How to mimic larger periodic array in Python

Question

I want to pass a pair of d-dimensional arrays to scipy.signal.correlate, but I want it to be calculated as though both inputs are periodic in every direction. So, in 1 dimension, if my arrays were [1,2,3] and [4,5,6], I'd like to pass to scipy.signal.correlate [1,2,3,1,2,3,1,2,3] and [4,5,6,4,5,6,4,5,6], which will give me back a new array of size 17 which I will then cut out the middle 9 elements of. However, if possible, I'd like to not have to actually replicate the full data of the input arrays in memory which would multiply the size of the inputs by 3^d, but just provide a view of the arrays as though they were tiled into a hypercube that was 3^d bigger. Though, I know the output from the correlate function will still give me a result that is much larger than 3^d time the size of the input arrays.

numpy.tile seems to do what I want.

a = [[1, 2, 3], 
     [2, 4, 6],  
     [3, 6, 9]]
tiled_a = numpy.tile(a, numpy.ones(a.ndim, int) * 3)
print(tiled)

correctly yeilds

[[1 2 3 1 2 3 1 2 3]
 [2 4 6 2 4 6 2 4 6]
 [3 6 9 3 6 9 3 6 9]
 [1 2 3 1 2 3 1 2 3]
 [2 4 6 2 4 6 2 4 6]
 [3 6 9 3 6 9 3 6 9]
 [1 2 3 1 2 3 1 2 3]
 [2 4 6 2 4 6 2 4 6]
 [3 6 9 3 6 9 3 6 9]]

But I don't believe this is just a view, but is actually taking up 9 times the original memory as the original array.

Answer 1

I'm not sure if that helps, but - w.r.t. your example above - look at:

l1 = [1, 2, 3] * 3
l2 = [2, 4, 6] * 3
l3 = [3, 6, 9] * 3
m = [l1, l2, l3, l1, l2, l3, l1, l2, l3]
print(m)
m[0][0] = 100
print(m)

The first 3 arrays in m have to store data, the rest points to the first 3. Let me know if that's not what you're interested in: I will delete the answer if not.