put 2d coordinate axis at the center of an array in python

Question

I am going to simulate a 2d area using a matrix in python and I should change the indexes somehow.. I need to find a relation between the original matrix and a new axis coordinate: I think it can be more clarified if I explain by a piece of my code:

originalMatrix=np.random.randint(0, 10, size=(5,5))

the output is:

[[4 8 3 2 5]
 [2 2 2 6 5]
 [2 4 7 9 9]
 [6 2 6 6 6]
 [2 8 3 8 2]]

we can access to number '7' by originalMatrix[2][2]. but in the coordinate system the index must be (0,0).Index of '4' in the left side of '7' in originalMatrix is [2][1] but in the new coordinate should be (-1,0) and so on... I hope I could explain well!

Answer 1

An easy way is to roll your array:

a = np.array([[4, 8, 3, 2, 5],
              [2, 2, 2, 6, 5],
              [2, 4, 7, 9, 9],
              [6, 2, 6, 6, 6],
              [2, 8, 3, 8, 2]])
center = np.array(a.shape)//2
# b will be indexed with the previous center being 0,0
b = np.roll(a, -center, axis=(0,1))

b[0, -1]
# 4

b[0, 0]
# 7

NB. You have to decide what is the center in case you have an even number as a dimension.

Answer 2

There is no way to do that with standard numpy arrays, but you could define a function that does it for you

def arrayByCoordinates(array, coords):
    coords = np.array(coords)
    center = np.array(array.shape) // 2
    return array[tuple(coords + center)]

>>> x
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14],
       [15, 16, 17, 18, 19],
       [20, 21, 22, 23, 24]])
>>> arrayByCoordinates(x,(0,0))
12

But keep in mind that if the shape of the array is even, there is no real center, so this will convert to the lowest one

Answer 3

Here is another possible approach, assuming the matrix is nxn where n is odd:

import numpy as np


def access_coordinate(matrix, x, y):
    center = (len(matrix)//2, len(matrix)//2)
    translated_coordinates = (center[0]+y, center[1] + x)
    return matrix[translated_coordinates[0], translated_coordinates[1]]
    

originalMatrix=np.array([[4, 8, 3, 2, 5],
 [2, 2, 2 ,6, 5],
 [2, 4, 7, 9, 9],
 [6, 2, 6, 6, 6],
 [2, 8, 3, 8, 2]])


print(access_coordinate(originalMatrix, -1, 0)) #4