Andreas Specovius / ctools

Commit 1c97acc16130d40cbc355f4ca45cee9157b9faee

Authored by Jürgen Knödlseder
1 parent fd516957

Add Fermi-LAT tutorials

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doc/source/users/tutorials/howto/fermi/howto_fermi_butterfly.png 0 → 100644
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doc/source/users/tutorials/howto/fermi/howto_fermi_butterfly.rst 0 → 100644
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  1 +.. _howto_fermi_butterfly:
  2 +
  3 +Generate a butterfly diagram for a model component
  4 +--------------------------------------------------
  5 +
  6 + .. admonition:: What you will learn
  7 +
  8 + You will learn how to use :ref:`ctbutterfly` to create a butterfly diagram
  9 + for a model component from Fermi-LAT data.
  10 +
  11 +A butterfly diagram shows the envelope of all spectral models that are
  12 +statistically compatible with the data. You can create such a butterfly
  13 +diagram for the Vela pulsar using the :ref:`ctbutterfly` tool by providing
  14 +the
  15 +:ref:`model definition file <glossary_moddef>`
  16 +output file from :ref:`ctlike` as input:
  17 +
  18 +.. code-block:: bash
  19 +
  20 + $ ctbutterfly
  21 + Input event list, counts cube or observation definition XML file [events.fits] obs.xml
  22 + Source of interest [Crab] Vela
  23 + Input model definition XML file [$CTOOLS/share/models/crab.xml] vela_results.xml
  24 + Start value for first energy bin in TeV [0.1] 0.0001
  25 + Stop value for last energy bin in TeV [100.0] 0.1
  26 + Output ASCII file [butterfly.txt]
  27 +
  28 +:ref:`ctbutterfly` produces the ASCII file ``butterfly.txt`` that contains
  29 +the envelope of the butterfly diagram. The figure below gives a graphical
  30 +representation of the envelope.
  31 +
  32 +.. figure:: howto_fermi_butterfly.png
  33 + :width: 600px
  34 + :align: center
  35 +
  36 + *Butterfly diagram of the fitted Vela pulsar spectrum*
  37 +..
  38 +
  39 + .. note::
  40 +
  41 + The figure was created using the ``show_butterfly.py`` script that is
  42 + located in the ctools example folder. The example script requires the
  43 + `matplotlib <http://matplotlib.org>`_ Python module for display.
  44 + You may reproduce the plot by typing
  45 +
  46 + .. code-block:: bash
  47 +
  48 + $ $CTOOLS/share/examples/python/show_butterfly.py butterfly.txt
doc/source/users/tutorials/howto/fermi/howto_fermi_data.jpg 0 → 100644
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doc/source/users/tutorials/howto/fermi/howto_fermi_errors.rst 0 → 100644
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  1 +.. _howto_fermi_errors:
  2 +
  3 +Determine asymmetric model parameter errors for a model component
  4 +-----------------------------------------------------------------
  5 +
  6 + .. admonition:: What you will learn
  7 +
  8 + You will learn how to use :ref:`cterror` to derive asymmetric model
  9 + parameter errors from Fermi-LAT data using a likelihood profile method.
  10 +
  11 +The :ref:`ctlike` tool computes errors for each fitted parameter value based
  12 +on the covariance matrix of the fit. This assumes a Gaussian approximation
  13 +of the uncertainties around the best fitting values. Uncertainties may however
  14 +by asymmetric.
  15 +
  16 +To test the symmetry of the uncertainties you can use the :ref:`cterror`
  17 +tool. :ref:`cterror` will make use of the likelihood profile to determine
  18 +the confidence interval for each fitted parameter, allowing thus also for
  19 +asymmetric errors. You use :ref:`cterror` as follows:
  20 +
  21 +.. code-block:: bash
  22 +
  23 + $ cterror
  24 + Input event list, counts cube or observation definition XML file [events.fits] obs.xml
  25 + Source of interest [Crab] Vela
  26 + Input model definiton XML file [$CTOOLS/share/models/crab.xml] vela_results.xml
  27 + Output model definiton XML file [results.xml] vela_errors.xml
  28 +
  29 +The confidence intervals can then be extracted from the ``cterror.log`` log file
  30 +that was created by :ref:`cterror`. As you will see, the parameter errors
  31 +are essentially symmetric and very close to the values determined using the
  32 +covariance matrix.
  33 +
  34 +.. code-block:: bash
  35 +
  36 + 2017-08-26T14:16:00: +=======================================================+
  37 + 2017-08-26T14:16:00: | Compute error for source "Vela" parameter "Prefactor" |
  38 + 2017-08-26T14:16:00: +=======================================================+
  39 + 2017-08-26T14:16:00: Confidence level ..........: 68 %
  40 + 2017-08-26T14:16:00: Log-likelihood difference .: 0.494473
  41 + 2017-08-26T14:16:00: Initial factor range ......: [1e-07, 9.10916268820218]
  42 + 2017-08-26T14:16:20: Lower parameter factor ....: 3.93549
  43 + 2017-08-26T14:16:20: Upper parameter factor ....: 4.89285
  44 + 2017-08-26T14:16:20: Error from curvature ......: 4.75365104151534e-10 ph/cm2/s/MeV
  45 + 2017-08-26T14:16:20: Error from profile ........: 4.78682555317737e-10 ph/cm2/s/MeV
  46 + 2017-08-26T14:16:20: Negative profile error ....: 4.20026137925122e-10 ph/cm2/s/MeV
  47 + 2017-08-26T14:16:20: Positive profile error ....: 5.37338972710351e-10 ph/cm2/s/MeV
  48 + 2017-08-26T14:16:20:
  49 + 2017-08-26T14:16:20: +====================================================+
  50 + 2017-08-26T14:16:20: | Compute error for source "Vela" parameter "Index1" |
  51 + 2017-08-26T14:16:20: +====================================================+
  52 + 2017-08-26T14:16:20: Confidence level ..........: 68 %
  53 + 2017-08-26T14:16:20: Log-likelihood difference .: 0.494473
  54 + 2017-08-26T14:16:20: Initial factor range ......: [1.03221907174349, 1.65479046234989]
