%%%%%%%%%%%%%%%%%%%%%%%%%%%% Geodesic Ray Matrix %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% RAYMATU
% Usage: RAYMATU(x,u)
%Inputs:  x= basepoint of ray  
%         u = direction of ray, 
%   
% Output:  a matrix L used to construct the ray from x in the direction u

function L = raymatu(x,u)             
   v = sqrt(1-abs(x)^2);          % a normalizing factor
   w = sqrt(u/abs(u));            % rotation factor (determined by u) 
   a = w/v;
   b = x*conj(a);
   L = [a  b; conj(b) conj(a)];