This file is indexed.

/usr/lib/python2.7/dist-packages/openturns/analytical.py is in python-openturns 1.5-7build2.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  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
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
# This file was automatically generated by SWIG (http://www.swig.org).
# Version 2.0.12
#
# Do not make changes to this file unless you know what you are doing--modify
# the SWIG interface file instead.




"""
Analytical uncertainty propagation algorithms.
"""


from sys import version_info
if version_info >= (2,6,0):
    def swig_import_helper():
        from os.path import dirname
        import imp
        fp = None
        try:
            fp, pathname, description = imp.find_module('_analytical', [dirname(__file__)])
        except ImportError:
            import _analytical
            return _analytical
        if fp is not None:
            try:
                _mod = imp.load_module('_analytical', fp, pathname, description)
            finally:
                fp.close()
            return _mod
    _analytical = swig_import_helper()
    del swig_import_helper
else:
    import _analytical
del version_info
try:
    _swig_property = property
except NameError:
    pass # Python < 2.2 doesn't have 'property'.
def _swig_setattr_nondynamic(self,class_type,name,value,static=1):
    if (name == "thisown"): return self.this.own(value)
    if (name == "this"):
        if type(value).__name__ == 'SwigPyObject':
            self.__dict__[name] = value
            return
    method = class_type.__swig_setmethods__.get(name,None)
    if method: return method(self,value)
    if (not static):
        self.__dict__[name] = value
    else:
        raise AttributeError("You cannot add attributes to %s" % self)

def _swig_setattr(self,class_type,name,value):
    return _swig_setattr_nondynamic(self,class_type,name,value,0)

def _swig_getattr(self,class_type,name):
    if (name == "thisown"): return self.this.own()
    method = class_type.__swig_getmethods__.get(name,None)
    if method: return method(self)
    raise AttributeError(name)

def _swig_repr(self):
    try: strthis = "proxy of " + self.this.__repr__()
    except: strthis = ""
    return "<%s.%s; %s >" % (self.__class__.__module__, self.__class__.__name__, strthis,)

try:
    _object = object
    _newclass = 1
except AttributeError:
    class _object : pass
    _newclass = 0


class SwigPyIterator(_object):
    __swig_setmethods__ = {}
    __setattr__ = lambda self, name, value: _swig_setattr(self, SwigPyIterator, name, value)
    __swig_getmethods__ = {}
    __getattr__ = lambda self, name: _swig_getattr(self, SwigPyIterator, name)
    def __init__(self, *args, **kwargs): raise AttributeError("No constructor defined - class is abstract")
    __repr__ = _swig_repr
    __swig_destroy__ = _analytical.delete_SwigPyIterator
    __del__ = lambda self : None;
    def value(self): return _analytical.SwigPyIterator_value(self)
    def incr(self, n=1): return _analytical.SwigPyIterator_incr(self, n)
    def decr(self, n=1): return _analytical.SwigPyIterator_decr(self, n)
    def distance(self, *args): return _analytical.SwigPyIterator_distance(self, *args)
    def equal(self, *args): return _analytical.SwigPyIterator_equal(self, *args)
    def copy(self): return _analytical.SwigPyIterator_copy(self)
    def next(self): return _analytical.SwigPyIterator_next(self)
    def __next__(self): return _analytical.SwigPyIterator___next__(self)
    def previous(self): return _analytical.SwigPyIterator_previous(self)
    def advance(self, *args): return _analytical.SwigPyIterator_advance(self, *args)
    def __eq__(self, *args): return _analytical.SwigPyIterator___eq__(self, *args)
    def __ne__(self, *args): return _analytical.SwigPyIterator___ne__(self, *args)
    def __iadd__(self, *args): return _analytical.SwigPyIterator___iadd__(self, *args)
    def __isub__(self, *args): return _analytical.SwigPyIterator___isub__(self, *args)
    def __add__(self, *args): return _analytical.SwigPyIterator___add__(self, *args)
    def __sub__(self, *args): return _analytical.SwigPyIterator___sub__(self, *args)
    def __iter__(self): return self
SwigPyIterator_swigregister = _analytical.SwigPyIterator_swigregister
SwigPyIterator_swigregister(SwigPyIterator)

GCC_VERSION = _analytical.GCC_VERSION
class TestFailed:
    """TestFailed is used to raise an uniform exception in tests."""

