GeneralKernel.logL

GeneralKernel.logL(hp: Any, x_l: Array, x_t: Array, R: Array, stored_values: Any) → Tuple[Any, Any]

Computes the log likelihood using Cholesky factorisation and also returns stored values from the matrix decomposition.

Parameters:

• hp (Pytree) – Hyperparameters needed to build the covariance matrix K. Will be unaffected if additional mean function parameters are also included.

• x_l (JAXArray) – Array containing wavelength/vertical dimension regression variable(s). May be of shape (N_l,) or (d_l,N_l) for d_l different wavelength/vertical regression variables.

• x_t (JAXArray) – Array containing time/horizontal dimension regression variable(s). May be of shape (N_t,) or (d_t,N_t) for d_t different time/horizontal regression variables.

• R (JAXArray) – Residuals to be fit calculated from the observed data by subtracting the deterministic mean function. Must have the same shape as the observed data (N_l, N_t).

• stored_values (PyTree) – Stored values from the decomposition of the covariance matrix. For GeneralKernel this consists of the Cholesky factor and the log determinant of K.

Returns:

A tuple where the first element is the value of the log likelihood. The second element is a PyTree which contains stored values from the decomposition of the covariance matrix.

Return type:

(Scalar, PyTree)