SobolIndicesExperiment

class SobolIndicesExperiment(*args)

Experiment to computeSobol’ indices.

Available constructors:

SobolIndicesExperiment(distribution, size, computeSecondOrder=True)

SobolIndicesExperiment(experiment, computeSecondOrder=True)

Parameters:

distribution : Distribution

Distribution \mu with an independent copula used to generate the set of input data.

size : positive int

Size N of each of the two independent initial samples. For the total size of the experiment see notes below.

experiment : WeightedExperiment

Design of experiment

computeSecondOrder : bool, defaults to True

Whether to add points to compute second order indices

Notes

Sensitivity algorithms rely on the definition of specific designs. The method generates design for the Saltelli method. Such designs could be used for Jansen, Martinez and MauntzKucherenko methods. This precomputes such input designs using distribution or experiment by generating two independent samples and mixing columns of these ones to define the huge sample (design). If computeSecondOrder is disabled, result design is of size N*(p+2) where p is the input dimension. If computeSecondOrder is enabled, design’s size is N*(2p+2), see [Saltelli2002]. Model’s answer could be evaluated outside the platform.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> formula = ['sin(_pi*X1)+7*sin(_pi*X2)*sin(_pi*X2)+' + \
...    '0.1*((_pi*X3)*(_pi*X3)*(_pi*X3)*(_pi*X3))*sin(_pi*X1)']
>>> model = ot.SymbolicFunction(['X1', 'X2', 'X3'], formula)
>>> distribution = ot.ComposedDistribution([ot.Uniform(-1.0, 1.0)] * 3, \
...                                         ot.IndependentCopula(3))
>>> size = 10
>>> experiment = ot.SobolIndicesExperiment(distribution, size, True)
>>> sample = experiment.generate()

Methods

generate() Generate points according to the type of the experiment.
generateWithWeights(weights) Generate points and their associated weight according to the type of the experiment.
getClassName() Accessor to the object’s name.
getDistribution() Accessor to the distribution.
getId() Accessor to the object’s id.
getName() Accessor to the object’s name.
getShadowedId() Accessor to the object’s shadowed id.
getSize() Accessor to the size of the generated sample.
getVisibility() Accessor to the object’s visibility state.
hasName() Test if the object is named.
hasUniformWeights() Ask whether the experiment has uniform weights.
hasVisibleName() Test if the object has a distinguishable name.
setDistribution(distribution) Accessor to the distribution.
setName(name) Accessor to the object’s name.
setShadowedId(id) Accessor to the object’s shadowed id.
setSize(size) Accessor to the size of the generated sample.
setVisibility(visible) Accessor to the object’s visibility state.
__init__(*args)

x.__init__(…) initializes x; see help(type(x)) for signature

generate()

Generate points according to the type of the experiment.

Returns:

sample : Sample

Points (\Xi_i)_{i \in I} which constitute the design of experiments with card I = size. The sampling method is defined by the nature of the weighted experiment.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> myExperiment = ot.MonteCarloExperiment(ot.Normal(2), 5)
>>> sample = myExperiment.generate()
>>> print(sample)
    [ X0        X1        ]
0 : [  0.608202 -1.26617  ]
1 : [ -0.438266  1.20548  ]
2 : [ -2.18139   0.350042 ]
3 : [ -0.355007  1.43725  ]
4 : [  0.810668  0.793156 ]
generateWithWeights(weights)

Generate points and their associated weight according to the type of the experiment.

Returns:

sample : Sample

The points which constitute the design of experiments. The sampling method is defined by the nature of the experiment.

weights : Point of size cardI

Weights (\omega_i)_{i \in I} associated with the points. By default, all the weights are equal to 1/cardI.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> myExperiment = ot.MonteCarloExperiment(ot.Normal(2), 5)
>>> sample, weights = myExperiment.generateWithWeights()
>>> print(sample)
    [ X0        X1        ]
0 : [  0.608202 -1.26617  ]
1 : [ -0.438266  1.20548  ]
2 : [ -2.18139   0.350042 ]
3 : [ -0.355007  1.43725  ]
4 : [  0.810668  0.793156 ]
>>> print(weights)
[0.2,0.2,0.2,0.2,0.2]
getClassName()

Accessor to the object’s name.

Returns:

class_name : str

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

getDistribution()

Accessor to the distribution.

Returns:

distribution : Distribution

Distribution used to generate the set of input data.

getId()

Accessor to the object’s id.

Returns:

id : int

Internal unique identifier.

getName()

Accessor to the object’s name.

Returns:

name : str

The name of the object.

getShadowedId()

Accessor to the object’s shadowed id.

Returns:

id : int

Internal unique identifier.

getSize()

Accessor to the size of the generated sample.

Returns:

size : positive int

Number cardI of points constituting the design of experiments.

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.

hasUniformWeights()

Ask whether the experiment has uniform weights.

Returns:

hasUniformWeights : bool

Whether the experiment has uniform weights.

hasVisibleName()

Test if the object has a distinguishable name.

Returns:

hasVisibleName : bool

True if the name is not empty and not the default one.

setDistribution(distribution)

Accessor to the distribution.

Parameters:

distribution : Distribution

Distribution used to generate the set of input data.

setName(name)

Accessor to the object’s name.

Parameters:

name : str

The name of the object.

setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters:

id : int

Internal unique identifier.

setSize(size)

Accessor to the size of the generated sample.

Parameters:

size : positive int

Number cardI of points constituting the design of experiments.

setVisibility(visible)

Accessor to the object’s visibility state.

Parameters:

visible : bool

Visibility flag.