    __type = "TestFailed"

    def __init__(self, reason=""):
        self.reason = reason

    def type(self):
        return TestFailed.__type

    def what(self):
        return self.reason

    def __str__(self):
        return TestFailed.__type + ": " + self.reason

    def __lshift__(self, ch):
        self.reason += ch
        return self

import openturns.base
import openturns.common
import openturns.wrapper
import openturns.typ
import openturns.statistics
import openturns.graph
import openturns.func
import openturns.geom
import openturns.diff
import openturns.optim
import openturns.solver
import openturns.algo
import openturns.experiment
import openturns.model_copula
import openturns.metamodel
import openturns.weightedexperiment
import openturns.orthogonalbasis
import openturns.randomvector
import openturns.transformation
class AnalyticalResult(openturns.common.PersistentObject):
    """
    Analytical result.

    Available constructors:
        AnalyticalResult()

        AnalyticalResult(*designPoint, limitStateVariable, isInFailureSpace*)

    Notes
    -----
    Structure created by the method run() of a :class:`~openturns.Analytical`
    and obtained thanks to the method getAnalyticalResult().

    Parameters
    ----------
    designPoint : float sequence
        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.
    """
    __swig_setmethods__ = {}
    for _s in [openturns.common.PersistentObject]: __swig_setmethods__.update(getattr(_s,'__swig_setmethods__',{}))
    __setattr__ = lambda self, name, value: _swig_setattr(self, AnalyticalResult, name, value)
    __swig_getmethods__ = {}
    for _s in [openturns.common.PersistentObject]: __swig_getmethods__.update(getattr(_s,'__swig_getmethods__',{}))
    __getattr__ = lambda self, name: _swig_getattr(self, AnalyticalResult, name)
    def getClassName(self):
        """
        Accessor to the object's name.

        Returns
        -------
        class_name : str
            The object class name (`object.__class__.__name__`).
        """
        return _analytical.AnalyticalResult_getClassName(self)

    ELLIPTICAL = _analytical.AnalyticalResult_ELLIPTICAL
    CLASSICAL = _analytical.AnalyticalResult_CLASSICAL
    PHYSICAL = _analytical.AnalyticalResult_PHYSICAL
    def getStandardSpaceDesignPoint(self):
        """
        Accessor to the design point in the standard space.

        Returns
        -------
        designPoint : float sequence
            Design point in the standard space resulting from the optimization
            algorithm.
        """
        return _analytical.AnalyticalResult_getStandardSpaceDesignPoint(self)

    def setStandardSpaceDesignPoint(self, *args):
        """
        Accessor to the design point in the standard space.

        Returns
        -------
        designPoint : float sequence
            Design point in the standard space resulting from the optimization
            algorithm.
        """
        return _analytical.AnalyticalResult_setStandardSpaceDesignPoint(self, *args)

    def getPhysicalSpaceDesignPoint(self):
        """
        Accessor to the design point in the physical space.

        Returns
        -------
        designPoint : float sequence
            Design point in the physical space resulting from the optimization
            algorithm.
        """
        return _analytical.AnalyticalResult_getPhysicalSpaceDesignPoint(self)

    def getLimitStateVariable(self):
        """
        Accessor to the event of which the probability is calculated.

        Returns
        -------
        limitStateVariable : :class:`~openturns.Event`
            Event of which the probability is calculated.
        """
        return _analytical.AnalyticalResult_getLimitStateVariable(self)

    def getIsStandardPointOriginInFailureSpace(self):
        """
        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.
        """
        return _analytical.AnalyticalResult_getIsStandardPointOriginInFailureSpace(self)

    def setIsStandardPointOriginInFailureSpace(self, *args):
        """
        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.
        """
        return _analytical.AnalyticalResult_setIsStandardPointOriginInFailureSpace(self, *args)

    def getMeanPointInStandardEventDomain(self):
        """
        Accessor to the mean point in the standard event domain.

