LowDiscrepancyExperiment¶

(Source code, svg)

class LowDiscrepancyExperiment(*args)¶

LowDiscrepancy experiment.

Available constructors:

LowDiscrepancyExperiment(size, restart)

LowDiscrepancyExperiment(sequence, size, restart)

LowDiscrepancyExperiment(sequence, distribution, size, restart)

Parameters:

sizepositive int

Number $\sampleSize$ of points of the sequence.

sequenceLowDiscrepancySequence

Low discrepancy sequence type.

If not specified, the sequence is a SobolSequence.

distributionDistribution

Distribution $\mu$ of dimension $\sampleSize$ .

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.

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.
`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.
`getSize`()	Accessor to the size of the generated sample.
`hasName`()	Test if the object is named.
`hasUniformWeights`()	Ask whether the experiment has uniform weights.
`isRandom`()	Accessor to the randomness of quadrature.
`setDistribution`(distribution)	Accessor to the distribution.
`setLevels`(levels)	Accessor to the experiment nesting levels.
`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.
`setSize`(size)	Accessor to the size of the generated sample.

See also

WeightedExperiment

Notes

The generate() method generates a low discrepancy sequence $(u_1, \cdots, u_\sampleSize)$ over $[0,1]^\sampleSize$ using the Sobol sequence if no particular other sequence has been fixed through the parameter sequence.

Then we use an Isoprobabilistic transformation that maps the independent copula of dimension $\sampleSize$ into the distribution given through the parameter distribution: the sample $(u_1, \cdots, u_\sampleSize)$ is transformed into the sample $(x_1, \cdots, x_\sampleSize)$ that is finally returned.

The weights are all equal to $\frac{1}{\sampleSize}$ .

When the generate() method is called again, the generated sample changes. But as soon as the parameter distribution is modified, the sequence is restarted at its initial state.

Refer to [cambou2017] to get more details especially when distribution has dependent components.

Examples

>>> import openturns as ot
>>> distribution = ot.JointDistribution([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  ]

__init__(*args)¶

generate()¶

Generate points according to the type of the experiment.

Returns:

sampleSample: Points $(\inputReal_i)_{i = 1, ..., \sampleSize}$ of the design of experiments. The sampling method is defined by the type 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 of the design of experiments. The sampling method is defined by the nature of the experiment.
weightsPoint of size $\sampleSize$: Weights $(w_i)_{i = 1, ..., \sampleSize}$ associated with the points. By default, all the weights are equal to $\frac{1}{\sampleSize}$ .

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 of the input random vector.

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 $(u_1, \cdots, u_N)$ with low discrepancy.

getSize()¶

Accessor to the size of the generated sample.

Returns:

sizepositive int: Number $\sampleSize$ of points constituting the design of experiments.

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.

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 of the input random vector.

setLevels(levels)¶

Accessor to the experiment nesting levels.

Parameters:

levelssequence of int: Nesting level for each component.

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.

setSize(size)¶

Accessor to the size of the generated sample.

Parameters: