Multi tool use

python numpy ndarray index permutations in all dimensions (variable dimension number)

'M' is a numpy ndarray, which dimension 'dim' number is variable (previously generated) but each dimension is of equal size 'size'. In my code it will be more like dim = 5, size = 7.

ex: (dim = 3,size = 4).

M = np.arange(size**dim).reshape((size,)*dim)

[[[ 0 1 2 3]
[ 4 5 6 7]
[ 8 9 10 11]
[12 13 14 15]]

[[16 17 18 19]
[20 21 22 23]
[24 25 26 27]
[28 29 30 31]]

[[32 33 34 35]
[36 37 38 39]
[40 41 42 43]
[44 45 46 47]]

[[48 49 50 51]
[52 53 54 55]
[56 57 58 59]
[60 61 62 63]]]


And I have a permutation generator of my own, 'per', that generates specific permutations (not random) of range(size).

print(next(per))
(1,0,3,2)


My need: transform M, by moving its elements according to as many permutations as I need. In the example: 21 (1 permutation for first dimension, 4 for second, 16 for third - generalised: size**d for d in range(dim) permutations). My permutations are not random, but they are independant, different from each other.

A result may be:

[[[36 39 37 38]
[33 34 32 35]
[46 44 45 47]]
[41 43 40 42]
[[9 10 11 8]
[2 1 3 0]
[6 7 5 4]
[13 12 14 15]]
[[56 59 57 58]
[63 61 62 60]
[53 54 52 55]
[51 50 49 48]]
[[28 30 29 31]
[27 25 24 26]
[17 18 16 19]
[23 21 20 22]]]


How can I do it directly from M as numpy array, whith my code remaining dynamic?

1 Answer
1

This is an exercise in broadcasting:

>>> import numpy as np
>>> from itertools import islice
>>>
>>> A = np.arange(27).reshape(3,3,3)
>>> def per(n):
... while True:
... yield np.random.permutation(n)
...
>>> pg = per(3)
>>>
>>> p0 = next(pg)[..., None, None]
>>> p1 = np.array([p for p in islice(pg, 3)])[..., None]
>>> p2 = np.array([[p for p in islice(pg, 3)] for _ in range(3)])
>>>
>>> p0
array([[[2]],

[[1]],

[[0]]])
>>> p1
array([[[1],
[0],
[2]],

[[1],
[0],
[2]],

[[0],
[2],
[1]]])
>>> p2
array([[[1, 0, 2],
[0, 2, 1],
[0, 1, 2]],

[[2, 1, 0],
[1, 2, 0],
[2, 1, 0]],

[[1, 2, 0],
[2, 1, 0],
[2, 1, 0]]])
>>> A[p0, p1, p2]
array([[[22, 21, 23],
[18, 20, 19],
[24, 25, 26]],

[[14, 13, 12],
[10, 11, 9],
[17, 16, 15]],

[[ 1, 2, 0],
[ 8, 7, 6],
[ 5, 4, 3]]])


General soln:

import numpy as np
from itertools import islice

def per(n=None):
while True:
n = (yield n if n is None else np.random.permutation(n)) or n

def sweep(shp):
pg = per()
pg.send(None)
redshp = len(shp)*[1]
sz = 1
for j, k in enumerate(shp):
pg.send(k)
redshp[j] = k
yield np.reshape((*islice(pg, sz),), redshp)
sz *= k

# example
a = np.arange(24).reshape((2,3,4))
idx = *sweep(a.shape),
for i in idx:
print(i)
print(a[idx])


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