# scipy.spatial.distance.mahalanobis

scipy.spatial.distance.mahalanobis(u, v, VI)

  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 array_like

      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