/usr/include/openturns/swig/FORM_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 | %feature("docstring") OT::FORM
"First Order Reliability Method (FORM).
Available constructors:
FORM(*nearestPointAlgorithm, event, physicalStartingPoint*)
Parameters
----------
nearestPointAlgorithm : :class:`~openturns.OptimizationSolver`
Optimization algorithm used to research the design point.
event : :class:`~openturns.Event`
Failure event.
physicalStartingPoint : sequence of float
Starting point of the optimization algorithm, declared in the physical
space.
Notes
-----
See :class:`~openturns.Analytical` for the description of the first steps of
the FORM analysis.
The First Order Reliability Method (FORM) consists in linearizing the limit state
function :math:`G(\\\\vect{U}\\\\,,\\\\,\\\\vect{d})` at the design point, denoted
:math:`P^*`, which is the point on the limit state surface
:math:`G(\\\\vect{U}\\\\,,\\\\,\\\\vect{d})=0` that is closest to the origin of the
standard space.
Then, the probability :math:`P_f` where the limit state surface has been
approximated by a linear surface (hyperplane) can be obtained exactly, thanks
to the rotation invariance of the standard distribution :math:`f_{\\\\vect{U}}` :
.. math::
P_f = \\\\left\\\\{
\\\\begin{array}{ll}
\\\\displaystyle E(-\\\\beta_{HL})
& \\\\text{if the origin of the }\\\\vect{u}\\\\text{-space lies in the domain }\\\\cD_f \\\\\\\\
\\\\displaystyle E(+\\\\beta_{HL}) & \\\\text{otherwise}
\\\\end{array}
\\\\right.
where :math:`\\\\beta_{HL}` is the Hasofer-Lind reliability index, defined as the
distance of the design point :math:`\\\\vect{u}^*` to the origin of the standard
space and :math:`E` the marginal cumulative density function of the spherical
distributions in the standard space.
The evaluation of the failure probability is stored in the data structure
:class:`~openturns.FORMResult` recoverable with the :meth:`getResult` method.
See also
--------
Analytical, AnalyticalResult, SORM, StrongMaximumTest, FORMResult
Examples
--------
>>> 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)
>>> # We create an OptimizationSolver algorithm
>>> myCobyla = ot.Cobyla()
>>> myAlgo = ot.FORM(myCobyla, myEvent, [50., 1., 10., 5.])"
// ---------------------------------------------------------------------
%feature("docstring") OT::FORM::getResult
"Accessor to the result of FORM.
Returns
-------
result : :class:`~openturns.FORMResult`
Structure containing all the results of the FORM analysis."
// ---------------------------------------------------------------------
%feature("docstring") OT::FORM::setResult
"Accessor to the result of FORM.
Parameters
----------
result : :class:`~openturns.FORMResult`
Structure containing all the results of the FORM analysis."
// ---------------------------------------------------------------------
%feature("docstring") OT::FORM::run
"Evaluate the failure probability.
Notes
-----
Evaluate the failure probability and create a :class:`~openturns.FORMResult`,
the structure result which is accessible with the method :meth:`getResult`."
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