function [x,y]=ellipse(X,p,q)



%  function [x,y]=ellipse(X,p,q)

%

%    Return coordinates which can be used to plot the ellipse described by the

%    2x2 symmetric matrix "X", centered at the point (p,q).

%

%  INPUTS:

%

%    X:     a 2x2 symmetric matrix which describes the ellipse as follows:

%

%            [x y]*X*[x y]' = 1,

%

%           or, with X = [a b 

%                         b c],

%

%	           ax^2 + 2bxy + cy^2  = 1;

%

%           for a beam ellipse, X=inv(sigma)=(1/emit)*[gamma alpha

%                                                      alpha  beta]

%

%    p:     ordinate of ellipse center

%    q:     abscissa of ellipse center

%

%  OUTPUTS:

%

%    x:     a 1001 element column vector of x-coordinates

%    y:     a 1001 element column vector of y-coordinates



%===============================================================================



[r,c]=size(X);

if ((r~=2)|(c~=2))

  error('X must be a 2x2 matrix')

end

if (abs(X(1,2)-X(2,1))>(abs(.001*X(1,2))+eps))

  error('X must be a symmetric matrix')

end



a=X(1,1);

b=X(1,2);

c=X(2,2);



delta=0.001;

theta=[0:delta:pi]';

C=cos(theta);

S=sin(theta);



r=sqrt((a*(C.^2)+2*b*(C.*S)+c*(S.^2)).^(-1));

r=[r,r];

C=[C,-C];

S=[S,-S];



x=r.*C;         

y=r.*S;