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

.. only:: html

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

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

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

.. _sphx_glr_auto_examples_plot_EP.py:


Clutter example for expectation propagation
===========================================

The code below uses the Expectation Propagation algorithm to solve the Clutter
problem, Bishop et al., 2006, section 10.7.1

.. GENERATED FROM PYTHON SOURCE LINES 13-19

Implementation Details
----------------------
Below is the code for the EP functions used in this example:

.. literalinclude:: /../../../src/ep/examples/clutter/core.py
   :language: python

.. GENERATED FROM PYTHON SOURCE LINES 21-23

Import requirments
------------------

.. GENERATED FROM PYTHON SOURCE LINES 23-33

.. code-block:: Python


    import numpy as np
    from scipy.stats import norm
    from IPython.display import display
    import plotly.graph_objects as go

    import ep.examples.clutter.utils
    import ep.examples.clutter.core
    import ep.examples.clutter.plot








.. GENERATED FROM PYTHON SOURCE LINES 34-36

Sample from the clutter model
-----------------------------

.. GENERATED FROM PYTHON SOURCE LINES 36-46

.. code-block:: Python


    theta = 3.0
    a = 10.0
    b = 100.0
    w = 0.5
    N = 30
    num_iter = 20

    samples = ep.examples.clutter.utils.sample(theta=theta, a=a, w=w, n_samples=N)








.. GENERATED FROM PYTHON SOURCE LINES 47-49

Plot sampled data
-----------------

.. GENERATED FROM PYTHON SOURCE LINES 49-72

.. code-block:: Python


    x_min = -10
    x_max = 10
    x_dt = 0.1

    x_dense = np.arange(x_min, x_max, x_dt)
    signal_pdf_values = norm.pdf(x_dense, loc=theta, scale=1.0)
    noise_pdf_values = norm.pdf(x_dense, loc=0, scale=np.sqrt(a))

    fig = go.Figure()
    trace = go.Scatter(x=samples, y=np.zeros(shape=samples.shape),
                       mode="markers", marker=dict(symbol="x", color="black"))
    fig.add_trace(trace)
    trace = go.Scatter(x=x_dense, y=signal_pdf_values, mode="lines",
                       line=dict(color="green"))
    fig.add_trace(trace)
    trace = go.Scatter(x=x_dense, y=noise_pdf_values, mode="lines",
                       line=dict(color="red"))
    fig.add_trace(trace)
    fig.update_xaxes(title=r"$\theta$")
    fig.update_layout(showlegend=False)
    fig






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                       {"responsive": true}                    )                };            </script>        </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 73-75

Expectation Propagation script
------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 75-116

.. code-block:: Python


    samples = [np.array([sample]) for sample in samples]
    D = len(samples[0])
    m, v, m_f, v_f, s_f = ep.examples.clutter.core.init(b=b, D=D, N=N)
    log_evidences = []
    snapshots = []

    for iter_num in range(num_iter):
        for n in range(N):
            v_cn = ep.examples.clutter.core.get_cavity_var(v=v, v_fn=v_f[n])
            m_cn = ep.examples.clutter.core.get_cavity_mean(m=m, m_fn=m_f[n], v_fn=v_f[n],
                                                            v_cn=v_cn)
            Z_n = ep.examples.clutter.core.get_zeroth_moment(w=w, a=a, m_cn=m_cn,
                                                             v_cn=v_cn,
                                                             x_n=samples[n])
            rho_n = ep.examples.clutter.core.get_site_strength(w=w, a=a, D=D,
                                                               Z_n=Z_n,
                                                               x_n=samples[n])
            m = ep.examples.clutter.core.get_q_mean(m_cn=m_cn, v_cn=v_cn,
                                                    rho_n=rho_n, x_n=samples[n])
            v = ep.examples.clutter.core.get_q_var(m_cn=m_cn, v_cn=v_cn,
                                                   rho_n=rho_n, x_n=samples[n])
            v_f[n] = ep.examples.clutter.core.get_factor_var(v_cn=v_cn, v=v)
            m_f[n] = ep.examples.clutter.core.get_factor_mean(m_cn=m_cn, v_cn=v_cn,
                                                              v_fn=v_f[n], m=m)
            s_f[n] = ep.examples.clutter.core.get_factor_scale(Z_n=Z_n, m_fn=m_f[n],
                                                               v_fn=v_f[n],
                                                               m_cn=m_cn, v_cn=v_cn)
        snapshots.append({
            "iter": iter_num,
            "v_cn": v_cn,
            "m_cn": m_cn.copy(),
            "v": v,
            "m": m.copy(),
            "v_fn": v_f[n],
            "m_fn": m_f[n].copy(),
        })
        log_evidence = ep.examples.clutter.core.get_log_evidence(m=m, v=v, m_f=m_f,
                                                        v_f=v_f, s_f=s_f, b=b)
        log_evidences.append(log_evidence)








