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 annotations

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

configure_logger()

<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.

discipline = create_discipline("SobieskiMission")

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

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

<gemseo.algos.design_space.DesignSpace object at 0x7f84a89c38e0>

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})

    INFO - 07:02:54:
    INFO - 07:02:54: *** Start DOEScenario execution ***
    INFO - 07:02:54: DOEScenario
    INFO - 07:02:54:    Disciplines: SobieskiMission
    INFO - 07:02:54:    MDO formulation: DisciplinaryOpt
    INFO - 07:02:54: Optimization problem:
    INFO - 07:02:54:    minimize y_4(x_shared, y_14, y_24, y_34)
    INFO - 07:02:54:    with respect to x_shared, y_14, y_24, y_34
    INFO - 07:02:54:    over the design space:
    INFO - 07:02:54:    +-------------+-------------+---------------+-------------+-------+
    INFO - 07:02:54:    | name        | lower_bound |     value     | upper_bound | type  |
    INFO - 07:02:54:    +-------------+-------------+---------------+-------------+-------+
    INFO - 07:02:54:    | x_shared[0] |     0.01    |      0.05     |     0.09    | float |
    INFO - 07:02:54:    | x_shared[1] |    30000    |     45000     |    60000    | float |
    INFO - 07:02:54:    | x_shared[2] |     1.4     |      1.6      |     1.8     | float |
    INFO - 07:02:54:    | x_shared[3] |     2.5     |      5.5      |     8.5     | float |
    INFO - 07:02:54:    | x_shared[4] |      40     |       55      |      70     | float |
    INFO - 07:02:54:    | x_shared[5] |     500     |      1000     |     1500    | float |
    INFO - 07:02:54:    | y_14[0]     |    24850    | 50606.9741711 |    77100    | float |
    INFO - 07:02:54:    | y_14[1]     |    -7700    | 7306.20262124 |    45000    | float |
    INFO - 07:02:54:    | y_24        |     0.44    |   4.15006276  |    11.13    | float |
    INFO - 07:02:54:    | y_34        |     0.44    |   1.10754577  |     1.98    | float |
    INFO - 07:02:54:    +-------------+-------------+---------------+-------------+-------+
    INFO - 07:02:54: Solving optimization problem with algorithm OT_MONTE_CARLO:
    INFO - 07:02:54: ...   0%|          | 0/100 [00:00<?, ?it]
    INFO - 07:02:54: ...   1%|          | 1/100 [00:00<00:00, 239.31 it/sec, obj=4.13e+3]
    INFO - 07:02:54: ...   2%|▏         | 2/100 [00:00<00:00, 390.22 it/sec, obj=2.69e+3]
    INFO - 07:02:54: ...   3%|▎         | 3/100 [00:00<00:00, 507.13 it/sec, obj=0.718]
    INFO - 07:02:54: ...   4%|▍         | 4/100 [00:00<00:00, 601.89 it/sec, obj=1.84e+3]
    INFO - 07:02:54: ...   5%|▌         | 5/100 [00:00<00:00, 678.27 it/sec, obj=1.47e+3]
    INFO - 07:02:54: ...   6%|▌         | 6/100 [00:00<00:00, 739.24 it/sec, obj=-76.6]
    INFO - 07:02:54: ...   7%|▋         | 7/100 [00:00<00:00, 792.36 it/sec, obj=2.92e+3]
   ERROR - 07:02:54: Failed to evaluate function y_4
   ERROR - 07:02:54: Problem with evaluation of sample :[1.29698918e-02 4.61506629e+04 1.54257893e+00 7.81530848e+00
   ERROR - 07:02:54:  5.05577274e+01 1.02006624e+03 3.16585883e+04 3.74764805e+04
   ERROR - 07:02:54:  1.02715165e+01 8.69196356e-01] result is not taken into account in DOE.
   ERROR - 07:02:54: Traceback (most recent call last):
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/doe/doe_library.py", line 401, in evaluate_samples
   ERROR - 07:02:54:     self.problem.evaluate_functions(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt_problem.py", line 1170, in evaluate_functions
   ERROR - 07:02:54:     outputs[function.name] = function.evaluate(preprocessed_x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 128, in _func_to_wrap
   ERROR - 07:02:54:     value = self.__evaluate_orig_func(xu_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_function.py", line 100, in _func_to_wrap
   ERROR - 07:02:54:     return self.__evaluate_orig_func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 123, in _func_to_wrap
   ERROR - 07:02:54:     return self.__out_x_func(x_vect[self.__x_mask])
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 412, in __call__
   ERROR - 07:02:54:     return self.evaluate(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_discipline_adapter.py", line 121, in _func_to_wrap
   ERROR - 07:02:54:     output_data = self.__discipline.execute(input_data)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/discipline.py", line 980, in execute
   ERROR - 07:02:54:     self._run()
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/disciplines.py", line 123, in _run
   ERROR - 07:02:54:     y_4 = self.sobieski_problem.mission.execute(x_shared, y_14, y_24, y_34)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 266, in execute
   ERROR - 07:02:54:     return self._execute(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 293, in _execute
   ERROR - 07:02:54:     [self.__compute_range(altitude, mach, w_t, w_f, cl_cd, sfc)],
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 153, in __compute_range
   ERROR - 07:02:54:     return ((mach * cl_cd) * 661.0 * sqrt_theta / sfc) * self.math.log(
   ERROR - 07:02:54: ValueError: math domain error
   ERROR - 07:02:54:
    INFO - 07:02:54: ...   8%|▊         | 8/100 [00:00<00:00, 614.47 it/sec, obj=2.41e+3]
    INFO - 07:02:54: ...   9%|▉         | 9/100 [00:00<00:00, 651.57 it/sec, obj=2.27e+3]
    INFO - 07:02:54: ...  10%|█         | 10/100 [00:00<00:00, 687.43 it/sec, obj=2.19e+3]
    INFO - 07:02:54: ...  11%|█         | 11/100 [00:00<00:00, 720.36 it/sec, obj=752]
   ERROR - 07:02:54: Failed to evaluate function y_4
   ERROR - 07:02:54: Problem with evaluation of sample :[5.48981321e-02 3.02492651e+04 1.78425506e+00 7.51304278e+00
   ERROR - 07:02:54:  5.91913274e+01 1.07102327e+03 3.89430460e+04 4.39972900e+04
   ERROR - 07:02:54:  5.23135403e+00 1.69750699e+00] result is not taken into account in DOE.
   ERROR - 07:02:54: Traceback (most recent call last):
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/doe/doe_library.py", line 401, in evaluate_samples
   ERROR - 07:02:54:     self.problem.evaluate_functions(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt_problem.py", line 1170, in evaluate_functions
