Question

from random import *
N = 100
gamma = 0.7
connect = zeros((N,N))

for i in range(N):
    for j in range(i+1):
        if random() < gamma:
            connect[i,j] = 1
            connect[j,i] = 1
        else:
            connect[i,j] = 0
            connect[j,i] = 0

What I try to do is to create a symmetrical matrix, filled with zeros and ones (ones with a probability of 0.7).
Here is the double for loop, very inefficient…I shall make something with numpy, which I believe could speed up thing a great deal?
Does anyone know how to proceed?
Thank you very much!

Answer 1

You could use the numpy random module to generate random vectors, and use those vectors to seed the matrix. For example:

import numpy as np

N = 100
gamma = 0.7
connect = np.zeros((N,N),dtype=np.int32)

for i in range(0,N):
        dval = np.diag((np.random.random_sample(size=(N-i))<gamma).astype(np.int32),i)
        connect += dval
        if (i>0):
                connect += dval.T

does this diagonally using numpy.diag, but you could do it row-wise to assemble the upper or lower triangular portion, then use addition to form the symmetrical matrix. I don’t have a feeling for which might be faster.

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EDIT:
In fact this row wise version is about 5 times faster than the diagonal version, which I guess shouldn’t be all that surprising given the memory access patterns it uses compared to diagonal assembly.

N = 100
gamma = 0.7
connect = np.zeros((N,N),dtype=np.int32)

for i in range(0,N):
    rval = (np.random.random_sample(size=(N-i))<gamma).astype(np.int32)
    connect[i,i:] = rval

connect += np.triu(connect,1).T

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EDIT 2

This is even simpler and about 4 times faster than the row-wise version above. Here a triangular matrix is formed directly from a full matrix of weights, then added to its transpose to produce the symmetric matrix:

N = 100
gamma = 0.7
a=np.triu((np.random.random_sample(size=(N,N))<gamma).astype(np.int32))
connect = a + np.triu(a,1).T

On the Linux system I tested it on, version 1 takes about 6.5 milliseconds, version 2 takes about 1.5 milliseconds, version 3 takes about 450 microseconds.