Mercurial > octave
view scripts/statistics/cov.m @ 30875:5d3faba0342e
doc: Ensure documentation lists output argument when it exists for all m-files.
For new users of Octave it is best to show explicit calling forms
in the documentation and to show a return argument when it exists.
* bp-table.cc, shift.m, accumarray.m, accumdim.m, bincoeff.m, bitcmp.m,
bitget.m, bitset.m, blkdiag.m, celldisp.m, cplxpair.m, dblquad.m, flip.m,
fliplr.m, flipud.m, idivide.m, int2str.m, interpft.m, logspace.m, num2str.m,
polyarea.m, postpad.m, prepad.m, randi.m, repmat.m, rng.m, rot90.m, rotdim.m,
structfun.m, triplequad.m, uibuttongroup.m, uicontrol.m, uipanel.m,
uipushtool.m, uitoggletool.m, uitoolbar.m, waitforbuttonpress.m, help.m,
__additional_help_message__.m, hsv.m, im2double.m, im2frame.m, javachk.m,
usejava.m, argnames.m, char.m, formula.m, inline.m, __vectorize__.m, findstr.m,
flipdim.m, strmatch.m, vectorize.m, commutation_matrix.m, cond.m, cross.m,
duplication_matrix.m, expm.m, orth.m, rank.m, rref.m, trace.m, vech.m, cast.m,
compare_versions.m, delete.m, dir.m, fileattrib.m, grabcode.m, gunzip.m,
inputname.m, license.m, list_primes.m, ls.m, mexext.m, movefile.m,
namelengthmax.m, nargoutchk.m, nthargout.m, substruct.m, swapbytes.m, ver.m,
verLessThan.m, what.m, fminunc.m, fsolve.m, fzero.m, optimget.m, __fdjac__.m,
matlabroot.m, savepath.m, campos.m, camroll.m, camtarget.m, camup.m, camva.m,
camzoom.m, clabel.m, diffuse.m, legend.m, orient.m, rticks.m, specular.m,
thetaticks.m, xlim.m, xtickangle.m, xticklabels.m, xticks.m, ylim.m,
ytickangle.m, yticklabels.m, yticks.m, zlim.m, ztickangle.m, zticklabels.m,
zticks.m, ellipsoid.m, isocolors.m, isonormals.m, stairs.m, surfnorm.m,
__actual_axis_position__.m, __pltopt__.m, close.m, graphics_toolkit.m, pan.m,
print.m, printd.m, __ghostscript__.m, __gnuplot_print__.m, __opengl_print__.m,
rotate3d.m, subplot.m, zoom.m, compan.m, conv.m, poly.m, polyaffine.m,
polyder.m, polyint.m, polyout.m, polyreduce.m, polyvalm.m, roots.m, prefdir.m,
prefsfile.m, profexplore.m, profexport.m, profshow.m, powerset.m, unique.m,
arch_rnd.m, arma_rnd.m, autoreg_matrix.m, bartlett.m, blackman.m, detrend.m,
durbinlevinson.m, fftconv.m, fftfilt.m, fftshift.m, fractdiff.m, hamming.m,
hanning.m, hurst.m, ifftshift.m, rectangle_lw.m, rectangle_sw.m, triangle_lw.m,
sinc.m, sinetone.m, sinewave.m, spectral_adf.m, spectral_xdf.m, spencer.m,
ilu.m, __sprand__.m, sprand.m, sprandn.m, sprandsym.m, treelayout.m, beta.m,
betainc.m, betaincinv.m, betaln.m, cosint.m, expint.m, factorial.m, gammainc.m,
gammaincinv.m, lcm.m, nthroot.m, perms.m, reallog.m, realpow.m, realsqrt.m,
sinint.m, hadamard.m, hankel.m, hilb.m, invhilb.m, magic.m, pascal.m, rosser.m,
toeplitz.m, vander.m, wilkinson.m, center.m, corr.m, cov.m, discrete_cdf.m,
discrete_inv.m, discrete_pdf.m, discrete_rnd.m, empirical_cdf.m,
empirical_inv.m, empirical_pdf.m, empirical_rnd.m, kendall.m, kurtosis.m,
mad.m, mean.m, meansq.m, median.m, mode.m, moment.m, range.m, ranks.m,
run_count.m, skewness.m, spearman.m, statistics.m, std.m, base2dec.m,
bin2dec.m, blanks.m, cstrcat.m, deblank.m, dec2base.m, dec2bin.m, dec2hex.m,
hex2dec.m, index.m, regexptranslate.m, rindex.m, strcat.m, strjust.m,
strtrim.m, strtrunc.m, substr.m, untabify.m, __have_feature__.m,
__prog_output_assert__.m, __run_test_suite__.m, example.m, fail.m, asctime.m,
calendar.m, ctime.m, date.m, etime.m:
Add return arguments to @deftypefn macros where they were missing. Rename
variables in functions (particularly generic "retval") to match documentation.
