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

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.

getFunction()

Accessor to the Function in case of a composite RandomVector.

getId()

Accessor to the object's id.

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.

getShadowedId()

Accessor to the object's shadowed id.

getThreshold()

Accessor to the threshold of the Event.

getVisibility()

Accessor to the object's visibility state.

hasName()

Test if the object is named.

hasVisibleName()

Test if the object has a distinguishable name.

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.

setShadowedId(id)

Accessor to the object's shadowed id.

setVisibility(visible)

Accessor to the object's visibility state.

__init__(*args)
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.

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}).

getId()

Accessor to the object’s id.

Returns:
idint

Internal unique identifier.

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:
aRealizationPoint

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).

See also

getSample

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).

See also

getRealization

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 ]
getShadowedId()

Accessor to the object’s shadowed id.

Returns:
idint

Internal unique identifier.

getThreshold()

Accessor to the threshold of the Event.

Returns:
thresholdfloat

Threshold of the RandomVector.

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.

hasVisibleName()

Test if the object has a distinguishable name.

Returns:
hasVisibleNamebool

True if the name is not empty and not the default one.

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.

setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters:
idint

Internal unique identifier.

setVisibility(visible)

Accessor to the object’s visibility state.

Parameters:
visiblebool

Visibility flag.

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

Estimate a probability with Latin Hypercube Sampling

Estimate a probability with Latin Hypercube Sampling

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

Estimate a flooding probability

Estimate a flooding probability

Specify a simulation algorithm

Specify a simulation algorithm

Use the Importance Sampling algorithm

Use the Importance Sampling algorithm

Create a threshold event

Create a threshold event

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

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

Non parametric Adaptive Importance Sampling (NAIS)

Non parametric Adaptive Importance Sampling (NAIS)

Subset Sampling

Subset Sampling

Use the FORM - SORM algorithms

Use the FORM - SORM algorithms

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

Axial stressed beam : comparing different methods to estimate a probability

Axial stressed beam : comparing different methods to estimate a probability

Create unions or intersections of events

Create unions or intersections of events

An illustrated example of a FORM probability estimate

An illustrated example of a FORM probability estimate

Cross Entropy Importance Sampling

Cross Entropy Importance Sampling

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