octave: scripts/statistics/base/skewness.m annotate

annotate scripts/statistics/base/skewness.m @ 11436:e151e23f73bc

Overhaul base statistics functions and documentation of same. Add or improve input validation. Add input validation tests. Add functional tests. Improve or re-write documentation strings.

author	Rik <octave@nomad.inbox5.com>
date	Mon, 03 Jan 2011 21:23:08 -0800
parents	4c335d398c8d
children	fd0a3ac60b0e

rev	line source
7017 a1dbe9d80eee [project @ 2007-10-12 21:27:11 by jwe] jwe parents: 7016 diff changeset	1 ## Copyright (C) 1996, 1997, 1998, 1999, 2000, 2002, 2004, 2005, 2006,
8920 eb63fbe60fab update copyright notices John W. Eaton <jwe@octave.org> parents: 8517 diff changeset	2 ## 2007, 2008, 2009 John W. Eaton
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	3 ##
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	4 ## This file is part of Octave.
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	5 ##
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	6 ## Octave is free software; you can redistribute it and/or modify it
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	7 ## under the terms of the GNU General Public License as published by
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6754 diff changeset	8 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6754 diff changeset	9 ## your option) any later version.
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	10 ##
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	11 ## Octave is distributed in the hope that it will be useful, but
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	14 ## General Public License for more details.
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	15 ##
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	16 ## You should have received a copy of the GNU General Public License
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6754 diff changeset	17 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6754 diff changeset	18 ## <http://www.gnu.org/licenses/>.
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	19
3367 0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe] jwe parents: 3200 diff changeset	20 ## -- texinfo --
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	21 ## @deftypefn {Function File} {} skewness (@var{x})
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	22 ## @deftypefnx {Function File} {} skewness (@var{x}, @var{dim})
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	23 ## Compute the skewness of the elements of the vector @var{x}.
3367 0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe] jwe parents: 3200 diff changeset	24 ## @tex
0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe] jwe parents: 3200 diff changeset	25 ## $$
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	26 ## {\rm skewness} (x) = {1\over N \sigma^3} \sum_{i=1}^N (x_i-\bar{x})^3
3367 0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe] jwe parents: 3200 diff changeset	27 ## $$
6754 451b346d8c2f [project @ 2007-06-25 17:31:46 by jwe] jwe parents: 6046 diff changeset	28 ## where $\bar{x}$ is the mean value of $x$.
3367 0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe] jwe parents: 3200 diff changeset	29 ## @end tex
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7411 diff changeset	30 ## @ifnottex
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3367 diff changeset	31 ##
3367 0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe] jwe parents: 3200 diff changeset	32 ## @example
0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe] jwe parents: 3200 diff changeset	33 ## skewness (x) = N^(-1) std(x)^(-3) sum ((x - mean(x)).^3)
0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe] jwe parents: 3200 diff changeset	34 ## @end example
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10669 diff changeset	35 ##
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7411 diff changeset	36 ## @end ifnottex
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3367 diff changeset	37 ##
3367 0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe] jwe parents: 3200 diff changeset	38 ## @noindent
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	39 ## If @var{x} is a matrix, return the skewness along the
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	40 ## first non-singleton dimension of the matrix. If the optional
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	41 ## @var{dim} argument is given, operate along this dimension.
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	42 ## @seealso{var,kurtosis,moment}
3367 0748b03c3510 [project @ 1999-11-20 14:52:38 by jwe] jwe parents: 3200 diff changeset	43 ## @end deftypefn
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	44
5428 2a16423e4aa0 [project @ 2005-08-23 18:38:27 by jwe] jwe parents: 5307 diff changeset	45 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	46 ## Created: 29 July 1994
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	47 ## Adapted-By: jwe
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	48
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	49 function retval = skewness (x, dim)
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	50
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	51 if (nargin != 1 && nargin != 2)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5428 diff changeset	52 print_usage ();
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	53 endif
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	54
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	55 if (!isnumeric(x))
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	56 error ("skewness: X must be a numeric vector or matrix");
10669 cab3b148d4e4 Improve validation of input arguments for base statistics functions. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	57 endif
cab3b148d4e4 Improve validation of input arguments for base statistics functions. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	58
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	59 nd = ndims (x);
28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	60 sz = size (x);
28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	61 if (nargin != 2)
4886 54b076a24718 [project @ 2004-04-30 04:31:51 by jwe] jwe parents: 4885 diff changeset	62 ## Find the first non-singleton dimension.
10669 cab3b148d4e4 Improve validation of input arguments for base statistics functions. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	63 dim = find (sz > 1, 1);
cab3b148d4e4 Improve validation of input arguments for base statistics functions. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	64 if (isempty (dim))
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	65 dim = 1;
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	66 endif
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	67 else
11149 fe3c3dfc07eb style fix: break lines before && and \|\|, not after John W. Eaton <jwe@octave.org> parents: 10821 diff changeset	68 if (!(isscalar (dim) && dim == round (dim))
fe3c3dfc07eb style fix: break lines before && and \|\|, not after John W. Eaton <jwe@octave.org> parents: 10821 diff changeset	69 \|\| !(1 <= dim && dim <= nd))
10669 cab3b148d4e4 Improve validation of input arguments for base statistics functions. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	70 error ("skewness: DIM must be an integer and a valid dimension");
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	71 endif
28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	72 endif
28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	73
4886 54b076a24718 [project @ 2004-04-30 04:31:51 by jwe] jwe parents: 4885 diff changeset	74 c = sz(dim);
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	75 idx = ones (1, nd);
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	76 idx(dim) = c;
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	77 x = x - repmat (mean (x, dim), idx);
4886 54b076a24718 [project @ 2004-04-30 04:31:51 by jwe] jwe parents: 4885 diff changeset	78 sz(dim) = 1;
11401 4c335d398c8d skewness.m: make returned value have the same class as the input John W. Eaton <jwe@octave.org> parents: 11149 diff changeset	79 retval = zeros (sz, class (x));
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	80 s = std (x, [], dim);
28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	81 ind = find (s > 0);
28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	82 x = sum (x .^ 3, dim);
4886 54b076a24718 [project @ 2004-04-30 04:31:51 by jwe] jwe parents: 4885 diff changeset	83 retval(ind) = x(ind) ./ (c * s(ind) .^ 3);
4885 28ab079d8f0e [project @ 2004-04-30 04:21:33 by jwe] jwe parents: 4030 diff changeset	84
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	85 endfunction
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	86
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	87 %!assert(skewness ([-1,0,1]), 0);
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	88 %!assert(skewness ([-2,0,1]) < 0);
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	89 %!assert(skewness ([-1,0,2]) > 0);
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	90 %!assert(skewness ([-3,0,1]) == -1*skewness([-1,0,3]));
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	91 %!test
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	92 %! x = [0; 0; 0; 1];
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	93 %! y = [x, 2*x];
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	94 %! assert(all (abs (skewness (y) - [0.75, 0.75]) < sqrt (eps)));
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	95
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	96 %% Test input validation
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	97 %!error skewness ()
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	98 %!error skewness (1, 2, 3)
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	99 %!error skewness ([true true])
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	100 %!error skewness (1, ones(2,2))
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	101 %!error skewness (1, 1.5)
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	102 %!error skewness (1, 0)
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 11401 diff changeset	103 %!error skewness (1, 3)

Mercurial > octave

annotate scripts/statistics/base/skewness.m @ 11436:e151e23f73bc