Note

Click here to download the full example code

Empirical estimation of statistics¶

In this example, we want to empirically estimate statistics associated with the range of the Mission discipline of the Sobieski’s SSBJ problem.

For simplification, we use uniform distributions for the discipline inputs based on the bounds of the design parameters.

from __future__ import division, unicode_literals

from gemseo.api import configure_logger, create_discipline, create_scenario
from gemseo.problems.sobieski.core import SobieskiProblem
from gemseo.uncertainty.api import create_statistics

configure_logger()

Out:

<RootLogger root (INFO)>

Create the dataset¶

First of all, we create the dataset. For that, we instantiate the discipline SobieskiMission of the Sobieski’s SSBJ problem which is known to GEMSEO. We update the cache policy so as to cache all data in memory.

discipline = create_discipline("SobieskiMission")
discipline.set_cache_policy(discipline.MEMORY_FULL_CACHE)

Then, we load the design space of the Sobieski’s SSBJ problem by means of the method SobieskiProblem.read_design_space() and DesignSpace.filter() the inputs of the discipline SobieskiMission.

parameter_space = SobieskiProblem().read_design_space()
parameter_space.filter(discipline.get_input_data_names())

Out:

<gemseo.algos.design_space.DesignSpace object at 0x7f3b58036d30>

Then, we sample the discipline over this design space by means of a DOEScenario executed with a Monte Carlo algorithm and 100 samples.

scenario = create_scenario(
    [discipline], "DisciplinaryOpt", "y_4", parameter_space, scenario_type="DOE"
)
scenario.execute({"algo": "OT_MONTE_CARLO", "n_samples": 100})

Out:

