Select from multiple slices in Numpy

Question

Say we have

a = np.ones((3,3,3))

and

slices = [(0, 1, slice(None)), (0, slice(None), 0),  (slice(None), 1, 0)]

Answer 1

Do you know what r_ does? It converts the slices into ranges, and then concatenates the whole mess together.

I don't know if you can use r_ or something similar to construct the required indices. But:

In [168]: idx = np.where(a==0)
In [169]: idx
Out[169]: 
(array([0, 0, 0, 0, 0, 1, 2]),
 array([0, 1, 1, 1, 2, 1, 1]),
 array([0, 0, 1, 2, 0, 0, 0]))

this is gives us an idea of the required indexing arrays (minus some likely duplicates).

---

It might be possible to concatenate these 3 ogrid lists into a composite:

In [181]: np.ogrid[0:1,1:2,:3]
Out[181]: [array([[[0]]]), array([[[1]]]), array([[[0, 1, 2]]])]

In [182]: np.ogrid[0:1,:3,0:1]
Out[182]: 
[array([[[0]]]), array([[[0],
         [1],
         [2]]]), array([[[0]]])]

In [183]: np.ogrid[:3,1:2,0:1]
Out[183]: 
[array([[[0]],

        [[1]],

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

Individually they select the 0s in a.

It may be easiest to convert them into their raveled equivalents, and join the resulting 1d arrays.

In [188]: np.ravel_multi_index(Out[181],(3,3,3))
Out[188]: array([[[3, 4, 5]]])
etc
In [195]: np.hstack([Out[188].ravel(), Out[189].ravel(), Out[190].ravel()])
Out[195]: array([ 3,  4,  5,  0,  3,  6,  3, 12, 21])
In [197]: a.flat[_]
Out[197]: array([0., 0., 0., 0., 0., 0., 0., 0., 0.])

In [199]: np.unravel_index(Out[195],(3,3,3))
Out[199]: 
(array([0, 0, 0, 0, 0, 0, 0, 1, 2]),
 array([1, 1, 1, 0, 1, 2, 1, 1, 1]),
 array([0, 1, 2, 0, 0, 0, 0, 0, 0]))

Out[169] and Out[199] have the same values, except for duplicates.

This is a generalization of the problem of joining several 1d slices. Indexing and then concatenating takes about as much time as concatenating the indices first.