LuasKernel.generate_noise

LuasKernel.generate_noise(hp: Any, x_l: Array, x_t: Array, size: int | None = 1) → Array

Generate noise with the covariance matrix returned by this kernel using the input hyperparameters hp.

Solves for the matrix square root of K and then multiplies this by a random normal vector. Doing it this way has numerical stability advantages over generating noise separately for each of the two kronecker products of K as they might not both be well-conditioned matrices.

Parameters:

• hp (Pytree) – Hyperparameters needed to build the covariance matrices Kl, Kt, Sl, St. Will be unaffected if additional mean function parameters are also included.

• x_l (JAXArray) – Array containing wavelength/vertical dimension regression variable(s) for the observed locations. 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) for the observed locations. May be of shape (N_t,) or (d_t,N_t) for d_t different time/horizontal regression variables.

• size (int, optional) – The number of different draws of noise to generate. Defaults to 1.

Returns:

If size = 1 will generate noise of shape (N_l, N_t), otherwise if size > 1 then generated noise will be of shape (N_l, N_t, size).

Return type:

JAXArray