        Returns
        -------
        meanPoint : float sequence
            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)du_1`
            where :math:`E_1` is the spheric univariate distribution of the standard
            space and :math:`\\beta` the reliability index.
        """
        return _analytical.AnalyticalResult_getMeanPointInStandardEventDomain(self)

    def setMeanPointInStandardEventDomain(self, *args):
        """
        Accessor to the mean point in the standard event domain.

        Parameters
        ----------
        meanPoint : float sequence
            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)du_1`
            where :math:`E_1` is the spheric univariate distribution of the standard
            space and :math:`\\beta` the reliability index.
        """
        return _analytical.AnalyticalResult_setMeanPointInStandardEventDomain(self, *args)

    def getImportanceFactors(self, *args):
        """
        Accessor to the importance factors.

        Parameters
        ----------
        type : int, optional
            By default, the importance factors are evaluated as the square of the
            co-factors of the design point in the U-space.
            When `AnalyticalResult.CLASSICAL` they are evaluated as the square of the co-factors
            of the design point in the Y-space.
            When `AnalyticalResult.PHYSICAL`, the importance factors are evaluated
            as the square of the physical sensitivities.

        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 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 : float sequence with description for each component
            List of the importance factors.
        """
        return _analytical.AnalyticalResult_getImportanceFactors(self, *args)

    def drawImportanceFactors(self, *args):
        """
        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.
        """
        return _analytical.AnalyticalResult_drawImportanceFactors(self, *args)

    def getHasoferReliabilityIndex(self):
        """
        Accessor to the Hasofer Reliability Index.

        Returns
        -------
        index : float
            Hasofer Reliability Index.
        """
        return _analytical.AnalyticalResult_getHasoferReliabilityIndex(self)

    def getHasoferReliabilityIndexSensitivity(self):
        """
        Accessor to the sensitivities of the Hasofer Reliability Index.

        Returns
        -------
        sensitivity : :class:`~openturns.Sensitivity`
            Sensitivities of the Hasofer Reliability Index to the parameters of the
            probabilistic input vector (marginals and dependence structure).
        """
        return _analytical.AnalyticalResult_getHasoferReliabilityIndexSensitivity(self)

    def getOptimizationResult(self):
        """
        Accessor to the result of the optimization problem.

        Returns
        -------
        result : :class:`~openturns.NearestPointAlgorithmImplementationResult`
            Contains the design point in the standard space and information concerning
            the convergence of the optimization algorithm.
        """
        return _analytical.AnalyticalResult_getOptimizationResult(self)

    def setOptimizationResult(self, *args):
        """
        Accessor to the result of the optimization problem.

        Returns
        -------
        result : :class:`~openturns.NearestPointAlgorithmImplementationResult`
            Contains the design point in the standard space and information concerning
            the convergence of the optimization algorithm.
        """
        return _analytical.AnalyticalResult_setOptimizationResult(self, *args)

    def drawHasoferReliabilityIndexSensitivity(self, *args):
        """
        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 : list 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.
        """
        return _analytical.AnalyticalResult_drawHasoferReliabilityIndexSensitivity(self, *args)

    def __repr__(self): return _analytical.AnalyticalResult___repr__(self)
    def __init__(self, *args): 
        this = _analytical.new_AnalyticalResult(*args)
        try: self.this.append(this)
        except: self.this = this
    __swig_destroy__ = _analytical.delete_AnalyticalResult
    __del__ = lambda self : None;
AnalyticalResult_swigregister = _analytical.AnalyticalResult_swigregister
AnalyticalResult_swigregister(AnalyticalResult)

class Analytical(openturns.common.PersistentObject):
    """
    Base class to find the design point.

