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

.. only:: html

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

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

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

.. _sphx_glr_examples_plot_eggbox.py:


======
Eggbox
======

A likelihood surface with multiple modes of equal height.

.. GENERATED FROM PYTHON SOURCE LINES 8-36

.. code-block:: Python


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

    import nestle


    # Define the posterior density to be sampled:
    tmax = 5.0 * np.pi
    constant = np.log(1.0 / tmax**2)

    def loglike(x):
        t = 2.0 * tmax * x - tmax
        return (2.0 + np.cos(t[0]/2.0)*np.cos(t[1]/2.0))**5.0

    def prior(x):
        return x

    # plot the surface
    plt.figure(figsize=(8., 8.))
    ax = plt.axes(aspect=1)
    xx, yy = np.meshgrid(np.linspace(0., 1., 50),
                         np.linspace(0., 1., 50))
    Z = loglike(np.array([xx, yy]))
    ax.contourf(xx, yy, Z, 12, cmap=plt.cm.Blues_r)
    plt.title("True Log likelihood surface")




.. image-sg:: /examples/images/sphx_glr_plot_eggbox_001.png
   :alt: True Log likelihood surface
   :srcset: /examples/images/sphx_glr_plot_eggbox_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    Text(0.5, 1.0, 'True Log likelihood surface')



.. GENERATED FROM PYTHON SOURCE LINES 37-38

Run nested sampling in multi-ellipsoid mode and print a summary of results:

.. GENERATED FROM PYTHON SOURCE LINES 38-43

.. code-block:: Python


    res = nestle.sample(loglike, prior, 2, npoints=200, method='multi',
                        update_interval=20)
    print(res.summary())





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

 .. code-block:: none

    niter: 1532
    ncall: 3095
    nsamples: 1732
    logz: 236.196 +/-  0.170
    h:  5.806




.. GENERATED FROM PYTHON SOURCE LINES 44-46

Plot the samples. Note that this represents the *likelihood* rather than
its log, hence it is much more highly peaked.

.. GENERATED FROM PYTHON SOURCE LINES 46-51

.. code-block:: Python


    fig = corner.corner(res.samples, weights=res.weights, bins=500,
                        range=[(0., 1.), (0., 1.)])
    fig.set_size_inches(8., 8.)




.. image-sg:: /examples/images/sphx_glr_plot_eggbox_002.png
   :alt: plot eggbox
   :srcset: /examples/images/sphx_glr_plot_eggbox_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 5.700 seconds)


.. _sphx_glr_download_examples_plot_eggbox.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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