.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_bimodal_kde_2d.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_plot_bimodal_kde_2d.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_plot_bimodal_kde_2d.py:


2D bimodal example
====================

This example shows how to use ``lightkde.kde_2d`` and how it compares to
``scipy.stats.gaussian_kde`` for a bimodal bivariate case.

.. GENERATED FROM PYTHON SOURCE LINES 9-10

Import packages:

.. GENERATED FROM PYTHON SOURCE LINES 10-16

.. code-block:: default

    import matplotlib.pyplot as plt
    import numpy as np
    from scipy.stats import gaussian_kde, multivariate_normal

    from lightkde import kde_2d








.. GENERATED FROM PYTHON SOURCE LINES 17-18

Generate synthetic data from two univariate normal distributions:

.. GENERATED FROM PYTHON SOURCE LINES 18-29

.. code-block:: default

    np.random.seed(42)
    sample = np.vstack(
        (
            multivariate_normal.rvs(mean=[0, 0], cov=0.3, size=2000),
            multivariate_normal.rvs(
                mean=[2, 2], cov=[[0.5, -0.48], [-0.48, 0.5]], size=2000
            ),
        )
    )









.. GENERATED FROM PYTHON SOURCE LINES 30-31

Estimate kernel density using ``lightkde``:

.. GENERATED FROM PYTHON SOURCE LINES 31-33

.. code-block:: default

    density_mx, x_mx, y_mx = kde_2d(sample_mx=sample)








.. GENERATED FROM PYTHON SOURCE LINES 34-35

Estimate kernel density using ``scipy``:

.. GENERATED FROM PYTHON SOURCE LINES 35-39

.. code-block:: default

    gkde = gaussian_kde(dataset=sample.T)
    xy_mx = np.hstack((x_mx.reshape(-1, 1), y_mx.reshape(-1, 1)))
    scipy_density_mx = gkde.evaluate(xy_mx.T).reshape(x_mx.shape)








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Plot the data against the kernel density estimates:

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.. code-block:: default


    # pre-process
    bins = (30, 30)
    data_density_mx, xedges, yedges = np.histogram2d(
        sample[:, 0], sample[:, 1], bins=bins, density=True
    )
    z_min = 0
    z_max = np.max(data_density_mx)
    x_min, x_max = min(xedges), max(xedges)
    y_min, y_max = min(yedges), max(yedges)

    # plot
    cmap = "afmhot_r"
    fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(10, 3), sharex="all", sharey="all")

    # data
    h = ax1.hist2d(
        sample[:, 0],
        sample[:, 1],
        bins=bins,
        density=True,
        vmin=z_min,
        vmax=z_max,
        cmap=cmap,
    )[-1]
    ax1.set_title("data")

    # lightkde
    ax2.contourf(x_mx, y_mx, density_mx, levels=50, vmin=z_min, vmax=z_max, cmap=cmap)
    ax2.set_title("lightkde")

    # scipy
    ax3.contourf(x_mx, y_mx, scipy_density_mx, levels=50, vmin=z_min, vmax=z_max, cmap=cmap)
    ax3.set_xlim(x_min, x_max)
    ax3.set_ylim(y_min, y_max)
    ax3.set_title("scipy.stats.gaussian_kde")

    fig.subplots_adjust(right=0.89)
    cbar_ax = fig.add_axes([0.90, 0.15, 0.05, 0.7], aspect=30)
    fig.colorbar(h, cax=cbar_ax, label="density")
    plt.show()





.. image-sg:: /auto_examples/images/sphx_glr_plot_bimodal_kde_2d_001.png
   :alt: data, lightkde, scipy.stats.gaussian_kde
   :srcset: /auto_examples/images/sphx_glr_plot_bimodal_kde_2d_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 85-87

The ``scipy`` method oversmooths the kernel density and it is far
from the histogram of the data that it is expected to follow.


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

   **Total running time of the script:** ( 0 minutes  5.877 seconds)


.. _sphx_glr_download_auto_examples_plot_bimodal_kde_2d.py:

.. only:: html

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


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

      :download:`Download Python source code: plot_bimodal_kde_2d.py <plot_bimodal_kde_2d.py>`

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

      :download:`Download Jupyter notebook: plot_bimodal_kde_2d.ipynb <plot_bimodal_kde_2d.ipynb>`