In numpy, is there a function to find the inverse of ix_? - numpy

Question

With numpy, my goal is to select a quadratic submatrix from a quadratic matrix, and then also look at the collection of elements that are not in the first submatrix.
For the first submatrix, I'm using np.ix_:
import numpy as np
r = np.random.rand(3,3)
l = [1,2]
r[np.ix_(l, l)]
Then, r[np.ix_(l, l)] will pick out a 2x2 matrix, marked by **:
0
1
2
0
r0,0
r0,1
r0,2
1
r1,0
** r1,1 **
** r1,2**
2
r2,0
** r2,1 **
** r2,2 **
But now what is the best approach to select the difference between the submatrix and the parent matrix?
I have looked at:
~np.ix_, like ~np.eye, but this doesn't seem to be supported
np.subtract, but the problem is that I need to select the elements by their indices and not by their values.

Answer 1

Based on a comment by #hpaulj, I followed the approach with the numpy.ma submodule:
import numpy as np
r = np.random.rand(3,3)
l = [1,2]
r[np.ix_(l, l)]
import numpy.ma as ma
mask = ma.zeros(r.shape)
mask[np.ix_(l, l)] = 1
Then, ma.compressed() gives the desired result:
ma.compressed(ma.array(r, mask=mask))

Answer 2

Using np.ix_ is equivalent to using basic indexing, but by triggering advanced indexing.
So it lets you fetch all the elements belonging to the 1st and 2nd rows and 1st and 2nd columns completely as a copy (basic indexing yields a view)
import numpy as np
r = np.random.rand(3,3)
l = [1,2]
r[np.ix_(l, l)]
array([[0.46899841, 0.49051596],
[0.00256912, 0.86447371]])
Equivalent to np.ix_, using basic indexing (this is a view and not a copy!) -
r[1:3, 1:3]
array([[0.46899841, 0.49051596],
[0.00256912, 0.86447371]])
If you, however, want to fetch the (1,1) and (2,2) index elements, then you can directly use advance indexing as below -
r[l,l]
array([0.46899841, 0.86447371])
As you can see, this returns the diagonal elements which you are looking for (with the np.eye for example)
Read more about how indexing (basic and advance) works here or check out a detailed answer where I explain this as well here.