  55 + 2017-08-26T14:16:42: Lower parameter factor ....: 1.31121
  56 + 2017-08-26T14:16:42: Upper parameter factor ....: 1.37307
  57 + 2017-08-26T14:16:42: Error from curvature ......: 0.03112856953032
  58 + 2017-08-26T14:16:42: Error from profile ........: 0.0309309760713872
  59 + 2017-08-26T14:16:42: Negative profile error ....: 0.0322989307870749
  60 + 2017-08-26T14:16:42: Positive profile error ....: 0.0295630213556994
  61 + 2017-08-26T14:16:42:
  62 + 2017-08-26T14:16:42: +==========================================================+
  63 + 2017-08-26T14:16:42: | Compute error for source "Vela" parameter "CutoffEnergy" |
  64 + 2017-08-26T14:16:42: +==========================================================+
  65 + 2017-08-26T14:16:42: Confidence level ..........: 68 %
  66 + 2017-08-26T14:16:42: Log-likelihood difference .: 0.494473
  67 + 2017-08-26T14:16:42: Initial factor range ......: [0.001, 2.8071605417966]
  68 + 2017-08-26T14:17:02: Lower parameter factor ....: 0.813181
  69 + 2017-08-26T14:17:02: Upper parameter factor ....: 1.17404
  70 + 2017-08-26T14:17:02: Error from curvature ......: 181.871842544747 MeV
  71 + 2017-08-26T14:17:02: Error from profile ........: 180.431484426618 MeV
  72 + 2017-08-26T14:17:02: Negative profile error ....: 175.261332662553 MeV
  73 + 2017-08-26T14:17:02: Positive profile error ....: 185.601636190684 MeV
  74 + 2017-08-26T14:17:02:
  75 + 2017-08-26T14:17:02: +====================================================+
  76 + 2017-08-26T14:17:02: | Compute error for source "Vela" parameter "Index2" |
  77 + 2017-08-26T14:17:02: +====================================================+
  78 + 2017-08-26T14:17:02: Confidence level ..........: 68 %
  79 + 2017-08-26T14:17:02: Log-likelihood difference .: 0.494473
  80 + 2017-08-26T14:17:02: Initial factor range ......: [0.307804018748382, 0.866425033775455]
  81 + 2017-08-26T14:17:24: Lower parameter factor ....: 0.559156
  82 + 2017-08-26T14:17:24: Upper parameter factor ....: 0.615141
  83 + 2017-08-26T14:17:24: Error from curvature ......: 0.0279310507513537
  84 + 2017-08-26T14:17:24: Error from profile ........: 0.0279924226890397
  85 + 2017-08-26T14:17:24: Negative profile error ....: 0.027958327168103
  86 + 2017-08-26T14:17:24: Positive profile error ....: 0.0280265182099764
doc/source/users/tutorials/howto/fermi/howto_fermi_fitting.rst 0 → 100644
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  1 +.. _howto_fermi_fitting:
  2 +
  3 +Fit a model to the data
  4 +-----------------------
  5 +
  6 + .. admonition:: What you will learn
  7 +
  8 + You will learn how to use :ref:`ctlike` to fit a parametric model to
  9 + Fermi-LAT data.
  10 +
  11 +Start with creating an
  12 +:ref:`observation definition file <glossary_obsdef>`
  13 +that defines the names of the counts map file, the exposure map file, the
  14 +live time cube file and the name of the instrument response function that
  15 +should be used for the analysis:
  16 +
  17 +.. code-block:: xml
  18 +
  19 + <?xml version="1.0" standalone="no"?>
  20 + <observation_list title="observation library">
  21 + <observation name="Vela" id="000001" instrument="LAT">
  22 + <parameter name="CountsMap" file="srcmaps.fits"/>
  23 + <parameter name="ExposureMap" file="expmap.fits"/>
  24 + <parameter name="LiveTimeCube" file="ltcube.fits"/>
  25 + <parameter name="IRF" value="P8R2_SOURCE_V6"/>
  26 + </observation>
  27 + </observation_list>
  28 +
  29 +This will be your input file to all tools.
  30 +Then you also need a
  31 +:ref:`model definition file <glossary_moddef>`
  32 +that describes the source and background model that you want to fit. In the
  33 +example below, a point source with a super exponentially cut-off power law is
  34 +fit at the position of the Vela pulsar on top of a Galactic diffuse and an
  35 +extragalactic isotropic source component.
  36 +
  37 +.. code-block:: xml
  38 +
  39 + <?xml version="1.0" standalone="no"?>
  40 + <source_library title="source library">
  41 + <source type="PointSource" name="Vela">
  42 + <spectrum type="SuperExponentialCutoffPowerLaw">
  43 + <parameter name="Prefactor" scale="1e-9" value="1.0" min="1e-07" max="1000.0" free="1"/>
  44 + <parameter name="Index1" scale="-1" value="2.0" min="0.0" max="+5.0" free="1"/>
  45 + <parameter name="CutoffEnergy" scale="1e3" value="1.0" min="1e-3" max="1e+3" free="1"/>
  46 + <parameter name="PivotEnergy" scale="1e3" value="1.0" min="0.01" max="1000.0" free="0"/>
  47 + <parameter name="Index2" scale="1.0" value="0.5" min="0.1" max="5.0" free="1"/>
  48 + </spectrum>
  49 + <spatialModel type="PointSource">
  50 + <parameter name="RA" scale="1.0" value="128.84" min="-360" max="360" free="0"/>
  51 + <parameter name="DEC" scale="1.0" value="-45.18" min="-90" max="90" free="0"/>
  52 + </spatialModel>
  53 + </source>
  54 + <source type="DiffuseSource" name="Galactic_diffuse">
  55 + <spectrum type="Constant">
  56 + <parameter name="Normalization" scale="1.0" value="1.0" min="0.1" max="1000.0" free="1"/>
  57 + </spectrum>
  58 + <spatialModel type="DiffuseMapCube" file="gll_iem_v06.fits">
  59 + <parameter name="Normalization" scale="1.0" value="1.0" min="0.1" max="10.0" free="0"/>
  60 + </spatialModel>
  61 + </source>
  62 + <source type="DiffuseSource" name="Extragalactic_diffuse">
  63 + <spectrum type="FileFunction" file="iso_P8R2_SOURCE_V6_v06.txt">
  64 + <parameter name="Normalization" scale="1.0" value="1.0" min="0.0" max="1000.0" free="0"/>
  65 + </spectrum>
  66 + <spatialModel type="DiffuseIsotropic">
  67 + <parameter name="Value" scale="1.0" value="1.0" min="0.0" max="10.0" free="0"/>
  68 + </spatialModel>
  69 + </source>
  70 + </source_library>
  71 +..
