SciPy

scipy.spatial.distance.mahalanobis

scipy.spatial.distance.mahalanobis(u, v, VI)[source]

Compute the Mahalanobis distance between two 1-D arrays.

The Mahalanobis distance between 1-D arrays u and v, is defined as

\[\sqrt{ (u-v) V^{-1} (u-v)^T }\]

where V is the covariance matrix. Note that the argument VI is the inverse of V.

Parameters:

u : (N,) array_like

Input array.

v : (N,) array_like

Input array.

VI : ndarray

The inverse of the covariance matrix.

Returns:

mahalanobis : double

The Mahalanobis distance between vectors u and v.

Examples

>>> from scipy.spatial import distance
>>> iv = [[1, 0.5, 0.5], [0.5, 1, 0.5], [0.5, 0.5, 1]]
>>> distance.mahalanobis([1, 0, 0], [0, 1, 0], iv)
1.0
>>> distance.mahalanobis([0, 2, 0], [0, 1, 0], iv)
1.0
>>> distance.mahalanobis([2, 0, 0], [0, 1, 0], iv)
1.7320508075688772