libopenturns-dev 1.7-3 / usr / include / openturns / swig / StrongMaximumTest_doc.i

%feature("docstring") OT::StrongMaximumTest
"Strong Maximum Test.

Available constructors:
    StrongMaximumTest(*event, designPoint, importanceLevel, accuracyLevel, confidenceLevel*)

    StrongMaximumTest(*event, designPoint, importanceLevel, accuracyLevel, pointNumber*)

Parameters
----------
event : :class:`~openturns.StandardEvent`
    Failure event :math:`\\\\cD_f` defining in the standard space (U-space).
designPoint : sequence of float
    Design point in the standard space resulting from the optimization
    algorithm.
importanceLevel : float, :math:`0. < \\\\varepsilon < 1.`
    Importance level.
accuracyLevel : float, :math:`\\\\tau > 0`
    Accuracy level. It is recommanded to take :math:`\\\\tau \\\\leq 4`.
confidenceLevel : positive float, :math:`(1-q) \\\\in ]0., 1.[`
    Confidence level.
pointNumber : int, :math:`N > 0`
    Number of points used to perform the Strong Maximum Test, evaluated by the
    limit state function.

Notes
-----
The Strong Maximum Test helps to evaluate the quality of the design point
:math:`P^*` resulting from the optimization algorithm launched for example by
the :class:`~openturns.Analytical` class or its derived classes
:class:`~openturns.FORM` and :class:`~openturns.SORM`.
It checks whether the design point computed is :

- the *true* design point, which means a global maximum point,

- a *strong* design point, which means that there is no other local maximum
  located on the event boundary and which likelihood is slightly inferior to
  the design point one.

The Strong Maximum Test will sample the sphere centered on the origin of the
standard space and of radius :
:math:`R = \\\\beta_{HL} (1 + \\\\tau \\\\delta_{\\\\varepsilon})` with :math:`\\\\tau > 0`,
:math:`\\\\delta_{\\\\varepsilon}=\\\\sqrt{1 - 2 \\\\frac{ln(\\\\varepsilon)}{\\\\beta_{HL}^2}} - 1`
and :math:`\\\\beta_{HL}` the Hasofer-Lind reliability index.

The number :math:`N` of the simulations sampling the sphere of radius :math:`R`
is determined to ensure that the test detects with a probability greater than
:math:`(1-q)` any point of :math:`\\\\cD_f` outside the design point vicinity
which contribution to :math:`P_f` is not negligeable (i.e. which density value
in the U-space is greater than :math:`\\\\varepsilon` times the density value at
the design point).

See also
--------
Analytical, SORM, FORM, SORMResult, 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)
>>> # FORM analyse to get the design point
>>> myAlgo = ot.FORM(ot.Cobyla(), myEvent, [50., 1., 10., 5.])
>>> myAlgo.run()
>>> FORMresult = myAlgo.getResult()
>>> designPoint = FORMresult.getStandardSpaceDesignPoint()
>>> # Strong Max Test
>>> myStandardEvent = ot.StandardEvent(myEvent)
>>> myTest = ot.StrongMaximumTest(myStandardEvent, designPoint, 0.15, 3, 0.99)
>>> myTest.run()"

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%feature("docstring") OT::StrongMaximumTest::getAccuracyLevel
"Accessor to the accuracy level.

Returns
-------
accuracy : positive float
    Accuracy level :math:`\\\\tau`."

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%feature("docstring") OT::StrongMaximumTest::getConfidenceLevel
"Accessor to the confidence level.

Returns
-------
level : positive float
    Confidence level :math:`(1-q)`."

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%feature("docstring") OT::StrongMaximumTest::getDeltaEpsilon
"Accessor to the parameter :math:`\\\\delta_{\\\\varepsilon}`.

Returns
-------
delta_epsilon : float
    :math:`\\\\delta_{\\\\varepsilon} = \\\\sqrt{1 - 2 \\\\frac{ln(\\\\varepsilon)}{\\\\beta^2}} - 1`."

