LowDiscrepancyExperiment¶
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class
LowDiscrepancyExperiment
(*args)¶ LowDiscrepancy experiment.
 Available constructors:
LowDiscrepancyExperiment(size, restart)
LowDiscrepancyExperiment(sequence, size, restart)
LowDiscrepancyExperiment(sequence, distribution, size, restart)
 Parameters
 sizepositive int
Number of points of the sequence.
 sequence
LowDiscrepancySequence
Sequence of points with low discrepancy. If not specified, the sequence is a
SobolSequence
. distribution
Distribution
Distribution of dimension . The low discrepancy sequence is uniformly distributed over . We use an isoprobabilistic transformation from the independent copula of dimension to the given distribution. The weights are all equal to .
 restartbool
Flag to tell if the low discrepancy sequence must be restarted from its initial state at each change of distribution or not. Default is True: the sequence is restarted at each change of distribution.
See also
Notes
The
generate()
method generates points according to the distribution . When thegenerate()
method is called again, the generated sample changes. In case of dependent marginals, the approach based on [cambou2017] is used.Examples
>>> import openturns as ot >>> distribution = ot.ComposedDistribution([ot.Uniform(0.0, 1.0)] * 2)
Generate the sample with a reinitialization of the sequence at each change of distribution:
>>> experiment = ot.LowDiscrepancyExperiment(ot.SobolSequence(), distribution, 5, True) >>> print(experiment.generate()) [ y0 y1 ] 0 : [ 0.5 0.5 ] 1 : [ 0.75 0.25 ] 2 : [ 0.25 0.75 ] 3 : [ 0.375 0.375 ] 4 : [ 0.875 0.875 ] >>> print(experiment.generate()) [ y0 y1 ] 0 : [ 0.625 0.125 ] 1 : [ 0.125 0.625 ] 2 : [ 0.1875 0.3125 ] 3 : [ 0.6875 0.8125 ] 4 : [ 0.9375 0.0625 ] >>> experiment.setDistribution(distribution) >>> print(experiment.generate()) [ y0 y1 ] 0 : [ 0.5 0.5 ] 1 : [ 0.75 0.25 ] 2 : [ 0.25 0.75 ] 3 : [ 0.375 0.375 ] 4 : [ 0.875 0.875 ]
Generate the sample keeping the previous state of the sequence at each change of distribution:
>>> experiment = ot.LowDiscrepancyExperiment(ot.SobolSequence(), distribution, 5, False) >>> print(experiment.generate()) [ y0 y1 ] 0 : [ 0.5 0.5 ] 1 : [ 0.75 0.25 ] 2 : [ 0.25 0.75 ] 3 : [ 0.375 0.375 ] 4 : [ 0.875 0.875 ] >>> print(experiment.generate()) [ y0 y1 ] 0 : [ 0.625 0.125 ] 1 : [ 0.125 0.625 ] 2 : [ 0.1875 0.3125 ] 3 : [ 0.6875 0.8125 ] 4 : [ 0.9375 0.0625 ] >>> experiment.setDistribution(distribution) >>> print(experiment.generate()) [ y0 y1 ] 0 : [ 0.4375 0.5625 ] 1 : [ 0.3125 0.1875 ] 2 : [ 0.8125 0.6875 ] 3 : [ 0.5625 0.4375 ] 4 : [ 0.0625 0.9375 ]
Generate a sample according to a distribution with dependent marginals:
>>> distribution = ot.Normal([0.0]*2, ot.CovarianceMatrix(2, [4.0, 1.0, 1.0, 9.0])) >>> experiment = ot.LowDiscrepancyExperiment(ot.SobolSequence(), distribution, 5, False) >>> print(experiment.generate()) [ y0 y1 ] 0 : [ 0 0 ] 1 : [ 1.34898 1.65792 ] 2 : [ 1.34898 1.65792 ] 3 : [ 0.637279 1.10187 ] 4 : [ 2.3007 3.97795 ]
Methods
generate
()Generate points according to the type of the experiment.
Generate points and their associated weight according to the type of the experiment.
Accessor to the object’s name.
Accessor to the distribution.
getId
()Accessor to the object’s id.
getName
()Accessor to the object’s name.
Return the value of the randomize flag.
Return the value of the restart flag.
Return the sequence.
Accessor to the object’s shadowed id.
getSize
()Accessor to the size of the generated sample.
Accessor to the object’s visibility state.
hasName
()Test if the object is named.
Ask whether the experiment has uniform weights.
Test if the object has a distinguishable name.
setDistribution
(distribution)Accessor to the distribution.
setName
(name)Accessor to the object’s name.
setRandomize
(randomize)Set the value of the randomize flag.
setRestart
(restart)Set the value of the restart flag.
setShadowedId
(id)Accessor to the object’s shadowed id.
setSize
(size)Accessor to the size of the generated sample.
setVisibility
(visible)Accessor to the object’s visibility state.

