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 used to sample the distribution.

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 can be used for Jansen, Martinez and MauntzKucherenko methods. This precomputes such input designs using distribution or experiment by generating two samples A and B according to the given experiment and mixing columns of these ones to define the huge sample (design). If computeSecondOrder is set to False, the result design is of size N(d+2) where d is the dimension of the distribution. If computeSecondOrder is set to True, the design size is N(2d+2), see [Saltelli2002], excepted in dimension 2. If the constructor based on the distribution is used, an experiment is built according to the value of ‘SobolIndicesExperiment-SamplingMethod’ in ResourceMap:

  • If it is equal to ‘LHS’, a LHSExperiment is used, with AlwaysShuffle and RandomShift set to True
  • If it is equal to ‘QMC’ and d\leq SobolSequence.MaximumNumberOfDimension, a LowDiscrepancyExperiment is used in conjunction with SobolSequence, with Restart and Randomize set to True. If d is too large, it falls back to the ‘LHS’ case.
  • Otherwise a MonteCarloExperiment is used. It is the default choice in order to allow SobolIndicesAlgorithm to use the asymptotic distribution of the indices estimates.

The corresponding output values of a model can be evaluated outside of 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.
getWeightedExperiment  
__init__(*args)

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