haversine_distances (original) (raw)

sklearn.metrics.pairwise.haversine_distances(X, Y=None)[source]#

Compute the Haversine distance between samples in X and Y.

The Haversine (or great circle) distance is the angular distance between two points on the surface of a sphere. The first coordinate of each point is assumed to be the latitude, the second is the longitude, given in radians. The dimension of the data must be 2.

\[D(x, y) = 2\arcsin[\sqrt{\sin^2((x_{lat} - y_{lat}) / 2) + \cos(x_{lat})\cos(y_{lat})\ sin^2((x_{lon} - y_{lon}) / 2)}]\]

Parameters:

X{array-like, sparse matrix} of shape (n_samples_X, 2)

A feature array.

Y{array-like, sparse matrix} of shape (n_samples_Y, 2), default=None

An optional second feature array. If None, uses Y=X.

Returns:

distancesndarray of shape (n_samples_X, n_samples_Y)

The distance matrix.

Notes

As the Earth is nearly spherical, the haversine formula provides a good approximation of the distance between two points of the Earth surface, with a less than 1% error on average.

Examples

We want to calculate the distance between the Ezeiza Airport (Buenos Aires, Argentina) and the Charles de Gaulle Airport (Paris, France).

from sklearn.metrics.pairwise import haversine_distances from math import radians bsas = [-34.83333, -58.5166646] paris = [49.0083899664, 2.53844117956] bsas_in_radians = [radians() for _ in bsas] paris_in_radians = [radians() for _ in paris] result = haversine_distances([bsas_in_radians, paris_in_radians]) result * 6371000/1000 # multiply by Earth radius to get kilometers array([[ 0. , 11099.54035582], [11099.54035582, 0. ]])