1 # Copyright (C) 2006 Sylvain Pelissier <sylvain.pelissier@gmail.com>
3 ## This program is free software; you can redistribute it and/or modify
4 ## it under the terms of the GNU General Public License as published by
5 ## the Free Software Foundation; either version 3 of the License, or
6 ## (at your option) any later version.
8 ## This program is distributed in the hope that it will be useful,
9 ## but WITHOUT ANY WARRANTY; without even the implied warranty of
10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
11 ## GNU General Public License for more details.
13 ## You should have received a copy of the GNU General Public License
14 ## along with this program; If not, see <http://www.gnu.org/licenses/>.
17 ## @deftypefn {Function File} {@var{y} = } psi (@var{x})
18 ## Compute the psi function, for each value of @var{x}.
22 ## psi(x) = __ log(gamma(x))
26 ## @seealso{gamma, gammainc, gammaln}
29 function [y] = psi (x)
33 elseif (imag(x) != zeros(size(x)))
34 error("unable to handle complex arguments");
40 y(x>0) = (gammaln(y(x>0)+h)-gammaln(y(x>0)-h))./(2.*h);
41 y(x<0) = (gammaln((1-y(x<0))+h)-gammaln((1-y(x<0))-h))./(2.*h) + pi.*cot(pi.*(1-y(x<0)));