    Available constructors:
        Analytical(*nearestPointAlgorithm, event, physicalStartingPoint*)

    Parameters
    ----------
    nearestPointAlgorithm : :class:`~openturns.NearestPointAlgorithm`
        Optimization algorithm used to research the design point.
    event : :class:`~openturns.Event`
        Failure event.
    physicalStartingPoint : float sequence
        Starting point of the optimization algorithm, declared in the physical
        space.

    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`:

    .. math::

        P_f = \\int_{g(\\vect{X},\\vect{d})\\le 0}f_\\vect{X}(\\vect{x})d\\vect{x}

    may be evaluated with the :class:`~openturns.FORM` or :class:`~openturns.SORM`
    methods.

    In order to evaluate an approximation of :math:`P_f`, these analytical methods
    uses the Nataf isoprobabilistic transformation which maps the probabilistic
    model in terms of :math:`\\vect{X}` onto an equivalent model in terms of
    :math:`n` independant standard normal random :math:`\\vect{U}`. In that new
    :math:`\\vect{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\\}`.

    These analytical methods rely on the assumption that most of the contribution
    to :math:`P_f` comes from points located in the vicinity of a particular point
    :math:`P^*`, the **design point**, defined in the :math:`\\vect{u}`-space as the
    point located on the limit state surface and of maximal likelihood.
    Given the probabilistic caracteristics of the :math:`\\vect{u}`-space,
    :math:`P^*` has a geometrical interpretation: it is the point located on the
    event boundary and at minimal distance from the center of the
    :math:`\\vect{u}`-space. Thus, the design point :math:`P^*` is the result of a
    constrained optimization problem.

    See also
    --------
    FORM, SORM, StrongMaximumTest

    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 a NearestPoint algorithm
    >>> myCobyla = ot.Cobyla()
    >>> myAlgo = ot.Analytical(myCobyla, myEvent, [50., 1., 10., 5.])
    """
    __swig_setmethods__ = {}
    for _s in [openturns.common.PersistentObject]: __swig_setmethods__.update(getattr(_s,'__swig_setmethods__',{}))
    __setattr__ = lambda self, name, value: _swig_setattr(self, Analytical, name, value)
    __swig_getmethods__ = {}
    for _s in [openturns.common.PersistentObject]: __swig_getmethods__.update(getattr(_s,'__swig_getmethods__',{}))
    __getattr__ = lambda self, name: _swig_getattr(self, Analytical, name)
    def getClassName(self):
        """
        Accessor to the object's name.

        Returns
        -------
        class_name : str
            The object class name (`object.__class__.__name__`).
        """
        return _analytical.Analytical_getClassName(self)

    def getPhysicalStartingPoint(self):
        """
        Accessor to the starting point of the optimization algorithm.

        Returns
        -------
        point : float sequence
            Starting point of the optimization algorithm, declared in the physical
            space.
        """
        return _analytical.Analytical_getPhysicalStartingPoint(self)

    def setPhysicalStartingPoint(self, *args):
        """
        Accessor to the starting point of the optimization algorithm.

        Parameters
        ----------
        point : float sequence
            Starting point of the optimization algorithm, declared in the physical
            space.
        """
        return _analytical.Analytical_setPhysicalStartingPoint(self, *args)

    def getEvent(self):
        """
        Accessor to the event of which the probability is calculated.

        Returns
        -------
        event : :class:`~openturns.Event`
            Event of which the probability is calculated.
        """
        return _analytical.Analytical_getEvent(self)

    def setEvent(self, *args):
        """
        Accessor to the event of which the probability is calculated.

        Parameters
        ----------
        event : :class:`~openturns.Event`
            Event of which the probability is calculated.
        """
        return _analytical.Analytical_setEvent(self, *args)

    def getNearestPointAlgorithm(self):
        """
        Accessor to the optimization algorithm used to find the design point.

        Returns
        -------
        algorithm : :class:`~openturns.NearestPointAlgorithm`
             Optimization algorithm used to research the design point.
        """
        return _analytical.Analytical_getNearestPointAlgorithm(self)

    def setNearestPointAlgorithm(self, *args):
        """
        Accessor to the optimization algorithm used to find the design point.

        Parameters
        ----------
        algorithm : :class:`~openturns.NearestPointAlgorithm`
             Optimization algorithm used to research the design point.
        """
        return _analytical.Analytical_setNearestPointAlgorithm(self, *args)

    def getAnalyticalResult(self):
        """
        Accessor to the result.

        Returns
        -------
        result : :class:`~openturns.AnalyticalResult`
            Result structure which contains the results of the optimisation problem.
        """
        return _analytical.Analytical_getAnalyticalResult(self)

    def __repr__(self): return _analytical.Analytical___repr__(self)
    def run(self):
        """
        Perform the research of the design point.

        Notes
        -----
        Performs the research of the design point and creates a
        :class:`~openturns.AnalyticalResult`, the structure result which is
        accessible with the method getAnalyticalResult.

        See also
        --------
        getAnalyticalResult
        """
        return _analytical.Analytical_run(self)

    def __init__(self, *args): 
        this = _analytical.new_Analytical(*args)
        try: self.this.append(this)
        except: self.this = this
    __swig_destroy__ = _analytical.delete_Analytical
    __del__ = lambda self : None;
Analytical_swigregister = _analytical.Analytical_swigregister
Analytical_swigregister(Analytical)

class FORMResult(AnalyticalResult):
    __swig_setmethods__ = {}
    for _s in [AnalyticalResult]: __swig_setmethods__.update(getattr(_s,'__swig_setmethods__',{}))
    __setattr__ = lambda self, name, value: _swig_setattr(self, FORMResult, name, value)
    __swig_getmethods__ = {}
    for _s in [AnalyticalResult]: __swig_getmethods__.update(getattr(_s,'__swig_getmethods__',{}))
    __getattr__ = lambda self, name: _swig_getattr(self, FORMResult, name)
    def getClassName(self):
        """
        Accessor to the object's name.

        Returns
        -------
        class_name : str
            The object class name (`object.__class__.__name__`).
        """
        return _analytical.FORMResult_getClassName(self)

    def getEventProbability(self): return _analytical.FORMResult_getEventProbability(self)
    def getGeneralisedReliabilityIndex(self): return _analytical.FORMResult_getGeneralisedReliabilityIndex(self)
    def getEventProbabilitySensitivity(self): return _analytical.FORMResult_getEventProbabilitySensitivity(self)
    def drawEventProbabilitySensitivity(self, *args): return _analytical.FORMResult_drawEventProbabilitySensitivity(self, *args)
    def __repr__(self): return _analytical.FORMResult___repr__(self)
    def __init__(self, *args): 
        this = _analytical.new_FORMResult(*args)
        try: self.this.append(this)
        except: self.this = this
    __swig_destroy__ = _analytical.delete_FORMResult
    __del__ = lambda self : None;
FORMResult_swigregister = _analytical.FORMResult_swigregister
FORMResult_swigregister(FORMResult)

class FORM(Analytical):
    __swig_setmethods__ = {}
    for _s in [Analytical]: __swig_setmethods__.update(getattr(_s,'__swig_setmethods__',{}))
    __setattr__ = lambda self, name, value: _swig_setattr(self, FORM, name, value)
    __swig_getmethods__ = {}
    for _s in [Analytical]: __swig_getmethods__.update(getattr(_s,'__swig_getmethods__',{}))
    __getattr__ = lambda self, name: _swig_getattr(self, FORM, name)
    def getClassName(self):
        """
        Accessor to the object's name.

        Returns
        -------
        class_name : str
            The object class name (`object.__class__.__name__`).
        """
        return _analytical.FORM_getClassName(self)

    def getResult(self): return _analytical.FORM_getResult(self)
    def setResult(self, *args): return _analytical.FORM_setResult(self, *args)
    def __repr__(self): return _analytical.FORM___repr__(self)
    def run(self):
        """
        Perform the research of the design point.

        Notes
        -----
        Performs the research of the design point and creates a
        :class:`~openturns.AnalyticalResult`, the structure result which is
        accessible with the method getAnalyticalResult.

        See also
        --------
        getAnalyticalResult
        """
        return _analytical.FORM_run(self)

    def __init__(self, *args): 
        this = _analytical.new_FORM(*args)
        try: self.this.append(this)
        except: self.this = this
    __swig_destroy__ = _analytical.delete_FORM
    __del__ = lambda self : None;
FORM_swigregister = _analytical.FORM_swigregister
FORM_swigregister(FORM)

class SORMResult(AnalyticalResult):
    __swig_setmethods__ = {}
    for _s in [AnalyticalResult]: __swig_setmethods__.update(getattr(_s,'__swig_setmethods__',{}))
    __setattr__ = lambda self, name, value: _swig_setattr(self, SORMResult, name, value)
    __swig_getmethods__ = {}
    for _s in [AnalyticalResult]: __swig_getmethods__.update(getattr(_s,'__swig_getmethods__',{}))
    __getattr__ = lambda self, name: _swig_getattr(self, SORMResult, name)
    def getClassName(self):
        """
        Accessor to the object's name.

        Returns
        -------
        class_name : str
            The object class name (`object.__class__.__name__`).
        """
        return _analytical.SORMResult_getClassName(self)

    def getEventProbabilityBreitung(self): return _analytical.SORMResult_getEventProbabilityBreitung(self)
    def getEventProbabilityHohenBichler(self): return _analytical.SORMResult_getEventProbabilityHohenBichler(self)
    def getEventProbabilityTvedt(self): return _analytical.SORMResult_getEventProbabilityTvedt(self)
    def getGeneralisedReliabilityIndexBreitung(self): return _analytical.SORMResult_getGeneralisedReliabilityIndexBreitung(self)
    def getGeneralisedReliabilityIndexHohenBichler(self): return _analytical.SORMResult_getGeneralisedReliabilityIndexHohenBichler(self)
    def getGeneralisedReliabilityIndexTvedt(self): return _analytical.SORMResult_getGeneralisedReliabilityIndexTvedt(self)
    def getSortedCurvatures(self): return _analytical.SORMResult_getSortedCurvatures(self)
    def __repr__(self): return _analytical.SORMResult___repr__(self)
    def __str__(self, offset=""): return _analytical.SORMResult___str__(self, offset)
    def __init__(self, *args): 
        this = _analytical.new_SORMResult(*args)
        try: self.this.append(this)
        except: self.this = this
    __swig_destroy__ = _analytical.delete_SORMResult
    __del__ = lambda self : None;
SORMResult_swigregister = _analytical.SORMResult_swigregister
SORMResult_swigregister(SORMResult)

class SORM(Analytical):
    __swig_setmethods__ = {}
    for _s in [Analytical]: __swig_setmethods__.update(getattr(_s,'__swig_setmethods__',{}))
    __setattr__ = lambda self, name, value: _swig_setattr(self, SORM, name, value)
    __swig_getmethods__ = {}
    for _s in [Analytical]: __swig_getmethods__.update(getattr(_s,'__swig_getmethods__',{}))
    __getattr__ = lambda self, name: _swig_getattr(self, SORM, name)
    def getClassName(self):
        """
        Accessor to the object's name.

        Returns
        -------
        class_name : str
            The object class name (`object.__class__.__name__`).
        """
        return _analytical.SORM_getClassName(self)

    def getResult(self): return _analytical.SORM_getResult(self)
    def setResult(self, *args): return _analytical.SORM_setResult(self, *args)
    def __repr__(self): return _analytical.SORM___repr__(self)
    def run(self):
        """
        Perform the research of the design point.

        Notes
        -----
        Performs the research of the design point and creates a
        :class:`~openturns.AnalyticalResult`, the structure result which is
        accessible with the method getAnalyticalResult.

