JanonSensitivityAlgorithm¶

class JanonSensitivityAlgorithm(inputDesign, outputDesign, size)¶

Methods

`DrawCorrelationCoefficients`(*args)	Draw the correlation coefficients.
`DrawImportanceFactors`(*args)	Draw the importance factors.
`DrawSobolIndices`(*args)	Draw the Sobol' indices.
`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`()	Returns 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.
`getImplementation`()	Accessor to the underlying implementation.
`getName`()	Accessor to the object's name.
`getSecondOrderIndices`([marginalIndex])	Get second order Sobol indices.
`getTotalOrderIndices`()	Returns 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.
`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.
`setUseAsymptoticDistribution`(...)	Select asymptotic or bootstrap confidence intervals.

__init__(inputDesign, outputDesign, size)¶

Estimates Sobol’ indices with Janon estimator.

This estimator only implements an output dimension equal to 1.

Parameters:

inputDesignot.Sample(size, dimension): The input sample.
outputDesignot.Sample(required_size, dimension): The output sample.
sizeint: The basic size of the sample.

Returns:

None.

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()¶

Returns first order Sobol’ indices.

Returns:

indicesot.Point(dimension): The 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.

getImplementation()¶

Accessor to the underlying implementation.

Returns:

implImplementation: A copy of the underlying implementation object.

getName()¶

Accessor to the object’s name.

Returns:

namestr: The name of the object.

getSecondOrderIndices(marginalIndex=0)¶

Get second order Sobol indices.

Parameters:

marginalIndexint, optional: Index of the output marginal of the function, equals to $0$ by default.

Returns:

indicesSymmetricMatrix: Tensor containing second order Sobol indices.

Notes

Let $n_X \in \Nset$ be the input dimension of the random vector. For any pair of indices $i, j \in \{1, ..., n_x\}$ such that $i \neq j$ , this method computes the Sobol’ interaction index between $i$ and $j$ :

$S_{\{i, j\}} = \frac{V_{\{i,j\}}}{\Var{Y}}$

The second order Sobol’ index $S_{i,j}$ measures the part of the variance of $Y$ explained by the interaction of $X_i$ and $X_j$ . Hence, the closed Sobol’ index of the group $\{i, j\}$ is:

$S_{\{i, j\}}^{\operatorname{cl}} = S_i + S_j + S_{\{i, j\}}.$

Conversely, if the closed Sobol’ index $S_{\{i, j\}}^{\operatorname{cl}}$ is known, then the interaction Sobol’ index can be computed from the equation:

$S_{\{i, j\}} = S_{\{i, j\}}^{\operatorname{cl}} - S_i - S_j.$

getTotalOrderIndices()¶

Returns total order Sobol’ indices.

Returns:

indicesot.Point(dimension): The 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

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.

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

otbenchmark

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JanonSensitivityAlgorithm¶