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, outputSample2d sequence of float
The samples and .
 metaModel
Function
The meta model: , defined in (3).
 residuals
Point
The residual errors.
 relativeErrors
Point
The relative errors.
 basiscollection of
Basis
Collection of the functional basis: for each with . Its size must be equal to zero if the trend is not estimated.
 trendCoefficientscollection of
Point
The trend coeffient vectors .
 covarianceModel
CovarianceModel
Covariance function of the Gaussian process.
 covarianceCoefficients2d 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
__call__
(*args)Compute the conditional Gaussian distribution on a new point / sample conditionally to the observed paths.
Accessor to the collection of basis.
Accessor to the object’s name.
getConditionalCovariance
(*args)Compute the conditional covariance of the Gaussian process on a point (or several points).
Compute the conditional covariance of the Gaussian process on a point (or several points).
Compute the conditional variance of the Gaussian process on a point (or several points).
getConditionalMean
(*args)Compute the conditional mean of the Gaussian process on a point or a sample of points.
Accessor to the covariance coefficients.
Accessor to the covariance model.
getId
()Accessor to the object’s id.
Accessor to the input sample.
Accessor to the metamodel.
getModel
()Accessor to the model.
getName
()Accessor to the object’s name.
Accessor to the output sample.
Accessor to the relative errors.
Accessor to the residuals.
Accessor to the object’s shadowed id.
Accessor to the trend coefficients.
Accessor to the object’s visibility state.
hasName
()Test if the object is named.
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.
setVisibility
(visible)Accessor to the object’s visibility state.

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

getBasisCollection
()¶ Accessor to the collection of basis.
 Returns
 basisCollectioncollection of
Basis
Collection of the function basis: for each with .
 basisCollectioncollection of
Notes
If the trend is not estimated, the collection is empty.

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

getConditionalCovariance
(*args)¶ Compute the conditional covariance of the Gaussian process on a point (or several points).
 Available usages:
getConditionalCovariance(x)
getConditionalCovariance(sampleX)
 Parameters
 xsequence of float
The point where the conditional covariance of the output has to be evaluated.
 sampleX2d sequence of float
The sample where the conditional covariance of the output has to be evaluated (M can be equal to 1).
 Returns
 condCov
CovarianceMatrix
The conditional covariance at point . Or the conditional covariance matrix at the sample :
where .
 condCov

getConditionalMarginalCovariance
(*args)¶ Compute the conditional covariance of the Gaussian process on a point (or several points).
 Available usages:
getConditionalMarginalCovariance(x)
getConditionalMarginalCovariance(sampleX)
 Parameters
 xsequence of float
The point where the conditional marginal covariance of the output has to be evaluated.
 sampleX2d sequence of float
The sample where the conditional marginal covariance of the output has to be evaluated (M can be equal to 1).
 Returns
 condCov
CovarianceMatrix
The conditional covariance at point .
 condCov
CovarianceMatrixCollection
The collection of conditional covariance matrices at each point of the sample :
 condCov
Notes
In case input parameter is a of type
Sample
, each element of the collection corresponds to the conditional covariance with respect to the input learning set (pointwise evaluation of the getConditionalCovariance).

getConditionalMarginalVariance
(*args)¶ Compute the conditional variance of the Gaussian process on a point (or several points).
 Available usages:
getConditionalMarginalVariance(x, marginalIndex)
getConditionalMarginalVariance(sampleX, marginalIndex)
getConditionalMarginalVariance(x, marginalIndices)
getConditionalMarginalVariance(sampleX, marginalIndices)
 Parameters
 xsequence of float
The point where the conditional variance of the output has to be evaluated.
 sampleX2d sequence of float
The sample where the conditional variance of the output has to be evaluated (M can be equal to 1).
 marginalIndexint
Marginal of interest (for multiple outputs). Default value is 0
 marginalIndicessequence of int
Marginals of interest (for multiple outputs).
 Returns
 varfloat
Variance of interest. float if one point (x) and one marginal of interest (x, marginalIndex)
 varPointsequence of float
The marginal variances
Notes
In case of fourth usage, the sequence of float is given as the concatenation of marginal variances for each point in sampleX.

getConditionalMean
(*args)¶ Compute the conditional mean of the Gaussian process on a point or a sample of points.
 Available usages:
getConditionalMean(x)
getConditionalMean(sampleX)
 Parameters
 xsequence of float
The point where the conditional mean of the output has to be evaluated.
 sampleX2d sequence of float
The sample where the conditional mean of the output has to be evaluated (M can be equal to 1).
 Returns
 condMean
Point
The conditional mean at point . Or the conditional mean matrix at the sample :
 condMean

getCovarianceCoefficients
()¶ Accessor to the covariance coefficients.

getCovarianceModel
()¶ Accessor to the covariance model.
 Returns
 covModel
CovarianceModel
The covariance model of the Gaussian process W with its optimized parameters.
 covModel

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

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

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.
 relativeErrors

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.
 residuals

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

getTrendCoefficients
()¶ Accessor to the trend coefficients.
 Returns
 trendCoefcollection of
Point
The trend coefficients vectors
 trendCoefcollection of

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

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

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

setModel
(model)¶ Accessor to the model.
 Parameters
 model
Function
Physical model approximated by a metamodel.
 model

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

setRelativeErrors
(relativeErrors)¶ Accessor to the relative errors.
 Parameters
 relativeErrorssequence 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
 residualssequence 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
 idint
Internal unique identifier.

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