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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_tutorials_api_irfs.py>`
        to download the full example code. or to run this example in your browser via Binder

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

.. _sphx_glr_tutorials_api_irfs.py:


Using Gammapy IRFs
==================

`gammapy.irf` contains classes for handling Instrument Response
Functions typically stored as multi-dimensional tables. For a list of
IRF classes internally supported, see
https://gamma-astro-data-formats.readthedocs.io/en/v0.3/irfs/full_enclosure/index.html

This tutorial is intended for advanced users typically creating IRFs.

.. GENERATED FROM PYTHON SOURCE LINES 13-34

.. code-block:: Python


    import numpy as np
    import astropy.units as u
    from astropy.coordinates import SkyCoord
    from astropy.visualization import quantity_support
    import matplotlib.pyplot as plt
    from gammapy.irf import (
        IRF,
        Background3D,
        EffectiveAreaTable2D,
        EnergyDependentMultiGaussPSF,
        EnergyDispersion2D,
    )
    from gammapy.irf.io import COMMON_IRF_HEADERS, IRF_DL3_HDU_SPECIFICATION
    from gammapy.makers.utils import (
        make_edisp_kernel_map,
        make_map_exposure_true_energy,
        make_psf_map,
    )
    from gammapy.maps import MapAxis, WcsGeom








.. GENERATED FROM PYTHON SOURCE LINES 35-38

Inbuilt Gammapy IRFs
--------------------


.. GENERATED FROM PYTHON SOURCE LINES 38-47

.. code-block:: Python


    irf_filename = (
        "$GAMMAPY_DATA/cta-1dc/caldb/data/cta/1dc/bcf/South_z20_50h/irf_file.fits"
    )

    aeff = EffectiveAreaTable2D.read(irf_filename, hdu="EFFECTIVE AREA")
    print(aeff)






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

 .. code-block:: none

    EffectiveAreaTable2D
    --------------------

      axes  : ['energy_true', 'offset']
      shape : (42, 6)
      ndim  : 2
      unit  : m2
      dtype : >f4





.. GENERATED FROM PYTHON SOURCE LINES 48-51

We can see that the Effective Area Table is defined in terms of
`energy_true` and `offset` from the camera center


.. GENERATED FROM PYTHON SOURCE LINES 51-66

.. code-block:: Python


    # To see the IRF axes binning, eg, offset
    print(aeff.axes["offset"])

    # To get the IRF data
    print(aeff.data)

    # the aeff is evaluated at a given energy and offset
    print(aeff.evaluate(energy_true=[1, 10] * u.TeV, offset=[0.2, 2.5] * u.deg))


    # The peek method gives a quick look into the IRF
    aeff.peek()





.. image-sg:: /tutorials/api/images/sphx_glr_irfs_001.png
   :alt: irfs
   :srcset: /tutorials/api/images/sphx_glr_irfs_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    MapAxis

            name       : offset    
            unit       : 'deg'     
            nbins      : 6         
            node type  : edges     
            edges min  : 0.0e+00 deg
            edges max  : 6.0e+00 deg
            interp     : lin       

