ccakirby

formulation in Johnson and Wichern but using SVD
let X, Y be data matrix of data set I, II X = [x1;x2;...]

0001 function [A,B,cc] = ccakirby(X,Y)
0002 %formulation in Johnson and Wichern but using SVD
0003 %let X, Y be data matrix of data set I, II X = [x1;x2;...]
0004 
0005 mx = mean(X);
0006 MX = repmat(mx,size(X,1),1);
0007 my=mean(Y);
0008 MY = repmat(my,size(Y,1),1);
0009 
0010 if 0
0011   S11 = (X-MX)'*(X-MX)/size(X,1);
0012   S22 = (Y-MY)'*(Y-MY)/size(Y,1);
0013   S12 = (X-MX)'*(Y-MY)/size(X,1);
0014 else
0015   S11 = cov(X);
0016   S22 = cov(Y);
0017 end  
0018 S12 = (X-MX)'*(Y-MY)/(size(X,1)-1);
0019 
0020 K = inv(real(sqrtm(S11)))*S12*inv(real(sqrtm(S22)));
0021 
0022 %The matrix RHO contains the correlation coefs along its diagonal
0023 
0024 [E,RHO,F] = svd(K);
0025 E = real(E);
0026 F = real(F);
0027 
0028 A = inv(real(sqrtm(S11)))*E;
0029 if nargout > 1
0030   B = inv(real(sqrtm(S22)))*F;
0031 end
0032 
0033 cc = diag(RHO);