scipy.spatial.distance.

chebyshev#

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

Compute the Chebyshev distance.

The Chebyshev distance between real vectors \(u \equiv (u_1, \cdots, u_n)\) and \(v \equiv (v_1, \cdots, v_n)\) is defined as [1]

\[d_\textrm{chebyshev}(u,v) := \max_{1 \le i \le n} |u_i-v_i|\]

If a (non-negative) weight vector \(w \equiv (w_1, \cdots, w_n)\) is supplied, the weighted Chebyshev distance is defined to be the weighted Minkowski distance of infinite order; that is,

\[\begin{split}\begin{align} d_\textrm{chebyshev}(u,v;w) &:= \lim_{p\rightarrow \infty} \left( \sum_{i=1}^n w_i | u_i-v_i |^p \right)^\frac{1}{p} \\ &= \max_{1 \le i \le n} 1_{w_i > 0} | u_i - v_i | \end{align}\end{split}\]

Parameters:

u(N,) array_like of floats: Input vector.
v(N,) array_like of floats: Input vector.
w(N,) array_like of floats, optional: Weight vector. Default is None, which gives all pairs \((u_i, v_i)\) the same weight 1.0.

Returns:

chebyshevfloat: The Chebyshev distance between vectors u and v, optionally weighted by w.

References

[1]

https://en.wikipedia.org/wiki/Chebyshev_distance

Examples

>>> from scipy.spatial import distance
>>> distance.chebyshev([1, 0, 0], [0, 1, 0])
1
>>> distance.chebyshev([1, 1, 0], [0, 1, 0])
1