Covariance

Covariance (Entity)

Nested Covariance class.

Attributes:

Name	Type	Description
dimension	int	Covariance dimension.
sill	float	Covariance sill.
metric	List[Metric]	Metric defining the covariances (angles and scales).

dimension: int property readonly

Return Covariance dimension.

Returns:

Type	Description
int	Covariance Dimension.

metric: List[Metric] property readonly

Return metrics.

Returns:

Type	Description
List[Metric]	List of Elementary Metric.

sill: float property readonly

Return Covariance sill.

Returns:

Type	Description
float	Covariance sill.

eval(self, x, y, method=<VariographyMethod.COVARIOGRAM: 'COVARIOGRAM'>)

Applies a covariance model to a distance matrix computed from a set of vectors.

Parameters:

Name	Type	Description	Default
x	Vector	First vector.	required
y	Vector	Second vector.	required
method	VariographyMethod	Method used for computation. Defaults to "COVARIOGRAM".	<VariographyMethod.COVARIOGRAM: 'COVARIOGRAM'>

Returns:

Type	Description
float	Computed covariance.

plot(self, angles=[0, 0, 0], method=<VariographyMethod.SEMIVARIOGRAM: 'SEMIVARIOGRAM'>, maxlag=None, save_file=None)

Plot covariance along a direction.

Parameters:

Name	Type	Description	Default
angles	Angles	Direction to plot covariance along, by default [0, 0, 0].	[0, 0, 0]
method	VariographyMethod	Method used for computation, by default 'SEMIVARIOGRAM'.	<VariographyMethod.SEMIVARIOGRAM: 'SEMIVARIOGRAM'>
maxlag	int	Maximum distance to compute covariance.	None
save_file	str	Filename of saved figure. Defaults to None.	None

CovarianceElem (Entity)

Elementary covariance base class. Abstract base class, to be defined by its children.

Attributes:

Name	Type	Description
dimension	int	Covariance dimension.
sill	float	Covariance sill.
metric	Metric	Metric information.

dimension: int property readonly

Return Covariance dimension.

Returns:

Type	Description
int	Covariance Dimension.

metric: Metric property readonly

Return covariance metric.

Returns:

Type	Description
Metric	Covariance Metric.

sill: float property readonly

Return Covariance sill.

Returns:

Type	Description
float	Covariance sill.

cov_func(self, h)

Return covariance function applied on a distance h.

Parameters:

Name	Type	Description	Default
h	np.ndarray	Metric to apply covariance function on.	required

eval(self, x, y, method=<VariographyMethod.COVARIOGRAM: 'COVARIOGRAM'>)

Applies a covariance model to a distance matrix computed from a set of vectors.

Parameters:

Name	Type	Description	Default
x	Vector	First vector.	required
y	Vector	Second vector.	required
method	VariographyMethod	Method used for computation, by default 'COVARIOGRAM'.	<VariographyMethod.COVARIOGRAM: 'COVARIOGRAM'>

Returns:

Type	Description
float	Computed covariance

plot(self, angles=[0, 0, 0], method=<VariographyMethod.SEMIVARIOGRAM: 'SEMIVARIOGRAM'>, maxlag=None, save_file=None)

Plot covariance along a direction.

Parameters:

Name	Type	Description	Default
angles	Angles	Direction to plot covariance along, by default [0, 0, 0].	[0, 0, 0]
method	VariographyMethod	Method used for computation, by default 'SEMIVARIOGRAM'.	<VariographyMethod.SEMIVARIOGRAM: 'SEMIVARIOGRAM'>
maxlag	int	Maximum distance to compute covariance.	None
save_file	str	Filename of saved figure. Defaults to None.	None

Exponential (CovarianceElem)

Exponential Covariance Elementary base class.

Attributes:

Name	Type	Description
dimension	int	Covariance dimension.
sill	float	Covariance sill.
metric	Metric	Metric.

cov_func(self, h)

Return covariance function applied on a distance h.

Parameters:

Name	Type	Description	Default
h	np.ndarray	Metric to apply covariance function on.	required

Gaussian (CovarianceElem)

Gaussian Covariance Elementary base class.

Attributes:

Name	Type	Description
dimension	int	Covariance dimension.
sill	float	Covariance sill.
metric	Metric	Metric.

cov_func(self, h)

Return covariance function applied on a distance h.

Parameters:

Name	Type	Description	Default
h	np.ndarray	Metric to apply covariance function on.	required

Returns:

Type	Description
np.ndarray	Covariance.

Nugget (CovarianceElem)

Nugget Covariance Elementary base class.

Attributes:

Name	Type	Description
dimension	int	Covariance dimension.
sill	float	Covariance sill.
metric	Metric	Metric.

cov_func(self, h)

Return covariance function applied on a distance h.

Parameters:

Name	Type	Description	Default
h	np.ndarray	Metric to apply covariance function on.	required

Spherical (CovarianceElem)

Spherical Covariance Elementary base class.

Attributes:

Name	Type	Description
dimension	int	Covariance dimension.
sill	float	Covariance sill.
metric	Metric	Metric.

cov_func(self, h)

Return covariance function applied on a distance h.

Parameters:

Name	Type	Description	Default
h	np.ndarray	Metric to apply covariance function on.	required

cvv(cov, cell_size, discr=None, lag=None)

Applies a covariance model to a given grid for variance calculus.

Parameters:

Name	Type	Description	Default
cov	Union[Covariance, CovarianceElem]	Covariance model to be applied.	required
cell_size	Vector	Size of cell for block covariance computation.	required
discr	Vector	Number of discretization per cell.	None
lag	List[float]	Lag for the computation of the spatial regularized covariance. If None, lag will be set to 0 (block variance).	None

Returns:

Type	Description
float	Regularized Covariance.