function CC = cov(X,Y,Mode); % COV covariance matrix % X and Y can contain missing values encoded with NaN. % NaN's are skipped, NaN do not result in a NaN output. % The output gives NaN only if there are insufficient input data % The mean is removed from the data. % % C = COV(X [,Mode]); % calculates the (auto-)correlation matrix of X % C = COV(X,Y [,Mode]); % calculates the crosscorrelation between X and Y. % C(i,j) is the correlation between the i-th and jth % column of X and Y, respectively. % NOTE: Octave and Matlab have (in some special cases) incompatible implemenations. % This implementation follows Octave. If the result could be ambigous or % incompatible, a warning will be presented in Matlab. To avoid this warning use: % a) use COV([X(:),Y(:)]) if you want the traditional Matlab result. % b) use C = COV([X,Y]), C = C(1:size(X,2),size(X,2)+1:size(C,2)); if you want to be compatible with this software. % % Mode = 0 [default] scales C by (N-1) % Mode = 1 scales C by N. % % see also: COVM, COR, CORRCOEF, SUMSKIPNAN % % REFERENCES: % http://mathworld.wolfram.com/Covariance.html % $Revision: 4585 $ % $Id: cov.m 4585 2008-02-04 13:47:45Z adb014 $ % Copyright (C) 2000-2003,2005 by Alois Schloegl <a.schloegl@ieee.org> % This function is part of the NaN-toolbox % http://www.dpmi.tu-graz.ac.at/~schloegl/matlab/NaN/ % This program 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 2 of the License, or % (at your option) any later version. % % This program 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 this program; If not, see <http://www.gnu.org/licenses/>. if nargin==1 Mode = 0; Y = []; elseif nargin==2, % if all(size(Y)==1) & any(Y==[0,1]); % This is not compatible with octave % short-circuit evaluation is required % but for compatibility to matlab, && is avoided SW = all(size(Y)==1); if SW, SW = any(Y==[0,1]); end; if SW, Mode = Y; Y = []; else Mode = 0; end; elseif nargin==3, else fprintf(2,'Error COV: invalid number of arguments\n'); end; if ~exist('OCTAVE_VERSION','builtin') & ~isempty(Y) & (size(X,2)+size(Y,2)~=2), % COV in Matlab is differently defined than COV in Octave. % For compatibility reasons, this branch reflects the difference. fprintf(2,'Warning NaN/COV: This kind of use of COV is discouraged because it produces different results for Matlab and Octave. \n'); fprintf(2,' (a) the traditional Matlab result can be obtained with: C = COV([X(:),Y(:)]).\n'); fprintf(2,' (b) the traditional Octave result can be obtained with: C = COV([X,Y]); C = C(1:size(X,2),size(X,2)+1:size(C,2)).\n'); if prod(size(Y))~=prod(size(X)), error('The lengths of X and Y must match.'); end; X = [X(:),Y(:)]; Y = []; end; if isempty(Y) CC = covm(X,['D',int2str(Mode>0)]); else CC = covm(X,Y,['D',int2str(Mode>0)]); end;

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