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

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

.. _sphx_glr_examples_uncertainty_plot_parameter_space.py:


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

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

.. GENERATED FROM PYTHON SOURCE LINES 28-37

.. code-block:: Python


    from __future__ import annotations

    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
    from gemseo.settings.probability_distributions import SPNormalDistribution_Settings








.. GENERATED FROM PYTHON SOURCE LINES 38-42

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

.. GENERATED FROM PYTHON SOURCE LINES 42-44

.. code-block:: Python

    parameter_space = ParameterSpace()








.. GENERATED FROM PYTHON SOURCE LINES 45-48

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

.. GENERATED FROM PYTHON SOURCE LINES 48-50

.. code-block:: Python

    parameter_space.add_variable("x", lower_bound=-2.0, upper_bound=2.0)








.. GENERATED FROM PYTHON SOURCE LINES 51-53

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

.. GENERATED FROM PYTHON SOURCE LINES 53-58

.. code-block:: Python

    parameter_space.add_random_variable(
        "y", SPNormalDistribution_Settings(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 59-81

or without Pydantic model:

.. code-block:: python

   parameter_space.add_random_variable("y", "SPNormalDistribution", mu=0.0, sigma=1.0)

.. warning::

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

.. note::
   :ref:`This page <gen_distribution_algos>`
   lists the available probability distributions.
   The names prefixed with SP correspond to distributions based on SciPy.
   while those prefixed with OT correspond to distributions based on OpenTURNS.
   The settings class ``DistributionClassName_Settings``
   associated with the distribution ``DistributionClassName`` can be imported
   from ``gemseo.settings.probability_distributions``.

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

.. GENERATED FROM PYTHON SOURCE LINES 81-83

.. 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 84-98

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_Settings(interface_distribution="norm", parameters={"loc": 1.0, "scale": 2.0}),
   )

.. GENERATED FROM PYTHON SOURCE LINES 100-117

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_Settings(interface_distribution="Normal", parameters=(1.0, 2.0)),
   )

.. GENERATED FROM PYTHON SOURCE LINES 119-124

Sample from the parameter space
-------------------------------
We can sample the uncertain variables from the :class:`.ParameterSpace`
and return the result either as a dictionary of NumPy arrays
indexed by the names of these variables:

.. GENERATED FROM PYTHON SOURCE LINES 124-127

.. code-block:: Python

    samples = parameter_space.compute_samples(n_samples=4)
    samples





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

 .. code-block:: none


    array([[ 0.18117067],
           [-0.98115293],
           [-0.23722144],
           [-0.02840998]])



.. GENERATED FROM PYTHON SOURCE LINES 128-130

or a unique NumPy array concatenating the values of these variables
according to the order in which they were added to the :class:`.ParameterSpace`:

.. GENERATED FROM PYTHON SOURCE LINES 130-133

.. code-block:: Python

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





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

 .. code-block:: none


    [{'y': array([-1.77667104])}, {'y': array([0.02361843])}]



.. GENERATED FROM PYTHON SOURCE LINES 134-139

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 139-141

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 142-147

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 147-151

.. 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

        INFO - 16:21:54: *** Start Sampling execution ***
        INFO - 16:21:54: Sampling
        INFO - 16:21:54:    Disciplines: AnalyticDiscipline
        INFO - 16:21:54:    MDO formulation: MDF
        INFO - 16:21:54: Running the algorithm PYDOE_LHS:
        INFO - 16:21:54:      1%|          | 1/100 [00:00<00:00, 548.99 it/sec]
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        INFO - 16:21:54:    100%|██████████| 100/100 [00:00<00:00, 3942.98 it/sec]
        INFO - 16:21:54: *** End Sampling execution ***




.. GENERATED FROM PYTHON SOURCE LINES 152-153

and visualize it in a tabular way:

.. GENERATED FROM PYTHON SOURCE LINES 153-155

.. 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 156-158

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

.. GENERATED FROM PYTHON SOURCE LINES 158-160

.. code-block:: Python

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




.. image-sg:: /examples/uncertainty/images/sphx_glr_plot_parameter_space_001.png
   :alt: plot parameter space
   :srcset: /examples/uncertainty/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 161-165

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 165-167

.. 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 168-170

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

.. GENERATED FROM PYTHON SOURCE LINES 170-172

.. code-block:: Python

    uncertain_space = parameter_space.extract_uncertain_space()








.. GENERATED FROM PYTHON SOURCE LINES 173-174

Then, we sample the discipline over this uncertain space:

.. GENERATED FROM PYTHON SOURCE LINES 174-178

.. 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

        INFO - 16:21:54: *** Start Sampling execution ***
        INFO - 16:21:54: Sampling
        INFO - 16:21:54:    Disciplines: AnalyticDiscipline
        INFO - 16:21:54:    MDO formulation: MDF
        INFO - 16:21:54: Running the algorithm PYDOE_LHS:
        INFO - 16:21:54:      1%|          | 1/100 [00:00<00:00, 3463.50 it/sec]
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        INFO - 16:21:54:    100%|██████████| 100/100 [00:00<00:00, 3923.14 it/sec]
        INFO - 16:21:54: *** End Sampling execution ***


.. 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 0.314 seconds)


.. _sphx_glr_download_examples_uncertainty_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>`_