Squared Mahalanobis distance

Computes \((\boldsymbol{x}-\boldsymbol{m})^{\mathsf{T}} \boldsymbol{\Sigma}^{-1}(\boldsymbol{x}-\boldsymbol{m})\) for a symmetric positive-definite covariance (or scatter) matrix \(\boldsymbol{\Sigma}\). This is the squared distance; take the square root for the Mahalanobis distance itself. Solves \(\boldsymbol{\Sigma}\boldsymbol{z}=\boldsymbol{\delta}\) instead of forming \(\boldsymbol{\Sigma}^{-1}\) explicitly.

Usage

.squared_mahalanobis_distance(x, center = numeric(length(x)), covariance)

Arguments

x

Numeric vector.

center

Numeric centre \(\boldsymbol{m}\) (default the origin).

covariance

Symmetric positive-definite \(G\times G\) matrix.

Value

Non-negative numeric scalar.