Mercurial > octave-nkf
annotate scripts/statistics/base/cov.m @ 8977:f464119ec165
further simplify some stats funcs
author | Jaroslav Hajek <highegg@gmail.com> |
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date | Fri, 13 Mar 2009 21:26:13 +0100 |
parents | eb63fbe60fab |
children | f0c3d3fc4903 |
rev | line source |
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7017 | 1 ## Copyright (C) 1995, 1996, 1997, 1998, 1999, 2000, 2002, 2004, 2005, |
8920 | 2 ## 2006, 2007, 2008 Kurt Hornik |
3426 | 3 ## |
3922 | 4 ## This file is part of Octave. |
5 ## | |
6 ## Octave is free software; you can redistribute it and/or modify it | |
7 ## under the terms of the GNU General Public License as published by | |
7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
9 ## your option) any later version. | |
3426 | 10 ## |
3922 | 11 ## Octave is distributed in the hope that it will be useful, but |
3200 | 12 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
3426 | 14 ## General Public License for more details. |
15 ## | |
3200 | 16 ## You should have received a copy of the GNU General Public License |
7016 | 17 ## along with Octave; see the file COPYING. If not, see |
18 ## <http://www.gnu.org/licenses/>. | |
3200 | 19 |
3367 | 20 ## -*- texinfo -*- |
21 ## @deftypefn {Function File} {} cov (@var{x}, @var{y}) | |
6754 | 22 ## Compute covariance. |
23 ## | |
3367 | 24 ## If each row of @var{x} and @var{y} is an observation and each column is |
4855 | 25 ## a variable, the (@var{i}, @var{j})-th entry of |
3367 | 26 ## @code{cov (@var{x}, @var{y})} is the covariance between the @var{i}-th |
6754 | 27 ## variable in @var{x} and the @var{j}-th variable in @var{y}. |
28 ## @iftex | |
29 ## @tex | |
30 ## $$ | |
31 ## \sigma_{ij} = {1 \over N-1} \sum_{i=1}^N (x_i - \bar{x})(y_i - \bar{y}) | |
32 ## $$ | |
33 ## where $\bar{x}$ and $\bar{y}$ are the mean values of $x$ and $y$. | |
34 ## @end tex | |
35 ## @end iftex | |
36 ## If called with one argument, compute @code{cov (@var{x}, @var{x})}. | |
3367 | 37 ## @end deftypefn |
3200 | 38 |
5428 | 39 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
3456 | 40 ## Description: Compute covariances |
3200 | 41 |
42 function c = cov (x, y) | |
43 | |
44 if (nargin < 1 || nargin > 2) | |
6046 | 45 print_usage (); |
3200 | 46 endif |
47 | |
48 if (rows (x) == 1) | |
49 x = x'; | |
50 endif | |
51 n = rows (x); | |
52 | |
53 if (nargin == 2) | |
54 if (rows (y) == 1) | |
55 y = y'; | |
56 endif | |
57 if (rows (y) != n) | |
3458 | 58 error ("cov: x and y must have the same number of observations"); |
3200 | 59 endif |
8977
f464119ec165
further simplify some stats funcs
Jaroslav Hajek <highegg@gmail.com>
parents:
8920
diff
changeset
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60 x = center (x, 1); |
f464119ec165
further simplify some stats funcs
Jaroslav Hajek <highegg@gmail.com>
parents:
8920
diff
changeset
|
61 y = center (y, 1); |
3200 | 62 c = conj (x' * y / (n - 1)); |
63 elseif (nargin == 1) | |
8977
f464119ec165
further simplify some stats funcs
Jaroslav Hajek <highegg@gmail.com>
parents:
8920
diff
changeset
|
64 x = center (x, 1); |
3200 | 65 c = conj (x' * x / (n - 1)); |
66 endif | |
67 | |
68 endfunction | |
7411 | 69 |
70 %!test | |
71 %! x = rand (10); | |
72 %! cx1 = cov (x); | |
73 %! cx2 = cov (x, x); | |
7939 | 74 %! assert(size (cx1) == [10, 10] && size (cx2) == [10, 10] && norm(cx1-cx2) < 1e1*eps); |
7411 | 75 |
76 %!error cov (); | |
77 | |
78 %!error cov (1, 2, 3); | |
79 |