  72 +
  73 + .. warning::
  74 +
  75 + The names of the diffuse model components have to be identical to the
  76 + names used when preparing the ``srcmaps.fits`` file using ``gtsrcmap``.
  77 +
  78 + **Positions of point sources can so far not be fitted for a Fermi-LAT
  79 + analysis**, hence the corresponding parameters are fixed.
  80 +
  81 +Now you are ready to fit the model using the :ref:`ctlike` model tool. You do
  82 +this as follows:
  83 +
  84 +.. code-block:: bash
  85 +
  86 + $ ctlike
  87 + Input event list, counts cube or observation definition XML file [events.fits] obs.xml
  88 + Input model definition XML file [$CTOOLS/share/models/crab.xml] models.xml
  89 + Output model definition XML file [crab_results.xml] vela_results.xml
  90 +
  91 +:ref:`ctlike` creates on output the
  92 +:ref:`model definition file <glossary_moddef>`
  93 +``vela_results.xml`` where the parameter values were updated by their
  94 +fitted values, and where the statistical uncertainties were added using the
  95 +``error`` attribute. To investigate how the fit went you should inspect the
  96 +log file ``ctlike.log`` that was also created by :ref:`ctlike`:
  97 +
  98 +.. code-block:: bash
  99 +
  100 + 2017-08-26T10:35:10: +=================================+
  101 + 2017-08-26T10:35:10: | Maximum likelihood optimisation |
  102 + 2017-08-26T10:35:10: +=================================+
  103 + 2017-08-26T10:35:12: >Iteration 0: -logL=-177232.327, Lambda=1.0e-03
  104 + 2017-08-26T10:35:12: >Iteration 1: -logL=-198931.081, Lambda=1.0e-03, delta=21698.754, step=1.0e+00, max(|grad|)=-22713.401202 [CutoffEnergy:4]
  105 + 2017-08-26T10:35:12: >Iteration 2: -logL=-200263.519, Lambda=1.0e-04, delta=1332.438, step=1.0e+00, max(|grad|)=-67648.133552 [CutoffEnergy:4]
  106 + 2017-08-26T10:35:12: >Iteration 3: -logL=-212350.035, Lambda=1.0e-05, delta=12086.515, step=1.0e+00, max(|grad|)=23036.151920 [Index2:6]
  107 + 2017-08-26T10:35:12: >Iteration 4: -logL=-213951.781, Lambda=1.0e-06, delta=1601.746, step=1.0e+00, max(|grad|)=-8297.648633 [CutoffEnergy:4]
  108 + 2017-08-26T10:35:13: >Iteration 5: -logL=-215341.362, Lambda=1.0e-07, delta=1389.581, step=1.0e+00, max(|grad|)=2747.034517 [Index2:6]
  109 + 2017-08-26T10:35:13: >Iteration 6: -logL=-215490.429, Lambda=1.0e-08, delta=149.067, step=1.0e+00, max(|grad|)=697.301361 [Index2:6]
  110 + 2017-08-26T10:35:13: Iteration 7: -logL=-215490.429, Lambda=1.0e-09, delta=-14.065, step=1.0e+00, max(|grad|)=-1205.683279 [Index1:3] (stalled)
  111 + 2017-08-26T10:35:13: Iteration 8: -logL=-215490.429, Lambda=1.0e-08, delta=-14.064, step=1.0e+00, max(|grad|)=-1205.659884 [Index1:3] (stalled)
  112 + 2017-08-26T10:35:14: Iteration 9: -logL=-215490.429, Lambda=1.0e-07, delta=-14.055, step=1.0e+00, max(|grad|)=-1205.425967 [Index1:3] (stalled)
  113 + 2017-08-26T10:35:14: Iteration 10: -logL=-215490.429, Lambda=1.0e-06, delta=-13.963, step=1.0e+00, max(|grad|)=-1203.090620 [Index1:3] (stalled)
  114 + 2017-08-26T10:35:14: Iteration 11: -logL=-215490.429, Lambda=1.0e-05, delta=-13.066, step=1.0e+00, max(|grad|)=-1180.113526 [Index1:3] (stalled)
  115 + 2017-08-26T10:35:14: Iteration 12: -logL=-215490.429, Lambda=1.0e-04, delta=-6.263, step=1.0e+00, max(|grad|)=-983.079153 [Index1:3] (stalled)
  116 + 2017-08-26T10:35:14: >Iteration 13: -logL=-215496.367, Lambda=1.0e-03, delta=5.937, step=1.0e+00, max(|grad|)=-285.734284 [Index1:3]
  117 + 2017-08-26T10:35:15: Iteration 14: -logL=-215496.367, Lambda=1.0e-04, delta=-8.812, step=1.0e+00, max(|grad|)=-731.894749 [Index1:3] (stalled)
  118 + 2017-08-26T10:35:15: >Iteration 15: -logL=-215497.536, Lambda=1.0e-03, delta=1.169, step=1.0e+00, max(|grad|)=-153.668138 [Index1:3]
  119 + 2017-08-26T10:35:15: Iteration 16: -logL=-215496.136, Lambda=1.0e-04, delta=-1.400, step=1.0e+00, max(|grad|)=-328.522942 [Index1:3] (stalled)
  120 + 2017-08-26T10:35:15: >Iteration 17: -logL=-215498.376, Lambda=1.0e-03, delta=2.240, step=1.0e+00, max(|grad|)=3.257091 [Index2:6]
  121 + 2017-08-26T10:35:16: >Iteration 18: -logL=-215498.383, Lambda=1.0e-04, delta=0.007, step=1.0e+00, max(|grad|)=-8.270351 [CutoffEnergy:4]
  122 + 2017-08-26T10:35:16: >Iteration 19: -logL=-215498.384, Lambda=1.0e-05, delta=0.002, step=1.0e+00, max(|grad|)=0.637485 [Index2:6]
  123 + 2017-08-26T10:35:16:
  124 + 2017-08-26T10:35:16: +=========================================+
  125 + 2017-08-26T10:35:16: | Maximum likelihood optimisation results |
  126 + 2017-08-26T10:35:16: +=========================================+
  127 + 2017-08-26T10:35:16: === GOptimizerLM ===
  128 + 2017-08-26T10:35:16: Optimized function value ..: -215498.384
  129 + 2017-08-26T10:35:16: Absolute precision ........: 0.005
  130 + 2017-08-26T10:35:16: Acceptable value decrease .: 2
