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

.. only:: html

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

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

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

.. _sphx_glr_examples_mlearning_dimension_reduction_plot_pca_burgers.py:


PCA on Burgers equation
=======================

Example using PCA on solutions of the Burgers equation.

.. GENERATED FROM PYTHON SOURCE LINES 27-40

.. code-block:: Python


    from __future__ import annotations

    import matplotlib.pyplot as plt
    from numpy import eye

    from gemseo import configure_logger
    from gemseo.mlearning.transformers.dimension_reduction.pca import PCA
    from gemseo.problems.dataset.burgers import create_burgers_dataset

    configure_logger()






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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 41-43

Load dataset
~~~~~~~~~~~~

.. GENERATED FROM PYTHON SOURCE LINES 43-50

.. code-block:: Python

    dataset = create_burgers_dataset(n_samples=20)
    dataset

    t = dataset.input_dataset.to_numpy()[:, 0]
    u_t = dataset.output_dataset.to_numpy()
    t_split = 0.87








.. GENERATED FROM PYTHON SOURCE LINES 51-53

Plot dataset
~~~~~~~~~~~~

.. GENERATED FROM PYTHON SOURCE LINES 53-76

.. code-block:: Python



    def lines_gen():
        """Linestyle generator."""
        yield "-"
        for i in range(1, dataset.n_samples):
            yield 0, (i, 1, 1, 1)


    color = "red"
    lines = lines_gen()
    for i in range(dataset.n_samples):
        # Switch mode if discontinuity is gone
        if color == "red" and t[i] > t_split:
            color = "blue"
            lines = lines_gen()  # reset linestyle generator

        plt.plot(u_t[i], color=color, linestyle=next(lines), label=f"t={t[i]:.2f}")

    plt.legend()
    plt.title("Solutions to Burgers equation")
    plt.show()




.. image-sg:: /examples/mlearning/dimension_reduction/images/sphx_glr_plot_pca_burgers_001.png
   :alt: Solutions to Burgers equation
   :srcset: /examples/mlearning/dimension_reduction/images/sphx_glr_plot_pca_burgers_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 77-79

Create PCA
~~~~~~~~~~

.. GENERATED FROM PYTHON SOURCE LINES 79-89

.. code-block:: Python

    n_components = 7
    pca = PCA(n_components=n_components)
    pca.fit(u_t)

    means = u_t.mean(axis=1)
    # u_t = u_t - means[:, None]

    u_t_reduced = pca.transform(u_t)
    u_t_restored = pca.inverse_transform(u_t_reduced)





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

 .. code-block:: none

     WARNING - 13:55:27: The Scaler.fit() function does nothing; the instance of Scaler uses the coefficient and offset passed at its initialization




.. GENERATED FROM PYTHON SOURCE LINES 90-92

Plot restored data
~~~~~~~~~~~~~~~~~~

.. GENERATED FROM PYTHON SOURCE LINES 92-109

.. code-block:: Python

    color = "red"
    lines = lines_gen()
    for i in range(dataset.n_samples):
        # Switch mode if discontinuity is gone
        if color == "red" and t[i] > t_split:
            color = "blue"
            lines = lines_gen()  # reset linestyle generator

        plt.plot(
            u_t_restored[i],
            color=color,  # linestyle=next(lines),
            label=f"t={t[i]:.2f}",
        )
    plt.legend()
    plt.title("Reconstructed solution after PCA reduction.")
    plt.show()




.. image-sg:: /examples/mlearning/dimension_reduction/images/sphx_glr_plot_pca_burgers_002.png
   :alt: Reconstructed solution after PCA reduction.
   :srcset: /examples/mlearning/dimension_reduction/images/sphx_glr_plot_pca_burgers_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 110-112

Plot principal components
~~~~~~~~~~~~~~~~~~~~~~~~~

.. GENERATED FROM PYTHON SOURCE LINES 112-118

.. code-block:: Python

    red_component = eye(n_components)
    components = pca.inverse_transform(red_component)
    for i in range(n_components):
        plt.plot(components[i])
    plt.title("Principal components")
    plt.show()



.. image-sg:: /examples/mlearning/dimension_reduction/images/sphx_glr_plot_pca_burgers_003.png
   :alt: Principal components
   :srcset: /examples/mlearning/dimension_reduction/images/sphx_glr_plot_pca_burgers_003.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.679 seconds)


.. _sphx_glr_download_examples_mlearning_dimension_reduction_plot_pca_burgers.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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