OpenTURNS

An Open source initiative for the Treatment of Uncertainties, Risks'N Statistics

CrossEntropyResult¶

class CrossEntropyResult(*args)¶

Cross Entropy result.

Methods

`drawImportanceFactors`()	Draw the importance factors.
`getAuxiliaryDistribution`()	Accessor to the auxiliary distribution at the final Cross Entropy algorithm step.
`getAuxiliaryInputSample`()	Accessor to the auxiliary distribution input sample at the final Cross Entropy algorithm step.
`getAuxiliaryOutputSample`()	Accessor to the auxiliary distribution output sample at the final Cross Entropy algorithm step.
`getBlockSize`()	Accessor to the block size.
`getClassName`()	Accessor to the object's name.
`getCoefficientOfVariation`()	Accessor to the coefficient of variation.
`getConfidenceLength`(*args)	Accessor to the confidence length.
`getEvent`()	Accessor to the event.
`getImportanceFactors`()	Accessor to the importance factors.
`getMeanPointInEventDomain`()	Accessor to the mean point conditioned to the event realization.
`getName`()	Accessor to the object's name.
`getOuterSampling`()	Accessor to the outer sampling.
`getProbabilityDistribution`()	Accessor to the asymptotic probability distribution.
`getProbabilityEstimate`()	Accessor to the probability estimate.
`getStandardDeviation`()	Accessor to the standard deviation.
`getTimeDuration`()	Accessor to the elapsed time.
`getVarianceEstimate`()	Accessor to the variance estimate.
`hasName`()	Test if the object is named.
`setAuxiliaryDistribution`(auxiliaryDistribution)	Accessor to the auxiliary distribution at the final Cross Entropy algorithm step.
`setAuxiliaryInputSample`(auxiliaryInputSample)	Accessor to the auxiliary distribution input sample at the final Cross Entropy algorithm step.
`setAuxiliaryOutputSample`(auxiliaryInputSample)	Accessor to the auxiliary distribution output sample at the final Cross Entropy algorithm step.
`setBlockSize`(blockSize)	Accessor to the block size.
`setEvent`(event)	Accessor to the event.
`setName`(name)	Accessor to the object's name.
`setOuterSampling`(outerSampling)	Accessor to the outer sampling.
`setProbabilityEstimate`(probabilityEstimate)	Accessor to the probability estimate.
`setTimeDuration`(time)	Accessor to the elapsed time.
`setVarianceEstimate`(varianceEstimate)	Accessor to the variance estimate.

See also

CrossEntropyImportanceSampling, PhysicalSpaceCrossEntropyImportanceSampling, StandardSpaceCrossEntropyImportanceSampling

__init__(*args)¶

drawImportanceFactors()¶

Draw the importance factors.

Warning

It is necessary to enable the history of the model to perform this analysis (see MemoizeFunction).

Returns:

graphGraph: Importance factor graph.

See also

getImportanceFactors

getAuxiliaryDistribution()¶

Accessor to the auxiliary distribution at the final Cross Entropy algorithm step.

Returns:

auxiliaryDistributionDistribution: Auxiliary distribution at the final Cross Entropy algorithm step.

getAuxiliaryInputSample()¶

Accessor to the auxiliary distribution input sample at the final Cross Entropy algorithm step.

Returns:

auxiliaryInputSampleSample: Auxiliary distribution input sample at the final Cross Entropy algorithm step.

getAuxiliaryOutputSample()¶

Accessor to the auxiliary distribution output sample at the final Cross Entropy algorithm step.

Returns:

auxiliaryOutputSampleSample: Auxiliary distribution output sample at the final Cross Entropy algorithm step.

getBlockSize()¶

Accessor to the block size.

Returns:

blockSizeint: Number of terms in the probability simulation estimator grouped together.

getClassName()¶

Accessor to the object’s name.

Returns:

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

getCoefficientOfVariation()¶

Accessor to the coefficient of variation.

Returns:

coefficientfloat: Coefficient of variation of the simulated sample which is equal to $\sqrt{Var_e} / P_e$ with $Var_e$ the variance estimate and $P_e$ the probability estimate.

getConfidenceLength(*args)¶

Accessor to the confidence length.

Parameters:

levelfloat, $level \in ]0, 1[$: Confidence level. By default, it is $0.95$ .

