LHSExperiment¶

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class LHSExperiment(*args)¶

LHS experiment.

Available constructors:

LHSExperiment(size, alwaysShuffle, randomShift)

LHSExperiment(distribution, size, alwaysShuffle, randomShift)

Parameters

distributionDistribution: Distribution $\mu$ with an independent copula used to generate the set of input data.
sizepositive int: Number $\mathrm{card}\,I$ of points that will be generated in the experiment.
alwaysShufflebool: Flag to tell if the shuffle must be regenerated at each call to generate or not. Default is False: the shuffle is generated once and for all.
randomShiftbool: Flag to tell if the point selected in each cell of the shuffle is the center of the cell (randomshift is False) or if it is drawn wrt the restriction of the distribution to the cell. Default is True.

See also

WeightedExperiment

Notes

LHSExperiment is a random weighted design of experiments. The method generates a sample of points $\Xi_i$ according to the distribution $\mu$ with the LHS technique: some cells are determined, with the same probabilistic content according to the distribution, each line and each column contains exactly one cell, then points are selected among these selected cells. The weights associated to the points are all equal to $1/\mathrm{card}\,I$ . When recalled, the generate() method generates a new sample: the point selection within the cells changes but not the cells selection. To change the cell selection, it is necessary to create a new LHS Experiment.

Examples

Create an LHSExperiment:

>>> import openturns as ot

Generate the sample reusing the initial shuffle and using a random shift:

>>> ot.RandomGenerator.SetSeed(0)
>>> experiment = ot.LHSExperiment(ot.Normal(2), 5, False, True)
>>> print(experiment.generate())
    [ X0        X1        ]
0 : [  0.887671 -0.647818 ]
1 : [  0.107683  1.15851  ]
2 : [  0.453077 -1.04742  ]
3 : [ -0.928012  0.409732 ]
4 : [ -0.290539  0.16153  ]
>>> print(experiment.generate())
    [ X0         X1         ]
0 : [  1.52938   -0.343515  ]
1 : [ -0.0703427  2.36353   ]
2 : [  0.576091  -1.79398   ]
3 : [ -2.11636    0.619315  ]
4 : [ -0.699601  -0.0570674 ]

Generate the sample using a new shuffle and a random shift:

>>> ot.RandomGenerator.SetSeed(0)
>>> experiment = ot.LHSExperiment(ot.Normal(2), 5, True, True)
>>> print(experiment.generate())
    [ X0        X1        ]
0 : [  0.887671 -0.647818 ]
1 : [  0.107683  1.15851  ]
2 : [  0.453077 -1.04742  ]
3 : [ -0.928012  0.409732 ]
4 : [ -0.290539  0.16153  ]
>>> print(experiment.generate())
    [ X0         X1         ]
0 : [ -1.72695   -0.591043  ]
1 : [ -0.240653  -0.0406593 ]
2 : [  0.828719   2.12547   ]
3 : [  2.37061    0.508903  ]
4 : [ -0.668296  -1.11573   ]

Generate the sample reusing the initial shuffle and using a constant shift:

>>> ot.RandomGenerator.SetSeed(0)
>>> experiment = ot.LHSExperiment(ot.Normal(2), 5, False, False)
>>> print(experiment.generate())
    [ X0        X1        ]
0 : [  1.28155  -0.524401 ]
1 : [  0         1.28155  ]
2 : [  0.524401 -1.28155  ]
3 : [ -1.28155   0.524401 ]
4 : [ -0.524401  0        ]
>>> print(experiment.generate())
    [ X0        X1        ]
0 : [  1.28155  -0.524401 ]
1 : [  0         1.28155  ]
2 : [  0.524401 -1.28155  ]
3 : [ -1.28155   0.524401 ]
4 : [ -0.524401  0        ]

Generate the sample using a new shuffle and using a constant shift:

>>> ot.RandomGenerator.SetSeed(0)
>>> experiment = ot.LHSExperiment(ot.Normal(2), 5, True, False)
>>> print(experiment.generate())
    [ X0        X1        ]
0 : [  1.28155  -0.524401 ]
1 : [  0         1.28155  ]
2 : [  0.524401 -1.28155  ]
3 : [ -1.28155   0.524401 ]
4 : [ -0.524401  0        ]
>>> print(experiment.generate())
    [ X0        X1        ]
0 : [  0.524401 -0.524401 ]
1 : [  0         1.28155  ]
2 : [ -1.28155   0        ]
3 : [ -0.524401  0.524401 ]
4 : [  1.28155  -1.28155  ]

Methods

`ComputeShuffle`(dimension, totalSize)	Generate a new cell randomization for external use.
`generate`()	Generate points according to the type of the experiment.
`generateWithWeights`()	Generate points and their associated weight according to the type of the experiment.
`getAlwaysShuffle`()	Cell randomization flag accessor.
`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.
`getRandomShift`()	Randomization flag accessor.
`getShadowedId`()	Accessor to the object’s shadowed id.
`getShuffle`()	Return the cell randomization.
`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.
`setAlwaysShuffle`(alwaysShuffle)	Cell randomization flag accessor.
`setDistribution`(distribution)	Accessor to the distribution.
`setName`(name)	Accessor to the object’s name.
`setRandomShift`(randomShift)	Randomization flag accessor.
`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.

generateStandard

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

static ComputeShuffle(dimension, totalSize)¶

Generate a new cell randomization for external use.

Parameters

dimensionpositive int: Number of input dimension.
totalSizepositive int: Number $\mathrm{card}\,I$ of points that need to be shuffled.

Returns

shuffleMatrix: For each point, the indices of the shuffled components.

generate()¶

Generate points according to the type of the experiment.

Returns

sampleSample: 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

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

getAlwaysShuffle()¶

Cell randomization flag accessor.

Returns

alwaysShufflebool: Flag to tell if the shuffle must be regenerated at each call to generate or not. Default is False: the shuffle is generated once and for all.

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.

getRandomShift()¶

Randomization flag accessor.

Returns

randomShiftbool: Flag to tell if the point selected in each cell of the shuffle is the center of the cell (randomshift is False) or if it is drawn wrt the restriction of the distribution to the cell. Default is True.

getShadowedId()¶

Accessor to the object’s shadowed id.

Returns

idint: Internal unique identifier.

getShuffle()¶

Return the cell randomization.

Returns

shuffleMatrix: For each point, the indices of the shuffled components.

getSize()¶

Accessor to the size of the generated sample.

Returns

sizepositive int: Number $cardI$ 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.

setAlwaysShuffle(alwaysShuffle)¶

Cell randomization flag accessor.

Parameters

alwaysShufflebool: Flag to tell if the shuffle must be regenerated at each call to generate or not. Default is False: the shuffle is generated once and for all.

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.

setRandomShift(randomShift)¶

Randomization flag accessor.

Parameters

randomShiftbool: Flag to tell if the point selected in each cell of the shuffle is the center of the cell (randomshift is False) or if it is drawn wrt the restriction of the distribution to the cell. Default is True.

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 $cardI$ of points constituting the design of experiments.

setVisibility(visible)¶

Accessor to the object’s visibility state.

Parameters

visiblebool: Visibility flag.

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