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...

Detector

...

Response

...

Matrix

...

(DRM) Implementation
#Convolution Approximations
#Performance
#Usage
#User Performance Studies

Here is a description of the binned likelihood calculation.

Detector Response Matrix (DRM) Implementation

The DRM is the matrix that transforms a binned counts spectrum from true energies to measured energies:

Wiki Markup
 Implementation|#Detector Response Matrix (DRM) Implementation]
[#Convolution Approximations]
[#Performance]
[#Usage]
[#User Performance Studies]


Here is a [description of the binned likelihood calculation|https://confluence.slac.stanford.edu/download/attachments/3342362/binned.pdf?version=1&modificationDate=1254102725000].

h3. Detector Response Matrix (DRM) Implementation

The DRM is the matrix that transforms a binned counts spectrum from true energies to measured energies:
{latex}
\begin{equation}
n_{k^\prime} = \sum_k D_{kk^\prime} n_k  \nonumber
\end{equation}
{latex}
where

where

Wiki Markup
{latex}$n_{k^\prime}${latex}

...

 are 
...
 the 
...
 counts 
...
 in 
...
 measured 
...
 energy 
...
bin 
 Wiki Markup
{latex}$k^\prime${latex}
...
 and 
 Wiki Markup
{latex}$n^k${latex}
...
 are 
...
 the 
...
 counts 
...
 in 
...
 true 
...
 energy 
...
bin 
 Wiki Markup
{latex}$k${latex}
. 
...
 The 
...
DRM 
...
 calculation 
...
 in 
...
 Likelihood
...
 follows 
...
 that 
...
 performed 
...
 in 
...
 gtrspgen:
 Wiki Markup
|http://glast.stanford.edu/cgi-bin/viewcvs/rspgen/src/PointResponse.cxx?view=markup]:
{latex}
\begin{equation}
D_{kk^\prime} = \frac{\int d\theta d\phi \left[\int_{\Delta E_{k^\prime}} dE^\prime D(E^\prime; E_k, \theta, \phi)\right] A(E_k, \theta, \phi) lt(\theta, \phi)}{\int d\theta d\phi A(E_k, \theta, \phi) lt(\theta, \phi)}  \nonumber
\end{equation}
{latex}
Here 
Here 
 Wiki Markup
{latex}$D(E^\prime; E, \theta, \phi$){latex}
...
 is 
...
 the 
...
 energy 
...
 dispersion 
...
 function, 
...
 Wiki Markup
{latex}$A(E, \theta, \phi)${latex}
...
 is 
...
 the 
...
 effective 
...
 area, 
...
and 
 Wiki Markup
{latex}$lt(\theta, \phi)${latex}
...
 is 
...
 the 
...
 integrated 
...
 livetime 
...
 as 
...
 a 
...
 function 
...
 of 
...
 detector 
...
 coordinates 
...
 associated 
...
 with 
...
 the 
...
 specified 
...
 sky 
...
 position. 
...
 Wiki Markup
{latex}$E_k${latex}
...
 is 
...
 the 
...
 logarithmic 
...
 center 
...
 of 
...
the 
 Wiki Markup
{latex}$k${latex}