  131 + 2017-08-26T10:35:16: Optimization status .......: converged
  132 + 2017-08-26T10:35:16: Number of parameters ......: 14
  133 + 2017-08-26T10:35:16: Number of free parameters .: 5
  134 + 2017-08-26T10:35:16: Number of iterations ......: 19
  135 + 2017-08-26T10:35:16: Lambda ....................: 1e-06
  136 + 2017-08-26T10:35:16: Maximum log likelihood ....: 215498.384
  137 + 2017-08-26T10:35:16: Observed events (Nobs) ...: 202330.000
  138 + 2017-08-26T10:35:16: Predicted events (Npred) ..: 202318.082 (Nobs - Npred = 11.9178772509331)
  139 + 2017-08-26T10:35:16: === GModels ===
  140 + 2017-08-26T10:35:16: Number of models ..........: 3
  141 + 2017-08-26T10:35:16: Number of parameters ......: 14
  142 + 2017-08-26T10:35:16: === GModelSky ===
  143 + 2017-08-26T10:35:16: Name ......................: Vela
  144 + 2017-08-26T10:35:16: Instruments ...............: all
  145 + 2017-08-26T10:35:16: Instrument scale factors ..: unity
  146 + 2017-08-26T10:35:16: Observation identifiers ...: all
  147 + 2017-08-26T10:35:16: Model type ................: PointSource
  148 + 2017-08-26T10:35:16: Model components ..........: "PointSource" * "SuperExponentialCutoffPowerLaw" * "Constant"
  149 + 2017-08-26T10:35:16: Number of parameters ......: 8
  150 + 2017-08-26T10:35:16: Number of spatial par's ...: 2
  151 + 2017-08-26T10:35:16: RA .......................: 128.84 [-360,360] deg (fixed,scale=1)
  152 + 2017-08-26T10:35:16: DEC ......................: -45.18 [-90,90] deg (fixed,scale=1)
  153 + 2017-08-26T10:35:16: Number of spectral par's ..: 5
  154 + 2017-08-26T10:35:16: Prefactor ................: 4.3553344038324e-09 +/- 4.75309654008435e-10 [1e-16,1e-06] ph/cm2/s/MeV (free,scale=1e-09,gradient)
  155 + 2017-08-26T10:35:16: Index1 ...................: -1.3435116067011 +/- 0.0311270092486095 [-0,-5] (free,scale=-1,gradient)
  156 + 2017-08-26T10:35:16: CutoffEnergy .............: 988.499237722443 +/- 181.86709257978 [1,1000000] MeV (free,scale=1000,gradient)
  157 + 2017-08-26T10:35:16: PivotEnergy ..............: 1000 [10,1000000] MeV (fixed,scale=1000,gradient)
  158 + 2017-08-26T10:35:16: Index2 ...................: 0.587129723482927 +/- 0.0279303486200403 [0.1,5] (free,scale=1,gradient)
  159 + 2017-08-26T10:35:16: Number of temporal par's ..: 1
  160 + 2017-08-26T10:35:16: Normalization ............: 1 (relative value) (fixed,scale=1,gradient)
  161 + 2017-08-26T10:35:16: === GModelSky ===
  162 + 2017-08-26T10:35:16: Name ......................: Galactic_diffuse
  163 + 2017-08-26T10:35:16: Instruments ...............: all
  164 + 2017-08-26T10:35:16: Instrument scale factors ..: unity
  165 + 2017-08-26T10:35:16: Observation identifiers ...: all
  166 + 2017-08-26T10:35:16: Model type ................: DiffuseSource
  167 + 2017-08-26T10:35:16: Model components ..........: "DiffuseMapCube" * "Constant" * "Constant"
  168 + 2017-08-26T10:35:16: Number of parameters ......: 3
  169 + 2017-08-26T10:35:16: Number of spatial par's ...: 1
  170 + 2017-08-26T10:35:16: Normalization ............: 1 [0.1,10] (fixed,scale=1,gradient)
  171 + 2017-08-26T10:35:16: Number of spectral par's ..: 1
  172 + 2017-08-26T10:35:16: Normalization ............: 1.10915296009432 +/- 0.00503367301009883 [0.1,1000] (free,scale=1,gradient)
  173 + 2017-08-26T10:35:16: Number of temporal par's ..: 1
  174 + 2017-08-26T10:35:16: Normalization ............: 1 (relative value) (fixed,scale=1,gradient)
  175 + 2017-08-26T10:35:16: === GModelSky ===
  176 + 2017-08-26T10:35:16: Name ......................: Extragalactic_diffuse
  177 + 2017-08-26T10:35:16: Instruments ...............: all
  178 + 2017-08-26T10:35:16: Instrument scale factors ..: unity
  179 + 2017-08-26T10:35:16: Observation identifiers ...: all
  180 + 2017-08-26T10:35:16: Model type ................: DiffuseSource
  181 + 2017-08-26T10:35:16: Model components ..........: "DiffuseIsotropic" * "FileFunction" * "Constant"
  182 + 2017-08-26T10:35:16: Number of parameters ......: 3
  183 + 2017-08-26T10:35:16: Number of spatial par's ...: 1
  184 + 2017-08-26T10:35:16: Value ....................: 1 [0,10] (fixed,scale=1,gradient)
  185 + 2017-08-26T10:35:16: Number of spectral par's ..: 1
  186 + 2017-08-26T10:35:16: Normalization ............: 1 [0,1000] (fixed,scale=1,gradient)
  187 + 2017-08-26T10:35:16: Number of temporal par's ..: 1
  188 + 2017-08-26T10:35:16: Normalization ............: 1 (relative value) (fixed,scale=1,gradient)
  189 +
  190 +
  191 +The fit converged after 19 iterations with spectral parameters that are
  192 +reasonably close to those found in
  193 +`Abdo et al. 2010, ApJ, 713, 154 <http://iopscience.iop.org/article/10.1088/0004-637X/713/1/154/pdf>`_
  194 +using the Fermi-LAT Science Tools.
