We have the following two-dimensional array with x and y coordinates:
x = np.array([[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11], [12, 13, 14, 15]])
We flatten it: x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) )
and our goal is to apply translations into x direction, y direction.
We are dealing with a 4×4 array (lattice), and the first transformation is 1 shift into x direction :
so from ‘[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]’ we get ‘[1, 2, 3, 0, 5, 6, 7, 4, 9, 10, 11, 8, 13, 14, 15, 12]’.
The next transformation is two shifts in x:
from ‘[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]’ we get ‘[2, 3, 0, 1, 6, 7, 4, 5, 10, 11, 8, 9, 14, 15, 12, 13]’.
We want to get this (flattened) array:
y = np.array([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],
[1, 2, 3, 0, 5, 6, 7, 4, 9, 10, 11, 8, 13, 14, 15, 12],
[2, 3, 0, 1, 6, 7, 4, 5, 10, 11, 8, 9, 14, 15, 12, 13],
[3, 0, 1, 2, 7, 4, 5, 6, 11, 8, 9, 10, 15, 12, 13, 14],
[4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3],
[5, 6, 7, 4, 9, 10, 11, 8, 13, 14, 15, 12, 1, 2, 3, 0],
[6, 7, 4, 5, 10, 11, 8, 9, 14, 15, 12, 13, 2, 3, 0, 1],
[7, 4, 5, 6, 11, 8, 9, 10, 15, 12, 13, 14, 3, 0, 1, 2],
[8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7],
[9, 10, 11, 8, 13, 14, 15, 12, 1, 2, 3, 0, 5, 6, 7, 4],
[10, 11, 8, 9, 14, 15, 12, 13, 2, 3, 0, 1, 6, 7, 4, 5],
[11, 8, 9, 10, 15, 12, 13, 14, 3, 0, 1, 2, 7, 4, 5, 6],
[12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11],
[13, 14, 15, 12, 1, 2, 3, 0, 5, 6, 7, 4, 9, 10, 11, 8],
[14, 15, 12, 13, 2, 3, 0, 1, 6, 7, 4, 5, 10, 11, 8, 9],
[15, 12, 13, 14, 3, 0, 1, 2, 7, 4, 5, 6, 11, 8, 9, 10]])
I tried using:
y = np.roll(np.roll(x, -1), -1)
>Solution :
Can concatenate two vstack operations. First, roll in axis=1 and then, roll in axis=0.
np.vstack([np.roll(np.roll(arr, -i, axis=0), -x, axis=1).flatten() \
for x in range(arr.shape[0])] \
for i in range(arr.shape[1]))
array([[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],
[ 1, 2, 3, 0, 5, 6, 7, 4, 9, 10, 11, 8, 13, 14, 15, 12],
[ 2, 3, 0, 1, 6, 7, 4, 5, 10, 11, 8, 9, 14, 15, 12, 13],
[ 3, 0, 1, 2, 7, 4, 5, 6, 11, 8, 9, 10, 15, 12, 13, 14],
[ 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3],
[ 5, 6, 7, 4, 9, 10, 11, 8, 13, 14, 15, 12, 1, 2, 3, 0],
[ 6, 7, 4, 5, 10, 11, 8, 9, 14, 15, 12, 13, 2, 3, 0, 1],
[ 7, 4, 5, 6, 11, 8, 9, 10, 15, 12, 13, 14, 3, 0, 1, 2],
[ 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7],
[ 9, 10, 11, 8, 13, 14, 15, 12, 1, 2, 3, 0, 5, 6, 7, 4],
[10, 11, 8, 9, 14, 15, 12, 13, 2, 3, 0, 1, 6, 7, 4, 5],
[11, 8, 9, 10, 15, 12, 13, 14, 3, 0, 1, 2, 7, 4, 5, 6],
[12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11],
[13, 14, 15, 12, 1, 2, 3, 0, 5, 6, 7, 4, 9, 10, 11, 8],
[14, 15, 12, 13, 2, 3, 0, 1, 6, 7, 4, 5, 10, 11, 8, 9],
[15, 12, 13, 14, 3, 0, 1, 2, 7, 4, 5, 6, 11, 8, 9, 10]])