Returns:

confidenceLengthfloat: Length of the confidence interval at the confidence level level.

getEvent()¶

Accessor to the event.

Returns:

eventRandomVector: Event we want to evaluate the probability.

getImportanceFactors()¶

Accessor to the importance factors.

Returns:

importanceFactorsPointWithDescription: Sequence containing the importance factors with a description for each component.

See also

drawImportanceFactors

Notes

The importance factors $\alpha_i$ are evaluated from the coordinates of the mean point of event domain $\vect{X}^*_{event}$ , mapped into the standard space as follows:

$\alpha_i = \displaystyle \frac{\left(U_{i}^*\right)^2}{||\vect{U}^*||^2}$

where $\vect{U}^* = T(\vect{X}^*_{event})$ with $T$ the iso-probabilistic transformation and the mean point $\vect{X}^*_{event} = \displaystyle \frac{1}{n} \sum_{i=1}^{n} \vect{X}_i 1_{event}(\vect{X}_i)$ .

Warning

This notion is only available if the history mechanism of the model is activated (see MemoizeFunction).

getMeanPointInEventDomain()¶

Accessor to the mean point conditioned to the event realization.

Returns:

meanPointPoint: Mean point in the physical space of all the simulations generated by the EventSimulation algorithm that failed into the event domain.

Notes

Warning

This notion is only available if the history mechanism of the model is activated (see MemoizeFunction).

getName()¶

Accessor to the object’s name.

Returns:

namestr: The name of the object.

getOuterSampling()¶

Accessor to the outer sampling.

Returns:

outerSamplingint: Number of groups of terms in the probability simulation estimator.

getProbabilityDistribution()¶

Accessor to the asymptotic probability distribution.

Returns:

probaDistributionNormal: Asymptotic normal distribution of the event probability estimate.

getProbabilityEstimate()¶

Accessor to the probability estimate.

Returns:

probaEstimatefloat: Estimate of the event probability.

getStandardDeviation()¶

Accessor to the standard deviation.

Returns:

sigmafloat: Standard deviation of the estimator at the end of the simulation.

getTimeDuration()¶

Accessor to the elapsed time.

Returns:

timefloat: Simulation duration in seconds

getVarianceEstimate()¶

Accessor to the variance estimate.

Returns:

varianceEstimatefloat: Variance estimate.

hasName()¶

Test if the object is named.

Returns:

hasNamebool: True if the name is not empty.

setAuxiliaryDistribution(auxiliaryDistribution)¶

Accessor to the auxiliary distribution at the final Cross Entropy algorithm step.

Parameters:

auxiliaryDistributionDistribution: Auxiliary distribution at the final Cross Entropy algorithm step.

setAuxiliaryInputSample(auxiliaryInputSample)¶

Accessor to the auxiliary distribution input sample at the final Cross Entropy algorithm step.

Parameters:

auxiliaryInputSampleSample: Auxiliary distribution input sample at the final Cross Entropy algorithm step.

setAuxiliaryOutputSample(auxiliaryInputSample)¶

Accessor to the auxiliary distribution output sample at the final Cross Entropy algorithm step.

Parameters:

auxiliaryOutputSampleSample: Auxiliary distribution output sample at the final Cross Entropy algorithm step.

setBlockSize(blockSize)¶

Accessor to the block size.

Parameters:

blockSizeint, $blockSize \geq 0$: Number of terms in the probability simulation estimator grouped together.

setEvent(event)¶

Accessor to the event.

Parameters:

eventRandomVector: Event we want to evaluate the probability.

setName(name)¶

Accessor to the object’s name.

Parameters:

namestr: The name of the object.

setOuterSampling(outerSampling)¶

Accessor to the outer sampling.

Parameters:

outerSamplingint, $outerSampling \geq 0$: Number of groups of terms in the probability simulation estimator.

setProbabilityEstimate(probabilityEstimate)¶

Accessor to the probability estimate.

Parameters:

probaEstimatefloat, $0 \leq P_e \leq 1$: Estimate of the event probability.

setTimeDuration(time)¶

Accessor to the elapsed time.

Parameters:

timefloat: Simulation duration in seconds

setVarianceEstimate(varianceEstimate)¶

Accessor to the variance estimate.

Parameters:

varianceEstimatefloat, $Var_e \geq 0$: Variance estimate.

Examples using the class¶

Cross Entropy Importance Sampling

Cross Entropy Importance Sampling