update packages

[CreaPhase.git] / octave_packages / m / statistics / distributions / kolmogorov_smirnov_cdf.m

diff --git a/octave_packages/m/statistics/distributions/kolmogorov_smirnov_cdf.m b/octave_packages/m/statistics/distributions/kolmogorov_smirnov_cdf.m
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+## Copyright (C) 2012 Rik Wehbring
+## Copyright (C) 1995-2012 Kurt Hornik
+##
+## This file is part of Octave.
+##
+## Octave is free software; you can redistribute it and/or modify it
+## under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 3 of the License, or (at
+## your option) any later version.
+##
+## Octave is distributed in the hope that it will be useful, but
+## WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+## General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with Octave; see the file COPYING.  If not, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} kolmogorov_smirnov_cdf (@var{x}, @var{tol})
+## Return the cumulative distribution function (CDF) at @var{x} of the 
+## Kolmogorov-Smirnov distribution,
+## @tex
+## $$ Q(x) = \sum_{k=-\infty}^\infty (-1)^k \exp (-2 k^2 x^2) $$
+## @end tex
+## @ifnottex
+##
+## @example
+## @group
+##          Inf
+## Q(x) =   SUM    (-1)^k exp (-2 k^2 x^2)
+##        k = -Inf
+## @end group
+## @end example
+##
+## @end ifnottex
+## @noindent
+## for @var{x} > 0.
+##
+## The optional parameter @var{tol} specifies the precision up to which
+## the series should be evaluated; the default is @var{tol} = @code{eps}.
+## @end deftypefn
+
+## Author: KH <Kurt.Hornik@wu-wien.ac.at>
+## Description: CDF of the Kolmogorov-Smirnov distribution
+
+function cdf = kolmogorov_smirnov_cdf (x, tol)
+
+  if (nargin < 1 || nargin > 2)
+    print_usage ();
+  endif
+
+  if (nargin == 1)
+    if (isa (x, "single"))
+      tol = eps ("single");
+    else
+      tol = eps;
+    endif
+  else
+    if (! (isscalar (tol) && (tol > 0)))
+      error ("kolmogorov_smirnov_cdf: TOL must be a positive scalar");
+    endif
+  endif
+
+  if (numel (x) == 0)
+    error ("kolmogorov_smirnov_cdf: X must not be empty");
+  endif
+
+  cdf = zeros (size (x));
+
+  ind = find (x > 0);
+  if (length (ind) > 0)
+    if (columns (ind) < rows (ind))
+      y = x(ind.');
+    else
+      y = x(ind);
+    endif
+    K   = ceil (sqrt (- log (tol) / 2) / min (y));
+    k   = (1:K)';
+    A   = exp (- 2 * k.^2 * y.^2);
+    odd = find (rem (k, 2) == 1);
+    A(odd,:) = -A(odd,:);
+    cdf(ind) = 1 + 2 * sum (A);
+  endif
+
+endfunction
+
+
+%% Test input validation
+%!error kolmogorov_smirnov_cdf ()
+%!error kolmogorov_smirnov_cdf (1,2,3)
+%!error kolmogorov_smirnov_cdf (1, ones(2))
+%!error kolmogorov_smirnov_cdf ([], 1)
+