Mercurial > octave
view scripts/statistics/var.m @ 30998:1bf26f913b9c
std.m, var.m: Cleanup functions.
* std.m: Re-write documentation to be in present tense per Octave convention.
Use lowercase for "all" parameter. Use Texinfo @. to end sentence ending with
capital N. Check for zero arguments to function and call print_usage().
Remove BIST tests for empty inputs and bug #62395 which are simply duplicating
tests in var.m. Remove input validation tests which are duplicating tests in
var.m.
* var.m: Re-write documentation to be in present tense per Octave convention.
Use lowercase for "all" parameter. Use Texinfo @. to end sentence ending with
capital N. Use default in function prototype for third input "dim" to eliminate
elseif branch in input validation. Put input validation as close to top of
function as possible. Rename "highest_dim" to "max_dim" for clarity & brevity.
Rename "ALL" to "all" in error() statements. Replace "strcmp (tolower (...))"
with strcmpi. Avoid slow call to isequal().
author | Rik <rik@octave.org> |
---|---|
date | Sat, 14 May 2022 18:03:35 -0700 |
parents | 5330efaf9476 |
children | ef3cd4d7691f |
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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{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 non-negative scalar weights. The length ## of @var{w} must equal 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(s). @var{dim} can either be a scalar dimension or a ## vector of non-repeating dimensions. 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. ## ## The optional second output variable @var{mu} contains the mean or weighted ## mean used to calculate @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 (); 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; # Compatibility hack for empty x, ndims==2 ## Find the first non-singleton dimension. (dim = find (sz != 1, 1)) || (dim = 1); else if (isscalar (dim)) if (dim < 1 || dim != fix (dim)) error ("var: DIM must be a positive integer scalar, vector, or 'all'"); endif elseif (isnumeric (dim)) if (! isvector (dim) && all (dim > 0) && all (rem (dim, 1) == 0)) error ("var: DIM must be a positive integer scalar, vector, or 'all'"); endif if (dim != unique (dim, "stable")) error ("var: vector DIM must contain non-repeating positive integers"); endif 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 = dim.'; endif collapsed_dims = dim; dim = dim(end); ## Permute X to cluster the dimensions to collapse max_dim = max ([nd, collapsed_dims]); perm_start = perm_end = [1:max_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, max_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) && strcmpi (dim, "all")) if (! isscalar (w)) error ("var: W must be either 0 or 1 when using 'all' as dimension"); endif ## "all" equates 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 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)) ## Empty matrix special case if (emptydimflag && nd == 2 && all (sz == [0, 0])) v = NaN; mu = NaN; else sz(dim) = 1; v = NaN (sz); mu = NaN (sz); endif elseif (n == 1) ## Scalar special case 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"]); endif if (isa (x, "single")) v = zeros (sz, "single"); mu = x; else v = zeros (sz); mu = x; endif else ## Regular algorithm if (isscalar (w)) v = sumsq (center (x, dim), dim) / (n - 1 + w); if (nargout == 2) mu = mean (x, dim); endif else ## Weighted variance if (numel (w) != n) error (["var: the length of W must be equal to the size of X " ... "in the dimension along which variance is calculated"]); endif if ((dim == 1 && isrow (w)) || (dim == 2 && iscolumn (w))) w = w.'; elseif (dim > 2) newdims = [ones(1, dim - 1), numel(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 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)