# scipy.spatial.distance.kulczynski1

scipy.spatial.distance.kulczynski1(u, v, *, w=None)

  Compute the Kulczynski 1 dissimilarity between two boolean 1-D arrays.

  The Kulczynski 1 dissimilarity between two boolean 1-D arrays u and v of length `n`, is defined as

  \[\frac{c_{11}} {c_{01} + c_{10}}\]

  where \(c_{ij}\) is the number of occurrences of \(\mathtt{u[k]} = i\) and \(\mathtt{v[k]} = j\) for \(k \in {0, 1, ..., n-1}\).

  Parameters:
    u(N,) array_like, bool

      Input array.

    v(N,) array_like, bool

      Input array.

    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:
    kulczynski1 float

      The Kulczynski 1 distance between vectors u and v.

  Notes

  This measure has a minimum value of 0 and no upper limit. It is un-defined when there are no non-matches.

  New in version 1.8.0.

  References

  [1]

  Kulczynski S. et al. Bulletin International de l’Academie Polonaise des Sciences et des Lettres, Classe des Sciences Mathematiques et Naturelles, Serie B (Sciences Naturelles). 1927; Supplement II: 57-203.

  Examples

      >>> from scipy.spatial import distance
      >>> distance.kulczynski1([1, 0, 0], [0, 1, 0])
      0.0
      >>> distance.kulczynski1([True, False, False], [True, True, False])
      1.0
      >>> distance.kulczynski1([True, False, False], [True])
      0.5
      >>> distance.kulczynski1([1, 0, 0], [3, 1, 0])
      -3.0