plotting Intensity function which consists of an exponential sum

hello,

Im trying to plot the followin function in matlab:

where k=10,d=1,A=1,0.1,0.01, epsilon is a random number between [0,1], the summation n is from 1 to 20 and theta goes from [-pi/2,pi/2]

I've written this code:

% param defenition %
L=100; N=20; d=1; k=10; Ar=1;
A=0.1;
theta=linspace(-pi/2,pi/2,200);
phase=(d+A*epsilon)*sin(theta);
epsilon=rand(0,1);


function psi = Psi(x)
    psi=1;
    for n=1:N
        psi=psi+(exp(i*k*phase).^n);
    end
end
I=([abs(psi)].^2);
fplot(I,[-pi/2,pi/2])

but when I try to run it, I get nothing printed in the figure. what did I do wrong?

Thank you very much for your time and attention.

[Sriram Tadavarty]

Remove function declaration and corresponding end, then replace fplot with plot(I)

[Elinor Ginzburg]

thank you for your reply, but it still doesn't work. perhaps you have another idea? now it looks like this:

%% Question 03 %%
% param defenition %
L=100; N=20; d=1; k=10; Ar=1;
A=0.1;
theta=linspace(-pi/2,pi/2,200);
epsilon=rand(0,1);
phase=(d+A*epsilon)*sin(theta);

psi=1;
for n=1:N
    psi=psi+(exp(i*k*phase).^n);
end
I=((abs(psi)).^2);
plot(I)

[Sriram Tadavarty]

rand(0,1) returns empty vector. So instead provide rand(1,1)

Answer 1

[Birdman]

Try this:

L=100; N=20; d=1; k=10; Ar=1;
A=0.1;
theta=linspace(-pi/2,pi/2,200);
epsilon=rand;
phase=(d+A*epsilon)*sin(theta);
psi=1;
for n=1:N
    psi=psi+(exp(1i*k*phase).^n);
end
I=((abs(psi)).^2);
plot(I)

[Elinor Ginzburg]

it worked! thank you so much! I had no idea I need to use rand instead of rand(0,1). how can you keep track between all the changes in different versions? thanks once again!

[Birdman]

I pay attention to details :) you are welcome.