    INFO - 14:41:26:
    INFO - 14:41:26: *** Start DOE Scenario execution ***
    INFO - 14:41:26: DOEScenario
    INFO - 14:41:26:    Disciplines: SobieskiMission
    INFO - 14:41:26:    MDOFormulation: DisciplinaryOpt
    INFO - 14:41:26:    Algorithm: OT_MONTE_CARLO
    INFO - 14:41:26: Optimization problem:
    INFO - 14:41:26:    Minimize: y_4(x_shared, y_14, y_24, y_34)
    INFO - 14:41:26:    With respect to: x_shared, y_14, y_24, y_34
    INFO - 14:41:26: Generation of OT_MONTE_CARLO DOE with OpenTurns
    INFO - 14:41:26: DOE sampling:   0%|          | 0/100 [00:00<?, ?it]
   ERROR - 14:41:26: Failed to evaluate function y_4
   ERROR - 14:41:26: Problem with evaluation of sample :[0.04202001 0.85228014 0.71690529 0.88633775 0.38606961 0.80108811
   ERROR - 14:41:26:  0.29051756 0.97472276 0.32130349 0.18516387] result is not taken into account in DOE.
   ERROR - 14:41:26: Traceback (most recent call last):
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/doe/doe_lib.py", line 349, in evaluate_samples
   ERROR - 14:41:26:     self.problem.evaluate_functions(x_norm, eval_jac)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/opt_problem.py", line 910, in evaluate_functions
   ERROR - 14:41:26:     outputs[func.name] = func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 122, in _func
   ERROR - 14:41:26:     value = self.__orig_func(xn_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/norm_function.py", line 93, in _func
   ERROR - 14:41:26:     return self.__orig_func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 121, in _func
   ERROR - 14:41:26:     obj_allx_val = self.__out_x_func(x_of_disc)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/make_function.py", line 103, in _func
   ERROR - 14:41:26:     computed_values = self.__mdo_function.discipline.execute(data)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/discipline.py", line 830, in execute
   ERROR - 14:41:26:     self._run()
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/wrappers.py", line 96, in _run
   ERROR - 14:41:26:     y_4 = self.sobieski_problem.blackbox_mission(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core.py", line 729, in blackbox_mission
   ERROR - 14:41:26:     return self.sobieski_mission.blackbox_mission(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core_mission.py", line 272, in blackbox_mission
   ERROR - 14:41:26:     y_4[0] = self.compute_range(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core_mission.py", line 157, in compute_range
   ERROR - 14:41:26:     return ((x_shared[2] * y_24[0]) * 661.0 * sqrt_theta / y_34[0]) * self.math.log(
   ERROR - 14:41:26: ValueError: math domain error
   ERROR - 14:41:26:
   ERROR - 14:41:26: Failed to evaluate function y_4
   ERROR - 14:41:26: Problem with evaluation of sample :[0.74844008 0.14099705 0.91790447 0.42207073 0.41108155 0.53920648
   ERROR - 14:41:26:  0.02652421 0.98955432 0.82365121 0.37878286] result is not taken into account in DOE.
   ERROR - 14:41:26: Traceback (most recent call last):
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/doe/doe_lib.py", line 349, in evaluate_samples
   ERROR - 14:41:26:     self.problem.evaluate_functions(x_norm, eval_jac)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/opt_problem.py", line 910, in evaluate_functions
   ERROR - 14:41:26:     outputs[func.name] = func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 122, in _func
   ERROR - 14:41:26:     value = self.__orig_func(xn_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/norm_function.py", line 93, in _func
   ERROR - 14:41:26:     return self.__orig_func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 121, in _func
   ERROR - 14:41:26:     obj_allx_val = self.__out_x_func(x_of_disc)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/make_function.py", line 103, in _func
   ERROR - 14:41:26:     computed_values = self.__mdo_function.discipline.execute(data)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/discipline.py", line 830, in execute
   ERROR - 14:41:26:     self._run()
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/wrappers.py", line 96, in _run
   ERROR - 14:41:26:     y_4 = self.sobieski_problem.blackbox_mission(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core.py", line 729, in blackbox_mission
   ERROR - 14:41:26:     return self.sobieski_mission.blackbox_mission(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core_mission.py", line 272, in blackbox_mission
   ERROR - 14:41:26:     y_4[0] = self.compute_range(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core_mission.py", line 157, in compute_range
   ERROR - 14:41:26:     return ((x_shared[2] * y_24[0]) * 661.0 * sqrt_theta / y_34[0]) * self.math.log(
   ERROR - 14:41:26: ValueError: math domain error
   ERROR - 14:41:26:
   ERROR - 14:41:26: Failed to evaluate function y_4
   ERROR - 14:41:26: Problem with evaluation of sample :[0.8665374  0.56122665 0.68417981 0.61383853 0.08187036 0.80519389
   ERROR - 14:41:26:  0.16149925 0.96544834 0.97133343 0.42997454] result is not taken into account in DOE.
   ERROR - 14:41:26: Traceback (most recent call last):
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/doe/doe_lib.py", line 349, in evaluate_samples
   ERROR - 14:41:26:     self.problem.evaluate_functions(x_norm, eval_jac)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/opt_problem.py", line 910, in evaluate_functions
