[2563] | 1 | /*************************************************************************
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| 2 | >>> SOURCE LICENSE >>>
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| 3 | This program is free software; you can redistribute it and/or modify
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| 4 | it under the terms of the GNU General Public License as published by
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| 5 | the Free Software Foundation (www.fsf.org); either version 2 of the
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| 6 | License, or (at your option) any later version.
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| 7 |
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| 8 | This program is distributed in the hope that it will be useful,
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| 9 | but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 10 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 11 | GNU General Public License for more details.
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| 12 |
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| 13 | A copy of the GNU General Public License is available at
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| 14 | http://www.fsf.org/licensing/licenses
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| 15 |
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| 16 | >>> END OF LICENSE >>>
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| 17 | *************************************************************************/
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| 18 |
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| 19 | using System;
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| 20 |
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| 21 | namespace alglib
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| 22 | {
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| 23 | public class hermite
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| 24 | {
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| 25 | /*************************************************************************
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| 26 | Calculation of the value of the Hermite polynomial.
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| 27 |
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| 28 | Parameters:
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| 29 | n - degree, n>=0
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| 30 | x - argument
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| 31 |
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| 32 | Result:
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| 33 | the value of the Hermite polynomial Hn at x
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| 34 | *************************************************************************/
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| 35 | public static double hermitecalculate(int n,
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| 36 | double x)
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| 37 | {
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| 38 | double result = 0;
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| 39 | int i = 0;
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| 40 | double a = 0;
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| 41 | double b = 0;
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| 42 |
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| 43 |
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| 44 | //
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| 45 | // Prepare A and B
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| 46 | //
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| 47 | a = 1;
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| 48 | b = 2*x;
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| 49 |
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| 50 | //
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| 51 | // Special cases: N=0 or N=1
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| 52 | //
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| 53 | if( n==0 )
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| 54 | {
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| 55 | result = a;
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| 56 | return result;
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| 57 | }
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| 58 | if( n==1 )
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| 59 | {
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| 60 | result = b;
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| 61 | return result;
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| 62 | }
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| 63 |
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| 64 | //
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| 65 | // General case: N>=2
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| 66 | //
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| 67 | for(i=2; i<=n; i++)
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| 68 | {
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| 69 | result = 2*x*b-2*(i-1)*a;
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| 70 | a = b;
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| 71 | b = result;
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| 72 | }
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| 73 | return result;
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| 74 | }
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| 75 |
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| 76 |
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| 77 | /*************************************************************************
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| 78 | Summation of Hermite polynomials using Clenshaws recurrence formula.
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| 79 |
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| 80 | This routine calculates
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| 81 | c[0]*H0(x) + c[1]*H1(x) + ... + c[N]*HN(x)
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| 82 |
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| 83 | Parameters:
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| 84 | n - degree, n>=0
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| 85 | x - argument
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| 86 |
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| 87 | Result:
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| 88 | the value of the Hermite polynomial at x
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| 89 | *************************************************************************/
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| 90 | public static double hermitesum(ref double[] c,
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| 91 | int n,
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| 92 | double x)
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| 93 | {
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| 94 | double result = 0;
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| 95 | double b1 = 0;
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| 96 | double b2 = 0;
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| 97 | int i = 0;
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| 98 |
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| 99 | b1 = 0;
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| 100 | b2 = 0;
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| 101 | for(i=n; i>=0; i--)
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| 102 | {
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| 103 | result = 2*(x*b1-(i+1)*b2)+c[i];
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| 104 | b2 = b1;
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| 105 | b1 = result;
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| 106 | }
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| 107 | return result;
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| 108 | }
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| 109 |
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| 110 |
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| 111 | /*************************************************************************
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| 112 | Representation of Hn as C[0] + C[1]*X + ... + C[N]*X^N
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| 113 |
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| 114 | Input parameters:
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| 115 | N - polynomial degree, n>=0
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| 116 |
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| 117 | Output parameters:
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| 118 | C - coefficients
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| 119 | *************************************************************************/
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| 120 | public static void hermitecoefficients(int n,
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| 121 | ref double[] c)
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| 122 | {
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| 123 | int i = 0;
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| 124 |
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| 125 | c = new double[n+1];
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| 126 | for(i=0; i<=n; i++)
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| 127 | {
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| 128 | c[i] = 0;
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| 129 | }
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| 130 | c[n] = Math.Exp(n*Math.Log(2));
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| 131 | for(i=0; i<=n/2-1; i++)
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| 132 | {
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| 133 | c[n-2*(i+1)] = -(c[n-2*i]*(n-2*i)*(n-2*i-1)/4/(i+1));
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| 134 | }
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| 135 | }
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| 136 | }
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| 137 | }
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