.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/design_space/plot_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_design_space_plot_parameter_space.py>`
        to download the full example code

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

.. _sphx_glr_examples_design_space_plot_parameter_space.py:


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

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

.. GENERATED FROM PYTHON SOURCE LINES 27-39

.. 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)>



.. GENERATED FROM PYTHON SOURCE LINES 40-44

Firstly, a :class:`.ParameterSpace` does not require any mandatory argument.

Create a parameter space
------------------------

.. GENERATED FROM PYTHON SOURCE LINES 44-46

.. code-block:: Python

    parameter_space = ParameterSpace()








.. GENERATED FROM PYTHON SOURCE LINES 47-50

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

.. GENERATED FROM PYTHON SOURCE LINES 50-52

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 53-55

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

.. GENERATED FROM PYTHON SOURCE LINES 55-58

.. 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 59-66

.. 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 66-68

.. 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 76-84

.. 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 85-95

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 95-103

.. code-block:: Python


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








.. GENERATED FROM PYTHON SOURCE LINES 104-108

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

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.. 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([-1.48921944])}, {'y': array([0.98435788])}]



.. GENERATED FROM PYTHON SOURCE LINES 112-113

or as a dictionary:

.. GENERATED FROM PYTHON SOURCE LINES 113-116

.. code-block:: Python

    sample = parameter_space.compute_samples(n_samples=4)
    sample





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

 .. code-block:: none


    array([[ 0.1842264 ],
           [-0.66728834],
           [ 1.01831895],
           [-0.8882144 ]])



.. GENERATED FROM PYTHON SOURCE LINES 117-122

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.

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.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 125-136

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:`.Scenario` deals with all variables available in the
   :class:`.DesignSpace`. By inheritance, a :class:`.DOEScenario` deals
   with all variables available in the :class:`.ParameterSpace`.
   Thus, if we do not filter the uncertain variables, the
   :class:`.DOEScenario` will consider all variables. In particular, the
   deterministic variables will be considered as uniformly distributed.

.. GENERATED FROM PYTHON SOURCE LINES 136-141

.. 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 - 13:56:52:  
        INFO - 13:56:52: *** Start DOEScenario execution ***
        INFO - 13:56:52: DOEScenario
        INFO - 13:56:52:    Disciplines: AnalyticDiscipline
        INFO - 13:56:52:    MDO formulation: DisciplinaryOpt
        INFO - 13:56:52: Optimization problem:
        INFO - 13:56:52:    minimize z(x, y)
        INFO - 13:56:52:    with respect to x, y
        INFO - 13:56:52:    over the design space:
        INFO - 13:56:52:       +------+-------------+-------+-------------+-------+-------------------------+
        INFO - 13:56:52:       | Name | Lower bound | Value | Upper bound | Type  |       Distribution      |
        INFO - 13:56:52:       +------+-------------+-------+-------------+-------+-------------------------+
        INFO - 13:56:52:       | x    |      -2     |  None |      2      | float |                         |
        INFO - 13:56:52:       | y    |     -inf    |   0   |     inf     | float | norm(mu=0.0, sigma=1.0) |
        INFO - 13:56:52:       +------+-------------+-------+-------------+-------+-------------------------+
        INFO - 13:56:52: Solving optimization problem with algorithm lhs:
        INFO - 13:56:52:      1%|          | 1/100 [00:00<00:00, 351.49 it/sec, obj=3.12]
        INFO - 13:56:52:      2%|▏         | 2/100 [00:00<00:00, 551.56 it/sec, obj=1.72]
        INFO - 13:56:52:      3%|▎         | 3/100 [00:00<00:00, 706.23 it/sec, obj=0.181]
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        INFO - 13:56:52:     93%|█████████▎| 93/100 [00:00<00:00, 1388.47 it/sec, obj=-0.0722]
        INFO - 13:56:52:     94%|█████████▍| 94/100 [00:00<00:00, 1390.86 it/sec, obj=-0.407]
        INFO - 13:56:52:     95%|█████████▌| 95/100 [00:00<00:00, 1393.28 it/sec, obj=0.194]
        INFO - 13:56:52:     96%|█████████▌| 96/100 [00:00<00:00, 1395.63 it/sec, obj=-0.207]
        INFO - 13:56:52:     97%|█████████▋| 97/100 [00:00<00:00, 1396.84 it/sec, obj=0.462]
        INFO - 13:56:52:     98%|█████████▊| 98/100 [00:00<00:00, 1398.57 it/sec, obj=-2.37]
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        INFO - 13:56:52:    100%|██████████| 100/100 [00:00<00:00, 1402.90 it/sec, obj=-2.21]
        INFO - 13:56:52: Optimization result:
        INFO - 13:56:52:    Optimizer info:
        INFO - 13:56:52:       Status: None
        INFO - 13:56:52:       Message: None
        INFO - 13:56:52:       Number of calls to the objective function by the optimizer: 100
        INFO - 13:56:52:    Solution:
        INFO - 13:56:52:       Objective: -3.3284373246961634
        INFO - 13:56:52:       Design space:
        INFO - 13:56:52:          +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 13:56:52:          | Name | Lower bound |       Value        | Upper bound | Type  |       Distribution      |
        INFO - 13:56:52:          +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 13:56:52:          | x    |      -2     | -1.959995425007306 |      2      | float |                         |
        INFO - 13:56:52:          | y    |     -inf    | -1.368441899688857 |     inf     | float | norm(mu=0.0, sigma=1.0) |
        INFO - 13:56:52:          +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 13:56:52: *** End DOEScenario execution (time: 0:00:00.096368) ***

