:orphan:

.. _general_examples:

Examples
========

Examples are included in the documentation to illustrate the usage of the package. The examples are divided into different categories, each corresponding to a specific functionality of the package.

.. toctree::
	:includehidden:
	:maxdepth: 2
	:titlesonly:



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Representation
--------------

These examples illustrate the use of the :mod:`FDApy.representation` module. It contains various functionalities to represent functional data in different formats.



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    <div class="sphx-glr-thumbcontainer" tooltip="Representation of univariate and dense functional data">

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  .. image:: /auto_examples/representation/images/thumb/sphx_glr_plot_dense_functional_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_representation_plot_dense_functional.py`

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      <div class="sphx-glr-thumbnail-title">Representation of univariate and dense functional data</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Representation of univariate and irregular functional data">

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  .. image:: /auto_examples/representation/images/thumb/sphx_glr_plot_irregular_functional_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_representation_plot_irregular_functional.py`

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      <div class="sphx-glr-thumbnail-title">Representation of univariate and irregular functional data</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Representation of functional data using a basis">

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  .. image:: /auto_examples/representation/images/thumb/sphx_glr_plot_basis_functional_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_representation_plot_basis_functional.py`

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      <div class="sphx-glr-thumbnail-title">Representation of functional data using a basis</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Representation of multivariate functional data">

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  .. image:: /auto_examples/representation/images/thumb/sphx_glr_plot_multivariate_functional_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_representation_plot_multivariate_functional.py`

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      <div class="sphx-glr-thumbnail-title">Representation of multivariate functional data</div>
    </div>


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Basis
-----

These examples illustrate the use of the :mod:`FDApy.basis` module. It contains examples of the different basis functions available in the package.


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    <div class="sphx-glr-thumbcontainer" tooltip="One-dimensional Basis">

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  .. image:: /auto_examples/basis/images/thumb/sphx_glr_plot_basis_1d_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_basis_plot_basis_1d.py`

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      <div class="sphx-glr-thumbnail-title">One-dimensional Basis</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Two-dimensional Basis">

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  .. image:: /auto_examples/basis/images/thumb/sphx_glr_plot_basis_2d_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_basis_plot_basis_2d.py`

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      <div class="sphx-glr-thumbnail-title">Two-dimensional Basis</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Multivariate Basis">

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  .. image:: /auto_examples/basis/images/thumb/sphx_glr_plot_basis_multivariate_1d_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_basis_plot_basis_multivariate_1d.py`

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      <div class="sphx-glr-thumbnail-title">Multivariate Basis</div>
    </div>


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Smoothing
---------

These examples illustrate the use of the :mod:`FDApy.preprocessing.smoothing` module. It contains various functionalities to smooth functional data.



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    <div class="sphx-glr-thumbcontainer" tooltip="Smoothing of dense one-dimensional functional data">

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  .. image:: /auto_examples/smoothing/images/thumb/sphx_glr_plot_smooth_data_1d_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_smoothing_plot_smooth_data_1d.py`

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      <div class="sphx-glr-thumbnail-title">Smoothing of dense one-dimensional functional data</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Smoothing of dense two-dimensional functional data">

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  .. image:: /auto_examples/smoothing/images/thumb/sphx_glr_plot_smooth_data_2d_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_smoothing_plot_smooth_data_2d.py`

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      <div class="sphx-glr-thumbnail-title">Smoothing of dense two-dimensional functional data</div>
    </div>


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Dimension Reduction
-------------------

These examples illustrate the use of the :mod:`FDApy.preprocessing.dim_reduction` module. It contains various functionalities to reduce the dimension of functional data.



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    <div class="sphx-glr-thumbcontainer" tooltip="FPCA of 1-dimensional data">

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  .. image:: /auto_examples/fpca/images/thumb/sphx_glr_plot_fpca_1d_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_fpca_plot_fpca_1d.py`

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      <div class="sphx-glr-thumbnail-title">FPCA of 1-dimensional data</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="FPCA of 1-dimensional sparse data">

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  .. image:: /auto_examples/fpca/images/thumb/sphx_glr_plot_fpca_1d_sparse_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_fpca_plot_fpca_1d_sparse.py`

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      <div class="sphx-glr-thumbnail-title">FPCA of 1-dimensional sparse data</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="FPCA of 2-dimensional data">

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  .. image:: /auto_examples/fpca/images/thumb/sphx_glr_plot_fpca_2d_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_fpca_plot_fpca_2d.py`

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      <div class="sphx-glr-thumbnail-title">FPCA of 2-dimensional data</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="MFPCA of 1-dimensional data">

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  .. image:: /auto_examples/fpca/images/thumb/sphx_glr_plot_mfpca_1d_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_fpca_plot_mfpca_1d.py`

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      <div class="sphx-glr-thumbnail-title">MFPCA of 1-dimensional data</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="MFPCA of 2-dimensional data">

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  .. image:: /auto_examples/fpca/images/thumb/sphx_glr_plot_mfpca_2d_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_fpca_plot_mfpca_2d.py`

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      <div class="sphx-glr-thumbnail-title">MFPCA of 2-dimensional data</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="MFPCA of 1- and 2-dimensional data">

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  .. image:: /auto_examples/fpca/images/thumb/sphx_glr_plot_mfpca_1d_2d_thumb.png
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  :ref:`sphx_glr_auto_examples_fpca_plot_mfpca_1d_2d.py`

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      <div class="sphx-glr-thumbnail-title">MFPCA of 1- and 2-dimensional data</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="MFPCA of 1-dimensional sparse data">

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  .. image:: /auto_examples/fpca/images/thumb/sphx_glr_plot_mfpca_1d_sparse_thumb.png
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  :ref:`sphx_glr_auto_examples_fpca_plot_mfpca_1d_sparse.py`

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      <div class="sphx-glr-thumbnail-title">MFPCA of 1-dimensional sparse data</div>
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Real data analysis
------------------

These examples illustrate the use of the package using real datasets.



