.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/smoothing/plot_smooth_data_2d.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_smoothing_plot_smooth_data_2d.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_smoothing_plot_smooth_data_2d.py:


Smoothing of dense two-dimensional functional data
==================================================

.. GENERATED FROM PYTHON SOURCE LINES 6-17

.. code-block:: Python


    # Author: Steven Golovkine <steven_golovkine@icloud.com>
    # License: MIT

    # Load packages
    import numpy as np

    from FDApy.representation import DenseArgvals
    from FDApy.simulation import KarhunenLoeve
    from FDApy.visualization import plot








.. GENERATED FROM PYTHON SOURCE LINES 18-19

The package includes different smoothing methods to smooth functional data. In this section, we are showing the building blocks of the smoothing of dense two-dimensional functional data. First, we simulate functional data using the Karhunen-Loève decomposition using B-splines basis functions. We then add some noise to the simulation.

.. GENERATED FROM PYTHON SOURCE LINES 19-43

.. code-block:: Python


    # Set general parameters
    rng = 42
    n_obs = 4

    # Parameters of the basis
    name = ("bsplines", "bsplines")
    n_functions = (5, 5)

    argvals = DenseArgvals({
        "input_dim_0": np.linspace(0, 1, 51),
        "input_dim_1": np.linspace(0, 1, 51)
    })


    kl = KarhunenLoeve(
        basis_name=name, argvals=argvals, n_functions=n_functions, random_state=rng
    )
    kl.new(n_obs=n_obs)
    data = kl.data

    # Add some noise to the simulation.
    kl.add_noise(0.05)








.. GENERATED FROM PYTHON SOURCE LINES 44-45

Smoothing two-dimensional functional data is similar to smoothing one-dimensional functional data. The main difference is that the smoothing is done in two dimensions. In this example, we will smooth the noisy data using the :func:`~FDApy.representation.DenseFunctionalData.smooth` function. This function allows to smooth the data using different methods such as local polynomials and P-splines. In this example, we will use the local polynomials smoothing method with an Epanechnikov kernel and a bandwidth of :math:`0.5`. We plot the smoothed data.

.. GENERATED FROM PYTHON SOURCE LINES 45-64

.. code-block:: Python


    # Smooth the data
    points = DenseArgvals({
        "input_dim_0": np.linspace(0, 1, 11),
        "input_dim_1": np.linspace(0, 1, 11)
    })
    kernel_name = "epanechnikov"
    bandwidth = 0.5
    degree = 1

    data_smooth = kl.noisy_data.smooth(
        points=points,
        method="LP",
        kernel_name=kernel_name,
        bandwidth=bandwidth,
        degree=degree,
    )

    _ = plot(data_smooth)



.. image-sg:: /auto_examples/smoothing/images/sphx_glr_plot_smooth_data_2d_001.png
   :alt: plot smooth data 2d
   :srcset: /auto_examples/smoothing/images/sphx_glr_plot_smooth_data_2d_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.235 seconds)


.. _sphx_glr_download_auto_examples_smoothing_plot_smooth_data_2d.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_smooth_data_2d.ipynb <plot_smooth_data_2d.ipynb>`

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

      :download:`Download Python source code: plot_smooth_data_2d.py <plot_smooth_data_2d.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_smooth_data_2d.zip <plot_smooth_data_2d.zip>`


.. only:: html

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

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