% abs2 of the part of the rotation result which is orthogonal to the desired solution
% want to make this zero
%
% options=optimset("Display","iter","TolX",10*eps,"TolFun",eps*eps)
% [X, FVAL] = fminsearch(@f,t0,options)
%
function r2 = f( t)
 phi0 = t(1); phi1 = t(2); e0 = exp(i*phi0); e1 = exp(i*phi1);
 N = 8; x = 0.883883476483184; y = 0.467707173346743;
 %
 r = ((e1*(1-e0)*sqrt(N-1))/N)*x + ((-e0*(N-1)-1)/N)*y;
 r2 = real(r)*real(r) + imag(r)*imag(r);
end
%
% N=8
% s=ones(8,1)/sqrt(N)
% w=zeros(8,1); w(2)=1
% sp = (sqrt(N)*s-w)/sqrt(N-1)
% H=[-(2-N), 2*sqrt(N-1); -2*sqrt(N-1), (N-2)]/N
% q=s
% x=1/sqrt(N)
% y=sqrt((N-1)/N)
% z=H*[x;y]
% z = x,y used above after one standard rotation