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

generate
()¶ Generate points according to the type of the experiment.
 Returns
 sample
Sample
Points which constitute the design of experiments with . The sampling method is defined by the nature of the weighted experiment.
 sample
Examples
>>> import openturns as ot >>> ot.RandomGenerator.SetSeed(0) >>> myExperiment = ot.MonteCarloExperiment(ot.Normal(2), 5) >>> sample = myExperiment.generate() >>> print(sample) [ X0 X1 ] 0 : [ 0.608202 1.26617 ] 1 : [ 0.438266 1.20548 ] 2 : [ 2.18139 0.350042 ] 3 : [ 0.355007 1.43725 ] 4 : [ 0.810668 0.793156 ]

generateWithWeights
()¶ Generate points and their associated weight according to the type of the experiment.
 Returns
Examples
>>> import openturns as ot >>> ot.RandomGenerator.SetSeed(0) >>> myExperiment = ot.MonteCarloExperiment(ot.Normal(2), 5) >>> sample, weights = myExperiment.generateWithWeights() >>> print(sample) [ X0 X1 ] 0 : [ 0.608202 1.26617 ] 1 : [ 0.438266 1.20548 ] 2 : [ 2.18139 0.350042 ] 3 : [ 0.355007 1.43725 ] 4 : [ 0.810668 0.793156 ] >>> print(weights) [0.2,0.2,0.2,0.2,0.2]

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

getDistribution
()¶ Accessor to the distribution.
 Returns
 distribution
Distribution
Distribution used to generate the set of input data.
 distribution

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

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

getRandomize
()¶ Return the value of the randomize flag.
 Returns
 randomizebool
The value of the randomize flag.

getRestart
()¶ Return the value of the restart flag.
 Returns
 restartbool
The value of the restart flag.

getSequence
()¶ Return the sequence.
 Returns
 sequence
LowDiscrepancySequence
Sequence of points with low discrepancy.
 sequence

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

getSize
()¶ Accessor to the size of the generated sample.
 Returns
 sizepositive int
Number of points constituting the design of experiments.

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

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

hasUniformWeights
()¶ Ask whether the experiment has uniform weights.
 Returns
 hasUniformWeightsbool
Whether the experiment has uniform weights.

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

setDistribution
(distribution)¶ Accessor to the distribution.
 Parameters
 distribution
Distribution
Distribution used to generate the set of input data.
 distribution

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

setRandomize
(randomize)¶ Set the value of the randomize flag.
 Parameters
 randomizebool
Use a cyclic scrambling of the low discrepancy sequence, it means, the whole low discrepancy sequence is translated by a random vector modulo 1. See [lecuyer2005] for the interest of such a scrambling. Default is False.

setRestart
(restart)¶ Set the value of the restart flag.
 Parameters
 restartbool
The value of the restart flag. If equals to True, the low discrepancy sequence is restarted at each change of distribution, else it is changed only if the new distribution has a dimension different from the current one.

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

setSize
(size)¶ Accessor to the size of the generated sample.
 Parameters
 sizepositive int
Number of points constituting the design of experiments.

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