fips.Covariance.quadratic_form#

Covariance.quadratic_form(x)[source]#

Return \(x^T S^{-1} x\), the squared Mahalanobis length of x.

Parameters:

x (Vector) – A vector on the covariance’s space, in any order.

Returns:

The quadratic form of the inverse covariance.

Return type:

float

Raises:

ValueError – If the labels of x do not match the covariance’s.
numpy.linalg.LinAlgError – If the covariance is singular.

Examples

>>> import pandas as pd
>>> from fips import Covariance, Space, Vector
>>> space = Space({"co2": pd.Index(["a", "b"], name="site")})
>>> S = Covariance.diagonal([4.0, 1.0], space)
>>> S.quadratic_form(Vector([2.0, 1.0], space))
2.0