SobolIndicesExperiment¶

class
SobolIndicesExperiment
(*args)¶ Experiment to computeSobol’ indices.
 Available constructors:
SobolIndicesExperiment(distribution, size, computeSecondOrder=False)
SobolIndicesExperiment(experiment, computeSecondOrder=False)
 Parameters
 distribution
Distribution
Distribution with an independent copula used to generate the set of input data.
 sizepositive int
Size 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.
 computeSecondOrderbool, defaults to False
Whether to add points to compute second order indices
 distribution
See also
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 distribution with repeated marginals, in order to also work with noniid samples such as those generated by
LHSExperiment
orLowDiscrepancyExperiment
. The sampling is done according to the given experiment, then it is split into samples and 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 where is the dimension of the distribution. If computeSecondOrder is set to True, the design size is , see [saltelli2002], excepted in dimension 2. If the constructor based on the distribution is used, an experiment is built according to the value of ‘SobolIndicesExperimentSamplingMethod’ inResourceMap
:If it is equal to ‘LHS’, a
LHSExperiment
is used, with AlwaysShuffle and RandomShift set to TrueIf it is equal to ‘QMC’ and , a
LowDiscrepancyExperiment
is used in conjunction withSobolSequence
, with Randomize set to False. If is too large, it falls back to the ‘LHS’ case.Otherwise a
MonteCarloExperiment
is used. It is the default choice in order to allowSobolIndicesAlgorithm
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
 sample
Sample
Points which constitute the design of experiments with . The sampling method is defined by the nature of the weighted experiment.
 sample
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
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
 distribution
Distribution
Distribution used to generate the set of input data.
 distribution

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 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
 distribution
Distribution
Distribution used to generate the set of input data.
 distribution

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 of points constituting the design of experiments.

setVisibility
(self, visible)¶ Accessor to the object’s visibility state.
 Parameters
 visiblebool
Visibility flag.