.. _sphx_glr_examples_plot_eggbox.py:


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

A likelihood surface with multiple modes of equal height.



.. 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:: /examples/images/sphx_glr_plot_eggbox_001.png
    :align: center




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



.. 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

 Out::

    niter: 1545
    ncall: 3035
    nsamples: 1745
    logz: 236.135 +/-  0.172
    h:  5.915


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



.. 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:: /examples/images/sphx_glr_plot_eggbox_002.png
    :align: center




**Total running time of the script:** ( 0 minutes  8.239 seconds)



.. container:: sphx-glr-footer


  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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

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

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