   ERROR - 07:02:54:     outputs[function.name] = function.evaluate(preprocessed_x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 128, in _func_to_wrap
   ERROR - 07:02:54:     value = self.__evaluate_orig_func(xu_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_function.py", line 100, in _func_to_wrap
   ERROR - 07:02:54:     return self.__evaluate_orig_func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 123, in _func_to_wrap
   ERROR - 07:02:54:     return self.__out_x_func(x_vect[self.__x_mask])
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 412, in __call__
   ERROR - 07:02:54:     return self.evaluate(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_discipline_adapter.py", line 121, in _func_to_wrap
   ERROR - 07:02:54:     output_data = self.__discipline.execute(input_data)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/discipline.py", line 980, in execute
   ERROR - 07:02:54:     self._run()
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/disciplines.py", line 123, in _run
   ERROR - 07:02:54:     y_4 = self.sobieski_problem.mission.execute(x_shared, y_14, y_24, y_34)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 266, in execute
   ERROR - 07:02:54:     return self._execute(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 293, in _execute
   ERROR - 07:02:54:     [self.__compute_range(altitude, mach, w_t, w_f, cl_cd, sfc)],
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 153, in __compute_range
   ERROR - 07:02:54:     return ((mach * cl_cd) * 661.0 * sqrt_theta / sfc) * self.math.log(
   ERROR - 07:02:54: ValueError: math domain error
   ERROR - 07:02:54:
    INFO - 07:02:54: ...  12%|█▏        | 12/100 [00:00<00:00, 647.13 it/sec, obj=3.07e+3]
    INFO - 07:02:54: ...  13%|█▎        | 13/100 [00:00<00:00, 674.63 it/sec, obj=4.9e+3]
    INFO - 07:02:54: ...  14%|█▍        | 14/100 [00:00<00:00, 698.28 it/sec, obj=1.19e+3]
    INFO - 07:02:54: ...  15%|█▌        | 15/100 [00:00<00:00, 722.60 it/sec, obj=8.3e+3]
    INFO - 07:02:54: ...  16%|█▌        | 16/100 [00:00<00:00, 744.70 it/sec, obj=5.59e+3]
    INFO - 07:02:54: ...  17%|█▋        | 17/100 [00:00<00:00, 764.79 it/sec, obj=-1.53e+3]
    INFO - 07:02:54: ...  18%|█▊        | 18/100 [00:00<00:00, 784.48 it/sec, obj=876]
    INFO - 07:02:54: ...  19%|█▉        | 19/100 [00:00<00:00, 803.52 it/sec, obj=529]
   ERROR - 07:02:54: Failed to evaluate function y_4
   ERROR - 07:02:54: Problem with evaluation of sample :[3.23734572e-02 5.75371340e+04 1.56588241e+00 3.92408088e+00
   ERROR - 07:02:54:  5.21270800e+01 6.95527982e+02 2.78544051e+04 2.90664780e+04
   ERROR - 07:02:54:  8.48303790e+00 1.07896745e+00] result is not taken into account in DOE.
   ERROR - 07:02:54: Traceback (most recent call last):
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/doe/doe_library.py", line 401, in evaluate_samples
   ERROR - 07:02:54:     self.problem.evaluate_functions(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt_problem.py", line 1170, in evaluate_functions
   ERROR - 07:02:54:     outputs[function.name] = function.evaluate(preprocessed_x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 128, in _func_to_wrap
   ERROR - 07:02:54:     value = self.__evaluate_orig_func(xu_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_function.py", line 100, in _func_to_wrap
   ERROR - 07:02:54:     return self.__evaluate_orig_func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 123, in _func_to_wrap
   ERROR - 07:02:54:     return self.__out_x_func(x_vect[self.__x_mask])
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 412, in __call__
   ERROR - 07:02:54:     return self.evaluate(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_discipline_adapter.py", line 121, in _func_to_wrap
   ERROR - 07:02:54:     output_data = self.__discipline.execute(input_data)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/discipline.py", line 980, in execute
   ERROR - 07:02:54:     self._run()
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/disciplines.py", line 123, in _run
   ERROR - 07:02:54:     y_4 = self.sobieski_problem.mission.execute(x_shared, y_14, y_24, y_34)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 266, in execute
   ERROR - 07:02:54:     return self._execute(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 293, in _execute
   ERROR - 07:02:54:     [self.__compute_range(altitude, mach, w_t, w_f, cl_cd, sfc)],
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 153, in __compute_range
   ERROR - 07:02:54:     return ((mach * cl_cd) * 661.0 * sqrt_theta / sfc) * self.math.log(
   ERROR - 07:02:54: ValueError: math domain error
   ERROR - 07:02:54:
    INFO - 07:02:54: ...  20%|██        | 20/100 [00:00<00:00, 742.97 it/sec, obj=4.49e+3]
   ERROR - 07:02:54: Failed to evaluate function y_4
   ERROR - 07:02:54: Problem with evaluation of sample :[8.65821820e-02 5.67282712e+04 1.63166519e+00 8.05650222e+00
   ERROR - 07:02:54:  6.64935582e+01 7.09872962e+02 2.82276678e+04 3.83552559e+04
   ERROR - 07:02:54:  1.00916432e+01 1.92827068e+00] result is not taken into account in DOE.
   ERROR - 07:02:54: Traceback (most recent call last):
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/doe/doe_library.py", line 401, in evaluate_samples
   ERROR - 07:02:54:     self.problem.evaluate_functions(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt_problem.py", line 1170, in evaluate_functions
   ERROR - 07:02:54:     outputs[function.name] = function.evaluate(preprocessed_x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 128, in _func_to_wrap
   ERROR - 07:02:54:     value = self.__evaluate_orig_func(xu_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_function.py", line 100, in _func_to_wrap
   ERROR - 07:02:54:     return self.__evaluate_orig_func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 123, in _func_to_wrap
   ERROR - 07:02:54:     return self.__out_x_func(x_vect[self.__x_mask])
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 412, in __call__
   ERROR - 07:02:54:     return self.evaluate(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_discipline_adapter.py", line 121, in _func_to_wrap
   ERROR - 07:02:54:     output_data = self.__discipline.execute(input_data)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/discipline.py", line 980, in execute
   ERROR - 07:02:54:     self._run()
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/disciplines.py", line 123, in _run