    [[3.9391360e+02 2.6772235e+02 1.1955810e+01 0.0000000e+00 0.0000000e+00
      0.0000000e+00]
     [2.1976572e+03 1.3710784e+03 6.6018166e+01 0.0000000e+00 0.0000000e+00
      0.0000000e+00]
     [7.2827988e+03 4.4933657e+03 1.9277492e+02 0.0000000e+00 0.0000000e+00
      0.0000000e+00]
     [1.6318811e+04 9.2217412e+03 3.9053906e+02 0.0000000e+00 0.0000000e+00
      0.0000000e+00]
     [2.7097381e+04 1.5188338e+04 7.1269263e+02 0.0000000e+00 0.0000000e+00
      0.0000000e+00]
     [3.5835918e+04 2.0376213e+04 1.4120719e+03 6.4971704e+00 0.0000000e+00
      0.0000000e+00]
     [4.8613613e+04 2.7351418e+04 4.6046689e+03 8.7537086e+01 0.0000000e+00
      0.0000000e+00]
     [6.8954039e+04 4.6218742e+04 1.8455480e+04 7.0139252e+02 0.0000000e+00
      0.0000000e+00]
     [1.0631757e+05 8.4360750e+04 5.2121164e+04 3.4875723e+03 0.0000000e+00
      0.0000000e+00]
     [1.4225631e+05 1.2825456e+05 9.6194453e+04 1.0149044e+04 0.0000000e+00
      0.0000000e+00]
     [1.8893600e+05 1.7755386e+05 1.4428634e+05 2.2362506e+04 6.2068682e+00
      0.0000000e+00]
     [2.3058422e+05 2.1899070e+05 1.8349780e+05 3.8943121e+04 1.1567629e+01
      0.0000000e+00]
     [2.8908866e+05 2.7990194e+05 2.3380311e+05 6.3812160e+04 1.5692809e+02
      0.0000000e+00]
     [3.7190994e+05 3.4834488e+05 2.9489822e+05 9.9163195e+04 8.5162628e+02
      5.3302565e+00]
     [4.1554106e+05 3.9529719e+05 3.3659253e+05 1.4420073e+05 3.4303606e+03
      0.0000000e+00]
     [4.9977859e+05 4.9269494e+05 4.0322775e+05 1.9834338e+05 1.1456479e+04
      0.0000000e+00]
     [5.9969731e+05 5.8570719e+05 4.8037638e+05 2.6652219e+05 2.7997221e+04
      3.0902437e+01]
     [6.7681656e+05 6.6181862e+05 5.3499075e+05 3.2443672e+05 5.7385727e+04
      1.8062607e+02]
     [8.1099306e+05 7.7395744e+05 6.1618850e+05 3.8555500e+05 1.0076540e+05
      9.7876233e+02]
     [9.5867488e+05 8.9280475e+05 7.2040469e+05 4.5892966e+05 1.5842497e+05
      4.7765957e+03]
     [1.2162670e+06 1.1264500e+06 9.0183519e+05 5.3590188e+05 2.2699878e+05
      1.5607778e+04]
     [1.5719922e+06 1.4968236e+06 1.2062580e+06 6.4819444e+05 2.9215375e+05
      5.0505949e+04]
     [2.0122385e+06 1.8475576e+06 1.5297030e+06 7.8799800e+05 3.7284447e+05
      1.0520119e+05]
     [2.4420222e+06 2.3037632e+06 1.9053655e+06 9.5194769e+05 4.5951631e+05
      1.8031431e+05]
     [2.7887840e+06 2.6253652e+06 2.2635108e+06 1.2041222e+06 5.3117988e+05
      2.5779092e+05]
     [3.0016288e+06 2.9912648e+06 2.5768262e+06 1.5230376e+06 5.9205875e+05
      3.4480056e+05]
     [3.3368855e+06 3.1926520e+06 2.8515948e+06 1.8699165e+06 6.9847406e+05
      4.2104353e+05]
     [3.4212028e+06 3.4642048e+06 3.0395135e+06 2.1510240e+06 9.4647544e+05
      5.1629219e+05]
     [3.6419578e+06 3.5427520e+06 3.3886270e+06 2.4904078e+06 1.1061971e+06
      5.8834862e+05]
     [3.8369650e+06 3.7596682e+06 3.4080942e+06 2.6554088e+06 1.3962942e+06
      6.9074812e+05]
     [3.6556248e+06 3.9023670e+06 3.7240965e+06 2.9912712e+06 1.7479085e+06
      8.0375512e+05]
     [4.0462798e+06 4.1072542e+06 3.8377268e+06 3.0739282e+06 1.9910796e+06
      9.9608912e+05]
     [4.7580410e+06 4.2058705e+06 3.5561760e+06 3.2560538e+06 2.3279955e+06
      1.1768896e+06]
     [3.5545130e+06 4.4198250e+06 3.8441040e+06 3.3812120e+06 2.5538942e+06
      1.6402822e+06]
     [4.7350380e+06 4.7123895e+06 4.2164425e+06 3.5192420e+06 2.7652512e+06
      1.9816452e+06]
     [4.8769240e+06 4.7692170e+06 4.2880470e+06 3.5438860e+06 3.0800792e+06
      2.2079930e+06]
     [4.5754970e+06 4.8475650e+06 4.2628525e+06 3.8222980e+06 3.0025508e+06
      2.4225498e+06]
     [4.9606540e+06 4.5763635e+06 4.6471115e+06 3.7471700e+06 3.1438465e+06
      2.7804888e+06]
     [3.6909290e+06 5.0354700e+06 4.0028272e+06 3.3364130e+06 3.3689322e+06
      3.1486415e+06]
     [4.0064830e+06 5.0474750e+06 4.1556008e+06 3.8290458e+06 3.0894640e+06
      2.9776920e+06]
     [4.2465055e+06 4.5345275e+06 4.1062535e+06 3.8885138e+06 3.2021345e+06
      3.0907128e+06]
     [4.6105760e+06 5.3715810e+06 4.0482342e+06 3.6259962e+06 3.3739292e+06
      2.9499210e+06]]
    [ 900269.83242471 3398360.62514628] m2




