PDF to CDF in MATLAB

Hi!
Im trying to extract a scattering angle for a photon using the Klein-Nishina scattering angle distribution (KN in the code) and for this I need the CDF (of KN) to be able to use the Monte Carlo method when that is achieved. All i've managed so far is to plot the PDF between 0 degrees and Pi to see that it looks alright, and that it has that "peanut shape". Ive tried to use the built in CDF function but it seems very slow.

E_gamma=0.140;
alpha=0.511;
P=zeros(3142,1);
KN_matrix=zeros(3142, 1);

for k=1:3142
j=(k-1)/1000;
PE=1/(1+((E_gamma/alpha)*(1-cos(j))));
KN=(PE^2*(PE+(1/PE)-1+(cos(j))^2))/2;
KN_matrix(k,1)=(KN);
plot(j,KN_matrix(k,1))
hold on
end

Thanks!
axis equal