th 
...
 true 
...
 energy 
...
 bin. 
...
 The 
...
 integral 
...
 over 
...
 measured 
...
 energy 
...
 is 
...
 taken 
...
 over 
...
 the 
...
 width 
...
 of 
...
the 
 Wiki Markup
{latex}$k^\prime${latex}
th 
...
 bin.
...
In 
...
 principle, 
...
 the 
...
 DRM 
...
 should 
...
 be 
...
 evaluated 
...
 at 
...
 each 
...
 sky 
...
 pixel 
...
 position 
...
 in 
...
 the 
...
 binned 
...
 counts 
...
 map, 
...
 but 
...
 we 
...
 make 
...
 the 
...
 approximation 
...
 that 
...
 the 
...
 DRM 
...
 does 
...
 not 
...
 change 
...
 much 
...
 over 
...
 the 
...
 counts 
...
 map 
...
 region 
...
 and 
...
 just 
...
 evaluate 
...
 it 
...
 at 
...
 the 
...
 map 
...
 center 
...
 and 
...
 assume 
...
 it 
...
 applies 
...
 everywhere 
...
 on 
...
 the 
...
 map. 
...
 This 
...
 is 
...
 supported 
...
 by 
...
 these 
...
 plots 
...
 of 
...
 the 
...
 energy 
...
 dispersion 
...
 evaluated 
...
 at 
...
 various 
...
 points 
...
 on 
...
 the 
...
 sky 
...
 for 
...
 a 
...
 one-day 
...
 survey 
...
 mode 
...
 integration:
...
Image Added
Convolution Approximations
The model counts cubes used by the binned analysis are 2D spatial arrays of sky pixels with a counts spectrum at each pixel location forming the third dimension. When energy dispersion is neglected, the model counts spectrum is a function of true energy, but with the other aspects of the instrument response applied (i.e., 
...
 effective 
...
 area 
...
 and 
...
 PSF). 
...
 To 
...
 complete 
...
 the 
...
 forward-folding 
...
 of 
...
 the 
...
 model 
...
 counts, 
...
 we 
...
 simply 
...
 need 
...
 to 
...
 apply 
...
 the 
...
 DRM 
...
 to 
...
 the 
...
 true 
...
 counts 
...
 spectrum 
...
 at 
...
 each 
...
 pixel. 
...
 Unfortunately, 
...
 there 
...
 are 
...
 two 
...
 constraints 
...
 that 
...
 prevent 
...
 us 
...
 from 
...
 doing 
...
 this:
...
  1. To 
...
  1.  save 
...
  1.  execution 
...
  1.  time, 
...
  1.  the 
...
  1.  log-likelihood 
...
  1.  is 
...
  1.  evaluated 
...
  1.  using 
...
  1.  only 
...
  1.  the 
...
  1.  pixels 
...
  1.  that 
...
  1.  have 
...
  1.  non-zero 
...
  1.  data 
...
  1.  counts 
...
  1.  (as 
...
  1.  opposed 
...
  1.  to 
...
  1.  model 
...
  1.  counts). 
...
  1.  This 
...
  1.  can 
...
  1.  be 
...
  1.  seen 
...
  1.  in 
...
  1.  the 
...
  1.  expression 
...
  1.  for 
...
  1.  the 
...
  1.  Poisson 
...
  1.  log-likelihood, 
...