        See also
        --------
        getAnalyticalResult
        """
        return _analytical.SORM_run(self)

    def __init__(self, *args): 
        this = _analytical.new_SORM(*args)
        try: self.this.append(this)
        except: self.this = this
    __swig_destroy__ = _analytical.delete_SORM
    __del__ = lambda self : None;
SORM_swigregister = _analytical.SORM_swigregister
SORM_swigregister(SORM)

class StrongMaximumTest(openturns.common.PersistentObject):
    __swig_setmethods__ = {}
    for _s in [openturns.common.PersistentObject]: __swig_setmethods__.update(getattr(_s,'__swig_setmethods__',{}))
    __setattr__ = lambda self, name, value: _swig_setattr(self, StrongMaximumTest, name, value)
    __swig_getmethods__ = {}
    for _s in [openturns.common.PersistentObject]: __swig_getmethods__.update(getattr(_s,'__swig_getmethods__',{}))
    __getattr__ = lambda self, name: _swig_getattr(self, StrongMaximumTest, name)
    def getClassName(self):
        """
        Accessor to the object's name.

        Returns
        -------
        class_name : str
            The object class name (`object.__class__.__name__`).
        """
        return _analytical.StrongMaximumTest_getClassName(self)

    def getStandardSpaceDesignPoint(self): return _analytical.StrongMaximumTest_getStandardSpaceDesignPoint(self)
    def getEvent(self): return _analytical.StrongMaximumTest_getEvent(self)
    def getImportanceLevel(self): return _analytical.StrongMaximumTest_getImportanceLevel(self)
    def getAccuracyLevel(self): return _analytical.StrongMaximumTest_getAccuracyLevel(self)
    def getConfidenceLevel(self): return _analytical.StrongMaximumTest_getConfidenceLevel(self)
    def getDesignPointVicinity(self): return _analytical.StrongMaximumTest_getDesignPointVicinity(self)
    def getPointNumber(self): return _analytical.StrongMaximumTest_getPointNumber(self)
    def getDeltaEpsilon(self): return _analytical.StrongMaximumTest_getDeltaEpsilon(self)
    def run(self): return _analytical.StrongMaximumTest_run(self)
    def getNearDesignPointVerifyingEventPoints(self): return _analytical.StrongMaximumTest_getNearDesignPointVerifyingEventPoints(self)
    def getFarDesignPointVerifyingEventPoints(self): return _analytical.StrongMaximumTest_getFarDesignPointVerifyingEventPoints(self)
    def getNearDesignPointViolatingEventPoints(self): return _analytical.StrongMaximumTest_getNearDesignPointViolatingEventPoints(self)
    def getFarDesignPointViolatingEventPoints(self): return _analytical.StrongMaximumTest_getFarDesignPointViolatingEventPoints(self)
    def getNearDesignPointVerifyingEventValues(self): return _analytical.StrongMaximumTest_getNearDesignPointVerifyingEventValues(self)
    def getFarDesignPointVerifyingEventValues(self): return _analytical.StrongMaximumTest_getFarDesignPointVerifyingEventValues(self)
    def getNearDesignPointViolatingEventValues(self): return _analytical.StrongMaximumTest_getNearDesignPointViolatingEventValues(self)
    def getFarDesignPointViolatingEventValues(self): return _analytical.StrongMaximumTest_getFarDesignPointViolatingEventValues(self)
    def __repr__(self): return _analytical.StrongMaximumTest___repr__(self)
    def __init__(self, *args): 
        this = _analytical.new_StrongMaximumTest(*args)
        try: self.this.append(this)
        except: self.this = this
    __swig_destroy__ = _analytical.delete_StrongMaximumTest
    __del__ = lambda self : None;
StrongMaximumTest_swigregister = _analytical.StrongMaximumTest_swigregister
StrongMaximumTest_swigregister(StrongMaximumTest)

# This file is compatible with both classic and new-style classes.