.. 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 27-38

.. 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 39-43

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

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

.. GENERATED FROM PYTHON SOURCE LINES 43-45

.. code-block:: default

    parameter_space = ParameterSpace()








.. GENERATED FROM PYTHON SOURCE LINES 46-50

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

.. GENERATED FROM PYTHON SOURCE LINES 50-55

.. 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 56-58

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

.. GENERATED FROM PYTHON SOURCE LINES 58-60

.. 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 61-65

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

.. GENERATED FROM PYTHON SOURCE LINES 65-68

.. 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([-0.97694264])}, {'y': array([-0.46624564])}]



.. GENERATED FROM PYTHON SOURCE LINES 69-70

or as a dictionary:

.. GENERATED FROM PYTHON SOURCE LINES 70-73

.. code-block:: default

    sample = parameter_space.compute_samples(n_samples=4)
    sample





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

 .. code-block:: none


    array([[-0.26843244],
           [ 0.27673196],
           [ 1.46675697],
           [-1.20904408]])



.. GENERATED FROM PYTHON SOURCE LINES 74-79

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 79-81

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 82-93

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 93-98

.. 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 - 13:55:42:  
        INFO - 13:55:42: *** Start DOEScenario execution ***
        INFO - 13:55:42: DOEScenario
        INFO - 13:55:42:    Disciplines: AnalyticDiscipline
        INFO - 13:55:42:    MDO formulation: DisciplinaryOpt
        INFO - 13:55:42: Optimization problem:
        INFO - 13:55:42:    minimize z(x, y)
        INFO - 13:55:42:    with respect to x, y
        INFO - 13:55:42:    over the design space:
        INFO - 13:55:42:    +------+-------------+-------+-------------+-------+-------------------------+
        INFO - 13:55:42:    | name | lower_bound | value | upper_bound | type  |   Initial distribution  |
        INFO - 13:55:42:    +------+-------------+-------+-------------+-------+-------------------------+
        INFO - 13:55:42:    | x    |      -2     |  None |      2      | float |                         |
        INFO - 13:55:42:    | y    |     -inf    |   0   |     inf     | float | norm(mu=0.0, sigma=1.0) |
        INFO - 13:55:42:    +------+-------------+-------+-------------+-------+-------------------------+
        INFO - 13:55:42: Solving optimization problem with algorithm lhs:
        INFO - 13:55:42: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 13:55:42: ...   1%|          | 1/100 [00:00<00:00, 301.51 it/sec, obj=3.12]
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        INFO - 13:55:42: ...  93%|█████████▎| 93/100 [00:00<00:00, 1284.05 it/sec, obj=-.0722]
        INFO - 13:55:42: ...  94%|█████████▍| 94/100 [00:00<00:00, 1284.86 it/sec, obj=-.407]
        INFO - 13:55:42: ...  95%|█████████▌| 95/100 [00:00<00:00, 1286.72 it/sec, obj=0.194]
        INFO - 13:55:42: ...  96%|█████████▌| 96/100 [00:00<00:00, 1288.84 it/sec, obj=-.207]
        INFO - 13:55:42: ...  97%|█████████▋| 97/100 [00:00<00:00, 1290.21 it/sec, obj=0.462]
        INFO - 13:55:42: ...  98%|█████████▊| 98/100 [00:00<00:00, 1290.43 it/sec, obj=-2.37]
        INFO - 13:55:42: ...  99%|█████████▉| 99/100 [00:00<00:00, 1291.22 it/sec, obj=1.32]
        INFO - 13:55:42: ... 100%|██████████| 100/100 [00:00<00:00, 1291.98 it/sec, obj=-2.21]
        INFO - 13:55:42: Optimization result:
        INFO - 13:55:42:    Optimizer info:
        INFO - 13:55:42:       Status: None
        INFO - 13:55:42:       Message: None
        INFO - 13:55:42:       Number of calls to the objective function by the optimizer: 100
        INFO - 13:55:42:    Solution:
        INFO - 13:55:42:       Objective: -3.3284373246961634
        INFO - 13:55:42:       Parameter space:
        INFO - 13:55:42:       +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 13:55:42:       | name | lower_bound |       value        | upper_bound | type  |   Initial distribution  |
        INFO - 13:55:42:       +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 13:55:42:       | x    |      -2     | -1.959995425007306 |      2      | float |                         |
        INFO - 13:55:42:       | y    |     -inf    | -1.368441899688857 |     inf     | float | norm(mu=0.0, sigma=1.0) |
        INFO - 13:55:42:       +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 13:55:42: *** End DOEScenario execution (time: 0:00:00.102768) ***

