Random and symmetric permutation matrix

permutation_matrix.py

import numpy as np
from itertools import product

def generatePermutationMatrix(n):
    d = np.zeros((n, n))
    index = np.random.permutation(range(n))

    p = index[:n/2]
    index1 = list(product(p, p))
    for i in index1:
        d[i] = 1

    p = index[n/2:]
    index2 = list(product(p, p))
    for i in index2:
        d[i] = 1

    return d

Sample output

print generatePermutationMatrix(6)
[[ 1. 1. 0. 0. 0. 1.]
[ 1. 1. 0. 0. 0. 1.]
[ 0. 0. 1. 1. 1. 0.]
[ 0. 0. 1. 1. 1. 0.]
[ 0. 0. 1. 1. 1. 0.]
[ 1. 1. 0. 0. 0. 1.]]