Mercurial > octave
view scripts/statistics/var.m @ 30564:796f54d4ddbf stable
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2021.
In all .txi and .texi files except gpl.txi and gpl.texi in the
doc/liboctave and doc/interpreter directories, change the copyright
to "Octave Project Developers", the same as used for other source
files. Update copyright notices for 2022 (not done since 2019). For
gpl.txi and gpl.texi, change the copyright notice to be "Free Software
Foundation, Inc." and leave the date at 2007 only because this file
only contains the text of the GPL, not anything created by the Octave
Project Developers.
Add Paul Thomas to contributors.in.
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Tue, 28 Dec 2021 18:22:40 -0500 |
parents | bc0de453fb6a |
children | 83f9f8bda883 9c7561dda313 |
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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 (@var{x}) ## @deftypefnx {} {} var (@var{x}, @var{w}) ## @deftypefnx {} {} var (@var{x}, @var{w}, @var{dim}) ## @deftypefnx {} {} var (@var{x}, @var{w}, @qcode{"ALL"}) ## 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 an array, compute the variance for each column and return ## them in a row vector (or for an n-D array, the result is returned as ## an array of dimension 1 x n x m x @dots{}). ## ## The optional argument @var{w} determines the weighting scheme to use. Valid ## values are ## ## @table @asis ## @item 0 [default]: ## Normalize with @math{N-1}. This provides the square root of the best ## unbiased estimator of the variance. ## ## @item 1: ## Normalize with @math{N}, this provides the square root of the second moment ## around the mean ## ## @item a vector: ## Compute the weighted variance with nonnegative scalar weights. The length of ## @var{w} must be equal to the size of @var{x} along dimension @var{dim}. ## @end table ## ## If @math{N} is equal to 1 the value of @var{W} is ignored and ## normalization by @math{N} is used. ## ## The optional variable @var{dim} forces @code{var} to operate over the ## specified dimension. @var{dim} can either be a scalar dimension or a vector ## of non-repeating dimensions over which to operate. Dimensions must be ## positive integers, and the variance is calculated over the array slice ## defined by @var{dim}. ## ## Specifying dimension @qcode{"ALL"} will force @code{var} to operate on all ## elements of @var{x}, and is equivalent to @code{var (@var{x}(:))}. ## ## When @var{dim} is a vector or @qcode{"ALL"}, @var{w} must be either 0 or 1. ## @seealso{cov, std, skewness, kurtosis, moment} ## @end deftypefn function retval = var (x, w = 0, dim) if (nargin < 1) print_usage (); elseif (nargin < 3) dim = []; endif if (! (isnumeric (x) || islogical (x))) error ("var: X must be a numeric vector or matrix"); endif nd = ndims (x); sz = size (x); emptydimflag = false; if (isempty (dim)) emptydimflag = true; ## Compatibliity hack for empty x, ndims==2 ## Find the first non-singleton dimension. (dim = find (sz != 1, 1)) || (dim = 1); else if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) if (isvector (dim) && isnumeric (dim) && all (dim > 0) && all (rem (dim, 1) == 0)) if (dim != unique (dim, "stable")) error (["var: vector DIM must contain non-repeating positive"... "integers"]); endif ## Check W if (! isscalar (w)) error ("var: W must be either 0 or 1 when DIM is a vector"); endif ## Reshape X to compute the variance over an array slice if (iscolumn (dim)) dim = transpose (dim); endif collapsed_dims = dim; dim = dim(end); ## Permute X to cluster the dimensions to collapse highest_dim = max ([nd, collapsed_dims]); perm_start = perm_end = [1:highest_dim]; perm_start(dim:end) = []; perm_start(ismember (perm_start, collapsed_dims)) = []; perm_end(1:dim) = []; perm_end(ismember (perm_end, collapsed_dims)) = []; perm = [perm_start, collapsed_dims, perm_end]; x = permute (x, perm); ## Collapse the given dimensions newshape = ones (1, highest_dim); newshape(1:nd) = sz; newshape(collapsed_dims(1:(end - 1))) = 1; newshape(dim) = prod (sz(collapsed_dims)); ## New X with collapsed dimensions x = reshape (x, newshape); elseif (ischar (dim) && strcmp (tolower (dim), "all")) ## Check W if (! isscalar (w)) error ("var: W must be either 0 or 1 when using 'ALL' as dimension"); endif ## "ALL" equals to collapsing all elements to a single vector x = x(:); dim = 1; sz = size (x); else error ("var: DIM must be a positive integer scalar, vector, or 'all'"); endif endif endif n = size (x, dim); if (isempty (w)) w = 0; elseif (! isvector (w) || ! isnumeric (w) || (isvector (w) && any (w < 0)) || (isscalar (w) && ((w != 0 && w != 1) && (n != 1)))) error ("var: W must be 0, 1, or a vector of positive integers"); endif if (isempty (x)) if (emptydimflag && isequal (sz, [0 0])) retval = NaN; else output_size = sz; output_size(dim) = 1; retval = NaN(output_size); endif else if (n == 1) if (! isscalar (w)) error (["var: the length of W must be equal to the size of X "... "in the dimension along which variance is calculated"]) else if (isa (x, "single")) retval = zeros (sz, "single"); else retval = zeros (sz); endif endif else if (isscalar (w)) retval = sumsq (center (x, dim), dim) / (n - 1 + w); else ## Weighted variance if (length (w) != n) error (["var: the length of W must be equal to the size of X "... "in the dimension along which variance is calculated"]); else if ((dim == 1 && rows (w) == 1) || (dim == 2 && columns (w) == 1)) w = transpose (w); elseif (dim > 2) newdims = [(ones (1, (dim - 1))), (length (w))]; w = reshape (w, newdims); endif den = sum (w); mu = sum (w .* x, dim) ./ sum (w); retval = sum (w .* ((x .- mu) .^ 2), dim) / den; endif endif endif 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]) %!assert (var (5, 99), 0) %!assert (var (5, 99, 1), 0) %!assert (var (5, 99, 2), 0) %!assert (var ([1:7], [1:7]), 3) %!assert (var ([eye(3)], [1:3]), [5/36, 2/9, 1/4], eps) %!assert (var (ones (2,2,2), [1:2], 3), [(zeros (2,2))]) %!assert (var ([1 2; 3 4], 0, 'all'), var ([1:4])) %!assert (var (reshape ([1:8], 2, 2, 2), 0, [1 3]), [17/3 17/3], eps) ##Test empty inputs %!assert (var ([]), NaN) %!assert (var ([],[],1), NaN(1,0)) %!assert (var ([],[],2), NaN(0,1)) %!assert (var ([],[],3), []) %!assert (var (ones (0,1)), NaN) %!assert (var (ones (1,0)), NaN) %!assert (var (ones (1,0), [], 1), NaN(1,0)) %!assert (var (ones (1,0), [], 2), NaN) %!assert (var (ones (1,0), [], 3), NaN(1,0)) %!assert (var (ones (0,1)), NaN) %!assert (var (ones (0,1), [], 1), NaN) %!assert (var (ones (0,1), [], 2), NaN(0,1)) %!assert (var (ones (0,1), [], 3), NaN(0,1)) %!assert (var (ones (1,3,0,2)), NaN(1,1,0,2)) %!assert (var (ones (1,3,0,2), [], 1), NaN(1,3,0,2)) %!assert (var (ones (1,3,0,2), [], 2), NaN(1,1,0,2)) %!assert (var (ones (1,3,0,2), [], 3), NaN(1,3,1,2)) %!assert (var (ones (1,3,0,2), [], 4), NaN(1,3,0)) ## Test input validation %!error <Invalid call> var () %!error <X must be a numeric> var (['A'; 'B']) %!error <W must be 0> var ([1 2 3], 2) %!error <W must be .* a vector of positive integers> var ([1 2], [-1 0]) %!error <W must be .* a vector of positive integers> var ([1 2], eye (2)) %!error <W must be either 0 or 1> var (ones (2, 2), [1 2], [1 2]) %!error <W must be either 0 or 1> var ([1 2], [1 2], 'all') %!error <the length of W must be> var ([1 2], [1 2 3]) %!error <the length of W must be> var (1, [1 2]) %!error <the length of W must be> var ([1 2], [1 2], 1) %!error <DIM must be a positive integer> var (1, [], ones (2,2)) %!error <DIM must be a positive integer> var (1, [], 1.5) %!error <DIM must be a positive integer> var (1, [], 0)