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



.. GENERATED FROM PYTHON SOURCE LINES 142-144

We can visualize the result by encapsulating the database in
a :class:`.Dataset`:

.. GENERATED FROM PYTHON SOURCE LINES 144-146

.. code-block:: Python

    dataset = scenario.to_dataset(opt_naming=False)








.. GENERATED FROM PYTHON SOURCE LINES 147-148

This visualization can be tabular for example:

.. GENERATED FROM PYTHON SOURCE LINES 148-150

.. 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">inputs</th>
          <th>outputs</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>0</th>
          <td>1.869403</td>
          <td>1.246453</td>
          <td>3.115855</td>
        </tr>
        <tr>
          <th>1</th>
          <td>-1.567970</td>
          <td>3.285041</td>
          <td>1.717071</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.282640</td>
          <td>-0.101706</td>
          <td>0.180934</td>
        </tr>
        <tr>
          <th>3</th>
          <td>1.916313</td>
          <td>1.848317</td>
          <td>3.764630</td>
        </tr>
        <tr>
          <th>4</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>95</th>
          <td>0.120633</td>
          <td>-0.327477</td>
          <td>-0.206844</td>
        </tr>
        <tr>
          <th>96</th>
          <td>-0.999225</td>
          <td>1.461403</td>
          <td>0.462178</td>
        </tr>
        <tr>
          <th>97</th>
          <td>-1.396066</td>
          <td>-0.972779</td>
          <td>-2.368845</td>
        </tr>
        <tr>
          <th>98</th>
          <td>1.090093</td>
          <td>0.225565</td>
          <td>1.315658</td>
        </tr>
        <tr>
          <th>99</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 151-152

or graphical by means of a scatter plot matrix for example:

.. GENERATED FROM PYTHON SOURCE LINES 152-154

.. code-block:: Python

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




.. image-sg:: /examples/design_space/images/sphx_glr_plot_parameter_space_001.png
   :alt: plot parameter space
   :srcset: /examples/design_space/images/sphx_glr_plot_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 155-159

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

.. GENERATED FROM PYTHON SOURCE LINES 159-161

.. code-block:: Python

    parameter_space.filter(parameter_space.uncertain_variables)






.. 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>y</td>
            <td>-inf</td>
            <td>-1.368441899688857</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 162-164

