I’ve always used Parallel Python but it’s not a complete analog since I believe it typically uses separate processes which can be expensive on certain operating systems. Still, if the body of your loops are chunky enough then this won’t matter and can actually have some benefits.

The one built-in to python would be multiprocessing docs are here. I always use multiprocessing.Pool with as many workers as processors. Then whenever I need to do a for-loop like structure I use Pool.imap

As long as the body of your function does not depend on any previous iteration then you should have near linear speed-up. This also requires that your inputs and outputs are pickle-able but this is pretty easy to ensure for standard types.

UPDATE:
Some code for your updated function just to show how easy it is:

from multiprocessing import Pool
from itertools import product

output = np.zeros((N,N))
pool = Pool() #defaults to number of available CPU's
chunksize = 20 #this may take some guessing ... take a look at the docs to decide
for ind, res in enumerate(pool.imap(Fun, product(xrange(N), xrange(N))), chunksize):
    output.flat[ind] = res

Jupyter Notebook

To see an example consider you want to write the equivalence of this Matlab code on in Python

matlabpool open 4
parfor n=0:9
   for i=1:10000
       for j=1:10000
           s=j*i   
       end
   end
   n
end
disp('done')

The way one may write this in python particularly in jupyter notebook. You have to create a function in the working directory (I called it FunForParFor.py) which has the following

def func(n):
    for i in range(10000):
        for j in range(10000):
            s=j*i
    print(n)

Then I go to my Jupyter notebook and write the following code

import multiprocessing  
import FunForParFor

if __name__ == '__main__':
    pool = multiprocessing.Pool(processes=4)
    pool.map(FunForParFor.func, range(10))
    pool.close()
    pool.join()   
    print('done')

This has worked for me! I just wanted to share it here to give you a particular example.

I tried all solutions here, but found that the simplest way and closest equivalent to matlabs parfor is numba’s prange.

Essentially you change a single letter in your loop, range to prange:

from numba import autojit, prange

@autojit
def parallel_sum(A):
    sum = 0.0
    for i in prange(A.shape[0]):
        sum += A[i]

    return sum

This can be done elegantly with Ray, a system that allows you to easily parallelize and distribute your Python code.

To parallelize your example, you’d need to define your functions with the @ray.remote decorator, and then invoke them with .remote.

import numpy as np
import time

import ray

ray.init()

# Define the function. Each remote function will be executed 
# in a separate process.
@ray.remote
def HeavyComputationThatIsThreadSafe(i, j):
    n = i*j
    time.sleep(0.5) # Simulate some heavy computation. 
    return n

N = 10
output_ids = []
for i in range(N):
    for j in range(N):
        # Remote functions return a future, i.e, an identifier to the 
        # result, rather than the result itself. This allows invoking
        # the next remote function before the previous finished, which
        # leads to the remote functions being executed in parallel.
        output_ids.append(HeavyComputationThatIsThreadSafe.remote(i,j))

# Get results when ready.
output_list = ray.get(output_ids)
# Move results into an NxN numpy array.
outputs = np.array(output_list).reshape(N, N)

# This program should take approximately N*N*0.5s/p, where
# p is the number of cores on your machine, N*N
# is the number of times we invoke the remote function,
# and 0.5s is the time it takes to execute one instance
# of the remote function. For example, for two cores this
# program will take approximately 25sec. 

There are a number of advantages of using Ray over the multiprocessing module. In particular, the same code will run on a single machine as well as on a cluster of machines. For more advantages of Ray see this related post.

Note: One point to keep in mind is that each remote function is executed in a separate process, possibly on a different machine, and thus the remote function’s computation should take more than invoking a remote function. As a rule of thumb a remote function’s computation should take at least a few 10s of msec to amortize the scheduling and startup overhead of a remote function.

I recommend trying joblib Parallel.

one liner

from joblib import Parallel, delayed
out = Parallel(n_jobs=2)(delayed(heavymethod)(i) for i in range(10)) 

instructional

instead of taking a for loop

from time import sleep
for _ in range(10):
   sleep(.2)

rewrite your operation into a list comprehension

[sleep(.2) for _ in range(10)]

Now let us not directly evaluate the expression, but collect what should be done.
This is what the delayed method is for.

from joblib import delayed
[delayed(sleep(.2)) for _ in range(10)]

Next instantiate a parallel process with n_workers and process the list.

from joblib import Parallel
r = Parallel(n_jobs=2, verbose=10)(delayed(sleep)(.2) for _ in range(10)) 

[Parallel(n_jobs=2)]: Done   1 tasks      | elapsed:    0.6s
[Parallel(n_jobs=2)]: Done   4 tasks      | elapsed:    0.8s
[Parallel(n_jobs=2)]: Done  10 out of  10 | elapsed:    1.4s finished

Ok, I’ll also give it a go, let’s see if my way is easier

from multiprocessing import Pool
def heavy_func(key):
    #do some heavy computation on each key 
    output = key**2
    return key, output 

output_data ={}     #<--this dict will store the results
keys = [1,5,7,8,10] #<--compute heavy_func over all the values of keys
with Pool(processes=40) as pool:
    for i in pool.imap_unordered(heavy_func, keys):
        output_data[i[0]] = i[1]

Now output_data is a dictionary that will contain for every key the result of the computation on this key.

That is it..