/***************************************************************************
* GModelSpatialRadialShell.cpp - Radial shell source model class *
* ----------------------------------------------------------------------- *
* copyright (C) 2011-2013 by Christoph Deil *
* ----------------------------------------------------------------------- *
* *
* This program is free software: you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
* the Free Software Foundation, either version 3 of the License, or *
* (at your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU General Public License for more details. *
* *
* You should have received a copy of the GNU General Public License *
* along with this program. If not, see . *
* *
***************************************************************************/
/**
* @file GModelSpatialRadialShell.cpp
* @brief Radial shell model class implementation
* @author Christoph Deil
*/
/* __ Includes ___________________________________________________________ */
#ifdef HAVE_CONFIG_H
#include
#endif
#include "GException.hpp"
#include "GTools.hpp"
#include "GMath.hpp"
#include "GModelSpatialRadialShell.hpp"
#include "GModelSpatialRegistry.hpp"
/* __ Constants __________________________________________________________ */
/* __ Globals ____________________________________________________________ */
const GModelSpatialRadialShell g_radial_shell_seed;
const GModelSpatialRegistry g_radial_shell_registry(&g_radial_shell_seed);
/* __ Method name definitions ____________________________________________ */
#define G_READ "GModelSpatialRadialShell::read(GXmlElement&)"
#define G_WRITE "GModelSpatialRadialShell::write(GXmlElement&)"
/* __ Macros _____________________________________________________________ */
/* __ Coding definitions _________________________________________________ */
/* __ Debug definitions __________________________________________________ */
//#define G_DEBUG_MC //!< Debug MC method
/*==========================================================================
= =
= Constructors/destructors =
= =
==========================================================================*/
/***********************************************************************//**
* @brief Void constructor
***************************************************************************/
GModelSpatialRadialShell::GModelSpatialRadialShell(void) : GModelSpatialRadial()
{
// Initialise members
init_members();
// Return
return;
}
/***********************************************************************//**
* @brief Shell constructor
*
* @param[in] dir Sky position of shell centre.
* @param[in] radius Inner shell radius (degrees).
* @param[in] width Shell width (degrees).
* @param[in] small_angle Use small angle approximation (default to true).
*
* Constructs the shell model from the shell centre (@p dir), the inner
* shell @p radius, and the shell @p width. The optional parameters
* @p small_angle specifies whether the small angle approximation
* should be used or not. The small angle approximation is (a little) faster,
* but incorrect for shells larger than a few degrees.
*
* @todo Measure speed difference between small angle approximation and
* full computation.
***************************************************************************/
GModelSpatialRadialShell::GModelSpatialRadialShell(const GSkyDir& dir,
const double& radius,
const double& width,
const bool& small_angle) :
GModelSpatialRadial()
{
// Initialise members
init_members();
// Assign parameters
this->dir(dir);
this->radius(radius);
this->width(width);
this->small_angle(small_angle);
// Return
return;
}
/***********************************************************************//**
* @brief XML constructor
*
* @param[in] xml XML element.
*
* Constructs shell spatial model by extracting information from an XML
* element. See the read() method for more information about the expected
* structure of the XML element.
***************************************************************************/
GModelSpatialRadialShell::GModelSpatialRadialShell(const GXmlElement& xml) :
GModelSpatialRadial()
{
// Initialise members
init_members();
// Read information from XML element
read(xml);
// Return
return;
}
/***********************************************************************//**
* @brief Copy constructor
*
* @param[in] model Radial shell source model.
***************************************************************************/
GModelSpatialRadialShell::GModelSpatialRadialShell(const GModelSpatialRadialShell& model) :
GModelSpatialRadial(model)
{
// Initialise members
init_members();
// Copy members
copy_members(model);
// Return
return;
}
/***********************************************************************//**
* @brief Destructor
***************************************************************************/
GModelSpatialRadialShell::~GModelSpatialRadialShell(void)
{
// Free members
free_members();
// Return
return;
}
/*==========================================================================
= =
= Operators =
= =
==========================================================================*/
/***********************************************************************//**
* @brief Assignment operator
*
* @param[in] model Radial shell source model.
* @return Radial shell source model.
