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########################################################################
##
## Copyright (C) 1994-2024 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## 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
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {@var{y} =} beta (@var{a}, @var{b})
## Compute the Beta function for real inputs @var{a} and @var{b}.
##
## The Beta function definition is
## @tex
## $$
## B (a, b) = {\Gamma (a) \Gamma (b) \over \Gamma (a + b)}.
## $$
## @end tex
## @ifnottex
##
## @example
## beta (a, b) = gamma (a) * gamma (b) / gamma (a + b).
## @end example
##
## @end ifnottex
##
## The Beta function can grow quite large and it is often more useful to work
## with the logarithm of the output rather than the function directly.
## @xref{XREFbetaln,,@code{betaln}}, for computing the logarithm of the Beta
## function in an efficient manner.
## @seealso{betaln, betainc, betaincinv}
## @end deftypefn
function y = beta (a, b)
if (nargin != 2)
print_usage ();
endif
if (! isreal (a) || ! isreal (b))
error ("beta: A and B must be real");
elseif (! size_equal (a, b) && numel (a) != 1 && numel (b) != 1)
error ("beta: A and B must have consistent sizes");
endif
y = real (exp (gammaln (a) + gammaln (b) - gammaln (a+b)));
endfunction
%!test
%! a = [1, 1.5, 2, 3];
%! b = [4, 3, 2, 1];
%! v1 = beta (a, b);
%! v2 = beta (b, a);
%! v3 = gamma (a).*gamma (b) ./ gamma (a+b);
%! assert (v1, v2, sqrt (eps));
%! assert (v2, v3, sqrt (eps));
%!assert (beta (1, 1), 1)
%!test
%! a = 2:10;
%! tol = 10 * max (a) * eps;
%! assert (-a, beta (-1./a, 1), tol);
%! assert (-a, beta (1, -1./a), tol);
%!test
%! a = 0.25 + (0:5) * 0.5;
%! tol = 10 * max (a) * eps;
%! assert (zeros (size (a)), beta (a, -a), tol);
%! assert (zeros (size (a)), beta (-a, a), tol);
%!error <Invalid call> beta ()
%!error <Invalid call> beta (1)
%!error <A and B must be real> beta (1i, 2)
%!error <A and B must be real> beta (2, 1i)
%!error <A and B must have consistent sizes> beta ([1 2], [1 2 3])
%!error <A and B must have consistent sizes> beta ([1 2 3], [1 2])
%!error <A and B must have consistent sizes> beta ([1 2 3], [1 2 3]')
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