# FunctionalChaosSobolIndices¶

class FunctionalChaosSobolIndices(*args)

Sensitivity analysis based on functional chaos expansion.

Parameters
resultFunctionalChaosResult

A functional chaos result resulting from a polynomial chaos decomposition.

Notes

This structure is created from a FunctionalChaosResult in order to evaluate the Sobol indices associated to the polynomial chaos decomposition of the model. The SobolIndicesAlgorithm.DrawSobolIndices static method can be used to draw the indices.

Examples

Create a polynomial chaos for the Ishigami function:

>>> import openturns as ot
>>> from math import pi
>>> import openturns.viewer as otv

Create the function:

>>> ot.RandomGenerator.SetSeed(0)
>>> formula = ['sin(X1) + 7. * sin(X2)^2 + 0.1 * X3^4 * sin(X1)']
>>> input_names = ['X1', 'X2', 'X3']
>>> g = ot.SymbolicFunction(input_names, formula)

Create the probabilistic model:

>>> distributionList = [ot.Uniform(-pi, pi)] * 3
>>> distribution = ot.ComposedDistribution(distributionList)

Create a training sample:

>>> N = 100
>>> inputTrain = distribution.getSample(N)
>>> outputTrain = g(inputTrain)

Create the chaos:

>>> chaosalgo = ot.FunctionalChaosAlgorithm(inputTrain, outputTrain)
>>> chaosalgo.run()
>>> result = chaosalgo.getResult()

Print Sobol’ indices :

>>> chaosSI = ot.FunctionalChaosSobolIndices(result)
>>> #print( chaosSI.summary() )

Get first order Sobol’ indices for X0:

>>> chaosSI.getSobolIndex(0)
0.322659...

Get total order Sobol’ indices for X0:

>>> chaosSI.getSobolTotalIndex(0)
0.4744650...

Get first order Sobol’ indices for group [X0,X1]:

>>> chaosSI.getSobolGroupedIndex([0,1])
0.78412698...

Get total order Sobol’ indices for group [X1,X2]:

>>> chaosSI.getSobolGroupedTotalIndex([1,2])
0.6773409...

Methods

 Accessor to the object’s name. Accessor to the functional chaos result. getId() Accessor to the object’s id. getName() Accessor to the object’s name. Accessor to the object’s shadowed id. getSobolGroupedIndex(*args) Get the grouped Sobol first order indices. getSobolGroupedTotalIndex(*args) Get the grouped Sobol total order indices. getSobolIndex(*args) Get the Sobol indices. getSobolTotalIndex(*args) Get the total Sobol indices. Accessor to the object’s visibility state. hasName() Test if the object is named. Test if the object has a distinguishable name. setName(name) Accessor to the object’s name. setShadowedId(id) Accessor to the object’s shadowed id. setVisibility(visible) Accessor to the object’s visibility state. summary() Summary accessor.
__init__(*args)

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

getClassName()

Accessor to the object’s name.

Returns
class_namestr

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

getFunctionalChaosResult()

Accessor to the functional chaos result.

Returns
functionalChaosResultFunctionalChaosResult

The functional chaos result resulting from a polynomial chaos decomposition.

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.

Accessor to the object’s shadowed id.

Returns
idint

Internal unique identifier.

getSobolGroupedIndex(*args)

Get the grouped Sobol first order indices.

Parameters
iint or sequence of int,

Indice(s) of the variable(s) we want the associated grouped Sobol indices. is the dimension of the input variables.

Returns
sfloat

The grouped Sobol first order indice.

getSobolGroupedTotalIndex(*args)

Get the grouped Sobol total order indices.

Parameters
iint or sequence of int,

Indice(s) of the variable(s) we want the associated grouped Sobol indices. is the dimension of the input variables.

Returns
sfloat

The grouped Sobol total order indice.

getSobolIndex(*args)

Get the Sobol indices.

Parameters
iint or sequence of int,

Indice(s) of the variable(s) we want the associated Sobol indices. is the dimension of the input variables.

out_marginalint

Output marginal Default value is 0

Returns
sfloat

The Sobol indice.

getSobolTotalIndex(*args)

Get the total Sobol indices.

Parameters
iint or sequence of int,

Indice(s) of the variable(s) we want the associated total Sobol indices. is the dimension of the input variables.

out_marginalint

Output marginal Default value is 0

Returns
sfloat

The total Sobol indice.

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.

setName(name)

Accessor to the object’s name.

Parameters
namestr

The name of the object.

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.

summary()

Summary accessor.

Returns
summarystr

A text summary of the sensitivity analysis to be shown in a console.