# FunctionalChaosResult¶

class FunctionalChaosResult(*args)

Functional chaos result.

Returned by functional chaos algorithms, see FunctionalChaosAlgorithm.

Parameters:
sampleX2-d sequence of float

Input sample of .

sampleY2-d sequence of float

Output sample of .

distributionDistribution

Distribution of the random vector

transformationFunction

The function that maps the physical input to the standardized input .

inverseTransformationFunction

The function that maps standardized input to the the physical input .

orthogonalBasisOrthogonalBasis

The multivariate orthogonal basis.

indicessequence of int

The indices of the selected basis function within the orthogonal basis.

alpha_k2-d sequence of float

The coefficients of the functional chaos expansion.

Psi_ksequence of Function

The functions of the multivariate basis selected by the algorithm.

residualssequence of float,

For each output component, the residual is the square root of the sum of squared differences between the model and the meta model, divided by the sample size.

The relative error is the empirical error divided by the sample variance of the output.

Notes

Let be the sample size. Let be the dimension of the output of the physical model. For any and any , let be the output of the physical model and let be the output of the metamodel. For any , let be the sample output and let be the output predicted by the metamodel. The marginal residual is:

for , where is the marginal sum of squares:

The marginal relative error is:

for , where is the unbiased sample variance of the -th output.

This structure is created by the method run() of FunctionalChaosAlgorithm, and obtained thanks to the getResult() method.

Methods

 Accessor to the object's name. Get the coefficients. Get the composed metamodel. Get the input distribution. Accessor to the object's id. Get the indices of the final basis. Accessor to the input sample. Get the inverse isoprobabilistic transformation. Accessor to the metamodel. Accessor to the object's name. Get the orthogonal basis. Accessor to the output sample. Get the reduced basis. Accessor to the relative errors. Accessor to the residuals. Accessor to the object's shadowed id. Get the isoprobabilistic transformation. Accessor to the object's visibility state. Test if the object is named. Test if the object has a distinguishable name. setInputSample(sampleX) Accessor to the input sample. setMetaModel(metaModel) Accessor to the metamodel. setName(name) Accessor to the object's name. setOutputSample(sampleY) Accessor to the output sample. setRelativeErrors(relativeErrors) Accessor to the relative errors. setResiduals(residuals) Accessor to the residuals. Accessor to the object's shadowed id. setVisibility(visible) Accessor to the object's visibility state.
__init__(*args)
getClassName()

Accessor to the object’s name.

Returns:
class_namestr

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

getCoefficients()

Get the coefficients.

Returns:
coefficients2-d sequence of float

Coefficients .

getComposedMetaModel()

Get the composed metamodel.

Returns:
composedMetamodelFunction

getDistribution()

Get the input distribution.

Returns:
distributionDistribution

Distribution of the input random vector .

getId()

Accessor to the object’s id.

Returns:
idint

Internal unique identifier.

getIndices()

Get the indices of the final basis.

Returns:
indicesIndices

Indices of the elements of the multivariate basis used in the decomposition.

getInputSample()

Accessor to the input sample.

Returns:
inputSampleSample

The input sample.

getInverseTransformation()

Get the inverse isoprobabilistic transformation.

Returns:
invTransfFunction

such that .

getMetaModel()

Accessor to the metamodel.

Returns:
metaModelFunction

Metamodel.

getName()

Accessor to the object’s name.

Returns:
namestr

The name of the object.

getOrthogonalBasis()

Get the orthogonal basis.

Returns:
basisOrthogonalBasis

Factory of the orthogonal basis.

getOutputSample()

Accessor to the output sample.

Returns:
outputSampleSample

The output sample.

getReducedBasis()

Get the reduced basis.

Returns:
basislist of Function

Collection of the K functions used in the decomposition.

getRelativeErrors()

Accessor to the relative errors.

Returns:
relativeErrorsPoint

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:
residualsPoint

The residual values defined as follows for each output of the model: with the model’s values and the metamodel’s values.

Accessor to the object’s shadowed id.

Returns:
idint

Internal unique identifier.

getTransformation()

Get the isoprobabilistic transformation.

Returns:
transformationFunction

Transformation such that .

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.

setInputSample(sampleX)

Accessor to the input sample.

Parameters:
inputSampleSample

The input sample.

setMetaModel(metaModel)

Accessor to the metamodel.

Parameters:
metaModelFunction

Metamodel.

setName(name)

Accessor to the object’s name.

Parameters:
namestr

The name of the object.

setOutputSample(sampleY)

Accessor to the output sample.

Parameters:
outputSampleSample

The output sample.

setRelativeErrors(relativeErrors)

Accessor to the relative errors.

Parameters:

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.

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.

## Examples using the class¶

Polynomial chaos exploitation

Polynomial chaos exploitation

Polynomial chaos over database

Polynomial chaos over database

Compute grouped indices for the Ishigami function

Compute grouped indices for the Ishigami function

Validate a polynomial chaos

Validate a polynomial chaos

Create a polynomial chaos metamodel by integration on the cantilever beam

Create a polynomial chaos metamodel by integration on the cantilever beam

Create a polynomial chaos metamodel

Create a polynomial chaos metamodel

Create a polynomial chaos for the Ishigami function: a quick start guide to polynomial chaos

Create a polynomial chaos for the Ishigami function: a quick start guide to polynomial chaos

Polynomial chaos expansion cross-validation

Polynomial chaos expansion cross-validation

Polynomial chaos is sensitive to the degree

Polynomial chaos is sensitive to the degree

Create a sparse chaos by integration

Create a sparse chaos by integration

Compute Sobol’ indices confidence intervals

Compute Sobol' indices confidence intervals

Metamodel of a field function

Metamodel of a field function

Sobol’ sensitivity indices from chaos

Sobol' sensitivity indices from chaos

Use the ANCOVA indices

Use the ANCOVA indices

Example of sensitivity analyses on the wing weight model

Example of sensitivity analyses on the wing weight model

Compute leave-one-out error of a polynomial chaos expansion

Compute leave-one-out error of a polynomial chaos expansion