atbeam

ATBEAM generates a particle distribution according to a sigma matrix
  PARTICLES=ATBEAM(NP,SIGMA)  Generate a particle distribution according to a sigma matrix
  PARTICLES=ATBEAM(NP,SIGMA,ORBIT) adds a center of mass to the distribution%

  INPUTS
    1. NP     number of particles
    2. SIGMA  beam matrix (2x2, 4x4, 6x6)
    3. ORBIT  closed orbit

  OUPUTS
    1. PARTICLES particle distribution

  NOTES
    1. random generator is randn

  See also atsigma

0001 function particle_dist = atbeam(np,sigma,orbit)
0002 %ATBEAM generates a particle distribution according to a sigma matrix
0003 %  PARTICLES=ATBEAM(NP,SIGMA)  Generate a particle distribution according to a sigma matrix
0004 %  PARTICLES=ATBEAM(NP,SIGMA,ORBIT) adds a center of mass to the distribution%
0005 %
0006 %  INPUTS
0007 %    1. NP     number of particles
0008 %    2. SIGMA  beam matrix (2x2, 4x4, 6x6)
0009 %    3. ORBIT  closed orbit
0010 %
0011 %  OUPUTS
0012 %    1. PARTICLES particle distribution
0013 %
0014 %  NOTES
0015 %    1. random generator is randn
0016 %
0017 %  See also atsigma
0018 
0019 %
0020 %See also ATPLOTBEAM, ATSIGMA
0021 
0022 % ampl=sqrt(-2*log(rand(3,np)));
0023 % phase=2*pi()*rand(3,np);
0024 % v=[ampl.*cos(phase);ampl.*sin(phase)];
0025 v=randn(size(sigma,1),np);
0026 try
0027     l=chol(sigma);
0028 catch
0029     a=[chol(sigma([1 2 5 6],[1 2 5 6])) zeros(4,2);zeros(2,6)];
0030     l=a([1 2 5 6 3 4],[1 2 5 6 3 4]);
0031 end
0032 if nargin < 3
0033     particle_dist=l'*v;
0034 else
0035     particle_dist=orbit(:,ones(1,np)) + l'*v;
0036 end
0037 end