%feature("docstring") OT::StandardEvent
"Event defined in the standard space.

Available constructor:
    StandardEvent(*antecedent, comparisonOperator, threshold*)

    StandardEvent(*event*)

Parameters
----------
antecedent : :class:`~openturns.RandomVector` of dimension 1
    Output variable of interest.
comparisonOperator : :class:`~openturns.ComparisonOperator`
    Comparison operator used to compare *antecedent* with *threshold*.
threshold : float
    *threshold* we want to compare to *antecedent*.
event : :class:`~openturns.Event`
    Physical event associated with the standard event to be created.

Notes
-----
An event is defined as follows:

.. math::

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

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

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

.. math::

    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
:math:`G : \cD_f = \{\vect{U} \in \Rset^n \, | \, G(\vect{U}\,,\,\vect{d}) \le 0\}`
and its boundary :
:math:`\{\vect{U} \in \Rset^n \, | \,G(\vect{U}\,,\,\vect{d}) = 0\}`.

See also
--------
Analytical, SORM, FORM, SORMResult, FORMResult, StrongMaximumTest

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.RandomVector(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)"
