/usr/include/openturns/swig/AnalyticalResult_doc.i is in libopenturns-dev 1.9-5.
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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 | %feature("docstring") OT::AnalyticalResult
"Analytical result.
Available constructors:
AnalyticalResult(*designPoint, limitStateVariable, isInFailureSpace*)
Notes
-----
Structure created by the method run() of the :class:`~openturns.Analytical`
class and obtained thanks to its method getAnalyticalResult().
Parameters
----------
designPoint : sequence of float
Design point in the standard space resulting from the optimization
algorithm.
limitStateVariable : :class:`~openturns.Event`
Event of which the probability is calculated.
isInFailureSpace : bool
Indicates whether the origin of the standard space is in the failure space."
// ---------------------------------------------------------------------
%feature("docstring") OT::AnalyticalResult::drawHasoferReliabilityIndexSensitivity
"Draw the sensitivity of the Hasofer Reliability Index.
Parameters
----------
width : float, optional
Value to calculate the shift position of the :class:`~openturns.BarPlot`.
By default it is 1.0.
Returns
-------
graphCollection : sequence of two :class:`~openturns.Graph` containing a barplot
The first graph drawing the sensitivity of the Hasofer Reliability Index to
the parameters of the marginals of the probabilistic input vector.
The second graph drawing the sensitivity of the Hasofer Reliability Index
to the parameters of the dependence structure of the probabilistic input
vector."
// ---------------------------------------------------------------------
%feature("docstring") OT::AnalyticalResult::drawImportanceFactors
"Draw the importance factors.
Parameters
----------
type : int, optional
See :meth:`getImportanceFactors`
Returns
-------
graph : :class:`~openturns.Graph`
Pie of the importance factors of the probabilistic variables."
// ---------------------------------------------------------------------
%feature("docstring") OT::AnalyticalResult::getImportanceFactors
"Accessor to the importance factors.
Parameters
----------
type : int, optional
- When *ot.AnalyticalResult.ELLIPTICAL*, the importance factors
are evaluated as the square of the co-factors of the design point in the
elliptical space of the iso-probabilistic transformation (Y-space).
- When *ot.AnalyticalResult.CLASSICAL* they are evaluated as the square of
the co-factors of the design point in the U-space.
- When *ot.AnalyticalResult.PHYSICAL*, the importance factors are evaluated
as the square of the physical sensitivities.
By default *type = ot.AnalyticalResult.ELLIPTICAL*.
Notes
-----
- If the importance factors are evaluated as the square of the
co-factors of the design point in the U-space :
.. math::
\\\\alpha_i^2 = \\\\frac{(u_i^*)^2}
{\\\\beta_{HL}^2}
- If the importance factors are evaluated as the square of the co-factors of the
design point in the Y-space :
.. math::
\\\\alpha_i^2 = \\\\frac{(y_i^*)^2}
{\\\\|\\\\vect{y}^*\\\\|^2}
where
.. math::
Y^* = \\\\left(
\\\\begin{array}{c}
E^{-1}\\\\circ F_1(X_1^*) \\\\\\\\
E^{-1}\\\\circ F_2(X_2^*) \\\\\\\\
\\\\vdots \\\\\\\\
E^{-1}\\\\circ F_n(X_n^*)
\\\\end{array}
\\\\right)
with :math:`\\\\vect{X}^*` is the design point in the physical space and :math:`E`
the univariate standard CDF of the elliptical space. In the case where the
input distribution of :math:`\\\\vect{X}` has an elliptical copula
:math:`C_E`, then :math:`E` has the same type as :math:`C_E`.
In the case where the input distribution of :math:`\\\\vect{X}` has a copula
:math:`C` which is not elliptical, then :math:`E=\\\\Phi` where :math:`\\\\Phi`
is the CDF of the standard normal.
- If the importance factors are evaluated as the square of the physical sensitivities :
.. math::
\\\\alpha_i^2 = \\\\displaystyle \\\\frac{s_i^2}{{\\\\|s\\\\|}^2}
where
.. math::
s_i = \\\\displaystyle \\\\frac{\\\\partial \\\\beta}{\\\\partial x_i} (x^*)
= \\\\sum_{j=1}^n \\\\frac{\\\\partial \\\\beta}{\\\\partial u_i} \\\\frac{\\\\partial u_j}{\\\\partial x_i} (x^*)
Returns
-------
factors : :class:`~openturns.PointWithDescription`
Sequence containing the importance factors with a description for each
component."
