Mercurial > octave
view scripts/statistics/var.m @ 30997:5330efaf9476
Add optional second output to var and std (bug #62395)
* scripts/statistics/var.m: Add optional second output containing the mean
used to calculate the variance. Move weight isempty check ahead of vector
dimension isscalar check to avoid triggering incompatability error. Add BISTs
testing second output with different calling options. Add BIST testing empty
value passed as variance weight treated as zero. Add new output behavior to
docstring, and update function definitions to show the primary variable.
* scripts/statistics/std.m: Add passthrough for second output from var when
std called with two outputs. Add BISTs testing second output with different
calling options. Update docstring noting new output behavior.
* etc/NEWS.8.md: Note output changes to var and std under Matlab Compatability.
author | Nicholas R. Jankowski <jankowski.nicholas@gmail.com> |
---|---|
date | Thu, 12 May 2022 13:10:52 -0400 |
parents | 586262153621 |
children | 1bf26f913b9c |
line wrap: on
line source
######################################################################## ## ## 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{v} =} var (@var{x}) ## @deftypefnx {} {@var{v} =} var (@var{x}, @var{w}) ## @deftypefnx {} {@var{v} =} var (@var{x}, @var{w}, @var{dim}) ## @deftypefnx {} {@var{v} =} var (@var{x}, @var{w}, @qcode{"ALL"}) ## @deftypefnx {} {[@var{v}, @var{m}] =} var (@dots{}) ## 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. ## ## If requested the optional second output variable @var{mu} will contain the ## mean or weighted mean used to calcluate @var{v}, and will be the same size ## as @var{v}. ## @seealso{cov, std, skewness, kurtosis, moment} ## @end deftypefn function [v, mu] = 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 if (isempty (w)) w = 0; 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 (! 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])) v = NaN; mu = NaN; else output_size = sz; output_size(dim) = 1; v = NaN(output_size); mu = 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")) v = zeros (sz, "single"); mu = x; else v = zeros (sz); mu = x; endif endif else if (isscalar (w)) v = sumsq (center (x, dim), dim) / (n - 1 + w); if (nargout == 2) mu = mean (x, dim); endif 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) ./ den; v = 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) %!assert (var ([1 2 3;1 2 3], [], [1 2]), 0.8, 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 second output %!test <*62395> %! [~, m] = var (13); %! assert (m, 13); %! [~, m] = var (single(13)); %! assert (m, single(13)); %! [~, m] = var ([1, 2, 3; 3 2 1], []); %! assert (m, [2 2 2]); %! [~, m] = var ([1, 2, 3; 3 2 1], [], 1); %! assert (m, [2 2 2]); %! [~, m] = var ([1, 2, 3; 3 2 1], [], 2); %! assert (m, [2 2]'); %! [~, m] = var ([1, 2, 3; 3 2 1], [], 3); %! assert (m, [1 2 3; 3 2 1]); ## 2nd output, weighted inputs, vector dims %!test <*62395> %! [~, m] = var(5,99); %! assert (m, 5); %! [~, m] = var ([1:7], [1:7]); %! assert (m, 5); %! [~, m] = var ([eye(3)], [1:3]); %! assert (m, [1/6, 1/3, 0.5], eps); %! [~, m] = var (ones (2,2,2), [1:2], 3); %! assert (m, ones (2,2)); %! [~, m] = var ([1 2; 3 4], 0, 'all'); %! assert (m, 2.5, eps); %! [~, m] = var (reshape ([1:8], 2, 2, 2), 0, [1 3]); %! assert (m, [3.5, 5.5], eps); ## 2nd output, empty inputs %!test <*62395> %! [~, m] = var ([]); %! assert (m, NaN); %! [~, m] = var ([],[],1); %! assert (m, NaN(1,0)); %! [~, m] = var ([],[],2); %! assert (m, NaN(0,1)); %! [~, m] = var ([],[],3); %! assert (m, []); %! [~, m] = var (ones (1,3,0,2)); %! assert (m, NaN(1,1,0,2)); ## 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)