LowDiscrepancyExperiment

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../../_images/LowDiscrepancyExperiment.png
class LowDiscrepancyExperiment(*args)

LowDiscrepancy experiment.

Available constructors:

LowDiscrepancyExperiment(size, restart)

LowDiscrepancyExperiment(sequence, size, restart)

LowDiscrepancyExperiment(sequence, distribution, size, restart)

Parameters:

size : positive int

Number N of points of the sequence.

sequence : LowDiscrepancySequence

Sequence of points (u_1, \cdots, u_N) with low discrepancy. If not specified, the sequence is a SobolSequence.

distribution :

Distribution \mu of dimension n with an independent copula. The low discrepancy sequence (u_1, \cdots, u_N) is uniformly distributed over [0,1]^n. We use the marginal transformation \Xi_i =F_i^{-1}(u_i) to generate points (\Xi_i)_{i\in I} according to the distribution \mu. The weights are all equal to 1/N.

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 (\Xi_i)_{i \in I} independently from the distribution \mu. When the generate() method is recalled, the generated sample changes.

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())
    [ X0    X1    ]
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())
    [ X0     X1     ]
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())
    [ X0    X1    ]
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())
    [ X0    X1    ]
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())
    [ X0     X1     ]
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())
    [ X0     X1     ]
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 ]

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.
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.
hasVisibleName() Test if the object has a distinguishable name.
setDistribution(distribution) Accessor to the distribution.
setName(name) Accessor to the object’s name.
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)
generate()

Generate points according to the type of the experiment.

Returns:

sample : Sample

Points (\Xi_i)_{i \in I} which constitute the design of experiments with card I = size. 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 cardI

Weights (\omega_i)_{i \in I} associated with the points. By default, all the weights are equal to 1/cardI.

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.

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 (u_1, \cdots, u_N) 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 cardI 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.

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.

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 cardI of points constituting the design of experiments.

setVisibility(visible)

Accessor to the object’s visibility state.

Parameters:

visible : bool

Visibility flag.