Scale/resize a square matrix into a larger size whilst retaining the grid structure/pattern (Python)

arr = [[1 0 0]    # 3x3
       [0 1 0]
       [0 0 1]]

largeArr = [[1 1 0 0 0 0]   # 6x6
            [1 1 0 0 0 0]
            [0 0 1 1 0 0]
            [0 0 1 1 0 0]
            [0 0 0 0 1 1]
            [0 0 0 0 1 1]]

Like above, I want to retain the same ‘grid’ format whilst increasing the dimensions of the 2D array. How would I go about doing this? I assume the original matrix can only be scaled up by an integer n.

Answer

You can use numba if performance is of importance (similar post) with no python jitting and in parallel mode if needed (this code can be written faster by some optimizations):

@nb.njit      # @nb.njit("int64[:, ::1](int64[:, ::1], int64)", parallel =True)
def numba_(arr, n):
    res = np.empty((arr.shape[0] * n, arr.shape[0] * n), dtype=np.int64)
    for i in range(arr.shape[0]):     # for i in nb.prange(arr.shape[0])
        for j in range(arr.shape[0]):
            res[n * i: n * (i + 1), n * j: n * (j + 1)] = arr[i, j]
    return res

So, as an example:

arr = [[0 0 0 1 1]
       [0 1 1 1 1]
       [1 1 0 0 1]
       [0 0 1 0 1]
       [0 1 1 0 1]]

res (n=3):
[[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1]
 [0 0 0 0 0 0 0 0 0 1 1 1 1 1 1]
 [0 0 0 0 0 0 0 0 0 1 1 1 1 1 1]
 [0 0 0 1 1 1 1 1 1 1 1 1 1 1 1]
 [0 0 0 1 1 1 1 1 1 1 1 1 1 1 1]
 [0 0 0 1 1 1 1 1 1 1 1 1 1 1 1]
 [1 1 1 1 1 1 0 0 0 0 0 0 1 1 1]
 [1 1 1 1 1 1 0 0 0 0 0 0 1 1 1]
 [1 1 1 1 1 1 0 0 0 0 0 0 1 1 1]
 [0 0 0 0 0 0 1 1 1 0 0 0 1 1 1]
 [0 0 0 0 0 0 1 1 1 0 0 0 1 1 1]
 [0 0 0 0 0 0 1 1 1 0 0 0 1 1 1]
 [0 0 0 1 1 1 1 1 1 0 0 0 1 1 1]
 [0 0 0 1 1 1 1 1 1 0 0 0 1 1 1]
 [0 0 0 1 1 1 1 1 1 0 0 0 1 1 1]]

Performances (perfplot)

In my benchmarks, numba will be the fastest (for large n, parallel mode will be better), after that BrokenBenchmark answer will be faster than scipy.ndimage.zoom. In the benchmarks, f is arr.shape[0] and n is the repeating count: