Veronika Vodeb / ctools

Commit 39991280aa6aed4432dfc232d9720a49e23b032b

Authored by Luigi Tibaldo
1 parent 070a0973

On/Off analysis in quickstart and reshuffling of material with 1DC tutorial

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Showing 4 changed files with 304 additions and 133 deletions
doc/source/users/tutorials/1dc/classical_analysis.rst
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... ... @@ -56,7 +56,7 @@ region. You can do this using the :ref:`ctskymap` tool.
56 56 Output skymap file [skymap.fits]
57 57  
58 58 In the spirit of the classical analysis we have chosen to derive the background
59   -using the RING method (e.g., Berge et al. 2007 A&A 466 1219B), in which for each
  59 +using the RING method, in which for each
60 60 point in the map (trial source position) the background is derived from a ring
61 61 centered at the same position. The RING method is fast and robust against linear
62 62 gradients of the background rates, but requires a model (from the :ref:`instrument response functions <glossary_irf>`
... ... @@ -133,22 +133,7 @@ Below you can see the new significance map with the source/exclusion region.
133 133  
134 134 For a classical spectral analysis we need to derive count spectra for the source
135 135 region and for background regions. This is accomplished by the :ref:`csphagen`
136   -script. This script saves the source (On) and background (Off) count spectra
137   -in `OGIP format <https://heasarc.gsfc.nasa.gov/docs/heasarc/ofwg/docs/spectra/ogip_92_007/node5.html>`_,
138   -along with the relevant information from the :ref:`instrument response functions <glossary_irf>`
139   -refashioned according to this format conventions.
140   -
141   -:ref:`csphagen` calculates the background counts using the REFLECTED algorithm
142   -(e.g., Berge et al. 2007 A&A 466 1219B), in which, for each individual
143   -observation the background regions have the same shape as the source region, and
144   -are rotated around the center of the camera keeping the same offset. As many
145   -reflected regions as possible are used, excluding the area of the camera near
146   -the source position. Since the background rates are expected to be approximately
147   -radially symmetric in camera coordinates, this method minimizes the impact of
148   -the background rate modeling from Monte Carlo. An optional exclusion map (in
149   -FITS WCS format) can be provided as input through the ``inexclusion`` hidden
150   -parameter if other regions of significant gamma-ray emission ought to be
151   -excluded from the background computation.
  136 +script.
152 137  
153 138 .. code-block:: bash
154 139  
... ... @@ -183,33 +168,9 @@ looks like.
183 168 </observation>
184 169 </observation_list>
185 170  
186   -The observation entails four FITS files. ``onoff_stacked_pha_on.fits`` and
187   -``onoff_stacked_pha_off.fits`` contain the On and Off spectra, respectively.
188   -These are stored in the SPECTRUM extension of the FITS file, along with ancillary
189   -information, notably the scaling factor to be applied to the background spectrum,
190   -BACKSCAL. The third extension, EBOUNDS, contains the boundaries of the energy
191   -bins, as defined by the binning parameters in input to csphagen. The file
192   -``onoff_stacked_arf.fits`` contains the spectral response of the instrument
193   -extracted fromt the :ref:`instrument response functions <glossary_irf>`,
194   -including effective area for gamma-ray detection and background rates, in the
195   -SPECRESP extension. The file ``onoff_stacked_rmf.fits`` contains the remaining
196   -part of the instrument response, i.e., an energy redistribution matrix (MATRIX),
197   -as well as another instance of the EBOUNDS table. Note that we are performing a
198   -1D analysis: the effect of the PSF is already folded into the effective area
199   -computation.
200   -
201   -.. note::
202   -
203   - The parameters specified control the energy binning of the count spectra in
204   - *reconstructed* energy. For the computation of the instrument response we
205   - need a fine binning in *true* energy, which is controlled by the hidden
206   - parameters ``etruemin``, ``etruemax``, and ``etruebins``.
207   -
208 171 .. note::
209 172  
210   - The first part of the FITS files names (and a full path to the desired
211   - location) can be set using the hidden ``prefix`` parameter of
212   - :ref:`csphagen`. If you decide not to stack multiple observations the string
  173 + If you decide not to stack multiple observations the string
213 174 ``stacked`` with be replaced in the file names by the observation id for
214 175 each of the original observations.