   ERROR - 14:41:26:     outputs[func.name] = func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 122, in _func
   ERROR - 14:41:26:     value = self.__orig_func(xn_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/norm_function.py", line 93, in _func
   ERROR - 14:41:26:     return self.__orig_func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 121, in _func
   ERROR - 14:41:26:     obj_allx_val = self.__out_x_func(x_of_disc)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/make_function.py", line 103, in _func
   ERROR - 14:41:26:     computed_values = self.__mdo_function.discipline.execute(data)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/discipline.py", line 830, in execute
   ERROR - 14:41:26:     self._run()
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/wrappers.py", line 96, in _run
   ERROR - 14:41:26:     y_4 = self.sobieski_problem.blackbox_mission(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core.py", line 729, in blackbox_mission
   ERROR - 14:41:26:     return self.sobieski_mission.blackbox_mission(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core_mission.py", line 272, in blackbox_mission
   ERROR - 14:41:26:     y_4[0] = self.compute_range(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core_mission.py", line 157, in compute_range
   ERROR - 14:41:26:     return ((x_shared[2] * y_24[0]) * 661.0 * sqrt_theta / y_34[0]) * self.math.log(
   ERROR - 14:41:26: ValueError: math domain error
   ERROR - 14:41:26:
   ERROR - 14:41:26: Failed to evaluate function y_4
   ERROR - 14:41:26: Problem with evaluation of sample :[0.49906918 0.90219506 0.71877658 0.69302534 0.79907863 0.76790717
   ERROR - 14:41:26:  0.02750403 0.68315107 0.59863483 0.98960888] result is not taken into account in DOE.
   ERROR - 14:41:26: Traceback (most recent call last):
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/doe/doe_lib.py", line 349, in evaluate_samples
   ERROR - 14:41:26:     self.problem.evaluate_functions(x_norm, eval_jac)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/opt_problem.py", line 910, in evaluate_functions
   ERROR - 14:41:26:     outputs[func.name] = func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 122, in _func
   ERROR - 14:41:26:     value = self.__orig_func(xn_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/norm_function.py", line 93, in _func
   ERROR - 14:41:26:     return self.__orig_func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 121, in _func
   ERROR - 14:41:26:     obj_allx_val = self.__out_x_func(x_of_disc)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/make_function.py", line 103, in _func
   ERROR - 14:41:26:     computed_values = self.__mdo_function.discipline.execute(data)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/discipline.py", line 830, in execute
   ERROR - 14:41:26:     self._run()
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/wrappers.py", line 96, in _run
   ERROR - 14:41:26:     y_4 = self.sobieski_problem.blackbox_mission(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core.py", line 729, in blackbox_mission
   ERROR - 14:41:26:     return self.sobieski_mission.blackbox_mission(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core_mission.py", line 272, in blackbox_mission
   ERROR - 14:41:26:     y_4[0] = self.compute_range(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core_mission.py", line 157, in compute_range
   ERROR - 14:41:26:     return ((x_shared[2] * y_24[0]) * 661.0 * sqrt_theta / y_34[0]) * self.math.log(
   ERROR - 14:41:26: ValueError: math domain error
   ERROR - 14:41:26:
   ERROR - 14:41:26: Failed to evaluate function y_4
   ERROR - 14:41:26: Problem with evaluation of sample :[0.12528728 0.72185944 0.38040214 0.31980013 0.86315212 0.92514122
   ERROR - 14:41:26:  0.23786315 0.85612668 0.98944314 0.03632122] result is not taken into account in DOE.
   ERROR - 14:41:26: Traceback (most recent call last):
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/doe/doe_lib.py", line 349, in evaluate_samples
   ERROR - 14:41:26:     self.problem.evaluate_functions(x_norm, eval_jac)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/opt_problem.py", line 910, in evaluate_functions
   ERROR - 14:41:26:     outputs[func.name] = func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 122, in _func
   ERROR - 14:41:26:     value = self.__orig_func(xn_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/norm_function.py", line 93, in _func
   ERROR - 14:41:26:     return self.__orig_func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 121, in _func
   ERROR - 14:41:26:     obj_allx_val = self.__out_x_func(x_of_disc)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/make_function.py", line 103, in _func
   ERROR - 14:41:26:     computed_values = self.__mdo_function.discipline.execute(data)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/discipline.py", line 830, in execute
   ERROR - 14:41:26:     self._run()
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/wrappers.py", line 96, in _run
   ERROR - 14:41:26:     y_4 = self.sobieski_problem.blackbox_mission(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core.py", line 729, in blackbox_mission
   ERROR - 14:41:26:     return self.sobieski_mission.blackbox_mission(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core_mission.py", line 272, in blackbox_mission
   ERROR - 14:41:26:     y_4[0] = self.compute_range(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core_mission.py", line 157, in compute_range
