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.. "auto_examples/simulation/plot_cluster_multivariate.py"
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.. only:: html

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

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

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

.. _sphx_glr_auto_examples_simulation_plot_cluster_multivariate.py:


Simulation of clusters of multivariate 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_multivariate








.. GENERATED FROM PYTHON SOURCE LINES 18-19

Similarly to the univariate case, the package provides a class to simulate clusters of multivariate 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 19-41

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








.. GENERATED FROM PYTHON SOURCE LINES 42-43

We simulate :math:`N = 20` curves of a multivariate process. The first component of the process is defined on the one-dimensional observation grid :math:`\{0, 0.01, 0.02, \cdots, 1\}`, based on the first :math:`K = 5` Fourier basis functions on :math:`[0, 1]` and the decreasing of the variance of the scores is exponential. The second component of the process is defined on the one-dimensional observation grid :math:`\{0, 0.01, 0.02, \cdots, 1\}`, based on the first :math:`K = 5` Wiener basis functions on :math:`[0, 1]` and the decreasing of the variance of the scores is exponential. The clusters are defined through the coefficients in the Karhunen-Loève decomposition. The centers of the clusters are generated as Gaussian random variables with parameters defined by `mean` and `covariance`.

.. GENERATED FROM PYTHON SOURCE LINES 43-50

.. code-block:: Python


    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, clusters_std="exponential")

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



.. image-sg:: /auto_examples/simulation/images/sphx_glr_plot_cluster_multivariate_001.png
   :alt: plot cluster multivariate
   :srcset: /auto_examples/simulation/images/sphx_glr_plot_cluster_multivariate_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.134 seconds)


.. _sphx_glr_download_auto_examples_simulation_plot_cluster_multivariate.py:

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

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


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