veccor1

 VECCOR1 computes the complex vector correlation.

 [a,theta]=VECCOR1(u1,v1,u2,v2) computes the complex vector correlation
 coefficient following Kundu (1976), JPO, 6, 238-242. Input are the 
 four time series vectors. Output is complex, with amplitude and 
 rotation angle in degrees. A positive angle indicates that series 1
 is rotated positively (counterclockwise) from series 2.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 ver. 1: 12/1/96 (RB)
 ver. 2:  allow for complex arguments, remove mean
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

0001  function   [a,theta]=veccor1(u1,v1,u2,v2)
0002 
0003 % VECCOR1 computes the complex vector correlation.
0004 %
0005 % [a,theta]=VECCOR1(u1,v1,u2,v2) computes the complex vector correlation
0006 % coefficient following Kundu (1976), JPO, 6, 238-242. Input are the
0007 % four time series vectors. Output is complex, with amplitude and
0008 % rotation angle in degrees. A positive angle indicates that series 1
0009 % is rotated positively (counterclockwise) from series 2.
0010 %
0011 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0012 % ver. 1: 12/1/96 (RB)
0013 % ver. 2:  allow for complex arguments, remove mean
0014 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0015 
0016 % make input column vectors
0017 if(nargin==2),
0018   X=u1(:);
0019   Y=v1(:);
0020 else
0021   X=u1(:)+i*v1;
0022   Y=u2(:)+i*v2;
0023 end
0024 
0025 % work on only the common good points
0026 ii=find((finite(X+Y)));
0027 % if no common good points, return NaNs
0028 if(length(ii)<1),amp=NaN;theta=NaN;trans=NaN;return;end
0029 X=X(ii); Y=Y(ii);
0030 
0031 % remove mean
0032 X=X-mean(X(:)); Y=Y-mean(Y(:));
0033 
0034 % compute a, theta
0035 c=(rot90(X)*conj(Y))./(sqrt(rot90(X)*conj(X))*sqrt(rot90(Y)*conj(Y)));
0036 a=abs(c);
0037 theta=180.*angle(c)./pi;
0038