215 176  
... ... @@ -226,12 +187,6 @@ the On and Off regions for a few observations (extracted using the
226 187  
227 188 *Sky map of the event counts in a larger region around Cas A (not background subtracted). The green crosses show the pointing directions, the magenta circles the Off regions, and the white circle the On region.*
228 189  
229   -.. note::
230   -
231   - If you wish to limit the number of observations considered to those pointed
232   - closer to the source, you can do this either at the observation selection
233   - level (see :ref:`csobsselect`), or directly in :ref:`csphagen` via the
234   - hidden ``maxoffset`` parameter.
235 190  
236 191 Next we need a model to be fit to the observations. It must contain a model for the
237 192 source, and, optionally, a model for the background. Here is what such a
... ... @@ -300,32 +255,9 @@ The output file ``CasA_results.xml`` contains the best fit parameter values.
300 255 Check the :ref:`ctlike` log file (by default ``ctlike.log``) to learn
301 256 about the fit convergence and investigate any issues.
302 257  
303   -:ref:`ctlike` has a hidden parameter called ``statistic`` that sets the
304   -statistic used for the fit.
305   -
306   -- The DEFAULT for OnOff osbervations is CSTAT, i.e., Poisson signal and Poisson
307   - background. A spectral model for the signal and a spectral model for the
308   - background are jointly fit to the On and Off spectra.
309   -- WSTAT is a special case of CSTAT, Poisson signal with Poisson background, in
310   - which you do not need to have a spectral model for the background and
311   - free parameters associated with it. The number of background counts in each
312   - energy bin is treated as a nuisance parameter, derived from the On and Off
313   - counts by profiling the likelihood function. In this case the only assumption
314   - is that the background rate spectrum is the same in the On and Off regions.
315   -
316   -.. warning::
317   - Beware that the profiling may yield unphysical results (negative background
318   - counts) if the number of events in the Off spectra are zero. In this case a
319   - null number of expected background events must be enforced,
320   - which can result in a bias on the source's parameters. You can address this
321   - issue by stacking multiple observations, using a coarser energy binning, or
322   - using CSTAT instead (if you have a spectral model for the background that is
323   - good enough). See the `XSPEC manual Appendix B <https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/XSappendixStatistics.html>`_
324   - for more information.
325   -
326   -- You can also use CHI2, a classical chi square, i.e., a Gaussian signal and
327   - Gaussian background. As for CSTAT, a spectral model for the signal and a
328   - spectral model for the background are jointly fit to the On and Off spectra.
  258 +The hidden parameter ``statistic`` in :ref:`ctlike` can be used to
  259 +set the fit statistic and in particular how the background is treated
  260 +in the fit.
329 261  
330 262 The :ref:`ctbutterfly` tool and :ref:`csspec` script can now be used to extract
331 263 the best-fit source spectrum.
... ... @@ -360,4 +292,4 @@ matplotlib).
360 292 :width: 400px
361 293 :align: center
362 294  
363   - *Spectral Energy Distribution of the source: the best-fit function over the whole energy range and its uncertainty range, along with the spectral points in energy bins.*
364 295 \ No newline at end of file
  296 + *Spectral Energy Distribution of the source: the best-fit function over the whole energy range and its uncertainty range, along with the spectral points in energy bins.*
... ...
doc/source/users/tutorials/quickstart/onoff.png 0 → 100644
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doc/source/users/tutorials/quickstart/onoff.rst
  View file @3999128
... ... @@ -6,7 +6,7 @@ Doing an On/Off analysis
6 6 .. admonition:: What you will learn
7 7  
8 8 You will learn how to **adjust a parametrised spectral model to
9   - the events deriving the bacground from the data**.
  9 + the events deriving the background from the data**.
10 10  
11 11 Gamma-ray events are rare compared to the background events,
12 12 hence small imperfections of the background model can have a
... ... @@ -17,3 +17,242 @@ Doing an On/Off analysis
17 17 (background) regions. An On/Off analysis is recommended if you
18 18 want to assure minimal dependency on the Monte Carlo background model.
19 19  
  20 +Last, we consider the classical technique for IACT spectral analysis,
  21 +in which 1D spectra for On and Off regions are used jointly to
  22 +determine the source parameters.
  23 +
  24 +The script :ref:`csphagen` is used to derive a set of On/Off
  25 +observations from the event lists. This script saves the source (On) and background (Off) count spectra
  26 +in `OGIP format <https://heasarc.gsfc.nasa.gov/docs/heasarc/ofwg/docs/spectra/ogip_92_007/node5.html>`_,
  27 +along with the relevant information from the :ref:`instrument response functions <glossary_irf>`
  28 +refashioned according to this format conventions.
