atTunesAndDampingRatesFromMat

find tunes and damping rates from one map matrix with radiation
note that in order to find the damping times, one needs the revolution
time T0, then
tau1 = T0/chi1, tau2 = T0/chi2, tau3 = T0/chi3
In the case that m66 is symplectic, the damping rates will be all 0.
note that we have taken absolute values, assumeing all these quantities
are positive.
B. Nash 24/07/2014

0001 function [nu,chi]=atTunesAndDampingRatesFromMat(m66)
0002 %find tunes and damping rates from one map matrix with radiation
0003 %note that in order to find the damping times, one needs the revolution
0004 %time T0, then
0005 %tau1 = T0/chi1, tau2 = T0/chi2, tau3 = T0/chi3
0006 %In the case that m66 is symplectic, the damping rates will be all 0.
0007 %note that we have taken absolute values, assumeing all these quantities
0008 %are positive.
0009 %B. Nash 24/07/2014
0010 
0011 aa=amat(m66);
0012 
0013 Rmat=aa\m66*aa;
0014 
0015 R1=Rmat([1 2],[1 2]);
0016 R2=Rmat([3 4],[3 4]);
0017 R3=Rmat([5 6],[5 6]);
0018 
0019 %ev=eigs(m66);
0020 
0021 ev1=eigs(R1);
0022 evlog1=log(ev1(1));
0023 
0024 ev2=eigs(R2);
0025 evlog2=log(ev2(1));
0026 
0027 ev3=eigs(R3);
0028 evlog3=log(ev3(1));
0029 
0030 %evlog123=log(ev([1,3,5]));
0031 
0032 nu(1)=abs(imag(evlog1)/(2*pi));
0033 chi(1)=abs(real(evlog1));
0034 
0035 nu(2)=abs(imag(evlog2)/(2*pi));
0036 chi(2)=abs(real(evlog2));
0037 
0038 nu(3)=abs(imag(evlog3)/(2*pi));
0039 chi(3)=abs(real(evlog3));