FunctionalChaosAnalysis¶

class persalys.FunctionalChaosAnalysis(*args)¶

Create a Functional chaos analysis.

Parameters:

namestr: Name
designOfExperimentDesignOfExperiment: Design of experiments

Methods

`analyticalValidation`()	Whether an analytical validation is requested.
`asPythonPhysicalModel`(study)	Create a Python model wrapping the metamodel created by the analysis.
`getChaosDegree`()	Chaos degree accessor.
`getClassName`()	Accessor to the object's name.
`getDesignOfExperiment`()	Design of experiments accessor.
`getDistribution`()	Input distribution accessor.
`getEffectiveInputSample`()	Effective input sample accessor.
`getEffectiveOutputSample`()	Effective output sample accessor.
`getErrorMessage`()	Error message accessor.
`getInterestVariables`()	Get the variables to analyse.
`getKFoldValidationNumberOfFolds`()	Number of folds accessor.
`getKFoldValidationSeed`()	Seed accessor.
`getMetaModel`()	metamodel accessor.
`getName`()	Accessor to the object's name.
`getPythonScript`()	Physical model accessor.
`getResult`()	Results accessor.
`getSparseChaos`()	Whether it is sparse.
`getTestSampleValidationPercentageOfPoints`()	Percentage of points accessor.
`getTestSampleValidationSeed`()	Seed accessor.
`getWarningMessage`()	Warning message accessor.
`hasName`()	Test if the object is named.
`hasValidResult`()	Whether the analysis has been run.
`isReliabilityAnalysis`()	Whether the analysis involves reliability.
`isRunning`()	Whether the analysis is running.
`kFoldValidation`()	Whether a k-Fold cross-validation is requested.
`leaveOneOutValidation`()	Whether a validation by leave-one-out is requested.
`run`()	Launch the analysis.
`setAnalyticalValidation`(validation)	Whether an analytical validation is requested.
`setChaosDegree`(degree)	Chaos degree accessor.
`setInterestVariables`(variablesNames)	Set the variables to analyse.
`setKFoldValidation`(validation)	Whether a k-Fold cross-validation is requested.
`setKFoldValidationNumberOfFolds`(nbFolds)	Number of folds accessor.
`setKFoldValidationSeed`(seed)	Seed accessor.
`setLeaveOneOutValidation`(validation)	Whether it is sparse.
`setName`(name)	Accessor to the object's name.
`setSparseChaos`(sparse)	Whether it is sparse.
`setTestSampleValidation`(validation)	Whether a validation with a test sample is requested.
`setTestSampleValidationPercentageOfPoints`(...)	Percentage of points accessor.
`setTestSampleValidationSeed`(seed)	Seed accessor.
`testSampleValidation`()	Whether a validation with a test sample is requested.

Examples

>>> import openturns as ot
>>> import persalys

Create the model:

>>> from math import pi
>>> ot.RandomGenerator.SetSeed(0)
>>> xi1 = persalys.Input('xi1', ot.Uniform(-pi, pi))
>>> xi2 = persalys.Input('xi2', ot.Uniform(-pi, pi))
>>> xi3 = persalys.Input('xi3', ot.Uniform(-pi, pi))
>>> y0 = persalys.Output('y0')
>>> myPhysicalModel = persalys.SymbolicPhysicalModel('myPhysicalModel', [xi1, xi2, xi3], [y0], ['sin(xi1) + 7. * (sin(xi2)) ^ 2 + 0.1 * xi3^4 * sin(xi1)'])

Create the design of experiments:

>>> aDesign = persalys.FixedDesignOfExperiment('aDesign', myPhysicalModel)
>>> inputSample = ot.LHSExperiment(myPhysicalModel.getDistribution(), 250).generate()
>>> aDesign.setOriginalInputSample(inputSample)
>>> aDesign.run()

Create the Functional Chaos Analysis:

>>> chaos = persalys.FunctionalChaosAnalysis('chaos', aDesign)
>>> chaos.setChaosDegree(6)
>>> chaos.setSparseChaos(False)
>>> chaos.setLeaveOneOutValidation(False)
>>> chaos.run()

Get the result:

>>> chaosResult = chaos.getResult()
>>> sobolResult = chaosResult.getSobolResult()

__init__(*args)¶

analyticalValidation()¶

Whether an analytical validation is requested.

Returns:

validationbool: Whether an analytical validation is requested. This method corresponds to an approximation of the Leave-one-out method result.

asPythonPhysicalModel(study)¶

Create a Python model wrapping the metamodel created by the analysis.

Parameters:

studyStudy: The study to which the analysis belong

Returns:

modelPythonPhysicalModel: The python model

getChaosDegree()¶

Chaos degree accessor.

Returns:

degreeint: Chaos degree. It is set by default to 2

getClassName()¶

Accessor to the object’s name.

Returns:

class_namestr: The object class name (object.__class__.__name__).

getDesignOfExperiment()¶

Design of experiments accessor.

Returns:

modelDesignOfExperiment: Design of experiments

getDistribution()¶

Input distribution accessor.