  195 +
  196 + .. note::
  197 +
  198 + The fit results can be compared to the corresponding output of gtlike
  199 + when the tool is applied to the same test data. As you will see below,
  200 + the fitted model parameters are basically identical.
  201 +
  202 + .. code-block:: bash
  203 +
  204 + Extragalactic_diffuse:
  205 + Normalization: 1
  206 + Flux: 0.000149604 photons/cm^2/s
  207 +
  208 + Galactic_diffuse:
  209 + Value: 1.11394 +/- 0.00508393
  210 + Flux: 0.00054415 +/- 2.48325e-06 photons/cm^2/s
  211 +
  212 + Vela:
  213 + Prefactor: 4.3344 +/- 0.65258
  214 + Index1: 1.34634 +/- 0.0429336
  215 + Scale: 1
  216 + Cutoff: 1.00992 +/- 0.25512
  217 + Index2: 0.595018 +/- 0.0398585
  218 + TS value: 326648
  219 + Flux: 1.0758e-05 +/- 4.33949e-08 photons/cm^2/s
  220 +
  221 + WARNING: Fit may be bad in range [100, 149.23] (MeV)
  222 + WARNING: Fit may be bad in range [182.299, 405.972] (MeV)
  223 + WARNING: Fit may be bad in range [6690.96, 8173.66] (MeV)
  224 + WARNING: Fit may be bad in range [14900.5, 18202.4] (MeV)
  225 + WARNING: Fit may be bad in range [33182.8, 40536] (MeV)
  226 + WARNING: Fit may be bad in range [49518.7, 60491.9] (MeV)
  227 +
  228 + Total number of observed counts: 202330
  229 + Total number of model events: 202327
  230 +
  231 + -log(Likelihood): -215606.3555
  232 +
  233 + Elapsed CPU time: 72.33
  234 +
  235 + You may also compute the Test Statistic value using :ref:`ctlike` by
  236 + adding the ``tscalc="1"`` attribute to the
  237 + :ref:`model definition file <glossary_moddef>`:
  238 +
  239 + .. code-block:: xml
  240 +
  241 + <?xml version="1.0" standalone="no"?>
  242 + <source_library title="source library">
  243 + <source type="PointSource" name="Vela" tscalc="1">
  244 + ...
  245 + </source_library>
  246 +
  247 + This results in
  248 +
  249 + .. code-block:: bash
  250 +
  251 + 2017-08-26T13:05:12: === GModelSky ===
  252 + 2017-08-26T13:05:12: Name ......................: Vela
  253 + 2017-08-26T13:05:12: Instruments ...............: all
  254 + 2017-08-26T13:05:12: Test Statistic ............: 326326.556902542
  255 +
  256 + which is also close to the value determined by gtlike.
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  1 +.. _howto_fermi_prepare:
  2 +
  3 +Prepare Fermi-LAT data
  4 +----------------------
  5 +
  6 + .. admonition:: What you will learn
  7 +
  8 + You will learn how to prepare Fermi-LAT data for an analysis with
  9 + ctools.
  10 +
  11 + You will find more information about the Fermi-LAT software and data
  12 + analysis at the
  13 + `Fermi Science Support Center (FSSC) <https://fermi.gsfc.nasa.gov/ssc/>`_
  14 + web site.
  15 +
  16 +
  17 +Prerequisits
  18 +~~~~~~~~~~~~
  19 +
  20 +The following sections assume that you have properly installed the Fermi-LAT
  21 +Science Tools. The Fermi-LAT Science Tools can be downloaded from the
  22 +`Fermi Science Support Center (FSSC) <https://fermi.gsfc.nasa.gov/ssc/>`_.
  23 +
  24 +
  25 +Get data from the Fermi-LAT data server
  26 +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  27 +
  28 +Start with requesting the data you are interested in from the
  29 +`Fermi-LAT Data server <https://fermi.gsfc.nasa.gov/cgi-bin/ssc/LAT/LATDataQuery.cgi>`_.
  30 +As example the figure below shows a request for data around the Vela pulsar.
  31 +
  32 +.. figure:: howto_fermi_query.jpg
  33 + :width: 600px
  34 + :align: center
  35 +
  36 + *Fermi-LAT data server interface*
  37 +
  38 +After submitting the request you will get information of how to retrieve the
  39 +data:
  40 +
  41 +.. figure:: howto_fermi_data.jpg
  42 + :width: 600px
  43 + :align: center
  44 +
  45 + *Fermi-LAT data retrieval information*
  46 +
  47 +Now you download the data using the ``wget`` tool. At the same time of
  48 +downloading the data you should also download the input files for the diffuse
  49 +galactic and extragalactic model components. In the current example the
  50 +following files were downloaded:
  51 +
  52 +.. code-block:: bash
  53 +
  54 + $ wget http://fermi.gsfc.nasa.gov/FTP/fermi/data/lat/queries/L1708251631252315B1AD08_SC00.fits
  55 + $ wget http://fermi.gsfc.nasa.gov/FTP/fermi/data/lat/queries/L1708251631252315B1AD08_PH00.fits
  56 + $ wget http://fermi.gsfc.nasa.gov/FTP/fermi/data/lat/queries/L1708251631252315B1AD08_PH01.fits
  57 + $ wget https://fermi.gsfc.nasa.gov/ssc/data/analysis/software/aux/gll_iem_v06.fits
  58 + $ wget https://fermi.gsfc.nasa.gov/ssc/data/analysis/software/aux/iso_P8R2_SOURCE_V6_v06.txt
  59 +..
  60 +
  61 + .. warning::
  62 +
  63 + In the current example data within a radius of only 10 degrees around the
  64 + source of interest were selected. This was mainly for getting a small
  65 + data set. The
  66 + `Fermi Science Support Center (FSSC) <https://fermi.gsfc.nasa.gov/ssc/>`_
  67 + recommends to use larger regions for the Fermi-LAT data analysis.
