SobolSimulationAlgorithm

class SobolSimulationAlgorithm(*args)

Sobol indices computation using iterative sampling.

The algorithm uses sampling of the distribution of the random vector \vect{X} through the model f to iteratively estimate the Sobol indices.

At each iteration a fixed number N = blockSize * (d + 2) of replications inputs is generated. These inputs are evaluated by blocks of size batchSize through the model f. Then the distribution of the indices (first and total order) is computed on this current replication sample. At the end of each iteration we update the global distribution of the indices.

Parameters:
X : Distribution

The random vector to study.

f : Function

The function to study.

estimator : SobolIndicesAlgorithm

The estimator of the indices.

Notes

The algorithm can operate on a multivariate model f, in this case it operates on aggregated indices.

Several estimators are available (Saltelli, Jansen, …).

The algorithms stops when, on all components, first and total order indices haved been estimated with enough precision or the first order indices are separable from the total order indices:

\forall{j}

\Phi^{F}_j(1-\alpha)-\Phi^{F}_j(\alpha) \leq \epsilon \cap \Phi^{T}_j(1-\alpha)-\Phi^{T}_j(\alpha) \leq \epsilon

or

\Phi^{T}_j(\alpha) \ge \Phi^{F}_j(1-\alpha)

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> distribution = ot.ComposedDistribution([ot.Uniform(-1.0, 1.0)] * 3)
>>> model = ot.SymbolicFunction(['x1', 'x2', 'x3'], ['x1*x2+x3'])
>>> estimator = ot.SaltelliSensitivityAlgorithm()
>>> estimator.setUseAsymptoticDistribution(True)
>>> algo = ot.SobolSimulationAlgorithm(distribution, model, estimator)
>>> algo.setMaximumOuterSampling(25) # number of iterations
>>> algo.setBlockSize(100) # size of Sobol experiment at each iteration
>>> algo.setBatchSize(4) # number of points evaluated simultaneously
>>> algo.setIndexQuantileLevel(0.05) # alpha
>>> algo.setIndexQuantileEpsilon(1e-2) # epsilon
>>> algo.run()
>>> result = algo.getResult()
>>> fo = result.getFirstOrderIndicesEstimate()
>>> foDist = result.getFirstOrderIndicesDistribution()

Methods

drawFirstOrderIndexConvergence(*args) Draw the first order Sobol index convergence at a given level.
drawTotalOrderIndexConvergence(*args) Draw the total order Sobol index convergence at a given level.
getBatchSize() Accessor to the batch size.
getBlockSize() Accessor to the block size.
getClassName() Accessor to the object’s name.
getConvergenceStrategy() Accessor to the convergence strategy.
getDistribution() Accessor to the batch size.
getEstimator() Sobol estimator accessor.
getId() Accessor to the object’s id.
getIndexQuantileEpsilon() Accessor to the criterion operator.
getIndexQuantileLevel() Accessor to the quantile level.
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 result.
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.
setBatchSize(replicationSize) Accessor to the batch size.
setBlockSize(blockSize) Accessor to the block size.
setConvergenceStrategy(convergenceStrategy) Accessor to the convergence strategy.
setEstimator(estimator) Sobol estimator accessor.
setIndexQuantileEpsilon(indexQuantileEpsilon) Accessor to the quantile tolerance.
setIndexQuantileLevel(indexQuantileLevel) Accessor to the quantile level.
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.
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)

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

drawFirstOrderIndexConvergence(*args)

Draw the first order Sobol index convergence at a given level.

Parameters:
marginalIndex : int

Index of the random vector component to consider

level : float, optional

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

Returns:
graph : a Graph

expectation convergence graph

drawTotalOrderIndexConvergence(*args)

Draw the total order Sobol index convergence at a given level.

Parameters:
marginalIndex : int

Index of the random vector component to consider

level : float, optional

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

Returns:
graph : a Graph

expectation convergence graph

getBatchSize()

Accessor to the batch size.

Returns:
batchSize : int

Number of points evaluated simultaneously.

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.

getDistribution()

Accessor to the batch size.

Returns:
distibution : Distribution

Distribution of the random variable.

getEstimator()

Sobol estimator accessor.

Returns:
estimator : SobolIndicesAlgorithm

The estimator of the indices.

getId()

Accessor to the object’s id.

Returns:
id : int

Internal unique identifier.

getIndexQuantileEpsilon()

Accessor to the criterion operator.

Returns:
epsilon : float

The quantile tolerance

getIndexQuantileLevel()

Accessor to the quantile level.

Returns:
alpha : float

The quantile level.

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, \sigma > 0

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 result.

Returns:
result : SobolSimulationResult

The simulation result.

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 on 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 > 2^{32} by a combination of blockSize and outerSampling.

setBatchSize(replicationSize)

Accessor to the batch size.

Parameters:
batchSize : int

Number of points evaluated simultaneously.

setBlockSize(blockSize)

Accessor to the block size.

Parameters:
blockSize : int, blockSize \geq 1

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.

setEstimator(estimator)

Sobol estimator accessor.

Parameters:
estimator : SobolIndicesAlgorithm

The estimator of the indices.

setIndexQuantileEpsilon(indexQuantileEpsilon)

Accessor to the quantile tolerance.

Parameters:
epsilon : float

The quantile tolerance

setIndexQuantileLevel(indexQuantileLevel)

Accessor to the quantile level.

Parameters:
alpha : float

The quantile level.

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, \sigma > 0

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.

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.