update packages

[CreaPhase.git] / octave_packages / m / miscellaneous / bincoeff.m

diff --git a/octave_packages/m/miscellaneous/bincoeff.m b/octave_packages/m/miscellaneous/bincoeff.m
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+## Copyright (C) 1995-2012 Kurt Hornik
+##
+## 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} {} bincoeff (@var{n}, @var{k})
+## Return the binomial coefficient of @var{n} and @var{k}, defined as
+## @tex
+## $$
+##  {n \choose k} = {n (n-1) (n-2) \cdots (n-k+1) \over k!}
+## $$
+## @end tex
+## @ifnottex
+##
+## @example
+## @group
+##  /   \
+##  | n |    n (n-1) (n-2) @dots{} (n-k+1)
+##  |   |  = -------------------------
+##  | k |               k!
+##  \   /
+## @end group
+## @end example
+##
+## @end ifnottex
+## For example:
+##
+## @example
+## @group
+## bincoeff (5, 2)
+##    @result{} 10
+## @end group
+## @end example
+##
+## In most cases, the @code{nchoosek} function is faster for small
+## scalar integer arguments.  It also warns about loss of precision for
+## big arguments.
+##
+## @seealso{nchoosek}
+## @end deftypefn
+
+## Author: KH <Kurt.Hornik@wu-wien.ac.at>
+## Created: 8 October 1994
+## Adapted-By: jwe
+
+function b = bincoeff (n, k)
+
+  if (nargin != 2)
+    print_usage ();
+  endif
+
+  [retval, n, k] = common_size (n, k);
+  if (retval > 0)
+    error ("bincoeff: N and K must be of common size or scalars");
+  endif
+
+  if (iscomplex (n) || iscomplex (k))
+    error ("bincoeff: N and K must not be complex");
+  endif
+
+  b = zeros (size (n));
+
+  ok = (k >= 0) & (k == fix (k)) & (! isnan (n));
+  b(! ok) = NaN;
+
+  n_int = (n == fix (n));
+  idx = n_int & (n < 0) & ok;
+  b(idx) = (-1) .^ k(idx) .* exp (gammaln (abs (n(idx)) + k(idx))
+                                  - gammaln (k(idx) + 1)
+                                  - gammaln (abs (n(idx))));
+
+  idx = (n >= k) & ok;
+  b(idx) = exp (gammaln (n(idx) + 1)
+                - gammaln (k(idx) + 1)
+                - gammaln (n(idx) - k(idx) + 1));
+
+  idx = (! n_int) & (n < k) & ok;
+  b(idx) = (1/pi) * exp (gammaln (n(idx) + 1)
+                         - gammaln (k(idx) + 1)
+                         + gammaln (k(idx) - n(idx))
+                         + log (sin (pi * (n(idx) - k(idx) + 1))));
+
+  ## Clean up rounding errors.
+  b(n_int) = round (b(n_int));
+
+  idx = ! n_int;
+  b(idx) = real (b(idx));
+
+endfunction
+
+
+%!assert(bincoeff (4, 2), 6)
+%!assert(bincoeff (2, 4), 0)
+%!assert(bincoeff (-4, 2), 10)
+%!assert(bincoeff (5, 2), 10)
+%!assert(bincoeff (50, 6), 15890700)
+%!assert(bincoeff (0.4, 2), -.12, 8*eps)
+
+%!assert(bincoeff ([4 NaN 4], [-1, 2, 2.5]), NaN (1, 3))
+
+%% Test input validation
+%!error bincoeff ();
+%!error bincoeff (1, 2, 3);
+%!error bincoeff (ones(3),ones(2))
+%!error bincoeff (ones(2),ones(3))
+