G4int
Definition: G4Types.hh:78
G4double solve(G4double IntervalMin, G4double IntervalMax)
G4PolynomialSolver(T *typeF, F func, F deriv, G4double precision)
double G4double
Definition: G4Types.hh:76