RandomVector

class RandomVector(*args)

Random vectors.

Available constructors:

RandomVector(points)

RandomVector(distribution)

RandomVector(distribution, randomParameters)

RandomVector(function, antecedent)

RandomVector(functionalChaosResult)

Parameters:

points : sequence of float

Sequence of values defining a ConstantRandomVector.

distribution : Distribution

Distribution of the UsualRandomVector to define.

randomParameters : RandomVector

RandomVector to define a distribution-based conditional vector. It defines random parameters for distribution.

antecedent : RandomVector

RandomVector \vect{X} of Usual type to define a CompositeRandomVector as the image through the function f of \vect{X}: \vect{Y}=f(\vect{X}).

function : NumericalMathFunction

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

functionalChaosResult : FunctionalChaosResult

Result to define a FunctionalChaosRandomVector as the image through a functional chaos approximation model of the associated UsualRandomVector.

Notes

A RandomVector provides at least a way to generate realizations. OpenTURNS provides two kinds of RandomVector :

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.
getFunction() Accessor to the NumericalMathFunction in case of a composite RandomVector.
getId() Accessor to the object’s id.
getImplementation(*args) Accessor to the underlying implementation.
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.
getRealization() Compute one realization of the RandomVector.
getSample(size) Compute realizations of the RandomVector.
getThreshold() Accessor to the threshold of the Event.
isComposite() Accessor to know if the RandomVector is a composite one.
setDescription(description) Accessor to the description of the RandomVector.
setName(name) Accessor to the object’s name.
__init__(*args)
getAntecedent()

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

Returns:

antecedent : RandomVector

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_name : str

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

getCovariance()

Accessor to the covariance of the RandomVector.

Returns:

covariance : CovarianceMatrix

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:

description : Description

Describes the components of the RandomVector.

getDimension()

Accessor to the dimension of the RandomVector.

Returns:

dimension : positive int

Dimension of the RandomVector.

getDistribution()

Accessor to the distribution of the RandomVector.

Returns:

distribution : Distribution

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 ]])
getFunction()

Accessor to the NumericalMathFunction in case of a composite RandomVector.

Returns:

function : NumericalMathFunction

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:

id : int

Internal unique identifier.

getImplementation(*args)

Accessor to the underlying implementation.

Returns:

impl : Implementation

The implementation class.

getMarginal(*args)

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

Parameters:

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

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

Returns:

vector : RandomVector

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:

mean : NumericalPoint

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:

name : str

The name of the object.

getOperator()

Accessor to the comparaison operator of the Event.

Returns:

operator : ComparisonOperator

Comparaison operator used to define the Event.

getRealization()

Compute one realization of the RandomVector.

Returns:

aRealization : NumericalPoint

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:

n : int, n \geq 0

Number of realizations needed.

Returns:

realizations : NumericalSample

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 ]
getThreshold()

Accessor to the threshold of the Event.

Returns:

threshold : float

Threshold of the Event.

isComposite()

Accessor to know if the RandomVector is a composite one.

Returns:

isComposite : bool

Indicates if the RandomVector is of type Composite or not.

setDescription(description)

Accessor to the description of the RandomVector.

Parameters:

description : str or sequence of str

Describes the components of the RandomVector.

setName(name)

Accessor to the object’s name.

Parameters:

name : str

The name of the object.