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annotate scripts/statistics/distributions/kolmogorov_smirnov_cdf.m @ 20641:c3c052b9192a

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Improve performance and error reporting of betainv, gaminv (bug #34363). * betainv.m: Replace for loop with do-until loop. Shorten max loop cycles to 40, rather than 10,000. Issue warning if algorithm fails. * gaminv.m: Replace for loop with do-until loop. Shorten max loop cycles to 40, rather than 100. Issue warning if algorithm fails.
author Rik <rik@octave.org>
date Sun, 11 Oct 2015 16:55:17 -0700
parents d9341b422488
children
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1 ## Copyright (C) 2012 Rik Wehbring
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2 ## Copyright (C) 1995-2015 Kurt Hornik
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3 ##
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4 ## This file is part of Octave.
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5 ##
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6 ## Octave is free software; you can redistribute it and/or modify it
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7 ## under the terms of the GNU General Public License as published by
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8 ## the Free Software Foundation; either version 3 of the License, or (at
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9 ## your option) any later version.
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10 ##
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11 ## Octave is distributed in the hope that it will be useful, but
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 ## General Public License for more details.
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15 ##
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16 ## You should have received a copy of the GNU General Public License
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17 ## along with Octave; see the file COPYING. If not, see
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18 ## <http://www.gnu.org/licenses/>.
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19
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20 ## -*- texinfo -*-
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21 ## @deftypefn {Function File} {} kolmogorov_smirnov_cdf (@var{x}, @var{tol})
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22 ## Return the cumulative distribution function (CDF) at @var{x} of the
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23 ## Kolmogorov-Smirnov distribution.
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24 ##
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25 ## This is defined as
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26 ## @tex
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27 ## $$ Q(x) = \sum_{k=-\infty}^\infty (-1)^k \exp (-2 k^2 x^2) $$
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28 ## @end tex
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29 ## @ifnottex
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30 ##
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31 ## @example
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32 ## @group
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33 ## Inf
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34 ## Q(x) = SUM (-1)^k exp (-2 k^2 x^2)
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35 ## k = -Inf
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36 ## @end group
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37 ## @end example
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38 ##
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39 ## @end ifnottex
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40 ## @noindent
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41 ## for @var{x} > 0.
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42 ##
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43 ## The optional parameter @var{tol} specifies the precision up to which
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44 ## the series should be evaluated; the default is @var{tol} = @code{eps}.
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45 ## @end deftypefn
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46
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47 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
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48 ## Description: CDF of the Kolmogorov-Smirnov distribution
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49
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50 function cdf = kolmogorov_smirnov_cdf (x, tol)
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51
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52 if (nargin < 1 || nargin > 2)
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53 print_usage ();
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54 endif
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55
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56 if (nargin == 1)
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57 if (isa (x, "single"))
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58 tol = eps ("single");
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59 else
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60 tol = eps;
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61 endif
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62 else
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63 if (! (isscalar (tol) && (tol > 0)))
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64 error ("kolmogorov_smirnov_cdf: TOL must be a positive scalar");
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65 endif
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66 endif
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67
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68 if (numel (x) == 0)
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69 error ("kolmogorov_smirnov_cdf: X must not be empty");
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70 endif
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71
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72 cdf = zeros (size (x));
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73
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74 ind = find (x > 0);
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75 if (length (ind) > 0)
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76 if (columns (ind) < rows (ind))
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77 y = x(ind.');
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78 else
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79 y = x(ind);
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80 endif
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81 K = ceil (sqrt (- log (tol) / 2) / min (y));
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82 k = (1:K)';
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83 A = exp (- 2 * k.^2 * y.^2);
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84 odd = find (rem (k, 2) == 1);
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85 A(odd,:) = -A(odd,:);
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86 cdf(ind) = 1 + 2 * sum (A);
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87 endif
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88
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89 endfunction
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90
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91
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92 ## Test input validation
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93 %!error kolmogorov_smirnov_cdf ()
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94 %!error kolmogorov_smirnov_cdf (1,2,3)
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95 %!error kolmogorov_smirnov_cdf (1, ones (2))
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96 %!error kolmogorov_smirnov_cdf ([], 1)
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97