# LowDiscrepancyExperiment¶

class LowDiscrepancyExperiment(*args)

LowDiscrepancy experiment.

Available constructors:

LowDiscrepancyExperiment(size, restart)

LowDiscrepancyExperiment(sequence, size, restart)

LowDiscrepancyExperiment(sequence, distribution, size, restart)

Parameters: size : positive 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 iso-probabilistic transformation from the independent copula of dimension to the given distribution. The weights are all equal to . restart : bool 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:

>>> myPlane = ot.LowDiscrepancyExperiment(ot.SobolSequence(), distribution, 5, True)
>>> print(myPlane.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(myPlane.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 ]
>>> myPlane.setDistribution(distribution)
>>> print(myPlane.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:

>>> myPlane = ot.LowDiscrepancyExperiment(ot.SobolSequence(), distribution, 5, False)
>>> print(myPlane.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(myPlane.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 ]
>>> myPlane.setDistribution(distribution)
>>> print(myPlane.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]))
>>> myPlane = ot.LowDiscrepancyExperiment(ot.SobolSequence(), distribution, 5, False)
>>> print(myPlane.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. generateWithWeights() Generate points and their associated weight according to the type of the experiment. getClassName() Accessor to the object’s name. getDistribution() Accessor to the distribution. getId() Accessor to the object’s id. getName() Accessor to the object’s name. getRandomize() Return the value of the randomize flag. getRestart() Return the value of the restart flag. getSequence() Return the sequence. getShadowedId() Accessor to the object’s shadowed id. getSize() Accessor to the size of the generated sample. getVisibility() Accessor to the object’s visibility state. hasName() Test if the object is named. hasUniformWeights() Ask whether the experiment has uniform weights. hasVisibleName() 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.

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: sample : Sample The points which constitute the design of experiments. The sampling method is defined by the nature of the experiment. weights : Point 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_name : str The object class name (object.__class__.__name__).
getDistribution()

Accessor to the distribution.

Returns: distribution : Distribution Distribution used to generate the set of input data.
getId()

Accessor to the object’s id.

Returns: id : int Internal unique identifier.
getName()

Accessor to the object’s name.

Returns: name : str The name of the object.
getRandomize()

Return the value of the randomize flag.

Returns: randomize : bool The value of the randomize flag.
getRestart()

Return the value of the restart flag.

Returns: restart : bool The value of the restart flag.
getSequence()

Return the sequence.

Returns: sequence : LowDiscrepancySequence Sequence of points with low discrepancy.
getShadowedId()

Accessor to the object’s shadowed id.

Returns: id : int Internal unique identifier.
getSize()

Accessor to the size of the generated sample.

Returns: size : positive int Number of points constituting the design of experiments.
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.
hasUniformWeights()

Ask whether the experiment has uniform weights.

Returns: hasUniformWeights : bool Whether the experiment has uniform weights.
hasVisibleName()

Test if the object has a distinguishable name.

Returns: hasVisibleName : bool 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.
setName(name)

Accessor to the object’s name.

Parameters: name : str The name of the object.
setRandomize(randomize)

Set the value of the randomize flag.

Parameters: randomize : bool Use a cyclic scrambling of the low discrepancy sequence. See [Lecuyer2005] for the interest of such a scrambling. Default is false.
setRestart(restart)

Set the value of the restart flag.

Parameters: restart : bool 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: id : int Internal unique identifier.
setSize(size)

Accessor to the size of the generated sample.

Parameters: size : positive int Number of points constituting the design of experiments.
setVisibility(visible)

Accessor to the object’s visibility state.

Parameters: visible : bool Visibility flag.