.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/dataset/use_cases/plot_rosenbrock.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_dataset_use_cases_plot_rosenbrock.py>`
        to download the full example code

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

.. _sphx_glr_examples_dataset_use_cases_plot_rosenbrock.py:


Rosenbrock dataset
==================

This :class:`.Dataset` contains 100 evaluations
of the well-known Rosenbrock function:

.. math::

   f(x,y)=(1-x)^2+100(y-x^2)^2

This function is known for its global minimum at point (1,1),
its banana valley and the difficulty to reach its minimum.

This :class:`.Dataset` is based on a full-factorial
design of experiments.

`More information about the Rosenbrock function
<https://en.wikipedia.org/wiki/Rosenbrock_function>`_

.. GENERATED FROM PYTHON SOURCE LINES 41-52

.. code-block:: Python


    from __future__ import annotations

    from gemseo import configure_logger
    from gemseo import create_benchmark_dataset
    from gemseo.post.dataset.yvsx import YvsX
    from gemseo.post.dataset.zvsxy import ZvsXY

    configure_logger()






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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 53-57

Load Rosenbrock dataset
-----------------------
We can easily load this dataset
by means of the high-level function :func:`.create_benchmark_dataset`:

.. GENERATED FROM PYTHON SOURCE LINES 57-61

.. code-block:: Python


    dataset = create_benchmark_dataset("RosenbrockDataset")
    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>objectives</th>
        </tr>
        <tr>
          <th>VARIABLE</th>
          <th colspan="2" halign="left">x</th>
          <th>rosen</th>
        </tr>
        <tr>
          <th>COMPONENT</th>
          <th>0</th>
          <th>1</th>
          <th>0</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>1</th>
          <td>-2.000000</td>
          <td>-2.0</td>
          <td>3609.000000</td>
        </tr>
        <tr>
          <th>2</th>
          <td>-1.555556</td>
          <td>-2.0</td>
          <td>1959.952599</td>
        </tr>
        <tr>
          <th>3</th>
          <td>-1.111111</td>
          <td>-2.0</td>
          <td>1050.699741</td>
        </tr>
        <tr>
          <th>4</th>
          <td>-0.666667</td>
          <td>-2.0</td>
          <td>600.308642</td>
        </tr>
        <tr>
          <th>5</th>
          <td>-0.222222</td>
          <td>-2.0</td>
          <td>421.490779</td>
        </tr>
        <tr>
          <th>...</th>
          <td>...</td>
          <td>...</td>
          <td>...</td>
        </tr>
        <tr>
          <th>6</th>
          <td>0.222222</td>
          <td>2.0</td>
          <td>381.095717</td>
        </tr>
        <tr>
          <th>7</th>
          <td>0.666667</td>
          <td>2.0</td>
          <td>242.086420</td>
        </tr>
        <tr>
          <th>8</th>
          <td>1.111111</td>
          <td>2.0</td>
          <td>58.600975</td>
        </tr>
        <tr>
          <th>9</th>
          <td>1.555556</td>
          <td>2.0</td>
          <td>17.927907</td>
        </tr>
        <tr>
          <th>10</th>
          <td>2.000000</td>
          <td>2.0</td>
          <td>401.000000</td>
        </tr>
      </tbody>
    </table>
    <p>100 rows × 3 columns</p>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 62-64

Show the design data
--------------------

.. GENERATED FROM PYTHON SOURCE LINES 64-66

.. code-block:: Python

    dataset.design_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>
        </tr>
        <tr>
          <th>VARIABLE</th>
          <th colspan="2" halign="left">x</th>
        </tr>
        <tr>
          <th>COMPONENT</th>
          <th>0</th>
          <th>1</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>1</th>
          <td>-2.000000</td>
          <td>-2.0</td>
        </tr>
        <tr>
          <th>2</th>
          <td>-1.555556</td>
          <td>-2.0</td>
        </tr>
        <tr>
          <th>3</th>
          <td>-1.111111</td>
          <td>-2.0</td>
        </tr>
        <tr>
          <th>4</th>
          <td>-0.666667</td>
          <td>-2.0</td>
        </tr>
        <tr>
          <th>5</th>
          <td>-0.222222</td>
          <td>-2.0</td>
        </tr>
        <tr>
          <th>...</th>
          <td>...</td>
          <td>...</td>
        </tr>
        <tr>
          <th>6</th>
          <td>0.222222</td>
          <td>2.0</td>
        </tr>
        <tr>
          <th>7</th>
          <td>0.666667</td>
          <td>2.0</td>
        </tr>
        <tr>
          <th>8</th>
          <td>1.111111</td>
          <td>2.0</td>
        </tr>
        <tr>
          <th>9</th>
          <td>1.555556</td>
          <td>2.0</td>
        </tr>
        <tr>
          <th>10</th>
          <td>2.000000</td>
          <td>2.0</td>
        </tr>
      </tbody>
    </table>
    <p>100 rows × 2 columns</p>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 67-69