   ERROR - 14:41:26:     return ((x_shared[2] * y_24[0]) * 661.0 * sqrt_theta / y_34[0]) * self.math.log(
   ERROR - 14:41:26: ValueError: math domain error
   ERROR - 14:41:26:
    INFO - 14:41:26: DOE sampling:  57%|█████▋    | 57/100 [00:00<00:00, 999.61 it/sec, obj=572]
   ERROR - 14:41:26: Failed to evaluate function y_4
   ERROR - 14:41:26: Problem with evaluation of sample :[0.0195634  0.16707163 0.19467861 0.07127645 0.41818136 0.50039841
   ERROR - 14:41:26:  0.12219384 0.93727158 0.38711987 0.63748152] result is not taken into account in DOE.
   ERROR - 14:41:26: Traceback (most recent call last):
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/doe/doe_lib.py", line 349, in evaluate_samples
   ERROR - 14:41:26:     self.problem.evaluate_functions(x_norm, eval_jac)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/opt_problem.py", line 910, in evaluate_functions
   ERROR - 14:41:26:     outputs[func.name] = func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 122, in _func
   ERROR - 14:41:26:     value = self.__orig_func(xn_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/norm_function.py", line 93, in _func
   ERROR - 14:41:26:     return self.__orig_func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 121, in _func
   ERROR - 14:41:26:     obj_allx_val = self.__out_x_func(x_of_disc)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/make_function.py", line 103, in _func
   ERROR - 14:41:26:     computed_values = self.__mdo_function.discipline.execute(data)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/discipline.py", line 830, in execute
   ERROR - 14:41:26:     self._run()
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/wrappers.py", line 96, in _run
   ERROR - 14:41:26:     y_4 = self.sobieski_problem.blackbox_mission(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core.py", line 729, in blackbox_mission
   ERROR - 14:41:26:     return self.sobieski_mission.blackbox_mission(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core_mission.py", line 272, in blackbox_mission
   ERROR - 14:41:26:     y_4[0] = self.compute_range(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core_mission.py", line 157, in compute_range
   ERROR - 14:41:26:     return ((x_shared[2] * y_24[0]) * 661.0 * sqrt_theta / y_34[0]) * self.math.log(
   ERROR - 14:41:26: ValueError: math domain error
   ERROR - 14:41:26:
   ERROR - 14:41:26: Failed to evaluate function y_4
   ERROR - 14:41:26: Problem with evaluation of sample :[0.91969285 0.43381704 0.70684137 0.16789262 0.5134998  0.21172817
   ERROR - 14:41:26:  0.24624098 0.92150389 0.69492076 0.56596376] result is not taken into account in DOE.
   ERROR - 14:41:26: Traceback (most recent call last):
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/doe/doe_lib.py", line 349, in evaluate_samples
   ERROR - 14:41:26:     self.problem.evaluate_functions(x_norm, eval_jac)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/opt_problem.py", line 910, in evaluate_functions
   ERROR - 14:41:26:     outputs[func.name] = func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 122, in _func
   ERROR - 14:41:26:     value = self.__orig_func(xn_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/norm_function.py", line 93, in _func
   ERROR - 14:41:26:     return self.__orig_func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 121, in _func
   ERROR - 14:41:26:     obj_allx_val = self.__out_x_func(x_of_disc)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/make_function.py", line 103, in _func
   ERROR - 14:41:26:     computed_values = self.__mdo_function.discipline.execute(data)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/discipline.py", line 830, in execute
   ERROR - 14:41:26:     self._run()
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/wrappers.py", line 96, in _run
   ERROR - 14:41:26:     y_4 = self.sobieski_problem.blackbox_mission(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core.py", line 729, in blackbox_mission
   ERROR - 14:41:26:     return self.sobieski_mission.blackbox_mission(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core_mission.py", line 272, in blackbox_mission
   ERROR - 14:41:26:     y_4[0] = self.compute_range(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core_mission.py", line 157, in compute_range
   ERROR - 14:41:26:     return ((x_shared[2] * y_24[0]) * 661.0 * sqrt_theta / y_34[0]) * self.math.log(
   ERROR - 14:41:26: ValueError: math domain error
   ERROR - 14:41:26:
   ERROR - 14:41:26: Failed to evaluate function y_4
   ERROR - 14:41:26: Problem with evaluation of sample :[0.84380318 0.59969063 0.97150445 0.62089097 0.60036934 0.20840372
   ERROR - 14:41:26:  0.21460579 0.83251048 0.14072065 0.53654164] result is not taken into account in DOE.
   ERROR - 14:41:26: Traceback (most recent call last):
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/doe/doe_lib.py", line 349, in evaluate_samples
   ERROR - 14:41:26:     self.problem.evaluate_functions(x_norm, eval_jac)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/opt_problem.py", line 910, in evaluate_functions
   ERROR - 14:41:26:     outputs[func.name] = func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 122, in _func
   ERROR - 14:41:26:     value = self.__orig_func(xn_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/norm_function.py", line 93, in _func
   ERROR - 14:41:26:     return self.__orig_func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 121, in _func
