.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/uncertainty/plot_u_parameter_space.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_uncertainty_plot_u_parameter_space.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_uncertainty_plot_u_parameter_space.py:


Parameter space
===============

In this example,
we will see the basics of :class:`.ParameterSpace`.

.. GENERATED FROM PYTHON SOURCE LINES 28-39

.. code-block:: default

    from __future__ import annotations

    from gemseo import configure_logger
    from gemseo import create_discipline
    from gemseo import create_scenario
    from gemseo.algos.parameter_space import ParameterSpace
    from gemseo.post.dataset.scatter_plot_matrix import ScatterMatrix

    configure_logger()






.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 40-44

Create a parameter space
------------------------
Firstly,
the creation of a :class:`.ParameterSpace` does not require any mandatory argument:

.. GENERATED FROM PYTHON SOURCE LINES 44-46

.. code-block:: default

    parameter_space = ParameterSpace()








.. GENERATED FROM PYTHON SOURCE LINES 47-52

Then, we can add either deterministic variables
from their lower and upper bounds
(use :meth:`.ParameterSpace.add_variable`)
or uncertain variables from their distribution names and parameters
(use :meth:`.ParameterSpace.add_random_variable`)

.. GENERATED FROM PYTHON SOURCE LINES 52-56

.. code-block:: default

    parameter_space.add_variable("x", l_b=-2.0, u_b=2.0)
    parameter_space.add_random_variable("y", "SPNormalDistribution", mu=0.0, sigma=1.0)
    parameter_space






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div style='background-color: #fafae2; padding: 10px;'>Parameter space:<br/><table>
        <tr>
            <th style='text-align: left;'>name</th>
            <th style='text-align: left;'>lower_bound</th>
            <th style='text-align: left;'>value</th>
            <th style='text-align: left;'>upper_bound</th>
            <th style='text-align: left;'>type</th>
            <th style='text-align: left;'>Initial distribution</th>
        </tr>
        <tr>
            <td>x</td>
            <td>-2</td>
            <td>None</td>
            <td>2</td>
            <td>float</td>
            <td></td>
        </tr>
        <tr>
            <td>y</td>
            <td>-inf</td>
            <td>0</td>
            <td>inf</td>
            <td>float</td>
            <td>norm(mu=0.0, sigma=1.0)</td>
        </tr>
    </table></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 57-59

We can check that the variables *x* and *y* are implemented
as deterministic and deterministic variables respectively:

.. GENERATED FROM PYTHON SOURCE LINES 59-61

.. code-block:: default

    parameter_space.is_deterministic("x"), parameter_space.is_uncertain("y")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    (True, True)



.. GENERATED FROM PYTHON SOURCE LINES 62-66

Sample from the parameter space
-------------------------------
We can sample the uncertain variables from the :class:`.ParameterSpace`
and get values either as a NumPy array (by default)

.. GENERATED FROM PYTHON SOURCE LINES 66-69

.. code-block:: default

    sample = parameter_space.compute_samples(n_samples=2, as_dict=True)
    sample





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    [{'y': array([0.80969516])}, {'y': array([2.46015528])}]



.. GENERATED FROM PYTHON SOURCE LINES 70-71

or as a dictionary of NumPy arrays indexed by the names of the variables:

.. GENERATED FROM PYTHON SOURCE LINES 71-74

.. code-block:: default

    sample = parameter_space.compute_samples(n_samples=4)
    sample





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    array([[0.36250283],
           [0.70154774],
           [0.34327059],
           [0.39628863]])



.. GENERATED FROM PYTHON SOURCE LINES 75-80

Sample a discipline over the parameter space
--------------------------------------------
We can also sample a discipline over the parameter space.
For simplicity,
we instantiate an :class:`.AnalyticDiscipline` from a dictionary of expressions:

.. GENERATED FROM PYTHON SOURCE LINES 80-82

.. code-block:: default

    discipline = create_discipline("AnalyticDiscipline", expressions={"z": "x+y"})








.. GENERATED FROM PYTHON SOURCE LINES 83-100

From these parameter space and discipline,
we build a :class:`.DOEScenario`
and execute it with a Latin Hypercube Sampling algorithm and 100 samples.

.. warning::

   A :class:`.DOEScenario` considers all the variables
   available in its :class:`.DesignSpace`.
   By inheritance,
   in the special case of a :class:`.ParameterSpace`,
   a :class:`.DOEScenario` considers all the variables
   available in this :class:`.ParameterSpace`.
   Thus,
   if we do not filter the uncertain variables,
   the :class:`.DOEScenario` will consider
   both the deterministic variables as uniformly distributed variables
   and the uncertain variables with their specified probability distributions.

.. GENERATED FROM PYTHON SOURCE LINES 100-106

.. code-block:: default


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





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

        INFO - 08:22:41:  
        INFO - 08:22:41: *** Start DOEScenario execution ***
        INFO - 08:22:41: DOEScenario
        INFO - 08:22:41:    Disciplines: AnalyticDiscipline
        INFO - 08:22:41:    MDO formulation: DisciplinaryOpt
        INFO - 08:22:41: Optimization problem:
        INFO - 08:22:41:    minimize z(x, y)
        INFO - 08:22:41:    with respect to x, y
        INFO - 08:22:41:    over the design space:
        INFO - 08:22:41:    +------+-------------+-------+-------------+-------+-------------------------+
        INFO - 08:22:41:    | name | lower_bound | value | upper_bound | type  |   Initial distribution  |
        INFO - 08:22:41:    +------+-------------+-------+-------------+-------+-------------------------+
        INFO - 08:22:41:    | x    |      -2     |  None |      2      | float |                         |
        INFO - 08:22:41:    | y    |     -inf    |   0   |     inf     | float | norm(mu=0.0, sigma=1.0) |
        INFO - 08:22:41:    +------+-------------+-------+-------------+-------+-------------------------+
        INFO - 08:22:41: Solving optimization problem with algorithm lhs:
        INFO - 08:22:41: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 08:22:41: ...   1%|          | 1/100 [00:00<00:00, 368.41 it/sec, obj=3.12]
        INFO - 08:22:41: ...   2%|▏         | 2/100 [00:00<00:00, 567.80 it/sec, obj=1.72]
        INFO - 08:22:41: ...   3%|▎         | 3/100 [00:00<00:00, 721.46 it/sec, obj=0.181]
        INFO - 08:22:41: ...   4%|▍         | 4/100 [00:00<00:00, 838.32 it/sec, obj=3.76]
        INFO - 08:22:41: ...   5%|▌         | 5/100 [00:00<00:00, 929.55 it/sec, obj=2.15]
        INFO - 08:22:41: ...   6%|▌         | 6/100 [00:00<00:00, 996.39 it/sec, obj=-.666]
        INFO - 08:22:41: ...   7%|▋         | 7/100 [00:00<00:00, 1052.71 it/sec, obj=1.53]
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        INFO - 08:22:41: ...  82%|████████▏ | 82/100 [00:00<00:00, 1541.26 it/sec, obj=0.505]
        INFO - 08:22:41: ...  83%|████████▎ | 83/100 [00:00<00:00, 1541.63 it/sec, obj=1.99]
        INFO - 08:22:41: ...  84%|████████▍ | 84/100 [00:00<00:00, 1542.37 it/sec, obj=0.574]
        INFO - 08:22:41: ...  85%|████████▌ | 85/100 [00:00<00:00, 1543.39 it/sec, obj=-2.06]
        INFO - 08:22:41: ...  86%|████████▌ | 86/100 [00:00<00:00, 1544.37 it/sec, obj=-1.49]
        INFO - 08:22:41: ...  87%|████████▋ | 87/100 [00:00<00:00, 1545.54 it/sec, obj=0.61]
        INFO - 08:22:41: ...  88%|████████▊ | 88/100 [00:00<00:00, 1546.62 it/sec, obj=0.542]
        INFO - 08:22:41: ...  89%|████████▉ | 89/100 [00:00<00:00, 1547.10 it/sec, obj=-1.5]
        INFO - 08:22:41: ...  90%|█████████ | 90/100 [00:00<00:00, 1547.96 it/sec, obj=0.201]
        INFO - 08:22:41: ...  91%|█████████ | 91/100 [00:00<00:00, 1548.48 it/sec, obj=0.949]
        INFO - 08:22:41: ...  92%|█████████▏| 92/100 [00:00<00:00, 1547.01 it/sec, obj=-1.86]
        INFO - 08:22:41: ...  93%|█████████▎| 93/100 [00:00<00:00, 1547.71 it/sec, obj=-.0722]
        INFO - 08:22:41: ...  94%|█████████▍| 94/100 [00:00<00:00, 1548.60 it/sec, obj=-.407]
        INFO - 08:22:41: ...  95%|█████████▌| 95/100 [00:00<00:00, 1549.49 it/sec, obj=0.194]
        INFO - 08:22:41: ...  96%|█████████▌| 96/100 [00:00<00:00, 1549.67 it/sec, obj=-.207]
        INFO - 08:22:41: ...  97%|█████████▋| 97/100 [00:00<00:00, 1550.09 it/sec, obj=0.462]
        INFO - 08:22:41: ...  98%|█████████▊| 98/100 [00:00<00:00, 1550.96 it/sec, obj=-2.37]
        INFO - 08:22:41: ...  99%|█████████▉| 99/100 [00:00<00:00, 1551.91 it/sec, obj=1.32]
        INFO - 08:22:41: ... 100%|██████████| 100/100 [00:00<00:00, 1552.82 it/sec, obj=-2.21]
        INFO - 08:22:41: Optimization result:
        INFO - 08:22:41:    Optimizer info:
        INFO - 08:22:41:       Status: None
        INFO - 08:22:41:       Message: None
        INFO - 08:22:41:       Number of calls to the objective function by the optimizer: 100
        INFO - 08:22:41:    Solution:
        INFO - 08:22:41:       Objective: -3.3284373246961634
        INFO - 08:22:41:       Parameter space:
        INFO - 08:22:41:       +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 08:22:41:       | name | lower_bound |       value        | upper_bound | type  |   Initial distribution  |
        INFO - 08:22:41:       +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 08:22:41:       | x    |      -2     | -1.959995425007306 |      2      | float |                         |
        INFO - 08:22:41:       | y    |     -inf    | -1.368441899688857 |     inf     | float | norm(mu=0.0, sigma=1.0) |
        INFO - 08:22:41:       +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 08:22:41: *** End DOEScenario execution (time: 0:00:00.089111) ***

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



.. GENERATED FROM PYTHON SOURCE LINES 107-108

We can export the optimization problem to a :class:`.Dataset`:

.. GENERATED FROM PYTHON SOURCE LINES 108-110

.. code-block:: default

    dataset = scenario.to_dataset(name="samples")








.. GENERATED FROM PYTHON SOURCE LINES 111-112

and visualize it in a tabular way:

.. GENERATED FROM PYTHON SOURCE LINES 112-114

.. code-block:: default

    dataset






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead tr th {
            text-align: left;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr>
          <th>GROUP</th>
          <th colspan="2" halign="left">designs</th>
          <th>functions</th>
        </tr>
        <tr>
          <th>VARIABLE</th>
          <th>x</th>
          <th>y</th>
          <th>z</th>
        </tr>
        <tr>
          <th>COMPONENT</th>
          <th>0</th>
          <th>0</th>
          <th>0</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>1</th>
          <td>1.869403</td>
          <td>1.246453</td>
          <td>3.115855</td>
        </tr>
        <tr>
          <th>2</th>
          <td>-1.567970</td>
          <td>3.285041</td>
          <td>1.717071</td>
        </tr>
        <tr>
          <th>3</th>
          <td>0.282640</td>
          <td>-0.101706</td>
          <td>0.180934</td>
        </tr>
        <tr>
          <th>4</th>
          <td>1.916313</td>
          <td>1.848317</td>
          <td>3.764630</td>
        </tr>
        <tr>
          <th>5</th>
          <td>1.562653</td>
          <td>0.586038</td>
          <td>2.148691</td>
        </tr>
        <tr>
          <th>...</th>
          <td>...</td>
          <td>...</td>
          <td>...</td>
        </tr>
        <tr>
          <th>6</th>
          <td>0.120633</td>
          <td>-0.327477</td>
          <td>-0.206844</td>
        </tr>
        <tr>
          <th>7</th>
          <td>-0.999225</td>
          <td>1.461403</td>
          <td>0.462178</td>
        </tr>
        <tr>
          <th>8</th>
          <td>-1.396066</td>
          <td>-0.972779</td>
          <td>-2.368845</td>
        </tr>
        <tr>
          <th>9</th>
          <td>1.090093</td>
          <td>0.225565</td>
          <td>1.315658</td>
        </tr>
        <tr>
          <th>10</th>
          <td>-1.433207</td>
          <td>-0.779330</td>
          <td>-2.212536</td>
        </tr>
      </tbody>
    </table>
    <p>100 rows × 3 columns</p>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 115-117

or with a graphical post-processing,
e.g. a scatter plot matrix:

.. GENERATED FROM PYTHON SOURCE LINES 117-119

.. code-block:: default

    ScatterMatrix(dataset).execute(save=False, show=True)




.. image-sg:: /examples/uncertainty/images/sphx_glr_plot_u_parameter_space_001.png
   :alt: plot u parameter space
   :srcset: /examples/uncertainty/images/sphx_glr_plot_u_parameter_space_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    [<Figure size 640x480 with 9 Axes>]



.. GENERATED FROM PYTHON SOURCE LINES 120-124

Sample a discipline over the uncertain space
--------------------------------------------
If we want to sample a discipline over the uncertain space,
we need to extract it:

.. GENERATED FROM PYTHON SOURCE LINES 124-126

.. code-block:: default

    uncertain_space = parameter_space.extract_uncertain_space()








.. GENERATED FROM PYTHON SOURCE LINES 127-129

Then, we clear the cache, create a new scenario from this parameter space
containing only the uncertain variables and execute it.

.. GENERATED FROM PYTHON SOURCE LINES 129-134

.. code-block:: default

    scenario = create_scenario(
        [discipline], "DisciplinaryOpt", "z", uncertain_space, scenario_type="DOE"
    )
    scenario.execute({"algo": "lhs", "n_samples": 100})





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

        INFO - 08:22:41:  
        INFO - 08:22:41: *** Start DOEScenario execution ***
        INFO - 08:22:41: DOEScenario
        INFO - 08:22:41:    Disciplines: AnalyticDiscipline
        INFO - 08:22:41:    MDO formulation: DisciplinaryOpt
        INFO - 08:22:41: Optimization problem:
        INFO - 08:22:41:    minimize z(y)
        INFO - 08:22:41:    with respect to y
        INFO - 08:22:41:    over the design space:
        INFO - 08:22:41:    +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 08:22:41:    | name | lower_bound |       value        | upper_bound | type  |   Initial distribution  |
        INFO - 08:22:41:    +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 08:22:41:    | y    |     -inf    | -1.368441899688857 |     inf     | float | norm(mu=0.0, sigma=1.0) |
        INFO - 08:22:41:    +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 08:22:41: Solving optimization problem with algorithm lhs:
        INFO - 08:22:41: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 08:22:41: ...   1%|          | 1/100 [00:00<00:00, 1786.33 it/sec, obj=-.641]
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        INFO - 08:22:41: ...   5%|▌         | 5/100 [00:00<00:00, 1591.77 it/sec, obj=-2.12]
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        INFO - 08:22:41: ...  43%|████▎     | 43/100 [00:00<00:00, 1578.09 it/sec, obj=1.4]
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        INFO - 08:22:41: ...  56%|█████▌    | 56/100 [00:00<00:00, 1580.42 it/sec, obj=-2.64]
        INFO - 08:22:41: ...  57%|█████▋    | 57/100 [00:00<00:00, 1579.87 it/sec, obj=-.0776]
        INFO - 08:22:41: ...  58%|█████▊    | 58/100 [00:00<00:00, 1580.42 it/sec, obj=1.08]
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        INFO - 08:22:41: ...  63%|██████▎   | 63/100 [00:00<00:00, 1581.38 it/sec, obj=-.195]
        INFO - 08:22:41: ...  64%|██████▍   | 64/100 [00:00<00:00, 1581.67 it/sec, obj=-.578]
        INFO - 08:22:41: ...  65%|██████▌   | 65/100 [00:00<00:00, 1582.16 it/sec, obj=-.977]
        INFO - 08:22:41: ...  66%|██████▌   | 66/100 [00:00<00:00, 1582.77 it/sec, obj=-.114]
        INFO - 08:22:41: ...  67%|██████▋   | 67/100 [00:00<00:00, 1583.34 it/sec, obj=0.587]
        INFO - 08:22:41: ...  68%|██████▊   | 68/100 [00:00<00:00, 1582.80 it/sec, obj=-.0679]
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        INFO - 08:22:41: ...  74%|███████▍  | 74/100 [00:00<00:00, 1583.43 it/sec, obj=1.67]
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        INFO - 08:22:41: ...  79%|███████▉  | 79/100 [00:00<00:00, 1585.00 it/sec, obj=-1.01]
        INFO - 08:22:41: ...  80%|████████  | 80/100 [00:00<00:00, 1585.38 it/sec, obj=0.246]
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        INFO - 08:22:41: ...  82%|████████▏ | 82/100 [00:00<00:00, 1584.67 it/sec, obj=0.75]
        INFO - 08:22:41: ...  83%|████████▎ | 83/100 [00:00<00:00, 1584.93 it/sec, obj=-1.54]
        INFO - 08:22:41: ...  84%|████████▍ | 84/100 [00:00<00:00, 1585.41 it/sec, obj=-.156]
        INFO - 08:22:41: ...  85%|████████▌ | 85/100 [00:00<00:00, 1585.88 it/sec, obj=1.87]
        INFO - 08:22:41: ...  86%|████████▌ | 86/100 [00:00<00:00, 1586.29 it/sec, obj=-1.08]
        INFO - 08:22:41: ...  87%|████████▋ | 87/100 [00:00<00:00, 1585.82 it/sec, obj=-.647]
        INFO - 08:22:41: ...  88%|████████▊ | 88/100 [00:00<00:00, 1586.16 it/sec, obj=0.968]
        INFO - 08:22:41: ...  89%|████████▉ | 89/100 [00:00<00:00, 1585.88 it/sec, obj=-.773]
        INFO - 08:22:41: ...  90%|█████████ | 90/100 [00:00<00:00, 1586.24 it/sec, obj=1.26]
        INFO - 08:22:41: ...  91%|█████████ | 91/100 [00:00<00:00, 1586.56 it/sec, obj=0.166]
        INFO - 08:22:41: ...  92%|█████████▏| 92/100 [00:00<00:00, 1585.71 it/sec, obj=0.29]
        INFO - 08:22:41: ...  93%|█████████▎| 93/100 [00:00<00:00, 1584.81 it/sec, obj=0.127]
        INFO - 08:22:41: ...  94%|█████████▍| 94/100 [00:00<00:00, 1584.94 it/sec, obj=-1.26]
        INFO - 08:22:41: ...  95%|█████████▌| 95/100 [00:00<00:00, 1584.77 it/sec, obj=1.01]
        INFO - 08:22:41: ...  96%|█████████▌| 96/100 [00:00<00:00, 1585.01 it/sec, obj=0.0819]
        INFO - 08:22:41: ...  97%|█████████▋| 97/100 [00:00<00:00, 1585.38 it/sec, obj=-1.09]
        INFO - 08:22:41: ...  98%|█████████▊| 98/100 [00:00<00:00, 1585.59 it/sec, obj=-.762]
        INFO - 08:22:41: ...  99%|█████████▉| 99/100 [00:00<00:00, 1585.86 it/sec, obj=-.0429]
        INFO - 08:22:41: ... 100%|██████████| 100/100 [00:00<00:00, 1585.35 it/sec, obj=-.813]
        INFO - 08:22:41: Optimization result:
        INFO - 08:22:41:    Optimizer info:
        INFO - 08:22:41:       Status: None
        INFO - 08:22:41:       Message: None
        INFO - 08:22:41:       Number of calls to the objective function by the optimizer: 100
        INFO - 08:22:41:    Solution:
        INFO - 08:22:41:       Objective: -2.6379682068246657
        INFO - 08:22:41:       Parameter space:
        INFO - 08:22:41:       +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 08:22:41:       | name | lower_bound |       value        | upper_bound | type  |   Initial distribution  |
        INFO - 08:22:41:       +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 08:22:41:       | y    |     -inf    | -2.637968206824666 |     inf     | float | norm(mu=0.0, sigma=1.0) |
        INFO - 08:22:41:       +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 08:22:41: *** End DOEScenario execution (time: 0:00:00.086681) ***

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



.. GENERATED FROM PYTHON SOURCE LINES 135-140

Finally,
we build a dataset from the disciplinary cache and visualize it.
We can see that the deterministic variable 'x' is set to its default value
for all evaluations,
contrary to the previous case where we were considering the whole parameter space:

.. GENERATED FROM PYTHON SOURCE LINES 140-142

.. code-block:: default

    dataset = scenario.to_dataset(name="samples")
    dataset





.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead tr th {
            text-align: left;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr>
          <th>GROUP</th>
          <th>designs</th>
          <th>functions</th>
        </tr>
        <tr>
          <th>VARIABLE</th>
          <th>y</th>
          <th>z</th>
        </tr>
        <tr>
          <th>COMPONENT</th>
          <th>0</th>
          <th>0</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>1</th>
          <td>-0.640726</td>
          <td>-0.640726</td>
        </tr>
        <tr>
          <th>2</th>
          <td>-0.393653</td>
          <td>-0.393653</td>
        </tr>
        <tr>
          <th>3</th>
          <td>0.550565</td>
          <td>0.550565</td>
        </tr>
        <tr>
          <th>4</th>
          <td>0.944369</td>
          <td>0.944369</td>
        </tr>
        <tr>
          <th>5</th>
          <td>-2.115275</td>
          <td>-2.115275</td>
        </tr>
        <tr>
          <th>...</th>
          <td>...</td>
          <td>...</td>
        </tr>
        <tr>
          <th>6</th>
          <td>0.081947</td>
          <td>0.081947</td>
        </tr>
        <tr>
          <th>7</th>
          <td>-1.085812</td>
          <td>-1.085812</td>
        </tr>
        <tr>
          <th>8</th>
          <td>-0.761651</td>
          <td>-0.761651</td>
        </tr>
        <tr>
          <th>9</th>
          <td>-0.042932</td>
          <td>-0.042932</td>
        </tr>
        <tr>
          <th>10</th>
          <td>-0.813354</td>
          <td>-0.813354</td>
        </tr>
      </tbody>
    </table>
    <p>100 rows × 2 columns</p>
    </div>
    </div>
    <br />
    <br />


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.640 seconds)


.. _sphx_glr_download_examples_uncertainty_plot_u_parameter_space.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example




    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_u_parameter_space.py <plot_u_parameter_space.py>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_u_parameter_space.ipynb <plot_u_parameter_space.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_