Preparing the data for communication

First, we will look into Step 2. It is a nice exercise to write a script that splits a vector into m pieces with a balanced number of elements. Here is one suggestion for such a script, among many others:

def split_array(vector, n_processors):
 # splits an array into a number of subarrays 
 # vector one dimensional ndarray or a list
 # n_processors integer, the number of subarrays to be formed
 
    n=len(vector)
    n_portions, rest = divmod(n,n_processors) # division with remainder
    # get the amount of data per processor and distribute the res on
    # the first processors so that the load is more or less equally 
    # distributed
    # Construction of the indexes needed for the splitting
    counts = [0]+ [n_portions + 1 \
                 if p < rest else n_portions for p in range(n_processors)]
    counts=numpy.cumsum(counts)
    start_end=zip(counts[:-1],counts[1:]) # a generator
    slice_list=(slice(*sl) for sl in start_end) # a generator comprehension...