.. 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 sample_disciplines
    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", lower_bound=-2.0, upper_bound=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='margin: 1em;'>Parameter space:<br/><table>
        <thead>
            <tr>
                <th>Name</th>
                <th>Lower bound</th>
                <th>Value</th>
                <th>Upper bound</th>
                <th>Type</th>
                <th>Distribution</th>
            </tr>
        </thead>
        <tbody>
            <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>
        </tbody>
    </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)



.. GENERATED FROM PYTHON SOURCE LINES 69-85

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>`__).

.. 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 87-106

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>`__).

.. code-block:: python

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

.. GENERATED FROM PYTHON SOURCE LINES 108-112

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 112-115

.. 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([2.20802034])}, {'y': array([-0.83830366])}]



.. GENERATED FROM PYTHON SOURCE LINES 116-117

or as a dictionary:

.. GENERATED FROM PYTHON SOURCE LINES 117-120

.. code-block:: Python

    sample = parameter_space.compute_samples(n_samples=4)
    sample





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

 .. code-block:: none


    array([[-0.25581204],
           [-1.87981732],
           [ 0.07967951],
           [ 0.67264765]])



.. GENERATED FROM PYTHON SOURCE LINES 121-126

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 126-128

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 129-134

Then,
we use the :func:`.sample_disciplines` function
with an :term:`LHS` algorithm
to generate 100 samples of the discipline
over the whole parameter space:

.. GENERATED FROM PYTHON SOURCE LINES 134-138

.. code-block:: Python

    dataset = sample_disciplines(
        [discipline], parameter_space, "z", algo_name="PYDOE_LHS", n_samples=100
    )





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

 .. code-block:: none

     WARNING - 11:49:09: No coupling in MDA, switching chain_linearize to True.
        INFO - 11:49:09: *** Start Sampling execution ***
        INFO - 11:49:09: Sampling
        INFO - 11:49:09:    Disciplines: AnalyticDiscipline
        INFO - 11:49:09:    MDO formulation: MDF
        INFO - 11:49:09: Running the algorithm PYDOE_LHS:
        INFO - 11:49:09:      1%|          | 1/100 [00:00<00:00, 438.92 it/sec]
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        INFO - 11:49:09:     95%|█████████▌| 95/100 [00:00<00:00, 2892.43 it/sec]
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        INFO - 11:49:09:     97%|█████████▋| 97/100 [00:00<00:00, 2900.71 it/sec]
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        INFO - 11:49:09:    100%|██████████| 100/100 [00:00<00:00, 2910.91 it/sec]
        INFO - 11:49:09: *** End Sampling execution (time: 0:00:00.046021) ***




.. GENERATED FROM PYTHON SOURCE LINES 139-140

and visualize it in a tabular way:

.. GENERATED FROM PYTHON SOURCE LINES 140-142

.. 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 143-144

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

.. GENERATED FROM PYTHON SOURCE LINES 144-146

.. 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 147-151

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 151-153

.. code-block:: Python

    parameter_space.filter(parameter_space.uncertain_variables)






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div style='margin: 1em;'>Parameter space:<br/><table>
        <thead>
            <tr>
                <th>Name</th>
                <th>Lower bound</th>
                <th>Value</th>
                <th>Upper bound</th>
                <th>Type</th>
                <th>Distribution</th>
            </tr>
        </thead>
        <tbody>
            <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>
        </tbody>
    </table></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 154-156

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

.. GENERATED FROM PYTHON SOURCE LINES 156-158

.. code-block:: Python

    uncertain_space = parameter_space.extract_uncertain_space()








.. GENERATED FROM PYTHON SOURCE LINES 159-160

Then, we sample the discipline over this uncertain space:

.. GENERATED FROM PYTHON SOURCE LINES 160-164

.. code-block:: Python

    dataset = sample_disciplines(
        [discipline], uncertain_space, "z", algo_name="PYDOE_LHS", n_samples=100
    )
    dataset




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

 .. code-block:: none

     WARNING - 11:49:09: No coupling in MDA, switching chain_linearize to True.
        INFO - 11:49:09: *** Start Sampling execution ***
        INFO - 11:49:09: Sampling
        INFO - 11:49:09:    Disciplines: AnalyticDiscipline
        INFO - 11:49:09:    MDO formulation: MDF
        INFO - 11:49:09: Running the algorithm PYDOE_LHS:
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        INFO - 11:49:09: *** End Sampling execution (time: 0:00:00.045086) ***


.. 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 0.477 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>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_parameter_space.zip <plot_parameter_space.zip>`


.. only:: html

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

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