CompositeRandomVector

(Source code, png)

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

Random Vector obtained by applying a function.

Allows one to define the random variable Y=f(X) from a function f and another random variable X.

Parameters:
fFunction

Function to apply to the antecedent.

XRandomVector

Random vector of the antecedent.

Examples

>>> import openturns as ot
>>> X = ot.RandomVector(ot.Normal())
>>> f = ot.SymbolicFunction(['x'], ['x^2*sin(x)'])
>>> Y = ot.CompositeRandomVector(f, X)

Draw a sample:

>>> sample = Y.getSample(5)

Methods

asComposedEvent()

If the random vector can be viewed as the composition of several ThresholdEvent objects, this method builds and returns the composition.

getAntecedent()

Accessor to the antecedent RandomVector in case of a composite RandomVector.

getClassName()

Accessor to the object's name.

getCovariance()

Accessor to the covariance of the RandomVector.

getDescription()

Accessor to the description of the RandomVector.

getDimension()

Accessor to the dimension of the RandomVector.

getDistribution()

Accessor to the distribution of the RandomVector.

getDomain()

Accessor to the domain of the Event.

getFrozenRealization(fixedPoint)

Compute realizations of the RandomVector.

getFrozenSample(fixedSample)

Compute realizations of the RandomVector.

getFunction()

Accessor to the Function in case of a composite RandomVector.

getMarginal(*args)

Get the random vector corresponding to the i^{th} marginal component(s).

getMean()

Accessor to the mean of the RandomVector.

getName()

Accessor to the object's name.

getOperator()

Accessor to the comparaison operator of the Event.

getParameter()

Accessor to the parameter of the distribution.

getParameterDescription()

Accessor to the parameter description of the distribution.

getProcess()

Get the stochastic process.

getRealization()

Compute one realization of the RandomVector.

getSample(size)

Compute realizations of the RandomVector.

getThreshold()

Accessor to the threshold of the Event.

hasName()

Test if the object is named.

isComposite()

Accessor to know if the RandomVector is a composite one.

isEvent()

Whether the random vector is an event.

setDescription(description)

Accessor to the description of the RandomVector.

setName(name)

Accessor to the object's name.

setParameter(parameters)

Accessor to the parameter of the distribution.

__init__(*args)
asComposedEvent()

If the random vector can be viewed as the composition of several ThresholdEvent objects, this method builds and returns the composition. Otherwise throws.

Returns:
composedRandomVector

Composed event.

getAntecedent()

Accessor to the antecedent RandomVector in case of a composite RandomVector.

Returns:
antecedentRandomVector

Antecedent RandomVector \vect{X} in case of a CompositeRandomVector such as: \vect{Y}=f(\vect{X}).

getClassName()

Accessor to the object’s name.

Returns:
class_namestr

The object class name (object.__class__.__name__).

getCovariance()

Accessor to the covariance of the RandomVector.

Returns:
covarianceCovarianceMatrix

Covariance of the considered UsualRandomVector.

Examples

>>> import openturns as ot
>>> distribution = ot.Normal([0.0, 0.5], [1.0, 1.5], ot.CorrelationMatrix(2))
>>> randomVector = ot.RandomVector(distribution)
>>> ot.RandomGenerator.SetSeed(0)
>>> print(randomVector.getCovariance())
[[ 1    0    ]
 [ 0    2.25 ]]
getDescription()

Accessor to the description of the RandomVector.

Returns:
descriptionDescription

Describes the components of the RandomVector.

getDimension()

Accessor to the dimension of the RandomVector.

Returns:
dimensionpositive int

Dimension of the RandomVector.

getDistribution()

Accessor to the distribution of the RandomVector.

Returns:
distributionDistribution

Distribution of the considered UsualRandomVector.

Examples

>>> import openturns as ot
>>> distribution = ot.Normal([0.0, 0.0], [1.0, 1.0], ot.CorrelationMatrix(2))
>>> randomVector = ot.RandomVector(distribution)
>>> ot.RandomGenerator.SetSeed(0)
>>> print(randomVector.getDistribution())
Normal(mu = [0,0], sigma = [1,1], R = [[ 1 0 ]
 [ 0 1 ]])
getDomain()

Accessor to the domain of the Event.

Returns:
domainDomain

Describes the domain of an event.

getFrozenRealization(fixedPoint)

Compute realizations of the RandomVector.

In the case of a CompositeRandomVector or an event of some kind, this method returns the value taken by the random vector if the root cause takes the value given as argument.

Parameters:
fixedPointPoint

Point chosen as the root cause of the random vector.

Returns:
realizationPoint

The realization corresponding to the chosen root cause.

