CHECK_SPECTRUM_AND_INTERNAL_RESONANCE

function check_spectrum_and_internal_resonance(lambdaRe,lambdaIm,mFreqs)
% The spectrum for internal resonances

flags1 = abs(lambdaRe(1:2:end-1)-lambdaRe(2:2:end))<1e-6*abs(lambdaRe(1:2:end-1)); % same real parts
flags1 = all(flags1);
flags2 = abs(lambdaIm(1:2:end-1)+lambdaIm(2:2:end))<1e-6*abs(lambdaIm(1:2:end-1)); % opposite imag parts
flags2 = all(flags2);
freqs  = lambdaIm(1:2:end-1);
freqso = freqs - dot(freqs,mFreqs(:))*mFreqs(:)/sum(mFreqs.^2);
flags3 = norm(freqso)<0.1*norm(freqs);
assert(flags1, 'Real parts do not follow complex conjugate relation');
assert(flags2, 'Imaginary parts do not follow complex conjugate relation');
assert(flags3, 'Internal resonnace is not detected for given master subspace');

end