.. GENERATED FROM PYTHON SOURCE LINES 117-119

Plot EP probability density functions after iteration 0
-------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 119-128

.. code-block:: Python


    iter_num = 0
    s = snapshots[iter_num]
    ep.examples.clutter.plot.plot_pdfs(theta=theta, m_cn=s["m_cn"], v_cn=s["v_cn"],
                                       m=s["m"], v=s["v"], m_fn=s["m_fn"],
                                       v_fn=s["v_fn"], samples=samples[:N],
                                       x_min=x_min, x_max=x_max, x_dt=x_dt,
                                       title=f"Iteration {iter_num}, Factor {N-1}")






.. raw:: html

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    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 129-131

Plot EP probability density functions after iteration 3
-------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 131-140

.. code-block:: Python


    iter_num = 3
    s = snapshots[iter_num]
    ep.examples.clutter.plot.plot_pdfs(theta=theta, m_cn=s["m_cn"], v_cn=s["v_cn"],
                                       m=s["m"], v=s["v"], m_fn=s["m_fn"],
                                       v_fn=s["v_fn"], samples=samples[:N],
                                       x_min=x_min, x_max=x_max, x_dt=x_dt,
                                       title=f"Iteration {iter_num}, Factor {N-1}")






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    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 141-143

Plot EP probability density functions after iteration 6
-------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 143-152

.. code-block:: Python


    iter_num = 6
    s = snapshots[iter_num]
    ep.examples.clutter.plot.plot_pdfs(theta=theta, m_cn=s["m_cn"], v_cn=s["v_cn"],
                                       m=s["m"], v=s["v"], m_fn=s["m_fn"],
                                       v_fn=s["v_fn"], samples=samples[:N],
                                       x_min=x_min, x_max=x_max, x_dt=x_dt,
                                       title=f"Iteration {iter_num}, Factor {N-1}")






.. raw:: html

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    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 153-155

Plot EP probability density functions after iteration 9
-------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 155-164

.. code-block:: Python


    iter_num = 9
    s = snapshots[iter_num]
    ep.examples.clutter.plot.plot_pdfs(theta=theta, m_cn=s["m_cn"], v_cn=s["v_cn"],
                                       m=s["m"], v=s["v"], m_fn=s["m_fn"],
                                       v_fn=s["v_fn"], samples=samples[:N],
                                       x_min=x_min, x_max=x_max, x_dt=x_dt,
                                       title=f"Iteration {iter_num}, Factor {N-1}")






.. raw:: html

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    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 165-167

Plot EP probability density functions after iteration 19
--------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 167-176

.. code-block:: Python


    iter_num = 19
    s = snapshots[iter_num]
    ep.examples.clutter.plot.plot_pdfs(theta=theta, m_cn=s["m_cn"], v_cn=s["v_cn"],
                                       m=s["m"], v=s["v"], m_fn=s["m_fn"],
                                       v_fn=s["v_fn"], samples=samples[:N],
                                       x_min=x_min, x_max=x_max, x_dt=x_dt,
                                       title=f"Iteration {iter_num}, Factor {N-1}")






.. raw:: html

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    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 177-179

Plot log evidences
------------------

.. GENERATED FROM PYTHON SOURCE LINES 179-181

.. code-block:: Python


    ep.examples.clutter.plot.plot_log_evidences(log_evidences)





.. raw:: html

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

   **Total running time of the script:** (0 minutes 1.249 seconds)


.. _sphx_glr_download_auto_examples_plot_EP.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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