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Chapter 2: Basic notions on reproducing kernels
===============================================

This gallery contains examples and tutorials for Chapter 2. The examples demonstrate how to use
the CodPy library for various machine learning and regression tasks.

Each example includes code and outputs, such as plots or results, to help you understand
how the library works.

Below are the examples for this chapter:


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="In this experiment, we plot in 2D and 3D various kernels available in CodPy.">

.. only:: html

  .. image:: /auto_ch2/images/thumb/sphx_glr_ch2_2_thumb.png
    :alt:

  :ref:`sphx_glr_auto_ch2_ch2_2.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">2.2 Reproducing kernels and transformation maps</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Objective --------- The goal of this experiment is to compare the performance of different models in predicting the output of a complex sinusoidal function (``periodic_fun``). The function is defined over a range of input values (``x``), and we generate predictions over a broader range (``z``) to see how each model generalizes beyond the training data.">

.. only:: html

  .. image:: /auto_ch2/images/thumb/sphx_glr_ch2_ex1D_thumb.png
    :alt:

  :ref:`sphx_glr_auto_ch2_ch2_ex1D.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">2.3 1D Periodic Function Extrapolation</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="2.3.2 Applying maps to kernels">

.. only:: html

  .. image:: /auto_ch2/images/thumb/sphx_glr_ch2_5_thumb.png
    :alt:

  :ref:`sphx_glr_auto_ch2_ch2_5.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">2.3.2 Applying maps to kernels</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This script demonstrates an experiment using CodPy and SciPy models to visualize a 2D periodic function. It generates random data points (``x``, fx) and (``z``, fz), applies both CodPy and SciPy models, and visualizes the results using 3D plots.">

.. only:: html

  .. image:: /auto_ch2/images/thumb/sphx_glr_ch2_ex2D_thumb.png
    :alt:

  :ref:`sphx_glr_auto_ch2_ch2_ex2D.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">2.4 2D Periodic Function Extrapolation</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="2.6.2 A study of the discrepancy functional">

.. only:: html

  .. image:: /auto_ch2/images/thumb/sphx_glr_ch2_discrepancy_functional_thumb.png
    :alt:

  :ref:`sphx_glr_auto_ch2_ch2_discrepancy_functional.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">2.6.2 A study of the discrepancy functional</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_ch2/ch2_2
   /auto_ch2/ch2_ex1D
   /auto_ch2/ch2_5
   /auto_ch2/ch2_ex2D
   /auto_ch2/ch2_discrepancy_functional



.. only:: html

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

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