/***********************************************************************//**
* @brief Return normalization of radial source for Monte Carlo simulations
*
* @param[in] dir Centre of simulation cone.
* @param[in] radius Radius of simulation cone (degrees).
* @return Normalization.
*
* Returns the normalization for a radial source within a circular region.
* The normalization is 1 if the radial source falls within the circle
* defined by @p dir and @p radius, 0 otherwise.
***************************************************************************/
inline
double GModelSpatialRadial::mc_norm(const GSkyDir& dir,
const double& radius) const
{
double norm = (dir.dist_deg(this->dir()) <= radius+theta_max()) ? 1.0 : 0.0;
return (norm);
}
/***********************************************************************//**
* @brief Checks where model contains specified sky direction
*
* @param[in] dir Sky direction.
* @param[in] margin Margin to be added to sky direction (degrees)
* @return True if the model contains the sky direction.
*
* Signals whether a sky direction is contained in the radial gauss model.
***************************************************************************/
bool GModelSpatialRadialGauss::contains(const GSkyDir& dir,
const double& margin) const
{
// Compute distance to centre (radians)
double distance = dir.dist(this->dir());
// Return flag
return (distance <= theta_max() + margin*gammalib::deg2rad);
}
/***********************************************************************//**
* @brief Evaluate function (in units of sr^-1)
*
* @param[in] theta Angular distance from disk centre (radians).
* @param[in] posangle Position angle (counterclockwise from North) (radians).
* @param[in] energy Photon energy.
* @param[in] time Photon arrival time.
* @return Model value.
*
* Evaluates the spatial component for an elliptical disk source model. The
* disk source model is an elliptical function
* \f$S_{\rm p}(\theta, \phi | E, t)\f$, where
* \f$\theta\f$ is the angular separation between elliptical disk centre and
* the actual location and \f$\phi\f$ the position angle with respect to the
* ellipse centre, counted counterclockwise from North.
*
* The function \f$f(\theta, \phi)\f$ is given by
*
* \f[
* S_{\rm p}(\theta, \phi | E, t) = \left \{
* \begin{array}{l l}
* {\tt m\_norm}
* & \mbox{if} \, \, \theta \le \theta_0 \\
* \\
* 0 & \mbox{else}
* \end{array}
* \right .
* \f]
*
* where \f$\theta_0\f$ is the effective radius of the ellipse on the sphere
* given by
*
* \f[\theta_0\ =
* \frac{ab}{\sqrt{b^2 \cos^2(\phi-\phi_0) + a^2 \sin^2(\phi-\phi_0)}}\f]
*
* and
* \f$a\f$ is the semi-major axis of the ellipse,
* \f$b\f$ is the semi-minor axis, and
* \f$\phi_0\f$ is the position angle of the ellipse, counted
* counterclockwise from North.
*
* The normalisation constant \f${\tt m\_norm}\f$ which is the inverse of the
* solid angle subtended by an ellipse is given by
*
* @todo Quote formula for ellipse solid angle
*
* (see the update() method).
***************************************************************************/
double GModelSpatialEllipticalDisk::eval(const double& theta,
const double& posangle,
const GEnergy& energy,
const GTime& time) const
{
// Initialise value
double value = 0.0;
// Continue only if we're inside circle enclosing the ellipse
if (theta <= theta_max()) {
// Update precomputation cache
update();
// Perform computations
double diff_angle = posangle - m_posangle.value() * gammalib::deg2rad;
double cosinus = std::cos(diff_angle);
double sinus = std::sin(diff_angle);
double arg1 = m_semiminor_rad * cosinus;
double arg2 = m_semimajor_rad * sinus;
double r_ell = m_semiminor_rad * m_semimajor_rad /
std::sqrt(arg1*arg1 + arg2*arg2);
// Set value
value = (theta <= r_ell) ? m_norm : 0.0;
// Compile option: Check for NaN/Inf
#if defined(G_NAN_CHECK)
if (gammalib::is_notanumber(value) || gammalib::is_infinite(value)) {
std::cout << "*** ERROR: GModelSpatialEllipticalDisk::eval";
std::cout << "(theta=" << theta << "): NaN/Inf encountered";
std::cout << "(posangle=" << posangle << "): NaN/Inf encountered";
std::cout << " (value=" << value;
std::cout << ", R_ellipse=" << r_ell;
std::cout << ", diff_angle=" << diff_angle;
std::cout << ", m_norm=" << m_norm;
std::cout << ")" << std::endl;
}
#endif
} // endif: position was inside enclosing circle
// Return value
return value;
}
/***********************************************************************//**
* @brief Evaluate function (in units of sr^-1)
*
* @param[in] theta Angular distance from disk centre (radians).
