MonteCarloExperiment¶

(Source code, svg)

class MonteCarloExperiment(*args)¶

MonteCarlo experiment.

Available constructors:

MonteCarloExperiment(distribution, size)

MonteCarloExperiment(size)

Parameters:

distributionDistribution: Distribution $\mu$ with an independent copula used to generate the set of input data.
sizepositive int: Number $\sampleSize$ of points that will be generated in the experiment.

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.
`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.
`setSize`(size)	Accessor to the size of the generated sample.

See also

WeightedExperiment

Notes

MonteCarloExperiment is a random weighted design of experiments (see [hammersley1961] page 51, [lemieux2009] page 3). The generate() method computes the nodes $(\inputReal_i)_{i = 1, ..., \sampleSize}$ by generating independent observations from the distribution $\mu$ . The weights associated to the points are all equal to $w_i = \frac{1}{\sampleSize}$ where $\sampleSize$ is the sample size. When the generate() method is called a second time, the generated sample changes.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> experiment = ot.MonteCarloExperiment(ot.Normal(2), 5)
>>> print(experiment.generate())
    [ 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 ]

__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]