Mercurial > octave
view scripts/general/bincoeff.m @ 30893:e1788b1a315f
maint: Use "fcn" as preferred abbreviation for "function" in m-files.
* accumarray.m, accumdim.m, quadl.m, quadv.m, randi.m, structfun.m,
__is_function__.m, uigetfile.m, uimenu.m, uiputfile.m, doc_cache_create.m,
colorspace_conversion_input_check.m, imageIO.m, argnames.m, vectorize.m,
vectorize.m, normest1.m, inputname.m, nthargout.m, display_info_file.m,
decic.m, ode15i.m, ode15s.m, ode23.m, ode23s.m, ode45.m, odeset.m,
check_default_input.m, integrate_adaptive.m, ode_event_handler.m,
runge_kutta_23.m, runge_kutta_23s.m, runge_kutta_45_dorpri.m,
runge_kutta_interpolate.m, starting_stepsize.m, __all_opts__.m, fminbnd.m,
fminsearch.m, fminunc.m, fsolve.m, fzero.m, sqp.m, fplot.m, plotyy.m,
__bar__.m, __ezplot__.m, flat_entry.html, profexport.m, movfun.m, bicg.m,
bicgstab.m, cgs.m, eigs.m, gmres.m, pcg.m, __alltohandles__.m, __sprand__.m,
qmr.m, tfqmr.m, dump_demos.m:
Replace "func", "fun", "fn" in documentation and variable names with "fcn".
author | Rik <rik@octave.org> |
---|---|
date | Mon, 04 Apr 2022 18:14:56 -0700 |
parents | 5d3faba0342e |
children | 597f3ee61a48 |
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######################################################################## ## ## Copyright (C) 1995-2022 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))