# KrigingResult¶

class KrigingResult(*args)

Kriging result.

Available constructors:

KrigingResult(inputSample, outputSample, metaModel, residuals, relativeErrors, basis, trendCoefficients, covarianceModel, covarianceCoefficients)

KrigingResult(inputSample, outputSample, metaModel, residuals, relativeErrors, basis, trendCoefficients, covarianceModel, covarianceCoefficients, covarianceCholeskyFactor, covarianceHMatrix)

Parameters: inputSample, outputSample : 2-d sequence of float The samples and . metaModel : Function The meta model: , defined in (3). residuals : Point The residual errors. relativeErrors : Point The relative errors. basis : collection of Basis Collection of the functional basis: for each with . Its size must be equal to zero if the trend is not estimated. trendCoefficients : collection of Point The trend coeffient vectors . covarianceModel : CovarianceModel Covariance function of the Gaussian process. covarianceCoefficients : 2-d sequence of float The defined in (2). covarianceCholeskyFactor : TriangularMatrix The Cholesky factor of . covarianceHMatrix : HMatrix The hmat implementation of .

Notes

The Kriging meta model is defined by:

(1)

where is the condition for each .

Equation (1) writes:

where

and

(2)

At the end, the meta model writes:

(3)

Examples

Create the model and the samples:

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x'],  ['x * sin(x)'])
>>> sampleX = [[1.0], [2.0], [3.0], [4.0], [5.0], [6.0]]
>>> sampleY = f(sampleX)


Create the algorithm:

>>> basis = ot.Basis([ot.SymbolicFunction(['x'], ['x']), ot.SymbolicFunction(['x'], ['x^2'])])
>>> covarianceModel = ot.GeneralizedExponential([2.0], 2.0)
>>> algoKriging = ot.KrigingAlgorithm(sampleX, sampleY, covarianceModel, basis)
>>> algoKriging.run()


Get the result:

>>> resKriging = algoKriging.getResult()


Get the meta model:

>>> metaModel = resKriging.getMetaModel()


Methods

 getBasisCollection() Accessor to the collection of basis. getClassName() Accessor to the object’s name. getConditionalCovariance(*args) Compute the expected covariance of the Gaussian process on a point (or several points). getConditionalMean(*args) Compute the expected mean of the Gaussian process on a point or a sample of points. getCovarianceCoefficients() Accessor to the covariance coefficients. getCovarianceModel() Accessor to the covariance model. getId() Accessor to the object’s id. getInputSample() Accessor to the input sample. getMetaModel() Accessor to the metamodel. getModel() Accessor to the model. getName() Accessor to the object’s name. getOutputSample() Accessor to the output sample. getRelativeErrors() Accessor to the relative errors. getResiduals() Accessor to the residuals. getShadowedId() Accessor to the object’s shadowed id. getTransformation() Accessor to the normalizing transformation. getTrendCoefficients() Accessor to the trend coefficients. getVisibility() Accessor to the object’s visibility state. hasName() Test if the object is named. hasVisibleName() Test if the object has a distinguishable name. setMetaModel(metaModel) Accessor to the metamodel. setModel(model) Accessor to the model. setName(name) Accessor to the object’s name. setRelativeErrors(relativeErrors) Accessor to the relative errors. setResiduals(residuals) Accessor to the residuals. setShadowedId(id) Accessor to the object’s shadowed id. setTransformation(transformation) Accessor to the normalizing transformation. setVisibility(visible) Accessor to the object’s visibility state.
 __call__
__init__(*args)

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

getBasisCollection()

Accessor to the collection of basis.

Returns: basisCollection : collection of Basis Collection of the function basis: for each with .

Notes

If the trend is not estimated, the collection is empty.

getClassName()

Accessor to the object’s name.

Returns: class_name : str The object class name (object.__class__.__name__).
getConditionalCovariance(*args)

Compute the expected covariance of the Gaussian process on a point (or several points).

Available usages:

getConditionalCovariance(x)

getConditionalCovariance(sampleX)

Parameters: x : sequence of float The point where the conditional mean of the output has to be evaluated. sampleX : 2-d sequence of float The sample where the conditional mean of the output has to be evaluated (M can be equal to 1). condCov : CovarianceMatrix The conditional covariance at point . Or the conditional covariance matrix at the sample : where .
getConditionalMean(*args)

Compute the expected mean of the Gaussian process on a point or a sample of points.

Available usages:

getConditionalMean(x)

getConditionalMean(sampleX)

Parameters: x : sequence of float The point where the conditional mean of the output has to be evaluated. sampleX : 2-d sequence of float The sample where the conditional mean of the output has to be evaluated (M can be equal to 1). condMean : Point The conditional mean at point . Or the conditional mean matrix at the sample :
getCovarianceCoefficients()

Accessor to the covariance coefficients.

Returns: covCoeff : Sample The defined in (2).
getCovarianceModel()

Accessor to the covariance model.

Returns: covModel : CovarianceModel The covariance model of the Gaussian process W with its optimized parameters.
getId()

Accessor to the object’s id.

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

Accessor to the input sample.

Returns: inputSample : Sample The input sample.
getMetaModel()

Accessor to the metamodel.

Returns: metaModel : Function Metamodel.
getModel()

Accessor to the model.

Returns: model : Function Physical model approximated by a metamodel.
getName()

Accessor to the object’s name.

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

Accessor to the output sample.

Returns: outputSample : Sample The output sample.
getRelativeErrors()

Accessor to the relative errors.

Returns: relativeErrors : Point The relative errors defined as follows for each output of the model: with the vector of the model’s values and the metamodel’s values.
getResiduals()

Accessor to the residuals.

Returns: residuals : Point The residual values defined as follows for each output of the model: with the model’s values and the metamodel’s values.
getShadowedId()

Accessor to the object’s shadowed id.

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

Accessor to the normalizing transformation.

Returns: transformation : Function The transformation T that normalizes the input sample.
getTrendCoefficients()

Accessor to the trend coefficients.

Returns: trendCoef : collection of Point The trend coefficients vectors
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.
setMetaModel(metaModel)

Accessor to the metamodel.

Parameters: metaModel : Function Metamodel.
setModel(model)

Accessor to the model.

Parameters: model : Function Physical model approximated by a metamodel.
setName(name)

Accessor to the object’s name.

Parameters: name : str The name of the object.
setRelativeErrors(relativeErrors)

Accessor to the relative errors.

Parameters: relativeErrors : sequence of float The relative errors defined as follows for each output of the model: with the vector of the model’s values and the metamodel’s values.
setResiduals(residuals)

Accessor to the residuals.

Parameters: residuals : sequence of float The residual values defined as follows for each output of the model: with the model’s values and the metamodel’s values.
setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters: id : int Internal unique identifier.
setTransformation(transformation)

Accessor to the normalizing transformation.

Parameters: transformation : Function The transformation T that normalizes the input sample.
setVisibility(visible)

Accessor to the object’s visibility state.

Parameters: visible : bool Visibility flag.