  29 +
  30 +:ref:`csphagen` calculates the background counts using the REFLECTED algorithm, in which, for each individual
  31 +observation the background regions have the same shape as the source region, and
  32 +are rotated around the center of the camera keeping the same offset. As many
  33 +reflected regions as possible are used, excluding the area of the camera near
  34 +the source position. Since the background rates are expected to be approximately
  35 +radially symmetric in camera coordinates, this method minimizes the impact of
  36 +the background rate modeling from Monte Carlo. An optional exclusion map (in
  37 +FITS WCS format) can be provided as input through the ``inexclusion`` hidden
  38 +parameter if other regions of significant gamma-ray emission ought to be
  39 +excluded from the background computation.
  40 +
  41 +.. code-block:: bash
  42 +
  43 + $ csphagen
  44 + Input event list or observation definition XML file [obs.xml] events_edisp.fits
  45 + Calibration database [prod2]
  46 + Instrument response function [South_0.5h]
  47 + Binning algorithm (LIN|LOG|FILE) [LOG]
  48 + Lower energy limit (TeV) [0.1]
  49 + Upper energy limit (TeV) [100.0]
  50 + Number of energy bins [120] 30
  51 + Coordinate system (CEL - celestial, GAL - galactic) (CEL|GAL) [CEL]
  52 + Right Ascension of source region centre (deg) (0-360) [83.63]
  53 + Declination of source region centre (deg) (-90-90) [22.01]
  54 + Radius of source region circle (deg) (0-180) [0.2]
  55 + Stack multiple observations into single PHA, ARF and RMF files? [no]
  56 + Output observation definition XML file [onoff_obs.xml]
  57 +
  58 +.. note::
  59 +
  60 + - We have used the events simulated accounting for energy
  61 + dispersion, since energy dispersion is always used in On/Off analysis.
  62 +
  63 + - If you wish to limit the number of observations considered to
  64 + those pointed closer to the source, you can do this either at the
  65 + observation selection level (see :ref:`csobsselect`), or directly
  66 + in :ref:`csphagen` via the hidden ``maxoffset`` parameter.
  67 +
  68 + - The parameters specified control the energy binning of the count
  69 + spectra in *reconstructed* energy. For the computation of the
  70 + instrument response we need a fine binning in *true* energy,
  71 + which is controlled by the hidden parameters ``etruemin``,
  72 + ``etruemax``, and ``etruebins``.
  73 +
  74 +This has produced in output several files. The xml observations file
  75 +contains a single On/Off observation.
  76 +
  77 +.. code-block:: bash
  78 +
  79 + <?xml version="1.0" encoding="UTF-8" standalone="no"?>
  80 + <observation_list title="observation list">
  81 + <observation name="" id="" instrument="CTAOnOff" statistic="cstat">
  82 + <parameter name="Pha_on" file="onoff_pha_on.fits" />
  83 + <parameter name="Pha_off" file="onoff_pha_off.fits" />
  84 + <parameter name="Arf" file="onoff_arf.fits" />
  85 + <parameter name="Rmf" file="onoff_rmf.fits" />
  86 + </observation>
  87 + </observation_list>
  88 +
  89 +The observation entails four FITS files. ``onoff_pha_on.fits`` and
  90 +``onoff_pha_off.fits`` contain the On and Off spectra, respectively.
  91 +These are stored in the SPECTRUM extension of the FITS file, along with ancillary
  92 +information, notably the scaling factor to be applied to the background spectrum,
  93 +BACKSCAL. The third extension, EBOUNDS, contains the boundaries of the energy
  94 +bins, as defined by the binning parameters in input to csphagen. The file
  95 +``onoff_arf.fits`` contains the spectral response of the instrument
  96 +extracted fromt the :ref:`instrument response functions <glossary_irf>`,
  97 +including effective area for gamma-ray detection and background rates, in the
  98 +SPECRESP extension. The file ``onoff_rmf.fits`` contains the remaining
  99 +part of the instrument response, i.e., an energy redistribution matrix (MATRIX),
  100 +as well as another instance of the EBOUNDS table. Note that we are performing a
  101 +1D analysis: the effect of the PSF is already folded into the effective area
  102 +computation.
  103 +
  104 +.. note::
  105 +
  106 + The first part of the FITS files names (and a full path to the desired
  107 + location) can be set using the hidden ``prefix`` parameter of
  108 + :ref:`csphagen`.
