/usr/share/octave/packages/interval-3.1.0/@infsupdec/gamma.m is in octave-interval 3.1.0-5.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 | ## Copyright 2015-2016 Oliver Heimlich
##
## This program 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.
##
## This program 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 this program; if not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @documentencoding UTF-8
## @defmethod {@@infsupdec} gamma (@var{X})
##
## Compute the gamma function.
##
## @tex
## $$
## {\rm gamma} (x) = \int_0^\infty t^(x-1) \exp (-t) dt
## $$
## @end tex
## @ifnottex
## @group
## @verbatim
## ∞
## /
## gamma (x) = | t^(x - 1) * exp (-t) dt
## /
## 0
## @end verbatim
## @end group
## @end ifnottex
##
## Accuracy: The result is a valid enclosure. The result is tightest for
## @var{X} >= -10.
##
## @example
## @group
## gamma (infsupdec (1.5))
## @result{} ans ⊂ [0.88622, 0.88623]_com
## @end group
## @end example
## @seealso{@@infsupdec/psi, @@infsupdec/gammaln, @@infsupdec/factorial}
## @end defmethod
## Author: Oliver Heimlich
## Keywords: interval
## Created: 2015-03-01
function result = gamma (x)
if (nargin ~= 1)
print_usage ();
return
endif
result = newdec (gamma (x.infsup));
## gamma is continuous where it is defined
undefined = (inf (x) <= 0 & fix (inf (x)) == inf (x)) | ...
(sup (x) <= 0 & fix (sup (x)) == sup (x)) | ...
(inf (x) < 0 & ceil (inf (x)) <= floor (sup (x)));
result.dec(undefined) = _trv ();
result.dec = min (result.dec, x.dec);
endfunction
%!# from the documentation string
%!assert (isequal (gamma (infsupdec (1.5)), infsupdec ("[0x1.C5BF891B4EF6Ap-1, 0x1.C5BF891B4EF6Bp-1]_com")));
|