StandardEvent

class StandardEvent(*args)

Event defined in the standard space.

Available constructor:

StandardEvent(antecedent, comparisonOperator, threshold)

StandardEvent(event)

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.

eventEvent

Physical event associated with the standard event to be created.

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.

One way to evaluate the probability content P_f of the event \cD_f:

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

is to use an isoprobabilistic transformation to move from the physical space to a standard normal space (U-space) where distributions are spherical (invariant by rotation by definition), with zero mean, unit variance and unit correlation matrix. The usual isoprobabilistic transformations are the Generalized Nataf transformation and the Rosenblatt one.

In that new U-space, the event has the new expression defined from the transformed limit state function of the model G : \cD_f = \{\vect{U} \in \Rset^n \, | \, G(\vect{U}\,,\,\vect{d}) \le 0\} and its boundary : \{\vect{U} \in \Rset^n \, | \,G(\vect{U}\,,\,\vect{d}) = 0\}.

Examples

A StandardEvent 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(4)
>>> vect = ot.RandomVector(myDistribution)
>>> output = ot.CompositeRandomVector(myFunction, vect)
>>> myStandardEvent = ot.StandardEvent(output, ot.Less(), 1.0)

A StandardEvent based on an event :

>>> myEvent = ot.Event(output, ot.Less(), 1.0)
>>> myStandardEvent = ot.StandardEvent(myEvent)

Methods

getAntecedent(self)

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

getClassName(self)

Accessor to the object’s name.

getCovariance(self)

Accessor to the covariance of the RandomVector.

getDescription(self)

Accessor to the description of the RandomVector.

getDimension(self)

Accessor to the dimension of the RandomVector.

getDistribution(self)

Accessor to the distribution of the RandomVector.

getDomain(self)

Accessor to the domain of the Event.

getFunction(self)

Accessor to the Function in case of a composite RandomVector.

getId(self)

Accessor to the object’s id.

getImplementation(self, \*args)

Accessor to the underlying implementation.

getMarginal(self, \*args)

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

getMean(self)

Accessor to the mean of the RandomVector.

getName(self)

Accessor to the object’s name.

getOperator(self)

Accessor to the comparaison operator of the Event.

getParameter(self)

Accessor to the parameter of the distribution.

getParameterDescription(self)

Accessor to the parameter description of the distribution.

getRealization(self)

Compute one realization of the RandomVector.

getSample(self, size)

Compute realizations of the RandomVector.

getThreshold(self)

Accessor to the threshold of the Event.

intersect(self, other)

Intersection of two events.

isComposite(self)

Accessor to know if the RandomVector is a composite one.

join(self, other)

Union of two events.

setDescription(self, description)

Accessor to the description of the RandomVector.

setName(self, name)

Accessor to the object’s name.

setParameter(self, parameters)

Accessor to the parameter of the distribution.

__init__(self, *args)

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

getAntecedent(self)

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(self)

Accessor to the object’s name.

Returns
class_namestr

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

getCovariance(self)

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(self)

Accessor to the description of the RandomVector.

Returns
descriptionDescription

Describes the components of the RandomVector.

getDimension(self)

Accessor to the dimension of the RandomVector.

Returns
dimensionpositive int

Dimension of the RandomVector.

getDistribution(self)

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(self)

Accessor to the domain of the Event.

Returns
domainDomain

Describes the domain of an event.

getFunction(self)

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(self)

Accessor to the object’s id.

Returns
idint

Internal unique identifier.

getImplementation(self, *args)

Accessor to the underlying implementation.

Returns
implImplementation

The implementation class.

getMarginal(self, *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(self)

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(self)

Accessor to the object’s name.

Returns
namestr

The name of the object.

getOperator(self)

Accessor to the comparaison operator of the Event.

Returns
operatorComparisonOperator

Comparaison operator used to define the Event.

getParameter(self)

Accessor to the parameter of the distribution.

Returns
parameterPoint

Parameter values.

getParameterDescription(self)

Accessor to the parameter description of the distribution.

Returns
descriptionDescription

Parameter names.

getRealization(self)

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(self, 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(self)

Accessor to the threshold of the Event.

Returns
thresholdfloat

Threshold of the Event.

intersect(self, other)

Intersection of two events.

Parameters
eventEvent

A composite event

Returns
eventEvent

Intersection event

isComposite(self)

Accessor to know if the RandomVector is a composite one.

Returns
isCompositebool

Indicates if the RandomVector is of type Composite or not.

join(self, other)

Union of two events.

Parameters
eventEvent

A composite event

Returns
eventEvent

Union event

setDescription(self, description)

Accessor to the description of the RandomVector.

Parameters
descriptionstr or sequence of str

Describes the components of the RandomVector.

setName(self, name)

Accessor to the object’s name.

Parameters
namestr

The name of the object.

setParameter(self, parameters)

Accessor to the parameter of the distribution.

Parameters
parametersequence of float

Parameter values.