ROTMAJAX rotates input vector velocity into direction of maximum variance. [ur,[vr],thetad]=ROTMAJAX(u,v) rotates input vector velocity into direction of maximum variance. Input can be either real u,v or complex (u+iv) vectors, ur,vr or (ur+ivr) is the vector velocity rotated by the angle theta counterclockwise. Assumes u,v are east,north components. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ver. 1: 11/17/96 (RG) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0001 function [ur,vr,thetad]=rotmajax(u,v) 0002 0003 % ROTMAJAX rotates input vector velocity into direction of maximum variance. 0004 % 0005 % [ur,[vr],thetad]=ROTMAJAX(u,v) rotates input vector velocity 0006 % into direction of maximum variance. Input can be either real 0007 % u,v or complex (u+iv) vectors, ur,vr or (ur+ivr) is the vector 0008 % velocity rotated by the angle theta counterclockwise. Assumes 0009 % u,v are east,north components. 0010 % 0011 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0012 % ver. 1: 11/17/96 (RG) 0013 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0014 0015 if nargin==1; 0016 v=imag(u); 0017 u=real(u); 0018 end 0019 0020 [N,M]=size(u); 0021 if M==1 0022 u=u';v=v'; 0023 end 0024 0025 if any( isnan(u(:)))|(isnan(v(:)) ) 0026 disp('NaNs found') 0027 ur=oness(u)*nan; 0028 vr=ur; 0029 g=find( (~isnan(u(:)))&(~isnan(v(:))) ); 0030 if length(g)>1; 0031 u=u(g); 0032 v=v(g); 0033 end 0034 else 0035 ur=u; 0036 vr=u; 0037 g=1:length(u(:)); 0038 end 0039 if length(g)>1 0040 cv1=cov([u(:) v(:)]); 0041 theta=0.5*atan2(2.*cv1(2,1),(cv1(1,1)-cv1(2,2)) ); 0042 thetad=theta*180./pi 0043 vr(g)=-u*sin(theta)+v*cos(theta); 0044 ur(g)=u*cos(theta)+v*sin(theta); 0045 0046 else; 0047 thetad=nan; 0048 end 0049 0050 if M==1 0051 ur=ur';vr=vr'; 0052 end 0053 0054 if nargin==1 0055 ur=ur+sqrt(-1)*vr; 0056 vr=thetad; 0057 thetad=[]; 0058 end