.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/plot_line.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_line.py>`
        to download the full example code.

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

.. _sphx_glr_examples_plot_line.py:


====
Line
====

Example of fitting a straight line to some data.

.. GENERATED FROM PYTHON SOURCE LINES 8-58

.. code-block:: Python


    from __future__ import print_function

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

    import nestle

    np.random.seed(0)

    def model(theta, x):
        m, c = theta
        return m*x + c

    # Generate some data
    theta_true = [0.5, 10.0]
    N = 50
    x = np.sort(10*np.random.rand(N))
    y = model(theta_true, x) 
    yerr = 0.1+0.5*np.random.rand(N)
    y += yerr * np.random.randn(N)


    # The likelihood function:
    def loglike(theta):
        return -0.5*(np.sum((y-model(theta, x))**2/yerr**2))


    # Defines a flat prior in 0 < m < 1, 0 < b < 100:
    def prior_transform(theta):
        return np.array([1., 100.]) * theta


    # Run nested sampling
    res = nestle.sample(loglike, prior_transform, 2, method='single',
                        npoints=1000)
    print(res.summary())

    # weighted average and covariance:
    p, cov = nestle.mean_and_cov(res.samples, res.weights)

    print("m = {0:5.2f} +/- {1:5.2f}".format(p[0], np.sqrt(cov[0, 0])))
    print("b = {0:5.2f} +/- {1:5.2f}".format(p[1], np.sqrt(cov[1, 1])))

    plt.figure()
    plt.errorbar(x, y, yerr=yerr, capsize=0, fmt='k.', ecolor='.7')
    plt.plot([0., 10.], model(p, np.array([0., 10.])), c='k')
    plt.show()




.. image-sg:: /examples/images/sphx_glr_plot_line_001.png
   :alt: plot line
   :srcset: /examples/images/sphx_glr_plot_line_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    niter: 11556
    ncall: 19613
    nsamples: 12556
    logz: -35.894 +/-  0.098
    h:  9.690
    m =  0.50 +/-  0.01
    b = 10.10 +/-  0.07




.. GENERATED FROM PYTHON SOURCE LINES 59-60

Plot samples to see the full posterior surface.

.. GENERATED FROM PYTHON SOURCE LINES 60-64

.. code-block:: Python


    fig = corner.corner(res.samples, weights=res.weights, labels=['m', 'b'],
                        range=[0.99999, 0.99999], truths=theta_true, bins=30)
    plt.show()



.. image-sg:: /examples/images/sphx_glr_plot_line_002.png
   :alt: plot line
   :srcset: /examples/images/sphx_glr_plot_line_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.304 seconds)


.. _sphx_glr_download_examples_plot_line.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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