# SaltelliSensitivityAlgorithm¶

class SaltelliSensitivityAlgorithm(*args)

Sensitivity analysis using Saltelli method.

Available constructors:

SaltelliSensitivityAlgorithm(inputDesign, outputDesign, N)

SaltelliSensitivityAlgorithm(distribution, N, model, computeSecondOrder)

SaltelliSensitivityAlgorithm(experiment, model, computeSecondOrder)

Parameters:
inputDesignSample

Design for the evaluation of sensitivity indices, obtained with the SobolIndicesExperiment.generate() method

outputDesignSample

Design for the evaluation of sensitivity indices, obtained as the evaluation of a Function (model) on the previous inputDesign

distributionDistribution

Input probabilistic model. Should have independent copula

experimentWeightedExperiment

Experiment for the generation of two independent samples.

Nint

Size of samples to generate

computeSecondOrderbool

If True, design that will be generated contains elements for the evaluation of second order indices.

Notes

This class analyzes the influence of each component of a random vector on a random vector by computing Sobol’ indices (see also [sobol1993]). The [saltelli2002] method is used to estimate both first and total order indices. Notations are defined in the documentation page of the SobolIndicesAlgorithm class. The estimators of and used by this class are respectively:

where is the centered model based on the sample.

The class constructor SaltelliSensitivityAlgorithm(inputDesign, outputDesign, N) requires a specific structure for the outputDesign, and therefore for the inputDesign . The latter should be generated using SobolIndicesExperiment (see example below). Otherwise, results will be worthless.

Examples

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)
>>> # Define designs to pre-compute
>>> size = 10000
>>> inputDesign = ot.SobolIndicesExperiment(distribution, size).generate()
>>> outputDesign = model(inputDesign)
>>> # sensitivity analysis algorithm
>>> sensitivityAnalysis = ot.SaltelliSensitivityAlgorithm(inputDesign, outputDesign, size)
>>> print(sensitivityAnalysis.getFirstOrderIndices())
[0.302745,0.460846,0.0066916]
>>> print(sensitivityAnalysis.getTotalOrderIndices())
[0.574996,0.427126,0.256689]


Methods

 Draw the correlation coefficients. Draw the importance factors. DrawSobolIndices(*args) Draw the Sobol' indices. draw(*args) Draw sensitivity indices. Get the evaluation of aggregated first order Sobol indices. Get the evaluation of aggregated total order Sobol indices. Get the number of bootstrap sampling size. Accessor to the object's name. Get the confidence interval level for confidence intervals. getFirstOrderIndices([marginalIndex]) Get first order Sobol indices. Get the distribution of the aggregated first order Sobol indices. Get interval for the aggregated first order Sobol indices. Accessor to the object's id. Accessor to the object's name. getSecondOrderIndices([marginalIndex]) Get second order Sobol indices. Accessor to the object's shadowed id. getTotalOrderIndices([marginalIndex]) Get total order Sobol indices. Get the distribution of the aggregated total order Sobol indices. Get interval for the aggregated total order Sobol indices. Select asymptotic or bootstrap confidence intervals. Accessor to the object's visibility state. Test if the object is named. 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. setDesign(inputDesign, outputDesign, size) Sample accessor. setName(name) Accessor to the object's name. Accessor to the object's shadowed id. Select asymptotic or bootstrap confidence intervals. setVisibility(visible) Accessor to the object's visibility state.
__init__(*args)
static DrawCorrelationCoefficients(*args)
Draw the correlation coefficients.

As correlation coefficients are considered, values might be positive or negative.

Available usages:

DrawCorrelationCoefficients(correlationCoefficients, title=’Correlation coefficients’)

DrawCorrelationCoefficients(values, names, title=’Correlation coefficients’)

Parameters:
correlationCoefficientsPointWithDescription

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

valuessequence of float

Correlation coefficients.

namessequence of str

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

titlestr

Title of the graph.

Returns:
graphGraph

A graph containing a Cloud and a Text of the correlation coefficients.

static DrawImportanceFactors(*args)

Draw the importance factors.

Available usages:

DrawImportanceFactors(importanceFactors, title=’Importance Factors’)

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

Parameters:
importanceFactorsPointWithDescription

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.

valuessequence of float

Importance factors.

namessequence of str

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

titlestr

Title of the graph.

Returns:
graphGraph

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

static DrawSobolIndices(*args)

Draw the Sobol’ indices.

Parameters:
inputDescriptionsequence of str

Variable names

firstOrderIndicessequence of float

First order indices values

totalOrderIndicessequence of float

Total order indices values

fo_ciInterval, optional

First order indices confidence interval

to_ciInterval, optional

Total order indices confidence interval

Returns:
graphGraph

For each variable, draws first and total indices

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)

Returns:
graphGraph

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:
indicesPoint

Sequence containing aggregated first order Sobol indices.

getAggregatedTotalOrderIndices()

Get the evaluation of aggregated total order Sobol indices.

Returns:
indicesPoint

Sequence containing aggregated total order Sobol indices.

getBootstrapSize()

Get the number of bootstrap sampling size.

Returns:
bootstrapSizeint

Number of bootstrap sampling

getClassName()

Accessor to the object’s name.

Returns:
class_namestr

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

getConfidenceLevel()

Get the confidence interval level for confidence intervals.

Returns:
confidenceLevelfloat

Confidence level for confidence intervals

getFirstOrderIndices(marginalIndex=0)

Get first order Sobol indices.

Parameters:
iint, optional

Index of the output marginal of the function, equal to by default.

Returns:
indicesPoint

Sequence containing first order Sobol indices.

getFirstOrderIndicesDistribution()

Get the distribution of the aggregated first order Sobol indices.

Returns:
distributionDistribution

Distribution for first order Sobol indices for each component.

getFirstOrderIndicesInterval()

Get interval for the aggregated first order Sobol indices.

Returns:
intervalInterval

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:
idint

Internal unique identifier.

getName()

Accessor to the object’s name.

Returns:
namestr

The name of the object.

getSecondOrderIndices(marginalIndex=0)

Get second order Sobol indices.

Parameters:
iint, optional

Index of the marginal of the function, equals to by default.

Returns:
indicesSymmetricMatrix

Tensor containing second order Sobol indices.

Accessor to the object’s shadowed id.

Returns:
idint

Internal unique identifier.

getTotalOrderIndices(marginalIndex=0)

Get total order Sobol indices.

Parameters:
iint, optional

Index of the output marginal of the function, equal to by default.

Returns:
indicesPoint

Sequence containing total order Sobol indices.

getTotalOrderIndicesDistribution()

Get the distribution of the aggregated total order Sobol indices.

Returns:
distributionDistribution

Distribution for total order Sobol indices for each component.

getTotalOrderIndicesInterval()

Get interval for the aggregated total order Sobol indices.

Returns:
intervalInterval

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:
useAsymptoticDistributionbool

Whether to use bootstrap or asymptotic intervals

getVisibility()

Accessor to the object’s visibility state.

Returns:
visiblebool

Visibility flag.

hasName()

Test if the object is named.

Returns:
hasNamebool

True if the name is not empty.

hasVisibleName()

Test if the object has a distinguishable name.

Returns:
hasVisibleNamebool

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:
bootstrapSizeint

Number of bootstrap sampling

setConfidenceLevel(confidenceLevel)

Set the confidence interval level for confidence intervals.

Parameters:
confidenceLevelfloat

Confidence level for confidence intervals

setDesign(inputDesign, outputDesign, size)

Sample accessor.

Allows one to estimate indices from a predefined Sobol design.

Parameters:
inputDesignSample

Design for the evaluation of sensitivity indices, obtained thanks to the SobolIndicesAlgorithmImplementation.Generate method

outputDesignSample

Design for the evaluation of sensitivity indices, obtained as the evaluation of a Function (model) on the previous inputDesign

Nint

Base size of the Sobol design

setName(name)

Accessor to the object’s name.

Parameters:
namestr

The name of the object.

Accessor to the object’s shadowed id.

Parameters:
idint

Internal unique identifier.

setUseAsymptoticDistribution(useAsymptoticDistribution)

Select asymptotic or bootstrap confidence intervals.

Default value is set by the SobolIndicesAlgorithm-DefaultUseAsymptoticDistribution key.

Parameters:
useAsymptoticDistributionbool

Whether to use bootstrap or asymptotic intervals

setVisibility(visible)

Accessor to the object’s visibility state.

Parameters:
visiblebool

Visibility flag.

## Examples using the class¶

Estimate Sobol’ indices for a function with multivariate output

Estimate Sobol' indices for a function with multivariate output

Estimate Sobol’ indices for the Ishigami function by a sampling method: a quick start guide to sensitivity analysis

Estimate Sobol' indices for the Ishigami function by a sampling method: a quick start guide to sensitivity analysis

Example of sensitivity analyses on the wing weight model

Example of sensitivity analyses on the wing weight model