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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