***************************************************************************/
GModelSpatialRadialShell& GModelSpatialRadialShell::operator=(const GModelSpatialRadialShell& model)
{
// Execute only if object is not identical
if (this != &model) {
// Copy base class members
this->GModelSpatialRadial::operator=(model);
// Free members
free_members();
// Initialise members
init_members();
// Copy members
copy_members(model);
} // endif: object was not identical
// Return
return *this;
}
/*==========================================================================
= =
= Public methods =
= =
==========================================================================*/
/***********************************************************************//**
* @brief Clear radial shell model
***************************************************************************/
void GModelSpatialRadialShell::clear(void)
{
// Free class members (base and derived classes, derived class first)
free_members();
this->GModelSpatialRadial::free_members();
this->GModelSpatial::free_members();
// Initialise members
this->GModelSpatial::init_members();
this->GModelSpatialRadial::init_members();
init_members();
// Return
return;
}
/***********************************************************************//**
* @brief Clone radial shell model
*
* @return Pointer to deep copy of radial shell model.
***************************************************************************/
GModelSpatialRadialShell* GModelSpatialRadialShell::clone(void) const
{
// Clone radial shell model
return new GModelSpatialRadialShell(*this);
}
/***********************************************************************//**
* @brief Evaluate function
*
* @param[in] theta Angular distance from shell centre (radians).
* @param[in] energy Photon energy.
* @param[in] time Photon arrival time.
* @return Model value.
*
* Evaluates the spatial part for a shell source model. The shell source
* model is a radial function \f$f(\theta)\f$, where \f$\theta\f$ is the
* angular separation between shell centre and the actual location.
*
* In the small angle approximation,
* \f[
* S_{\rm p}(\vec{p} | E, t) = {\tt m\_norm} \left \{
* \begin{array}{l l}
* \displaystyle
* \sqrt{ \theta_{\rm out}^2 - \theta^2 } -
* \sqrt{ \theta_{\rm in}^2 - \theta^2 }
* & \mbox{if $\theta \le \theta_{\rm in}$} \\
* \\
* \displaystyle
* \sqrt{ \theta_{\rm out}^2 - \theta^2 }
* & \mbox{if $\theta_{\rm in} < \theta \le \theta_{\rm out}$} \\
* \\
* \displaystyle
* 0 & \mbox{if $\theta > \theta_{\rm out}$}
* \end{array}
* \right .
* \f]
* where \f${\tt m\_norm}\f$ is a normalization constant (see the update()
* method).
*
* In the general form that is also valid for large angles
* \f[
* S_{\rm p}(\vec{p} | E, t) = {\tt m\_norm} \left \{
* \begin{array}{l l}
* \displaystyle
* \sqrt{ \sin^2 \theta_{\rm out} - \sin^2 \theta } -
* \sqrt{ \sin^2 \theta_{\rm in} - \sin^2 \theta }
* & \mbox{if $\theta \le \theta_{\rm in}$} \\
* \\
* \displaystyle
* \sqrt{ \sin^2 \theta_{\rm out} - \sin^2 \theta }
* & \mbox{if $\theta_{\rm in} < \theta \le \theta_{\rm out}$} \\
* \\
* \displaystyle
* 0 & \mbox{if $\theta > \theta_{\rm out}$}
* \end{array}
* \right .
* \f]
*
* Here, \f$\theta_{\rm in}\f$ and \f$\theta_{\rm out}\f$ are the shell inner
* and outer radius.
***************************************************************************/
double GModelSpatialRadialShell::eval(const double& theta,
const GEnergy& energy,
const GTime& time) const
{
// Update precomputation cache
update();
// Set x appropriately for the small angle approximation or not
double x;
if (m_small_angle) {
x = theta * theta;
}
else {
x = std::sin(theta);
x *= x;
}
// Compute value
double value = 0.0;
if (x < m_x_out) {
value = std::sqrt(m_x_out - x);
if (x < m_x_in) {
value -= std::sqrt(m_x_in - x);
}
}
// Normalise value
double result = m_norm * value;
// Compile option: Check for NaN/Inf
#if defined(G_NAN_CHECK)
if (gammalib::is_notanumber(result) || gammalib::is_infinite(result)) {
std::cout << "*** ERROR: GModelSpatialRadialShell::eval";
std::cout << "(theta=" << theta << "): NaN/Inf encountered";
std::cout << " (result=" << result;
std::cout << ", m_norm=" << m_norm;
std::cout << ", value=" << value;
std::cout << ", x=" << x;
std::cout << ", m_x_out=" << m_x_out;
std::cout << ", m_x_in=" << m_x_in;
std::cout << ", m_small_angle=" << m_small_angle;
std::cout << ")" << std::endl;
}
#endif
// Return normalised value
return result;
}
/***********************************************************************//**
* @brief Evaluate function and gradients
*
* @param[in] theta Angular distance from shell centre (radians).
