Mercurial > octave
view scripts/general/bincoeff.m @ 33577:2506c2d30b32 bytecode-interpreter tip
maint: Merge default to bytecode-interpreter
author | Arun Giridhar <arungiridhar@gmail.com> |
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date | Sat, 11 May 2024 18:49:01 -0400 |
parents | 2e484f9f1f18 |
children |
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######################################################################## ## ## Copyright (C) 1995-2024 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{b} =} bincoeff (@var{n}, @var{k}) ## Return the binomial coefficient of @var{n} and @var{k}. ## ## The binomial coefficient is 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 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 <Invalid call> bincoeff () %!error <Invalid call> bincoeff (1) %!error bincoeff (ones (3), ones (2)) %!error bincoeff (ones (2), ones (3))