How to construct a rank array with numpy? (What is a rank array?)

Question

I hope all of you are having a great day. In my python class, we are learning how to use Numpy, so we got an assignment about that. My question is this: What is a rank array and how can I construct that with using python? My instructor tried to explain that with these lines but I did not understand anything actually :( These are the instructions:

rank_calculator(A) - 5 pts

Given a numpy ndarray A, return its rank array.

Input: [[ 9 4 15 0 18]
        [16 19 8 10 1]]

Return value: [[4 2 6 0 8]
               [7 9 3 5 1]]

The return value should be an ndarray of the same size and shape as the original array A.

So, can someone explain that? I am not so good at Python, unfortunately :(

Answer 1

Q) What is a rank array?

Ans: It's basically the elements in their sorted order.

Basically what your teacher is asking you is to return each elements positions if they were sorted in ascending order.

CODE:

import numpy as np

A = np.array([[9, 4, 15, 0, 18],
              [16, 19, 8, 10, 1]])

flatA = A.flatten()
sorted_flatA = sorted(flatA)  # will become -> [0, 1, 4, 8, 9, 10, 15, 16, 18, 19]

# Using a 'MAP' to map the values of sorted_faltA to the index of sorted_faltA.
MAP = {}
for i in range(len(sorted_flatA)):
    MAP[sorted_flatA[i]] = i

# Then simply going through the 2D array snd replacing the with their ranks.
res = np.zeros(A.shape)
for i in range(A.shape[0]):
    for j in range(A.shape[1]):
        res[i][j] = MAP[A[i][j]]

print(res)

Answer 2

You can use numpy.argsort multiple times to handle a matrix, as suggested in this answer on SO.

import numpy as np

inp = np.array([[9,4,15,0,18],
                [16,19,8,10,1]])

inp.ravel().argsort().argsort().reshape(inp.shape)

array([[4, 2, 6, 0, 8],
       [7, 9, 3, 5, 1]])

What is a rank matrix?

In summary, if I were to take all the integers in the matrix, and sort them smallest to largest, then assign each one a rank from 0 to 9, that would result in the rank matrix. Notice that the smallest is 0 which gets a rank of 0, while largest is 19, which gets the last rank of 9.

How the double argsort works

#printing them so they align nicely
print('Array ->', end='')
for i in inp.ravel().astype('str'):
    print(i.center(4), end='')
print('\n')
print('Sort1 ->', end='')
for i in inp.ravel().argsort().astype('str'):
    print(i.center(4), end='')
print('\n')
print('Sort2 ->', end='')
for i in inp.ravel().argsort().argsort().astype('str'):
    print(i.center(4), end='')

Array -> 9   4   15  0   18  16  19  8   10  1  

Sort1 -> 3   9   1   7   0   8   2   5   4   6  

Sort2 -> 4   2   6   0   8   7   9   3   5   1  

Let's first summarize what argsort does. It takes the position of each element and puts them where they belong after sorting. Knowing this, we can write a backward logic which is sort of triangular in nature. Lets start from sort2, then sort1 and then array.

1. 0th (in sort2) is 4th (in sort1), 4th (in sort1) is 0th (in array). So 0th (in array) is 0th (in sort2)

2. 9th (in sort2) is 1st (in sort1), 1st (in sort1) is 9th (in array). So, 9th (in array) is 9th (in sort2)

3. 6th (in sort2) is 9th (in sort1), 9th (in sort1) is 6th (in array). So, 6th (in array) is 6th (in sort2)

Its a bit confusing to wrap your head around it, but once you can understand how argsort() works, you shouldn't have a problem.