  1.  Wiki Markup
    {latex}
\begin{equation}
\log{\cal L} = \sum_j \left[n_j\log\theta_j - \theta_j\right] \nonumber
\end{equation}
{latex}
...

  1.  where 
     Wiki Markup
    {latex}$n_j${latex}
...
  1.  is 
...
  1.  the 
...
  1.  observed 
...
  1.  count 
...
  1.  in 
...
  1. pixel 
     Wiki Markup
    {latex}$j${latex}
...
  1.  and 
     Wiki Markup
    {latex}$\theta_j${latex}
...
  1.  is 
...
  1.  the 
...
  1.  model 
...
  1.  counts 
...
  1.  for 
...
  1.  that 
...
  1.  pixel. 
...
  1.  In 
...
  1.  the 
...
  1.  current 
...
  1.  implementation, 
...
  1.  this 
...
  1.  means 
...
  1.  that 
...
  1.  model 
...
  1.  counts 
...
  1.  are 
...
  1.  only 
...
  1.  computed 
...
  1.  for 
...
  1.  those 
...
  1.  non-zero 
...
  1.  pixels. 
...
  1.  For 
...
  1.  sparse 
...
  1.  datasets 
...
  1.  (e.g., 
...
  1.  short 
...
  1.  integration 
...
  1.  times 
...
  1.  or 
...
  1.  at 
...
  1.  higher 
...
  1.  energies), 
...
  1.  this 
...
  1.  speeds 
...
  1.  up 
...
  1.  the 
...
  1.  calculation 
...
  1.  substantially: 
...
  1.  at 
...
  1.  least 
...
  1.  an 
...
  1.  order 
...
  1.  of 
...
  1.  magnitude 
...
  1.  for 
...
  1.  1 
...
  1.  day 
...
  1.  integrations. 
...
  1.  Applying 
...
  1.  the 
...
  1.  DRM 
...
  1.  to 
...
  1.  each 
...
  1.  pixel 
...
  1.  counts 
...
  1.  spectrum 
...
  1.  would 
...
  1.  require 
...
  1.  the 
...
  1.  model 
...
  1.  calcuation 
...
  1.  to 
...
  1.  be 
...
  1.  made 
...
  1.  for 
...
  1.  every 
...
  1.  pixel 
...
  1.  in 
...
  1.  the 
...
  1.  counts 
...
  1.  cube, 
...
  1.  even 
...
  1.  if 
...
  1.  it 
...
  1.  is 
...
  1.  empty. 
...
  1.  However, 
...
  1.  assuming 
...
  1.  binned 
...
  1.  analysis 
...
  1.  is 
...
  1.  generally 
...
  1.  used 
...
  1.  for 
...
  1.  longer 
...
  1.  observations, 
...
  1.  and 
...
  1.  most 
...
  1.  pixels 
...
  1.  are 
...
  1.  occupied, 
...
  1.  this 
...
  1.  may 
...
  1.  not 
...
  1.  be 
...
  1.  a 
...
  1.  real 
...
  1.  limitation.
...
  2. A 
...
  1.  more 
...
  1.  serious 
...
  1.  problem 
...
  1.  is 
...
  1.  applying 
...
  1.  the 
...
  1.  DRM 
...
  1.  convolution 
...
  1.  to 
...
  1.  the 
...
  1.  true 
...
  1.  counts 
...
  1.  spectrum 
...
  1.  at 
...
  1.  each 
...
  1.  pixel 
...
  1.  location. 
...
  1.  If 
...
  1.  the 
...
  1.  number 
...
  1.  of 
...
  1.  energy 
...
  1.  bins 
...
  1. is 
     Wiki Markup
    {latex}$n_e${latex}
    , 
...
  1.  the 
...
  1.  convolution 
...
  1.  is 
...
  1. an 
     Wiki Markup
    {latex}${\cal O}(n_e^2)${latex}
...
  1.  operation. 
...
  1. For 
     Wiki Markup
    {latex}$n_e = 30${latex}
    , 
...
  1.  this 
...
  1.  results 
...
  1.  in 
...
  1.  about 
...
  1.  a 
...
  1.  factor 
...
  1.  of 
...
  1.  900 
...
  1.  slow 
...
  1.  down 
...
  1.  in 
...
  1.  computing 
...
  1.  the 
...
  1.  expected 
...
  1.  pixel 
...
  1.  counts 
...
  1.  that 
...
  1.  go 