Examples

>>> import openturns as ot
>>> distribution = ot.Normal()
>>> randomVector = ot.RandomVector(distribution)
>>> f = ot.SymbolicFunction('x', 'x')
>>> compositeRandomVector = ot.CompositeRandomVector(f, randomVector)
>>> event = ot.ThresholdEvent(compositeRandomVector, ot.Less(), 0.0)
>>> print(event.getFrozenRealization([0.2]))
[0]
>>> print(event.getFrozenRealization([-0.1]))
[1]
getFrozenSample(fixedSample)

Compute realizations of the RandomVector.

In the case of a CompositeRandomVector or an event of some kind, this method returns the different values taken by the random vector when the root cause takes the values given as argument.

Parameters:
fixedSampleSample

Sample of root causes of the random vector.

Returns:
sampleSample

Sample of the realizations corresponding to the chosen root causes.

Examples

>>> import openturns as ot
>>> distribution = ot.Normal()
>>> randomVector = ot.RandomVector(distribution)
>>> f = ot.SymbolicFunction('x', 'x')
>>> compositeRandomVector = ot.CompositeRandomVector(f, randomVector)
>>> event = ot.ThresholdEvent(compositeRandomVector, ot.Less(), 0.0)
>>> print(event.getFrozenSample([[0.2], [-0.1]]))
    [ y0 ]
0 : [ 0  ]
1 : [ 1  ]
getFunction()

Accessor to the Function in case of a composite RandomVector.

Returns:
functionFunction

Function used to define a CompositeRandomVector as the image through this function of the antecedent \vect{X}: \vect{Y}=f(\vect{X}).

getMarginal(*args)

Get the random vector corresponding to the i^{th} marginal component(s).

Parameters:
iint or list of ints, 0\leq i < dim

Indicates the component(s) concerned. dim is the dimension of the RandomVector.

Returns:
vectorRandomVector

RandomVector restricted to the concerned components.

Notes

Let’s note \vect{Y}=\Tr{(Y_1,\dots,Y_n)} a random vector and I \in [1,n] a set of indices. If \vect{Y} is a UsualRandomVector, the subvector is defined by \tilde{\vect{Y}}=\Tr{(Y_i)}_{i \in I}. If \vect{Y} is a CompositeRandomVector, defined by \vect{Y}=f(\vect{X}) with f=(f_1,\dots,f_n), f_i some scalar functions, the subvector is \tilde{\vect{Y}}=(f_i(\vect{X}))_{i \in I}.

Examples

>>> import openturns as ot
>>> distribution = ot.Normal([0.0, 0.0], [1.0, 1.0], ot.CorrelationMatrix(2))
>>> randomVector = ot.RandomVector(distribution)
>>> ot.RandomGenerator.SetSeed(0)
>>> print(randomVector.getMarginal(1).getRealization())
[0.608202]
>>> print(randomVector.getMarginal(1).getDistribution())
Normal(mu = 0, sigma = 1)
getMean()

Accessor to the mean of the RandomVector.

Returns:
meanPoint

Mean of the considered UsualRandomVector.

Examples

>>> import openturns as ot
>>> distribution = ot.Normal([0.0, 0.5], [1.0, 1.5], ot.CorrelationMatrix(2))
>>> randomVector = ot.RandomVector(distribution)
>>> ot.RandomGenerator.SetSeed(0)
>>> print(randomVector.getMean())
[0,0.5]
getName()

Accessor to the object’s name.

Returns:
namestr

The name of the object.

getOperator()

Accessor to the comparaison operator of the Event.

Returns:
operatorComparisonOperator

Comparaison operator used to define the RandomVector.

getParameter()

Accessor to the parameter of the distribution.

Returns:
parameterPoint

Parameter values.

getParameterDescription()

Accessor to the parameter description of the distribution.

Returns:
descriptionDescription

Parameter names.

getProcess()

Get the stochastic process.

Returns:
processProcess

Stochastic process used to define the RandomVector.

getRealization()

Compute one realization of the RandomVector.

Returns:
realizationPoint

Sequence of values randomly determined from the RandomVector definition. In the case of an event: one realization of the event (considered as a Bernoulli variable) which is a boolean value (1 for the realization of the event and 0 else).

Examples

>>> import openturns as ot
>>> distribution = ot.Normal([0.0, 0.0], [1.0, 1.0], ot.CorrelationMatrix(2))
>>> randomVector = ot.RandomVector(distribution)
>>> ot.RandomGenerator.SetSeed(0)
>>> print(randomVector.getRealization())
[0.608202,-1.26617]
>>> print(randomVector.getRealization())
[-0.438266,1.20548]
getSample(size)

Compute realizations of the RandomVector.

