IntersectionEvent¶

class IntersectionEvent(*args)¶

Event defined as the intersection of several events.

The occurrence of all the events is necessary for the system event to occur (parallel system):

$E_{sys} = \bigcap_{i=1}^N E_i$

Parameters:

collsequence of RandomVector: Collection of events

See also

Event

Examples

>>> import openturns as ot
>>> dim = 2
>>> X = ot.RandomVector(ot.Normal(dim))
>>> f1 = ot.SymbolicFunction(['x1', 'x2'], ['x1'])
>>> f2 = ot.SymbolicFunction(['x1', 'x2'], ['x2'])
>>> Y1 = ot.CompositeRandomVector(f1, X)
>>> Y2 = ot.CompositeRandomVector(f2, X)
>>> e1 = ot.ThresholdEvent(Y1, ot.Less(), 0.0)
>>> e2 = ot.ThresholdEvent(Y2, ot.Greater(), 0.0)
>>> event = ot.IntersectionEvent([e1, e2])

Then it can be used for sampling (or with simulation algorithms):

>>> p = event.getSample(1000).computeMean()

Methods

`getAntecedent`()	Accessor to the antecedent random vector.
`getClassName`()	Accessor to the object's name.
`getComposedEvent`()	Accessor to the composed event.
`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.
`getEventCollection`()	Accessor to sub events.
`getFunction`()	Accessor to the function.
`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.
`setEventCollection`(collection)	Accessor to sub events.
`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 random vector.

Returns:

antecedentRandomVector: Defined as the root cause.

getClassName()¶

Accessor to the object’s name.

Returns:

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

getComposedEvent()¶

Accessor to the composed event.

Returns:

composedRandomVector: Composed event.

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.

getEventCollection()¶

Accessor to sub events.

Returns:

eventsRandomVectorCollection: List of sub events.

getFunction()¶

Accessor to the function.

Returns:

functionFunction: Composed function.

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

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.

setEventCollection(collection)¶

Accessor to sub events.

Parameters:

eventssequence of RandomVector: List of sub events.

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¶

Time variant system reliability problem

Create unions or intersections of events

OpenTURNS

An Open source initiative for the Treatment of Uncertainties, Risks'N Statistics

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IntersectionEvent¶

Examples using the class¶