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

annotate scripts/statistics/base/var.m @ 13836:519390f1b67f

maint: periodic merge of stable to default.

author	Rik <octave@nomad.inbox5.com>
date	Sun, 06 Nov 2011 21:22:49 -0800
parents	6b2f14af2360 50ceb5c51271
children	72c96de7a403

rev	line source
11523 fd0a3ac60b0e update copyright notices John W. Eaton <jwe@octave.org> parents: 11436 diff changeset	1 ## Copyright (C) 1995-2011 Kurt Hornik
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	2 ##
3922 38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3456 diff changeset	3 ## This file is part of Octave.
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3456 diff changeset	4 ##
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3456 diff changeset	5 ## 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	6 ## 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	7 ## 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	8 ## your option) any later version.
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	9 ##
3922 38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3456 diff changeset	10 ## 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	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	12 ## 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	13 ## General Public License for more details.
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	14 ##
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	15 ## 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	16 ## 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	17 ## <http://www.gnu.org/licenses/>.
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	18
3453 71d2e09c15a2 [project @ 2000-01-18 08:32:09 by jwe] jwe parents: 3426 diff changeset	19 ## -- texinfo --
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	20 ## @deftypefn {Function File} {} var (@var{x})
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	21 ## @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	22 ## @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	23 ## 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	24 ## @tex
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	25 ## $$
13795 50ceb5c51271 var.m: Fix bug in docstring referring to std (Bug #34729). Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	26 ## {\rm var} (x) = \sigma^2 = {\sum_{i=1}^N (x_i - \bar{x})^2 \over N - 1}
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	27 ## $$
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	28 ## 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	29 ## @end tex
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	30 ## @ifnottex
4849 a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	31 ##
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	32 ## @example
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	33 ## @group
13795 50ceb5c51271 var.m: Fix bug in docstring referring to std (Bug #34729). Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	34 ## var (x) = 1/(N-1) SUM_i (x(i) - mean(x))^2
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	35 ## @end group
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	36 ## @end example
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	37 ##
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	38 ## @end ifnottex
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	39 ## 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	40 ## and return them in a row vector.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	41 ##
5435 66ad03c58880 [project @ 2005-08-31 20:41:47 by jwe] jwe parents: 5428 diff changeset	42 ## 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	43 ## Valid values are
4849 a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	44 ##
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	45 ## @table @asis
4849 a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	46 ## @item 0:
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	47 ## 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	48 ## variance [default]
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	49 ##
4849 a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	50 ## @item 1:
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	51 ## 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	52 ## @end table
a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	53 ##
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	54 ## If the optional argument @var{dim} is given, operate along this dimension.
12575 d0b799dafede Grammarcheck files for 3.4.1 release. Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	55 ## @seealso{cov, std, skewness, kurtosis, moment}
3453 71d2e09c15a2 [project @ 2000-01-18 08:32:09 by jwe] jwe parents: 3426 diff changeset	56 ## @end deftypefn
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	57
5428 2a16423e4aa0 [project @ 2005-08-23 18:38:27 by jwe] jwe parents: 5307 diff changeset	58 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
3456 434790acb067 [project @ 2000-01-19 06:58:51 by jwe] jwe parents: 3453 diff changeset	59 ## Description: Compute variance
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	60
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	61 function retval = var (x, opt = 0, dim)
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	62
4849 a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	63 if (nargin < 1 \|\| nargin > 3)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 6024 diff changeset	64 print_usage ();
4849 a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	65 endif
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	66
12656 6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	67 if (! (isnumeric (x) \|\| islogical (x)))
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	68 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	69 endif
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	70
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	71 if (isempty (opt))
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	72 opt = 0;
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	73 endif
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	74 if (opt != 0 && opt != 1)
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	75 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	76 endif
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	77
12656 6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	78 nd = ndims (x);
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	79 sz = size (x);
4849 a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	80 if (nargin < 3)
12656 6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	81 ## Find the first non-singleton dimension.
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	82 (dim = find (sz > 1, 1)) \|\| (dim = 1);
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	83 else
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	84 if (!(isscalar (dim) && dim == fix (dim))
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	85 \|\| !(1 <= dim && dim <= nd))
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	86 error ("var: DIM must be an integer and a valid dimension");
4849 a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	87 endif
a3440ff5eb14 [project @ 2004-04-06 15:23:56 by jwe] jwe parents: 4171 diff changeset	88 endif
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	89
12656 6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	90 n = sz(dim);
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	91 if (n == 1)
12656 6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	92 if (isa (x, 'single'))
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	93 retval = zeros (sz, 'single');
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	94 else
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	95 retval = zeros (sz);
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	96 endif
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	97 elseif (numel (x) > 0)
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	98 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	99 else
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	100 error ("var: X must not be empty");
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	101 endif
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	102
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	103 endfunction
9371 56751dfc6ebd fix var for scalar and empty arguments John W. Eaton <jwe@octave.org> parents: 9245 diff changeset	104
12656 6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	105
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	106 %!assert(var (13), 0);
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	107 %!assert(var (single(13)), single(0));
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	108 %!assert(var ([1,2,3]), 1);
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	109 %!assert(var ([1,2,3], 1), 2/3, eps);
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	110 %!assert(var ([1,2,3], [], 1), [0,0,0]);
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	111
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	112 %% Test input validation
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	113 %!error var ()
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	114 %!error var (1,2,3,4)
12656 6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	115 %!error var (['A'; 'B'])
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	116 %!error var (1, -1);
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	117 %!error var ([],1)
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	118

Mercurial > octave-nkf

annotate scripts/statistics/base/var.m @ 13836:519390f1b67f