* @param[in] posangle Position angle (counterclockwise from North) (radians).
* @param[in] energy Photon energy.
* @param[in] time Photon arrival time.
* @return Model value.
*
* Evaluates the spatial component for an elliptical Gaussian source model.
*
* The elliptical Gaussian function is defined by
* \f$S_{\rm p}(\theta, \phi | E, t)\f$, where
* \f$\theta\f$ is the angular separation between elliptical Gaussian centre
* and the actual location and \f$\phi\f$ the position angle with respect to
* the model centre, counted counterclockwise from North.
*
* The function \f$S_{\rm p}(\theta, \phi | E, t)\f$ is given by
*
* \f[
* S_{\rm p}(\theta, \phi | E, t) = {\tt m\_norm} \times
* \exp \left( -\frac{\theta^2}{2 r_{\rm eff}^2} \right)
* \f]
*
* where the effective ellipse radius \f$r_{\rm eff}\f$ towards a given
* position angle is given by
*
* \f[
* r_{\rm eff} = \frac{ab}
* {\sqrt{\left( a \sin (\phi - \phi_0) \right)^2} +
* \sqrt{\left( b \cos (\phi - \phi_0) \right)^2}}
* \f]
* and
* \f$a\f$ is the semi-major axis of the ellipse,
* \f$b\f$ is the semi-minor axis, and
* \f$\phi_0\f$ is the position angle of the ellipse, counted
* counterclockwise from North.
* \f${\tt m\_norm}\f$ is a normalization constant given by
*
* \f[
* {\tt m\_norm} = \frac{1}{2 \pi \times a \times b}
* \f]
*
* @warning
* The above formula for an elliptical Gaussian are accurate for small
* angles, with semimajor and semiminor axes below a few degrees. This
* should be fine for most use cases, but you should be aware that the
* ellipse will get distorted for larger angles.
*
* @warning
* For numerical reasons the elliptical Gaussian will be truncated for
* \f$\theta\f$ angles that correspond to 3.0 times the effective ellipse
* radius.
***************************************************************************/
double GModelSpatialEllipticalGauss::eval(const double& theta,
const double& posangle,
const GEnergy& energy,
const GTime& time) const
{
// Initialise value
double value = 0.0;
// Continue only if we're inside circle enclosing the ellipse
if (theta <= theta_max()) {
// Update precomputation cache
update();
// Perform computations to compute exponent
#if defined(G_SMALL_ANGLE_APPROXIMATION)
double rel_posangle = posangle - this->posangle() * gammalib::deg2rad;
double cosinus = std::cos(rel_posangle);
double sinus = std::sin(rel_posangle);
double arg1 = m_minor_rad * cosinus;
double arg2 = m_major_rad * sinus;
double r_ellipse = m_minor_rad * m_major_rad /
std::sqrt(arg1*arg1 + arg2*arg2); //!< small angle
double r_relative = theta/r_ellipse;
double exponent = 0.5*r_relative*r_relative;
#else
// Perform computations
double sinphi = std::sin(posangle);
double cosphi = std::cos(posangle);
// Compute help term
double term1 = m_term1 * cosphi * cosphi;
double term2 = m_term2 * sinphi * sinphi;
double term3 = m_term3 * sinphi * cosphi;
// Compute exponent
double exponent = theta * theta * (term1 + term2 + term3);
#endif
// Set value if the exponent is within the truncation region
if (exponent <= c_max_exponent) {
value = m_norm * std::exp(-exponent);
}
// Compile option: Check for NaN/Inf
#if defined(G_NAN_CHECK)
if (gammalib::is_notanumber(value) || gammalib::is_infinite(value)) {
std::cout << "*** ERROR: GModelSpatialEllipticalGauss::eval";
std::cout << "(theta=" << theta << "): NaN/Inf encountered";
std::cout << "(posangle=" << posangle << "): NaN/Inf encountered";
std::cout << " (value=" << value;
std::cout << ", MinorAxis^2=" << m_minor2;
std::cout << ", MaxjorAxis^2=" << m_major2;
std::cout << ", m_norm=" << m_norm;
std::cout << ")" << std::endl;
}
#endif
} // endif: position was inside enclosing circle
// Return value
return value;
}