Mercurial > octave
view scripts/statistics/var.m @ 27919:1891570abac8
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2020.
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Mon, 06 Jan 2020 22:29:51 -0500 |
parents | b442ec6dda5c |
children | bd51beb6205e |
line wrap: on
line source
## Copyright (C) 1995-2020 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this distribution ## or <https://octave.org/COPYRIGHT.html/>. ## ## ## 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 (@var{x}) ## @deftypefnx {} {} var (@var{x}, @var{opt}) ## @deftypefnx {} {} var (@var{x}, @var{opt}, @var{dim}) ## Compute the variance of the elements of the vector @var{x}. ## ## The variance is defined as ## @tex ## $$ ## {\rm var} (x) = \sigma^2 = {\sum_{i=1}^N (x_i - \bar{x})^2 \over N - 1} ## $$ ## where $\bar{x}$ is the mean value of @var{x} and $N$ is the number of ## elements of @var{x}. ## ## @end tex ## @ifnottex ## ## @example ## @group ## var (@var{x}) = 1/(N-1) SUM_i (@var{x}(i) - mean(@var{x}))^2 ## @end group ## @end example ## ## @noindent ## where @math{N} is the length of the @var{x} vector. ## ## @end ifnottex ## If @var{x} is a matrix, compute the variance for each column and return ## them in a row vector. ## ## The argument @var{opt} determines the type of normalization to use. ## Valid values are ## ## @table @asis ## @item 0: ## normalize with @math{N-1}, provides the best unbiased estimator of the ## variance [default] ## ## @item 1: ## normalizes with @math{N}, this provides the second moment around the mean ## @end table ## ## If @math{N} is equal to 1 the value of @var{opt} is ignored and ## normalization by @math{N} is used. ## ## If the optional argument @var{dim} is given, operate along this dimension. ## @seealso{cov, std, skewness, kurtosis, moment} ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.ac.at> ## Description: Compute variance function retval = var (x, opt = 0, dim) if (nargin < 1 || nargin > 3) print_usage (); endif if (! (isnumeric (x) || islogical (x))) error ("var: X must be a numeric vector or matrix"); endif if (isempty (opt)) opt = 0; elseif (opt != 0 && opt != 1) error ("var: normalization OPT must be 0 or 1"); endif nd = ndims (x); sz = size (x); if (nargin < 3) ## Find the first non-singleton dimension. (dim = find (sz > 1, 1)) || (dim = 1); else if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) error ("var: DIM must be an integer and a valid dimension"); endif endif n = size (x, dim); if (n == 1) if (isa (x, "single")) retval = zeros (sz, "single"); else retval = zeros (sz); endif elseif (numel (x) > 0) retval = sumsq (center (x, dim), dim) / (n - 1 + opt); else error ("var: X must not be empty"); endif endfunction %!assert (var (13), 0) %!assert (var (single (13)), single (0)) %!assert (var ([1,2,3]), 1) %!assert (var ([1,2,3], 1), 2/3, eps) %!assert (var ([1,2,3], [], 1), [0,0,0]) %!assert (var ([1,2,3], [], 3), [0,0,0]) ## Test input validation %!error var () %!error var (1,2,3,4) %!error <X must be a numeric> var (['A'; 'B']) %!error <OPT must be 0 or 1> var (1, -1) %!error <FLAG must be 0 or 1> skewness (1, 2) %!error <FLAG must be 0 or 1> skewness (1, [1 0]) %!error <DIM must be an integer> var (1, [], ones (2,2)) %!error <DIM must be an integer> var (1, [], 1.5) %!error <DIM must be .* a valid dimension> var (1, [], 0) %!error <X must not be empty> var ([], 1)