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LuasKernel

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LuasKernel#

class luas.LuasKernel(Kl: Callable = None, Kt: Callable = None, Sl: Callable = None, St: Callable = None, use_stored_values: bool | None = True)[source]#

Bases: Kernel

Kernel class which solves for the log likelihood for any covariance matrix which is the sum of two kronecker products of the covariance matrix in each of two dimensions i.e. the full covariance matrix K is given by:

\[K = K_l \otimes K_t + S_l \otimes S_t\]

although we can avoid calculating K for many calculations implemented here.

The Kl and Sl functions should both return (N_l, N_l) matrices which will be the covariance matrices in the wavelength/vertical direction.

The Kt and St functions should both return (N_t, N_t) matrices which will by the covariance matrices in the time/horizontal direction.

>>> from luas import LuasKernel, kernels
>>> def Kl_fn(hp, x_l1, x_l2, wn = True):
>>> ... return hp["h"]**2*kernels.squared_exp(x_l1, x_l2, hp["l_l"])
>>> def Kt_fn(hp, x_t1, x_t2, wn = True):
>>> ... return kernels.squared_exp(x_t1, x_t2, hp["l_t"])
>>> # ... And similarly for Sl_fn, St_fn
>>> kernel = LuasKernel(Kl = Kl_fn, Kt = Kt_fn, Sl = Sl_fn, St = St_fn)
... )

See https://luas.readthedocs.io/en/latest/tutorials.html for more detailed tutorials on how to use.

Parameters:

  • Kl (Callable) – Function which returns the covariance matrix Kl, should be of the form Kl(hp, x_l1, x_l2, wn = True).

  • Kt (Callable) – Function which returns the covariance matrix Kt, should be of the form Kt(hp, x_t1, x_t2, wn = True).

  • Sl (Callable) – Function which returns the covariance matrix Sl, should be of the form Sl(hp, x_l1, x_l2, wn = True).

  • St (Callable) – Function which returns the covariance matrix St, should be of the form St(hp, x_t1, x_t2, wn = True).

  • use_stored_values (bool, optional) – Whether to perform checks if any of the component covariance matrices have changed and to make use of previously stored values for the decomposition of those matrices if they’re the same. If False then will not perform these checks and will compute the eigendecomposition of all matrices for every calculation.

LuasKernel.eigendecomp_no_stored_values(hp, ...)

Required calculations for the decomposition of the overall matrix K where the previously stored decomposition of K cannot be used for the calculation of a new decomposition.

LuasKernel.eigendecomp_use_stored_values(hp, ...)

Required calculations for the decomposition of the overall matrix K where the previously stored decomposition of K may be used for the calculation of a new decomposition.

LuasKernel.generate_noise(hp, x_l, x_t[, size])

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

LuasKernel.logL(hp, x_l, x_t, R, stored_values)

Computes the log likelihood using the method originally presented in Rakitsch et al. (2013) and also outlined in Fortune at al.

LuasKernel.logL_hessianable(hp, x_l, x_t, R, ...)

Computes the log likelihood using the method originally presented in Rakitsch et al. (2013) and also outlined in Fortune at al.

LuasKernel.predict(hp, x_l, x_l_pred, x_t, ...)

Performs GP regression and computes the GP predictive mean and the GP predictive uncertainty as the standard devation at each location or else can return the full covariance matrix.

LuasKernel.K(hp, x_l1, x_l2, x_t1, x_t2, ...)

Generates the full covariance matrix K formed from the sum of two kronecker products:

LuasKernel.visualise_covariance_in_data(hp, ...)

Creates a plot to aid in visualising how the kernel function is defining the covariance between different points in the observed data.

LuasKernel.visualise_covariance_matrix(hp, ...)

Visualise the covariance matrix/matrices generated by the input hyperparameters.

LuasKernel.K_inv_by_vec(hp, x_l, x_t, R)

Calculates the product of the inverse of the covariance matrix with a vector, represented by a JAXArray of shape (N_l, N_t).

LuasKernel.K_by_vec(hp, x_l, x_t, R)

Calculates the product of the covariance matrix with a vector, represented by a JAXArray of shape ``(N_l, N_t)`. Useful for testing for numerical stability.
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