  68 +
  69 +
  70 +Data preparation
  71 +~~~~~~~~~~~~~~~~
  72 +
  73 +First you need to combine the event lists into a single file. At the same
  74 +time you will select the region of interest for the analysis. You do this
  75 +using the ``gtselect`` tool:
  76 +
  77 +.. code-block:: bash
  78 +
  79 + $ ls *_PH* > events.txt
  80 + $ gtselect evclass=128 evtype=3
  81 + Input FT1 file[] @events.txt
  82 + Output FT1 file[] events_fermi.fits
  83 + RA for new search center (degrees) (0:360) [INDEF] 128.84
  84 + Dec for new search center (degrees) (-90:90) [INDEF] -45.18
  85 + radius of new search region (degrees) (0:180) [INDEF] 10.0
  86 + start time (MET in s) (0:) [INDEF]
  87 + end time (MET in s) (0:) [INDEF]
  88 + lower energy limit (MeV) (0:) [30] 100.0
  89 + upper energy limit (MeV) (0:) [300000] 300000.0
  90 + maximum zenith angle value (degrees) (0:180) [180] 90.0
  91 +
  92 +Now you have to select from all events those which fall into periods where
  93 +data quality is good, the telescope is configured for science, and the rocking
  94 +angle is not too large. You do this using the ``gtmktime`` tool that defines
  95 +the Good Time Intervals for your analysis:
  96 +
  97 +.. code-block:: bash
  98 +
  99 + $ gtmktime
  100 + Spacecraft data file[] L1708251631252315B1AD08_SC00.fits
  101 + Filter expression[DATA_QUAL>0 && LAT_CONFIG==1 && ABS(ROCK_ANGLE)<52]
  102 + Apply ROI-based zenith angle cut[yes] no
  103 + Event data file[] events_fermi.fits
  104 + Output event file name[] events_fermi_gti.fits
  105 +
  106 +The events are now ready to be binned into a counts cube using the
  107 +``gtbin`` tool:
  108 +
  109 +.. code-block:: bash
  110 +
  111 + $ gtbin
  112 + This is gtbin version ScienceTools-10-01-01
  113 + Type of output file (CCUBE|CMAP|LC|PHA1|PHA2|HEALPIX) [PHA2] CCUBE
  114 + Event data file name[] events_fermi_gti.fits
  115 + Output file name[] cntmap.fits
  116 + Spacecraft data file name[NONE] L1708251631252315B1AD08_SC00.fits
  117 + Size of the X axis in pixels[] 60
  118 + Size of the Y axis in pixels[] 60
  119 + Image scale (in degrees/pixel)[] 0.2
  120 + Coordinate system (CEL - celestial, GAL -galactic) (CEL|GAL) [CEL]
  121 + First coordinate of image center in degrees (RA or galactic l)[] 128.84
  122 + Second coordinate of image center in degrees (DEC or galactic b)[] -45.18
  123 + Rotation angle of image axis, in degrees[0.]
  124 + Projection method e.g. AIT|ARC|CAR|GLS|MER|NCP|SIN|STG|TAN:[AIT] TAN
  125 + Algorithm for defining energy bins (FILE|LIN|LOG) [LOG]
  126 + Start value for first energy bin in MeV[30] 100.0
  127 + Stop value for last energy bin in MeV[200000] 300000.0
  128 + Number of logarithmically uniform energy bins[] 40
  129 +
  130 +As next step you need to compute a livetime cube which is a computational
  131 +intensive task. You do this using the ``gtltcube`` tool:
  132 +
  133 +.. code-block:: bash
  134 +
  135 + $ gtltcube zmax=90
  136 + Event data file[] events_fermi_gti.fits
  137 + Spacecraft data file[] L1708251631252315B1AD08_SC00.fits
  138 + Output file[expCube.fits] ltcube.fits
  139 + Step size in cos(theta) (0.:1.) [0.025]
  140 + Pixel size (degrees)[1]
  141 + Working on file L1708251631252315B1AD08_SC00.fits
  142 + .....................!
  143 +
  144 +The little dots indicate the progress while the tool is computing. Once
  145 +finished you need to compute the binned exposure map using the ``gtexpcube2``
  146 +tool:
  147 +
  148 +.. code-block:: bash
  149 +
  150 + $ gtexpcube2
  151 + Livetime cube file[] ltcube.fits
  152 + Counts map file[] none
  153 + Output file name[] expmap.fits
  154 + Response functions to use[CALDB] P8R2_SOURCE_V6
  155 + Size of the X axis in pixels[INDEF] 200
  156 + Size of the Y axis in pixels[INDEF] 200
  157 + Image scale (in degrees/pixel)[INDEF] 0.2
  158 + Coordinate system (CEL - celestial, GAL -galactic) (CEL|GAL) [GAL] CEL
  159 + First coordinate of image center in degrees (RA or galactic l)[INDEF] 128.84
  160 + Second coordinate of image center in degrees (DEC or galactic b)[INDEF] -45.18
  161 + Rotation angle of image axis, in degrees[0]
  162 + Projection method e.g. AIT|ARC|CAR|GLS|MER|NCP|SIN|STG|TAN[CAR] TAN
  163 + Start energy (MeV) of first bin[INDEF] 100.0
  164 + Stop energy (MeV) of last bin[INDEF] 300000.0
  165 + Number of logarithmically-spaced energy bins[INDEF] 40
  166 + Computing binned exposure map....................!
  167 +
  168 +
  169 +Generate source maps
  170 +~~~~~~~~~~~~~~~~~~~~
  171 +
  172 +Now you are ready to produce source maps for all diffuse model components.