...
  1.  into 
...
  1.  the 
...
  1.  log-likelihood.
...
Since 
...
 we 
...
 need 
...
 to 
...
 compute 
...
 the 
...
 total 
...
 predicted 
...
 counts 
...
 for 
...
 each 
...
 component, 
...
 we 
...
 have 
...
 the 
...
 total 
...
 counts 
...
 spectrum 
...
 in 
...
 true 
...
 energy 
...
 space 
...
 (This 
...
 is 
...
 easily 
...
 obtained 
...
 for 
...
 each 
...
 source 
...
 by 
...
 integrating 
...
 each 
...
 energy 
...
 plane 
...
 over 
...
 angle 
...
 in 
...
 the 
...
 associated 
...
 source 
...
 map 
...
 and 
...
 multiplying 
...
 by 
...
 the 
...
 spectral 
...
 function.) 
...
 We 
...
 can 
...
 then 
...
 convolve 
...
 the 
...
 spatially 
...
 integrated 
...
 true 
...
 energy 
...
 counts 
...
 spectrum 
...
 with 
...
 the 
...
 DRM 
...
 to 
...
 obtain 
...
 the 
...
 overall 
...
 measured 
...
 energy 
...
 counts 
...
 spectrum. 
...
 We 
...
 form 
...
 the 
...
 ratio 
...
 of 
...
 the 
...
 convolved 
...
 model 
...
 counts 
...
 to 
...
 unconvolved 
...
 model 
...
 counts 
...
 in 
...
 each 
...
 energy 
...
 bin. 
...
 When 
...
 computing 
...
 the 
...
 contribution 
...
 to 
...
 the 
...
 log-likelihood 
...
 from 
...
 each 
...
pixel 
 Wiki Markup
{latex}$j${latex}
, 
...
 we 
...
 multiply 
...
 the 
...
 unconvolved 
...
 model 
...
 counts 
...
 for 
...
 that 
...
 pixel 
...
 by 
...
 the 
...
 ratio 
...
 of 
...
 convolved 
...
 to 
...
 unconvolved 
...
 model 
...
 counts 
...
 from 
...
 the 
...
 spatially 
...
 integrated 
...
 spectrum. 
...
 This 
...
 procedure 
...
 does 
...
 not 
...
 really 
...
 account 
...
 for 
...
 any 
...
 differences 
...
 in 
...
 counts 
...
 spectra 
...
 that 
...
 arise 
...
 from 
...
 spatial 
...
 variation 
...
 of 
...
 the 
...
 source 
...
 spectrum 
...
 (for 
...
 diffuse 
...
 sources), 
...
 exposure 
...
 variations 
...
 across 
...
 the 
...
 map 
...
 region, 
...
 and 
...
 the 
...
 effect 
...
 of 
...
 the 
...
 energy-dependence 
...
 of 
...
 the 
...
 PSF 
...
 on 
...
 the 
...
 counts 
...
 spectrum 
...
 (the 
...
 observed 
...
 counts 
...
 spectrum 
...
 for 
...
 a 
...
 point 
...
 source 
...
 should 
...
 be 
...
 softer 
...
 near 
...
 the 
...
 source 
...
 location). 
...
 All 
...
 of 
...
 these 
...
 neglected 
...
 effects 
...
 (they 
...
 may 
...
 be 
...
 others 
...
 I 
...
 am 
...
 missing) 
...
 are 
...
 ameliorated 
...
 somewhat 
...
 by 
...
 the 
...
 fact 
...
 that 
...
 this 
...
 procedure 
...
 has 
...
 the 
...
 right 
...
 local 
...
 effect, 
...
 i.e., 
...
 energy 
...
 bins 
...
 on 
...
 the 
...
 falling 
...
 part 
...
 of 
...
 the 
...
 counts 
...
 spectrum 
...
 tend 
...
 to 
...
 have 
...
 their 
...
 count 
...
 increased 
...
 while 
...
 bins 
...
 on 
...
 the 
...
 rising 
...
 part 
...
 have 
...
 their 
...
 count 
...
 decreased. 
...
 This 
...
 procedure 
...
 will 
...
 probably 
...
 not 
...
 work 
...
 very 
...
 well 
...
 for 
...
 sharp 
...
 spectral 
...
 features.
Performance
 Wiki Markup