Show the objective data
-----------------------

.. GENERATED FROM PYTHON SOURCE LINES 69-71

.. code-block:: Python

    dataset.objective_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>objectives</th>
        </tr>
        <tr>
          <th>VARIABLE</th>
          <th>rosen</th>
        </tr>
        <tr>
          <th>COMPONENT</th>
          <th>0</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>1</th>
          <td>3609.000000</td>
        </tr>
        <tr>
          <th>2</th>
          <td>1959.952599</td>
        </tr>
        <tr>
          <th>3</th>
          <td>1050.699741</td>
        </tr>
        <tr>
          <th>4</th>
          <td>600.308642</td>
        </tr>
        <tr>
          <th>5</th>
          <td>421.490779</td>
        </tr>
        <tr>
          <th>...</th>
          <td>...</td>
        </tr>
        <tr>
          <th>6</th>
          <td>381.095717</td>
        </tr>
        <tr>
          <th>7</th>
          <td>242.086420</td>
        </tr>
        <tr>
          <th>8</th>
          <td>58.600975</td>
        </tr>
        <tr>
          <th>9</th>
          <td>17.927907</td>
        </tr>
        <tr>
          <th>10</th>
          <td>401.000000</td>
        </tr>
      </tbody>
    </table>
    <p>100 rows × 1 columns</p>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 72-74

Load the data with an input-output naming
-----------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 74-77

.. code-block:: Python

    dataset = create_benchmark_dataset("RosenbrockDataset", 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 colspan="2" halign="left">inputs</th>
          <th>outputs</th>
        </tr>
        <tr>
          <th>VARIABLE</th>
          <th colspan="2" halign="left">x</th>
          <th>rosen</th>
        </tr>
        <tr>
          <th>COMPONENT</th>
          <th>0</th>
          <th>1</th>
          <th>0</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>-2.000000</td>
          <td>-2.0</td>
          <td>3609.000000</td>
        </tr>
        <tr>
          <th>1</th>
          <td>-1.555556</td>
          <td>-2.0</td>
          <td>1959.952599</td>
        </tr>
        <tr>
          <th>2</th>
          <td>-1.111111</td>
          <td>-2.0</td>
          <td>1050.699741</td>
        </tr>
        <tr>
          <th>3</th>
          <td>-0.666667</td>
          <td>-2.0</td>
          <td>600.308642</td>
        </tr>
        <tr>
          <th>4</th>
          <td>-0.222222</td>
          <td>-2.0</td>
          <td>421.490779</td>
        </tr>
        <tr>
          <th>...</th>
          <td>...</td>
          <td>...</td>
          <td>...</td>
        </tr>
        <tr>
          <th>95</th>
          <td>0.222222</td>
          <td>2.0</td>
          <td>381.095717</td>
        </tr>
        <tr>
          <th>96</th>
          <td>0.666667</td>
          <td>2.0</td>
          <td>242.086420</td>
        </tr>
        <tr>
          <th>97</th>
          <td>1.111111</td>
          <td>2.0</td>
          <td>58.600975</td>
        </tr>
        <tr>
          <th>98</th>
          <td>1.555556</td>
          <td>2.0</td>
          <td>17.927907</td>
        </tr>
        <tr>
          <th>99</th>
          <td>2.000000</td>
          <td>2.0</td>
          <td>401.000000</td>
        </tr>
      </tbody>
    </table>
    <p>100 rows × 3 columns</p>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 78-80

Plot the data
-------------

.. GENERATED FROM PYTHON SOURCE LINES 80-83

.. code-block:: Python

    ZvsXY(dataset, x=("x", 0), y=("x", 1), z="rosen").execute(save=False, show=True)

    YvsX(dataset, x=("x", 0), y="rosen").execute(save=False, show=True)



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /examples/dataset/use_cases/images/sphx_glr_plot_rosenbrock_001.png
         :alt: rosen
         :srcset: /examples/dataset/use_cases/images/sphx_glr_plot_rosenbrock_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/dataset/use_cases/images/sphx_glr_plot_rosenbrock_002.png
         :alt: plot rosenbrock
         :srcset: /examples/dataset/use_cases/images/sphx_glr_plot_rosenbrock_002.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none


    [<Figure size 640x480 with 1 Axes>]




.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.314 seconds)


.. _sphx_glr_download_examples_dataset_use_cases_plot_rosenbrock.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

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

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

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

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


.. only:: html

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

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