Computing the Minkowski distance using Python

Overview:

Minkowski distance between two n-dimensional points (x1, y1... Dn) and (x2, y2... Dn) is given by ((x₁-y₁)^p+ (x₂-y₁)^p...+(x_n - y_n)^p)^1/p
The Minkowski distance is a metric that gives specialised distance for each value of the parameter p.
- When p = 1, the resultant metric is the Manhattan distance.
- When p = 2, the resultant metric is the Euclidean distance.
- When p = ∞, the resultant metric is the Chebyshev distance.

# Example Python program that finds the Minkowski distance between

# two points on a 2-dimensional real plane for the parameter value 1, 2

# and ∞
import scipy.spatial.distance as dist
import numpy as np

# Points on a 2-dimensional plane
x = (2, 2)
y = (4, 5)

# Manhattan distance
d = dist.minkowski(x, y, p = 1)
print("Minkowski distance when p = 1")
print(d)

# Euclidean distance
d = dist.minkowski(x, y, p = 2)
print("Minkowski distance when p = 2")
print(d)

# Chebyshev distance
d = dist.minkowski(x, y, p = np.inf)
print("Minkowski distance when p = 3")
print(d)

Minkowski distance when p = 1
5.0
Minkowski distance when p = 2
3.605551275463989
Minkowski distance when p = 3
3.0