LHS¶

class
LHS
(*args)¶ Latin Hypercube Sampling (LHS) method.
 Available constructors:
LHS(event=ot.Event())
 Parameters
 event
RandomVector
Event we are computing the probability of.
 event
Notes
Using the probability distribution of a random vector , we seek to evaluate the following probability:
Here, is a random vector, a deterministic vector, the function known as limit state function which enables the definition of the event . describes the indicator function equal to 1 if and equal to 0 otherwise.
LHS or Latin Hypercube Sampling is a sampling method enabling to better cover the domain of variations of the input variables, thanks to a stratified sampling strategy. This method is applicable in the case of independent input variables. The sampling procedure is based on dividing the range of each variable into several intervals of equal probability. The sampling is undertaken as follows:
Step 1: The range of each input variable is stratified into isoprobabilistic cells,
Step 2: A cell is uniformly chosen among all the available cells,
Step 3: The random number is obtained by inverting the Cumulative Density Function locally in the chosen cell,
Step 4: All the cells having a common strate with the previous cell are put apart from the list of available cells.
The estimator of the probability of failure with LHS is given by:
where the sample of is obtained as described previously.
Examples
>>> import openturns as ot >>> ot.RandomGenerator.SetSeed(0) >>> myFunction = ot.SymbolicFunction(['E', 'F', 'L', 'I'], ['F*L^3/(3*E*I)']) >>> myDistribution = ot.Normal([50.0, 1.0, 10.0, 5.0], [1.0]*4, ot.IdentityMatrix(4)) >>> # We create a 'usual' RandomVector from the Distribution >>> vect = ot.RandomVector(myDistribution) >>> # We create a composite random vector >>> output = ot.CompositeRandomVector(myFunction, vect) >>> # We create an Event from this RandomVector >>> myEvent = ot.ThresholdEvent(output, ot.Less(), 3.0) >>> # We create a LHS algorithm >>> myAlgo = ot.LHS(myEvent) >>> myAlgo.setMaximumOuterSampling(150) >>> myAlgo.setBlockSize(4) >>> myAlgo.setMaximumCoefficientOfVariation(0.1) >>> # Perform the simulation >>> myAlgo.run() >>> print('Probability estimate=%.6f' % myAlgo.getResult().getProbabilityEstimate()) Probability estimate=0.151667
Methods
drawProbabilityConvergence
(self, \*args)Draw the probability convergence at a given level.
getBlockSize
(self)Accessor to the block size.
getClassName
(self)Accessor to the object’s name.
getConvergenceStrategy
(self)Accessor to the convergence strategy.
getEvent
(self)Accessor to the event.
getId
(self)Accessor to the object’s id.
Accessor to the maximum coefficient of variation.
getMaximumOuterSampling
(self)Accessor to the maximum sample size.
Accessor to the maximum standard deviation.
getName
(self)Accessor to the object’s name.
getResult
(self)Accessor to the results.
getShadowedId
(self)Accessor to the object’s shadowed id.
getVerbose
(self)Accessor to verbosity.
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.
run
(self)Launch simulation.
setBlockSize
(self, blockSize)Accessor to the block size.
setConvergenceStrategy
(self, convergenceStrategy)Accessor to the convergence strategy.
setMaximumCoefficientOfVariation
(self, …)Accessor to the maximum coefficient of variation.
setMaximumOuterSampling
(self, …)Accessor to the maximum sample size.
setMaximumStandardDeviation
(self, …)Accessor to the maximum standard deviation.
setName
(self, name)Accessor to the object’s name.
setProgressCallback
(self, \*args)Set up a progress callback.
setShadowedId
(self, id)Accessor to the object’s shadowed id.
setStopCallback
(self, \*args)Set up a stop callback.
setVerbose
(self, verbose)Accessor to verbosity.
setVisibility
(self, visible)Accessor to the object’s visibility state.

