There is a function np.split()
which can split an array along 1 axis. I was wondering if there was a multi axis version where you can split along axes (0,1,2) for e
I don't think there is a multi axis version where you can split along some given axes. But you can split it up one dimension at a time. For example like this:
def split2(arys, sections, axis=[0, 1]):
if not isinstance(arys, list):
arys = [arys]
for ax in axis:
arys = [np.split(ary, sections, axis=ax) for ary in arys]
arys = [ary for aa in arys for ary in aa] # Flatten
return arys
It can be used like this:
In [1]: a = np.array(range(100)).reshape(10, 10)
In [2]: split2(a, 2, axis=[0, 1])
Out[2]:
[array([[ 0, 1, 2, 3, 4],
[10, 11, 12, 13, 14],
[20, 21, 22, 23, 24],
[30, 31, 32, 33, 34],
[40, 41, 42, 43, 44]]),
array([[ 5, 6, 7, 8, 9],
[15, 16, 17, 18, 19],
[25, 26, 27, 28, 29],
[35, 36, 37, 38, 39],
[45, 46, 47, 48, 49]]),
array([[50, 51, 52, 53, 54],
[60, 61, 62, 63, 64],
[70, 71, 72, 73, 74],
[80, 81, 82, 83, 84],
[90, 91, 92, 93, 94]]),
array([[55, 56, 57, 58, 59],
[65, 66, 67, 68, 69],
[75, 76, 77, 78, 79],
[85, 86, 87, 88, 89],
[95, 96, 97, 98, 99]])]
Suppose the cube
has shape (W, H, D)
and you wish to break it up into N
little cubes of shape (w, h, d)
. Since NumPy arrays have axes of fixed length, w
must evenly divide W
, and similarly for h
and d
.
Then there is a way to reshape the cube of shape (W, H, D)
into a new array of shape (N, w, h, d)
.
For example, if arr = np.arange(4*4*4).reshape(4,4,4)
(so (W,H,D) = (4,4,4)
) and we wish to break it up into cubes of shape (2,2,2)
, then we could use
In [283]: arr.reshape(2,2,2,2,2,2).transpose(0,2,4,1,3,5).reshape(-1,2,2,2)
Out[283]:
array([[[[ 0, 1],
[ 4, 5]],
[[16, 17],
[20, 21]]],
...
[[[42, 43],
[46, 47]],
[[58, 59],
[62, 63]]]])
The idea here is to add extra axes to the array which sort of act as place markers:
number of repeats act as placemarkers
o---o---o
| | |
v v v
(2,2,2,2,2,2)
^ ^ ^
| | |
o---o---o
newshape
We can then reorder the axes (using transpose
) so that the number of repeats comes first, and the newshape comes at the end:
arr.reshape(2,2,2,2,2,2).transpose(0,2,4,1,3,5)
And finally, call reshape(-1, w, h, d)
to squash all the placemarking axes into a single axis. This produces an array of shape (N, w, h, d)
where N
is the number of little cubes.
The idea used above is a generalization of this idea to 3 dimensions. It can be further generalized to ndarrays of any dimension:
import numpy as np
def cubify(arr, newshape):
oldshape = np.array(arr.shape)
repeats = (oldshape / newshape).astype(int)
tmpshape = np.column_stack([repeats, newshape]).ravel()
order = np.arange(len(tmpshape))
order = np.concatenate([order[::2], order[1::2]])
# newshape must divide oldshape evenly or else ValueError will be raised
return arr.reshape(tmpshape).transpose(order).reshape(-1, *newshape)
print(cubify(np.arange(4*6*16).reshape(4,6,16), (2,3,4)).shape)
print(cubify(np.arange(8*8*8*8).reshape(8,8,8,8), (2,2,2,2)).shape)
yields new arrays of shapes
(16, 2, 3, 4)
(256, 2, 2, 2, 2)
To "uncubify" the arrays:
def uncubify(arr, oldshape):
N, newshape = arr.shape[0], arr.shape[1:]
oldshape = np.array(oldshape)
repeats = (oldshape / newshape).astype(int)
tmpshape = np.concatenate([repeats, newshape])
order = np.arange(len(tmpshape)).reshape(2, -1).ravel(order='F')
return arr.reshape(tmpshape).transpose(order).reshape(oldshape)
Here is some test code to check that cubify
and uncubify
are inverses.
import numpy as np
def cubify(arr, newshape):
oldshape = np.array(arr.shape)
repeats = (oldshape / newshape).astype(int)
tmpshape = np.column_stack([repeats, newshape]).ravel()
order = np.arange(len(tmpshape))
order = np.concatenate([order[::2], order[1::2]])
# newshape must divide oldshape evenly or else ValueError will be raised
return arr.reshape(tmpshape).transpose(order).reshape(-1, *newshape)
def uncubify(arr, oldshape):
N, newshape = arr.shape[0], arr.shape[1:]
oldshape = np.array(oldshape)
repeats = (oldshape / newshape).astype(int)
tmpshape = np.concatenate([repeats, newshape])
order = np.arange(len(tmpshape)).reshape(2, -1).ravel(order='F')
return arr.reshape(tmpshape).transpose(order).reshape(oldshape)
tests = [[np.arange(4*6*16), (4,6,16), (2,3,4)],
[np.arange(8*8*8*8), (8,8,8,8), (2,2,2,2)]]
for arr, oldshape, newshape in tests:
arr = arr.reshape(oldshape)
assert np.allclose(uncubify(cubify(arr, newshape), oldshape), arr)
# cuber = Cubify(oldshape,newshape)
# assert np.allclose(cuber.uncubify(cuber.cubify(arr)), arr)
In addition to my extra question to @unutbu's answer I think I have got the reverse to work (in case you want to split a cube into cubes, apply a function to each one and then combine them back).
import numpy as np
import pdb
np.set_printoptions(precision=3,linewidth=300)
class Cubify():
def __init__(self,oldshape,newshape):
self.newshape = np.array(newshape)
self.oldshape = np.array(oldshape)
self.repeats = (oldshape / newshape).astype(int)
self.tmpshape = np.column_stack([self.repeats, newshape]).ravel()
order = np.arange(len(self.tmpshape))
self.order = np.concatenate([order[::2], order[1::2]])
self.reverseOrder = self.order.copy()
self.reverseOrder = np.arange(len(self.tmpshape)).reshape(2, -1).ravel(order='F')
self.reverseReshape = np.concatenate([self.repeats,self.newshape])
def cubify(self,arr):
# newshape must divide oldshape evenly or else ValueError will be raised
return arr.reshape(self.tmpshape).transpose(self.order).reshape(-1, *self.newshape)
def uncubify(self,arr):
return arr.reshape(self.reverseReshape).transpose(self.reverseOrder).reshape(self.oldshape)
if __name__ == "__main__":
N = 9
x = np.arange(N**3).reshape(N,N,N)
oldshape = x.shape
newshape = np.array([3,3,3])
cuber = Cubify(oldshape,newshape)
out = cuber.cubify(x)
back = cuber.uncubify(out)