  173 +Start with putting the diffuse model components into a
  174 +:ref:`model definition XML file <glossary_moddef>`:
  175 +
  176 +.. code-block:: xml
  177 +
  178 + <?xml version="1.0" standalone="no"?>
  179 + <source_library title="source library">
  180 + <source type="DiffuseSource" name="Galactic_diffuse" instrument="LAT">
  181 + <spectrum type="ConstantValue">
  182 + <parameter name="Value" scale="1.0" value="1.0" min="0.1" max="1000.0" free="1"/>
  183 + </spectrum>
  184 + <spatialModel type="MapCubeFunction" file="gll_iem_v06.fits">
  185 + <parameter name="Normalization" scale="1.0" value="1.0" min="0.1" max="10.0" free="0"/>
  186 + </spatialModel>
  187 + </source>
  188 + <source type="DiffuseSource" name="Extragalactic_diffuse" instrument="LAT">
  189 + <spectrum type="FileFunction" file="iso_P8R2_SOURCE_V6_v06.txt">
  190 + <parameter name="Normalization" scale="1.0" value="1.0" min="0.0" max="1000.0" free="1"/>
  191 + </spectrum>
  192 + <spatialModel type="ConstantValue">
  193 + <parameter name="Value" scale="1.0" value="1.0" min="0.0" max="10.0" free="0"/>
  194 + </spatialModel>
  195 + </source>
  196 + </source_library>
  197 +..
  198 +
  199 + .. warning::
  200 +
  201 + While ctools also implements the syntax used for Fermi-LAT Science Tools
  202 + :ref:`model definition files <glossary_moddef>`,
  203 + the Fermi-LAT Science Tools naming conventions are not very homogenous,
  204 + hence we usually advocate to use the more coherent ctools syntax. For the
  205 + Fermi-LAT Science Tools you have to use however the Fermi-LAT syntax.
  206 +
  207 +Now you can generate the source maps using ``gtsrcmaps``:
  208 +
  209 +.. code-block:: bash
  210 +
  211 + $ gtsrcmaps ptsrc=no
  212 + Exposure hypercube file[] ltcube.fits
  213 + Counts map file[] cntmap.fits
  214 + Source model file[] diffuse.xml
  215 + Binned exposure map[none] expmap.fits
  216 + Source maps output file[] srcmaps.fits
  217 + Response functions[CALDB] P8R2_SOURCE_V6
  218 + Generating SourceMap for Extragalactic_diffuse....................!
  219 + Generating SourceMap for Galactic_diffuse....................!
  220 +
  221 +And you are done with the preparation of the Fermi-LAT data. You now have
  222 +the following files in your working directory:
  223 +
  224 +* ``srcmaps.fits`` - Counts cube including source maps
  225 +* ``ltcube.fits`` - Livetime cube
  226 +* ``expmap.fits`` - Exposure map
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  1 +.. _howto_fermi_spectrum:
  2 +
  3 +Generate a spectral energy distribution for a source
  4 +----------------------------------------------------
  5 +
  6 + .. admonition:: What you will learn
  7 +
  8 + You will learn how to use :ref:`ctlike` to derive the spectral energy
  9 + density of a source from Fermi-LAT data.
  10 +
  11 +So far the :ref:`csspec` script does not work for Fermi-LAT data, but you
  12 +will learn here a method that you can use to derive the spectrum of any
  13 +source using Fermi-LAT data. For this you first need a little Python code
  14 +to transform the spectral component of the Vela source in the
  15 +:ref:`model definition file <glossary_moddef>`
  16 +from a super exponentially cut-off power law into a node function.
  17 +You do this as follows:
  18 +
  19 +.. code-block:: python
  20 +
  21 + >>> import gammalib
  22 + >>> models = gammalib.GModels('vela_results.xml')
  23 + >>> energies = gammalib.GEnergies(10, gammalib.GEnergy(100.0, 'MeV'), gammalib.GEnergy(100.0, 'GeV'))
  24 + >>> nodes = gammalib.GModelSpectralNodes()
  25 + >>> for energy in energies:
  26 + >>> nodes.append(energy, models['Vela'].spectral().eval(energy))
  27 + >>> for par in nodes:
  28 + >>> if 'Energy' in par.name():
  29 + >>> par.fix()
  30 + >>> if 'Intensity' in par.name():
  31 + >>> par.min(1.0e-30)
  32 + >>> models['Vela'].spectral(nodes)
  33 + >>> models.save('model_nodes.xml')
  34 +
  35 +This will create a
  36 +:ref:`model definition file <glossary_moddef>`
  37 +with the following structure:
  38 +
  39 +.. code-block:: xml
  40 +
  41 + <?xml version="1.0" encoding="UTF-8" standalone="no"?>
  42 + <source_library title="source library">
  43 + <source name="Vela" type="PointSource">
  44 + <spectrum type="NodeFunction">
  45 + <node>
  46 + <parameter name="Energy" value="100" scale="1" free="0" />
  47 + <parameter name="Intensity" value="7.40280399439422e-08" error="0" scale="1" min="1e-30" free="1" />
  48 + </node>
  49 + <node>
  50 + <parameter name="Energy" value="215.443469003188" scale="1" free="0" />
  51 + <parameter name="Intensity" value="2.27587615163047e-08" error="0" scale="1" min="1e-30" free="1" />
  52 + </node>
  53 + ...
  54 + </source_library>
  55 +
  56 +Instead of the super exponentially cut-off power law the model now contains
  57 +a node function with ten intensity nodes between 100 MeV and 100 GeV, and the
  58 +:ref:`ctlike` tool will now adjust the intensities of each of the nodes which
  59 +will result in a spectrum. To do this type now:
  60 +
  61 +.. code-block:: bash
  62 +
  63 + $ ctlike debug=yes
  64 + Input event list, counts cube or observation definition XML file [obs.xml]
  65 + Input model definition XML file [models.xml] model_nodes.xml
  66 + Output model definition XML file [vela_results.xml] vela_nodes_results.xml
  67 +
  68 +This will produce the
  69 +:ref:`model definition file <glossary_moddef>`
  70 +``vela_nodes_results.xml`` with the intensities of the fitted source at
  71 +each energy. The results are displayed graphically below.
  72 +
  73 +.. figure:: howto_fermi_spectrum.png
  74 + :width: 600px
  75 + :align: center
  76 +
  77 + *Spectrum of the Vela pulsar derived using a node function*
  78 +..
  79 +
  80 + .. note::
  81 +
  82 + The ``NodeFunction`` spectral models implements a piece-wise power law
  83 + that is defined by the intensity values at each node.
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  1 +.. _howto_fermi_ulimit:
  2 +
  3 +Derive upper flux limits for a source
  4 +-------------------------------------
  5 +
  6 + .. admonition:: What you will learn
  7 +
  8 + You will learn how to use :ref:`ctulimit` to determine upper flux limits
  9 + from Fermi-LAT data using a likelihood profile method.