__init__
(self, *args)¶ Initialize self. See help(type(self)) for accurate signature.

drawProbabilityConvergence
(self, *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
 grapha

getBlockSize
(self)¶ Accessor to the block size.
 Returns
 blockSizeint
Number of terms in the probability simulation estimator grouped together. It is set by default to 1.

getClassName
(self)¶ Accessor to the object’s name.
 Returns
 class_namestr
The object class name (object.__class__.__name__).

getConvergenceStrategy
(self)¶ Accessor to the convergence strategy.
 Returns
 storage_strategy
HistoryStrategy
Storage strategy used to store the values of the probability estimator and its variance during the simulation algorithm.
 storage_strategy

getEvent
(self)¶ Accessor to the event.
 Returns
 event
RandomVector
Event we want to evaluate the probability.
 event

getId
(self)¶ Accessor to the object’s id.
 Returns
 idint
Internal unique identifier.

getMaximumCoefficientOfVariation
(self)¶ Accessor to the maximum coefficient of variation.
 Returns
 coefficientfloat
Maximum coefficient of variation of the simulated sample.

getMaximumOuterSampling
(self)¶ Accessor to the maximum sample size.
 Returns
 outerSamplingint
Maximum number of groups of terms in the probability simulation estimator.

getMaximumStandardDeviation
(self)¶ Accessor to the maximum standard deviation.
 Returns
 sigmafloat,
Maximum standard deviation of the estimator.

getName
(self)¶ Accessor to the object’s name.
 Returns
 namestr
The name of the object.

getResult
(self)¶ Accessor to the results.
 Returns
 results
SimulationResult
Structure containing all the results obtained after simulation and created by the method
run()
.
 results

getShadowedId
(self)¶ Accessor to the object’s shadowed id.
 Returns
 idint
Internal unique identifier.

getVerbose
(self)¶ Accessor to verbosity.
 Returns
 verbosity_enabledbool
If True, the computation is verbose. By default it is verbose.

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.

run
(self)¶ Launch simulation.
Notes
It launches the simulation and creates a
SimulationResult
, structure containing all the results obtained after simulation. It computes the probability of occurence 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 to use efficiently the distribution of the computation as well as it allows to deal with a sample size by a combination of blockSize and outerSampling.

setBlockSize
(self, blockSize)¶ Accessor to the block size.
 Parameters
 blockSizeint,
Number of terms in the probability simulation estimator grouped together. It is set by default to 1.
Notes
For Monte Carlo, LHS and Importance Sampling methods, this allows to save space while allowing multithreading, when available we recommend to use the number of available CPUs; for the Directional Sampling, we recommend to set it to 1.

setConvergenceStrategy
(self, convergenceStrategy)¶ Accessor to the convergence strategy.
 Parameters
 storage_strategy
HistoryStrategy
Storage strategy used to store the values of the probability estimator and its variance during the simulation algorithm.
 storage_strategy

setMaximumCoefficientOfVariation
(self, maximumCoefficientOfVariation)¶ Accessor to the maximum coefficient of variation.
 Parameters
 coefficientfloat
Maximum coefficient of variation of the simulated sample.

setMaximumOuterSampling
(self, maximumOuterSampling)¶ Accessor to the maximum sample size.
 Parameters
 outerSamplingint
Maximum number of groups of terms in the probability simulation estimator.

setMaximumStandardDeviation
(self, maximumStandardDeviation)¶ Accessor to the maximum standard deviation.
 Parameters
 sigmafloat,
Maximum standard deviation of the estimator.

setName
(self, name)¶ Accessor to the object’s name.
 Parameters
 namestr
The name of the object.

setProgressCallback
(self, *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()

setShadowedId
(self, id)¶ Accessor to the object’s shadowed id.
 Parameters
 idint
Internal unique identifier.

setStopCallback
(self, *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) >>> timer = ot.TimerCallback(0.1) >>> algo.setStopCallback(timer) >>> algo.run()

setVerbose
(self, verbose)¶ Accessor to verbosity.
 Parameters
 verbosity_enabledbool
If True, make the computation verbose. By default it is verbose.

setVisibility
(self, visible)¶ Accessor to the object’s visibility state.
 Parameters
 visiblebool
Visibility flag.