   ERROR - 14:41:26:     obj_allx_val = self.__out_x_func(x_of_disc)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/make_function.py", line 103, in _func
   ERROR - 14:41:26:     computed_values = self.__mdo_function.discipline.execute(data)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/discipline.py", line 830, in execute
   ERROR - 14:41:26:     self._run()
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/wrappers.py", line 96, in _run
   ERROR - 14:41:26:     y_4 = self.sobieski_problem.blackbox_mission(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core.py", line 729, in blackbox_mission
   ERROR - 14:41:26:     return self.sobieski_mission.blackbox_mission(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core_mission.py", line 272, in blackbox_mission
   ERROR - 14:41:26:     y_4[0] = self.compute_range(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core_mission.py", line 157, in compute_range
   ERROR - 14:41:26:     return ((x_shared[2] * y_24[0]) * 661.0 * sqrt_theta / y_34[0]) * self.math.log(
   ERROR - 14:41:26: ValueError: math domain error
   ERROR - 14:41:26:
   ERROR - 14:41:26: Failed to evaluate function y_4
   ERROR - 14:41:26: Problem with evaluation of sample :[0.37219004 0.22260347 0.43802788 0.63178147 0.76788982 0.91416354
   ERROR - 14:41:26:  0.22861302 0.90193946 0.98410142 0.80413149] result is not taken into account in DOE.
   ERROR - 14:41:26: Traceback (most recent call last):
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/doe/doe_lib.py", line 349, in evaluate_samples
   ERROR - 14:41:26:     self.problem.evaluate_functions(x_norm, eval_jac)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/opt_problem.py", line 910, in evaluate_functions
   ERROR - 14:41:26:     outputs[func.name] = func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 122, in _func
   ERROR - 14:41:26:     value = self.__orig_func(xn_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/norm_function.py", line 93, in _func
   ERROR - 14:41:26:     return self.__orig_func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 121, in _func
   ERROR - 14:41:26:     obj_allx_val = self.__out_x_func(x_of_disc)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 313, in __call__
   ERROR - 14:41:26:     val = self.evaluate(x_vect, self.force_real)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 330, in evaluate
   ERROR - 14:41:26:     val = self.__counted_f(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 286, in __counted_f
   ERROR - 14:41:26:     val = self._func(x_vect)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/mdofunctions/make_function.py", line 103, in _func
   ERROR - 14:41:26:     computed_values = self.__mdo_function.discipline.execute(data)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/core/discipline.py", line 830, in execute
   ERROR - 14:41:26:     self._run()
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/wrappers.py", line 96, in _run
   ERROR - 14:41:26:     y_4 = self.sobieski_problem.blackbox_mission(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core.py", line 729, in blackbox_mission
   ERROR - 14:41:26:     return self.sobieski_mission.blackbox_mission(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core_mission.py", line 272, in blackbox_mission
   ERROR - 14:41:26:     y_4[0] = self.compute_range(x_shared, y_14, y_24, y_34)
   ERROR - 14:41:26:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/problems/sobieski/core_mission.py", line 157, in compute_range
   ERROR - 14:41:26:     return ((x_shared[2] * y_24[0]) * 661.0 * sqrt_theta / y_34[0]) * self.math.log(
   ERROR - 14:41:26: ValueError: math domain error
   ERROR - 14:41:26:
    INFO - 14:41:26: DOE sampling:  91%|█████████ | 91/100 [00:00<00:00, 627.15 it/sec, obj=9.38e+3]
    INFO - 14:41:26: Optimization result:
    INFO - 14:41:26: Objective value = -2378.708862411289
    INFO - 14:41:26: The result is feasible.
    INFO - 14:41:26: Status: None
    INFO - 14:41:26: Optimizer message: None
    INFO - 14:41:26: Number of calls to the objective function by the optimizer: 100
    INFO - 14:41:26: Design space:
    INFO - 14:41:26: +----------+-------------+---------------------+-------------+-------+
    INFO - 14:41:26: | name     | lower_bound |        value        | upper_bound | type  |
    INFO - 14:41:26: +----------+-------------+---------------------+-------------+-------+
    INFO - 14:41:26: | x_shared |     0.01    | 0.02013857927148241 |     0.09    | float |
    INFO - 14:41:26: | x_shared |    30000    |  53979.33921433108  |    60000    | float |
    INFO - 14:41:26: | x_shared |     1.4     |  1.568672471180504  |     1.8     | float |
    INFO - 14:41:26: | x_shared |     2.5     |  6.335453391896027  |     8.5     | float |
    INFO - 14:41:26: | x_shared |      40     |  59.27324692282826  |      70     | float |
    INFO - 14:41:26: | x_shared |     500     |  1382.959881676765  |     1500    | float |
    INFO - 14:41:26: | y_14     |    24850    |  45556.08529012231  |    77100    | float |
    INFO - 14:41:26: | y_14     |    -7700    |  -7410.461821391603 |    45000    | float |
    INFO - 14:41:26: | y_24     |     0.44    |    8.32480856994    |    11.13    | float |
    INFO - 14:41:26: | y_34     |     0.44    |  0.4742496457352351 |     1.98    | float |
    INFO - 14:41:26: +----------+-------------+---------------------+-------------+-------+
    INFO - 14:41:26: *** DOE Scenario run terminated ***

