Name error in the command window when running function

Question

I have created a function that shall take as input two columns( arrays), use the central difference for the gradient, and return a column/array with the gradient values.

This is what I have written:

def central_diff_method (array_vert_disp , array_chain):

# Compute the difference formula for f'(a) with step size h.

import pandas as pd 

length_of_column= len(array_vert_disp)

array_diff=pd.DataFrame()
array_chain_diff=pd.DataFrame()
grad_inc=pd.DataFrame()

k=0

for i in range (1,length_of_column-1):
    
    array_diff[k]=array_chain[i+1]-array_chain[i-1]
    array_chain_diff[k]=array_chain[i+1]-array_chain[i-1]
    grad_inc[k]=array_diff[k]/(array_chain_diff[k]*2)
            
    k=k+1
    
return  grad_inc

And this is how I call it in the main script:

disps['grad_inc']=central_diff_method(disps['z_disps'], disps['chainage'])

I get a nameerror in the command window: disps['grad_inc']=central_diff_method(disps['z_disps'], disps['chainage'])

NameError: name 'central_diff_method' is not defined

What am I doing wrong ? Apart from that, do you see anything else wrong in my function?