# NonStationaryCovarianceModelFactory¶

class NonStationaryCovarianceModelFactory(*args)

Estimation of a non stationary covariance model.

Notes

We consider be a multivariate process of dimension d where . We denote the vertices of the mesh .

X is supposed to be a second order process and we note its covariance function. X may be stationary or non stationary as well.

We suppose that we have K fields and we note the values of the field k on the mesh .

We recall that the covariance function C writes:

where the mean function is defined by:

First, we estimate the covariance function C on the vertices of the mesh using the empirical mean estimator:

Then, we build a covariance function defined on which is a piecewise constant function defined on by:

where k is such that is the vertex of the nearest to and the nearest to .

Methods

 build(*args) Estimate the covariance model. buildAsCovarianceMatrix(sample[, isCentered]) Estimate the covariance model as a covariance matrix. buildAsUserDefinedCovarianceModel(sample[, …]) Estimate the covariance model as a User defined covariance model. getClassName() Accessor to the object’s name. getId() Accessor to the object’s id. getName() Accessor to the object’s name. getShadowedId() Accessor to the object’s shadowed id. getVisibility() Accessor to the object’s visibility state. hasName() Test if the object is named. hasVisibleName() Test if the object has a distinguishable name. setName(name) Accessor to the object’s name. setShadowedId(id) Accessor to the object’s shadowed id. setVisibility(visible) Accessor to the object’s visibility state.
__init__(*args)

Initialize self. See help(type(self)) for accurate signature.

build(*args)

Estimate the covariance model.

Parameters: sampleFields : ProcessSample The fields used to estimate the covariance model which is not supposed to be stationary. covEst : CovarianceModelImplementation The estimated covariance model.

Examples

Create the covariance model, a mesh and a process:

>>> import openturns as ot
>>> myModel = ot.AbsoluteExponential([0.1]*2)
>>> myMesh = ot.IntervalMesher([10]*2).build(ot.Interval([0.0]*2, [1.0]*2))
>>> myProcess = ot.GaussianProcess(myModel, myMesh)


Generate 10 fields:

>>> mySample = myProcess.getSample(10)


Estimate the covariance model without supposing the stationarity:

>>> myEstCov = ot.NonStationaryCovarianceModelFactory().build(mySample)

buildAsCovarianceMatrix(sample, isCentered=False)

Estimate the covariance model as a covariance matrix.

Parameters: sampleFields : ProcessSample The fields used to estimate the covariance model. isCentered : bool, optional Flag telling if the given sample is from a centered process or if it has to be centered by the empirical mean. Default value is False. covEst : CovarianceMatrix The unbiased estimation of the discretization of the covariance function over the mesh defining the given sample.
buildAsUserDefinedCovarianceModel(sample, isCentered=False)

Estimate the covariance model as a User defined covariance model.

Parameters: sampleFields : ProcessSample The fields used to estimate the covariance model. isCentered : bool, optional Flag telling if the given sample is from a centered process or if it has to be centered by the empirical mean. Default value is False. covEst : UserDefinedCovarianceModel The estimated covariance model that can be used as a UserDefinedCovarianceModel.
getClassName()

Accessor to the object’s name.

Returns: class_name : str The object class name (object.__class__.__name__).
getId()

Accessor to the object’s id.

Returns: id : int Internal unique identifier.
getName()

Accessor to the object’s name.

Returns: name : str The name of the object.
getShadowedId()

Accessor to the object’s shadowed id.

Returns: id : int Internal unique identifier.
getVisibility()

Accessor to the object’s visibility state.

Returns: visible : bool Visibility flag.
hasName()

Test if the object is named.

Returns: hasName : bool True if the name is not empty.
hasVisibleName()

Test if the object has a distinguishable name.

Returns: hasVisibleName : bool True if the name is not empty and not the default one.
setName(name)

Accessor to the object’s name.

Parameters: name : str The name of the object.
setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters: id : int Internal unique identifier.
setVisibility(visible)

Accessor to the object’s visibility state.

Parameters: visible : bool Visibility flag.