Dmitry Malyshev / gammalib

Commit 3c035092958b99c6ccfb2d84b1fe78c42f71638a

Authored by Jürgen Knödlseder
1 parent e6609470

Adjusted model documentation.

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Showing 1 changed file with 16 additions and 14 deletions
doc/source/user_manual/modules/model.rst
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... ... @@ -89,11 +89,11 @@ Power law
89 89 The ``GModelSpectralPlaw`` class implements the power law function
90 90  
91 91 .. math::
92   - \frac{dN}{dE} = N_0 \left( \frac{E}{E_0} \right)^{\gamma}
  92 + \frac{dN}{dE} = k_0 \left( \frac{E}{E_0} \right)^{\gamma}
93 93  
94 94 where the parameters in the XML definition have the following mappings:
95 95  
96   -* :math:`N_0` = ``Prefactor``
  96 +* :math:`k_0` = ``Prefactor``
97 97 * :math:`\gamma` = ``Index``
98 98 * :math:`E_0` = ``Scale``
99 99  
... ... @@ -145,12 +145,12 @@ Exponentially cut-off power law
145 145 The ``GModelSpectralExpPlaw`` class implements the exponentially cut-off power law function
146 146  
147 147 .. math::
148   - \frac{dN}{dE} = N_0 \left( \frac{E}{E_0} \right)^{\gamma}
  148 + \frac{dN}{dE} = k_0 \left( \frac{E}{E_0} \right)^{\gamma}
149 149 \exp \left( \frac{-E}{\tt E_{\rm cut}} \right)
150 150  
151 151 where the parameters in the XML definition have the following mappings:
152 152  
153   -* :math:`N_0` = ``Prefactor``
  153 +* :math:`k_0` = ``Prefactor``
154 154 * :math:`\gamma` = ``Index``
155 155 * :math:`E_0` = ``Scale``
156 156 * :math:`E_{\rm cut}` = ``Cutoff``
... ... @@ -174,7 +174,7 @@ The ``GModelSpectralBrokenPlaw`` class implements the broken power law function
174 174  
175 175 .. math::
176 176  
177   - \frac{dN}{dE} = N_0 \times \left \{
  177 + \frac{dN}{dE} = k_0 \times \left \{
178 178 \begin{eqnarray}
179 179 \left( \frac{E}{E_b} \right)^{\gamma_1} & {\rm if\,\,} E < E_b \\
180 180 \left( \frac{E}{E_b} \right)^{\gamma_2} & {\rm otherwise}
... ... @@ -183,7 +183,7 @@ The ``GModelSpectralBrokenPlaw`` class implements the broken power law function
183 183  
184 184 where the parameters in the XML definition have the following mappings:
185 185  
186   -* :math:`N_0` = ``Prefactor``
  186 +* :math:`k_0` = ``Prefactor``
187 187 * :math:`\gamma_1` = ``Index1``
188 188 * :math:`\gamma_2` = ``Index2``
189 189 * :math:`E_b` = ``BreakValue``
... ... @@ -198,22 +198,24 @@ The XML format for specifying a broken power law is:
198 198 <parameter name="BreakValue" scale="1e6" value="0.3" min="0.01" max="1000.0" free="1"/>
199 199 <parameter name="Index2" scale="-1" value="2.70" min="0.01" max="1000.0" free="1"/>
200 200 </spectrum>
201   -
  201 +
  202 +
202 203 Gaussian
203 204 ^^^^^^^^
204 205  
205 206 The ``GModelSpectralGauss`` class implements the gaussian function
206 207  
207 208 .. math::
208   - \frac{dN}{dE} = \frac{N_0}{\sqrt{2\pi}\sigma}\exp(\frac{-(E-E_bar)^2}{2 \sigma^2})
  209 + \frac{dN}{dE} = \frac{N_0}{\sqrt{2\pi}\sigma}
  210 + \exp \left( \frac{-(E-\bar{E})^2}{2 \sigma^2} \right)
209 211  
210 212 where the parameters in the XML definition have the following mappings:
211 213  
212   -* :math:`N_0` = ``Prefactor``
213   -* :math:`E_bar` = ``Mean Energy``
214   -* :math:`sigma` = ``Energy Standard Deviation``
  214 +* :math:`N_0` = ``Normalization``
  215 +* :math:`\bar{E}` = ``Mean``
  216 +* :math:`\sigma` = ``Sigma``
215 217  
216   -The XML format for specifying a power law is:
  218 +The XML format for specifying a Gaussian is:
217 219  
218 220 .. code-block:: xml
219 221  
... ... @@ -256,11 +258,11 @@ Log parabola
256 258 The ``GModelSpectralLogParabola`` class implements the log parabola function
257 259  
258 260 .. math::
259   - \frac{dN}{dE} = N_0 \left( \frac{E}{E_0} \right)^{\gamma+\eta \ln(E/E_0)}
  261 + \frac{dN}{dE} = k_0 \left( \frac{E}{E_0} \right)^{\gamma+\eta \ln(E/E_0)}
260 262  
261 263 where the parameters in the XML definition have the following mappings:
262 264  
263   -* :math:`N_0` = ``Prefactor``
  265 +* :math:`k_0` = ``Prefactor``
264 266 * :math:`\gamma` = ``Index``
265 267 * :math:`\eta` = ``Curvature``
266 268 * :math:`E_0` = ``Scale``
... ...