DirectionalSampling¶

class
DirectionalSampling
(*args)¶ Directional simulation.
 Available constructors:
DirectionalSampling(event=ot.Event())
DirectionalSampling(event, rootStrategy, samplingStrategy)
Parameters: event :
Event
Event we are computing the probability of.
rootStrategy :
RootStrategy
Strategy adopted to evaluate the intersections of each direction with the limit state function and take into account the contribution of the direction to the event probability. By default, rootStrategy = ot.RootStrategy(ot.SafeAndSlow()).
samplingStrategy :
SamplingStrategy
Strategy adopted to sample directions. By default, samplingStrategy=ot.SamplingStrategy(ot.RandomDirection()).
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.
The directional simulation method is an accelerated sampling method. It implies a preliminary isoprobabilistic transformation, as for
FORM
andSORM
methods; however, it remains based on sampling and is thus not an approximation method. In the transformed space, the (transformed) uncertain variables are independent standard gaussian variables (mean equal to zero and standard deviation equal to 1).Roughly speaking, each simulation of the directional simulation algorithm is made of three steps. For the iteration, these steps are the following:
 Let . A point is drawn randomly on according to an uniform distribution.
 In the direction starting from the origin and passing through , solutions of the equation (i.e. limits of ) are searched. The set of values of that belong to is deduced for these solutions: it is a subset .
 Then, one calculates the probability . By property of independent standard variable, is a random variable distributed according to a chisquare distribution, which makes the computation effortless.
Finally, the estimate of the probability after simulations is the following:
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.RandomVector(myFunction, vect) >>> # We create an Event from this RandomVector >>> myEvent = ot.Event(output, ot.Less(), 3.0) >>> # We create a DirectionalSampling algorithm >>> myAlgo = ot.DirectionalSampling(myEvent, ot.MediumSafe(), ot.OrthogonalDirection()) >>> myAlgo.setMaximumOuterSampling(150) >>> myAlgo.setBlockSize(4) >>> myAlgo.setMaximumCoefficientOfVariation(0.1) >>> # Perform the simulation >>> myAlgo.run() >>> print('Probability estimate=%.6f' % myAlgo.getResult().getProbabilityEstimate()) Probability estimate=0.169716
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. getId
()Accessor to the object’s id. getMaximumCoefficientOfVariation
()Accessor to the maximum coefficient of variation. getMaximumOuterSampling
()Accessor to the maximum sample size. getMaximumStandardDeviation
()Accessor to the maximum standard deviation. getName
()Accessor to the object’s name. getResult
()Accessor to the results. getRootStrategy
()Get the root strategy. getSamplingStrategy
()Get the direction sampling strategy. getShadowedId
()Accessor to the object’s shadowed id. getVerbose
()Accessor to verbosity. getVisibility
()Accessor to the object’s visibility state. hasName
()Test if the object is named. hasVisibleName
()Test if the object has a distinguishable name. run
()Launch simulation. setBlockSize
(blockSize)Accessor to the block size. setConvergenceStrategy
(convergenceStrategy)Accessor to the convergence strategy. setMaximumCoefficientOfVariation
(…)Accessor to the maximum coefficient of variation. setMaximumOuterSampling
(maximumOuterSampling)Accessor to the maximum sample size. setMaximumStandardDeviation
(…)Accessor to the maximum standard deviation. setName
(name)Accessor to the object’s name. setProgressCallback
(*args)Set up a progress callback. setRootStrategy
(rootStrategy)Set the root strategy. setSamplingStrategy
(samplingStrategy)Set the direction sampling strategy. setShadowedId
(id)Accessor to the object’s shadowed id. setStopCallback
(*args)Set up a stop callback. setVerbose
(verbose)Accessor to verbosity. setVisibility
(visible)Accessor to the object’s visibility state. 
__init__
(*args)¶

drawProbabilityConvergence
(*args)¶ Draw the probability convergence at a given level.
Parameters: level : float, optional
The probability convergence is drawn at this given confidence length level. By default level is 0.95.
Returns: graph : a
Graph
probability convergence graph

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

getClassName
()¶ Accessor to the object’s name.
Returns: class_name : str
The object class name (object.__class__.__name__).

getConvergenceStrategy
()¶ 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.

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

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

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

getMaximumStandardDeviation
()¶ Accessor to the maximum standard deviation.
Returns: sigma : float,
Maximum standard deviation of the estimator.

getName
()¶ Accessor to the object’s name.
Returns: name : str
The name of the object.

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

getRootStrategy
()¶ Get the root strategy.
Returns: strategy :
RootStrategy
Root strategy adopted.

getSamplingStrategy
()¶ Get the direction sampling strategy.
Returns: strategy :
SamplingStrategy
Direction sampling strategy adopted.

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

getVerbose
()¶ Accessor to verbosity.
Returns: verbosity_enabled : bool
If True, the computation is verbose. By default it is verbose.

getVisibility
()¶ Accessor to the object’s visibility state.
Returns: visible : bool
Visibility flag.

hasName
()¶ Test if the object is named.
Returns: hasName : bool
True if the name is not empty.

hasVisibleName
()¶ Test if the object has a distinguishable name.
Returns: hasVisibleName : bool
True if the name is not empty and not the default one.

run
()¶ 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
(blockSize)¶ Accessor to the block size.
Parameters: blockSize : int,
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
(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.

setMaximumCoefficientOfVariation
(maximumCoefficientOfVariation)¶ Accessor to the maximum coefficient of variation.
Parameters: coefficient : float
Maximum coefficient of variation of the simulated sample.

setMaximumOuterSampling
(maximumOuterSampling)¶ Accessor to the maximum sample size.
Parameters: outerSampling : int
Maximum number of groups of terms in the probability simulation estimator.

setMaximumStandardDeviation
(maximumStandardDeviation)¶ Accessor to the maximum standard deviation.
Parameters: sigma : float,
Maximum standard deviation of the estimator.

setName
(name)¶ Accessor to the object’s name.
Parameters: name : str
The name of the object.

setProgressCallback
(*args)¶ Set up a progress callback.
Parameters: callback : callable
Takes a float as argument as percentage of progress.

setRootStrategy
(rootStrategy)¶ Set the root strategy.
Parameters: strategy :
RootStrategy
Root strategy adopted.

setSamplingStrategy
(samplingStrategy)¶ Set the direction sampling strategy.
Parameters: strategy :
SamplingStrategy
Direction sampling strategy adopted.

setShadowedId
(id)¶ Accessor to the object’s shadowed id.
Parameters: id : int
Internal unique identifier.

setStopCallback
(*args)¶ Set up a stop callback.
Parameters: callback : callable
Returns an int deciding whether to stop or continue.

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

setVisibility
(visible)¶ Accessor to the object’s visibility state.
Parameters: visible : bool
Visibility flag.