.. GENERATED FROM PYTHON SOURCE LINES 67-69

Similarly, we can access other IRFs as well


.. GENERATED FROM PYTHON SOURCE LINES 69-77

.. code-block:: Python


    psf = EnergyDependentMultiGaussPSF.read(irf_filename, hdu="Point Spread Function")
    bkg = Background3D.read(irf_filename, hdu="BACKGROUND")
    edisp = EnergyDispersion2D.read(irf_filename, hdu="ENERGY DISPERSION")

    print(bkg)






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

 .. code-block:: none

    Background3D
    ------------

      axes  : ['energy', 'fov_lon', 'fov_lat']
      shape : (21, 36, 36)
      ndim  : 3
      unit  : 1 / (MeV s sr)
      dtype : >f4





.. GENERATED FROM PYTHON SOURCE LINES 78-85

Note that the background is given in FoV coordiantes with `fov_lon`
and `fov_lat` axis, and not in `offset` from the camera center. We
can also check the Field of view alignment. Currently, two possible
alignments are supported: alignment with the horizontal coordinate
system (ALTAZ) and alignment with the equatorial coordinate system
(RADEC).


.. GENERATED FROM PYTHON SOURCE LINES 85-89

.. code-block:: Python


    print(bkg.fov_alignment)






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

 .. code-block:: none

    FoVAlignment.RADEC




.. GENERATED FROM PYTHON SOURCE LINES 90-93

To evaluate the IRFs, pass the values for each axis. To know the default
interpolation scheme for the data


.. GENERATED FROM PYTHON SOURCE LINES 93-109

.. code-block:: Python


    print(bkg.interp_kwargs)

    # Evaluate background
    # Note that evaluate functions support  numpy-style broadcasting
    energy = [1, 10, 100, 1000] * u.TeV
    fov_lon = [1, 2] * u.deg
    fov_lat = [1, 2] * u.deg
    ev = bkg.evaluate(
        energy=energy.reshape(-1, 1, 1),
        fov_lat=fov_lat.reshape(1, -1, 1),
        fov_lon=fov_lon.reshape(1, 1, -1),
    )
    print(ev)






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

 .. code-block:: none

    {'bounds_error': False, 'fill_value': 0.0, 'values_scale': 'log'}
    [[[1.27093776e-04 1.12423250e-04]
      [1.12423250e-04 9.85188496e-05]]

     [[7.67759236e-07 9.01235137e-07]
      [9.01235137e-07 1.05901956e-06]]

     [[5.74465974e-09 5.24685677e-09]
      [5.24685677e-09 4.65357608e-09]]

     [[0.00000000e+00 0.00000000e+00]
      [0.00000000e+00 0.00000000e+00]]] 1 / (MeV s sr)




.. GENERATED FROM PYTHON SOURCE LINES 110-113

We can customise the interpolation scheme. Here, we adapt to fill
`nan` instead of `0` for extrapolated values


.. GENERATED FROM PYTHON SOURCE LINES 113-124

.. code-block:: Python


    bkg.interp_kwargs["fill_value"] = np.nan

    ev2 = bkg.evaluate(
        energy=energy.reshape(-1, 1, 1),
        fov_lat=fov_lat.reshape(1, -1, 1),
        fov_lon=fov_lon.reshape(1, 1, -1),
    )
    print(ev2)






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

 .. code-block:: none

    [[[1.27093776e-04 1.12423250e-04]
      [1.12423250e-04 9.85188496e-05]]

     [[7.67759236e-07 9.01235137e-07]
      [9.01235137e-07 1.05901956e-06]]

     [[5.74465974e-09 5.24685677e-09]
      [5.24685677e-09 4.65357608e-09]]

     [[           nan            nan]
      [           nan            nan]]] 1 / (MeV s sr)




.. GENERATED FROM PYTHON SOURCE LINES 125-128

The interpolation scheme along each axis is taken from the `MapAxis`
specification. eg


.. GENERATED FROM PYTHON SOURCE LINES 128-145

.. code-block:: Python


    print(
        "Interpolation scheme for energy axis is: ",
        bkg.axes["energy"].interp,
        "and for the fov_lon axis is: ",
        bkg.axes["fov_lon"].interp,
    )

    # Evaluate energy dispersion
    ev = edisp.evaluate(energy_true=1 * u.TeV, offset=[0, 1] * u.deg, migra=[1, 1.2])
    print(ev)

    edisp.peek()

    print(psf)





.. image-sg:: /tutorials/api/images/sphx_glr_irfs_002.png
   :alt: irfs
   :srcset: /tutorials/api/images/sphx_glr_irfs_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    Interpolation scheme for energy axis is:  log and for the fov_lon axis is:  lin
    [189.80982039  54.28382603]
    EnergyDependentMultiGaussPSF
    ----------------------------

      axes      : ['energy_true', 'offset']
      shape     : (25, 6)
      ndim      : 2
      parameters: ['sigma_1', 'sigma_2', 'sigma_3', 'scale', 'ampl_2', 'ampl_3']





.. GENERATED FROM PYTHON SOURCE LINES 146-151

The PointSpreadFunction for the CTA DC1 is stored as a combination of 3
Gaussians. Other PSFs, like a `PSF_TABLE` and analytic expressions
like KING function are also supported. All PSF classes inherit from a
common base `PSF` class.


.. GENERATED FROM PYTHON SOURCE LINES 151-169

.. code-block:: Python


    print(psf.axes.names)

    # To get the containment radius for a fixed fraction at a given position
    print(
        psf.containment_radius(
            fraction=0.68, energy_true=1.0 * u.TeV, offset=[0.2, 4.0] * u.deg
        )
    )

    # Alternatively, to get the containment fraction for at a given position
    print(
        psf.containment(
            rad=0.05 * u.deg, energy_true=1.0 * u.TeV, offset=[0.2, 4.0] * u.deg
        )
    )






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

 .. code-block:: none

    ['energy_true', 'offset']
    [0.05075 0.08075] deg
    [0.66984341 0.35569283]




.. GENERATED FROM PYTHON SOURCE LINES 170-173

Support for Asymmetric IRFs
---------------------------


.. GENERATED FROM PYTHON SOURCE LINES 176-184

While Gammapy does not have inbuilt classes for supporting asymmetric
IRFs (except for `Background3D`), custom classes can be created. For
this to work correctly with the `MapDatasetMaker`, only variations
with `fov_lon` and `fov_lat` can be allowed.

The main idea is that the list of required axes should be correctly
mentioned in the class definition.


.. GENERATED FROM PYTHON SOURCE LINES 187-190

Effective Area
~~~~~~~~~~~~~~


.. GENERATED FROM PYTHON SOURCE LINES 190-238

.. code-block:: Python



    class EffectiveArea3D(IRF):
        tag = "aeff_3d"
        required_axes = ["energy_true", "fov_lon", "fov_lat"]
        default_unit = u.m**2


    energy_axis = MapAxis.from_energy_edges(
        [0.1, 0.3, 1.0, 3.0, 10.0] * u.TeV, name="energy_true"
    )

    nbin = 7
    fov_lon_axis = MapAxis.from_edges([-1.5, -0.5, 0.5, 1.5] * u.deg, name="fov_lon")
    fov_lat_axis = MapAxis.from_edges([-1.5, -0.5, 0.5, 1.5] * u.deg, name="fov_lat")

    data = np.ones((4, 3, 3))
    for i in range(1, 4):
        data[i] = data[i - 1] * 2.0
        data[i][-1] = data[i][0] * 1.2


    aeff_3d = EffectiveArea3D(
        [energy_axis, fov_lon_axis, fov_lat_axis], data=data, unit=u.m**2
    )
    print(aeff_3d)

    res = aeff_3d.evaluate(
        fov_lon=[-0.5, 0.8] * u.deg,
        fov_lat=[-0.5, 1.0] * u.deg,
        energy_true=[0.2, 8.0] * u.TeV,
    )
    print(res)

    # to visualise at a given energy
    # sphinx_gallery_thumbnail_number = 1
    aeff_eval = aeff_3d.evaluate(energy_true=[1.0] * u.TeV)

    ax = plt.subplot()
    with quantity_support():
        caxes = ax.pcolormesh(
            fov_lat_axis.edges, fov_lon_axis.edges, aeff_eval.value.squeeze()
        )
    fov_lat_axis.format_plot_xaxis(ax)
    fov_lon_axis.format_plot_yaxis(ax)
    ax.set_title("Asymmetric effective area")





.. image-sg:: /tutorials/api/images/sphx_glr_irfs_003.png
   :alt: Asymmetric effective area
   :srcset: /tutorials/api/images/sphx_glr_irfs_003.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    EffectiveArea3D
    ---------------

      axes  : ['energy_true', 'fov_lon', 'fov_lat']
      shape : (4, 3, 3)
      ndim  : 3
      unit  : m2
      dtype : float64

    [ 1.12493874 10.80683246] m2

    Text(0.5, 1.0, 'Asymmetric effective area')



.. GENERATED FROM PYTHON SOURCE LINES 239-241

Unless specified, it is assumed these IRFs are in the RADEC frame


.. GENERATED FROM PYTHON SOURCE LINES 241-245

.. code-block:: Python


    aeff_3d.fov_alignment






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

 .. code-block:: none


    <FoVAlignment.RADEC: 'RADEC'>



.. GENERATED FROM PYTHON SOURCE LINES 246-252

Serialisation
~~~~~~~~~~~~~

For serialisation, we need to add the class definition to the
`IRF_DL3_HDU_SPECIFICATION` dictionary


.. GENERATED FROM PYTHON SOURCE LINES 252-270

.. code-block:: Python


    IRF_DL3_HDU_SPECIFICATION["aeff_3d"] = {
        "extname": "EFFECTIVE AREA",
        "column_name": "EFFAREA",
        "mandatory_keywords": {
            **COMMON_IRF_HEADERS,
            "HDUCLAS2": "EFF_AREA",
            "HDUCLAS3": "FULL-ENCLOSURE",  # added here to have HDUCLASN in order
            "HDUCLAS4": "AEFF_3D",
        },
    }

    aeff_3d.write("test_aeff3d.fits", overwrite=True)

    aeff_new = EffectiveArea3D.read("test_aeff3d.fits")
    print(aeff_new)






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

 .. code-block:: none

    EffectiveArea3D
    ---------------

      axes  : ['energy_true', 'fov_lon', 'fov_lat']
      shape : (4, 3, 3)
      ndim  : 3
      unit  : m2
      dtype : >f8





