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25 //
26 // G4GaussLegendreQ
27 //
28 // Class description:
29 //
30 // Class for Gauss-Legendre integration method
31 // Roots of ortogonal polynoms and corresponding weights are calculated based on
32 // iteration method (by bisection Newton algorithm). Constant values for initial
33 // approximations were derived from the book:
34 // M. Abramowitz, I. Stegun, Handbook of mathematical functions,
35 // DOVER Publications INC, New York 1965 ; chapters 9, 10, and 22.
36
37 // Author: V.Grichine, 13.05.1997
38 // --------------------------------------------------------------------
39 #ifndef G4GAUSSLEGENDREQ_HH
40 #define G4GAUSSLEGENDREQ_HH 1
41
42 #include "G4VGaussianQuadrature.hh"
43
44 class G4GaussLegendreQ : public G4VGaussianQuadrature
45 {
46 public:
47 explicit G4GaussLegendreQ(function pFunction);
48
49 G4GaussLegendreQ(function pFunction, G4int nLegendre);
50 // Constructor for GaussLegendre quadrature method. The value nLegendre set
51 // the accuracy required, i.e the number of points where the function
52 // pFunction will be evaluated during integration. The constructor creates
53 // the arrays for abscissas and weights that used in Gauss-Legendre
54 // quadrature method.
55 // The values a and b are the limits of integration of the pFunction.
56
57 G4GaussLegendreQ(const G4GaussLegendreQ&) = delete;
58 G4GaussLegendreQ& operator=(const G4GaussLegendreQ&) = delete;
59
60 G4double Integral(G4double a, G4double b) const;
61 // Returns the integral of the function to be pointed by fFunction between a
62 // and b, by 2*fNumber point Gauss-Legendre integration: the function is
63 // evaluated exactly 2*fNumber Times at interior points in the range of
64 // integration. Since the weights and abscissas are, in this case, symmetric
65 // around the midpoint of the range of integration, there are actually only
66 // fNumber distinct values of each.
67
68 G4double QuickIntegral(G4double a, G4double b) const;
69 // Returns the integral of the function to be pointed by fFunction between a
70 // and b, by ten point Gauss-Legendre integration: the function is evaluated
71 // exactly ten Times at interior points in the range of integration. Since
72 // the weights and abscissas are, in this case, symmetric around the midpoint
73 // of the range of integration, there are actually only five distinct values
74 // of each.
75
76 G4double AccurateIntegral(G4double a, G4double b) const;
77 // Returns the integral of the function to be pointed by fFunction between a
78 // and b, by 96 point Gauss-Legendre integration: the function is evaluated
79 // exactly ten Times at interior points in the range of integration. Since
80 // the weights and abscissas are, in this case, symmetric around the midpoint
81 // of the range of integration, there are actually only five distinct values
82 // of each.
83 };
84
85 #endif
86