Mercurial > hg > octave-lyh
view scripts/statistics/base/cov.m @ 14138:72c96de7a403 stable
maint: update copyright notices for 2012
author | John W. Eaton <jwe@octave.org> |
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date | Mon, 02 Jan 2012 14:25:41 -0500 |
parents | cad4cba03f19 |
children | 34af9f9ff98b |
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## Copyright (C) 1995-2012 Kurt Hornik ## ## 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 {Function File} {} cov (@var{x}) ## @deftypefnx {Function File} {} cov (@var{x}, @var{opt}) ## @deftypefnx {Function File} {} cov (@var{x}, @var{y}) ## @deftypefnx {Function File} {} cov (@var{x}, @var{y}, @var{opt}) ## Compute the covariance matrix. ## ## If each row of @var{x} and @var{y} is an observation, and each column is ## a variable, then the @w{(@var{i}, @var{j})-th} entry of ## @code{cov (@var{x}, @var{y})} is the covariance between the @var{i}-th ## variable in @var{x} and the @var{j}-th variable in @var{y}. ## @tex ## $$ ## \sigma_{ij} = {1 \over N-1} \sum_{i=1}^N (x_i - \bar{x})(y_i - \bar{y}) ## $$ ## where $\bar{x}$ and $\bar{y}$ are the mean values of $x$ and $y$. ## @end tex ## @ifnottex ## ## @example ## cov (x) = 1/N-1 * SUM_i (x(i) - mean(x)) * (y(i) - mean(y)) ## @end example ## ## @end ifnottex ## ## If called with one argument, compute @code{cov (@var{x}, @var{x})}, the ## covariance between the columns of @var{x}. ## ## 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 best unbiased estimator of the ## covariance [default] ## ## @item 1: ## normalize with @math{N}, this provides the second moment around the mean ## @end table ## @seealso{corr} ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.ac.at> ## Description: Compute covariances function c = cov (x, y = [], opt = 0) if (nargin < 1 || nargin > 3) print_usage (); endif if ( ! (isnumeric (x) || islogical (x)) || ! (isnumeric (y) || islogical (y))) error ("cov: X and Y must be numeric matrices or vectors"); endif if (ndims (x) != 2 || ndims (y) != 2) error ("cov: X and Y must be 2-D matrices or vectors"); endif if (nargin == 2 && isscalar (y)) opt = y; endif if (opt != 0 && opt != 1) error ("cov: normalization OPT must be 0 or 1"); endif ## Special case, scalar has zero covariance if (isscalar (x)) if (isa (x, 'single')) c = single (0); else c = 0; endif return; endif if (isrow (x)) x = x.'; endif n = rows (x); if (nargin == 1 || isscalar (y)) x = center (x, 1); c = conj (x' * x / (n - 1 + opt)); else if (isrow (y)) y = y.'; endif if (rows (y) != n) error ("cov: X and Y must have the same number of observations"); endif x = center (x, 1); y = center (y, 1); c = conj (x' * y / (n - 1 + opt)); endif endfunction %!test %! x = rand (10); %! cx1 = cov (x); %! cx2 = cov (x, x); %! assert(size (cx1) == [10, 10] && size (cx2) == [10, 10]); %! assert(cx1, cx2, 1e1*eps); %!test %! x = [1:3]'; %! y = [3:-1:1]'; %! assert (cov (x,y), -1, 5*eps) %! assert (cov (x,flipud (y)), 1, 5*eps) %! assert (cov ([x, y]), [1 -1; -1 1], 5*eps) %!test %! x = single ([1:3]'); %! y = single ([3:-1:1]'); %! assert (cov (x,y), single (-1), 5*eps) %! assert (cov (x,flipud (y)), single (1), 5*eps) %! assert (cov ([x, y]), single ([1 -1; -1 1]), 5*eps) %!test %! x = [1:5]; %! c = cov (x); %! assert (isscalar (c)); %! assert (c, 2.5); %!assert(cov (5), 0); %!assert(cov (single(5)), single(0)); %!test %! x = [1:5]; %! c = cov (x, 0); %! assert(c, 2.5); %! c = cov (x, 1); %! assert(c, 2); %% Test input validation %!error cov (); %!error cov (1, 2, 3, 4); %!error cov ([1; 2], ["A", "B"]); %!error cov (ones (2,2,2)); %!error cov (ones (2,2), ones (2,2,2)); %!error cov (1, 3); %!error cov (ones (2,2), ones (3,2));