.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_composition.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_plot_composition.py>`
        to download the full example code or to run this example in your browser via Binder

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

.. _sphx_glr_auto_examples_plot_composition.py:


Function composition
====================

This example shows the composition of multidimensional FDataGrids.

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.. code-block:: Python


    # Author: Pablo Marcos Manchón
    # License: MIT

    # sphinx_gallery_thumbnail_number = 3

    import numpy as np
    from mpl_toolkits.mplot3d import axes3d

    import skfda








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Function composition can be applied to our data once is in functional
form using the method :func:`~skfda.representation.FData.compose`.

Let :math:`f: X \rightarrow Y` and :math:`g: Y \rightarrow Z`, the
composition will produce a third function :math:`g \circ f: X \rightarrow Z`
which maps :math:`x \in X` to :math:`g(f(x))` [1].

In :ref:`sphx_glr_auto_examples_plot_landmark_registration.py` it is shown
the simplest case, where it is used to apply a transformation of the time
scale of unidimensional data to register its features.

The following example shows the basic usage applied to a surface and a
curve, although the method will work for data with arbitrary dimensions to.

Firstly we will create a data object containing a surface
:math:`g: \mathbb{R}^2 \rightarrow \mathbb{R}`.

Constructs example surface

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.. code-block:: Python

    X, Y, Z = axes3d.get_test_data(1.2)
    data_matrix = [Z.T]
    grid_points = [X[0, :], Y[:, 0]]

    g = skfda.FDataGrid(data_matrix, grid_points)

    # Plots the surface
    g.plot()




.. image-sg:: /auto_examples/images/sphx_glr_plot_composition_001.png
   :alt: plot composition
   :srcset: /auto_examples/images/sphx_glr_plot_composition_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <Figure size 640x480 with 1 Axes>



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We will create a parametric curve
:math:`f(t)=(10 \, \cos(t), 10 \, sin(t))`. The result of the composition,
:math:`g \circ f:\mathbb{R} \rightarrow \mathbb{R}` will be another
functional object with the values of :math:`g` along the path given by
:math:`f`.

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.. code-block:: Python



    # Creation of circunference in parametric form
    t = np.linspace(0, 2 * np.pi, 100)

    data_matrix = [10 * np.array([np.cos(t), np.sin(t)]).T]
    f = skfda.FDataGrid(data_matrix, t)

    # Composition of function
    gof = g.compose(f)

    gof.plot()




.. image-sg:: /auto_examples/images/sphx_glr_plot_composition_002.png
   :alt: plot composition
   :srcset: /auto_examples/images/sphx_glr_plot_composition_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <Figure size 640x480 with 1 Axes>



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In the following chart it is plotted the curve
:math:`(10 \, \cos(t), 10 \, sin(t), g \circ f (t))` and the surface.

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.. code-block:: Python


    # Plots surface
    fig = g.plot(alpha=0.8)

    # Plots path along the surface
    path = f(t)[0]
    fig.axes[0].plot(path[:, 0], path[:, 1], gof(t)[0, ..., 0], color="orange")

    fig




.. image-sg:: /auto_examples/images/sphx_glr_plot_composition_003.png
   :alt: plot composition
   :srcset: /auto_examples/images/sphx_glr_plot_composition_003.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <Figure size 640x480 with 1 Axes>



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[1] Function composition `https://en.wikipedia.org/wiki/Function_composition
<https://en.wikipedia.org/wiki/Function_composition>`_.


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

   **Total running time of the script:** (0 minutes 0.496 seconds)


.. _sphx_glr_download_auto_examples_plot_composition.py:

.. only:: html

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

    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/GAA-UAM/scikit-fda/develop?filepath=examples/plot_composition.py
        :alt: Launch binder
        :width: 150 px

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

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

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

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


.. only:: html

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

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