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    <div class="sphx-glr-thumbcontainer" tooltip="Canadian weather dataset">

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  .. image:: /auto_examples/data_analysis/images/thumb/sphx_glr_plot_canadian_weather_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_data_analysis_plot_canadian_weather.py`

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      <div class="sphx-glr-thumbnail-title">Canadian weather dataset</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="CD4 dataset">

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  .. image:: /auto_examples/data_analysis/images/thumb/sphx_glr_plot_cd4_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_data_analysis_plot_cd4.py`

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      <div class="sphx-glr-thumbnail-title">CD4 dataset</div>
    </div>


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    </div>


Simulation
----------

These examples illustrate the use of the :mod:`FDApy.simulation` module. It contains various functionalities to simulate functional data.


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    <div class="sphx-glr-thumbcontainer" tooltip="Simulation using Karhunen-Loève decomposition">

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  .. image:: /auto_examples/simulation/images/thumb/sphx_glr_plot_karhunen_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_simulation_plot_karhunen.py`

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      <div class="sphx-glr-thumbnail-title">Simulation using Karhunen-Loève decomposition</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Simulation using multivariate Karhunen-Loève decomposition">

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  .. image:: /auto_examples/simulation/images/thumb/sphx_glr_plot_karhunen_multivariate_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_simulation_plot_karhunen_multivariate.py`

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      <div class="sphx-glr-thumbnail-title">Simulation using multivariate Karhunen-Loève decomposition</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Simulation of Brownian motion">

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  .. image:: /auto_examples/simulation/images/thumb/sphx_glr_plot_brownian_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_simulation_plot_brownian.py`

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      <div class="sphx-glr-thumbnail-title">Simulation of Brownian motion</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Simulation of functional data">

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  .. image:: /auto_examples/simulation/images/thumb/sphx_glr_plot_simulation_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_simulation_plot_simulation.py`

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      <div class="sphx-glr-thumbnail-title">Simulation of functional data</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Simulation of clusters of univariate functional data">

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  .. image:: /auto_examples/simulation/images/thumb/sphx_glr_plot_cluster_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_simulation_plot_cluster.py`

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      <div class="sphx-glr-thumbnail-title">Simulation of clusters of univariate functional data</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Simulation of clusters of multivariate functional data">

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  .. image:: /auto_examples/simulation/images/thumb/sphx_glr_plot_cluster_multivariate_thumb.png
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  :ref:`sphx_glr_auto_examples_simulation_plot_cluster_multivariate.py`

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      <div class="sphx-glr-thumbnail-title">Simulation of clusters of multivariate functional data</div>
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Miscellaneous
-------------

These examples illustrate diverse functionalities of the package that are not directly related to the main modules and to functional data analysis. They could be useful for the user to understand how to use the package in a more general context.




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    <div class="sphx-glr-thumbcontainer" tooltip="Smoothing of 1D data using local polynomial regression">

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  .. image:: /auto_examples/misc/images/thumb/sphx_glr_plot_local_polynomials_1d_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_misc_plot_local_polynomials_1d.py`

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      <div class="sphx-glr-thumbnail-title">Smoothing of 1D data using local polynomial regression</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Smoothing of 2D data using local polynomial regression">

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  .. image:: /auto_examples/misc/images/thumb/sphx_glr_plot_local_polynomials_2d_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_misc_plot_local_polynomials_2d.py`

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      <div class="sphx-glr-thumbnail-title">Smoothing of 2D data using local polynomial regression</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Smoothing of 1D data using P-Splines">

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  .. image:: /auto_examples/misc/images/thumb/sphx_glr_plot_psplines_1d_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_misc_plot_psplines_1d.py`

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      <div class="sphx-glr-thumbnail-title">Smoothing of 1D data using P-Splines</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Smoothing of 2D data using P-Splines">

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  .. image:: /auto_examples/misc/images/thumb/sphx_glr_plot_psplines_2d_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_misc_plot_psplines_2d.py`

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      <div class="sphx-glr-thumbnail-title">Smoothing of 2D data using P-Splines</div>
    </div>


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    </div>


.. toctree::
   :hidden:
   :includehidden:


   /auto_examples/representation/index.rst
   /auto_examples/basis/index.rst
   /auto_examples/smoothing/index.rst
   /auto_examples/fpca/index.rst
   /auto_examples/data_analysis/index.rst
   /auto_examples/simulation/index.rst
   /auto_examples/misc/index.rst


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      :download:`Download all examples in Python source code: auto_examples_python.zip </auto_examples/auto_examples_python.zip>`

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

      :download:`Download all examples in Jupyter notebooks: auto_examples_jupyter.zip </auto_examples/auto_examples_jupyter.zip>`


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