* @param[in] energy Photon energy.
* @param[in] time Photon arrival time.
* @return Model value.
*
* This method simply calls the eval() method as no analytical gradients will
* be computed. See the eval() method for details.
***************************************************************************/
double GModelSpatialRadialShell::eval_gradients(const double& theta,
const GEnergy& energy,
const GTime& time) const
{
// Return value
return (eval(theta, energy, time));
}
/***********************************************************************//**
* @brief Returns MC sky direction
*
* @param[in] energy Photon energy.
* @param[in] time Photon arrival time.
* @param[in,out] ran Random number generator.
* @return Sky direction.
*
* Draws an arbitrary sky position from the 2D shell distribution.
***************************************************************************/
GSkyDir GModelSpatialRadialShell::mc(const GEnergy& energy,
const GTime& time,
GRan& ran) const
{
// Update precomputation cache
update();
// Simulate offset from photon arrival direction
#if defined(G_DEBUG_MC)
int n_samples = 0;
#endif
double theta_max = this->theta_max();
double sin_theta_max = std::sin(theta_max);
double u_max = (m_small_angle) ? m_norm * sin_theta_max * theta_max
: m_norm * sin_theta_max * sin_theta_max;
double value = 0.0;
double u = 1.0;
double theta = 0.0;
do {
theta = ran.uniform() * theta_max;
value = eval(theta, energy, time) * std::sin(theta);
u = ran.uniform() * u_max;
#if defined(G_DEBUG_MC)
n_samples++;
#endif
} while (u > value);
#if defined(G_DEBUG_MC)
std::cout << "#=" << n_samples << " ";
#endif
// Simulate azimuth angle
double phi = 360.0 * ran.uniform();
// Rotate pointing direction by offset and azimuth angle
GSkyDir sky_dir = dir();
sky_dir.rotate_deg(phi, theta * gammalib::rad2deg);
// Return sky direction
return sky_dir;
}
/***********************************************************************//**
* @brief Return maximum model radius (in radians)
*
* @return Maximum model radius (in radians).
***************************************************************************/
double GModelSpatialRadialShell::theta_max(void) const
{
// Return value
return ((radius()+width()) * gammalib::deg2rad);
}
/***********************************************************************//**
* @brief Read model from XML element
*
* @param[in] xml XML element.
*
* @exception GException::model_invalid_parnum
* Invalid number of model parameters found in XML element.
* @exception GException::model_invalid_parnames
* Invalid model parameter names found in XML element.
*
* Reads the radial shell model information from an XML element. The XML
* element shall have either the format
*
*
*
*
*
*
*
*
* or
*
*
*
*
*
*
*
*
* @todo Implement tests of the radius and radius boundary and the width and
* width boundary. The radius and radius boundary should be >=0, the
* width and width boundary should be >0.
***************************************************************************/
void GModelSpatialRadialShell::read(const GXmlElement& xml)
{
// Determine number of parameter nodes in XML element
int npars = xml.elements("parameter");
// Verify that XML element has exactly 4 parameters
if (xml.elements() != 4 || npars != 4) {
throw GException::model_invalid_parnum(G_READ, xml,
"Shell model requires exactly 4 parameters.");
}
// Read shell location
GModelSpatialRadial::read(xml);
// Extract remaining model parameters. Note that we have to loop over
// all parameters to find the remaining 2 parameters that are
// implemented by this class (the location is implemented by the base
// class)
int npar[2] = {0, 0};
for (int i = 0; i < npars; ++i) {
// Get parameter element
const GXmlElement* par = xml.element("parameter", i);
// Handle Radius
if (par->attribute("name") == "Radius") {
// Read parameter
m_radius.read(*par);
//TODO: Check parameter
// Increment parameter counter
npar[0]++;
}
// Handle Width
else if (par->attribute("name") == "Width") {
// Read parameter
m_width.read(*par);
//TODO: Check parameter
// Increment parameter counter
npar[1]++;
}
} // endfor: looped over all parameters
// Verify that all parameters were found
if (npar[0] != 1 || npar[1] != 1) {
throw GException::model_invalid_parnames(G_READ, xml,
"Require \"Radius\" and \"Width\" parameters.");
}
// Return
return;
}
/***********************************************************************//**
* @brief Write model into XML element
*
* @param[in] xml XML element into which model information is written.
