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# 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.

    p scalar

      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:
    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