/usr/share/octave/packages/specfun-1.1.0/psi.m is in octave-specfun 1.1.0-1build1.
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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 | # Copyright (C) 2006 Sylvain Pelissier <sylvain.pelissier@gmail.com>
##
## 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 -*-
## @deftypefn {Function File} {@var{y} = } psi (@var{x})
## Compute the psi function, for each value of @var{x}.
##
## @verbatim
## d
## psi(x) = __ log(gamma(x))
## dx
## @end verbatim
##
## @seealso{gamma, gammainc, gammaln}
## @end deftypefn
function [y] = psi (x)
if (nargin != 1)
print_usage;
elseif (imag(x) != zeros(size(x)))
error("unable to handle complex arguments");
endif
h = 1e-9;
y = x;
y(x == 0) = -Inf;
y(x>0) = (gammaln(y(x>0)+h)-gammaln(y(x>0)-h))./(2.*h);
y(x<0) = (gammaln((1-y(x<0))+h)-gammaln((1-y(x<0))-h))./(2.*h) + pi.*cot(pi.*(1-y(x<0)));
endfunction
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