.. GENERATED FROM PYTHON SOURCE LINES 271-276

Create exposure map
~~~~~~~~~~~~~~~~~~~

DL4 data products can be created from these IRFs.


.. GENERATED FROM PYTHON SOURCE LINES 276-291

.. code-block:: Python


    axis = MapAxis.from_energy_bounds(0.1 * u.TeV, 10 * u.TeV, 6, name="energy_true")
    pointing = SkyCoord(2, 1, unit="deg")
    geom = WcsGeom.create(npix=(4, 3), binsz=2, axes=[axis], skydir=pointing)

    print(geom)

    exposure_map = make_map_exposure_true_energy(
        pointing=pointing, livetime="42 h", aeff=aeff_3d, geom=geom
    )

    exposure_map.plot_grid(add_cbar=True, figsize=(17, 7))
    plt.show()





.. image-sg:: /tutorials/api/images/sphx_glr_irfs_004.png
   :alt: Energy_true 100 GeV - 215 GeV, Energy_true 215 GeV - 464 GeV, Energy_true 464 GeV - 1.00 TeV, Energy_true 1.00 TeV - 2.15 TeV, Energy_true 2.15 TeV - 4.64 TeV, Energy_true 4.64 TeV - 10.0 TeV
   :srcset: /tutorials/api/images/sphx_glr_irfs_004.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    WcsGeom

            axes       : ['lon', 'lat', 'energy_true']
            shape      : (4, 3, 6)
            ndim       : 3
            frame      : icrs
            projection : CAR
            center     : 2.0 deg, 1.0 deg
            width      : 8.0 deg x 6.0 deg
            wcs ref    : 2.0 deg, 1.0 deg





.. GENERATED FROM PYTHON SOURCE LINES 292-295

Energy Dispersion
-----------------


.. GENERATED FROM PYTHON SOURCE LINES 295-303

.. code-block:: Python



    class EnergyDispersion3D(IRF):
        tag = "edisp_3d"
        required_axes = ["energy_true", "migra", "fov_lon", "fov_lat"]
        default_unit = u.one









.. GENERATED FROM PYTHON SOURCE LINES 304-307

Note that most functions defined on the inbuilt IRF classes can be
easily generalised to higher dimensions.


.. GENERATED FROM PYTHON SOURCE LINES 307-380

.. code-block:: Python


    # Make a test case
    energy_axis_true = MapAxis.from_energy_bounds(
        "0.1 TeV", "100 TeV", nbin=3, name="energy_true"
    )

    migra_axis = MapAxis.from_bounds(0, 4, nbin=2, node_type="edges", name="migra")

    fov_lon_axis = MapAxis.from_edges([-1.5, -0.5, 0.5, 1.5] * u.deg, name="fov_lon")
    fov_lat_axis = MapAxis.from_edges([-1.5, -0.5, 0.5, 1.5] * u.deg, name="fov_lat")

    data = np.array(
        [
            [
                [
                    [5.00e-01, 5.10e-01, 5.20e-01],
                    [6.00e-01, 6.10e-01, 6.30e-01],
                    [6.00e-01, 6.00e-01, 6.00e-01],
                ],
                [
                    [2.0e-02, 2.0e-02, 2.0e-03],
                    [2.0e-02, 2.0e-02, 2.0e-03],
                    [2.0e-02, 2.0e-02, 2.0e-03],
                ],
            ],
            [
                [
                    [5.00e-01, 5.10e-01, 5.20e-01],
                    [6.00e-01, 6.10e-01, 6.30e-01],
                    [6.00e-01, 6.00e-01, 6.00e-01],
                ],
                [
                    [2.0e-02, 2.0e-02, 2.0e-03],
                    [2.0e-02, 2.0e-02, 2.0e-03],
                    [2.0e-02, 2.0e-02, 2.0e-03],
                ],
            ],
            [
                [
                    [5.00e-01, 5.10e-01, 5.20e-01],
                    [6.00e-01, 6.10e-01, 6.30e-01],
                    [6.00e-01, 6.00e-01, 6.00e-01],
                ],
                [
                    [3.0e-02, 6.0e-02, 2.0e-03],
                    [3.0e-02, 5.0e-02, 2.0e-03],
                    [3.0e-02, 4.0e-02, 2.0e-03],
                ],
            ],
        ]
    )


    edisp3d = EnergyDispersion3D(
        [energy_axis_true, migra_axis, fov_lon_axis, fov_lat_axis], data=data
    )

    print(edisp3d)

    energy = [1, 2] * u.TeV
    migra = np.array([0.98, 0.97, 0.7])
    fov_lon = [0.1, 1.5] * u.deg
    fov_lat = [0.0, 0.3] * u.deg

    edisp_eval = edisp3d.evaluate(
        energy_true=energy.reshape(-1, 1, 1, 1),
        migra=migra.reshape(1, -1, 1, 1),
        fov_lon=fov_lon.reshape(1, 1, -1, 1),
        fov_lat=fov_lat.reshape(1, 1, 1, -1),
    )
    print(edisp_eval[0])






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

 .. code-block:: none

    EnergyDispersion3D
    ------------------

      axes  : ['energy_true', 'migra', 'fov_lon', 'fov_lat']
      shape : (3, 2, 3, 3)
      ndim  : 4
      unit  : 
      dtype : float64

    [[[0.61489  0.620398]
      [0.60075  0.597774]]

     [[0.617835 0.623397]
      [0.603625 0.600661]]

     [[0.69735  0.70437 ]
      [0.68125  0.67861 ]]]




.. GENERATED FROM PYTHON SOURCE LINES 381-384

Serialisation
~~~~~~~~~~~~~


