# MartinezSensitivityAlgorithm¶

class MartinezSensitivityAlgorithm(*args)

Sensitivity analysis using Martinez method.

Available constructors:

MartinezSensitivityAlgorithm(inputDesign, outputDesign, N, computeSecondOrder)

MartinezSensitivityAlgorithm(distribution, N, model, computeSecondOrder)

MartinezSensitivityAlgorithm(experiment, model, computeSecondOrder)

Parameters: inputDesign : Sample Design for the evaluation of sensitivity indices, obtained thanks to the SobolIndicesAlgorithmImplementation.Generate method outputDesign : Sample Design for the evaluation of sensitivity indices, obtained as the evaluation of a Function (model) on the previous inputDesign distribution : Distribution Input probabilistic model. Should have independent copula experiment : WeightedExperiment Experiment for the generation of two independent samples. N : int Size of samples to generate computeSecondOrder : bool If True, design that will be generated contains elements for the evaluation of second order indices.

Notes

This class is concerned with analyzing the influence the random vector has on a random variable which is being studied for uncertainty, by using the [Martinez2011] method for the evaluation of both first and total order indices.

These last ones are respectively given as follows:

where is the empirical correlation defined by:

The variance of the estimator is computed using:

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))
>>> # Define designs to pre-compute
>>> size = 100
>>> inputDesign = ot.SobolIndicesExperiment(distribution, size, True).generate()
>>> outputDesign = model(inputDesign)
>>> # sensitivity analysis algorithm
>>> sensitivityAnalysis = ot.MartinezSensitivityAlgorithm(inputDesign, outputDesign, size)
>>> print(sensitivityAnalysis.getFirstOrderIndices())
[0.30449,0.448506,-0.0711394]


Methods

 DrawImportanceFactors(*args) Draw the importance factors. draw(*args) Draw sensitivity indices. getAggregatedFirstOrderIndices() Get the evaluation of aggregated first order Sobol indices. getAggregatedTotalOrderIndices() Get the evaluation of aggregated total order Sobol indices. getBootstrapSize() Get the number of bootstrap sampling size. getClassName() Accessor to the object’s name. getConfidenceLevel() Get the confidence interval level for confidence intervals. getFirstOrderIndices([marginalIndex]) Get first order Sobol indices. getFirstOrderIndicesDistribution() Get the distribution of the aggregated first order Sobol indices. getFirstOrderIndicesInterval() Get interval for the aggregated first order Sobol indices. getId() Accessor to the object’s id. getName() Accessor to the object’s name. getSecondOrderIndices([marginalIndex]) Get second order Sobol indices. getShadowedId() Accessor to the object’s shadowed id. getTotalOrderIndices([marginalIndex]) Get total order Sobol indices. getTotalOrderIndicesDistribution() Get the distribution of the aggregated total order Sobol indices. getTotalOrderIndicesInterval() Get interval for the aggregated total order Sobol indices. getUseAsymptoticDistribution() Select asymptotic or bootstrap confidence intervals. getVisibility() Accessor to the object’s visibility state. hasName() Test if the object is named. hasVisibleName() Test if the object has a distinguishable name. setBootstrapSize(bootstrapSize) Set the number of bootstrap sampling size. setConfidenceLevel(confidenceLevel) Set the confidence interval level for confidence intervals. setName(name) Accessor to the object’s name. setShadowedId(id) Accessor to the object’s shadowed id. setUseAsymptoticDistribution(…) Select asymptotic or bootstrap confidence intervals. setVisibility(visible) Accessor to the object’s visibility state.
__init__(*args)

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

static DrawImportanceFactors(*args)

Draw the importance factors.

Available usages:

DrawImportanceFactors(importanceFactors, title=’Importance Factors’)

DrawImportanceFactors(values, names, title=’Importance Factors’)

Parameters:
importanceFactors : PointWithDescription

Sequence containing the importance factors with a description for each component. The descriptions are used to build labels for the created Pie. If they are not mentioned, default labels will be used.

values : sequence of float

Importance factors.

names : sequence of str

Variables’ names used to build labels for the created Pie.

title : str

Title of the graph.

