SciPy

scipy.spatial.distance.sqeuclidean

scipy.spatial.distance.sqeuclidean(u, v, w=None)[source]

Compute the squared Euclidean distance between two 1-D arrays.

The squared Euclidean distance between u and v is defined as

\[ \begin{align}\begin{aligned}{||u-v||}_2^2\\\left(\sum{(w_i |(u_i - v_i)|^2)}\right)\end{aligned}\end{align} \]
Parameters:

u : (N,) array_like

Input array.

v : (N,) array_like

Input array.

w : (N,) array_like, optional

The weights for each value in u and v. Default is None, which gives each value a weight of 1.0

Returns:

sqeuclidean : double

The squared Euclidean distance between vectors u and v.

Examples

>>> from scipy.spatial import distance
>>> distance.sqeuclidean([1, 0, 0], [0, 1, 0])
2.0
>>> distance.sqeuclidean([1, 1, 0], [0, 1, 0])
1.0