Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / specfun-1.1.0 / psi.m

diff --git a/octave_packages/specfun-1.1.0/psi.m b/octave_packages/specfun-1.1.0/psi.m
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+++ b/octave_packages/specfun-1.1.0/psi.m
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+# 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