Create a random array of specified shape and then sort along the axis where you want to keep the limits, thus giving us a vectorized and very efficient solution. This would be based on this smart answer
to MATLAB randomly permuting columns differently
. Here's the implementation -
Sample run -
In [122]: N = 10
In [123]: np.argsort(np.random.rand(8,N),axis=0)+1
Out[123]:
array([[7, 3, 5, 1, 1, 5, 2, 4, 1, 4],
[8, 4, 3, 2, 2, 8, 5, 5, 6, 2],
[1, 2, 4, 6, 5, 4, 4, 3, 4, 7],
[5, 6, 2, 5, 8, 2, 7, 8, 5, 8],
[2, 8, 6, 3, 4, 7, 1, 1, 2, 6],
[6, 7, 7, 8, 6, 6, 3, 2, 7, 3],
[4, 1, 1, 4, 3, 3, 8, 6, 8, 1],
[3, 5, 8, 7, 7, 1, 6, 7, 3, 5]], dtype=int64)
Runtime tests -
In [124]: def sortbased_rand8(N):
...: return np.argsort(np.random.rand(8,N),axis=0)+1
...:
...: def rand_M(N):
...: M = np.zeros(shape = (8, N))
...: for i in range (0, N):
...: M[:, i] = np.random.choice(8, size = 8, replace = False) + 1
...: return M
...:
In [125]: N = 5000
In [126]: %timeit sortbased_rand8(N)
100 loops, best of 3: 1.95 ms per loop
In [127]: %timeit rand_M(N)
1 loops, best of 3: 233 ms per loop
Thus, awaits a 120x
speedup!