LHSExperiment

(Source code, png)

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

LHS experiment.

Available constructors:

LHSExperiment(size, alwaysShuffle, randomShift)

LHSExperiment(distribution, size, alwaysShuffle, randomShift)

Parameters:
distributionDistribution

Distribution \mu 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.

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.

Warning

When the distribution has a non-independent copula, the sample obtained by inverse isoprobabilistic transformation of an LHS experiment does not have the same properties as the original LHS experiment but can still be used to efficiently estimate threshold exceedance probabilities, especially when the copula is normal (as in this case the isoprobabilistic transformation is linear) and the limit-state is linear.

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.

isRandom()

Accessor to the randomness of quadrature.

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(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.

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.

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.

Examples using the class

Create a polynomial chaos metamodel by integration on the cantilever beam

Create a polynomial chaos metamodel by integration on the cantilever beam

Kriging: propagate uncertainties

Kriging: propagate uncertainties

Example of multi output Kriging on the fire satellite model

Example of multi output Kriging on the fire satellite model

Kriging: metamodel of the Branin-Hoo function

Kriging: metamodel of the Branin-Hoo function

Sequentially adding new points to a kriging

Sequentially adding new points to a kriging

Advanced kriging

Advanced kriging

Kriging :configure the optimization solver

Kriging :configure the optimization solver

Axial stressed beam : comparing different methods to estimate a probability

Axial stressed beam : comparing different methods to estimate a probability

Probabilistic design of experiments

Probabilistic design of experiments

Create a random design of experiments

Create a random design of experiments

Create a design of experiments with discrete and continuous variables

Create a design of experiments with discrete and continuous variables

Various design of experiments in OpenTURNS

Various design of experiments in OpenTURNS

Optimize an LHS design of experiments

Optimize an LHS design of experiments

EfficientGlobalOptimization examples

EfficientGlobalOptimization examples