How to compute eccentricity for elliptical

how to make matlab compute eccentricity for elliptical figure that I am creating. I am creating elliptical using numerical method. See code below and attached.

clear all
clc
%* Set initial position and velocity of the comet.
r0 = 1 ;
v0 = pi;
r = [r0 0];  v = [0 v0];

%* Set physical parameters (mass, G*M)
GM = 4*pi^2;      % Grav. const. * Mass of Sun (au^3/yr^2)
mass = 1.;        % Mass of comet 
adaptErr = 1.e-4; % Error parameter used by adaptive Runge-Kutta
time = 0;

%* Loop over desired number of steps using specified
%  numerical method.
nStep = 1000;
tau = 0.001;

for iStep=1:nStep  

    %* Record position and energy for plotting.
    rplot(iStep) = norm(r);           % Record position for polar plot
    thplot(iStep) = atan2(r(2),r(1));
    tplot(iStep) = time;
    kinetic(iStep) = .5*mass*norm(v)^2;   % Record energies
    potential(iStep) = - GM*mass/norm(r);

% Euler-Cromer step
 accel = -GM*r/norm(r)^3;   
 v = v + tau*accel; 
 r = r + tau*v;             
 time = time + tau;     

   unwrap_theta=unwrap(thplot);

      if unwrap_theta(iStep) > 2*pi 
          break
      end

end

%* Graph the trajectory of the comet.
figure(1); clf;  % Clear figure 1 window and bring forward
q=polar(thplot,rplot,'-');  % Use polar plot for graphing orbit
xlabel('Distance (AU)');  grid;

[James Tursa]

Are you simply asking how to calculate eccentricity from your initial state vector r and v?

Answer 1

[James Tursa]

To calculate the eccentricity of an orbit, e.g. see this link:

http://space.stackexchange.com/questions/1904/how-to-programmatically-calculate-orbital-elements-using-position-velocity-vecto

[Mohammed Alshehri]

I am trying to find out if there is a function in matlab that can calculate the eccentricity from the figure or from theta and r coordinates