  10 +
  11 +Suppose there is another potential source in the field of view but you cannot
  12 +see this source in a counts map, hence you want to derive an upper flux limit
  13 +for the source. To do this you first have to add an additional source to the
  14 +:ref:`model definition file <glossary_moddef>`. An example for a source at
  15 +:math:`\alpha=122^\circ` and :math:`\delta=-42^\circ` is shown below:
  16 +
  17 +.. code-block:: xml
  18 +
  19 + <?xml version="1.0" standalone="no"?>
  20 + <source_library title="source library">
  21 + <source type="PointSource" name="Test">
  22 + <spectrum type="PowerLaw">
  23 + <parameter name="PhotonFlux" scale="1e-12" value="1.0" min="1e-07" max="1000.0" free="1"/>
  24 + <parameter name="Index" scale="1.0" value="-2.0" min="-5.0" max="+5.0" free="0"/>
  25 + <parameter name="LowerLimit" scale="1.0" value="100.0" min="10.0" max="1000000.0" free="0"/>
  26 + <parameter name="UpperLimit" scale="1.0" value="100000.0" min="10.0" max="1000000.0" free="0"/>
  27 + </spectrum>
  28 + <spatialModel type="PointSource">
  29 + <parameter name="RA" scale="1.0" value="122.00" min="-360" max="360" free="0"/>
  30 + <parameter name="DEC" scale="1.0" value="-42.00" min="-90" max="90" free="0"/>
  31 + </spatialModel>
  32 + </source>
  33 + <source type="PointSource" name="Vela">
  34 + ...
  35 + </source_library>
  36 +
  37 +Now you can run the :ref:`ctulimit` tool. Since the tool is normally tuned
  38 +for Cherenkov Telescope data analysis, energies are by default given in TeV.
  39 +To specify a reference energy of the differential flux limit of 1 GeV you
  40 +need to provide the hidden parameter ``eref=0.001``. You can also set the
  41 +flux interval for the intergal flux computation to 100 MeV - 100 GeV by
  42 +specifying ``emin=0.0001 emax=0.1`` (all values are given in TeV):
  43 +
  44 +.. code-block:: bash
  45 +
  46 + $ ctulimit eref=0.001 emin=0.0001 emax=0.1
  47 + Input event list, counts cube or observation definition XML file [obs.xml]
  48 + Source of interest [Test]
  49 + Input model definition XML file [model_lat_ulimit.xml]
  50 +
  51 +The results of the upper limit computation can then be extracted from the
  52 +``ctulimit.log`` file that is created by :ref:`ctulimit`:
  53 +
  54 +.. code-block:: bash
  55 +
  56 + 2017-08-26T14:37:48: +=====================+
  57 + 2017-08-26T14:37:48: | Upper limit results |
  58 + 2017-08-26T14:37:48: +=====================+
  59 + 2017-08-26T14:37:48: Differential flux limit ...: 1.00100099727198e-13 ph/cm2/s/MeV at 0.001 TeV
  60 + 2017-08-26T14:37:48: Integral flux limit .......: 9.9999999627471e-10 ph/cm2/s within [0.0001-0.1] TeV
  61 + 2017-08-26T14:37:48: Energy flux limit .........: 1.10785216561628e-12 erg/cm2/s within [0.0001-0.1] TeV
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  1 +.. _howto_fermi:
  2 +
  3 +Analysing Fermi-LAT data
  4 +------------------------
  5 +
  6 + .. admonition:: What you will learn
  7 +
  8 + You will learn how to analyse data from the LAT telescope about NASA's
  9 + `Fermi <https://fermi.gsfc.nasa.gov/ssc/>`_ satellite with ctools.
  10 +
  11 +You can use ctools to analyse data from the LAT telescope about NASA's
  12 +`Fermi <https://fermi.gsfc.nasa.gov/ssc/>`_ satellite.
  13 +To do this you need to be familar with the Fermi-LAT Science Tools that you
  14 +will use to prepare the Fermi-LAT data for the analysis. You can download the
  15 +Fermi-LAT Science Tools from the
  16 +`Fermi Science Support Center (FSSC) <https://fermi.gsfc.nasa.gov/ssc/>`_
  17 +which provides also more detailed information about how to prepare the data.
  18 +What you need for a given observation are the following files:
  19 +
  20 +* ``srcmaps.fits`` - source maps file that include a counts cube and maps of the
  21 + diffuse model components
  22 +* ``ltcube.fits`` - livetime cube file that corresponds to the Good Time Intervals
  23 + of the data
  24 +* ``expmap.fits`` - exposure map file
  25 +
  26 +To demonstrate how the Fermi-LAT analysis works with ctools, here is a short
  27 +tutorial that is based on a simple analysis of the Vela pulsar.
  28 +
  29 +.. toctree::
  30 + :maxdepth: 1
  31 +
  32 + howto_fermi_prepare
  33 + howto_fermi_fitting
  34 + howto_fermi_butterfly
  35 + howto_fermi_spectrum
  36 + howto_fermi_ulimit
  37 + howto_fermi_errors
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@@ -21,4 +21,6 @@ These examples can be easily adapted to any data you have at your disposal. @@ -21,4 +21,6 @@ These examples can be easily adapted to any data you have at your disposal.
21 howto_lightcurve 21 howto_lightcurve
22 howto_phasecurve 22 howto_phasecurve
23 howto_exclude 23 howto_exclude
24 - howto_vo  
25 \ No newline at end of file 24 \ No newline at end of file
  25 + howto_vo
  26 + How to analyse Fermi-LAT data with ctools? <fermi/index>
  27 + How to analyse H.E.S.S. data with ctools? <iact/index>
26 \ No newline at end of file 28 \ No newline at end of file
doc/source/users/tutorials/index.rst
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@@ -8,6 +8,5 @@ Tutorials @@ -8,6 +8,5 @@ Tutorials
8 8
9 quickstart/index 9 quickstart/index
10 beyond/index 10 beyond/index
11 - 1dc/index  
12 howto/index 11 howto/index
13 - iact_analysis/index 12 + 1dc/index
14 \ No newline at end of file 13 \ No newline at end of file