  109 +
  110 +There are also come ancillary `ds9 <http://ds9.si.edu>`_ region files, that show
  111 +the On region and the Off regions, ``onoff_on.reg`` and
  112 +``onoff_off.reg``, respectively. Below there is
  113 +a skymap where you can see the pointing direction along with the position of
  114 +the On and Off regions.
  115 +
  116 +.. figure:: onoff.png
  117 + :width: 400px
  118 + :align: center
  119 +
  120 + *Sky map of the events. The cross shows the pointing directions,
  121 + the green circles the Off regions, and the white circle the On
  122 + region.*
  123 +
  124 +The model to be fit to the observations needs to specify for the
  125 +background component that we are dealing with a ``CTAOnOff`` analysis.
  126 +
  127 +.. code-block:: bash
  128 +
  129 + <?xml version="1.0" standalone="no"?>
  130 + <source_library title="source library">
  131 + <source name="Crab" type="PointSource">
  132 + <spectrum type="PowerLaw">
  133 + <parameter name="Prefactor" scale="1e-16" value="5.7" min="1e-07" max="1000.0" free="1"/>
  134 + <parameter name="Index" scale="-1" value="2.48" min="0.0" max="+5.0" free="1"/>
  135 + <parameter name="PivotEnergy" scale="1e6" value="0.3" min="0.01" max="1000.0" free="0"/>
  136 + </spectrum>
  137 + <spatialModel type="PointSource">
  138 + <parameter name="RA" scale="1.0" value="83.6331" min="-360" max="360" free="0"/>
  139 + <parameter name="DEC" scale="1.0" value="22.0145" min="-90" max="90" free="0"/>
  140 + </spatialModel>
  141 + </source>
  142 + <source name="CTABackgroundModel" type="CTAIrfBackground" instrument="CTAOnOff">
  143 + <spectrum type="PowerLaw">
  144 + <parameter name="Prefactor" scale="1.0" value="1.0" min="1e-3" max="1e+3" free="1"/>
  145 + <parameter name="Index" scale="1.0" value="0.0" min="-5.0" max="+5.0" free="1"/>
  146 + <parameter name="PivotEnergy" scale="1e6" value="1.0" min="0.01" max="1000.0" free="0"/>
  147 + </spectrum>
  148 + </source>
  149 + </source_library>
  150 +
  151 +At this point we can run an On/Off analysis just by passing the On/Off
  152 +observation container to :ref:`ctlike`.
  153 +
  154 +.. code-block:: bash
  155 + Input event list, counts cube or observation definition XML file [selected_events.fits] onoff_obs.xml
  156 + Input model definition XML file [$CTOOLS/share/models/crab.xml] crab_onoff.xml
  157 + Output model definition XML file [crab_results.xml]
  158 +
  159 +Below you see the corresponding output from the ``ctlike.log``
  160 +file.The fitted parameters are still the same within statistical
  161 +uncertainties as the ones found in binned/unbinned mode. This may not
  162 +always be the case, especially if the background is not well known a priori.
  163 +
  164 +.. code-block:: bash
  165 +
  166 + 2017-11-28T17:26:56: +=================================+
  167 + 2017-11-28T17:26:56: | Maximum likelihood optimisation |
  168 + 2017-11-28T17:26:56: +=================================+
  169 + 2017-11-28T17:26:56: >Iteration 0: -logL=-48350.908, Lambda=1.0e-03
  170 + 2017-11-28T17:26:56: >Iteration 1: -logL=-48352.759, Lambda=1.0e-03, delta=1.852, step=1.0e+00, max(|grad|)=2.829489 [Index:7]
  171 + 2017-11-28T17:26:56: >Iteration 2: -logL=-48352.760, Lambda=1.0e-04, delta=0.000, step=1.0e+00, max(|grad|)=0.002408 [Index:3]
  172 + 2017-11-28T17:26:56:
  173 + 2017-11-28T17:26:56: +=========================================+
  174 + 2017-11-28T17:26:56: | Maximum likelihood optimisation results |
  175 + 2017-11-28T17:26:56: +=========================================+
  176 + 2017-11-28T17:26:56: === GOptimizerLM ===
  177 + 2017-11-28T17:26:56: Optimized function value ..: -48352.760
