# scipy.spatial.distance.minkowski¶

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

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. p : int The order of the norm of the difference $${||u-v||}_p$$. 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 minkowski : double 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


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