Geant4  10.02.p02
G4GaussLegendreQ.hh
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27 // $Id: G4GaussLegendreQ.hh 67970 2013-03-13 10:10:06Z gcosmo $
28 //
29 // Class description:
30 //
31 // Class for Gauss-Legendre integration method
32 // Roots of ortogonal polynoms and corresponding weights are calculated based on
33 // iteration method (by bisection Newton algorithm). Constant values for initial
34 // approximations were derived from the book: M. Abramowitz, I. Stegun, Handbook
35 // of mathematical functions, DOVER Publications INC, New York 1965 ; chapters 9,
36 // 10, and 22 .
37 //
38 // ------------------------- CONSTRUCTORS: -------------------------------
39 //
40 // Constructor for GaussLegendre quadrature method. The value nLegendre set the
41 // accuracy required, i.e the number of points where the function pFunction will
42 // be evaluated during integration. The constructor creates the arrays for
43 // abscissas and weights that used in Gauss-Legendre quadrature method.
44 // The values a and b are the limits of integration of the pFunction.
45 //
46 // G4GaussLegendreQ( function pFunction,
47 // G4int nLegendre )
48 //
49 // -------------------------- METHODS: ---------------------------------------
50 //
51 // Returns the integral of the function to be pointed by fFunction between a and b,
52 // by 2*fNumber point Gauss-Legendre integration: the function is evaluated exactly
53 // 2*fNumber Times at interior points in the range of integration. Since the weights
54 // and abscissas are, in this case, symmetric around the midpoint of the range of
55 // integration, there are actually only fNumber distinct values of each.
56 //
57 // G4double Integral(G4double a, G4double b) const
58 //
59 // -----------------------------------------------------------------------
60 //
61 // Returns the integral of the function to be pointed by fFunction between a and b,
62 // by ten point Gauss-Legendre integration: the function is evaluated exactly
63 // ten Times at interior points in the range of integration. Since the weights
64 // and abscissas are, in this case, symmetric around the midpoint of the range of
65 // integration, there are actually only five distinct values of each
66 //
67 // G4double
68 // QuickIntegral(G4double a, G4double b) const
69 //
70 // ---------------------------------------------------------------------
71 //
72 // Returns the integral of the function to be pointed by fFunction between a and b,
73 // by 96 point Gauss-Legendre integration: the function is evaluated exactly
74 // ten Times at interior points in the range of integration. Since the weights
75 // and abscissas are, in this case, symmetric around the midpoint of the range of
76 // integration, there are actually only five distinct values of each
77 //
78 // G4double
79 // AccurateIntegral(G4double a, G4double b) const
80 
81 // ------------------------------- HISTORY --------------------------------
82 //
83 // 13.05.97 V.Grichine (Vladimir.Grichine@cern.chz0
84 
85 #ifndef G4GAUSSLEGENDREQ_HH
86 #define G4GAUSSLEGENDREQ_HH
87 
88 #include "G4VGaussianQuadrature.hh"
89 
91 {
92 public:
93  explicit G4GaussLegendreQ( function pFunction ) ;
94 
95 
96  G4GaussLegendreQ( function pFunction,
97  G4int nLegendre ) ;
98 
99  // Methods
100 
101  G4double Integral(G4double a, G4double b) const ;
102 
104 
106 
107 private:
108 
111 };
112 
113 #endif
G4double QuickIntegral(G4double a, G4double b) const
G4double Integral(G4double a, G4double b) const
G4GaussLegendreQ & operator=(const G4GaussLegendreQ &)
G4double a
Definition: TRTMaterials.hh:39
int G4int
Definition: G4Types.hh:78
G4GaussLegendreQ(function pFunction)
double G4double
Definition: G4Types.hh:76
G4double AccurateIntegral(G4double a, G4double b) const