Mercurial > octave
view scripts/statistics/base/std.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) 1996-2017 John W. Eaton ## ## 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 {} {} std (@var{x}) ## @deftypefnx {} {} std (@var{x}, @var{opt}) ## @deftypefnx {} {} std (@var{x}, @var{opt}, @var{dim}) ## Compute the standard deviation of the elements of the vector @var{x}. ## ## The standard deviation is defined as ## @tex ## $$ ## {\rm std} (x) = \sigma = \sqrt{{\sum_{i=1}^N (x_i - \bar{x})^2 \over N - 1}} ## $$ ## 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 ## std (@var{x}) = sqrt ( 1/(N-1) SUM_i (@var{x}(i) - mean(@var{x}))^2 ) ## @end group ## @end example ## ## @noindent ## where @math{N} is the number of elements of the @var{x} vector. ## @end ifnottex ## ## If @var{x} is a matrix, compute the standard deviation for each column and ## return them in a row vector. ## ## 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 square root of the best unbiased ## estimator of the variance [default] ## ## @item 1: ## normalize with @math{N}, this provides the square root of the second ## moment around the mean ## @end table ## ## If the optional argument @var{dim} is given, operate along this dimension. ## @seealso{var, range, iqr, mean, median} ## @end deftypefn ## Author: jwe function retval = std (x, opt = 0, dim) if (nargin < 1 || nargin > 3) print_usage (); endif if (! (isnumeric (x) || islogical (x))) error ("std: X must be a numeric vector or matrix"); endif if (isempty (opt)) opt = 0; elseif (! isscalar (opt) || (opt != 0 && opt != 1)) error ("std: normalization OPT must be 0 or 1"); endif nd = ndims (x); sz = size (x); if (nargin < 3) ## Find the first non-singleton dimension. (dim = find (sz > 1, 1)) || (dim = 1); else if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) error ("std: DIM must be an integer and a valid dimension"); endif endif n = size (x, dim); if (n == 1 || isempty (x)) if (isa (x, "single")) retval = zeros (sz, "single"); else retval = zeros (sz); endif else retval = sqrt (sumsq (center (x, dim), dim) / (n - 1 + opt)); endif endfunction %!test %! x = ones (10, 2); %! y = [1, 3]; %! assert (std (x), [0, 0]); %! assert (std (y), sqrt (2), sqrt (eps)); %! assert (std (x, 0, 2), zeros (10, 1)); %!assert (std (ones (3, 1, 2), 0, 2), zeros (3, 1, 2)) %!assert (std ([1 2], 0), sqrt (2)/2, 5*eps) %!assert (std ([1 2], 1), 0.5, 5*eps) %!assert (std (1), 0) %!assert (std (single (1)), single (0)) %!assert (std ([]), []) %!assert (std (ones (1,3,0,2)), ones (1,3,0,2)) %!assert (std ([1 2 3], [], 3), [0 0 0]) ## Test input validation %!error std () %!error std (1, 2, 3, 4) %!error <X must be a numeric> std (['A'; 'B']) %!error <OPT must be 0 or 1> std (1, 2) %!error <DIM must be an integer> std (1, [], ones (2,2)) %!error <DIM must be an integer> std (1, [], 1.5) %!error <DIM must be .* a valid dimension> std (1, [], 0)