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.
- basisCollection : collection of
-
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).
Returns: - 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).
Returns: - condMean :
Point
The conditional mean
at point
. Or the conditional mean matrix at the sample
:
-
getCovarianceCoefficients
()¶ Accessor to the covariance coefficients.
Returns:
-
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: - id : int
Internal unique identifier.
-
getModel
()¶ Accessor to the model.
Returns: - model :
Function
Physical model approximated by a metamodel.
- model :
-
getName
()¶ Accessor to the object’s name.
Returns: - name : str
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: - id : int
Internal unique identifier.
-
getTransformation
()¶ Accessor to the normalizing transformation.
Returns: - transformation :
Function
The transformation T that normalizes the input sample.
- transformation :
-
getTrendCoefficients
()¶ Accessor to the trend coefficients.
Returns: - trendCoef : collection of
Point
The trend coefficients vectors
- trendCoef : collection of
-
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.
-
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: - 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.
- transformation :
-
setVisibility
(visible)¶ Accessor to the object’s visibility state.
Parameters: - visible : bool
Visibility flag.