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[CreaPhase.git] / octave_packages / m / specfun / betaln.m

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+## Copyright (C) 1998-2012 Nicol N. Schraudolph
+##
+## 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 {Mapping Function} {} betaln (@var{a}, @var{b})
+## Return the natural logarithm of the Beta function,
+## @tex
+## $$
+##  {\rm betaln} (a, b) = \ln (B (a,b)) \equiv \ln ({\Gamma (a) \Gamma (b) \over \Gamma (a + b)}).
+## $$
+## @end tex
+## @ifnottex
+##
+## @example
+## betaln (a, b) = log (beta (a, b))
+## @end example
+##
+## @end ifnottex
+## calculated in a way to reduce the occurrence of underflow.
+## @seealso{beta, betainc, gammaln}
+## @end deftypefn
+
+## Author:   Nicol N. Schraudolph <nic@idsia.ch>
+## Created:  06 Aug 1998
+## Keywords: log beta special function
+
+function retval = betaln (a, b)
+
+  if (nargin != 2)
+    print_usage ();
+  endif
+
+  retval = gammaln (a) + gammaln (b) - gammaln (a + b);
+
+endfunction
+
+
+%!assert (betaln (3,4), log (beta(3,4)),eps);
+
+%% Test input validation
+%!error (betaln (1))
+%!error (betaln (1,2,3))