ProbabilitySimulationResult

class ProbabilitySimulationResult(*args)

Probability simulation result.

Notes

Structure created by the method run() of a EventSimulation, and obtained thanks to the method getResult().

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> limitState = ot.SymbolicFunction(['E', 'F', 'L', 'I'], ['-F*L^3/(3.*E*I)'])
>>> # Enable the history mecanism in order to use the getImportanceFactors method
>>> limitState = ot.MemoizeFunction(limitState)
>>> myDistribution = ot.Normal([50.0, 1.0, 10.0, 5.0], [1.0]*4, ot.IdentityMatrix(4))
>>> output = ot.CompositeRandomVector(limitState, ot.RandomVector(myDistribution))
>>> myEvent = ot.ThresholdEvent(output, ot.Less(), -3.0)
>>> myLHS = ot.LHS(myEvent)
>>> myLHS.run()
>>> SimulationLHSResult = myLHS.getResult()
>>> print(SimulationLHSResult.getImportanceFactors())
[X0 : 0.000722617, X1 : 0.635094, X2 : 0.275692, X3 : 0.0884917]

Methods

drawImportanceFactors(self)

Draw the importance factors.

getBlockSize(self)

Accessor to the block size.

getClassName(self)

Accessor to the object’s name.

getCoefficientOfVariation(self)

Accessor to the coefficient of variation.

getConfidenceLength(self, \*args)

Accessor to the confidence length.

getEvent(self)

Accessor to the event.

getId(self)

Accessor to the object’s id.

getImportanceFactors(self)

Accessor to the importance factors.

getMeanPointInEventDomain(self)

Accessor to the mean point conditioned to the event realization.

getName(self)

Accessor to the object’s name.

getOuterSampling(self)

Accessor to the outer sampling.

getProbabilityDistribution(self)

Accessor to the asymptotic probability distribution.

getProbabilityEstimate(self)

Accessor to the probability estimate.

getShadowedId(self)

Accessor to the object’s shadowed id.

getStandardDeviation(self)

Accessor to the standard deviation.

getVarianceEstimate(self)

Accessor to the variance estimate.

getVisibility(self)

Accessor to the object’s visibility state.

hasName(self)

Test if the object is named.

hasVisibleName(self)

Test if the object has a distinguishable name.

setBlockSize(self, blockSize)

Accessor to the block size.

setEvent(self, event)

Accessor to the event.

setName(self, name)

Accessor to the object’s name.

setOuterSampling(self, outerSampling)

Accessor to the outer sampling.

setProbabilityEstimate(self, probabilityEstimate)

Accessor to the probability estimate.

setShadowedId(self, id)

Accessor to the object’s shadowed id.

setVarianceEstimate(self, varianceEstimate)

Accessor to the variance estimate.

setVisibility(self, visible)

Accessor to the object’s visibility state.
__init__(self, \*args)

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

drawImportanceFactors(self)

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
getBlockSize(self)

Accessor to the block size.

Returns
blockSizeint

Number of terms in the probability simulation estimator grouped together.

getClassName(self)

Accessor to the object’s name.

Returns
class_namestr

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

getCoefficientOfVariation(self)

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(self, \*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(self)

Accessor to the event.

Returns
eventRandomVector

Event we want to evaluate the probability.

getId(self)

Accessor to the object’s id.

Returns
idint

Internal unique identifier.

getImportanceFactors(self)

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 mecanism of the model is activated (see MemoizeFunction).

getMeanPointInEventDomain(self)

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 mecanism of the model is activated (see MemoizeFunction).

getName(self)

Accessor to the object’s name.

Returns
namestr

The name of the object.

getOuterSampling(self)

Accessor to the outer sampling.

Returns
outerSamplingint

Number of groups of terms in the probability simulation estimator.

getProbabilityDistribution(self)

Accessor to the asymptotic probability distribution.

Returns
probaDistributionNormal

Asymptotic normal distribution of the event probability estimate.

getProbabilityEstimate(self)

Accessor to the probability estimate.

Returns
probaEstimatefloat

Estimate of the event probability.

getShadowedId(self)

Accessor to the object’s shadowed id.

Returns
idint

Internal unique identifier.

getStandardDeviation(self)

Accessor to the standard deviation.

Returns
sigmafloat

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

getVarianceEstimate(self)

Accessor to the variance estimate.

Returns
varianceEstimatefloat

Variance estimate.

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.

hasVisibleName(self)

Test if the object has a distinguishable name.

Returns
hasVisibleNamebool

True if the name is not empty and not the default one.

setBlockSize(self, blockSize)

Accessor to the block size.

Parameters
blockSizeint, blockSize \geq 0

Number of terms in the probability simulation estimator grouped together.

setEvent(self, event)

Accessor to the event.

Parameters
eventRandomVector

Event we want to evaluate the probability.

setName(self, name)

Accessor to the object’s name.

Parameters
namestr

The name of the object.

setOuterSampling(self, outerSampling)

Accessor to the outer sampling.

Parameters
outerSamplingint, outerSampling \geq 0

Number of groups of terms in the probability simulation estimator.

setProbabilityEstimate(self, probabilityEstimate)

Accessor to the probability estimate.

Parameters
probaEstimatefloat, 0 \leq P_e \leq 1

Estimate of the event probability.

setShadowedId(self, id)

Accessor to the object’s shadowed id.

Parameters
idint

Internal unique identifier.

setVarianceEstimate(self, varianceEstimate)

Accessor to the variance estimate.

Parameters
varianceEstimatefloat, Var_e \geq 0

Variance estimate.

setVisibility(self, visible)

Accessor to the object’s visibility state.

Parameters
visiblebool

Visibility flag.