Why this output?

Question

Hi guys, I'have started Numpy and I have to admit I pretty hate its "syntax".
Here my problem:

import numpy as np
a= np.arange(12).reshape(3,4)
print(a)
i= np.array([[0,1],[1,2]])
j= np.array([[2,1],[3,3]])

print(a[i,j])

OUTPUT=
array([[ 2, 5],
[ 7, 11]])

Why?????? I don't understand how it is referring to indexes and dimensions! why these numbers as output?
Seriously I'm getting crazy...

Answer 1

"The resultant array has the same shape as the index arrays, and the values correspond to the index set for each position in the index arrays".

This means the printed values correspond to a[0,2] == 2, a[1,1] == 5, a[1,3] == 7, a[2,3] == 11.

https://docs.scipy.org/doc/numpy/user/basics.indexing.html#indexing-multi-dimensional-arrays

Answer 2

You're right: a[0,1] == 1. The thins is your code prints a[0,2] == 2.

The problem is the indexes of the resultant array aren't [0,1], [1,2], [2,1], [3,3].

To get the correct ones take each index from array "i" and pair it with the corresponding index of array "j" as follows:

1. The first element of "i" (0) goes with the first element of "j" (2) resulting in [0,2].

2. The second element of "i" (1) goes with the second element of "j" (1) resulting in [1,1].

At the end you get [0,2], [1,1], [1,3], [2,3].

Answer 3

That’s how numpy's multidimensional array indexing works.

https://scipy-cookbook.readthedocs.io/items/Indexing.html#Multidimensional-list-of-locations-indexing

https://docs.scipy.org/doc/numpy-1.15.0/user/basics.indexing.html#indexing-multi-dimensional-arrays

Answer 4

Ok, so far I understand that it's indexing the element in 2 rows and two columns. The point is why THOSE numbers? I mean, I thought that a[0,1] was supposed to be nrow=0 and ncol=1.
So, in a= arange(12).reshape(3,4) is:
a = [0,1,2,3,
4,5,6,7,
8,9,10,11]
First element [0,1] Line 0, element 1 = 1. Why 2?
Second element [1,2] Line 1,element 2 = 6. Why 5?
Third element [2,1] """"""""""""""""""""""""""""""""
Fourth element [3,3] """""""""""""""""""""""""""""""""

It's clear I didn't understand how to proceed in this indexing

Answer 5

Ok perfect, I got it now!!
I only have one doubt left: why do I have to "joining" the couples as columns ([0,2],[1,1],[1,3],[2,3])? Anyway THANKS MATE!