// ---------------------------------------------------------------------
%feature("docstring") OT::AnalyticalResult::getOptimizationResult
"Accessor to the result of the optimization problem.
Returns
-------
result : :class:`~openturns.OptimizationResult`
Contains the design point in the standard space and information concerning
the convergence of the optimization algorithm."
// ---------------------------------------------------------------------
%feature("docstring") OT::AnalyticalResult::setOptimizationResult
"Accessor to the result of the optimization problem.
Parameters
----------
result : :class:`~openturns.OptimizationResult`
Contains the design point in the standard space and information concerning
the convergence of the optimization algorithm."
// ---------------------------------------------------------------------
%feature("docstring") OT::AnalyticalResult::getHasoferReliabilityIndex
"Accessor to the Hasofer Reliability Index.
Returns
-------
index : float
Hasofer Reliability Index which is the distance of the design point from
the origin of the standard space :math:`\\\\beta_{HL}=||\\\\vect{u}^*||`."
// ---------------------------------------------------------------------
%feature("docstring") OT::AnalyticalResult::getHasoferReliabilityIndexSensitivity
"Accessor to the sensitivities of the Hasofer Reliability Index.
Returns
-------
sensitivity : :class:`~openturns.PointWithDescription`
Sequence containing the sensitivities of the Hasofer Reliability Index to
the parameters of the probabilistic input vector (marginals and dependence
structure) with a description for each component."
// ---------------------------------------------------------------------
%feature("docstring") OT::AnalyticalResult::getLimitStateVariable
"Accessor to the event of which the probability is calculated.
Returns
-------
limitStateVariable : :class:`~openturns.Event`
Event of which the probability is calculated."
// ---------------------------------------------------------------------
%feature("docstring") OT::AnalyticalResult::getMeanPointInStandardEventDomain
"Accessor to the mean point in the standard event domain.
Returns
-------
meanPoint : :class:`~openturns.Point`
Mean point of the standard space distribution restricted to the event
domain:
:math:`\\\\displaystyle \\\\frac{1}{E_1(-\\\\beta)}\\\\int_{\\\\beta}^{\\\\infty} u_1 p_1(u_1)\\\\di{u_1}`
where :math:`E_1` is the spheric univariate distribution of the standard
space and :math:`\\\\beta` the reliability index."
// ---------------------------------------------------------------------
%feature("docstring") OT::AnalyticalResult::setMeanPointInStandardEventDomain
"Accessor to the mean point in the standard event domain.
Parameters
----------
meanPoint : sequence of float
Mean point of the standard space distribution restricted to the event
domain:
:math:`\\\\displaystyle \\\\frac{1}{E_1(-\\\\beta)}\\\\int_{\\\\beta}^{\\\\infty} u_1 p_1(u_1)\\\\di{u_1}`
where :math:`E_1` is the spheric univariate distribution of the standard
space and :math:`\\\\beta` the reliability index."
// ---------------------------------------------------------------------
%feature("docstring") OT::AnalyticalResult::getPhysicalSpaceDesignPoint
"Accessor to the design point in the physical space.
Returns
-------
designPoint : :class:`~openturns.Point`
Design point in the physical space resulting from the optimization
algorithm."
// ---------------------------------------------------------------------
%feature("docstring") OT::AnalyticalResult::getStandardSpaceDesignPoint
"Accessor to the design point in the standard space.
Returns
-------
designPoint : :class:`~openturns.Point`
Design point in the standard space resulting from the optimization
algorithm."
// ---------------------------------------------------------------------
%feature("docstring") OT::AnalyticalResult::setStandardSpaceDesignPoint
"Accessor to the design point in the standard space.
Parameters
----------
designPoint : sequence of float
Design point in the standard space resulting from the optimization
algorithm."
// ---------------------------------------------------------------------
%feature("docstring") OT::AnalyticalResult::getIsStandardPointOriginInFailureSpace
"Accessor to know if the standard point origin is in the failure space.
Returns
-------
isInFailureSpace : bool
Indicates whether the origin of the standard space is in the failure space."
// ---------------------------------------------------------------------
%feature("docstring") OT::AnalyticalResult::setIsStandardPointOriginInFailureSpace
"Accessor to specify if the standard point origin is in the failure space.
Parameters
----------
isInFailureSpace : bool
Indicates whether the origin of the standard space is in the failure space."
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