h3. Performance

{composition-setup}
{deck:id=My Deck}
{composition-setup}
 Wiki Markup
{deck:id=My Deck}
 Wiki Markup
{card:label=Power-law model counts spectra for various photon indices}

I've 
...
 simulated 
...
 a 
...
 single 
...
 point 
...
 source 
...
 with 
...
 indices 
...
 1.25, 
...
 1.50, 
...
 2.00, 
...
 2.50, 
...
 3.00, 
...
 generating 
...
 70-100k 
...
 events 
...
 for 
...
 each 
...
 case 
...
 for 
...
 a 
...
 week 
...
 long 
...
 observation 
...
 with 
...
 idealized 
...
 +/-50 
...
 deg 
...
 rocking 
...
 and 
...
 fit 
...
 those 
...
 data 
...
 with 
...
 and 
...
 without 
...
 energy 
...
 dispersion 
...
 handling 
...
enabled:
Image Added
Image Added
Image Added
Image Added
Image Added
data
data
data
data
data
The blue model curves and residual points correspond to the fit with energy dispersion turned off, while the red curves and residual points correspond to energy dispersion turned on. The corresponding data files have columns of 
 Emin 
 Emax 
 obs. counts 
 model counts w/ edisp 
 model counts w/out edisp 
The input spectra to gtobssim covered 20 to 1e6 MeV and the energy range selection for the binned analysis was 30 to 3e5 MeV, with 40 logarithmically spaced bins.
Photon index best-fit values
 MC index 
 edisp handling 
 no edisp handling
 1.25 
 -1.253 +/- 1.86e-03 
 -1.260 +/- 1.86e-03 
 1.50 
 -1.505 +/- 2.19e-03 
 -1.516 +/- 2.19e-03 
 2.00 
 -2.007 +/- 3.20e-03 
 -2.031 +/- 3.20e-03 
 2.50 
 -2.525 +/- 4.17e-03 
 -2.557 +/- 4.03e-03 
 3.00 
 -3.036 +/- 4.97e-03 
 -3.063 +/- 4.74e-03 
 Wiki Markup
{card}
 Wiki Markup
{card:label=Exponential cut-off power-law, various photon indices}
For these tests, a point source with an exponentially cut-off power-law spectrum is modeled and fit for different values of the photon index. The cutoff energy is fixed at 1 GeV, and values of photon index = 1.25, 1.5, 2.0, 2.5, 3.0 are used. These tests are similar to those shown in fig. 68 of v1r0 of the LAT performance paper.
Simulations are performed for P7SOURCE_V6 and DC1A IRFs and these simulations are analyzed with and without the energy dispersion handling turned on for the standard gtobssim output and without the energy dispersion handling but using the MC values for the ENERGY column which is attained simply by swapping the labels on the ENERGY and MCENERGY columns in the FT1 file. Note that this swap was done prior to making an energy range selection.
  • Input XML model to gtobssim 
     Code Block
    
<source_library title="cutoff_pl_source">
  <source name="cutoff_pl_source_3">
    <spectrum escale="MeV" flux="20" particle_name="gamma">
      <SpectrumClass name="FileSpectrum"
                     params = "flux=1, specFile=Cutoff_PowerLaw_-3.00.txt"/>
      <celestial_dir ra="266.4" dec="-28.9"/>
    </spectrum>
  </source>
  <source name="cutoff_pl_source_2.5">
    <spectrum escale="MeV" flux="7.8" particle_name="gamma">
      <SpectrumClass name="FileSpectrum"
                     params = "flux=1, specFile=Cutoff_PowerLaw_-2.50.txt"/>
      <celestial_dir ra="266.4" dec="-28.9"/>
    </spectrum>
  </source>
  <source name="cutoff_pl_source_2">
    <spectrum escale="MeV" flux="3" particle_name="gamma">
      <SpectrumClass name="FileSpectrum"
                     params = "flux=1, specFile=Cutoff_PowerLaw_-2.00.txt"/>
      <celestial_dir ra="266.4" dec="-28.9"/>
    </spectrum>
  </source>
  <source name="cutoff_pl_source_1.5">
    <spectrum escale="MeV" flux="1.14" particle_name="gamma">
      <SpectrumClass name="FileSpectrum"
                     params = "flux=1, specFile=Cutoff_PowerLaw_-1.50.txt"/>
      <celestial_dir ra="266.4" dec="-28.9"/>
    </spectrum>
  </source>
  <source name="cutoff_pl_source_1.25">
    <spectrum escale="MeV" flux="0.73" particle_name="gamma">
      <SpectrumClass name="FileSpectrum"
                     params = "flux=1, specFile=Cutoff_PowerLaw_-
...
  • 1.
...
  • 25.txt"/>
      <celestial_dir ra="266.4" dec="-28.9"/>
    </spectrum>
  </source>

