SobolIndicesExperiment

class SobolIndicesExperiment(*args)

Experiment to computeSobol’ indices.

Available constructors:

SobolIndicesExperiment(distribution, size, computeSecondOrder=False)

SobolIndicesExperiment(experiment, computeSecondOrder=False)

Parameters
distributionDistribution

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

sizepositive int

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

experimentWeightedExperiment

Design of experiment used to sample the distribution.

computeSecondOrderbool, defaults to False

Whether to add points to compute second order indices

See also

SobolIndicesAlgorithm

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 a sample of twice the dimension by duplicating the distribution into a 2d distribution with repeated marginals, in order to also work with non-iid samples such as those generated by LHSExperiment or LowDiscrepancyExperiment. The sampling is done according to the given experiment, then it is split into samples A and B and the columns of these ones are mixed 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 Randomize set to False. 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

Create a sample suitable to estimate first and total order Sobol’ indices: >>> import openturns as ot >>> ot.RandomGenerator.SetSeed(0) >>> formula = [‘sin(pi_*X1)+7*sin(pi_*X2)^2+0.1*(pi_*X3)^4*sin(pi_*X1)’] >>> model = ot.SymbolicFunction([‘X1’, ‘X2’, ‘X3’], formula) >>> distribution = ot.ComposedDistribution([ot.Uniform(-1.0, 1.0)] * 3) >>> size = 10 >>> experiment = ot.SobolIndicesExperiment(distribution, size) >>> sample = experiment.generate()

Create a sample suitable to estimate first, total order and second order Sobol’ indices: >>> import openturns as ot >>> ot.RandomGenerator.SetSeed(0) >>> formula = [‘sin(pi_*X1)+7*sin(pi_*X2)^2+0.1*(pi_*X3)^4*sin(pi_*X1)’] >>> model = ot.SymbolicFunction([‘X1’, ‘X2’, ‘X3’], formula) >>> distribution = ot.ComposedDistribution([ot.Uniform(-1.0, 1.0)] * 3) >>> size = 10 >>> computeSecondOrder = True >>> experiment = ot.SobolIndicesExperiment(distribution, size, computeSecondOrder) >>> sample = experiment.generate()

Methods

generate(self)

Generate points according to the type of the experiment.

generateWithWeights(self, weights)

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

getClassName(self)

Accessor to the object’s name.

getDistribution(self)

Accessor to the distribution.

getId(self)

Accessor to the object’s id.

getName(self)

Accessor to the object’s name.

getShadowedId(self)

Accessor to the object’s shadowed id.

getSize(self)

Accessor to the size of the generated sample.

getVisibility(self)

Accessor to the object’s visibility state.

hasName(self)

Test if the object is named.

hasUniformWeights(self)

Ask whether the experiment has uniform weights.

hasVisibleName(self)

Test if the object has a distinguishable name.

setDistribution(self, distribution)

Accessor to the distribution.

setName(self, name)

Accessor to the object’s name.

setShadowedId(self, id)

Accessor to the object’s shadowed id.

setSize(self, size)

Accessor to the size of the generated sample.

setVisibility(self, visible)

Accessor to the object’s visibility state.

getWeightedExperiment
__init__(self, \*args)

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

generate(self)

Generate points according to the type of the experiment.

Returns
sampleSample

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(self, weights)

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

Returns
sampleSample

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

weightsPoint 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(self)

Accessor to the object’s name.

Returns
class_namestr

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

getDistribution(self)

Accessor to the distribution.

Returns
distributionDistribution

Distribution used to generate the set of input data.

getId(self)

Accessor to the object’s id.

Returns
idint

Internal unique identifier.

getName(self)

Accessor to the object’s name.

Returns
namestr

The name of the object.

getShadowedId(self)

Accessor to the object’s shadowed id.

Returns
idint

Internal unique identifier.

getSize(self)

Accessor to the size of the generated sample.

Returns
sizepositive int

Number cardI of points constituting the design of experiments.

getVisibility(self)

Accessor to the object’s visibility state.

Returns
visiblebool

Visibility flag.

hasName(self)

Test if the object is named.

Returns
hasNamebool

True if the name is not empty.

hasUniformWeights(self)

Ask whether the experiment has uniform weights.

Returns
hasUniformWeightsbool

Whether the experiment has uniform weights.

hasVisibleName(self)

Test if the object has a distinguishable name.

Returns
hasVisibleNamebool

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

setDistribution(self, distribution)

Accessor to the distribution.

Parameters
distributionDistribution

Distribution used to generate the set of input data.

setName(self, name)

Accessor to the object’s name.

Parameters
namestr

The name of the object.

setShadowedId(self, id)

Accessor to the object’s shadowed id.

Parameters
idint

Internal unique identifier.

setSize(self, size)

Accessor to the size of the generated sample.

Parameters
sizepositive int

Number cardI of points constituting the design of experiments.

setVisibility(self, visible)

Accessor to the object’s visibility state.

Parameters
visiblebool

Visibility flag.