NonStationaryCovarianceModelFactory¶
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class
NonStationaryCovarianceModelFactory
(*args)¶ Estimation of a non stationary covariance model.
Refer to Estimation of a non stationary cov. 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
(self, \*args)Estimate the covariance model.
buildAsCovarianceMatrix
(self, sample[, …])Estimate the covariance model as a covariance matrix.
buildAsUserDefinedCovarianceModel
(self, sample)Estimate the covariance model as a User defined covariance model.
getClassName
(self)Accessor to the object’s name.
getId
(self)Accessor to the object’s id.
getName
(self)Accessor to the object’s name.
getShadowedId
(self)Accessor to the object’s shadowed id.
getVisibility
(self)Accessor to the object’s visibility state.
hasName
(self)Test if the object is named.
hasVisibleName
(self)Test if the object has a distinguishable name.
setName
(self, name)Accessor to the object’s name.
setShadowedId
(self, id)Accessor to the object’s shadowed id.
setVisibility
(self, visible)Accessor to the object’s visibility state.

__init__
(self, \*args)¶ Initialize self. See help(type(self)) for accurate signature.

build
(self, \*args)¶ Estimate the covariance model.
 Parameters
 sampleFields
ProcessSample
The fields used to estimate the covariance model which is not supposed to be stationary.
 sampleFields
 Returns
 covEst
CovarianceModelImplementation
The estimated covariance model.
 covEst
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
(self, sample, isCentered=False)¶ Estimate the covariance model as a covariance matrix.
 Parameters
 sampleFields
ProcessSample
The fields used to estimate the covariance model.
 isCenteredbool, 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.
 sampleFields
 Returns
 covEst
CovarianceMatrix
The unbiased estimation of the discretization of the covariance function over the mesh defining the given sample.
 covEst

buildAsUserDefinedCovarianceModel
(self, sample, isCentered=False)¶ Estimate the covariance model as a User defined covariance model.
 Parameters
 sampleFields
ProcessSample
The fields used to estimate the covariance model.
 isCenteredbool, 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.
 sampleFields
 Returns
 covEst
UserDefinedCovarianceModel
The estimated covariance model that can be used as a
UserDefinedCovarianceModel
.
 covEst

getClassName
(self)¶ Accessor to the object’s name.
 Returns
 class_namestr
The object class name (object.__class__.__name__).

getId
(self)¶ Accessor to the object’s id.
 Returns
 idint
Internal unique identifier.

getName
(self)¶ Accessor to the object’s name.
 Returns
 namestr
The name of the object.

getShadowedId
(self)¶ Accessor to the object’s shadowed id.
 Returns
 idint
Internal unique identifier.

getVisibility
(self)¶ Accessor to the object’s visibility state.
 Returns
 visiblebool
Visibility flag.

hasName
(self)¶ Test if the object is named.
 Returns
 hasNamebool
True if the name is not empty.

hasVisibleName
(self)¶ Test if the object has a distinguishable name.
 Returns
 hasVisibleNamebool
True if the name is not empty and not the default one.

setName
(self, name)¶ Accessor to the object’s name.
 Parameters
 namestr
The name of the object.

setShadowedId
(self, id)¶ Accessor to the object’s shadowed id.
 Parameters
 idint
Internal unique identifier.

setVisibility
(self, visible)¶ Accessor to the object’s visibility state.
 Parameters
 visiblebool
Visibility flag.
