Mercurial > octave
view scripts/statistics/moment.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{m} =} moment (@var{x}, @var{p}) ## @deftypefnx {} {@var{m} =} moment (@var{x}, @var{p}, @var{type}) ## @deftypefnx {} {@var{m} =} moment (@var{x}, @var{p}, @var{dim}) ## @deftypefnx {} {@var{m} =} moment (@var{x}, @var{p}, @var{type}, @var{dim}) ## @deftypefnx {} {@var{m} =} moment (@var{x}, @var{p}, @var{dim}, @var{type}) ## Compute the @var{p}-th central moment of the vector @var{x}. ## ## The @var{p}-th central moment of @var{x} is defined as: ## ## @tex ## $$ ## {\sum_{i=1}^N (x_i - \bar{x})^p \over N} ## $$ ## 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 ## 1/N SUM_i (@var{x}(i) - mean(@var{x}))^@var{p} ## @end group ## @end example ## ## @noindent ## where @math{N} is the length of the @var{x} vector. ## ## @end ifnottex ## ## If @var{x} is a matrix, return the row vector containing the @var{p}-th ## central moment of each column. ## ## If the optional argument @var{dim} is given, operate along this dimension. ## ## The optional string @var{type} specifies the type of moment to be computed. ## Valid options are: ## ## @table @asis ## @item @qcode{"c"} ## Central Moment (default). ## ## @item @qcode{"a"} ## @itemx @qcode{"ac"} ## Absolute Central Moment. The moment about the mean ignoring sign ## defined as ## @tex ## $$ ## {\sum_{i=1}^N {\left| x_i - \bar{x} \right|}^p \over N} ## $$ ## @end tex ## @ifnottex ## ## @example ## @group ## 1/N SUM_i (abs (@var{x}(i) - mean(@var{x})))^@var{p} ## @end group ## @end example ## ## @end ifnottex ## ## @item @qcode{"r"} ## Raw Moment. The moment about zero defined as ## ## @tex ## $$ ## {\rm moment} (x) = { \sum_{i=1}^N {x_i}^p \over N } ## $$ ## @end tex ## @ifnottex ## ## @example ## @group ## moment (@var{x}) = 1/N SUM_i @var{x}(i)^@var{p} ## @end group ## @end example ## ## @end ifnottex ## ## @item @nospell{@qcode{"ar"}} ## Absolute Raw Moment. The moment about zero ignoring sign defined as ## @tex ## $$ ## {\sum_{i=1}^N {\left| x_i \right|}^p \over N} ## $$ ## @end tex ## @ifnottex ## ## @example ## @group ## 1/N SUM_i ( abs (@var{x}(i)) )^@var{p} ## @end group ## @end example ## ## @end ifnottex ## @end table ## ## If both @var{type} and @var{dim} are given they may appear in any order. ## @seealso{var, skewness, kurtosis} ## @end deftypefn ## Can easily be made to work for continuous distributions (using quad) ## as well, but how does the general case work? function m = moment (x, p, opt1, opt2) if (nargin < 2) print_usage (); endif if (! (isnumeric (x) || islogical (x)) || isempty (x)) error ("moment: X must be a non-empty numeric matrix or vector"); endif if (! (isnumeric (p) && isscalar (p))) error ("moment: P must be a numeric scalar"); endif need_dim = false; if (nargin == 2) type = ""; need_dim = true; elseif (nargin == 3) if (ischar (opt1)) type = opt1; need_dim = true; else dim = opt1; type = ""; endif elseif (nargin == 4) if (ischar (opt1)) type = opt1; dim = opt2; elseif (ischar (opt2)) type = opt2; dim = opt1; else error ("moment: TYPE must be a string"); endif endif nd = ndims (x); sz = size (x); if (need_dim) ## Find the first non-singleton dimension. (dim = find (sz > 1, 1)) || (dim = 1); else if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) error ("moment: DIM must be an integer and a valid dimension"); endif endif n = size (x, dim); if (! any (type == "r")) x = center (x, dim); endif if (any (type == "a")) x = abs (x); endif m = sum (x .^ p, dim) / n; endfunction %!shared x %! x = rand (10); %!assert (moment (x,1), mean (center (x)), eps) %!assert (moment (x,2), meansq (center (x)), eps) %!assert (moment (x,1,2), mean (center (x, 2), 2), eps) %!assert (moment (x,1,"a"), mean (abs (center (x))), eps) %!assert (moment (x,1,"r"), mean (x), eps) %!assert (moment (x,1,"ar"), mean (abs (x)), eps) %!assert (moment (single ([1 2 3]), 1, "r"), single (2)) %!assert (moment (1, 2, 4), 0) ## Test input validation %!error <Invalid call> moment () %!error <Invalid call> moment (1) %!error <X must be a non-empty numeric matrix> moment (['A'; 'B'], 2) %!error <X must be a non-empty numeric matrix> moment (ones (2,0,3), 2) %!error <P must be a numeric scalar> moment (1, true) %!error <P must be a numeric scalar> moment (1, ones (2,2)) %!error <TYPE must be a string> moment (1, 2, 3, 4) %!error <DIM must be an integer and a valid dimension> moment (1, 2, ones (2,2)) %!error <DIM must be an integer and a valid dimension> moment (1, 2, 1.5)