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

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

.. _sphx_glr_examples_mlearning_transformer_plot_scaler.py:


Scalers
=======

.. GENERATED FROM PYTHON SOURCE LINES 25-35

.. code-block:: Python


    from __future__ import annotations

    import matplotlib.pyplot as plt
    from numpy import linspace

    from gemseo.mlearning.transformers.scaler.min_max_scaler import MinMaxScaler
    from gemseo.mlearning.transformers.scaler.scaler import Scaler
    from gemseo.mlearning.transformers.scaler.standard_scaler import StandardScaler








.. GENERATED FROM PYTHON SOURCE LINES 36-39

Scaling data may be important, as discussed in another example.
Different scalers are available
and this example illustrate them with these simple data:

.. GENERATED FROM PYTHON SOURCE LINES 39-41

.. code-block:: Python

    data = linspace(-2, 2, 100)








.. GENERATED FROM PYTHON SOURCE LINES 42-46

First,
a :class:`.Scaler` transforms a value :math:`x` into a new value :math:`\tilde{x}`
based on the linear function :math:`\tilde{x}=a+bx`.
By default, the offset :math:`a` is zero and the coefficient :math:`b` is one:

.. GENERATED FROM PYTHON SOURCE LINES 46-48

.. code-block:: Python

    default_scaler = Scaler()








.. GENERATED FROM PYTHON SOURCE LINES 49-50

We can set these coefficient and offset at instantiation:

.. GENERATED FROM PYTHON SOURCE LINES 50-52

.. code-block:: Python

    custom_scaler = Scaler(offset=-1, coefficient=0.5)








.. GENERATED FROM PYTHON SOURCE LINES 53-55

or use a specific :class:`.Scaler` for that,
e.g. a :class:`.MinMaxScaler`:

.. GENERATED FROM PYTHON SOURCE LINES 55-57

.. code-block:: Python

    min_max_scaler = MinMaxScaler()








.. GENERATED FROM PYTHON SOURCE LINES 58-59

or a :class:`.StandardScaler`:

.. GENERATED FROM PYTHON SOURCE LINES 59-61

.. code-block:: Python

    standard_scaler = StandardScaler()








.. GENERATED FROM PYTHON SOURCE LINES 62-64

In this case,
the coefficient and offset will be computed from ``data``.

.. GENERATED FROM PYTHON SOURCE LINES 66-68

Now,
we fit each scaler from ``data`` and transform these ``data``:

.. GENERATED FROM PYTHON SOURCE LINES 68-83

.. code-block:: Python

    same_data = default_scaler.fit_transform(data)
    scaled_data = custom_scaler.fit_transform(data)
    min_max_scaled_data = min_max_scaler.fit_transform(data)
    standard_scaled_data = standard_scaler.fit_transform(data)

    #
    # We can plot the transformed data versus the original one:
    plt.plot(data, default_scaler.fit_transform(data), label="Default scaler")
    plt.plot(data, custom_scaler.fit_transform(data), label="Custom scaler")
    plt.plot(data, min_max_scaler.fit_transform(data), label="Min-max scaler")
    plt.plot(data, standard_scaler.fit_transform(data), label="Standard scaler")
    plt.legend()
    plt.grid()
    plt.show()




.. image-sg:: /examples/mlearning/transformer/images/sphx_glr_plot_scaler_001.png
   :alt: plot scaler
   :srcset: /examples/mlearning/transformer/images/sphx_glr_plot_scaler_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 84-94

The specific features of the different scalers are clearly visible.
In particular,
the :class:`.MinMaxScaler` projects the data onto the interval :math:`[0,1]`
as long as this data is included in the fitting interval.
The :class:`.StandardScaler` guarantees that
the transformed ``data`` have zero mean and unit variance.

Lastly,
every scaler can compute the Jacobian,
e.g.

.. GENERATED FROM PYTHON SOURCE LINES 94-95

.. code-block:: Python

    custom_scaler.compute_jacobian(data)




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

 .. code-block:: none


    array([[0.5]])




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

   **Total running time of the script:** (0 minutes 0.159 seconds)


.. _sphx_glr_download_examples_mlearning_transformer_plot_scaler.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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