  178 + 2017-11-28T17:26:56: Absolute precision ........: 0.005
  179 + 2017-11-28T17:26:56: Acceptable value decrease .: 2
  180 + 2017-11-28T17:26:56: Optimization status .......: converged
  181 + 2017-11-28T17:26:56: Number of parameters ......: 10
  182 + 2017-11-28T17:26:56: Number of free parameters .: 4
  183 + 2017-11-28T17:26:56: Number of iterations ......: 2
  184 + 2017-11-28T17:26:56: Lambda ....................: 1e-05
  185 + 2017-11-28T17:26:56: Maximum log likelihood ....: 48352.760
  186 + 2017-11-28T17:26:56: Observed events (Nobs) ...: 6656.000
  187 + 2017-11-28T17:26:56: Predicted events (Npred) ..: 6655.663 (Nobs - Npred = 0.337440257160779)
  188 + 2017-11-28T17:26:56: === GModels ===
  189 + 2017-11-28T17:26:56: Number of models ..........: 2
  190 + 2017-11-28T17:26:56: Number of parameters ......: 10
  191 + 2017-11-28T17:26:56: === GModelSky ===
  192 + 2017-11-28T17:26:56: Name ......................: Crab
  193 + 2017-11-28T17:26:56: Instruments ...............: all
  194 + 2017-11-28T17:26:56: Instrument scale factors ..: unity
  195 + 2017-11-28T17:26:56: Observation identifiers ...: all
  196 + 2017-11-28T17:26:56: Model type ................: PointSource
  197 + 2017-11-28T17:26:56: Model components ..........: "PointSource" * "PowerLaw" * "Constant"
  198 + 2017-11-28T17:26:56: Number of parameters ......: 6
  199 + 2017-11-28T17:26:56: Number of spatial par's ...: 2
  200 + 2017-11-28T17:26:56: RA .......................: 83.6331 [-360,360] deg (fixed,scale=1)
  201 + 2017-11-28T17:26:56: DEC ......................: 22.0145 [-90,90] deg (fixed,scale=1)
  202 + 2017-11-28T17:26:56: Number of spectral par's ..: 3
  203 + 2017-11-28T17:26:56: Prefactor ................: 5.69533666063277e-16 +/- 7.77619410705106e-18 [1e-23,1e-13] ph/cm2/s/MeV (free,scale=1e-16,gradient)
  204 + 2017-11-28T17:26:56: Index ....................: -2.47347083803876 +/- 0.0114544870463654 [-0,-5] (free,scale=-1,gradient)
  205 + 2017-11-28T17:26:56: PivotEnergy ..............: 300000 [10000,1000000000] MeV (fixed,scale=1000000,gradient)
  206 + 2017-11-28T17:26:56: Number of temporal par's ..: 1
  207 + 2017-11-28T17:26:56: Normalization ............: 1 (relative value) (fixed,scale=1,gradient)
  208 + 2017-11-28T17:26:56: === GCTAModelIrfBackground ===
  209 + 2017-11-28T17:26:56: Name ......................: CTABackgroundModel
  210 + 2017-11-28T17:26:56: Instruments ...............: CTAOnOff
  211 + 2017-11-28T17:26:56: Instrument scale factors ..: unity
  212 + 2017-11-28T17:26:56: Observation identifiers ...: all
  213 + 2017-11-28T17:26:56: Model type ................: "PowerLaw" * "Constant"
  214 + 2017-11-28T17:26:56: Number of parameters ......: 4
  215 + 2017-11-28T17:26:56: Number of spectral par's ..: 3
  216 + 2017-11-28T17:26:56: Prefactor ................: 1.00017594707712 +/- 0.0373732914079376 [0.001,1000] ph/cm2/s/MeV (free,scale=1,gradient)
  217 + 2017-11-28T17:26:56: Index ....................: 0.0190520959815092 +/- 0.0220805114253248 [-5,5] (free,scale=1,gradient)
  218 + 2017-11-28T17:26:56: PivotEnergy ..............: 1000000 [10000,1000000000] MeV (fixed,scale=1000000,gradient)
  219 + 2017-11-28T17:26:56: Number of temporal par's ..: 1
  220 + 2017-11-28T17:26:56: Normalization ............: 1 (relative value) (fixed,scale=1,gradient)
  221 +
  222 +:ref:`ctlike` has a hidden parameter called ``statistic`` that sets the
  223 +statistic used for the fit.
  224 +
  225 +- The DEFAULT for OnOff osbervations is CSTAT, i.e., Poisson signal and Poisson
  226 + background. A spectral model for the signal and a spectral model for the
  227 + background are jointly fit to the On and Off spectra.
