## How To Calculate Euclidean And Manhattan Distance By Using Python

#### Euclidean Distance Euclidean metric is the "ordinary" straight-line distance between two points. if p = (p1, p2) and q = (q1, q2) then the distance is given by ![Euclidean Distance](https://wikimedia.org/api/rest_v1/media/math/render/svg/4febdae84cbc320c19dd13eac5060a984fd438d8) For three dimension, formula is ![Euclidean Distance](https://wikimedia.org/api/rest_v1/media/math/render/svg/b48fad52918eb76d14c4f17973ae210f7c1a6312) ```python ################################### # name: eudistance_samples.py # desc: Simple scatter plot # date: 2018-08-28 # Author: conquistadorjd ################################### from scipy import spatial import numpy from sklearn.metrics.pairwise import euclidean_distances import math print('*** Program started ***') ############ Calculating distance by using python math function ############# 2 D array x1 = [1,1] x2 = [2,9] eudistance =math.sqrt(math.pow(x1[0]-x2[0],2) + math.pow(x1[1]-x2[1],2) ) print("eudistance Using math ", eudistance) ############# 3 D array # x1 = [1,1,4] # x2 = [10,2,7] # # Calculating distance by using math # eudistance = math.sqrt(math.pow(x1[0]-x2[0],2) + math.pow(x1[1]-x2[1],2) + math.pow(x1[2]-x2[2],2) ) # print("eudistance Using math ", eudistance) ############ Calculating distance by using scipy eudistance = spatial.distance.euclidean(x1, x2) print("eudistance Using scipy", eudistance) ############ Calculating distance by using numpy x1np=numpy.array(x1) x2np=numpy.array(x2) eudistance = numpy.sqrt(numpy.sum((x1np-x2np)**2)) print("eudistance Using numpy", eudistance) eudistance = numpy.linalg.norm(x1np-x2np) print("eudistance Using numpy", eudistance) ############ Calculating distance by using sklearn eudistance = euclidean_distances([x1np], [x2np]) # for some strange reasons, values needs be in 2-D array print("eudistance Using sklearn", eudistance) print('*** Program ended ***') ``` ### Manhattan distance The distance between two points measured along axes at right angles. The Manhattan distance between two vectors (or points) a and b is defined as ∑i|ai−bi| over the dimensions of the vectors. ![Manhattan distance](https://wikimedia.org/api/rest_v1/media/math/render/svg/02436c34fc9562eb170e2e2cfddbb3303075b28e) All paths from the bottom left to top right of this idealized city have the same distance. ![Manhattan Distance](https://upload.wikimedia.org/wikipedia/commons/thumb/0/08/Manhattan_distance.svg/200px-Manhattan_distance.svg.png) Reference: https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.spatial.distance.euclidean.html

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