*
* @exception GException::model_invalid_spatial
* Existing XML element is not of type 'GaussFunction'
* @exception GException::model_invalid_parnum
* Invalid number of model parameters found in XML element.
* @exception GException::model_invalid_parnames
* Invalid model parameter names found in XML element.
*
* Writes the radial shell model information into an XML element. The XML
* element will have the format
*
*
*
*
*
*
*
*
***************************************************************************/
void GModelSpatialRadialShell::write(GXmlElement& xml) const
{
// Write shell location
GModelSpatialRadial::write(xml);
// If XML element has 2 nodes (which should be the location nodes)
// then append 2 parameter nodes
if (xml.elements() == 2) {
xml.append(GXmlElement("parameter name=\"Radius\""));
xml.append(GXmlElement("parameter name=\"Width\""));
}
// Determine number of parameter nodes in XML element
int npars = xml.elements("parameter");
// Verify that XML element has exactly 4 parameters
if (xml.elements() != 4 || npars != 4) {
throw GException::model_invalid_parnum(G_WRITE, xml,
"Shell source model requires exactly 4 parameters.");
}
// Set or update model parameter attributes
int npar[2] = {0, 0};
for (int i = 0; i < npars; ++i) {
// Get parameter element
GXmlElement* par = xml.element("parameter", i);
// Handle Radius
if (par->attribute("name") == "Radius") {
m_radius.write(*par);
npar[0]++;
}
// Handle Width
else if (par->attribute("name") == "Width") {
m_width.write(*par);
npar[1]++;
}
} // endfor: looped over all parameters
// Check of all required parameters are present
if (npar[0] != 1 || npar[1] != 1) {
throw GException::model_invalid_parnames(G_WRITE, xml,
"Require \"Radius\" and \"Width\" parameters.");
}
// Return
return;
}
/***********************************************************************//**
* @brief Print information
*
* @param[in] chatter Chattiness (defaults to NORMAL).
* @return String containing model information.
***************************************************************************/
std::string GModelSpatialRadialShell::print(const GChatter& chatter) const
{
// Initialise result string
std::string result;
// Continue only if chatter is not silent
if (chatter != SILENT) {
// Append header
result.append("=== GModelSpatialRadialShell ===");
// Append parameters
result.append("\n"+gammalib::parformat("Number of parameters"));
result.append(gammalib::str(size()));
for (int i = 0; i < size(); ++i) {
result.append("\n"+m_pars[i]->print(chatter));
}
} // endif: chatter was not silent
// Return result
return result;
}
/*==========================================================================
= =
= Private methods =
= =
==========================================================================*/
/***********************************************************************//**
* @brief Initialise class members
***************************************************************************/
void GModelSpatialRadialShell::init_members(void)
{
// Initialise Radius
m_radius.clear();
m_radius.name("Radius");
m_radius.unit("deg");
m_radius.value(0.0);
m_radius.min(0.0);
m_radius.free();
m_radius.scale(1.0);
m_radius.gradient(0.0);
m_radius.has_grad(false); // Radial components never have gradients
// Initialise Width
m_width.clear();
m_width.name("Width");
m_width.unit("deg");
m_width.value(2.778e-4);
m_width.min(2.778e-4); // 1 arcsec
m_width.free();
m_width.scale(1.0);
m_width.gradient(0.0);
m_width.has_grad(false); // Radial components never have gradients
// Set parameter pointer(s)
m_pars.push_back(&m_radius);
m_pars.push_back(&m_width);
// Initialise other members
m_small_angle = false;
// Initialise precomputation cache. Note that zero values flag
// uninitialised as a zero radius and width shell is not meaningful
m_last_radius = 0.0;
m_last_width = 0.0;
m_theta_in = 0.0;
m_x_in = 0.0;
m_theta_out = 0.0;
m_x_out = 0.0;
m_norm = 0.0;
// Return
return;
}
/***********************************************************************//**
* @brief Copy class members
*
* @param[in] model Radial shell source model.