...
  • </source_library>

     The flux for each source was adjusted so that 100000 events are generated for a week long idealized survey mode observation using P7SOURCE_V6.
  • The template spectra were generated with this python script, using the PLSuperExpCutoff model that is available from pyLikelihood. This same model was used in the spectral fitting to ensure consistency. 
    Results
  • P7SOURCE_V6
     Image Added
     edisp-off 
     edisp handling turned off 
     edisp-on 
     edisp handling turned on 
     MC 
     edisp handling turned off, but using MCENERGY values 
     The red and green points substantially agree, as one would hope, and the trend is towards a harder measured spectra, as expected. However, there seems to be a residual bias in the edisp-on and MC results towards harder spectra.
  • DC1A (source fluxes were adjust to produce 200000 events)
     Image Added
     Here the differences between the three cases is much smaller, but edisp-on and MC still agree better. The same residual bias persists. 
     Wiki Markup
    {card}
     Wiki Markup
    {card:label=Comparison with Instrument Performance Paper Figure}
     Figure 68 of the instrument performance paper (v1r0) shows the "fractional" error on the photon index for a power-law and cutoff power-law model for different input indices:
     Image Added
     Using the same data that went into those simulations, here are the comparisons using energy dispersion handling: 
     Image Added 
     Image Added 
     In each plot, the black points are obtained from refitting the data without energy dispersion handling (consistent with the paper figure), and the red points are the results obtained with energy dispersion turned on. 
     Wiki Markup
    {card}
     Wiki Markup
    {card:label=Soft power-law source, isotropic diffuse background}
  • The xml model that was input to gtobssim 
     Code Block
    
<source_library title="soft_source">
  <source flux="1" name="soft_source">
    <spectrum escale="MeV">
      <particle name="gamma">
        
...
  • <power_law emax="1000000.0" emin="20.0" gamma="2.5"/>
      </particle>
      <celestial_dir 
...
  • dec="
...
  • -28.
...
  • 9" 
...
  • ra="
...
  • 266.
...
  • 4"/>
    </spectrum>
  </source>
  <source name="
...
  • test_isotropic">
    <spectrum escale="MeV
...
  • "
...
  • >
      <SpectrumClass name="
...
  • Isotropic"
...
  •  params="100, 2.1, 20., 2e5"/>
      
...
  • <use_spectrum frame="galaxy"/>
    </spectrum>
  
...
  • </source>
</source_library>

  • The model used in the binned analysis 
     Code Block
    
<?xml version="1.0" ?>
<source_library title="source library">
  
...
  • <source name="
...
  • test_
...
  • source" type="PointSource">
<!-- point source units are 
...
  • cm^-2 s^-1 MeV^-1 -->
    <spectrum 
...
  • type="
...
  • PowerLaw2">
      <parameter free="1" max="1000.0" min="1e-05" name="Integral" scale="1e-06" value="1.0"/>
      <parameter free="1" 
...
  • max="-1.0" min="-5.0" name="Index" scale="1.0" value="-2.0"/>
      
