# scipy.spatial.distance.kulsinski¶

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

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

The Kulsinski dissimilarity between two boolean 1-D arrays u and v, is defined as

$\frac{c_{TF} + c_{FT} - c_{TT} + n} {c_{FT} + c_{TF} + n}$

where $$c_{ij}$$ is the number of occurrences of $$\mathtt{u[k]} = i$$ and $$\mathtt{v[k]} = j$$ for $$k < n$$.

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
kulsinskidouble

The Kulsinski distance between vectors u and v.

Examples

>>> from scipy.spatial import distance
>>> distance.kulsinski([1, 0, 0], [0, 1, 0])
1.0
>>> distance.kulsinski([1, 0, 0], [1, 1, 0])
0.75
>>> distance.kulsinski([1, 0, 0], [2, 1, 0])
0.33333333333333331
>>> distance.kulsinski([1, 0, 0], [3, 1, 0])
-0.5


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