Manhattan distance between 2 vectors

Question

I need to calculate the manhattan distance between 2 vectors

I found this code https://www.geeksforgeeks.org/sum-manhattan-distances-pairs-points/

def distancesum (x, y, n): 
    sum = 0
      
    # for each point, finding distance 
    # to rest of the point 
    for i in range(n): 
        for j in range(i+1,n): 
            sum += (abs(x[i] - x[j]) +
                        abs(y[i] - y[j])) 
      
    return sum

But in another documentation I found this code for manhattan

so the code for this is:

def manhattan_distance(instance1, instance2):
    n = len(instance1)-1
    sum = 0
    # for each point, finding distance
    # to rest of the point
    for i in range(n):
        sum += abs(float(instance1[i]) - float(instance2[i]))
    return sum

What is the algorithm for manhattan distance

Answer 1

Here's an example for calculating the manhattan distance.

In [1]: %paste                                                                                                                                               
import numpy as np

def manhattan_distance(a, b):
    return np.abs(a - b).sum()

a = np.array([1, 2])
b = np.array([-1, 4])
print(manhattan_distance(a, b))

## -- End pasted text --
4

If dealing with vectors that are strings

In [1]: %paste                                                                                                                                               
import numpy as np

def manhattan_distance(a, b):
    return np.abs(a - b).sum()

a = ['1', '2']
b = ['-1', '4']
print(manhattan_distance(np.array(a, dtype=float), np.array(b, dtype=float)))
## -- End pasted text --
4.0

Answer 2

In the referenced formula, you have n points each with 2 coordinates and you compute the distance of one vectors to the others. So apart from the notations, both formula are the same. The Manhattan distance between 2 vectors is the sum of the absolute value of the difference of their coordinates. An easy way to remember it, is that the distance of a vector to itself must be 0.

Answer 3

You probably need this Scipy function:

Y = cdist(XA, XB, 'cityblock')