.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/simulation/plot_cluster.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_simulation_plot_cluster.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_simulation_plot_cluster.py:


Simulation of clusters of univariate 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 provides a class to simulate clusters of univariate functional data based on the Karhunen-Loève decomposition. The class :class:`~FDApy.simulation.KarhunenLoeve` allows to simulate functional data based on the truncated Karhunen-Loève representation of a functional process.

.. GENERATED FROM PYTHON SOURCE LINES 21-22

We simulate :math:`N = 20` curves on the one-dimensional observation grid :math:`\{0, 0.01, 0.02, \cdots, 1\}`, based on the first :math:`K = 25` Fourier basis functions on :math:`[0, 1]`. The clusters are defined through the coefficients in the Karhunen-Loève decomposition and parametrize using the `centers` parameter. The centers of the clusters are generated as Gaussian random variables with parameters defined by a `mean` and a `covariance`. We also consider an exponential decreasing of the eigenvalues.

.. GENERATED FROM PYTHON SOURCE LINES 22-48

.. code-block:: Python



    # Set general parameters
    rng = 42
    n_obs = 20

    # Define the random state
    random_state = np.random.default_rng(rng)

    # Parameters of the basis
    name = "fourier"
    n_functions = 25
    argvals = DenseArgvals({"input_dim_0": np.linspace(0, 1, 101)})

    # Parameters of the clusters
    n_clusters = 2
    mean = np.array([0, 0])
    covariance = np.array([[1, -0.6], [-0.6, 1]])
    centers = random_state.multivariate_normal(mean, covariance, size=n_functions)

    kl = KarhunenLoeve(
        basis_name=name, argvals=argvals, n_functions=n_functions, random_state=rng
    )
    kl.new(n_obs=n_obs, n_clusters=n_clusters, centers=centers, cluster_std="exponential")

    _ = plot(kl.data, kl.labels)



.. image-sg:: /auto_examples/simulation/images/sphx_glr_plot_cluster_001.png
   :alt: plot cluster
   :srcset: /auto_examples/simulation/images/sphx_glr_plot_cluster_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.112 seconds)


.. _sphx_glr_download_auto_examples_simulation_plot_cluster.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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