.. _sphx_glr_gallery_statistics_hexbin_demo.py:


===========
Hexbin Demo
===========

Plotting hexbins with Matplotlib.

Hexbin is an axes method or pyplot function that is essentially
a pcolor of a 2-D histogram with hexagonal cells.  It can be
much more informative than a scatter plot. In the first subplot
below, try substituting 'scatter' for 'hexbin'.



.. code-block:: python


    import numpy as np
    import matplotlib.pyplot as plt
    import matplotlib.mlab as mlab

    # Fixing random state for reproducibility
    np.random.seed(19680801)

    n = 100000
    x = np.random.standard_normal(n)
    y = 2.0 + 3.0 * x + 4.0 * np.random.standard_normal(n)
    xmin = x.min()
    xmax = x.max()
    ymin = y.min()
    ymax = y.max()

    fig, axs = plt.subplots(ncols=2, sharey=True, figsize=(7, 4))
    fig.subplots_adjust(hspace=0.5, left=0.07, right=0.93)
    ax = axs[0]
    hb = ax.hexbin(x, y, gridsize=50, cmap='inferno')
    ax.axis([xmin, xmax, ymin, ymax])
    ax.set_title("Hexagon binning")
    cb = fig.colorbar(hb, ax=ax)
    cb.set_label('counts')

    ax = axs[1]
    hb = ax.hexbin(x, y, gridsize=50, bins='log', cmap='inferno')
    ax.axis([xmin, xmax, ymin, ymax])
    ax.set_title("With a log color scale")
    cb = fig.colorbar(hb, ax=ax)
    cb.set_label('log10(N)')

    plt.show()





.. image:: /gallery/statistics/images/sphx_glr_hexbin_demo_001.png
    :align: center




Below we'll simulate some 2-D probability distributions, and show how to
visualize them with Matplotlib.



.. code-block:: python


    delta = 0.025
    x = y = np.arange(-3.0, 3.0, delta)
    X, Y = np.meshgrid(x, y)
    Z1 = mlab.bivariate_normal(X, Y, 1.0, 1.0, 0.0, 0.0)
    Z2 = mlab.bivariate_normal(X, Y, 1.5, 0.5, 1, 1)
    Z = Z2 - Z1  # difference of Gaussians

    x = X.ravel()
    y = Y.ravel()
    z = Z.ravel()

    # make some points 20 times more common than others, but same mean
    xcond = (-1 < x) & (x < 1)
    ycond = (-2 < y) & (y < 0)
    cond = xcond & ycond
    xnew = x[cond]
    ynew = y[cond]
    znew = z[cond]
    for i in range(20):
        x = np.hstack((x, xnew))
        y = np.hstack((y, ynew))
        z = np.hstack((z, znew))

    xmin = x.min()
    xmax = x.max()
    ymin = y.min()
    ymax = y.max()

    gridsize = 30

    fig, (ax0, ax1) = plt.subplots(2, 1)

    c = ax0.hexbin(x, y, C=z, gridsize=gridsize, marginals=True, cmap=plt.cm.RdBu,
                   vmax=abs(z).max(), vmin=-abs(z).max())
    ax0.axis([xmin, xmax, ymin, ymax])
    cb = fig.colorbar(c, ax=ax0)
    cb.set_label('mean value')

    c = ax1.hexbin(x, y, gridsize=gridsize, cmap=plt.cm.Blues_r)
    ax1.axis([xmin, xmax, ymin, ymax])
    cb = fig.colorbar(c, ax=ax1)
    cb.set_label('N observations')

    plt.show()



.. image:: /gallery/statistics/images/sphx_glr_hexbin_demo_002.png
    :align: center




**Total running time of the script:** ( 0 minutes  0.548 seconds)



.. only :: html

 .. container:: sphx-glr-footer


  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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