scipy.spatial.distance.

minkowski#

scipy.spatial.distance.minkowski(u, v, p=2, w=None)[source]#

Compute the Minkowski distance between two arrays.

The Minkowski distance between arrays u and v, is defined as

\[ \begin{align}\begin{aligned}{\|u-v\|}_p = (\sum{|u_i - v_i|^p})^{1/p}.\\\left(\sum{w_i(|(u_i - v_i)|^p)}\right)^{1/p}.\end{aligned}\end{align} \]

Parameters:

u(…, N) array_like: Input array.
v(…, N) array_like: Input array.
pscalar: The order of the norm of the difference \({\|u-v\|}_p\). Note that for \(0 < p < 1\), the triangle inequality only holds with an additional multiplicative factor, i.e. it is only a quasi-metric.
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:

minkowskifloat or ndarray: The Minkowski distance between vectors u and v.

Notes

Array API Standard Support

minkowski 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.minkowski([1, 0, 0], [0, 1, 0], 1)
2.0
>>> distance.minkowski([1, 0, 0], [0, 1, 0], 2)
1.4142135623730951
>>> distance.minkowski([1, 0, 0], [0, 1, 0], 3)
1.2599210498948732
>>> distance.minkowski([1, 1, 0], [0, 1, 0], 1)
1.0
>>> distance.minkowski([1, 1, 0], [0, 1, 0], 2)
1.0
>>> distance.minkowski([1, 1, 0], [0, 1, 0], 3)
1.0