MATLAB: Plotting contours of a probability density

contourpdfplotting

How do you create a script file to plot contours of a probability density in the y=0 plane? This is what I have done, but it's obviously wrong. Please help!
z=[-6:0.01:6];
x=[-6:0.01:6];
r=sqrt(x.^2+z.^2);
u1=(8*pi)^(-0.5)*(1-(r./2)).*exp(-r./2);
u2=(8*pi)^(-0.5)*(r./2).*(z/r).*exp(-r./2);
v1=(u1-u2).^(2).*0.5;
contour(x,z,v1)
xlabel('x')
zlabel('z')
I have attached the plot I am supposed to get.

Best Answer

You’re missing a meshgrid call and some element-wise dot-operator division
Otherwise, your code is correct:
z=[-6:0.01:6];
x=[-6:0.01:6];  
[X,Z] = meshgrid(x,z);  
r=sqrt(X.^2+Z.^2);  
u1=sqrt(8*pi)*(1-(r./2)).*exp(-r./2);  
u2=sqrt(8*pi)*(r./2).*(Z./r).*exp(-r./2);  
v1=(u1-u2).^(2).*0.5;
figure(1)
contour(X,Z,v1,20)
xlabel('x')
zlabel('z')
This isn’t exactly like the plot you posted, but it’s close! I’ll leave it to you to supply the necessary refinements to get it looking the way you want. You may want to adjust the number of contours the plot draws (I opted for 20 here).
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