keeping track of indices change in numpy.reshape

Question

While using numpy.reshape in Python, is there a way to keep track of the change in indices?

For example, if a numpy array with the shape (m,n,l,k) is reshaped into an array with the shape (m*n,k*l); is there a way to get the initial index ([x,y,w,z]) for the current [X,Y] index and vice versa?

Answer 1

Yes there is, it's called raveling and unraveling the index. For example you have two arrays:

import numpy as np

arr1 = np.arange(10000).reshape(20, 10, 50)
arr2 = arr.reshape(20, 500)

say you want to index the (10, 52) (equivalent to arr2[10, 52]) element but in arr1:

>>> np.unravel_index(np.ravel_multi_index((10, 52), arr2.shape), arr1.shape)
(10, 1, 2)

or in the other direction:

>>> np.unravel_index(np.ravel_multi_index((10, 1, 2), arr1.shape), arr2.shape)
(10, 52)

Answer 2

You don't keep track of it, but you can calculate it. The original m x n is mapped onto the new m*n dimension, e.g. n*x+y == X. But we can verify with a couple of multidimensional ravel/unravel functions (as answered by @MSeifert).

In [671]: m,n,l,k=2,3,4,5
In [672]: np.ravel_multi_index((1,2,3,4), (m,n,l,k))
Out[672]: 119
In [673]: np.unravel_index(52, (m*n,l*k))
Out[673]: (2, 12)