/usr/include/openturns/swig/Event_doc.i is in libopenturns-dev 1.7-3.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 | %feature("docstring") OT::Event
"Event.
Available constructor:
Event()
Event(*antecedent, comparisonOperator, threshold*)
Event(*antecedent, domain*)
Event(*process, domain*)
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*.
domain : :class:`~openturns.Domain`
Domain failure.
process : :class:`~openturns.Process`
Stochastic process.
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.
The probability content of the event :math:`\\\\cD_f` is :math:`P_f`:
.. math::
P_f = \\\\int_{g(\\\\vect{X},\\\\vect{d})\\\\le 0}f_\\\\vect{X}(\\\\vect{x})d\\\\vect{x}
Here, the event considered is explicited directly from the limit state function
:math:`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 :math:`Z=\\\\tilde{g}(\\\\vect{X}\\\\,,\\\\,\\\\vect{d})`,
evaluated from the model :math:`\\\\tilde{g}(.)`. In that case, the event
considered, associated to the threshold :math:`z_s` has the formulation:
.. math::
\\\\cD_f = \\\\{ \\\\vect{X} \\\\in \\\\Rset^n \\\\, / \\\\, Z=\\\\tilde{g}(\\\\vect{X}\\\\,,\\\\,\\\\vect{d}) > z_s \\\\}
and the limit state function is:
.. math::
g(\\\\vect{X}\\\\,,\\\\,\\\\vect{d}) &= z_s - Z \\\\\\\\
&= z_s - \\\\tilde{g}(\\\\vect{X}\\\\,,\\\\,\\\\vect{d})
:math:`P_f` is the threshold exceedance probability, defined as:
.. math::
P_f &= P(Z \\\\geq z_s) \\\\\\\\
&= \\\\int_{g(\\\\vect{X}\\\\,,\\\\,\\\\vect{d}) \\\\le 0} \\\\pdf\\\\, d\\\\vect{x}
Examples
--------
An event created from a limit state function:
>>> import openturns as ot
>>> myFunction = ot.NumericalMathFunction(['E', 'F', 'L', 'I'], ['d'], ['-F*L^3/(3*E*I)'])
>>> myDistribution = ot.Normal([50., 1., 10., 5.], [1.]*4, ot.IdentityMatrix(4))
>>> vect = ot.RandomVector(myDistribution)
>>> output = ot.RandomVector(myFunction, vect)
>>> myEvent = ot.Event(output, ot.Less(), -3.0)
A composite random vector based event:
>>> X = ot.RandomVector(ot.Normal(2))
>>> model = ot.NumericalMathFunction(['x0', 'x1'], ['x0', 'x1'])
>>> Y = ot.RandomVector(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)
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