LowDiscrepancyExperiment¶

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.

sequenceLowDiscrepancySequence

Sequence of points with low discrepancy. If not specified, the sequence is a SobolSequence.

distributionDistribution

Distribution of dimension . The low discrepancy sequence is uniformly distributed over . We use an iso-probabilistic 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.

Notes

The generate() method generates points according to the distribution . When the generate() 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 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. Accessor to the object's id. 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. Accessor to the size of the generated sample. Accessor to the object's visibility state. Test if the object is named. Ask whether the experiment has uniform weights. Test if the object has a distinguishable name. Accessor to the randomness of quadrature. 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. 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)
generate()

Generate points according to the type of the experiment.

Returns:
sampleSample

Points which constitute the design of experiments with . The sampling method is defined by the nature of the weighted experiment.

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:
sampleSample

The points which constitute the design of experiments. The sampling method is defined by the nature of the experiment.

weightsPoint of size

Weights associated with the points. By default, all the weights are equal to .

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:
distributionDistribution

Distribution used to generate the set of input data.

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:
sequenceLowDiscrepancySequence

Sequence of points with low discrepancy.

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.

isRandom()

Accessor to the randomness of quadrature.

Parameters:
isRandombool

Is true if the design of experiments is random. Otherwise, the design of experiment is assumed to be deterministic.

setDistribution(distribution)

Accessor to the distribution.

Parameters:
distributionDistribution

Distribution used to generate the set of input data.

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.

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.

Examples using the class¶

Create a polynomial chaos metamodel by integration on the cantilever beam

Create a polynomial chaos metamodel by integration on the cantilever beam

Use a randomized QMC algorithm

Use a randomized QMC algorithm

Time variant system reliability problem

Time variant system reliability problem

Various design of experiments in OpenTURNS

Various design of experiments in OpenTURNS

Optimization of the Rastrigin test function

Optimization of the Rastrigin test function