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

.. only:: html

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

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

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

.. _sphx_glr_auto_examples_gaussian_processes_plot_prior.py:


Gaussian Process Prior
======================

Hello world

.. GENERATED FROM PYTHON SOURCE LINES 8-16

.. code-block:: default


    import numpy as np

    import tensorflow as tf
    import tensorflow_probability as tfp

    import matplotlib.pyplot as plt








.. GENERATED FROM PYTHON SOURCE LINES 18-36

.. code-block:: default


    # shortcuts
    tfd = tfp.distributions
    kernels = tfp.math.psd_kernels

    # constants
    num_features = 1  # dimensionality
    num_index_points = 256  # nbr of index points
    num_samples = 8

    x_min, x_max = -5.0, 5.0
    X_grid = np.linspace(x_min, x_max, num_index_points).reshape(-1, num_features)

    seed = 23  # set random seed for reproducibility
    random_state = np.random.RandomState(seed)

    kernel = kernels.ExponentiatedQuadratic()








.. GENERATED FROM PYTHON SOURCE LINES 37-41

Kernel profile
--------------
The exponentiated quadratic kernel is *stationary*.
That is, :math:`k(x, x') = k(x, 0)` for all :math:`x, x'`.

.. GENERATED FROM PYTHON SOURCE LINES 41-51

.. code-block:: default


    fig, ax = plt.subplots()

    ax.plot(X_grid, kernel.apply(X_grid, np.zeros((1, num_features))))

    ax.set_xlabel(r'$x$')
    ax.set_ylabel(r'$k(x, 0)$')

    plt.show()




.. image:: /auto_examples/gaussian_processes/images/sphx_glr_plot_prior_001.png
    :alt: plot prior
    :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 52-54

Kernel matrix
-------------

.. GENERATED FROM PYTHON SOURCE LINES 54-65

.. code-block:: default

    fig, ax = plt.subplots()

    ax.pcolormesh(*np.broadcast_arrays(X_grid, X_grid.T),
                  kernel.matrix(X_grid, X_grid), cmap="cividis")
    ax.invert_yaxis()

    ax.set_xlabel(r'$x$')
    ax.set_ylabel(r'$x$')

    plt.show()




.. image:: /auto_examples/gaussian_processes/images/sphx_glr_plot_prior_002.png
    :alt: plot prior
    :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    /usr/src/app/examples/gaussian_processes/plot_prior.py:57: MatplotlibDeprecationWarning: shading='flat' when X and Y have the same dimensions as C is deprecated since 3.3.  Either specify the corners of the quadrilaterals with X and Y, or pass shading='auto', 'nearest' or 'gouraud', or set rcParams['pcolor.shading'].  This will become an error two minor releases later.
      kernel.matrix(X_grid, X_grid), cmap="cividis")




.. GENERATED FROM PYTHON SOURCE LINES 66-68

Prior samples
-------------

.. GENERATED FROM PYTHON SOURCE LINES 68-71

.. code-block:: default


    gp = tfd.GaussianProcess(kernel=kernel, index_points=X_grid)
    samples = gp.sample(num_samples, seed=seed)







.. GENERATED FROM PYTHON SOURCE LINES 72-82

.. code-block:: default


    fig, ax = plt.subplots()

    ax.plot(X_grid, samples.numpy().T)

    ax.set_xlabel(r'$x$')
    ax.set_ylabel(r'$f(x)$')
    ax.set_title(r'Draws of $f(x)$ from GP prior')

    plt.show()



.. image:: /auto_examples/gaussian_processes/images/sphx_glr_plot_prior_003.png
    :alt: Draws of $f(x)$ from GP prior
    :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  1.068 seconds)


.. _sphx_glr_download_auto_examples_gaussian_processes_plot_prior.py:


.. only :: html

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



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

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



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

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


.. only:: html

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

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