  228 +- WSTAT is a special case of CSTAT, Poisson signal with Poisson background, in
  229 + which you do not need to have a spectral model for the background and
  230 + free parameters associated with it. The number of background counts in each
  231 + energy bin is treated as a nuisance parameter, derived from the On and Off
  232 + counts by profiling the likelihood function. In this case the only assumption
  233 + is that the background rate spectrum is the same in the On and Off regions.
  234 +
  235 +.. warning::
  236 + Beware that the profiling may yield unphysical results (negative background
  237 + counts) if the number of events in the Off spectra are zero. In this case a
  238 + null number of expected background events must be enforced,
  239 + which can result in a bias on the source's parameters. You can address this
  240 + issue by stacking multiple observations, using a coarser energy binning, or
  241 + using CSTAT instead (if you have a spectral model for the background that is
  242 + good enough). See the `XSPEC manual Appendix B <https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/XSappendixStatistics.html>`_
  243 + for more information.
  244 +
  245 +- You can also use CHI2, a classical chi square, i.e., a Gaussian signal and
  246 + Gaussian background. As for CSTAT, a spectral model for the signal and a
  247 + spectral model for the background are jointly fit to the On and Off
  248 + spectra.
  249 +
  250 +.. note::
  251 +
  252 + Many scripts can also be used in On/Off mode, including
  253 + :ref:`ctbutterfly` and :ref:`csspec` that were used earlier. It is
  254 + sufficient to replace the input counts cube/event list with an
  255 + On/Off observation container to activate On/Off mode for these
  256 + tools.
  257 +
  258 +
... ...
doc/source/users/tutorials/quickstart/unbinned.rst
  View file @3999128
... ... @@ -56,64 +56,64 @@ the same events for both analyses.
56 56  
57 57 .. code-block:: none
58 58  
59   - 2017-11-28T16:26:57: +=================================+
60   - 2017-11-28T16:26:57: | Maximum likelihood optimisation |
61   - 2017-11-28T16:26:57: +=================================+
62   - 2017-11-28T16:26:57: >Iteration 0: -logL=134457.962, Lambda=1.0e-03
63   - 2017-11-28T16:26:57: >Iteration 1: -logL=134437.621, Lambda=1.0e-03, delta=20.342, step=1.0e+00, max(|grad|)=43.475634 [Index:7]
64   - 2017-11-28T16:26:57: >Iteration 2: -logL=134437.595, Lambda=1.0e-04, delta=0.026, step=1.0e+00, max(|grad|)=0.121800 [Index:7]
65   - 2017-11-28T16:26:57: >Iteration 3: -logL=134437.595, Lambda=1.0e-05, delta=0.000, step=1.0e+00, max(|grad|)=0.001202 [Index:7]
66   - 2017-11-28T16:26:57:
67   - 2017-11-28T16:26:57: +=========================================+
68   - 2017-11-28T16:26:57: | Maximum likelihood optimisation results |
69   - 2017-11-28T16:26:57: +=========================================+
70   - 2017-11-28T16:26:57: === GOptimizerLM ===
71   - 2017-11-28T16:26:57: Optimized function value ..: 134437.595
72   - 2017-11-28T16:26:57: Absolute precision ........: 0.005
73   - 2017-11-28T16:26:57: Acceptable value decrease .: 2
74   - 2017-11-28T16:26:57: Optimization status .......: converged
75   - 2017-11-28T16:26:57: Number of parameters ......: 10
76   - 2017-11-28T16:26:57: Number of free parameters .: 4
77   - 2017-11-28T16:26:57: Number of iterations ......: 3
78   - 2017-11-28T16:26:57: Lambda ....................: 1e-06
79   - 2017-11-28T16:26:57: Maximum log likelihood ....: -134437.595
80   - 2017-11-28T16:26:57: Observed events (Nobs) ...: 20877.000