Returns:
Graph : Graph

A graph containing a Pie of the importance factors of the variables.

draw(*args)

Draw sensitivity indices.

Usage:

draw()

draw(marginalIndex)

With the first usage, draw the aggregated first and total order indices. With the second usage, draw the first and total order indices of a specific marginal in case of vectorial output

Parameters: marginalIndex: int marginal of interest (case of second usage) Graph : Graph A graph containing the aggregated first and total order indices.

Notes

If number of bootstrap sampling is not 0, and confidence level associated > 0, the graph includes confidence interval plots in the first usage.

getAggregatedFirstOrderIndices()

Get the evaluation of aggregated first order Sobol indices.

Returns: indices : Point Sequence containing aggregated first order Sobol indices.
getAggregatedTotalOrderIndices()

Get the evaluation of aggregated total order Sobol indices.

Returns: indices : Point Sequence containing aggregated total order Sobol indices.
getBootstrapSize()

Get the number of bootstrap sampling size.

Returns: bootstrapSize : int Number of bootsrap sampling
getClassName()

Accessor to the object’s name.

Returns: class_name : str The object class name (object.__class__.__name__).
getConfidenceLevel()

Get the confidence interval level for confidence intervals.

Returns: confidenceLevel : float Confidence level for confidence intervals
getFirstOrderIndices(marginalIndex=0)

Get first order Sobol indices.

Parameters: i : int, optional Index of the marginal of the function, equals to by default. indices : Point Sequence containing first order Sobol indices.
getFirstOrderIndicesDistribution()

Get the distribution of the aggregated first order Sobol indices.

Returns: distribution : Distribution Distribution for first order Sobol indices for each component.
getFirstOrderIndicesInterval()

Get interval for the aggregated first order Sobol indices.

Returns: interval : Interval Interval for first order Sobol indices for each component. Computed marginal by marginal (not from the joint distribution).
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.
getSecondOrderIndices(marginalIndex=0)

Get second order Sobol indices.

Parameters: i : int, optional Index of the marginal of the function, equals to by default. indices : SymmetricMatrix Tensor containing second order Sobol indices.
getShadowedId()

Accessor to the object’s shadowed id.

Returns: id : int Internal unique identifier.
getTotalOrderIndices(marginalIndex=0)

Get total order Sobol indices.

Parameters: i : int, optional Index of the marginal of the function, equals to by default. indices : Point Sequence containing total order Sobol indices.
getTotalOrderIndicesDistribution()

Get the distribution of the aggregated total order Sobol indices.

Returns: distribution : Distribution Distribution for total order Sobol indices for each component.
getTotalOrderIndicesInterval()

Get interval for the aggregated total order Sobol indices.

Returns: interval : Interval Interval for total order Sobol indices for each component. Computed marginal by marginal (not from the joint distribution).
getUseAsymptoticDistribution()

Select asymptotic or bootstrap confidence intervals.

Returns: useAsymptoticDistribution : bool Whether to use bootstrap or asymptotic intervals
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.
hasVisibleName()

Test if the object has a distinguishable name.

Returns: hasVisibleName : bool True if the name is not empty and not the default one.
setBootstrapSize(bootstrapSize)

Set the number of bootstrap sampling size.

Default value is 0.

Parameters: bootstrapSize : int Number of bootsrap sampling
setConfidenceLevel(confidenceLevel)

Set the confidence interval level for confidence intervals.

Parameters: confidenceLevel : float Confidence level for confidence intervals
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.
setUseAsymptoticDistribution(useAsymptoticDistribution)

Select asymptotic or bootstrap confidence intervals.

Default value is set by the SobolIndicesAlgorithm-DefaultUseAsymptoticDistribution key.

Parameters: useAsymptoticDistribution : bool Whether to use bootstrap or asymptotic intervals
setVisibility(visible)

Accessor to the object’s visibility state.

Parameters: visible : bool Visibility flag.