Parameters:
nint, n \geq 0

Number of realizations needed.

Returns:
realizationsSample

n sequences of values randomly determined from the RandomVector definition. In the case of an event: n realizations of the event (considered as a Bernoulli variable) which are boolean values (1 for the realization of the event and 0 else).

Examples

>>> import openturns as ot
>>> distribution = ot.Normal([0.0, 0.0], [1.0, 1.0], ot.CorrelationMatrix(2))
>>> randomVector = ot.RandomVector(distribution)
>>> ot.RandomGenerator.SetSeed(0)
>>> print(randomVector.getSample(3))
    [ X0        X1        ]
0 : [  0.608202 -1.26617  ]
1 : [ -0.438266  1.20548  ]
2 : [ -2.18139   0.350042 ]
getThreshold()

Accessor to the threshold of the Event.

Returns:
thresholdfloat

Threshold of the RandomVector.

hasName()

Test if the object is named.

Returns:
hasNamebool

True if the name is not empty.

isComposite()

Accessor to know if the RandomVector is a composite one.

Returns:
isCompositebool

Indicates if the RandomVector is of type Composite or not.

isEvent()

Whether the random vector is an event.

Returns:
isEventbool

Whether it takes it values in {0, 1}.

setDescription(description)

Accessor to the description of the RandomVector.

Parameters:
descriptionstr or sequence of str

Describes the components of the RandomVector.

setName(name)

Accessor to the object’s name.

Parameters:
namestr

The name of the object.

setParameter(parameters)

Accessor to the parameter of the distribution.

Parameters:
parametersequence of float

Parameter values.

Examples using the class

Estimate moments from sample

Estimate moments from sample

Sample manipulation

Sample manipulation

Estimate Wilks and empirical quantile

Estimate Wilks and empirical quantile

Visualize sensitivity

Visualize sensitivity

Composite random vector

Composite random vector

Create a polynomial chaos for the Ishigami function: a quick start guide to polynomial chaos

Create a polynomial chaos for the Ishigami function: a quick start guide to polynomial chaos

Kriging: propagate uncertainties

Kriging: propagate uncertainties

Evaluate the mean of a random vector by simulations

Evaluate the mean of a random vector by simulations

Analyse the central tendency of a cantilever beam

Analyse the central tendency of a cantilever beam

Estimate moments from Taylor expansions

Estimate moments from Taylor expansions

Simulate an Event

Simulate an Event

Estimate a probability with Monte Carlo

Estimate a probability with Monte Carlo

Use a randomized QMC algorithm

Use a randomized QMC algorithm

Use the Adaptive Directional Stratification Algorithm

Use the Adaptive Directional Stratification Algorithm

Use the post-analytical importance sampling algorithm

Use the post-analytical importance sampling algorithm

Use the Directional Sampling Algorithm

Use the Directional Sampling Algorithm

Create a threshold event

Create a threshold event

Specify a simulation algorithm

Specify a simulation algorithm

Estimate a flooding probability

Estimate a flooding probability

Use the Importance Sampling algorithm

Use the Importance Sampling algorithm

Estimate a probability with Monte-Carlo on axial stressed beam: a quick start guide to reliability

Estimate a probability with Monte-Carlo on axial stressed beam: a quick start guide to reliability

Estimate a buckling probability

Estimate a buckling probability

Exploitation of simulation algorithm results

Exploitation of simulation algorithm results

Use the FORM algorithm in case of several design points

Use the FORM algorithm in case of several design points

Subset Sampling

Subset Sampling

Use the FORM - SORM algorithms

Use the FORM - SORM algorithms

Non parametric Adaptive Importance Sampling (NAIS)

Non parametric Adaptive Importance Sampling (NAIS)

Create a domain event

Create a domain event

Test the design point with the Strong Maximum Test

Test the design point with the Strong Maximum Test

Time variant system reliability problem

Time variant system reliability problem

Create unions or intersections of events

Create unions or intersections of events

Axial stressed beam : comparing different methods to estimate a probability

Axial stressed beam : comparing different methods to estimate a probability

An illustrated example of a FORM probability estimate

An illustrated example of a FORM probability estimate

Cross Entropy Importance Sampling

Cross Entropy Importance Sampling

Using the FORM - SORM algorithms on a nonlinear function

Using the FORM - SORM algorithms on a nonlinear function

Parallel coordinates graph as sensitivity tool

Parallel coordinates graph as sensitivity tool

Example of sensitivity analyses on the wing weight model

Example of sensitivity analyses on the wing weight model

Defining Python and symbolic functions: a quick start introduction to functions

Defining Python and symbolic functions: a quick start introduction to functions

Control algorithm termination

Control algorithm termination