81   - 2017-11-28T16:26:57: Predicted events (Npred) ..: 20877.000 (Nobs - Npred = -1.41397322295234e-07)
82   - 2017-11-28T16:26:57: === GModels ===
83   - 2017-11-28T16:26:57: Number of models ..........: 2
84   - 2017-11-28T16:26:57: Number of parameters ......: 10
85   - 2017-11-28T16:26:57: === GModelSky ===
86   - 2017-11-28T16:26:57: Name ......................: Crab
87   - 2017-11-28T16:26:57: Instruments ...............: all
88   - 2017-11-28T16:26:57: Instrument scale factors ..: unity
89   - 2017-11-28T16:26:57: Observation identifiers ...: all
90   - 2017-11-28T16:26:57: Model type ................: PointSource
91   - 2017-11-28T16:26:57: Model components ..........: "PointSource" * "PowerLaw" * "Constant"
92   - 2017-11-28T16:26:57: Number of parameters ......: 6
93   - 2017-11-28T16:26:57: Number of spatial par's ...: 2
94   - 2017-11-28T16:26:57: RA .......................: 83.6331 [-360,360] deg (fixed,scale=1)
95   - 2017-11-28T16:26:57: DEC ......................: 22.0145 [-90,90] deg (fixed,scale=1)
96   - 2017-11-28T16:26:57: Number of spectral par's ..: 3
97   - 2017-11-28T16:26:57: Prefactor ................: 5.85495471291474e-16 +/- 1.08121595582131e-17 [1e-23,1e-13] ph/cm2/s/MeV (free,scale=1e-16,gradient)
98   - 2017-11-28T16:26:57: Index ....................: -2.48742680094013 +/- 0.0155955916697299 [-0,-5] (free,scale=-1,gradient)
99   - 2017-11-28T16:26:57: PivotEnergy ..............: 300000 [10000,1000000000] MeV (fixed,scale=1000000,gradient)
100   - 2017-11-28T16:26:57: Number of temporal par's ..: 1
101   - 2017-11-28T16:26:57: Normalization ............: 1 (relative value) (fixed,scale=1,gradient)
102   - 2017-11-28T16:26:57: === GCTAModelIrfBackground ===
103   - 2017-11-28T16:26:57: Name ......................: CTABackgroundModel
104   - 2017-11-28T16:26:57: Instruments ...............: CTA
105   - 2017-11-28T16:26:57: Instrument scale factors ..: unity
106   - 2017-11-28T16:26:57: Observation identifiers ...: all
107   - 2017-11-28T16:26:57: Model type ................: "PowerLaw" * "Constant"
108   - 2017-11-28T16:26:57: Number of parameters ......: 4
109   - 2017-11-28T16:26:57: Number of spectral par's ..: 3
110   - 2017-11-28T16:26:57: Prefactor ................: 0.966210894921824 +/- 0.0131220642906203 [0.001,1000] ph/cm2/s/MeV (free,scale=1,gradient)
111   - 2017-11-28T16:26:57: Index ....................: 0.00879946195443994 +/- 0.00825144420159423 [-5,5] (free,scale=1,gradient)
112   - 2017-11-28T16:26:57: PivotEnergy ..............: 1000000 [10000,1000000000] MeV (fixed,scale=1000000,gradient)
113   - 2017-11-28T16:26:57: Number of temporal par's ..: 1
114   - 2017-11-28T16:26:57: Normalization ............: 1 (relative value) (fixed,scale=1,gradient)
  59 + 2017-11-28T16:26:57: +=================================+
  60 + 2017-11-28T16:26:57: | Maximum likelihood optimisation |
  61 + 2017-11-28T16:26:57: +=================================+
  62 + 2017-11-28T16:26:57: >Iteration 0: -logL=134457.962, Lambda=1.0e-03
  63 + 2017-11-28T16:26:57: >Iteration 1: -logL=134437.621, Lambda=1.0e-03, delta=20.342, step=1.0e+00, max(|grad|)=43.475634 [Index:7]
  64 + 2017-11-28T16:26:57: >Iteration 2: -logL=134437.595, Lambda=1.0e-04, delta=0.026, step=1.0e+00, max(|grad|)=0.121800 [Index:7]
  65 + 2017-11-28T16:26:57: >Iteration 3: -logL=134437.595, Lambda=1.0e-05, delta=0.000, step=1.0e+00, max(|grad|)=0.001202 [Index:7]
  66 + 2017-11-28T16:26:57:
  67 + 2017-11-28T16:26:57: +=========================================+
  68 + 2017-11-28T16:26:57: | Maximum likelihood optimisation results |
  69 + 2017-11-28T16:26:57: +=========================================+