.. GENERATED FROM PYTHON SOURCE LINES 384-402

.. code-block:: Python


    IRF_DL3_HDU_SPECIFICATION["edisp_3d"] = {
        "extname": "ENERGY DISPERSION",
        "column_name": "MATRIX",
        "mandatory_keywords": {
            **COMMON_IRF_HEADERS,
            "HDUCLAS2": "EDISP",
            "HDUCLAS3": "FULL-ENCLOSURE",  # added here to have HDUCLASN in order
            "HDUCLAS4": "EDISP_3D",
        },
    }

    edisp3d.write("test_edisp.fits", overwrite=True)

    edisp_new = EnergyDispersion3D.read("test_edisp.fits")
    edisp_new







.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <pre>EnergyDispersion3D
    ------------------

      axes  : [&#x27;energy_true&#x27;, &#x27;migra&#x27;, &#x27;fov_lon&#x27;, &#x27;fov_lat&#x27;]
      shape : (3, 2, 3, 3)
      ndim  : 4
      unit  : 
      dtype : &gt;f8
    </pre>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 403-406

Create edisp kernel map
~~~~~~~~~~~~~~~~~~~~~~~


.. GENERATED FROM PYTHON SOURCE LINES 406-421

.. code-block:: Python


    migra = MapAxis.from_edges(np.linspace(0.5, 1.5, 50), unit="", name="migra")
    etrue = MapAxis.from_energy_bounds(0.5, 2, 6, unit="TeV", name="energy_true")
    ereco = MapAxis.from_energy_bounds(0.5, 2, 3, unit="TeV", name="energy")
    geom = WcsGeom.create(10, binsz=0.5, axes=[ereco, etrue], skydir=pointing)

    edispmap = make_edisp_kernel_map(edisp3d, pointing, geom)

    edispmap.peek()
    plt.show()

    #
    print(edispmap.edisp_map.data[3][1][3])





.. image-sg:: /tutorials/api/images/sphx_glr_irfs_005.png
   :alt: irfs
   :srcset: /tutorials/api/images/sphx_glr_irfs_005.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    [0.         0.         0.19932878 0.20009124 0.20072608 0.20099855
     0.2009851  0.20097159 0.         0.        ]




.. GENERATED FROM PYTHON SOURCE LINES 422-432

PSF
---

There are two types of asymmetric PSFs that can be considered
- Asymmetry about the camera center: Such PSF Tables can be supported
- Asymmetry about the source position: These PSF models cannot be supported
correctly within the data reduction scheme at present
Also, analytic PSF models defined within the GADF scheme cannot be
directly generalised to the 3D case for use within Gammapy.


.. GENERATED FROM PYTHON SOURCE LINES 432-474

.. code-block:: Python



    class PSF_assym(IRF):
        tag = "psf_assym"
        required_axes = ["energy_true", "fov_lon", "fov_lat", "rad"]
        default_unit = u.sr**-1


    energy_axis = MapAxis.from_energy_edges(
        [0.1, 0.3, 1.0, 3.0, 10.0] * u.TeV, name="energy_true"
    )

    nbin = 7
    fov_lon_axis = MapAxis.from_edges([-1.5, -0.5, 0.5, 1.5] * u.deg, name="fov_lon")
    fov_lat_axis = MapAxis.from_edges([-1.5, -0.5, 0.5, 1.5] * u.deg, name="fov_lat")

    rad_axis = MapAxis.from_edges([0, 1, 2], unit="deg", name="rad")

    data = 0.1 * np.ones((4, 3, 3, 2))
    for i in range(1, 4):
        data[i] = data[i - 1] * 1.5


    psf_assym = PSF_assym(
        axes=[energy_axis, fov_lon_axis, fov_lat_axis, rad_axis],
        data=data,
    )
    print(psf_assym)

    energy = [1, 2] * u.TeV
    rad = np.array([0.98, 0.97, 0.7]) * u.deg
    fov_lon = [0.1, 1.5] * u.deg
    fov_lat = [0.0, 0.3] * u.deg

    psf_assym.evaluate(
        energy_true=energy.reshape(-1, 1, 1, 1),
        rad=rad.reshape(1, -1, 1, 1),
        fov_lon=fov_lon.reshape(1, 1, -1, 1),
        fov_lat=fov_lat.reshape(1, 1, 1, -1),
    )






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

 .. code-block:: none

    PSF_assym
    ---------

      axes  : ['energy_true', 'fov_lon', 'fov_lat', 'rad']
      shape : (4, 3, 3, 2)
      ndim  : 4
      unit  : 
      dtype : float64


    <Quantity [[[[0.18921591, 0.18921591],
                 [0.18921591, 0.18921591]],

                [[0.18921591, 0.18921591],
                 [0.18921591, 0.18921591]],

                [[0.18921591, 0.18921591],
                 [0.18921591, 0.18921591]]],


               [[[0.23905561, 0.23905561],
                 [0.23905561, 0.23905561]],

                [[0.23905561, 0.23905561],
                 [0.23905561, 0.23905561]],

                [[0.23905561, 0.23905561],
                 [0.23905561, 0.23905561]]]]>



.. GENERATED FROM PYTHON SOURCE LINES 475-478

Serialisation
~~~~~~~~~~~~~


