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source: trunk/sources/ALGLIB/legendre.cs @ 2575

Last change on this file since 2575 was 2563, checked in by gkronber, 15 years ago

Updated ALGLIB to latest version. #751 (Plugin for for data-modeling with ANN (integrated into CEDMA))

File size: 3.8 KB
Line 
1/*************************************************************************
2>>> SOURCE LICENSE >>>
3This program is free software; you can redistribute it and/or modify
4it under the terms of the GNU General Public License as published by
5the Free Software Foundation (www.fsf.org); either version 2 of the
6License, or (at your option) any later version.
7
8This program is distributed in the hope that it will be useful,
9but WITHOUT ANY WARRANTY; without even the implied warranty of
10MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
11GNU General Public License for more details.
12
13A copy of the GNU General Public License is available at
14http://www.fsf.org/licensing/licenses
15
16>>> END OF LICENSE >>>
17*************************************************************************/
18
19using System;
20
21namespace alglib
22{
23    public class legendre
24    {
25        /*************************************************************************
26        Calculation of the value of the Legendre polynomial Pn.
27
28        Parameters:
29            n   -   degree, n>=0
30            x   -   argument
31
32        Result:
33            the value of the Legendre polynomial Pn at x
34        *************************************************************************/
35        public static double legendrecalculate(int n,
36            double x)
37        {
38            double result = 0;
39            double a = 0;
40            double b = 0;
41            int i = 0;
42
43            result = 1;
44            a = 1;
45            b = x;
46            if( n==0 )
47            {
48                result = a;
49                return result;
50            }
51            if( n==1 )
52            {
53                result = b;
54                return result;
55            }
56            for(i=2; i<=n; i++)
57            {
58                result = ((2*i-1)*x*b-(i-1)*a)/i;
59                a = b;
60                b = result;
61            }
62            return result;
63        }
64
65
66        /*************************************************************************
67        Summation of Legendre polynomials using Clenshaw’s recurrence formula.
68
69        This routine calculates
70            c[0]*P0(x) + c[1]*P1(x) + ... + c[N]*PN(x)
71
72        Parameters:
73            n   -   degree, n>=0
74            x   -   argument
75
76        Result:
77            the value of the Legendre polynomial at x
78        *************************************************************************/
79        public static double legendresum(ref double[] c,
80            int n,
81            double x)
82        {
83            double result = 0;
84            double b1 = 0;
85            double b2 = 0;
86            int i = 0;
87
88            b1 = 0;
89            b2 = 0;
90            for(i=n; i>=0; i--)
91            {
92                result = (2*i+1)*x*b1/(i+1)-(i+1)*b2/(i+2)+c[i];
93                b2 = b1;
94                b1 = result;
95            }
96            return result;
97        }
98
99
100        /*************************************************************************
101        Representation of Pn as C[0] + C[1]*X + ... + C[N]*X^N
102
103        Input parameters:
104            N   -   polynomial degree, n>=0
105
106        Output parameters:
107            C   -   coefficients
108        *************************************************************************/
109        public static void legendrecoefficients(int n,
110            ref double[] c)
111        {
112            int i = 0;
113
114            c = new double[n+1];
115            for(i=0; i<=n; i++)
116            {
117                c[i] = 0;
118            }
119            c[n] = 1;
120            for(i=1; i<=n; i++)
121            {
122                c[n] = c[n]*(n+i)/2/i;
123            }
124            for(i=0; i<=n/2-1; i++)
125            {
126                c[n-2*(i+1)] = -(c[n-2*i]*(n-2*i)*(n-2*i-1)/2/(i+1)/(2*(n-i)-1));
127            }
128        }
129    }
130}
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