  70 + 2017-11-28T16:26:57: === GOptimizerLM ===
  71 + 2017-11-28T16:26:57: Optimized function value ..: 134437.595
  72 + 2017-11-28T16:26:57: Absolute precision ........: 0.005
  73 + 2017-11-28T16:26:57: Acceptable value decrease .: 2
  74 + 2017-11-28T16:26:57: Optimization status .......: converged
  75 + 2017-11-28T16:26:57: Number of parameters ......: 10
  76 + 2017-11-28T16:26:57: Number of free parameters .: 4
  77 + 2017-11-28T16:26:57: Number of iterations ......: 3
  78 + 2017-11-28T16:26:57: Lambda ....................: 1e-06
  79 + 2017-11-28T16:26:57: Maximum log likelihood ....: -134437.595
  80 + 2017-11-28T16:26:57: Observed events (Nobs) ...: 20877.000
  81 + 2017-11-28T16:26:57: Predicted events (Npred) ..: 20877.000 (Nobs - Npred = -1.41397322295234e-07)
  82 + 2017-11-28T16:26:57: === GModels ===
  83 + 2017-11-28T16:26:57: Number of models ..........: 2
  84 + 2017-11-28T16:26:57: Number of parameters ......: 10
  85 + 2017-11-28T16:26:57: === GModelSky ===
  86 + 2017-11-28T16:26:57: Name ......................: Crab
  87 + 2017-11-28T16:26:57: Instruments ...............: all
  88 + 2017-11-28T16:26:57: Instrument scale factors ..: unity
  89 + 2017-11-28T16:26:57: Observation identifiers ...: all
  90 + 2017-11-28T16:26:57: Model type ................: PointSource
  91 + 2017-11-28T16:26:57: Model components ..........: "PointSource" * "PowerLaw" * "Constant"
  92 + 2017-11-28T16:26:57: Number of parameters ......: 6
  93 + 2017-11-28T16:26:57: Number of spatial par's ...: 2
  94 + 2017-11-28T16:26:57: RA .......................: 83.6331 [-360,360] deg (fixed,scale=1)
  95 + 2017-11-28T16:26:57: DEC ......................: 22.0145 [-90,90] deg (fixed,scale=1)
  96 + 2017-11-28T16:26:57: Number of spectral par's ..: 3
  97 + 2017-11-28T16:26:57: Prefactor ................: 5.85495471291474e-16 +/- 1.08121595582131e-17 [1e-23,1e-13] ph/cm2/s/MeV (free,scale=1e-16,gradient)
  98 + 2017-11-28T16:26:57: Index ....................: -2.48742680094013 +/- 0.0155955916697299 [-0,-5] (free,scale=-1,gradient)
  99 + 2017-11-28T16:26:57: PivotEnergy ..............: 300000 [10000,1000000000] MeV (fixed,scale=1000000,gradient)
  100 + 2017-11-28T16:26:57: Number of temporal par's ..: 1
  101 + 2017-11-28T16:26:57: Normalization ............: 1 (relative value) (fixed,scale=1,gradient)
  102 + 2017-11-28T16:26:57: === GCTAModelIrfBackground ===
  103 + 2017-11-28T16:26:57: Name ......................: CTABackgroundModel
  104 + 2017-11-28T16:26:57: Instruments ...............: CTA
  105 + 2017-11-28T16:26:57: Instrument scale factors ..: unity
  106 + 2017-11-28T16:26:57: Observation identifiers ...: all
  107 + 2017-11-28T16:26:57: Model type ................: "PowerLaw" * "Constant"
  108 + 2017-11-28T16:26:57: Number of parameters ......: 4
  109 + 2017-11-28T16:26:57: Number of spectral par's ..: 3
  110 + 2017-11-28T16:26:57: Prefactor ................: 0.966210894921824 +/- 0.0131220642906203 [0.001,1000] ph/cm2/s/MeV (free,scale=1,gradient)
  111 + 2017-11-28T16:26:57: Index ....................: 0.00879946195443994 +/- 0.00825144420159423 [-5,5] (free,scale=1,gradient)
  112 + 2017-11-28T16:26:57: PivotEnergy ..............: 1000000 [10000,1000000000] MeV (fixed,scale=1000000,gradient)
  113 + 2017-11-28T16:26:57: Number of temporal par's ..: 1
  114 + 2017-11-28T16:26:57: Normalization ............: 1 (relative value) (fixed,scale=1,gradient)
115 115  
116   - .. note::
  116 +.. note::
117 117  
118 118 Many tools or scripts can also be used in unbinned mode, including
119 119 :ref:`csresmap`, :ref:`ctbutterfly` and :ref:`csspec` that were used
... ...