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

.. GENERATED FROM PYTHON SOURCE LINES 164-169

.. 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 - 13:56:53:  
        INFO - 13:56:53: *** Start DOEScenario execution ***
        INFO - 13:56:53: DOEScenario
        INFO - 13:56:53:    Disciplines: AnalyticDiscipline
        INFO - 13:56:53:    MDO formulation: DisciplinaryOpt
        INFO - 13:56:53: Optimization problem:
        INFO - 13:56:53:    minimize z(y)
        INFO - 13:56:53:    with respect to y
        INFO - 13:56:53:    over the design space:
        INFO - 13:56:53:       +------+-------------------------+
        INFO - 13:56:53:       | Name |       Distribution      |
        INFO - 13:56:53:       +------+-------------------------+
        INFO - 13:56:53:       |  y   | norm(mu=0.0, sigma=1.0) |
        INFO - 13:56:53:       +------+-------------------------+
        INFO - 13:56:53: Solving optimization problem with algorithm lhs:
        INFO - 13:56:53:      1%|          | 1/100 [00:00<00:00, 1248.30 it/sec, obj=-0.641]
        INFO - 13:56:53:      2%|▏         | 2/100 [00:00<00:00, 1263.53 it/sec, obj=-0.394]
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        INFO - 13:56:53:     85%|████████▌ | 85/100 [00:00<00:00, 1546.76 it/sec, obj=1.87]
        INFO - 13:56:53:     86%|████████▌ | 86/100 [00:00<00:00, 1547.45 it/sec, obj=-1.08]
        INFO - 13:56:53:     87%|████████▋ | 87/100 [00:00<00:00, 1548.62 it/sec, obj=-0.647]
        INFO - 13:56:53:     88%|████████▊ | 88/100 [00:00<00:00, 1548.62 it/sec, obj=0.968]
        INFO - 13:56:53:     89%|████████▉ | 89/100 [00:00<00:00, 1549.63 it/sec, obj=-0.773]
        INFO - 13:56:53:     90%|█████████ | 90/100 [00:00<00:00, 1550.71 it/sec, obj=1.26]
        INFO - 13:56:53:     91%|█████████ | 91/100 [00:00<00:00, 1551.77 it/sec, obj=0.166]
        INFO - 13:56:53:     92%|█████████▏| 92/100 [00:00<00:00, 1552.85 it/sec, obj=0.29]
        INFO - 13:56:53:     93%|█████████▎| 93/100 [00:00<00:00, 1553.93 it/sec, obj=0.127]
        INFO - 13:56:53:     94%|█████████▍| 94/100 [00:00<00:00, 1553.89 it/sec, obj=-1.26]
        INFO - 13:56:53:     95%|█████████▌| 95/100 [00:00<00:00, 1554.74 it/sec, obj=1.01]
        INFO - 13:56:53:     96%|█████████▌| 96/100 [00:00<00:00, 1555.77 it/sec, obj=0.0819]
        INFO - 13:56:53:     97%|█████████▋| 97/100 [00:00<00:00, 1556.78 it/sec, obj=-1.09]
        INFO - 13:56:53:     98%|█████████▊| 98/100 [00:00<00:00, 1557.72 it/sec, obj=-0.762]
        INFO - 13:56:53:     99%|█████████▉| 99/100 [00:00<00:00, 1558.68 it/sec, obj=-0.0429]
        INFO - 13:56:53:    100%|██████████| 100/100 [00:00<00:00, 1559.56 it/sec, obj=-0.813]
        INFO - 13:56:53: Optimization result:
        INFO - 13:56:53:    Optimizer info:
        INFO - 13:56:53:       Status: None
        INFO - 13:56:53:       Message: None
        INFO - 13:56:53:       Number of calls to the objective function by the optimizer: 100
        INFO - 13:56:53:    Solution:
        INFO - 13:56:53:       Objective: -2.6379682068246657
        INFO - 13:56:53:       Design space:
        INFO - 13:56:53:          +------+-------------------------+
        INFO - 13:56:53:          | Name |       Distribution      |
        INFO - 13:56:53:          +------+-------------------------+
        INFO - 13:56:53:          |  y   | norm(mu=0.0, sigma=1.0) |
        INFO - 13:56:53:          +------+-------------------------+
        INFO - 13:56:53: *** End DOEScenario execution (time: 0:00:00.087398) ***

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



.. GENERATED FROM PYTHON SOURCE LINES 170-174

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 174-176

.. code-block:: Python

    dataset = scenario.to_dataset(opt_naming=False)
    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>inputs</th>
          <th>outputs</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>0</th>
          <td>-0.640726</td>
          <td>-0.640726</td>
        </tr>
        <tr>
          <th>1</th>
          <td>-0.393653</td>
          <td>-0.393653</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.550565</td>
          <td>0.550565</td>
        </tr>
        <tr>
          <th>3</th>
          <td>0.944369</td>
          <td>0.944369</td>
        </tr>
        <tr>
          <th>4</th>
          <td>-2.115275</td>
          <td>-2.115275</td>
        </tr>
        <tr>
          <th>...</th>
          <td>...</td>
          <td>...</td>
        </tr>
        <tr>
          <th>95</th>
          <td>0.081947</td>
          <td>0.081947</td>
        </tr>
        <tr>
          <th>96</th>
          <td>-1.085812</td>
          <td>-1.085812</td>
        </tr>
        <tr>
          <th>97</th>
          <td>-0.761651</td>
          <td>-0.761651</td>
        </tr>
        <tr>
          <th>98</th>
          <td>-0.042932</td>
          <td>-0.042932</td>
        </tr>
        <tr>
          <th>99</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 0.608 seconds)


.. _sphx_glr_download_examples_design_space_plot_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_parameter_space.ipynb <plot_parameter_space.ipynb>`

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

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


.. only:: html

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

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