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## -*- texinfo -*-
## @deftypefn {} {@var{lnb} =} betaln (@var{a}, @var{b})
## Compute the natural logarithm of the Beta function for real inputs @var{a}
## and @var{b}.
##
## @code{betaln} is defined as
## @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
## and is calculated in a way to reduce the occurrence of underflow.
##
## 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.
## @seealso{beta, betainc, betaincinv, gammaln}
## @end deftypefn

function lnb = betaln (a, b)

  if (nargin != 2)
    print_usage ();
  endif

  if (! isreal (a) || ! isreal (b))
    error ("betaln: A and B must be real");
  endif

  lnb = gammaln (a) + gammaln (b) - gammaln (a + b);

endfunction


%!assert (betaln (3,4), log (beta (3,4)), eps)

## Test input validation
%!error <Invalid call> betaln ()
%!error <Invalid call> betaln (1)
%!error <A and B must be real> betaln (1i, 2)
%!error <A and B must be real> betaln (2, 1i)