Rename some return variables for (hopefully) better clarity (e.g., 'ax' to 'hax'
to indicate it is a graphics handle to an axes object).
author | Rik <rik@octave.org> |
---|---|
date | Wed, 30 Mar 2022 20:40:27 -0700 |
parents | 796f54d4ddbf |
children | 597f3ee61a48 |
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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{c} =} cov (@var{x}) ## @deftypefnx {} {@var{c} =} cov (@var{x}, @var{opt}) ## @deftypefnx {} {@var{c} =} cov (@var{x}, @var{y}) ## @deftypefnx {} {@var{c} =} cov (@var{x}, @var{y}, @var{opt}) ## Compute the covariance matrix. ## ## If each row of @var{x} and @var{y} is an observation, and each column is ## a variable, then the @w{(@var{i}, @var{j})-th} entry of ## @code{cov (@var{x}, @var{y})} is the covariance between the @var{i}-th ## variable in @var{x} and the @var{j}-th variable in @var{y}. ## @tex ## $$ ## \sigma_{ij} = {1 \over N-1} \sum_{i=1}^N (x_i - \bar{x})(y_i - \bar{y}) ## $$ ## where $\bar{x}$ and $\bar{y}$ are the mean values of @var{x} and @var{y}. ## @end tex ## @ifnottex ## ## @example ## cov (@var{x}) = 1/(N-1) * SUM_i (@var{x}(i) - mean(@var{x})) * (@var{y}(i) - mean(@var{y})) ## @end example ## ## @noindent ## where @math{N} is the length of the @var{x} and @var{y} vectors. ## ## @end ifnottex ## ## If called with one argument, compute @code{cov (@var{x}, @var{x})}, the ## covariance between the columns of @var{x}. ## ## 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 ## covariance [default] ## ## @item 1: ## normalize with @math{N}, this provides the second moment around the mean ## @end table ## ## Compatibility Note:: Octave always treats rows of @var{x} and @var{y} ## as multivariate random variables. ## For two inputs, however, @sc{matlab} treats @var{x} and @var{y} as two ## univariate distributions regardless of their shapes, and will calculate ## @code{cov ([@var{x}(:), @var{y}(:)])} whenever the number of elements in ## @var{x} and @var{y} are equal. This will result in a 2x2 matrix. ## Code relying on @sc{matlab}'s definition will need to be changed when ## running in Octave. ## @seealso{corr} ## @end deftypefn function c = cov (x, y = [], opt = 0) if (nargin < 1) print_usage (); endif if ( ! (isnumeric (x) || islogical (x)) || ! (isnumeric (y) || islogical (y))) error ("cov: X and Y must be numeric matrices or vectors"); endif if (ndims (x) != 2 || ndims (y) != 2) error ("cov: X and Y must be 2-D matrices or vectors"); endif if (nargin == 2 && isscalar (y)) opt = y; endif if (opt != 0 && opt != 1) error ("cov: normalization OPT must be 0 or 1"); endif ## Special case, scalar has zero covariance if (isscalar (x)) if (isa (x, "single")) c = single (0); else c = 0; endif return; endif if (isrow (x)) x = x.'; endif n = rows (x); if (nargin == 1 || isscalar (y)) x = center (x, 1); c = x' * x / (n - 1 + opt); else if (isrow (y)) y = y.'; endif if (rows (y) != n) error ("cov: X and Y must have the same number of observations"); endif x = center (x, 1); y = center (y, 1); c = x' * y / (n - 1 + opt); endif endfunction %!test %! x = rand (10); %! cx1 = cov (x); %! cx2 = cov (x, x); %! assert (size (cx1) == [10, 10] && size (cx2) == [10, 10]); %! assert (cx1, cx2, 1e1*eps); %!test %! x = [1:3]'; %! y = [3:-1:1]'; %! assert (cov (x, y), -1, 5*eps); %! assert (cov (x, flipud (y)), 1, 5*eps); %! assert (cov ([x, y]), [1 -1; -1 1], 5*eps); %!test %! x = single ([1:3]'); %! y = single ([3:-1:1]'); %! assert (cov (x, y), single (-1), 5*eps); %! assert (cov (x, flipud (y)), single (1), 5*eps); %! assert (cov ([x, y]), single ([1 -1; -1 1]), 5*eps); %!test %! x = [1:5]; %! c = cov (x); %! assert (isscalar (c)); %! assert (c, 2.5); %!assert (cov (5), 0) %!assert (cov (single (5)), single (0)) %!test %! x = [1:5]; %! c = cov (x, 0); %! assert (c, 2.5); %! c = cov (x, 1); %! assert (c, 2); ## Test input validation %!error <Invalid call> cov () %!error cov ([1; 2], ["A", "B"]) %!error cov (ones (2,2,2)) %!error cov (ones (2,2), ones (2,2,2)) %!error <normalization OPT must be 0 or 1> cov (1, 3) %!error cov (ones (2,2), ones (3,2))