Mercurial > octave
view scripts/statistics/base/mean.m @ 24511:4f0e6ee6c9b8 stable
Make documentation Sec 26.1 more consistent and Sec 25.4 clearer (bug #52685)
* corr.m: Add space in LaTeX formula. For the example, place variables in a
@var qualifier.
* cov.m: Use @var in LaTeX for x and y when referring to function input vector.
Correct Octave-help formula by placing parentheses around N-1 so that -1 is
in the denominator. Define N after the formula in which it is used.
* gls.m: Define what GLS stands for. Use @var instead of @math for function
input and output variables. Move the description of matrix O and scalar s
to a third paragraph, ensuring s is lower case. Give a little more context
to the description of X and Y in the second paragraph. Add an expansive
paragraph three for details about the error variables E including the
description of O and s along with their dimensions. Add "matrix" before
B and "scalar" before s for clarity. Place @var around variables r, y, x
and beta to make those upper case in Octave-help.
* histc.m: Use LaTeX math rather than @code for the @tex scenario.
* kendall.m: Treat tau differently for LaTeX and Octave-help scenarios. Add
space in LaTeX formulas. Treat tau as @var in Octave-help case. Use lower
case 'i' for index variable and upper case 'N' for vector length.
* kurtosis.m: For mean value of x, use script rather than non-script. Define
N after the formula in which it is used for Octave-help case.
* mean.m: Indicate N is number of elements. Use @var on input vector x for
Octave-help case.
* meansq.m: Indicate N is number of elements, but drop the reference to mean
value because there is none. Use @var on input vector x for Octave-help
case. Use "If x is a matrix" consistent with all others.
* median.m: Indicate N is number of elements for LaTeX case. For Octave-help
place some vertical lines to represent case curly-bracket. Place @math
around N. Define an intermediate vector S representing sorted X and use
that in the math formula.
* moment.m: Define x-bar as mean and N as number of elements. Use @var on
x and p in the Octave-help formulas.
* ols.m: Define meaning of OLS. Add @var to LaTeX variables to make them
non-script vectors. Use @var instead of @math for function input and output
variables. Use hyphens for matrix dimensions in Octave-help formula. Move
the description of matrix S to a third paragraph. Give a little more context
to the description of X and Y in the second paragraph. Add an expansive
paragraph three for details about the error variables E including the
description of matrix S along with its dimensions, ensuring S is upper case.
Add "matrix" before B for clarity. Make the definition of SIGMA one line for
appearance in Octave-help.
* prctile.m: Change a mistaken 'y' to 'q' to work in LaTeX as well.
* quantile.m: Use @var{method} rather than METHOD. Break up all the method
formulas for p(k) into LaTeX and Octave-help versions for better control.
Use upper case N for the length of P.
* skewness.m: Remove @var from x when referring to vector elements in LaTeX.
Indicate N is number of elements.
* spearman.m: Break into separate LaTeX and Octave-help cases rather than
use @code for LaTeX. Use Greek symbol rho in LaTeX.
* std.m: Add @var to x variable to indicate LaTeX or Octave-help vector. Add
clarification about N being number elements of x to both LaTeX and
Octave-help formulas.
* var.m: Indicate N is number of elements. Apply @var to x to show it is a
vector. Change == to "is equal to" for normal text.
author | Daniel J Sebald <daniel.sebald@ieee.org> |
---|---|
date | Wed, 27 Dec 2017 23:38:25 -0600 |
parents | 3ac9f9ecfae5 |
children | 3fc1c8ebe5c3 |
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## Copyright (C) 1995-2017 Kurt Hornik ## ## 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 ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {} {} mean (@var{x}) ## @deftypefnx {} {} mean (@var{x}, @var{dim}) ## @deftypefnx {} {} mean (@var{x}, @var{opt}) ## @deftypefnx {} {} mean (@var{x}, @var{dim}, @var{opt}) ## Compute the mean of the elements of the vector @var{x}. ## ## The mean is defined as ## ## @tex ## $$ {\rm mean}(x) = \bar{x} = {1\over N} \sum_{i=1}^N x_i $$ ## where $N$ is the number of elements of @var{x}. ## ## @end tex ## @ifnottex ## ## @example ## mean (@var{x}) = SUM_i @var{x}(i) / N ## @end example ## ## where @math{N} is the length of the @var{x} vector. ## ## @end ifnottex ## If @var{x} is a matrix, compute the mean for each column and return them ## in a row vector. ## ## If the optional argument @var{dim} is given, operate along this dimension. ## ## The optional argument @var{opt} selects the type of mean to compute. ## The following options are recognized: ## ## @table @asis ## @item @qcode{"a"} ## Compute the (ordinary) arithmetic mean. [default] ## ## @item @qcode{"g"} ## Compute the geometric mean. ## ## @item @qcode{"h"} ## Compute the harmonic mean. ## @end table ## ## Both @var{dim} and @var{opt} are optional. If both are supplied, either ## may appear first. ## @seealso{median, mode} ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.ac.at> ## Description: Compute arithmetic, geometric, and harmonic mean function y = mean (x, opt1, opt2) if (nargin < 1 || nargin > 3) print_usage (); endif if (! (isnumeric (x) || islogical (x))) error ("mean: X must be a numeric vector or matrix"); endif need_dim = false; if (nargin == 1) opt = "a"; need_dim = true; elseif (nargin == 2) if (ischar (opt1)) opt = opt1; need_dim = true; else dim = opt1; opt = "a"; endif elseif (nargin == 3) if (ischar (opt1)) opt = opt1; dim = opt2; elseif (ischar (opt2)) opt = opt2; dim = opt1; else error ("mean: OPT must be a string"); endif else print_usage (); 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 ("mean: DIM must be an integer and a valid dimension"); endif endif n = size (x, dim); if (strcmp (opt, "a")) y = sum (x, dim) / n; elseif (strcmp (opt, "g")) if (all (x(:) >= 0)) y = exp (sum (log (x), dim) ./ n); else error ("mean: X must not contain any negative values"); endif elseif (strcmp (opt, "h")) y = n ./ sum (1 ./ x, dim); else error ("mean: option '%s' not recognized", opt); endif endfunction %!test %! x = -10:10; %! y = x'; %! z = [y, y+10]; %! assert (mean (x), 0); %! assert (mean (y), 0); %! assert (mean (z), [0, 10]); ## Test small numbers %!assert (mean (repmat (0.1,1,1000), "g"), 0.1, 20*eps) %!assert (mean (magic (3), 1), [5, 5, 5]) %!assert (mean (magic (3), 2), [5; 5; 5]) %!assert (mean ([2 8], "g"), 4) %!assert (mean ([4 4 2], "h"), 3) %!assert (mean (logical ([1 0 1 1])), 0.75) %!assert (mean (single ([1 0 1 1])), single (0.75)) %!assert (mean ([1 2], 3), [1 2]) ## Test input validation %!error mean () %!error mean (1, 2, 3, 4) %!error <X must be a numeric> mean ({1:5}) %!error <OPT must be a string> mean (1, 2, 3) %!error <DIM must be an integer> mean (1, ones (2,2)) %!error <DIM must be an integer> mean (1, 1.5) %!error <DIM must be .* a valid dimension> mean (1, 0) %!error <X must not contain any negative values> mean ([1 -1], "g") %!error <option 'b' not recognized> mean (1, "b")