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



.. GENERATED FROM PYTHON SOURCE LINES 99-101

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

.. GENERATED FROM PYTHON SOURCE LINES 101-103

.. code-block:: default

    dataset = scenario.to_dataset(opt_naming=False)








.. GENERATED FROM PYTHON SOURCE LINES 104-105

This visualization can be tabular for example:

.. GENERATED FROM PYTHON SOURCE LINES 105-107

.. 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">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 108-109

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

.. GENERATED FROM PYTHON SOURCE LINES 109-111

.. code-block:: default

    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 112-116

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 116-118

.. code-block:: default

    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;'>Initial 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 119-121

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

.. GENERATED FROM PYTHON SOURCE LINES 121-126

.. 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 - 13:55:43:  
        INFO - 13:55:43: *** Start DOEScenario execution ***
        INFO - 13:55:43: DOEScenario
        INFO - 13:55:43:    Disciplines: AnalyticDiscipline
        INFO - 13:55:43:    MDO formulation: DisciplinaryOpt
        INFO - 13:55:43: Optimization problem:
        INFO - 13:55:43:    minimize z(y)
        INFO - 13:55:43:    with respect to y
        INFO - 13:55:43:    over the design space:
        INFO - 13:55:43:    +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 13:55:43:    | name | lower_bound |       value        | upper_bound | type  |   Initial distribution  |
        INFO - 13:55:43:    +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 13:55:43:    | y    |     -inf    | -1.368441899688857 |     inf     | float | norm(mu=0.0, sigma=1.0) |
        INFO - 13:55:43:    +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 13:55:43: Solving optimization problem with algorithm lhs:
        INFO - 13:55:43: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 13:55:43: ...   1%|          | 1/100 [00:00<00:00, 1092.27 it/sec, obj=-.641]
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        INFO - 13:55:43: ...  91%|█████████ | 91/100 [00:00<00:00, 1469.06 it/sec, obj=0.166]
        INFO - 13:55:43: ...  92%|█████████▏| 92/100 [00:00<00:00, 1469.44 it/sec, obj=0.29]
        INFO - 13:55:43: ...  93%|█████████▎| 93/100 [00:00<00:00, 1470.56 it/sec, obj=0.127]
        INFO - 13:55:43: ...  94%|█████████▍| 94/100 [00:00<00:00, 1471.66 it/sec, obj=-1.26]
        INFO - 13:55:43: ...  95%|█████████▌| 95/100 [00:00<00:00, 1448.26 it/sec, obj=1.01]
        INFO - 13:55:43: ...  96%|█████████▌| 96/100 [00:00<00:00, 1447.17 it/sec, obj=0.0819]
        INFO - 13:55:43: ...  97%|█████████▋| 97/100 [00:00<00:00, 1447.78 it/sec, obj=-1.09]
        INFO - 13:55:43: ...  98%|█████████▊| 98/100 [00:00<00:00, 1448.78 it/sec, obj=-.762]
        INFO - 13:55:43: ...  99%|█████████▉| 99/100 [00:00<00:00, 1449.95 it/sec, obj=-.0429]
        INFO - 13:55:43: ... 100%|██████████| 100/100 [00:00<00:00, 1450.62 it/sec, obj=-.813]
        INFO - 13:55:43: Optimization result:
        INFO - 13:55:43:    Optimizer info:
        INFO - 13:55:43:       Status: None
        INFO - 13:55:43:       Message: None
        INFO - 13:55:43:       Number of calls to the objective function by the optimizer: 100
        INFO - 13:55:43:    Solution:
        INFO - 13:55:43:       Objective: -2.6379682068246657
        INFO - 13:55:43:       Parameter space:
        INFO - 13:55:43:       +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 13:55:43:       | name | lower_bound |       value        | upper_bound | type  |   Initial distribution  |
        INFO - 13:55:43:       +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 13:55:43:       | y    |     -inf    | -2.637968206824666 |     inf     | float | norm(mu=0.0, sigma=1.0) |
        INFO - 13:55:43:       +------+-------------+--------------------+-------------+-------+-------------------------+
        INFO - 13:55:43: *** End DOEScenario execution (time: 0:00:00.093859) ***

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



.. GENERATED FROM PYTHON SOURCE LINES 127-131

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 131-133

.. code-block:: default

    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 0.653 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-python

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

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

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


.. only:: html

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

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