How to Efficiently Calculate Euclidean Distance in 3D Space Using NumPy?

Calculating Euclidean Distance with NumPy

You are given two points in 3D space, represented as NumPy arrays a and b. Your goal is to calculate the Euclidean distance between these points.

The Euclidean distance between two points is calculated using the following formula:

dist = sqrt((ax-bx)^2 + (ay-by)^2 + (az-bz)^2)

To calculate this distance with NumPy, you can utilize the numpy.linalg.norm function. This function computes the vector norm, which is the length of the vector. The Euclidean distance between two points is simply the l2 norm of their difference.

Therefore, you can calculate the distance as follows:

import numpy

a = numpy.array((ax, ay, az))
b = numpy.array((bx, by, bz))

dist = numpy.linalg.norm(a - b)

The numpy.linalg.norm function takes a vector as input and returns its norm. The default value of the ord parameter in this function is 2, which corresponds to the l2 norm, also known as the Euclidean distance.

For a more in-depth understanding of the Euclidean distance and its relationship with the l2 norm, refer to the excerpt from the book "Introduction to Data Mining".

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