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

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

.. _sphx_glr_auto_examples_basic.py:


Basic Example
=============

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.. code-block:: Python


    import numpy as np








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Formulating the possible associations between targets and measurements
----------------------------------------------------------------------

Both :class:`~.EHM` and :class:`~.EHM2` operate on a ``validation_matrix`` and a ``likelihood_matrix``. The
``validation_matrix`` is an indicator matrix that represents the possible associations between different targets
and measurements, while the ``likelihood_matrix`` contains the respective likelihoods/probabilities of these
associations. Both matrices have a shape ``(N_T, N_M+1)``, where ``N_T`` is the number of targets and ``N_M`` is
the numer of measurements.

For example, assume we have the following scenario of 4 targets and 4 measurements (taken from Section 4.4 of
[EHM2]_):

+---------------+---------------------------+
| Target index  | Gated measurement indices |
+===============+===========================+
| 0             | 0, 1                      |
+---------------+---------------------------+
| 1             | 0, 1, 2, 3                |
+---------------+---------------------------+
| 2             | 0, 1, 2                   |
+---------------+---------------------------+
| 3             | 0, 3, 4                   |
+---------------+---------------------------+

where the null measurement hypothesis is given the index of 0. Then the ``validation_matrix`` would be a ``(4, 5)``
numpy array of the following form:

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.. code-block:: Python


    validation_matrix = np.array([[1, 1, 0, 0, 0],   # 0 -> 0,1
                                  [1, 1, 1, 1, 0],   # 1 -> 0,1,2,3
                                  [1, 1, 1, 0, 0],   # 2 -> 0,1,2
                                  [1, 0, 0, 1, 1]])  # 3 -> 0,3,4








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The ``likelihood_matrix`` is such that each element ``likelihood_matrix[i, j]`` contains the respective likelihood
of target ``i`` being associated to measurement ``j``. Therefore, based on the above example, the
``likelihood_matrix`` could be the following:

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.. code-block:: Python


    likelihood_matrix = np.array([[0.1, 0.9, 0, 0, 0],
                                  [0.1, 0.3, 0.2, 0.4, 0],
                                  [0.7, 0.1, 0.2, 0, 0],
                                  [0.2, 0, 0, 0.75, 0.05]])








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Computing joint association probabilities
-----------------------------------------
Based on the above, we can use :class:`~.EHM` or :class:`~.EHM2` to compute the joint association probabilities
matrix ``assoc_matrix`` as follows:

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.. code-block:: Python


    from pyehm.core import EHM, EHM2

    assoc_matrix_ehm = EHM().run(validation_matrix, likelihood_matrix)
    print('assoc_matrix_ehm =\n {}\n'.format(assoc_matrix_ehm))
    # or
    assoc_matrix_ehm2 = EHM2().run(validation_matrix, likelihood_matrix)
    print('assoc_matrix_ehm2 =\n {}'.format(assoc_matrix_ehm2))





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

 .. code-block:: none

    assoc_matrix_ehm =
     [[0.17948718 0.82051282 0.         0.         0.        ]
     [0.25925926 0.07692308 0.4045584  0.25925926 0.        ]
     [0.85754986 0.01139601 0.13105413 0.         0.        ]
     [0.35555556 0.         0.         0.55555556 0.08888889]]

    assoc_matrix_ehm2 =
     [[0.17948718 0.82051282 0.         0.         0.        ]
     [0.25925926 0.07692308 0.4045584  0.25925926 0.        ]
     [0.85754986 0.01139601 0.13105413 0.         0.        ]
     [0.35555556 0.         0.         0.55555556 0.08888889]]




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Note that both :class:`~.EHM` and :class:`~.EHM2` should produce the same results, although :class:`~.EHM2` should,
in principle, be significantly faster for large numbers of targets and measurements.

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.. code-block:: Python


    # Check if the probability matrices produced by EHM and EHM2 are equal
    print(np.allclose(assoc_matrix_ehm, assoc_matrix_ehm2))



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

 .. code-block:: none

    True





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

   **Total running time of the script:** (0 minutes 0.005 seconds)


.. _sphx_glr_download_auto_examples_basic.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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