CrossEntropyImportanceSampling

class CrossEntropyImportanceSampling(*args)

Cross-Entropy Importance Sampling algorithm.

Methods

drawProbabilityConvergence(*args)	Draw the probability convergence at a given level.
getBlockSize()	Accessor to the block size.
getClassName()	Accessor to the object's name.
getConvergenceStrategy()	Accessor to the convergence strategy.
getEvent()	Accessor to the event.
getInputSample(*args)	Input sample accessor.
getMaximumCoefficientOfVariation()	Accessor to the maximum coefficient of variation.
getMaximumOuterSampling()	Accessor to the maximum iterations number.
getMaximumStandardDeviation()	Accessor to the maximum standard deviation.
getMaximumTimeDuration()	Accessor to the maximum duration.
getName()	Accessor to the object's name.
getOutputSample(*args)	Output sample accessor.
getQuantileLevel()	Accessor to the intermediate quantile level.
getResult()	Accessor to the intermediate quantile level.
getStepsNumber()	Subset steps number accessor.
getThresholdPerStep()	Threshold accessor.
hasName()	Test if the object is named.
run()	Launch simulation.
setBlockSize(blockSize)	Accessor to the block size.
setConvergenceStrategy(convergenceStrategy)	Accessor to the convergence strategy.
setKeepSample(keepSample)	Sample storage accessor.
setMaximumCoefficientOfVariation(...)	Accessor to the maximum coefficient of variation.
setMaximumOuterSampling(maximumOuterSampling)	Accessor to the maximum iterations number.
setMaximumStandardDeviation(...)	Accessor to the maximum standard deviation.
setMaximumTimeDuration(maximumTimeDuration)	Accessor to the maximum duration.
setName(name)	Accessor to the object's name.
setProgressCallback(*args)	Set up a progress callback.
setQuantileLevel(quantileLevel)	Accessor to the intermediate quantile level.
setStopCallback(*args)	Set up a stop callback.

See also

StandardSpaceCrossEntropyImportanceSampling, PhysicalSpaceCrossEntropyImportanceSampling, CrossEntropyResult

Notes

This class inherits from EventSimulation.

The principle is to perform a simulation study to evaluate the threshold exceedance probability according to an importance density obtained using Cross Entropy algorithm.

A CrossEntropyImportanceSampling object can be created only through its derivative classes, StandardSpaceCrossEntropyImportanceSampling or PhysicalSpaceCrossEntropyImportanceSampling.

__init__(*args)

drawProbabilityConvergence(*args)

Draw the probability convergence at a given level.

Parameters:

levelfloat, optional

The probability convergence is drawn at this given confidence length level. By default level is 0.95.

Returns:

grapha Graph

probability convergence graph

getBlockSize()

Accessor to the block size.

Returns:

blockSizeint

Number of simultaneous evaluations of the limit-state function. It is set by default to 1.

getClassName()

Accessor to the object’s name.

Returns:

class_namestr

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

getConvergenceStrategy()

Accessor to the convergence strategy.

Returns:

storage_strategyHistoryStrategy

Storage strategy used to store the values of the probability estimator and its variance during the simulation algorithm.

getEvent()

Accessor to the event.

Returns:

eventRandomVector

Event we want to evaluate the probability.

getInputSample(*args)

Input sample accessor.

Parameters:

stepint

Iteration index

selectint, optional

Selection flag:

• EVENT0 : points not realizing the event are selected

• EVENT1 : points realizing the event are selected

• BOTH : all points are selected (default)

Returns:

inputSampleSample

Input sample.

getMaximumCoefficientOfVariation()

Accessor to the maximum coefficient of variation.

Returns:

coefficientfloat

Maximum coefficient of variation of the simulated sample.

getMaximumOuterSampling()

Accessor to the maximum iterations number.

Returns:

outerSamplingint

Maximum number of iterations, each iteration performing a block of evaluations.

getMaximumStandardDeviation()

Accessor to the maximum standard deviation.

Returns:

sigmafloat,

Maximum standard deviation of the estimator.

getMaximumTimeDuration()

Accessor to the maximum duration.

Returns:

maximumTimeDurationfloat

Maximum optimization duration in seconds.

getName()

Accessor to the object’s name.

Returns:

namestr

The name of the object.

getOutputSample(*args)

Output sample accessor.

Parameters:

stepint

Iteration index

selectint, optional

Selection flag:

• EVENT0 : points not realizing the event are selected

• EVENT1 : points realizing the event are selected

• BOTH : all points are selected (default)

Returns:

outputSampleSample

Output sample.

getQuantileLevel()

Accessor to the intermediate quantile level.

Returns:

quantileLevelfloat

Result of Cross Entropy algorithm.

getResult()

Accessor to the intermediate quantile level.

