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.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_representation_plot_basis_functional.py>`
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.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_representation_plot_basis_functional.py:


Representation of functional data using a basis
===============================================

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.. code-block:: Python


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

    # Load packages
    import matplotlib.pyplot as plt
    import numpy as np

    from FDApy.representation import Basis, BasisFunctionalData
    from FDApy.representation import DenseArgvals
    from FDApy.visualization import plot








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In this section, we are showing the building blocks of the representation of functional data using a basis. To define a :class:`~FDApy.representation.BasisFunctionalData` object, we need a :class:`~FDApy.representation.Basis` object and a set of coefficients. The basis object contains the information about the basis functions and the argvals. The coefficients are the weights of the basis functions. The basis functions are evaluated at the argvals and multiplied by the coefficients to obtain the functional data.

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For unidimensional functional data
----------------------------------
First, we will consider unidimensional functional data. We represent a functional data using a Fourier basis. The coefficients are drawn from a normal distribution.

.. GENERATED FROM PYTHON SOURCE LINES 26-39

.. code-block:: Python


    n_functions = 5
    argvals = DenseArgvals({"input_dim_0": np.linspace(0, 1, 101)})

    basis = Basis(name="fourier", n_functions=n_functions, argvals=argvals)
    coefs = np.random.normal(size=(3, n_functions))

    data = BasisFunctionalData(basis=basis, coefficients=coefs)

    plot(data)
    plt.show()





.. image-sg:: /auto_examples/representation/images/sphx_glr_plot_basis_functional_001.png
   :alt: plot basis functional
   :srcset: /auto_examples/representation/images/sphx_glr_plot_basis_functional_001.png
   :class: sphx-glr-single-img





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For two-dimensional functional data
-----------------------------------
Second, we will consider two-dimensional functional data. We represent a functional data using a tensor product of two Fourier basis. The coefficients are drawn from a normal distribution.

.. GENERATED FROM PYTHON SOURCE LINES 43-57

.. code-block:: Python


    name = ("fourier", "fourier")
    n_functions = (5, 5)
    argvals = DenseArgvals(
        {"input_dim_0": np.linspace(0, 1, 101), "input_dim_1": np.linspace(0, 1, 51)}
    )

    basis = Basis(name=name, n_functions=n_functions, argvals=argvals)
    coefs = np.random.normal(size=(3, np.prod(n_functions)))

    data_2d = BasisFunctionalData(basis=basis, coefficients=coefs)

    plot(data_2d)
    plt.show()



.. image-sg:: /auto_examples/representation/images/sphx_glr_plot_basis_functional_002.png
   :alt: plot basis functional
   :srcset: /auto_examples/representation/images/sphx_glr_plot_basis_functional_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.510 seconds)


.. _sphx_glr_download_auto_examples_representation_plot_basis_functional.py:

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