...
  • <parameter free="0" max="
...
  • 200000.
...
  • 0" 
...
  • min="
...
  • 20.
...
  • 0"
...
  •  name="LowerLimit" scale="1.0" value="20.0"/>
      <parameter free="0" max="200000.0" min="20.0" name="UpperLimit" scale="1.0" value="2e5"/>
    </spectrum>
    <spatialModel type="SkyDirFunction">
      <parameter free="0" max="360.0" min="-360.0" name="RA" scale="1.0" value="266.4"/>
      <parameter free="0" max="90.0" min="-90.0" name="DEC" scale="1.0" value="-28.9"/>
    </spatialModel>
  </source>
  <source name="Extragalactic Diffuse" type="DiffuseSource">
    <spectrum type="PowerLaw2">
      <parameter free="1" max="1000.0" min="0.0" name="Integral" scale="1e-06" value="1.0"/>
      <parameter free="1" max="-1.0" min="-5.0" name="Index" scale="1.0" value="-2.1"/>
      <parameter free="0" max="200000.0" min="20.0" name="LowerLimit" scale="1.0" value="20.0"/>
      <parameter free="0" max="200000.0" min="20.0" name="UpperLimit" scale="1.0" value="200000.0"/>
    </spectrum>
    <spatialModel type="ConstantValue">
      <parameter free="0" max="10.0" min="0.0" name="Value" scale="1.0" value="1.0"/>
      <parameter free="0" max="10.0" min="0.0" name="Value" scale="1.0" value="1.0"/>
    </spatialModel>
  </source>
</source_library>

  • Distributions from simulations. The leftmost plot in each row is the parameter distribution obtained from the standard analysis with the energy dispersion handling turned off. The middle plot has energy dispersion handling turned on. The rightmost plot uses the MC energy values in the analysis and has energy dispersion handling turned off. 
    • Photon Index of the soft point source. 
       Image Added 
       Image Added 
       Image Added 
    • Photon Index of the isotropic component. 
       Image Added 
       Image Added 
       Image Added 
       Wiki Markup
      {card}
       Wiki Markup
      {card:label=Exponential cut-off with isotropic diffuse}
  • Input model to gtobssim: 
     Code Block
    
<source_library title="cutoff_pl_source">
  <source name="cutoff_pl_source">
    <spectrum escale="MeV" flux="1" particle_name="gamma">
      <SpectrumClass name="
...
  • FileSpectrum"
                     params = "flux=1e-2, specFile=$(rootdir)/Cutoff_PowerLaw.txt"/>
      
...
  • <celestial_dir ra="266.4" dec="-28.9"/>
    </spectrum>
  </source>
...
  • 
  <source name="test_
...
  • isotropic">
    <spectrum 
...
  • escale="
...
  • MeV">
      
...
  • <SpectrumClass name="Isotropic" params="100, 2.1, 20., 2e5"/>
      <use_spectrum frame="galaxy"/>
    </spectrum>
  </source>
</source_library>

  • Likelihood model 
     Code Block
    
<?xml version="1.0" ?>
<source_library title="source library">
  <source name="test_source" type="PointSource">
<!-- point source units are cm^-2 s^-1 MeV^-1 -->
    <spectrum type="PLSuperExpCutoff">
      <parameter free="
...
  • 1" max="
...
  • 1e3" min="
...
  • 1e-5" name="
...
  • Prefactor" scale="
...
  • 1e-07" value="
...
  • 1.0"/>
      <parameter free="1" max="
...
  • 0.0" min="
...
  • -5.0" name="
...
  • Index1" scale="1.0" value="
...
  • -1.
...
  • 7"/>
      <parameter free="0" max="
...
  • 1000.0" min="
...
  • 50.0" name="
...
  • Scale" scale="1.0" value="
...
  • 200.0
...
  • "/>
      <parameter free="
...
  • 1" max="
...
  • 30000.0" min="
...
  • 500.0" name="
...
  • Cutoff" scale="1.0" value="
...
  • 3000.
...
  • 0"/>
      <parameter free="0" max="
...
  • 5.0" min="
...
  • 0.0" name="
...
  • Index2" scale="1.0" value="
...
  • 1.
...
  • 0"/>
    </
...
  • spectrum>
  