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%feature("docstring") OT::StrongMaximumTest::getDesignPointVicinity
"Accessor to the design point vinicity.

Returns
-------
vicinity : float, :math:`v > 0`
    Design point vinicity :math:`v = \\\\frac{1} {1 + \\\\tau \\\\delta_{\\\\varepsilon}}`."

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%feature("docstring") OT::StrongMaximumTest::getEvent
"Accessor to the event in the standard space.

Returns
-------
event : :class:`~openturns.StandardEvent`
    Failure event :math:`\\\\cD_f` in the standard space on which is based the
    Strong Maximum Test."

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%feature("docstring") OT::StrongMaximumTest::getFarDesignPointVerifyingEventPoints
"Accessor to the points verifying the event and far of the design point.

Returns
-------
points : :class:`~openturns.NumericalSample`
    The points of the discretized sphere which are out of the vicinity of
    the standard design point and which verify the event."

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%feature("docstring") OT::StrongMaximumTest::getFarDesignPointVerifyingEventValues
"Accessor to values of the limit state function.

Returns
-------
values : :class:`~openturns.NumericalSample`
    The values of the limit state function on the points of the
    discretized sphere which are out of the vicinity of the standard design
    point and which verify the event."

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%feature("docstring") OT::StrongMaximumTest::getFarDesignPointViolatingEventPoints
"Accessor to the points not verifying the event and far of the design point.

Returns
-------
points : :class:`~openturns.NumericalSample`
    The points of the discretized sphere which are out of the vicinity of
    the standard design point and which don't verify the event."

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%feature("docstring") OT::StrongMaximumTest::getFarDesignPointViolatingEventValues
"Accessor to values of the limit state function.

Returns
-------
values : :class:`~openturns.NumericalSample`
    The values of the limit state function on the points of the
    discretized sphere which are out of the vicinity of the standard design
    point and which don't verify the event."

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%feature("docstring") OT::StrongMaximumTest::getImportanceLevel
"Accessor to the importance level.

Returns
-------
level : float
    Importance level :math:`\\\\varepsilon`."

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%feature("docstring") OT::StrongMaximumTest::getNearDesignPointVerifyingEventPoints
"Accessor to the points verifying the event and near of the design point.

Returns
-------
points : :class:`~openturns.NumericalSample`
    The points of the discretized sphere which are inside the vicinity of
    the standard design point and which verify the event."

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%feature("docstring") OT::StrongMaximumTest::getNearDesignPointVerifyingEventValues
"Accessor to values of the limit state function.

Returns
-------
values : :class:`~openturns.NumericalSample`
    The values of the limit state function on the points of the
    discretized sphere which are inside the vicinity of the standard design
    point and which verify the event."

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%feature("docstring") OT::StrongMaximumTest::getNearDesignPointViolatingEventPoints
"Accessor to the points not verifying the event and near of the design point.

Returns
-------
point : :class:`~openturns.NumericalSample`
    The points of the discretized sphere which are out of the vicinity of
    the standard design point and which don't verify the event."

// ---------------------------------------------------------------------

%feature("docstring") OT::StrongMaximumTest::getNearDesignPointViolatingEventValues
"Accessor to values of the limit state function.

Returns
-------
values : :class:`~openturns.NumericalSample`
    The values of the limit state function on the points of the
    discretized sphere which are inside the vicinity of the standard design
    point and which don't verify the event."

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%feature("docstring") OT::StrongMaximumTest::getPointNumber
"Accessor to the number of points.

Returns
-------
number : int, :math:`N > 0`
    Number of points used to perform the Strong Maximum Test, evaluated by the
    limit state function."

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%feature("docstring") OT::StrongMaximumTest::getStandardSpaceDesignPoint
"Accessor to the design point in the standard space.

Returns
-------
point : :class:`~openturns.NumericalPoint`
    Design point in the standard space."

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%feature("docstring") OT::StrongMaximumTest::run
"Perform the Strong Maximum Test."