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

annotate scripts/statistics/base/var.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	693e22af08ae
children	fd0a3ac60b0e

rev	line source
7017 a1dbe9d80eee [project @ 2007-10-12 21:27:11 by jwe] jwe parents: 7016 diff changeset	1 ## Copyright (C) 1995, 1996, 1997, 1998, 2000, 2002, 2004, 2005, 2006,
9245 16f53d29049f update copyright notices John W. Eaton <jwe@octave.org> parents: 8980 diff changeset	2 ## 2007, 2009 Kurt Hornik
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	3 ##
3922 38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3456 diff changeset	4 ## This file is part of Octave.
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3456 diff changeset	5 ##
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3456 diff changeset	6 ## Octave is free software; you can redistribute it and/or modify it
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3456 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: 7001 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: 7001 diff changeset	9 ## your option) any later version.
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	10 ##
3922 38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3456 diff changeset	11 ## Octave is distributed in the hope that it will be useful, but
3200 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
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	14 ## General Public License for more details.
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	15 ##
3200 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: 7001 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: 7001 diff changeset	18 ## <http://www.gnu.org/licenses/>.
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	19
3453 71d2e09c15a2 [project @ 2000-01-18 08:32:09 by jwe] jwe parents: 3426 diff changeset	20 ## -- texinfo --
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	21 ## @deftypefn {Function File} {} var (@var{x})
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	22 ## @deftypefnx {Function File} {} var (@var{x}, @var{opt})
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	23 ## @deftypefnx {Function File} {} var (@var{x}, @var{opt}, @var{dim})
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	24 ## Compute the variance of the elements of the vector @var{x}.
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	25 ## @tex
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	26 ## $$
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	27 ## {\rm std} (x) = \sigma^2 = {\sum_{i=1}^N (x_i - \bar{x})^2 \over N - 1}
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	28 ## $$
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	29 ## where $\bar{x}$ is the mean value of $x$.
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	30 ## @end tex
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	31 ## @ifnottex
4849 a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	32 ##
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	33 ## @example
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	34 ## @group
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	35 ## std (x) = 1/(N-1) SUM_i (x(i) - mean(x))^2
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	36 ## @end group
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	37 ## @end example
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	38 ##
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	39 ## @end ifnottex
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	40 ## If @var{x} is a matrix, compute the variance for each column
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	41 ## and return them in a row vector.
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	42 ##
5435 66ad03c58880 [project @ 2005-08-31 20:41:47 by jwe] jwe parents: 5428 diff changeset	43 ## The argument @var{opt} determines the type of normalization to use.
66ad03c58880 [project @ 2005-08-31 20:41:47 by jwe] jwe parents: 5428 diff changeset	44 ## Valid values are
4849 a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	45 ##
a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	46 ## @table @asis
a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	47 ## @item 0:
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	48 ## normalize with @math{N-1}, provides the best unbiased estimator of the
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	49 ## variance [default]
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	50 ##
4849 a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	51 ## @item 1:
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	52 ## normalizes with @math{N}, this provides the second moment around the mean
4849 a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	53 ## @end table
a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	54 ##
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	55 ## If the optional argument @var{dim} is given, operate along this dimension.
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	56 ## @seealso{cov,std,skewness,kurtosis,moment}
3453 71d2e09c15a2 [project @ 2000-01-18 08:32:09 by jwe] jwe parents: 3426 diff changeset	57 ## @end deftypefn
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	58
5428 2a16423e4aa0 [project @ 2005-08-23 18:38:27 by jwe] jwe parents: 5307 diff changeset	59 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
3456 434790acb067 [project @ 2000-01-19 06:58:51 by jwe] jwe parents: 3453 diff changeset	60 ## Description: Compute variance
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	61
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	62 function retval = var (x, opt = 0, dim)
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	63
4849 a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	64 if (nargin < 1 \|\| nargin > 3)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 6024 diff changeset	65 print_usage ();
4849 a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	66 endif
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	67
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	68 if (!isnumeric (x))
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	69 error ("var: X must be a numeric vector or matrix");
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	70 endif
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	71
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	72 if (isempty (opt))
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	73 opt = 0;
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	74 endif
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	75 if (opt != 0 && opt != 1)
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	76 error ("var: normalization OPT must be 0 or 1");
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	77 endif
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	78
4849 a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	79 if (nargin < 3)
6024 500d884ae373 [project @ 2006-10-03 14:27:33 by jwe] jwe parents: 5435 diff changeset	80 dim = find (size (x) > 1, 1);
4849 a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	81 if (isempty (dim))
a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	82 dim = 1;
a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	83 endif
a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	84 endif
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	85
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	86 n = size (x, dim);
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	87 if (n == 1)
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	88 retval = zeros (size (x), class (x));
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	89 elseif (numel (x) > 0)
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	90 retval = sumsq (center (x, dim), dim) / (n - 1 + opt);
9371 56751dfc6ebd fix var for scalar and empty arguments John W. Eaton <jwe@octave.org> parents: 9245 diff changeset	91 else
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	92 error ("var: X must not be empty");
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	93 endif
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	94
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	95 endfunction
9371 56751dfc6ebd fix var for scalar and empty arguments John W. Eaton <jwe@octave.org> parents: 9245 diff changeset	96
56751dfc6ebd fix var for scalar and empty arguments John W. Eaton <jwe@octave.org> parents: 9245 diff changeset	97 %!assert (var (13), 0)
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	98 %!assert (var ([1,2,3]), 1)
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	99 %!assert (var ([1,2,3], 1), 2/3, eps)
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	100 %!assert (var ([1,2,3], [], 1), [0,0,0])
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	101
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	102 %% Test input validation
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	103 %!error var ()
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	104 %!error var (1,2,3,4)
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	105 %!error var (true(1,2))
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	106 %!error var (1, -1);
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	107 %!error var ([],1)
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	108

Mercurial > octave

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