Event

class Event(*args)

Event.

Available constructor:

Event()

Event(antecedent, comparisonOperator, threshold)

Event(antecedent, domain)

Event(process, domain)

Parameters:
antecedentRandomVector of dimension 1

Output variable of interest.

comparisonOperatorComparisonOperator

Comparison operator used to compare antecedent with threshold.

thresholdfloat

threshold we want to compare to antecedent.

domainDomain

Domain failure.

processProcess

Stochastic process.

Notes

An event is defined as follows:

\cD_f = \{\vect{X} \in \Rset^n \, / \, g(\vect{X},\vect{d}) \le 0\}

where \vect{X} denotes a random input vector, representing the sources of uncertainties, \vect{d} is a determinist vector, representing the fixed variables and g(\vect{X},\vect{d}) is the limit state function of the model. The probability content of the event \cD_f is P_f:

P_f = \int_{g(\vect{X},\vect{d})\le 0}f_\vect{X}(\vect{x})\di{\vect{x}}

Here, the event considered is explicited directly from the limit state function g(\vect{X}\,,\,\vect{d}) : this is the classical structural reliability formulation. However, if the event is a threshold exceedance, it is useful to explicite the variable of interest Z=\tilde{g}(\vect{X}\,,\,\vect{d}), evaluated from the model \tilde{g}(.). In that case, the event considered, associated to the threshold z_s has the formulation:

\cD_f = \{ \vect{X} \in \Rset^n \, / \, Z=\tilde{g}(\vect{X}\,,\,\vect{d}) > z_s \}

and the limit state function is:

g(\vect{X}\,,\,\vect{d}) &= z_s - Z \\
                         &= z_s - \tilde{g}(\vect{X}\,,\,\vect{d})

P_f is the threshold exceedance probability, defined as:

P_f &= P(Z \geq z_s) \\
    &= \int_{g(\vect{X}, \vect{d}) \le 0} \pdf\di{\vect{x}}

Examples

An event created from a limit state function:

>>> import openturns as ot
>>> myFunction = ot.SymbolicFunction(['E', 'F', 'L', 'I'], ['-F*L^3/(3*E*I)'])
>>> myDistribution = ot.Normal([50.0, 1.0, 10.0, 5.0], [1.0]*4, ot.IdentityMatrix(4))
>>> vect = ot.RandomVector(myDistribution)
>>> output = ot.CompositeRandomVector(myFunction, vect)
>>> myEvent = ot.Event(output, ot.Less(), -3.0)

A composite random vector based event:

>>> X = ot.RandomVector(ot.Normal(2))
>>> model = ot.SymbolicFunction(['x0', 'x1'], ['x0', 'x1'])
>>> Y = ot.CompositeRandomVector(model, X)
>>> # The domain: [0, 1]^2
>>> domain = ot.Interval(2)
>>> # The event
>>> event = ot.Event(Y, domain)

A process based event:

>>> # The input process
>>> X = ot.WhiteNoise(ot.Normal(2))
>>> # The domain: [0, 1]^2
>>> domain = ot.Interval(2)
>>> # The event
>>> event = ot.Event(X, domain)
Attributes:
thisown

The membership flag

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.
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.
getParameter() Accessor to the parameter of the distribution.
getParameterDescription() Accessor to the parameter description of the distribution.
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.
setParameter(parameters) Accessor to the parameter of the distribution.
__init__(*args)

Initialize self. See help(type(self)) for accurate signature.

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.

getImplementation(*args)

Accessor to the underlying implementation.

Returns:
implImplementation

The implementation class.

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 Event.

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.

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 ]
getThreshold()

Accessor to the threshold of the Event.

Returns:
thresholdfloat

Threshold of the Event.

isComposite()

Accessor to know if the RandomVector is a composite one.

Returns:
isCompositebool

Indicates if the RandomVector is of type Composite or not.

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.

thisown

The membership flag