.. GENERATED FROM PYTHON SOURCE LINES 478-494

.. code-block:: Python


    IRF_DL3_HDU_SPECIFICATION["psf_assym"] = {
        "extname": "POINT SPREAD FUNCTION",
        "column_name": "MATRIX",
        "mandatory_keywords": {
            **COMMON_IRF_HEADERS,
            "HDUCLAS2": "PSF",
            "HDUCLAS3": "FULL-ENCLOSURE",
            "HDUCLAS4": "PSFnD",
        },
    }

    psf_assym.write("test_psf.fits.gz", overwrite=True)

    psf_new = PSF_assym.read("test_psf.fits.gz")








.. GENERATED FROM PYTHON SOURCE LINES 495-498

Create DL4 product - `PSFMap`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


.. GENERATED FROM PYTHON SOURCE LINES 498-509

.. code-block:: Python


    rad = MapAxis.from_edges(np.linspace(0.5, 3.0, 10), unit="deg", name="rad")
    etrue = MapAxis.from_energy_bounds(0.5, 2, 6, unit="TeV", name="energy_true")
    geom = WcsGeom.create(10, binsz=0.5, axes=[rad, etrue], skydir=pointing)

    psfmap = make_psf_map(psf_assym, pointing, geom)

    psfmap.peek()
    plt.show()





.. image-sg:: /tutorials/api/images/sphx_glr_irfs_006.png
   :alt: Exposure, Containment radius at 1 TeV, Containment radius at center of map, PSF at center of map
   :srcset: /tutorials/api/images/sphx_glr_irfs_006.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 510-515

Containers for asymmetric analytic PSFs are not supported at present.

**NOTE**: Support for asymmetric IRFs is preliminary at the moment, and
will evolve depending on feedback.



.. _sphx_glr_download_tutorials_api_irfs.py:

.. only:: html

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

    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/gammapy/gammapy-webpage/v1.3?urlpath=lab/tree/notebooks/1.3/tutorials/api/irfs.ipynb
        :alt: Launch binder
        :width: 150 px

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

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

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

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

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

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


.. only:: html

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

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