Returns:

distributionopenturns.JointDistribution: The distribution defined in the probabilistic model or a distribution composed of Uniform laws if there is no stochastic input variable.

getEffectiveInputSample()¶

Effective input sample accessor.

Returns:

sampleopenturns.Sample: Sample of all the input variables if all of them are deterministic. Otherwise, sample of the stochastic input variables.

getEffectiveOutputSample()¶

Effective output sample accessor.

Returns:

sampleopenturns.Sample: Sample of the interest output variables.

getErrorMessage()¶

Error message accessor.

Returns:

messagestr: Error message if the analysis failed

getInterestVariables()¶

Get the variables to analyse.

Returns:

variablesNamessequence of str: Names of the variables to analyse

getKFoldValidationNumberOfFolds()¶

Number of folds accessor.

Returns:

foldsint: Number of folds. By default it is 3.

getKFoldValidationSeed()¶

Seed accessor.

Returns:

seedint: Seed value for k-Fold cross-validation

getMetaModel()¶

metamodel accessor.

Returns:

metamodelPhysicalModel: The metamodel created by the analysis

getName()¶

Accessor to the object’s name.

Returns:

namestr: The name of the object.

getPythonScript()¶

Physical model accessor.

Returns:

scriptstr: Python script to replay the analysis

getResult()¶

Results accessor.

Returns:

resultFunctionalChaosAnalysisResult: Results

getSparseChaos()¶

Whether it is sparse.

Returns:

isSparsebool: Whether it is sparse. By default, the chaos is not sparse

getTestSampleValidationPercentageOfPoints()¶

Percentage of points accessor.

Returns:

percentageint: Percentage of points used to validate the metamodel. By default it is 20%.

getTestSampleValidationSeed()¶

Seed accessor.

Returns:

seedint: Seed value for the validation with a test sample

getWarningMessage()¶

Warning message accessor.

Returns:

messagestr: Warning message which can appear during the analysis computation

hasName()¶

Test if the object is named.

Returns:

hasNamebool: True if the name is not empty.

hasValidResult()¶

Whether the analysis has been run.

Returns:

hasValidResultbool: Whether the analysis has already been run

isReliabilityAnalysis()¶

Whether the analysis involves reliability.

Returns:

isReliabilityAnalysisbool: Whether the analysis involves a reliability analysis

isRunning()¶

Whether the analysis is running.

Returns:

isRunningbool: Whether the analysis is running

kFoldValidation()¶

Whether a k-Fold cross-validation is requested.

Returns:

validationbool: Whether a k-Fold cross-validation is requested

leaveOneOutValidation()¶

Whether a validation by leave-one-out is requested.

Returns:

validationbool: Whether a validation by leave-one-out is requested

run()¶: Launch the analysis.

setAnalyticalValidation(validation)¶

Whether an analytical validation is requested.

Parameters:

validationbool: Whether an analytical validation is requested. This method corresponds to an approximation of the Leave-one-out method result.

setChaosDegree(degree)¶

Chaos degree accessor.

Parameters:

degreeint: Chaos degree

setInterestVariables(variablesNames)¶

Set the variables to analyse.

Parameters:

variablesNamessequence of str: Names of the variables to analyse

setKFoldValidation(validation)¶

Whether a k-Fold cross-validation is requested.

Parameters:

validationbool: Whether a k-Fold cross-validation is requested

setKFoldValidationNumberOfFolds(nbFolds)¶

Number of folds accessor.

Parameters:

foldsint: Number of folds. By default it is 3.

setKFoldValidationSeed(seed)¶

Seed accessor.

Parameters:

seedint: Seed value for k-Fold cross-validation

setLeaveOneOutValidation(validation)¶

Whether it is sparse.

Parameters:

validationbool: Whether a validation by leave-one-out is requested

setName(name)¶

Accessor to the object’s name.

Parameters:

namestr: The name of the object.

setSparseChaos(sparse)¶

Whether it is sparse.

Parameters:

isSparsebool: Whether it is sparse

setTestSampleValidation(validation)¶

Whether a validation with a test sample is requested.

Parameters:

validationbool: Whether a validation with a test sample is requested. The data sample is dividing into two sub-samples: a training sample (default: 80% of the sample points) and a test sample (default: 20% of the sample points). A new metamodel is built with the training sample and is validated with the test sample. The points are randomly picked in the data sample (by default the seed is 1).

setTestSampleValidationPercentageOfPoints(percentage)¶

Percentage of points accessor.

Parameters:

percentageint: Percentage of points used to validate the metamodel. By default it is 20%.

setTestSampleValidationSeed(seed)¶

Seed accessor.

Parameters:

seedint: Seed value for the validation with a test sample

testSampleValidation()¶

Whether a validation with a test sample is requested.

Returns:

validationbool: Whether a validation with a test sample is requested. The data sample is dividing into two sub-samples: a training sample (default: 80% of the sample points) and a test sample (default: 20% of the sample points). A new metamodel is built with the training sample and is validated with the test sample. The points are randomly picked in the data sample (by default the seed is 1).

FunctionalChaosAnalysis¶

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