FunctionalChaosSobolIndices¶

class FunctionalChaosSobolIndices(*args)¶

Sensitivity analysis based on functional chaos expansion.

Parameters:

resultFunctionalChaosResult: A functional chaos result resulting from a polynomial chaos decomposition.

See also

FunctionalChaosAlgorithm, FunctionalChaosResult

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:

>>> s0 = chaosSI.getSobolIndex(0)

Get total order Sobol’ indices for X0:

>>> st0 = chaosSI.getSobolTotalIndex(0)

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

>>> stg01 = chaosSI.getSobolGroupedIndex([0,1])

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

>>> stg12 = chaosSI.getSobolGroupedTotalIndex([1,2])

Methods

`getClassName`()	Accessor to the object's name.
`getFunctionalChaosResult`()	Accessor to the functional chaos result.
`getId`()	Accessor to the object's id.
`getName`()	Accessor to the object's name.
`getShadowedId`()	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.
`getVisibility`()	Accessor to the object's visibility state.
`hasName`()	Test if the object is named.
`hasVisibleName`()	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

__init__(*args)¶

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.

getShadowedId()¶

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, $0 \leq i < d - 1$: Indice(s) of the variable(s) we want the associated grouped Sobol indices. $d$ is the dimension of the input variables.
marginalIndexint: Output marginal index. Default value is 0, i.e. the first output.

Returns:

sfloat: The grouped Sobol first order index.

getSobolGroupedTotalIndex(*args)¶

Get the grouped Sobol total order indices.

Parameters:

iint or sequence of int, $0 \leq i < d - 1$: Indice(s) of the variable(s) we want the associated grouped Sobol indices. $d$ is the dimension of the input variables.
marginalIndexint: Output marginal index. Default value is 0, i.e. the first output.

Returns:

sfloat: The grouped Sobol total order index.

getSobolIndex(*args)¶

Get the Sobol indices.

Parameters:

iint or sequence of int, $0 \leq i < d - 1$: Indice(s) of the variable(s) we want the associated Sobol indices. $d$ is the dimension of the input variables.
marginalIndexint: Output marginal index. Default value is 0, i.e. the first output.

Returns:

sfloat: The first order Sobol index.

getSobolTotalIndex(*args)¶

Get the total Sobol indices.

Parameters:

iint or sequence of int, $0 \leq i < d - 1$: Indice(s) of the variable(s) we want the associated total Sobol indices. $d$ is the dimension of the input variables.
marginalIndexint: Output marginal index. Default value is 0, i.e. the first output.

Returns: