Mercurial > octave
view scripts/statistics/iqr.m @ 30353:212461a26e9c stable
doc: grammarcheck m-files in scripts/ directory ahead of 7.1 release.
* Map.m, disable_diagonal_matrix.m, disable_permutation_matrix.m,
disable_range.m, warning_ids.m, colormap.m, inputParser.m, jupyter_notebook.m,
stem3.m, print.m, eigs.m, iqr.m, validatestring.m, weboptions.m:
grammarcheck m-files ahead of 7.1 release.
author | Rik <rik@octave.org> |
---|---|
date | Wed, 24 Nov 2021 14:57:21 -0800 |
parents | 01de0045b2e3 |
children | 1c114a55f4fb |
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######################################################################## ## ## Copyright (C) 1995-2021 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{Z} =} iqr (@var{x}) ## @deftypefnx {} {@var{Z} =} iqr (@var{x}, @var{dim}) ## @deftypefnx {} {@var{Z} =} iqr (@var{x}, @qcode{"ALL"}) ## Return the interquartile range of @var{x}, defined as the distance between ## the 25th and 75th percentile values of @var{x} calculated using: ## quantile (x, [0.25 0.75]) ## ## If @var{x} is a vector, @code{iqr (@var{x})} will operate on the data in ## @var{x}. ## ## If @var{x} is a matrix, @code{iqr (@var{x})} will operate independently on ## each column in @var{x} returning a row vector @var{Z}. ## ## If @var{x} is a n-dimensional array, @code{iqr (@var{x})} will operate ## independently on the first non-singleton dimension in @var{x}, returning an ## array @var{Z} the same shape as @var{x} with the non-singleton dimenion ## reduced to 1. ## ## The optional variable @var{dim} can be used to force @code{iqr} 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. In either case ## @var{dim} must be positive integers. A vector @var{dim} concatenates all ## specified diminsions for independent operation by @code{iqr}. ## ## Specifying dimension @qcode{"ALL"} will force @code{iqr} to operate ## on all elements of @var{x}, and is equivalent to @code{iqr (@var{x}(:))}. ## Similarly, specifying a vector dimension including all non-singleton ## dimensions of @var{x} is equivalent to @code{iqr (@var{x}, @qcode{"ALL"})}. ## ## If @var{x} is a scalar, or only singleton dimensions are specified for ## @var{dim}, the output will be @code{zeros (size (@var{x}))}. ## ## As a measure of dispersion, the interquartile range is less affected by ## outliers than either @code{range} or @code{std}. ## ## @seealso{bounds, mad, range, std, prctile, quantile} ## @end deftypefn ## TODO: When Probability Distribution Objects are implemented, enable ## handling for those object types. function z = iqr (x, dim) ## input checks if (nargin < 1) print_usage (); elseif (nargin < 2) dim = []; endif if (! (isnumeric (x) || islogical (x))) error ("iqr: X must be a numeric vector or matrix"); endif vecdim_flag = false; nd = ndims (x); sz = size (x); if isempty (dim) ## Find first non-singleton dimension. if (max (sz) == 1) dim = 2; else dim = find ((sz > 1), 1); endif else if (isvector (dim) && isnumeric (dim) && all (dim > 0) && all (rem (dim, 1) == 0)) if (((num_vecdims = numel (dim)) > 1) && all (diff (sort (dim)))) ## DIM must be 1D and non repeating. ## Detect trivial case of DIM being all dimensions (same as "all"). highest_dim = (max (nd, max (dim))); if ((num_vecdims == nd) && (highest_dim == nd)) x = x(:); sz = size (x); dim = 1; else ## Move dimensions for operation to the front, keeping the order of ## the remaining dimensions. ## Reshape those into a single dimension. ## Process as normal for a dim1 iqr on X, reshape when done. vecdim_flag = true; ## flag for final reshape if (iscolumn (dim)) dim = dim.'; endif ## Permutation vector with DIM at front perm = [1:highest_dim]; perm(dim) = []; perm = [dim, perm]; ## Reshape X to put dims to process at front. x = permute (x, perm); sz_x_new = size (x); ## Preserve trailing singletons when dim > ndims (x). sz_x_new = [sz_x_new, ones(1, highest_dim - numel (sz_x_new))]; newshape = [prod(sz_x_new(1:num_vecdims)), ... ones(1, (num_vecdims-1)), ... sz_x_new((num_vecdims+1):end)]; if (numel (newshape) == 1) newshape = [newshape, 1]; endif ## Collapse dimensions to be processses into single column. x = reshape (x, newshape); ## Operate column-wise. dim = 1; endif elseif (! isscalar (dim)) error ("iqr: vector DIM must contain non-repeating positive integers"); endif elseif (strcmp (tolower (dim), "all")) ## "ALL" simplifies to collapsing all elements to single vector x = x(:); dim = 1; sz = size (x); else error ("iqr: DIM must be a positive integer scalar, vector, or 'all'"); endif endif if (((dim > nd) || (sz(dim) == 1)) && all (isfinite (x))) ## shortcut easy zeros z = zeros (sz); elseif (iscolumn (x) && (dim == 1)) ## detect col vector with quantile/diff dim requirement mismatch z = abs (diff (quantile (x, [0.25, 0.75], 1), [], 2)); else z = abs (diff (quantile (x, [0.25, 0.75], dim), [], dim)); endif if (vecdim_flag) z = ipermute (z, perm); endif endfunction %!assert (iqr (17), 0) %!assert (iqr (17, 1), 0) %!assert (iqr (17, 4), 0) %!assert (iqr (1:3), 1.5) %!assert (iqr (1:4), 2) %!assert (iqr (1:5), 2.5) %!assert (iqr (1:10), 5) %!assert (iqr ((1:10).'), 5) %!assert (iqr (1:10, 2), 5) %!assert (iqr (1:10, 1), zeros(1, 10)) %!assert (iqr (1:10, 3), zeros(1, 10)) %!assert (iqr ([1:5; 2:6], "all"), 3) %!test %! x = reshape (1:6, [1 2 3]); %! assert (iqr (x), ones (1, 1, 3)); %! assert (iqr (x, 1), zeros (1, 2, 3)); %! assert (iqr (x, 2), ones( 1, 1, 3)); %! assert (iqr (x, 3), [3 3]); ## n-D arrays %!test %! x = magic (4); x = cat (3,x, 2*x, 3*x); x = cat (4, x, 2*x); %! y = cat (3, 8*[1 1 1 1], 16*[1 1 1 1], 24*[1 1 1 1]); %! assert (iqr (x), cat (4, y, 2*y)); %! assert (iqr (x, 1), cat (4, y, 2*y)); %! y = cat (3, 4*[3 1 1 3].', 8*[3 1 1 3].', 12*[3 1 1 3].'); %! assert (iqr (x, 2), cat (4, y, 2*y)); %! y = [24 3 4.5 19.5; 7.5 16.5 15 12; 13.5 10.5 9, 18; 6 21 22.5 1.5]; %! assert (iqr (x, 3), cat (4, y, 2*y)); %! y = [16 2 3 13; 5 11 10 8; 9 7 6 12; 4 14 15 1]; %! assert (iqr (x, 4), cat (3, y, 2*y, 3*y)); %! assert (iqr (x, 5), zeros (size (x))); ## vector dimensions %!assert (iqr (17, [1 8]), 0) %!assert (iqr ([[1 2 5]; [2 5 6]], [1 2]), 3) %!assert (iqr (cat (3, [1 2 5; 2 5 6], [1 2 5; 2 5 6]), [1 2]), cat(3, 3, 3)) %!assert (iqr (cat (3, [1 2 5; 2 5 6], [1 2 5; 2 5 6]), [1 2]'), cat(3, 3, 3)) %!test %! x = magic (4); x = cat (3, x, 2*x, 3*x); x = cat (4, x, 2*x); %! y = cat (3, 8, 16, 24); %! assert (iqr (x, [1 2]), cat (4, y, 2*y)); %! y = [14, 18.5, 17.5 19.5]; %! assert (iqr (x, [1 3]), cat (4, y, 2*y)); %! y = [10.5 12.5 11.5 15.0000]; %! assert (iqr (x, [1 4]), cat (3, y, 2*y, 3*y)); %! assert (iqr (x, [1 5]), iqr (x, 1)); %! y = [24 13 12 25.5]'; %! assert (iqr (x, [2 3]), cat (4, y, 2*y)); %! y = [17.5, 9, 8, 18.5]'; %! assert (iqr (x, [2 4]), cat (3, y, 2*y, 3*y)); %! assert (iqr (x, [3 4]), [32 4 6 26; 10 22 20 16; 18 14 12 24; 8 28 30 2]); %! assert (iqr (x, [3 4]), iqr (x, [4 3])); %! assert (iqr (x, [1 2 3]), cat (4, 17.5, 35)); %! assert (iqr (x, [2 3 4]), [29.5 19.5 23 31]'); %! assert (iqr (x, [1 3 4]), [22 28 22 30.5]); %! assert (iqr (x, [1 2 4]), cat (3, 11, 22, 33)); %! assert (iqr (x, [1 2 5]), iqr (x, [1 2])); %! assert (iqr (x, [5 6]), zeros (size (x))); ## Inf, NaN %!assert (iqr (Inf), NaN) %!assert (iqr (-Inf), NaN) %!assert (iqr (NaN), NaN) %!assert (iqr (NaN), NaN) %!assert (iqr ([1 2 Inf], 1), [0 0 NaN]) %!assert (iqr ([1 2 Inf], 2), Inf) %!assert (iqr ([1 2 -Inf], 1), [0 0 NaN]) %!assert (iqr ([1 2 -Inf], 2), Inf) %!assert (iqr ([1 2 3 NaN], 1), [0 0 0 NaN]) %!assert (iqr ([1 2 3 NaN], 2), 1.5) %!assert (iqr ([1 NaN 2 3], 2), 1.5) %!assert (iqr (NaN (2), 1), [NaN, NaN]) %!assert (iqr (NaN (2), 2), [NaN; NaN]) %!assert (iqr (NaN (2), 3), NaN (2)) %!assert (iqr ([[1 2 5], [2 NaN 6]], "all"), 3.5) ## input validation %!error iqr () %!error iqr (1, 2, 3) %!error <X .* numeric> iqr (['A'; 'B']) %!error <DIM .* positive integer> iqr (1, 'A') %!error <DIM .* positive integer> iqr (1, 0) %!error <DIM .* positive integer> iqr (1, -2) %!error <DIM .* positive integer> iqr (1, 1.4) %!error <DIM .* positive integer> iqr (1, [1 -2]) %!error <DIM .* positive integer> iqr (1, [1 1.4]) %!error <DIM .* positive integer> iqr ([1 2 3], NaN) %!error <DIM .* positive integer> iqr ([1 2 3], [2 NaN]) %!error <DIM .* positive integer> iqr ([1 2 3], Inf) %!error <DIM .* positive integer> iqr ([1 2 3], [2 Inf]) %!error <vector DIM .* non-repeating> iqr ([1 2 3], [1 2 1]) %!error <DIM .* vector> iqr (1, [1 2; 3 4])