sampling

This package provides tools to efficiently sample from covariance models on grids using circulant embeddings and the Fast Fourier Transform.

simulation

SamplerOnRectangularGrid(model: CovarianceModel, grid: RectangularGrid, exact: bool = True)

Class that allows to define efficient samplers on rectangular grids for fixed models.

Attributes:

Name	Type	Description
model	CovarianceModel	Covariance model used for sampling.
grid	RectangularGrid	Grid on which we wish to sample
n_sims	int	Simulations can be carried out in 'blocks'. This parameter allows to choose how many i.i.d. samples are generated in each block computation.
f	ndarray	Spectral amplitudes

Notes

This sampler accounts for the grid's mask by setting missing values to zero.

Examples:

>>> from debiased_spatial_whittle.models.univariate import ExponentialModel
>>> from debiased_spatial_whittle.grids.base import RectangularGrid
>>> model = ExponentialModel(rho=12., sigma=1.)
>>> grid = RectangularGrid((256, 128))
>>> sampler = SamplerOnRectangularGrid(model, grid)
>>> sample = sampler()
>>> sample.shape
(256, 128)

model: CovarianceModel property writable

Model from which we sample

grid: RectangularGrid property writable

Sampling grid

n_sims property writable

number of simulations in each block computation. By increasing this value, one allows parallel simulation, at the expense of increased memory usage.

spectral_amplitudes property

Spectral amplitudes of the covariance matrix on the circulant embedded grid.

__call__()

Samples a realization of a Gaussian Process specified by the provided covariance model, on the provided rectangular grid.

Returns:

Name	Type	Description
sample	ndarray	Sample values corresponding to the grid and covariance model. Shape is equal to the n attribute of grid.

Raises:

Type	Description
ValueError	If a non-negative definite circulant embedding could not be achieved. In that case a solution is to increase the grid size.

MultivariateSamplerOnRectangularGrid(model: CovarianceModel, grid: RectangularGrid, p: int)

Implements circulant embedding for multivariate random fields, as proposed by Chan & Wood (1999).

Parameters:

Name	Type	Description	Default
model	CovarianceModel	Model from which we sample	required
grid	RectangularGrid	Sampling grid	required
p	int	Number of variates of the model	required

model: CovarianceModel property writable

Model from which we sample

grid: RectangularGrid property writable

Sampling grid

__call__() -> xp.ndarray

Generate a realization from the specified covariance model on the grid.

Returns:

Type	Description
sample	Simulated sample.

SamplerSeparable(model: SeparableModel, grid: RectangularGrid, n_sim: int = 100)

Class for approximate sampling of Separable models.

SamplerBUCOnRectangularGrid(model: BivariateUniformCorrelation, grid: RectangularGrid)

Class to sample from the BivariateUniformCorrelation model on a rectangular grid with nvars=2.

Attributes:

Name	Type	Description
grid	RectangularGrid	Sampling grid. Should have attribute nvars=2.
model	BivariateUniformCorrelation	Bivariate covariance model
f	ndarray	Spectral amplitudes

__call__(periodic: bool = False, return_spectral: bool = False) -> xp.ndarray

Sample a realization.

Parameters:

Name	Type	Description	Default
periodic	bool	if true, returns a periodic sample on an embedding grid	False
return_spectral	bool	if true, returns the spectral amplitudes as well	False

Returns:

Name	Type	Description
sample	ndarray	shape (n1, ..., nd, 2) where the last dimension indexes the two variates.

samples

Sample(grid: RectangularGrid, values: np.ndarray)

General class for the definition of a sampled random field. Allows to store computed quantities such as periodograms etc.

SampleOnRectangularGrid(grid: RectangularGrid, values: np.ndarray)

Bases: Sample

Class for a sample on a Rectangular grid. In the case of a grid with missing observations, the values at missing locations are not used.