   ERROR - 07:02:54:     y_4 = self.sobieski_problem.mission.execute(x_shared, y_14, y_24, y_34)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 266, in execute
   ERROR - 07:02:54:     return self._execute(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 293, in _execute
   ERROR - 07:02:54:     [self.__compute_range(altitude, mach, w_t, w_f, cl_cd, sfc)],
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 153, in __compute_range
   ERROR - 07:02:54:     return ((mach * cl_cd) * 661.0 * sqrt_theta / sfc) * self.math.log(
   ERROR - 07:02:54: ValueError: math domain error
   ERROR - 07:02:54:
    INFO - 07:02:54: ...  21%|██        | 21/100 [00:00<00:00, 696.75 it/sec, obj=1.49e+3]
    INFO - 07:02:54: ...  22%|██▏       | 22/100 [00:00<00:00, 712.49 it/sec, obj=996]
    INFO - 07:02:54: ...  23%|██▎       | 23/100 [00:00<00:00, 728.11 it/sec, obj=8.56e+3]
    INFO - 07:02:54: ...  24%|██▍       | 24/100 [00:00<00:00, 741.76 it/sec, obj=1.26e+3]
    INFO - 07:02:54: ...  25%|██▌       | 25/100 [00:00<00:00, 755.70 it/sec, obj=2.07e+3]
    INFO - 07:02:54: ...  26%|██▌       | 26/100 [00:00<00:00, 768.83 it/sec, obj=1.71e+3]
    INFO - 07:02:54: ...  27%|██▋       | 27/100 [00:00<00:00, 782.10 it/sec, obj=1.49e+3]
    INFO - 07:02:54: ...  28%|██▊       | 28/100 [00:00<00:00, 794.46 it/sec, obj=6.55e+3]
    INFO - 07:02:54: ...  29%|██▉       | 29/100 [00:00<00:00, 805.66 it/sec, obj=821]
    INFO - 07:02:54: ...  30%|███       | 30/100 [00:00<00:00, 817.18 it/sec, obj=978]
   ERROR - 07:02:54: Failed to evaluate function y_4
   ERROR - 07:02:54: Problem with evaluation of sample :[8.73940398e-02 3.67026184e+04 1.56476942e+00 4.19812099e+00
   ERROR - 07:02:54:  6.17650588e+01 1.19302534e+03 3.41482711e+04 4.38203117e+04
   ERROR - 07:02:54:  1.00305508e+01 1.32482248e+00] result is not taken into account in DOE.
   ERROR - 07:02:54: Traceback (most recent call last):
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/doe/doe_library.py", line 401, in evaluate_samples
   ERROR - 07:02:54:     self.problem.evaluate_functions(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt_problem.py", line 1170, in evaluate_functions
   ERROR - 07:02:54:     outputs[function.name] = function.evaluate(preprocessed_x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 128, in _func_to_wrap
   ERROR - 07:02:54:     value = self.__evaluate_orig_func(xu_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_function.py", line 100, in _func_to_wrap
   ERROR - 07:02:54:     return self.__evaluate_orig_func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 123, in _func_to_wrap
   ERROR - 07:02:54:     return self.__out_x_func(x_vect[self.__x_mask])
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 412, in __call__
   ERROR - 07:02:54:     return self.evaluate(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_discipline_adapter.py", line 121, in _func_to_wrap
   ERROR - 07:02:54:     output_data = self.__discipline.execute(input_data)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/discipline.py", line 980, in execute
   ERROR - 07:02:54:     self._run()
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/disciplines.py", line 123, in _run
   ERROR - 07:02:54:     y_4 = self.sobieski_problem.mission.execute(x_shared, y_14, y_24, y_34)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 266, in execute
   ERROR - 07:02:54:     return self._execute(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 293, in _execute
   ERROR - 07:02:54:     [self.__compute_range(altitude, mach, w_t, w_f, cl_cd, sfc)],
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 153, in __compute_range
   ERROR - 07:02:54:     return ((mach * cl_cd) * 661.0 * sqrt_theta / sfc) * self.math.log(
   ERROR - 07:02:54: ValueError: math domain error
   ERROR - 07:02:54:
    INFO - 07:02:54: ...  31%|███       | 31/100 [00:00<00:00, 774.27 it/sec, obj=730]
    INFO - 07:02:54: ...  32%|███▏      | 32/100 [00:00<00:00, 784.85 it/sec, obj=1.69e+4]
    INFO - 07:02:54: ...  33%|███▎      | 33/100 [00:00<00:00, 795.29 it/sec, obj=2.2e+3]
    INFO - 07:02:54: ...  34%|███▍      | 34/100 [00:00<00:00, 805.31 it/sec, obj=4.98e+3]
    INFO - 07:02:54: ...  35%|███▌      | 35/100 [00:00<00:00, 815.10 it/sec, obj=126]
    INFO - 07:02:54: ...  36%|███▌      | 36/100 [00:00<00:00, 824.58 it/sec, obj=1.21e+3]
   ERROR - 07:02:54: Failed to evaluate function y_4
   ERROR - 07:02:54: Problem with evaluation of sample :[6.31287105e-02 4.23324465e+04 1.41438529e+00 4.38495848e+00
   ERROR - 07:02:54:  5.18016406e+01 9.81706178e+02 4.02684763e+04 4.04292612e+04
   ERROR - 07:02:54:  1.63495128e+00 1.58647382e+00] result is not taken into account in DOE.
   ERROR - 07:02:54: Traceback (most recent call last):
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/doe/doe_library.py", line 401, in evaluate_samples
   ERROR - 07:02:54:     self.problem.evaluate_functions(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt_problem.py", line 1170, in evaluate_functions
   ERROR - 07:02:54:     outputs[function.name] = function.evaluate(preprocessed_x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 128, in _func_to_wrap
   ERROR - 07:02:54:     value = self.__evaluate_orig_func(xu_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_function.py", line 100, in _func_to_wrap
   ERROR - 07:02:54:     return self.__evaluate_orig_func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 123, in _func_to_wrap
   ERROR - 07:02:54:     return self.__out_x_func(x_vect[self.__x_mask])
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 412, in __call__
   ERROR - 07:02:54:     return self.evaluate(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_discipline_adapter.py", line 121, in _func_to_wrap
   ERROR - 07:02:54:     output_data = self.__discipline.execute(input_data)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/discipline.py", line 980, in execute
   ERROR - 07:02:54:     self._run()
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/disciplines.py", line 123, in _run
   ERROR - 07:02:54:     y_4 = self.sobieski_problem.mission.execute(x_shared, y_14, y_24, y_34)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 266, in execute
   ERROR - 07:02:54:     return self._execute(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 293, in _execute
   ERROR - 07:02:54:     [self.__compute_range(altitude, mach, w_t, w_f, cl_cd, sfc)],
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 153, in __compute_range
   ERROR - 07:02:54:     return ((mach * cl_cd) * 661.0 * sqrt_theta / sfc) * self.math.log(
   ERROR - 07:02:54: ValueError: math domain error
   ERROR - 07:02:54:
    INFO - 07:02:54: ...  37%|███▋      | 37/100 [00:00<00:00, 788.84 it/sec, obj=-93.8]
   ERROR - 07:02:54: Failed to evaluate function y_4
   ERROR - 07:02:54: Problem with evaluation of sample :[4.70074524e-02 4.40740007e+04 1.62275117e+00 4.39813380e+00
   ERROR - 07:02:54:  6.53898046e+01 1.27066268e+03 3.10026856e+04 3.93852349e+04
   ERROR - 07:02:54:  5.25707580e+00 4.69709094e-01] result is not taken into account in DOE.
   ERROR - 07:02:54: Traceback (most recent call last):
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/doe/doe_library.py", line 401, in evaluate_samples
   ERROR - 07:02:54:     self.problem.evaluate_functions(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt_problem.py", line 1170, in evaluate_functions
   ERROR - 07:02:54:     outputs[function.name] = function.evaluate(preprocessed_x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 128, in _func_to_wrap
   ERROR - 07:02:54:     value = self.__evaluate_orig_func(xu_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_function.py", line 100, in _func_to_wrap
   ERROR - 07:02:54:     return self.__evaluate_orig_func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 123, in _func_to_wrap
   ERROR - 07:02:54:     return self.__out_x_func(x_vect[self.__x_mask])
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 412, in __call__
   ERROR - 07:02:54:     return self.evaluate(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_discipline_adapter.py", line 121, in _func_to_wrap
   ERROR - 07:02:54:     output_data = self.__discipline.execute(input_data)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/discipline.py", line 980, in execute
   ERROR - 07:02:54:     self._run()
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/disciplines.py", line 123, in _run
   ERROR - 07:02:54:     y_4 = self.sobieski_problem.mission.execute(x_shared, y_14, y_24, y_34)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 266, in execute
   ERROR - 07:02:54:     return self._execute(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 293, in _execute
   ERROR - 07:02:54:     [self.__compute_range(altitude, mach, w_t, w_f, cl_cd, sfc)],
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 153, in __compute_range
   ERROR - 07:02:54:     return ((mach * cl_cd) * 661.0 * sqrt_theta / sfc) * self.math.log(
   ERROR - 07:02:54: ValueError: math domain error
   ERROR - 07:02:54:
    INFO - 07:02:54: ...  38%|███▊      | 38/100 [00:00<00:00, 757.86 it/sec, obj=2.62e+3]
   ERROR - 07:02:54: Failed to evaluate function y_4
   ERROR - 07:02:54: Problem with evaluation of sample :[5.02116961e-02 4.11016864e+04 1.76501712e+00 7.39553905e+00
   ERROR - 07:02:54:  4.03455877e+01 8.42798741e+02 3.16404732e+04 3.77881168e+04
   ERROR - 07:02:54:  4.99873191e+00 5.33732657e-01] result is not taken into account in DOE.
   ERROR - 07:02:54: Traceback (most recent call last):
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/doe/doe_library.py", line 401, in evaluate_samples
   ERROR - 07:02:54:     self.problem.evaluate_functions(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt_problem.py", line 1170, in evaluate_functions
   ERROR - 07:02:54:     outputs[function.name] = function.evaluate(preprocessed_x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 128, in _func_to_wrap
   ERROR - 07:02:54:     value = self.__evaluate_orig_func(xu_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_function.py", line 100, in _func_to_wrap
   ERROR - 07:02:54:     return self.__evaluate_orig_func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 123, in _func_to_wrap
   ERROR - 07:02:54:     return self.__out_x_func(x_vect[self.__x_mask])
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 412, in __call__
   ERROR - 07:02:54:     return self.evaluate(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_discipline_adapter.py", line 121, in _func_to_wrap
   ERROR - 07:02:54:     output_data = self.__discipline.execute(input_data)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/discipline.py", line 980, in execute
   ERROR - 07:02:54:     self._run()
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/disciplines.py", line 123, in _run
   ERROR - 07:02:54:     y_4 = self.sobieski_problem.mission.execute(x_shared, y_14, y_24, y_34)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 266, in execute
   ERROR - 07:02:54:     return self._execute(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 293, in _execute
   ERROR - 07:02:54:     [self.__compute_range(altitude, mach, w_t, w_f, cl_cd, sfc)],
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 153, in __compute_range
   ERROR - 07:02:54:     return ((mach * cl_cd) * 661.0 * sqrt_theta / sfc) * self.math.log(
   ERROR - 07:02:54: ValueError: math domain error
   ERROR - 07:02:54:
    INFO - 07:02:54: ...  39%|███▉      | 39/100 [00:00<00:00, 730.53 it/sec, obj=2.4e+3]
    INFO - 07:02:54: ...  40%|████      | 40/100 [00:00<00:00, 738.62 it/sec, obj=3.82e+3]
    INFO - 07:02:54: ...  41%|████      | 41/100 [00:00<00:00, 747.20 it/sec, obj=5.76e+3]
   ERROR - 07:02:54: Failed to evaluate function y_4
   ERROR - 07:02:54: Problem with evaluation of sample :[1.79955568e-02 4.13572866e+04 1.53514395e+00 6.06896708e+00
   ERROR - 07:02:54:  6.30366946e+01 5.07973536e+02 3.06338667e+04 3.54965135e+04
   ERROR - 07:02:54:  6.15365417e-01 1.38454066e+00] result is not taken into account in DOE.
   ERROR - 07:02:54: Traceback (most recent call last):
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/doe/doe_library.py", line 401, in evaluate_samples
   ERROR - 07:02:54:     self.problem.evaluate_functions(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt_problem.py", line 1170, in evaluate_functions
   ERROR - 07:02:54:     outputs[function.name] = function.evaluate(preprocessed_x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 128, in _func_to_wrap
   ERROR - 07:02:54:     value = self.__evaluate_orig_func(xu_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_function.py", line 100, in _func_to_wrap
   ERROR - 07:02:54:     return self.__evaluate_orig_func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 123, in _func_to_wrap
   ERROR - 07:02:54:     return self.__out_x_func(x_vect[self.__x_mask])
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 412, in __call__
   ERROR - 07:02:54:     return self.evaluate(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_discipline_adapter.py", line 121, in _func_to_wrap
   ERROR - 07:02:54:     output_data = self.__discipline.execute(input_data)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/discipline.py", line 980, in execute
   ERROR - 07:02:54:     self._run()
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/disciplines.py", line 123, in _run
   ERROR - 07:02:54:     y_4 = self.sobieski_problem.mission.execute(x_shared, y_14, y_24, y_34)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 266, in execute
   ERROR - 07:02:54:     return self._execute(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 293, in _execute
   ERROR - 07:02:54:     [self.__compute_range(altitude, mach, w_t, w_f, cl_cd, sfc)],
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 153, in __compute_range
   ERROR - 07:02:54:     return ((mach * cl_cd) * 661.0 * sqrt_theta / sfc) * self.math.log(
   ERROR - 07:02:54: ValueError: math domain error
   ERROR - 07:02:54:
    INFO - 07:02:54: ...  42%|████▏     | 42/100 [00:00<00:00, 721.69 it/sec, obj=3.15e+3]
    INFO - 07:02:54: ...  43%|████▎     | 43/100 [00:00<00:00, 729.78 it/sec, obj=1.47e+4]
    INFO - 07:02:54: ...  44%|████▍     | 44/100 [00:00<00:00, 737.71 it/sec, obj=342]
    INFO - 07:02:54: ...  45%|████▌     | 45/100 [00:00<00:00, 745.06 it/sec, obj=149]
    INFO - 07:02:54: ...  46%|████▌     | 46/100 [00:00<00:00, 752.63 it/sec, obj=3.48e+3]
   ERROR - 07:02:54: Failed to evaluate function y_4
   ERROR - 07:02:54: Problem with evaluation of sample :[7.34156617e-02 4.29755065e+04 1.65638244e+00 4.73092799e+00
   ERROR - 07:02:54:  6.39497950e+01 7.54812818e+02 3.75942160e+04 4.10549422e+04
   ERROR - 07:02:54:  1.01970094e+01 1.93999914e+00] result is not taken into account in DOE.
   ERROR - 07:02:54: Traceback (most recent call last):
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/doe/doe_library.py", line 401, in evaluate_samples
   ERROR - 07:02:54:     self.problem.evaluate_functions(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt_problem.py", line 1170, in evaluate_functions
   ERROR - 07:02:54:     outputs[function.name] = function.evaluate(preprocessed_x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 128, in _func_to_wrap
   ERROR - 07:02:54:     value = self.__evaluate_orig_func(xu_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_function.py", line 100, in _func_to_wrap
   ERROR - 07:02:54:     return self.__evaluate_orig_func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 123, in _func_to_wrap
   ERROR - 07:02:54:     return self.__out_x_func(x_vect[self.__x_mask])
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 412, in __call__
   ERROR - 07:02:54:     return self.evaluate(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_discipline_adapter.py", line 121, in _func_to_wrap
   ERROR - 07:02:54:     output_data = self.__discipline.execute(input_data)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/discipline.py", line 980, in execute
   ERROR - 07:02:54:     self._run()
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/disciplines.py", line 123, in _run
   ERROR - 07:02:54:     y_4 = self.sobieski_problem.mission.execute(x_shared, y_14, y_24, y_34)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 266, in execute
   ERROR - 07:02:54:     return self._execute(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 293, in _execute
   ERROR - 07:02:54:     [self.__compute_range(altitude, mach, w_t, w_f, cl_cd, sfc)],
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 153, in __compute_range
   ERROR - 07:02:54:     return ((mach * cl_cd) * 661.0 * sqrt_theta / sfc) * self.math.log(
   ERROR - 07:02:54: ValueError: math domain error
   ERROR - 07:02:54:
    INFO - 07:02:54: ...  47%|████▋     | 47/100 [00:00<00:00, 730.32 it/sec, obj=-121]
    INFO - 07:02:54: ...  48%|████▊     | 48/100 [00:00<00:00, 737.46 it/sec, obj=3.52e+3]
   ERROR - 07:02:54: Failed to evaluate function y_4
   ERROR - 07:02:54: Problem with evaluation of sample :[8.69811400e-02 3.42276221e+04 1.48336149e+00 4.28449805e+00
   ERROR - 07:02:54:  4.74431990e+01 9.08368407e+02 3.06851402e+04 4.29931580e+04
   ERROR - 07:02:54:  9.77470946e+00 9.51964086e-01] result is not taken into account in DOE.
   ERROR - 07:02:54: Traceback (most recent call last):
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/doe/doe_library.py", line 401, in evaluate_samples
   ERROR - 07:02:54:     self.problem.evaluate_functions(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt_problem.py", line 1170, in evaluate_functions
   ERROR - 07:02:54:     outputs[function.name] = function.evaluate(preprocessed_x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 128, in _func_to_wrap
   ERROR - 07:02:54:     value = self.__evaluate_orig_func(xu_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_function.py", line 100, in _func_to_wrap
   ERROR - 07:02:54:     return self.__evaluate_orig_func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 123, in _func_to_wrap
   ERROR - 07:02:54:     return self.__out_x_func(x_vect[self.__x_mask])
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 412, in __call__
   ERROR - 07:02:54:     return self.evaluate(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_discipline_adapter.py", line 121, in _func_to_wrap
   ERROR - 07:02:54:     output_data = self.__discipline.execute(input_data)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/discipline.py", line 980, in execute
   ERROR - 07:02:54:     self._run()
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/disciplines.py", line 123, in _run
   ERROR - 07:02:54:     y_4 = self.sobieski_problem.mission.execute(x_shared, y_14, y_24, y_34)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 266, in execute
   ERROR - 07:02:54:     return self._execute(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 293, in _execute
   ERROR - 07:02:54:     [self.__compute_range(altitude, mach, w_t, w_f, cl_cd, sfc)],
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 153, in __compute_range
   ERROR - 07:02:54:     return ((mach * cl_cd) * 661.0 * sqrt_theta / sfc) * self.math.log(
   ERROR - 07:02:54: ValueError: math domain error
   ERROR - 07:02:54:
    INFO - 07:02:54: ...  49%|████▉     | 49/100 [00:00<00:00, 701.90 it/sec, obj=6.03e+3]
    INFO - 07:02:54: ...  50%|█████     | 50/100 [00:00<00:00, 704.90 it/sec, obj=143]
   ERROR - 07:02:54: Failed to evaluate function y_4
   ERROR - 07:02:54: Problem with evaluation of sample :[8.44564380e-02 3.07957264e+04 1.54087352e+00 5.88383336e+00
   ERROR - 07:02:54:  4.21051139e+01 5.91254283e+02 3.08786610e+04 3.32313216e+04
   ERROR - 07:02:54:  4.95940225e+00 7.91759531e-01] result is not taken into account in DOE.
   ERROR - 07:02:54: Traceback (most recent call last):
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/doe/doe_library.py", line 401, in evaluate_samples
   ERROR - 07:02:54:     self.problem.evaluate_functions(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt_problem.py", line 1170, in evaluate_functions
   ERROR - 07:02:54:     outputs[function.name] = function.evaluate(preprocessed_x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 128, in _func_to_wrap
   ERROR - 07:02:54:     value = self.__evaluate_orig_func(xu_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_function.py", line 100, in _func_to_wrap
   ERROR - 07:02:54:     return self.__evaluate_orig_func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 123, in _func_to_wrap
   ERROR - 07:02:54:     return self.__out_x_func(x_vect[self.__x_mask])
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 412, in __call__
   ERROR - 07:02:54:     return self.evaluate(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_discipline_adapter.py", line 121, in _func_to_wrap
   ERROR - 07:02:54:     output_data = self.__discipline.execute(input_data)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/discipline.py", line 980, in execute
   ERROR - 07:02:54:     self._run()
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/disciplines.py", line 123, in _run
   ERROR - 07:02:54:     y_4 = self.sobieski_problem.mission.execute(x_shared, y_14, y_24, y_34)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 266, in execute
   ERROR - 07:02:54:     return self._execute(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 293, in _execute
   ERROR - 07:02:54:     [self.__compute_range(altitude, mach, w_t, w_f, cl_cd, sfc)],
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 153, in __compute_range
   ERROR - 07:02:54:     return ((mach * cl_cd) * 661.0 * sqrt_theta / sfc) * self.math.log(
   ERROR - 07:02:54: ValueError: math domain error
   ERROR - 07:02:54:
    INFO - 07:02:54: ...  51%|█████     | 51/100 [00:00<00:00, 681.84 it/sec, obj=2.77e+3]
    INFO - 07:02:54: ...  52%|█████▏    | 52/100 [00:00<00:00, 685.26 it/sec, obj=114]
    INFO - 07:02:54: ...  53%|█████▎    | 53/100 [00:00<00:00, 688.31 it/sec, obj=1.64e+4]
    INFO - 07:02:54: ...  54%|█████▍    | 54/100 [00:00<00:00, 691.05 it/sec, obj=1.54e+3]
    INFO - 07:02:54: ...  55%|█████▌    | 55/100 [00:00<00:00, 693.77 it/sec, obj=3.24e+4]
    INFO - 07:02:54: ...  56%|█████▌    | 56/100 [00:00<00:00, 699.56 it/sec, obj=390]
    INFO - 07:02:54: ...  57%|█████▋    | 57/100 [00:00<00:00, 704.04 it/sec, obj=-139]
    INFO - 07:02:54: ...  58%|█████▊    | 58/100 [00:00<00:00, 707.59 it/sec, obj=4.99e+3]
    INFO - 07:02:54: ...  59%|█████▉    | 59/100 [00:00<00:00, 713.37 it/sec, obj=157]
    INFO - 07:02:54: ...  60%|██████    | 60/100 [00:00<00:00, 719.32 it/sec, obj=4.78e+3]
    INFO - 07:02:54: ...  61%|██████    | 61/100 [00:00<00:00, 724.69 it/sec, obj=2.81e+3]
    INFO - 07:02:54: ...  62%|██████▏   | 62/100 [00:00<00:00, 730.31 it/sec, obj=8.8e+3]
    INFO - 07:02:54: ...  63%|██████▎   | 63/100 [00:00<00:00, 735.72 it/sec, obj=371]
   ERROR - 07:02:54: Failed to evaluate function y_4
   ERROR - 07:02:54: Problem with evaluation of sample :[6.77585739e-02 3.79793238e+04 1.74373635e+00 3.43230716e+00
   ERROR - 07:02:54:  4.13701698e+01 1.31335579e+03 2.88266747e+04 3.74178761e+04
   ERROR - 07:02:54:  8.88078902e+00 1.83214824e+00] result is not taken into account in DOE.
   ERROR - 07:02:54: Traceback (most recent call last):
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/doe/doe_library.py", line 401, in evaluate_samples
   ERROR - 07:02:54:     self.problem.evaluate_functions(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt_problem.py", line 1170, in evaluate_functions
   ERROR - 07:02:54:     outputs[function.name] = function.evaluate(preprocessed_x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 128, in _func_to_wrap
   ERROR - 07:02:54:     value = self.__evaluate_orig_func(xu_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_function.py", line 100, in _func_to_wrap
   ERROR - 07:02:54:     return self.__evaluate_orig_func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 123, in _func_to_wrap
   ERROR - 07:02:54:     return self.__out_x_func(x_vect[self.__x_mask])
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 412, in __call__
   ERROR - 07:02:54:     return self.evaluate(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_discipline_adapter.py", line 121, in _func_to_wrap
   ERROR - 07:02:54:     output_data = self.__discipline.execute(input_data)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/discipline.py", line 980, in execute
   ERROR - 07:02:54:     self._run()
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/disciplines.py", line 123, in _run
   ERROR - 07:02:54:     y_4 = self.sobieski_problem.mission.execute(x_shared, y_14, y_24, y_34)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 266, in execute
   ERROR - 07:02:54:     return self._execute(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 293, in _execute
   ERROR - 07:02:54:     [self.__compute_range(altitude, mach, w_t, w_f, cl_cd, sfc)],
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 153, in __compute_range
   ERROR - 07:02:54:     return ((mach * cl_cd) * 661.0 * sqrt_theta / sfc) * self.math.log(
   ERROR - 07:02:54: ValueError: math domain error
   ERROR - 07:02:54:
    INFO - 07:02:54: ...  64%|██████▍   | 64/100 [00:00<00:00, 718.49 it/sec, obj=6.2e+4]
    INFO - 07:02:54: ...  65%|██████▌   | 65/100 [00:00<00:00, 723.68 it/sec, obj=4.9e+4]
    INFO - 07:02:54: ...  66%|██████▌   | 66/100 [00:00<00:00, 727.08 it/sec, obj=1.49e+3]
    INFO - 07:02:54: ...  67%|██████▋   | 67/100 [00:00<00:00, 729.19 it/sec, obj=7.4e+3]
    INFO - 07:02:54: ...  68%|██████▊   | 68/100 [00:00<00:00, 732.61 it/sec, obj=2.16e+3]
    INFO - 07:02:54: ...  69%|██████▉   | 69/100 [00:00<00:00, 737.41 it/sec, obj=2.42e+3]
    INFO - 07:02:54: ...  70%|███████   | 70/100 [00:00<00:00, 742.30 it/sec, obj=1.26e+3]
    INFO - 07:02:54: ...  71%|███████   | 71/100 [00:00<00:00, 747.28 it/sec, obj=1.1e+3]
    INFO - 07:02:54: ...  72%|███████▏  | 72/100 [00:00<00:00, 752.11 it/sec, obj=1.25e+4]
   ERROR - 07:02:54: Failed to evaluate function y_4
   ERROR - 07:02:54: Problem with evaluation of sample :[1.63329215e-02 5.97324226e+04 1.56766182e+00 4.71404767e+00
   ERROR - 07:02:54:  4.44948320e+01 1.24758949e+03 4.39269694e+04 4.44436533e+04
   ERROR - 07:02:54:  6.30023047e+00 8.37747853e-01] result is not taken into account in DOE.
   ERROR - 07:02:54: Traceback (most recent call last):
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/doe/doe_library.py", line 401, in evaluate_samples
   ERROR - 07:02:54:     self.problem.evaluate_functions(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt_problem.py", line 1170, in evaluate_functions
   ERROR - 07:02:54:     outputs[function.name] = function.evaluate(preprocessed_x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_db_function.py", line 128, in _func_to_wrap
   ERROR - 07:02:54:     value = self.__evaluate_orig_func(xu_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/norm_function.py", line 100, in _func_to_wrap
   ERROR - 07:02:54:     return self.__evaluate_orig_func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/function_from_discipline.py", line 123, in _func_to_wrap
   ERROR - 07:02:54:     return self.__out_x_func(x_vect[self.__x_mask])
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 412, in __call__
   ERROR - 07:02:54:     return self.evaluate(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 424, in evaluate
   ERROR - 07:02:54:     val = self.__counted_f(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_function.py", line 353, in __counted_f
   ERROR - 07:02:54:     self.last_eval = self._func(x_vect)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/mdofunctions/mdo_discipline_adapter.py", line 121, in _func_to_wrap
   ERROR - 07:02:54:     output_data = self.__discipline.execute(input_data)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/core/discipline.py", line 980, in execute
   ERROR - 07:02:54:     self._run()
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/disciplines.py", line 123, in _run
   ERROR - 07:02:54:     y_4 = self.sobieski_problem.mission.execute(x_shared, y_14, y_24, y_34)
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 266, in execute
   ERROR - 07:02:54:     return self._execute(
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 293, in _execute
   ERROR - 07:02:54:     [self.__compute_range(altitude, mach, w_t, w_f, cl_cd, sfc)],
   ERROR - 07:02:54:   File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/problems/sobieski/core/mission.py", line 153, in __compute_range
   ERROR - 07:02:54:     return ((mach * cl_cd) * 661.0 * sqrt_theta / sfc) * self.math.log(
   ERROR - 07:02:54: ValueError: math domain error
   ERROR - 07:02:54:
    INFO - 07:02:54: ...  73%|███████▎  | 73/100 [00:00<00:00, 737.49 it/sec, obj=6.65e+3]
    INFO - 07:02:54: ...  74%|███████▍  | 74/100 [00:00<00:00, 742.17 it/sec, obj=-185]
    INFO - 07:02:54: ...  75%|███████▌  | 75/100 [00:00<00:00, 746.51 it/sec, obj=5.26e+3]
    INFO - 07:02:54: ...  76%|███████▌  | 76/100 [00:00<00:00, 749.10 it/sec, obj=3.58e+3]
    INFO - 07:02:54: ...  77%|███████▋  | 77/100 [00:00<00:00, 752.61 it/sec, obj=2.08e+3]
    INFO - 07:02:54: ...  78%|███████▊  | 78/100 [00:00<00:00, 756.94 it/sec, obj=2.15e+3]
    INFO - 07:02:54: ...  79%|███████▉  | 79/100 [00:00<00:00, 761.36 it/sec, obj=1.28e+3]
    INFO - 07:02:54: ...  80%|████████  | 80/100 [00:00<00:00, 765.37 it/sec, obj=1.31e+3]
    INFO - 07:02:54: ...  81%|████████  | 81/100 [00:00<00:00, 769.61 it/sec, obj=538]
    INFO - 07:02:54: ...  82%|████████▏ | 82/100 [00:00<00:00, 773.75 it/sec, obj=-268]
    INFO - 07:02:54: ...  83%|████████▎ | 83/100 [00:00<00:00, 778.01 it/sec, obj=92.5]
    INFO - 07:02:54: ...  84%|████████▍ | 84/100 [00:00<00:00, 782.09 it/sec, obj=-108]
    INFO - 07:02:54: ...  85%|████████▌ | 85/100 [00:00<00:00, 785.91 it/sec, obj=141]
    INFO - 07:02:54: ...  86%|████████▌ | 86/100 [00:00<00:00, 789.88 it/sec, obj=7.2e+3]
    INFO - 07:02:54: Optimization result:
    INFO - 07:02:54:    Optimizer info:
    INFO - 07:02:54:       Status: None
    INFO - 07:02:54:       Message: None
    INFO - 07:02:54:       Number of calls to the objective function by the optimizer: 100
    INFO - 07:02:54:    Solution:
    INFO - 07:02:54:       Objective: -1532.410845601642
    INFO - 07:02:54:       Design space:
    INFO - 07:02:54:       +-------------+-------------+---------------------+-------------+-------+
    INFO - 07:02:54:       | name        | lower_bound |        value        | upper_bound | type  |
    INFO - 07:02:54:       +-------------+-------------+---------------------+-------------+-------+
    INFO - 07:02:54:       | x_shared[0] |     0.01    | 0.07639739427791871 |     0.09    | float |
    INFO - 07:02:54:       | x_shared[1] |    30000    |  30382.18560041557  |    60000    | float |
    INFO - 07:02:54:       | x_shared[2] |     1.4     |  1.639876251582323  |     1.8     | float |
    INFO - 07:02:54:       | x_shared[3] |     2.5     |  6.678131125265034  |     8.5     | float |
    INFO - 07:02:54:       | x_shared[4] |      40     |  48.22252066873557  |      70     | float |
    INFO - 07:02:54:       | x_shared[5] |     500     |  1398.577963779934  |     1500    | float |
    INFO - 07:02:54:       | y_14[0]     |    24850    |  73521.45283526971  |    77100    | float |
    INFO - 07:02:54:       | y_14[1]     |    -7700    |  -6556.014595540449 |    45000    | float |
    INFO - 07:02:54:       | y_24        |     0.44    |  8.311658540076003  |    11.13    | float |
    INFO - 07:02:54:       | y_34        |     0.44    |  0.4466759405180455 |     1.98    | float |
    INFO - 07:02:54:       +-------------+-------------+---------------------+-------------+-------+
    INFO - 07:02:54: *** End DOEScenario execution (time: 0:00:00.125602) ***

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

Create an EmpiricalStatistics object for all variables

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

dataset = scenario.to_dataset(opt_naming=False)
analysis = create_statistics(dataset, name="SobieskiMission")

print(analysis)

    INFO - 07:02:54: Create SobieskiMission, a EmpiricalStatistics library.
SobieskiMission
   n_samples: 86
   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())

{'x_shared': array([1.13352258e-02, 3.01398316e+04, 1.40041295e+00, 2.55929483e+00,
       4.05869021e+01, 5.05494083e+02]), 'y_14': array([26794.72022057, -6556.01459554]), 'y_24': array([0.48388241]), 'y_34': array([0.44667594]), 'y_4': array([-1532.4108456])}

Create an EmpiricalStatistics object for the range

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

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

    INFO - 07:02:54: Create SobieskiMission.range, a EmpiricalStatistics library.
SobieskiMission.range
   n_samples: 86
   n_variables: 1
   variables: y_4

Get minimum

Here is the minimum value:

print(analysis.compute_minimum())

{'y_4': array([-1532.4108456])}

Get maximum

Here is the maximum value:

print(analysis.compute_maximum())

{'y_4': array([62030.01439676])}

Get range

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

print(analysis.compute_range())

{'y_4': array([63562.42524236])}

Get mean

Here is the mean value:

print(analysis.compute_mean())

{'y_4': array([4539.61303269])}

Get central moment

Here is the second central moment:

print(analysis.compute_moment(2))

{'y_4': array([85150303.53546816])}

Get standard deviation

Here is the standard deviation:

print(analysis.compute_standard_deviation())

{'y_4': array([9227.6922107])}

Get variance

Here is the variance.

print(analysis.compute_variance())

{'y_4': array([85150303.53546816])}

Get quantile

Here is the quantile with level equal to 80%:

print(analysis.compute_quantile(0.8))

{'y_4': array([5261.95981236])}

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))
print(analysis.compute_probability(default_output, greater=False))

{'y_4': array([0.76744186])}
{'y_4': array([0.23255814])}

Get quartile

Here is the second quartile:

print(analysis.compute_quartile(2))

{'y_4': array([2117.20788623])}

Get percentile

Here is the 50the percentile:

print(analysis.compute_percentile(50))

{'y_4': array([2117.20788623])}

Get median

Here is the median:

print(analysis.compute_median())

{'y_4': array([2117.20788623])}