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, evaluated from left to right. Ordering the least probable events first can help to avoid evaluating the last ones. In case the ranking of the probabilities of the events is unknown, it can be quickly estimated with (for example) a FORM analysis of each individual event.

See also

UnionEvent

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

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 random vector.

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.

getEventCollection()

Accessor to sub events.

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.

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)
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 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__).

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.

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}).

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.

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

Time variant system reliability problem

Create unions or intersections of events

Create unions or intersections of events