Returns:

CrossEntropyResultCrossEntropyResult

Contains all the results of the Cross Entropy algorithm simulation.

getStepsNumber()

Subset steps number accessor.

Returns:

nint

Number of subset steps, including the initial Monte Carlo sampling.

getThresholdPerStep()

Threshold accessor.

Returns:

thresholdPoint

Threshold values at each step.

hasName()

Test if the object is named.

Returns:

hasNamebool

True if the name is not empty.

run()

Launch simulation.

See also

openturns.EventSimulation.setBlockSize

openturns.EventSimulation.setMaximumOuterSampling

openturns.ResourceMap

openturns.SimulationResult

Notes

It launches the simulation and creates a SimulationResult, structure containing all the results obtained after simulation. It computes the probability of occurrence of the given event by computing the empirical mean of a sample of size at most outerSampling * blockSize, this sample being built by blocks of size blockSize. It allows one to use efficiently the distribution of the computation as well as it allows one to deal with a sample size by a combination of blockSize and outerSampling.

setBlockSize(blockSize)

Accessor to the block size.

Parameters:

blockSizeint,

Number of simultaneous evaluations of the limit-state function. It is set by default to 1.

Notes

If the function supports batch evaluations this parameter can be set to the number of available CPUs to benefit from parallel execution (multithreading, multiprocessing, …); except for the Directional Sampling, where we recommend to set it to 1. It also decides the frequency of the stopping criteria and progress callbacks update as they are called once the whole block of fonction evaluations is completed.

setConvergenceStrategy(convergenceStrategy)

Accessor to the convergence strategy.

Parameters:

storage_strategyHistoryStrategy

Storage strategy used to store the values of the probability estimator and its variance during the simulation algorithm.

setKeepSample(keepSample)

Sample storage accessor.

Parameters:

keepsamplebool

Whether to keep the working samples at each iteration.

setMaximumCoefficientOfVariation(maximumCoefficientOfVariation)

Accessor to the maximum coefficient of variation.

Parameters:

coefficientfloat

Maximum coefficient of variation of the simulated sample.

setMaximumOuterSampling(maximumOuterSampling)

Accessor to the maximum iterations number.

Parameters:

outerSamplingint

Maximum number of iterations, each iteration performing a block of evaluations.

setMaximumStandardDeviation(maximumStandardDeviation)

Accessor to the maximum standard deviation.

Parameters:

sigmafloat,

Maximum standard deviation of the estimator.

setMaximumTimeDuration(maximumTimeDuration)

Accessor to the maximum duration.

Parameters:

maximumTimeDurationfloat

Maximum optimization duration in seconds.

setName(name)

Accessor to the object’s name.

Parameters:

namestr

The name of the object.

setProgressCallback(*args)

Set up a progress callback.

Can be used to programmatically report the progress of a simulation.

Parameters:

callbackcallable

Takes a float as argument as percentage of progress.

Examples

>>> import sys
>>> import openturns as ot
>>> experiment = ot.MonteCarloExperiment()
>>> X = ot.RandomVector(ot.Normal())
>>> Y = ot.CompositeRandomVector(ot.SymbolicFunction(['X'], ['1.1*X']), X)
>>> event = ot.ThresholdEvent(Y, ot.Less(), -2.0)
>>> algo = ot.ProbabilitySimulationAlgorithm(event, experiment)
>>> algo.setMaximumOuterSampling(100)
>>> algo.setMaximumCoefficientOfVariation(-1.0)
>>> def report_progress(progress):
...     sys.stderr.write('-- progress=' + str(progress) + '%\n')
>>> algo.setProgressCallback(report_progress)
>>> algo.run()

setQuantileLevel(quantileLevel)

Accessor to the intermediate quantile level.

Parameters:

quantileLevelfloat

Intermediate quantile level, must belong to the interval (0,1).

setStopCallback(*args)

Set up a stop callback.

Can be used to programmatically stop a simulation.

Parameters:

callbackcallable

Returns an int deciding whether to stop or continue.

Examples

Stop a Monte Carlo simulation algorithm using a time limit

>>> import openturns as ot
>>> experiment = ot.MonteCarloExperiment()
>>> X = ot.RandomVector(ot.Normal())
>>> Y = ot.CompositeRandomVector(ot.SymbolicFunction(['X'], ['1.1*X']), X)
>>> event = ot.ThresholdEvent(Y, ot.Less(), -2.0)
>>> algo = ot.ProbabilitySimulationAlgorithm(event, experiment)
>>> algo.setMaximumOuterSampling(10000000)
>>> algo.setMaximumCoefficientOfVariation(-1.0)
>>> algo.setMaximumTimeDuration(0.1)
>>> algo.run()

Examples using the class

Cross Entropy Importance Sampling

Cross Entropy Importance Sampling