added analytic calculation of containment radius to GCTAPsfVector

nkelhos
1 parent 096c1001
Showing 1 changed file with 23 additions and 1 deletions
inst/cta/src/GCTAPsfVector.cpp
@@ -564,6 +564,26 @@ void GCTAPsfVector::update(const double&amp; logE) const
  * @param[in] azimuth Azimuth angle in Earth system (rad). Not used.
  * @param[in] etrue Use true energy (true/false). Not used.
  *
+ * Evaluates:
+ * 
+ * \f[
+ *
+ * radius = \sqrt{ \frac{\ln{\left( \frac{ fraction * m\_par\_width}
+ *          {\pi*m\_par\_scale} +1\right)}}{m\_par\_width} }
+ *
+ * \f]
+ *
+ * which is derived from integrating
+ *
+ * \f[
+ *
+ * fraction = \int_{0}^{2\pi}\int_{0}^{radius}r * 
+ *            e^{ m\_par\_width * r^{2}}dr d\phi
+ *
+ * \f]
+ *
+ * and solving for radius.
+ *  
  * Calculate the radius from the center that contains 'fraction' percent
  * of the events.  fraction * 100. = Containment % .
  ***************************************************************************/
@@ -579,7 +599,9 @@ double GCTAPsfVector::containment_radius(const double&amp; fraction,
     update(logE);
  
     // Compute radius
-    double radius = 0.0 ; // TODO implement calculation
+    // for gaussian
+    double arg = fraction * m_par_width / ( gammalib::pi * m_par_scale ) ;
+    double radius = std::sqrt( std::log( arg + 1 ) / m_par_width ) ;
  
     // Return maximum PSF radius
     return radius;