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annotate scripts/specfun/expint.m @ 16584:2f766ceeb03e

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Add ellipj, ellipke, and expint functions from Octave Forge * ellipj.cc, ellipke.m, expint.m: New files. * libinterp/corefcn/module.mk (COREFCN_SRC): Add ellipj.cc to the list. * scripts/specfun/module.mk (specfun_FCN_FILES): Add ellipke.m and expint.m to the list. * __unimplemented__.m (missing_functions): Remove ellipj, ellipke, and expint from the list. * arith.txi: Include ellipj, ellipke, and expint docstrings. * NEWS: Mention ellipj, ellipke, and expint.
author Mike Miller <mtmiller@ieee.org>
date Wed, 24 Apr 2013 23:22:50 -0400
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children 1a3bfb14b5da
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16584
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1 ## Copyright (C) 2006 Sylvain Pelissier <sylvain.pelissier@gmail.com>
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2 ##
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3 ## This program is free software; you can redistribute it and/or modify it under
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4 ## the terms of the GNU General Public License as published by the Free Software
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5 ## Foundation; either version 3 of the License, or (at your option) any later
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6 ## version.
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7 ##
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8 ## This program is distributed in the hope that it will be useful, but WITHOUT
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9 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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10 ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
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11 ## details.
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12 ##
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13 ## You should have received a copy of the GNU General Public License along with
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14 ## this program; if not, see <http://www.gnu.org/licenses/>.
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15
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16 ## -*- texinfo -*-
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17 ## @deftypefn {Function File} {@var{y} =} expint (@var{x})
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18 ## Compute the exponential integral,
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19 ## @verbatim
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20 ## infinity
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21 ## /
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22 ## expint(x) = | exp(t)/t dt
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23 ## /
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24 ## x
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25 ## @end verbatim
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26 ## @seealso{expint_E1, expint_Ei}
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27 ## @end deftypefn
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28
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29 function y = expint(x)
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30 if (nargin != 1)
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31 print_usage;
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32 endif
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33 y = expint_E1(x);
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34 endfunction
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35
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36 ## -*- texinfo -*-
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37 ## @deftypefn {Function File} {@var{y} =} expint_E1 (@var{x})
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38 ## Compute the exponential integral,
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39 ## @verbatim
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40 ## infinity
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41 ## /
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42 ## expint(x) = | exp(t)/t dt
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43 ## /
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44 ## x
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45 ## @end verbatim
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46 ## @seealso{expint, expint_Ei}
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47 ## @end deftypefn
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48
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49 function y = expint_E1(x)
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50 if (nargin != 1)
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51 print_usage;
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52 endif
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53 y = x;
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54 y(imag(x) > 0 & imag(x) != 0) = -expint_Ei(-y(imag(x) > 0 & imag(x) != 0)) -i.*pi;
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55 y(imag(x) < 0 & imag(x) != 0) = -expint_Ei(-y(imag(x) < 0 & imag(x) != 0)) +i.*pi;
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56 y(real(x) >= 0 & imag(x)==0) = -expint_Ei(-y(real(x) >= 0 & imag(x)==0));
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57 y(real(x) < 0 & imag(x)==0) = -expint_Ei(-y(real(x) < 0 & imag(x)==0)) -i.*pi;
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58 endfunction
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59
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60 ## -*- texinfo -*-
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61 ## @deftypefn {Function File} {@var{y} =} expint_Ei (@var{x})
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62 ## Compute the exponential integral,
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63 ## @verbatim
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64 ## infinity
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65 ## /
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66 ## expint_Ei(x) = - | exp(t)/t dt
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67 ## /
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68 ## -x
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69 ## @end verbatim
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70 ## @seealso{expint, expint_E1}
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71 ## @end deftypefn
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72
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73 function y = expint_Ei(x)
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74 if (nargin != 1)
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75 print_usage;
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76 endif
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77 y = zeros(size(x));
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78 F = @(x) exp(-x)./x;
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79 s = prod(size(x));
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80 for t = 1:s;
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81 if(x(t)<0 && imag(x(t)) == 0)
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82 y(t) = -quad(F,-x(t),Inf);
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83 else
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84 if(abs(x(t)) > 2 && imag(x(t)) == 0)
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85 y(t) = expint_Ei(2) - quad(F,-x(t),-2);
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86 else
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87 if(abs(x(t)) >= 10)
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88 if(imag(x(t)) <= 0)
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89 a1 = 4.03640;
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90 a2 = 1.15198;
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91 b1 = 5.03637;
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92 b2 = 4.19160;
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93 y(t) = -(x(t).^2 - a1.*x(t) + a2)./((x(t).^2-b1.*x(t)+b2).*(-x(t)).*exp(-x(t)))-i.*pi;
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94 else
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95 y(t) = conj(expint_Ei(conj(x(t))));
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96 endif;
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97 ## Serie Expansion
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98 else
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99 for k = 1:100;
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100 y(t) = y(t) + x(t).^k./(k.*factorial(k));
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101 endfor
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102 y(t) = 0.577215664901532860606512090082402431 + log(x(t)) + y(t);
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103 endif
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104 endif
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105 endif
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106 endfor
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107 endfunction