/src/utils/t2r.m

function R=t2r(E1,P1,E2,P2,mu)

%

% Compute pseudo-4x4 R-matrix (diagonal 2x2's) between two points from

% twiss parameters.

%

% (NOTE: Pn=[psix,betax,alphax,etax,etapx,psiy,betay,alphay,etay,etapy])

%

% INPUTs:

%

%   E1 = energy at point 1 (GeV)

%   P1 = twiss at point 1

%   E2 = energy at point 2 (GeV)

%   P2 = twiss at point 2

%   mu = (optional) if provided and nonzero, convert phases in tune units

%        to radians

%

% OUTPUT:

%

%   R=[R11 R12  0   0

%      R21 R22  0   0  

%       0   0  R33 R34

%       0   0  R43 R44]



if (nargin<5)

  mu=0;

end

if (mu)

  conv=2*pi;

else

  conv=1;

end



R=eye(4);



psi1=conv*P1(1);beta1=P1(2);alpha1=P1(3);

psi2=conv*P2(1);beta2=P2(2);alpha2=P2(3);

dpsi=psi2-psi1;

S=sin(dpsi);

C=cos(dpsi);

R(1,1)=sqrt(beta2/beta1)*(C+alpha1*S);

R(1,2)=sqrt(beta1*beta2)*S;

R(2,1)=-((1+alpha1*alpha2)*S+(alpha2-alpha1)*C)/sqrt(beta1*beta2);

R(2,2)=sqrt(beta1/beta2)*(C-alpha2*S);



psi1=conv*P1(6);beta1=P1(7);alpha1=P1(8);

psi2=conv*P2(6);beta2=P2(7);alpha2=P2(8);

dpsi=psi2-psi1;

S=sin(dpsi);

C=cos(dpsi);

R(3,3)=sqrt(beta2/beta1)*(C+alpha1*S);

R(3,4)=sqrt(beta1*beta2)*S;

R(4,3)=-((1+alpha1*alpha2)*S+(alpha2-alpha1)*C)/sqrt(beta1*beta2);

R(4,4)=sqrt(beta1/beta2)*(C-alpha2*S);



R=sqrt(E1/E2)*R;