--- /dev/null
+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.
+%
+% Remark: for data contains missing values, the resulting
+% matrix might not be positiv definite, and its elements have magnitudes
+% larger than one. This ill-behavior is more likely for small sample
+% sizes, but there is no garantee that the result "behaves well" for larger
+% sample sizes. If you want the a "well behaved" result (i.e. positive
+% definiteness and magnitude of elements not larger than 1), use CORRCOEF.
+% However, COV is faster than CORRCOEF and might be good enough in some cases.
+%
+% 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
+
+% $Id: cov.m 9803 2012-03-09 20:03:49Z schloegl $
+% Copyright (C) 2000-2003,2005,2009,2011,2012 by Alois Schloegl <alois.schloegl@ist.ac.at>
+% This function is part of the NaN-toolbox
+% http://pub.ist.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 numel(Y)~=numel(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;
+
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff