.. 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 28-40

.. code-block:: Python


    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)>



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

.. GENERATED FROM PYTHON SOURCE LINES 45-47

.. code-block:: Python

    parameter_space = ParameterSpace()








.. GENERATED FROM PYTHON SOURCE LINES 48-51

Then, we can add either deterministic variables
from their lower and upper bounds
(use :meth:`.ParameterSpace.add_variable`):

.. GENERATED FROM PYTHON SOURCE LINES 51-53

.. code-block:: Python

    parameter_space.add_variable("x", l_b=-2.0, u_b=2.0)








.. GENERATED FROM PYTHON SOURCE LINES 54-56

or uncertain variables from their distribution names and parameters
(use :meth:`.ParameterSpace.add_random_variable`):

.. GENERATED FROM PYTHON SOURCE LINES 56-59

.. code-block:: Python

    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;'>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 60-67

.. warning::

   We cannot mix probability distributions from different families,
   e.g. an :class:`.OTDistribution` and a :class:`.SPDistribution`.

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

.. GENERATED FROM PYTHON SOURCE LINES 67-69

.. code-block:: Python

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





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

 .. code-block:: none


    (True, True)



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Note that when GEMSEO does not offer a class for the SciPy distribution,
we can use the generic GEMSEO class :class:`.SPDistribution`
to create any SciPy distribution
by setting ``interfaced_distribution`` to its SciPy name
and ``parameters`` as a dictionary of SciPy parameter names and values
(`see the documentation of SciPy
<https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html>`__).

.. GENERATED FROM PYTHON SOURCE LINES 77-85

.. code-block:: Python


    # parameter_space.add_random_variable(
    #     "y",
    #     "SPDistribution",
    #     interfaced_distribution="norm",
    #     parameters={"loc": 1.0, "scale": 2.0},
    # )








.. GENERATED FROM PYTHON SOURCE LINES 86-96

A similar procedure can be followed
for OpenTURNS distributions for which
GEMSEO does not offer a class directly.
We can use the generic GEMSEO class :class:`.OTDistribution`
to create any OpenTURNS distribution
by setting ``interfaced_distribution`` to its OpenTURNS name
and ``parameters`` as a tuple of OpenTURNS parameter values
(`see the documentation of OpenTURNS
<https://openturns.github.io/openturns/latest/user_manual/_generated/
openturns.Normal.html#openturns.Normal>`__).

.. GENERATED FROM PYTHON SOURCE LINES 96-104

.. code-block:: Python


    # parameter_space.add_random_variable(
    #     "y",
    #     "OTDistribution",
    #     interfaced_distribution="Normal",
    #     parameters=(1.0, 2.0),
    # )








.. GENERATED FROM PYTHON SOURCE LINES 105-109

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 109-112

.. code-block:: Python

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





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

 .. code-block:: none


    [{'y': array([-0.45949272])}, {'y': array([-2.84088122])}]



.. GENERATED FROM PYTHON SOURCE LINES 113-114

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

.. GENERATED FROM PYTHON SOURCE LINES 114-117

.. code-block:: Python

    sample = parameter_space.compute_samples(n_samples=4)
    sample





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

 .. code-block:: none


    array([[ 0.5770075 ],
           [ 0.53609591],
           [ 0.84681924],
           [-0.34940697]])



.. GENERATED FROM PYTHON SOURCE LINES 118-123

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 123-125

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 126-143

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 143-149

.. code-block:: Python


    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 - 13:52:19:  
        INFO - 13:52:19: *** Start DOEScenario execution ***
        INFO - 13:52:19: DOEScenario
        INFO - 13:52:19:    Disciplines: AnalyticDiscipline
        INFO - 13:52:19:    MDO formulation: DisciplinaryOpt
        INFO - 13:52:19: Optimization problem:
        INFO - 13:52:19:    minimize z(x, y)
        INFO - 13:52:19:    with respect to x, y
        INFO - 13:52:19:    over the design space:
        INFO - 13:52:19:       +------+-------------+-------+-------------+-------+-------------------------+
        INFO - 13:52:19:       | Name | Lower bound | Value | Upper bound | Type  |       Distribution      |
        INFO - 13:52:19:       +------+-------------+-------+-------------+-------+-------------------------+
        INFO - 13:52:19:       | x    |      -2     |  None |      2      | float |                         |
        INFO - 13:52:19:       | y    |     -inf    |   0   |     inf     | float | norm(mu=0.0, sigma=1.0) |
        INFO - 13:52:19:       +------+-------------+-------+-------------+-------+-------------------------+
        INFO - 13:52:19: Solving optimization problem with algorithm lhs:
        INFO - 13:52:19:      1%|          | 1/100 [00:00<00:00, 391.19 it/sec, obj=3.12]
        INFO - 13:52:19:      2%|▏         | 2/100 [00:00<00:00, 612.44 it/sec, obj=1.72]
        INFO - 13:52:19:      3%|▎         | 3/100 [00:00<00:00, 771.67 it/sec, obj=0.181]
        INFO - 13:52:19:      4%|▍         | 4/100 [00:00<00:00, 880.19 it/sec, obj=3.76]
        INFO - 13:52:19:      5%|▌         | 5/100 [00:00<00:00, 970.95 it/sec, obj=2.15]
        INFO - 13:52:19:      6%|▌         | 6/100 [00:00<00:00, 1042.71 it/sec, obj=-0.666]
        INFO - 13:52:19:      7%|▋         | 7/100 [00:00<00:00, 1101.03 it/sec, obj=1.53]
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        INFO - 13:52:19:     86%|████████▌ | 86/100 [00:00<00:00, 1573.85 it/sec, obj=-1.49]
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        INFO - 13:52:19:     89%|████████▉ | 89/100 [00:00<00:00, 1575.64 it/sec, obj=-1.5]
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        INFO - 13:52:19:     92%|█████████▏| 92/100 [00:00<00:00, 1578.06 it/sec, obj=-1.86]
        INFO - 13:52:19:     93%|█████████▎| 93/100 [00:00<00:00, 1578.82 it/sec, obj=-0.0722]
        INFO - 13:52:19:     94%|█████████▍| 94/100 [00:00<00:00, 1579.63 it/sec, obj=-0.407]
        INFO - 13:52:19:     95%|█████████▌| 95/100 [00:00<00:00, 1579.61 it/sec, obj=0.194]
        INFO - 13:52:19:     96%|█████████▌| 96/100 [00:00<00:00, 1580.23 it/sec, obj=-0.207]
        INFO - 13:52:19:     97%|█████████▋| 97/100 [00:00<00:00, 1581.10 it/sec, obj=0.462]
        INFO - 13:52:19:     98%|█████████▊| 98/100 [00:00<00:00, 1581.39 it/sec, obj=-2.37]
        INFO - 13:52:19:     99%|█████████▉| 99/100 [00:00<00:00, 1582.11 it/sec, obj=1.32]
        INFO - 13:52:19:    100%|██████████| 100/100 [00:00<00:00, 1582.88 it/sec, obj=-2.21]
        INFO - 13:52:19: Optimization result:
        INFO - 13:52:19:    Optimizer info:
        INFO - 13:52:19:       Status: None
        INFO - 13:52:19:       Message: None
        INFO - 13:52:19:       Number of calls to the objective function by the optimizer: 100
        INFO - 13:52:19:    Solution:
        INFO - 13:52:19:       Objective: -3.3284373246961634
        INFO - 13:52:19:       Design space:
        INFO - 13:52:19:          +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 13:52:19:          | Name | Lower bound |       Value        | Upper bound | Type  |       Distribution      |
        INFO - 13:52:19:          +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 13:52:19:          | x    |      -2     | -1.959995425007306 |      2      | float |                         |
        INFO - 13:52:19:          | y    |     -inf    | -1.368441899688857 |     inf     | float | norm(mu=0.0, sigma=1.0) |
        INFO - 13:52:19:          +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 13:52:19: *** End DOEScenario execution (time: 0:00:00.088497) ***

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



.. GENERATED FROM PYTHON SOURCE LINES 150-151

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

.. GENERATED FROM PYTHON SOURCE LINES 151-153

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 154-155

and visualize it in a tabular way:

.. GENERATED FROM PYTHON SOURCE LINES 155-157

.. code-block:: Python

    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 158-160

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

.. GENERATED FROM PYTHON SOURCE LINES 160-162

.. code-block:: Python

    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 163-167

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 167-169

.. code-block:: Python

    uncertain_space = parameter_space.extract_uncertain_space()








.. GENERATED FROM PYTHON SOURCE LINES 170-172

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 172-177

.. code-block:: Python

    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 - 13:52:20:  
        INFO - 13:52:20: *** Start DOEScenario execution ***
        INFO - 13:52:20: DOEScenario
        INFO - 13:52:20:    Disciplines: AnalyticDiscipline
        INFO - 13:52:20:    MDO formulation: DisciplinaryOpt
        INFO - 13:52:20: Optimization problem:
        INFO - 13:52:20:    minimize z(y)
        INFO - 13:52:20:    with respect to y
        INFO - 13:52:20:    over the design space:
        INFO - 13:52:20:       +------+-------------------------+
        INFO - 13:52:20:       | Name |       Distribution      |
        INFO - 13:52:20:       +------+-------------------------+
        INFO - 13:52:20:       |  y   | norm(mu=0.0, sigma=1.0) |
        INFO - 13:52:20:       +------+-------------------------+
        INFO - 13:52:20: Solving optimization problem with algorithm lhs:
        INFO - 13:52:20:      1%|          | 1/100 [00:00<00:00, 1480.52 it/sec, obj=-0.641]
        INFO - 13:52:20:      2%|▏         | 2/100 [00:00<00:00, 1457.62 it/sec, obj=-0.394]
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        INFO - 13:52:20:      4%|▍         | 4/100 [00:00<00:00, 1535.53 it/sec, obj=0.944]
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        INFO - 13:52:20:     62%|██████▏   | 62/100 [00:00<00:00, 1615.07 it/sec, obj=0.4]
        INFO - 13:52:20:     63%|██████▎   | 63/100 [00:00<00:00, 1608.39 it/sec, obj=-0.195]
        INFO - 13:52:20:     64%|██████▍   | 64/100 [00:00<00:00, 1602.40 it/sec, obj=-0.578]
        INFO - 13:52:20:     65%|██████▌   | 65/100 [00:00<00:00, 1601.73 it/sec, obj=-0.977]
        INFO - 13:52:20:     66%|██████▌   | 66/100 [00:00<00:00, 1600.44 it/sec, obj=-0.114]
        INFO - 13:52:20:     67%|██████▋   | 67/100 [00:00<00:00, 1601.03 it/sec, obj=0.587]
        INFO - 13:52:20:     68%|██████▊   | 68/100 [00:00<00:00, 1601.63 it/sec, obj=-0.0679]
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        INFO - 13:52:20:     73%|███████▎  | 73/100 [00:00<00:00, 1603.35 it/sec, obj=0.513]
        INFO - 13:52:20:     74%|███████▍  | 74/100 [00:00<00:00, 1604.31 it/sec, obj=1.67]
        INFO - 13:52:20:     75%|███████▌  | 75/100 [00:00<00:00, 1604.82 it/sec, obj=0.557]
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        INFO - 13:52:20:     77%|███████▋  | 77/100 [00:00<00:00, 1605.80 it/sec, obj=-1.31]
        INFO - 13:52:20:     78%|███████▊  | 78/100 [00:00<00:00, 1601.04 it/sec, obj=-0.678]
        INFO - 13:52:20:     79%|███████▉  | 79/100 [00:00<00:00, 1594.59 it/sec, obj=-1.01]
        INFO - 13:52:20:     80%|████████  | 80/100 [00:00<00:00, 1594.16 it/sec, obj=0.246]
        INFO - 13:52:20:     81%|████████  | 81/100 [00:00<00:00, 1594.67 it/sec, obj=1.29]
        INFO - 13:52:20:     82%|████████▏ | 82/100 [00:00<00:00, 1595.30 it/sec, obj=0.75]
        INFO - 13:52:20:     83%|████████▎ | 83/100 [00:00<00:00, 1595.80 it/sec, obj=-1.54]
        INFO - 13:52:20:     84%|████████▍ | 84/100 [00:00<00:00, 1592.36 it/sec, obj=-0.156]
        INFO - 13:52:20:     85%|████████▌ | 85/100 [00:00<00:00, 1592.92 it/sec, obj=1.87]
        INFO - 13:52:20:     86%|████████▌ | 86/100 [00:00<00:00, 1593.36 it/sec, obj=-1.08]
        INFO - 13:52:20:     87%|████████▋ | 87/100 [00:00<00:00, 1593.96 it/sec, obj=-0.647]
        INFO - 13:52:20:     88%|████████▊ | 88/100 [00:00<00:00, 1594.52 it/sec, obj=0.968]
        INFO - 13:52:20:     89%|████████▉ | 89/100 [00:00<00:00, 1585.94 it/sec, obj=-0.773]
        INFO - 13:52:20:     90%|█████████ | 90/100 [00:00<00:00, 1584.84 it/sec, obj=1.26]
        INFO - 13:52:20:     91%|█████████ | 91/100 [00:00<00:00, 1586.05 it/sec, obj=0.166]
        INFO - 13:52:20:     92%|█████████▏| 92/100 [00:00<00:00, 1586.95 it/sec, obj=0.29]
        INFO - 13:52:20:     93%|█████████▎| 93/100 [00:00<00:00, 1587.36 it/sec, obj=0.127]
        INFO - 13:52:20:     94%|█████████▍| 94/100 [00:00<00:00, 1587.90 it/sec, obj=-1.26]
        INFO - 13:52:20:     95%|█████████▌| 95/100 [00:00<00:00, 1588.41 it/sec, obj=1.01]
        INFO - 13:52:20:     96%|█████████▌| 96/100 [00:00<00:00, 1588.93 it/sec, obj=0.0819]
        INFO - 13:52:20:     97%|█████████▋| 97/100 [00:00<00:00, 1588.43 it/sec, obj=-1.09]
        INFO - 13:52:20:     98%|█████████▊| 98/100 [00:00<00:00, 1588.77 it/sec, obj=-0.762]
        INFO - 13:52:20:     99%|█████████▉| 99/100 [00:00<00:00, 1589.26 it/sec, obj=-0.0429]
        INFO - 13:52:20:    100%|██████████| 100/100 [00:00<00:00, 1589.73 it/sec, obj=-0.813]
        INFO - 13:52:20: Optimization result:
        INFO - 13:52:20:    Optimizer info:
        INFO - 13:52:20:       Status: None
        INFO - 13:52:20:       Message: None
        INFO - 13:52:20:       Number of calls to the objective function by the optimizer: 100
        INFO - 13:52:20:    Solution:
        INFO - 13:52:20:       Objective: -2.6379682068246657
        INFO - 13:52:20:       Design space:
        INFO - 13:52:20:          +------+-------------------------+
        INFO - 13:52:20:          | Name |       Distribution      |
        INFO - 13:52:20:          +------+-------------------------+
        INFO - 13:52:20:          |  y   | norm(mu=0.0, sigma=1.0) |
        INFO - 13:52:20:          +------+-------------------------+
        INFO - 13:52:20: *** End DOEScenario execution (time: 0:00:00.086388) ***

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



.. GENERATED FROM PYTHON SOURCE LINES 178-183

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 183-185

.. code-block:: Python

    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 0.668 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-jupyter

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

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

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


.. only:: html

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

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