...
  •   
...
  • <spatialModel type="
...
  • SkyDirFunction">
    
...
  •  
...
  •  
...
  • <parameter free="
...
  • 0" max="
...
  • 360.0" min="
...
  • -
...
  • 360.0" name="
...
  • RA" scale="
...
  • 1.0" value="
...
  • 266.
...
  • 4"/>
      <parameter free="
...
  • 0" max="
...
  • 90.0" min="-
...
  • 90.0" name="
...
  • DEC" scale="1.0" value="-
...
  • 28.
...
  • 9"/>
    </spatialModel>
  </source>
  <source name="Extragalactic Diffuse" type="DiffuseSource">
    <spectrum type="PowerLaw2">
      <parameter free="
...
  • 1" max="
...
  • 1e3" min="
...
  • 1e-5" name="
...
  • Integral" scale="
...
  • 1e-06" value="
...
  • 1.0"/>
      <parameter free="
...
  • 1" max="
...
  • -1.0" min="
...
  • -5.0" name="
...
  • Index" scale="1.0" value="
...
  • -2.1"/>
      <parameter free="0" max="
...
  • 200000.0" min="
...
  • 20.0" name="
...
  • LowerLimit" scale="1.0" value="
...
  • 20.0"/>
    
...
  •   
...
  • <parameter free="0" max="200000.0" min="20.0" name="UpperLimit" scale="1.0" value="2e5"/>
    </spectrum>
    <spatialModel type="ConstantValue">
      <parameter free="0" max="10.0" min="0.0" name="Value" scale="1.0" value="1.0"/>
    </spatialModel>
  </source>
</source_library>

  • Distributions 
    • Photon index (Index1) of the exponentially cutoff power-law of the point source. 
       Image Added 
       Image Added 
       Image Added 
    • Cutoff energy of the point source. 
       Image Added 
       Image Added 
       Image Added 
    • Photon index of the isotropic component. 
       Image Added 
       Image Added 
       Image Added 
       Wiki Markup
      {card}
       Wiki Markup
      {deck}
Usage
To enable the energy dispersion handling (in ST-09-26-00 
...
 and 
...
 later), 
...
 set 
...
 the 
...
 USE_BL_EDISP 
...
 environment 
...
 variable:

{
 Code Block
}
% setenv USE_BL_EDISP
{code}

To 
...
 disable 
...
 it, 
...
 unset 
...
 the 
...
 env 
...
 var:

{
 Code Block
}
% unsetenv USE_BL_EDISP
{code}

This 
...
 functionality 
...
 can 
...
 also 
...
 be 
...
 turned 
...
 on 
...
 and 
...
 off 
...
 in 
...
 python 
...
 at 
...
 runtime:

{
 Code Block
}
>>> import os
>>> os.environ['USE_BL_EDISP'] = "1"     # The precise value doesn't matter
>>> del os.environ['USE_BL_EDISP']       # In a script, this should probably be enclosed in a try/except block
{code}

In 
...
 ST-09-28-00 
...
 and 
...
 later, 
...
 energy 
...
 dispersion 
...
 handling 
...
 may 
...
 be 
...
 turned 
...
 on 
...
 in 
...
 python 
...
 for 
...
 individual 
...
 binned 
...
 analysis 
...
 objects:

{
 Code Block
}
>>> like = binnedAnalysis(...)

>>> like.logLike.set_edisp_flag(True)    # Turn on energy dispersion handling
>>> print like.logLike.use_edisp()       # Check if edisp handling is turned on
>>> like.logLike.set_edisp_flag(False)   # Turn off
{code}

This 
...
 will 
...
 allow 
...
 binned 
...
 analysis 
...
 objects 
...
 within 
...
 a 
...
 single 
...
 python 
...
 script 
...
 to 
...
 have 
...
 energy 
...
 dispersion 
...
 handling 
...
 turned 
...
 on 
...
 or 
...
 off 
...
 independently, 
...
 whereas 
...
 the 
...
 environment 
...
 variable 
...
 switch 
...
 will 
...
 affect 
...
 all 
...
 analysis 
...
 objects 
...
 within 
...
 the 
...
 script 
...
 the 
...
 same 
...
 way.
...
User 
...
 Performance 
...
Studies