scipy.spatial.distance.

seuclidean#

scipy.spatial.distance.seuclidean(u, v, V)[source]#

Return the standardized Euclidean distance between two arrays.

The standardized Euclidean distance between arrays u and v is

\[\sqrt{\sum\limits_i \frac{1}{V_i} \left(u_i-v_i \right)^2}\]

V is the variance vector; V[I] is the variance computed over all the i-th components of the points. If not passed, it is automatically computed.

Parameters:

u(…, N) array_like: Input array.
v(…, N) array_like: Input array.
V(…, N) array_like: V is an array of component variances. It is usually computed among a larger collection of vectors.

Returns:

seuclideanfloat or array: The standardized Euclidean distance between vectors u and v.

Notes

Array API Standard Support

seuclidean has support for Python Array API Standard compatible backends in addition to NumPy. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	✅
PyTorch	✅	✅
JAX	✅	✅
Dask	✅	n/a

See Support for the array API standard for more information.

Examples

>>> from scipy.spatial import distance
>>> distance.seuclidean([1, 0, 0], [0, 1, 0], [0.1, 0.1, 0.1])
4.4721359549995796
>>> distance.seuclidean([1, 0, 0], [0, 1, 0], [1, 0.1, 0.1])
3.3166247903553998
>>> distance.seuclidean([1, 0, 0], [0, 1, 0], [10, 0.1, 0.1])
3.1780497164141406