I have a code that uses two parameters (r,t) to create a matrix H. I then find the eigenvalues of this matrix and do some computations using the eigenvalues. Now, I need to do this for many different values of (r,t), (around 200). Since each operation is independent I tried to use multiprocessing in python to have all these operations done simultaneously.

When I run the code for a single (r,t), it takes around 1.5 hours. I was under the impression that running it for 200 (r,t)s should take around the same time using multiprocessing. However, it seems t be taking significantly longer. I am well into the 2nd day of the code running. I am using my university’s high performance unit so I believe there should be enough cores to assign. My code is something like below-

import numpy as np
import multiprocessing

rs = np.linspace(0.5,1.5,20)
thetas = np.linspace(0,np.pi/2,10)

def matrix_stuff(r,t):
#constructs a matrix H(r,t). Diagonalize and do stuff.


processes = []
rets = []
q = multiprocessing.Queue()

for i in range(len(thetas)):
    for j in range(len(rs)):
        theta = thetas[i]
        r = rs[I]
        p = multiprocessing.Process(target=matrix_stuff, args = (r,theta,i,j))
        processes.append(p)
        p.start()

for p in processes:
    ret = q.get()
    rets.append(ret)

for p in processes:
    p.join()


#store output in deltas

deltas = np.zeros((len(rs),len(thetas)))


for ret in rets:
    # ret has format (value, i,j)
    deltas[rets[1],rets[2]] = rets[0]

np.savetxt('new_deltas.txt',deltas)

My question is then are there some other areas where my program could be getting bottlenecked that I am not considering? This my is first time using multiprocessing so I am still not very clear on the details.