LHSExperiment

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

LHS experiment.

Available constructors:

LHSExperiment(size, alwaysShuffle, randomShift)

LHSExperiment(distribution, size, alwaysShuffle, randomShift)

Parameters:

distribution : Distribution

Distribution \mu with an independent copula used to generate the set of input data.

size : positive int

Number \mathrm{card}\,I of points that will be generated in the experiment.

alwaysShuffle : bool

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.

randomShift : bool

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.

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(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.
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.
__init__(*args)
static ComputeShuffle(totalSize)

Generate a new cell randomization for external use.

Parameters:

dimension : positive int

Number of input dimension.

totalSize : positive int

Number \mathrm{card}\,I of points that need to be shuffled.

Returns:

shuffle : Matrix

For each point, the indices of the shuffled components.

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]
getAlwaysShuffle()

Cell randomization flag accessor.

Returns:

alwaysShuffle : bool

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_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.

getRandomShift()

Randomization flag accessor.

Returns:

randomShift : bool

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:

id : int

Internal unique identifier.

getShuffle()

Return the cell randomization.

Returns:

shuffle : Matrix

For each point, the indices of the shuffled components.

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.

setAlwaysShuffle(alwaysShuffle)

Cell randomization flag accessor.

Parameters:

alwaysShuffle : bool

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:

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.

setRandomShift(randomShift)

Randomization flag accessor.

Parameters:

randomShift : bool

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:

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.