Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / nan-2.5.5 / decovm.m

diff --git a/octave_packages/nan-2.5.5/decovm.m b/octave_packages/nan-2.5.5/decovm.m
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+function [mu,sd,COV,xc,M,R2]=decovm(XCN,NN)
+% decompose extended covariance matrix into mean (mu), 
+% standard deviation, the (pure) Covariance (COV), 
+% correlation (xc) matrix and the correlation coefficients R2.
+% NaN's are condsidered as missing values. 
+% [mu,sd,COV,xc,N,R2]=decovm(ECM[,NN])
+%
+% ECM  is the extended covariance matrix
+% NN   is the number of elements, each estimate (in ECM) is based on 
+%
+% see also: MDBC, COVM, R2
+
+%      $Id: decovm.m 2140 2009-07-02 12:03:55Z schloegl $
+%      Copyright (c) 1999-2002,2009 by  Alois Schloegl
+%       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 3
+% 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, write to the Free Software
+% Foundation, Inc., 51 Franklin Street - Fifth Floor, Boston, MA 02110-1301, USA.
+
+[r,c]=size(XCN);
+if r~=c,
+        fprintf(2,'Warning DECOVM: input argument is not a square matrix\n');
+        XCN = ecovm(XCN);
+        c = c + 1;
+else
+       M = XCN(1,1);
+       if nargin<2,
+                XCN = XCN/(XCN(1,1));
+        else %if nargin==2
+                XCN = XCN./(NN);
+       end;
+
+       if any(isnan(XCN(:))),
+               warning('DECOVM: Extended Covariance Matrix should not contain NaN''s');
+       end;
+       if 0, %det(XCN)<0; % check removed for performance reasons
+               warning('DECOVM: Extended Covariance Matrix must be non-negative definite');
+       end;
+end;
+
+mu  = XCN(1,2:c);
+COV = XCN(2:c,2:c) - mu'*mu;
+sd  = sqrt(diag(COV))';
+if nargout<4, return; end; 
+xc  = COV./(sd'*sd);
+M   = XCN(1,1);
+if nargout<6, return; end; 
+R2  = xc.*xc;
+
+return;
+        
+mu=XCN(2:N,1)/XCN(1,1);
+COV=(XCN(2:N,2:N)/XCN(1,1)-XCN(2:N,1)*XCN(1,2:N)/XCN(1,1)^2);
+sd=sqrt(diag(COV));
+xc=COV./(sd*sd');
+
+% function [ECM] = ecovm(signal);
+% Generates extended Covariance matrix, 
+% ECM= [l signal]'*[l signal]; % l is a matching column of 1's
+% ECM is additive, i.e. it can be applied to subsequent blocks and summed up afterwards
+% [ECM1] = ecovm(s1);
+% [ECM2] = ecovm(s1);
+% [ECM]  = ecovm([s1;s2]);
+% ECM1+ECM2==ECM;
+%
+% SS=sum(signal); ECM=[[size(signal,1),SS];[SS',signal'*signal]];