scipy.spatial.distance.minkowski

scipy.spatial.distance.minkowski(u, v, p=2, w=None)

Compute the Minkowski distance between two 1-D arrays.

The Minkowski distance between 1-D 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:

minkowskidouble

The Minkowski distance between vectors u and v.

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