{'eval_jac': False, 'algo': 'OT_MONTE_CARLO', 'n_samples': 100}

Create an `EmpiricalStatistics` object for all variables¶

In this second stage, we create an EmpiricalStatistics from the cached data encapsulated in a Dataset:

dataset = discipline.cache.export_to_dataset()
analysis = create_statistics(dataset, name="SobieskiMission")

print(analysis)

Out:

    INFO - 14:41:26: Create SobieskiMission, a EmpiricalStatistics library.
SobieskiMission
   n_samples: 91
   n_variables: 5
   variables: x_shared, y_14, y_24, y_34, y_4

and easily obtain statistics, such as the minimum values of the different variables over the dataset:

print(analysis.compute_minimum())

Out:

{'x_shared': array([1.00825898e-02, 3.01300508e+04, 1.40601814e+00, 2.52462998e+00,
       4.02392061e+01, 5.21348495e+02]), 'y_14': array([26023.76214534, -7410.46182139]), 'y_24': array([0.54564362]), 'y_34': array([0.44717802]), 'y_4': array([-2378.70886241])}

Create an `EmpiricalStatistics` object for the range¶

We can only reduce the statistical analysis to the range variable:

analysis = create_statistics(
    dataset, variables_names=["y_4"], name="SobieskiMission.range"
)
print(analysis)

Out:

    INFO - 14:41:26: Create SobieskiMission.range, a EmpiricalStatistics library.
SobieskiMission.range
   n_samples: 91
   n_variables: 5
   variables: y_4

Get minimum¶

Here is the minimum value:

print(analysis.compute_minimum())

Out:

{'y_4': array([-2378.70886241])}

Get maximum¶

Here is the maximum value:

print(analysis.compute_maximum())

Out:

{'y_4': array([29542.75904538])}

Get range¶

Here is the (different between minimum and maximum values):

print(analysis.compute_range())

Out:

{'y_4': array([31921.46790779])}

Get mean¶

Here is the mean value:

print(analysis.compute_mean())

Out:

{'y_4': array([4033.24520293])}

Get central moment¶

Here is the second central moment:

print(analysis.compute_moment(2))

Out:

{'y_4': array([33202359.23030903])}

Get standard deviation¶

Here is the standard deviation:

print(analysis.compute_standard_deviation())

Out:

{'y_4': array([5762.14883792])}

Get variance¶

Here is the variance.

print(analysis.compute_variance())

Out:

{'y_4': array([33202359.23030903])}

Get quantile¶

Here is the quantile with level equal to 80%:

print(analysis.compute_quantile(0.8))

Out:

{'y_4': array([6389.01477707])}

Get probability¶

Here are the probability to respectively be greater and lower than the default output value:

default_output = discipline.execute()
print(analysis.compute_probability(default_output, greater=True))
print(analysis.compute_probability(default_output, greater=False))

Out:

{'y_4': 0.7252747252747253}
{'y_4': 0.27472527472527475}

Get quartile¶

Here is the second quartile:

print(analysis.compute_quartile(2))

Out:

{'y_4': array([1886.05710293])}

Get percentile¶

Here is the 50the percentile:

print(analysis.compute_percentile(50))

Out:

{'y_4': array([1886.05710293])}

Get median¶

Here is the median:

print(analysis.compute_median())

Out:

{'y_4': array([1886.05710293])}

Total running time of the script: ( 0 minutes 0.315 seconds)

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Empirical estimation of statistics¶

Create the dataset¶

Create an EmpiricalStatistics object for all variables¶

Create an EmpiricalStatistics object for the range¶

Get minimum¶

Get maximum¶

Get range¶

Get mean¶

Get central moment¶

Get standard deviation¶

Get variance¶

Get quantile¶

Get probability¶

Get quartile¶

Get percentile¶

Get median¶

Create an `EmpiricalStatistics` object for all variables¶

Create an `EmpiricalStatistics` object for the range¶