*
* We do not have to push back the members on the parameter stack as this
* should have been done by init_members() that was called before. Otherwise
* we would have the radius and width twice on the stack.
***************************************************************************/
void GModelSpatialRadialShell::copy_members(const GModelSpatialRadialShell& model)
{
// Copy members
m_radius = model.m_radius;
m_width = model.m_width;
m_small_angle = model.m_small_angle;
// Copy precomputation cache
m_last_radius = model.m_last_radius;
m_last_width = model.m_last_width;
m_theta_in = model.m_theta_in;
m_x_in = model.m_x_in;
m_theta_out = model.m_theta_out;
m_x_out = model.m_x_out;
m_norm = model.m_norm;
// Return
return;
}
/***********************************************************************//**
* @brief Delete class members
***************************************************************************/
void GModelSpatialRadialShell::free_members(void)
{
// Return
return;
}
/***********************************************************************//**
* @brief Update precomputation cache
*
* Performs precomputations that are valid for a given pair of radius and
* width values. The following members are set by this method:
* m_last_radius, m_last_width, m_theta_in, m_theta_out, m_x_in, m_x_out
* and m_norm.
*
* m_theta_in contains the inner shell radius in radians, while m_theta_out
* contains the outer shell radius in radians.
*
* In the small angle approximation,
* \f${\tt m\_x\_in} = {\tt m\_theta\_in}^2\f$,
* \f${\tt m\_x\_out} = {\tt m\_theta\_out}^2\f$, and
* \f[{\tt m\_norm} = \frac{3}{2 \pi}
* \frac{1}{\left( {\tt m\_theta\_out}^3 - {\tt m\_theta\_in}^3 \right)}\f].
*
* In the general case that is also valid for large angles,
* \f${\tt m\_x\_in} = \sin^2 {\tt m\_theta\_in}\f$,
* \f${\tt m\_x\_out} = \sin^2 {\tt m\_theta\_out}\f$, and
* \f[{\tt m\_norm} = \frac{1}{2 \pi}
* \frac{\sqrt{1-\cos 2 {\tt m\_theta\_out}} -
* \sqrt{1-\cos 2 {\tt m\_theta\_in}}}{2 \sqrt{2}} +
* \frac{1+\cos 2 {\tt m\_theta\_out}}{4} \ln \left(
* \frac{\sqrt{2} \cos {\tt m\_theta\_out}}
* {\sqrt{2} + \sqrt{1 - \cos 2 {\tt m\_theta\_out}}} \right) -
* \frac{1+\cos 2 {\tt m\_theta\_in}}{4} \ln \left(
* \frac{\sqrt{2} \cos {\tt m\_theta\_in}}
* {\sqrt{2} + \sqrt{1 - \cos 2 {\tt m\_theta\_in}}} \right)\f]
***************************************************************************/
void GModelSpatialRadialShell::update() const
{
// Set constants
const double c1 = gammalib::twopi / 3.0;
const double c2 = 1.0 / (2.0 * gammalib::sqrt_two);
// Update if radius or width have changed
if (m_last_radius != radius() || m_last_width != width()) {
// Store last values
m_last_radius = radius();
m_last_width = width();
// Perform precomputations
m_theta_in = radius() * gammalib::deg2rad;
m_theta_out = (radius() + width()) * gammalib::deg2rad;
if (m_small_angle) {
m_x_in = m_theta_in * m_theta_in;
m_x_out = m_theta_out * m_theta_out;
double denom = c1 * (m_x_out*m_theta_out - m_x_in*m_theta_in);
m_norm = (denom > 0.0) ? 1.0 / denom : 0.0;
}
else {
double sin_theta_in = std::sin(m_theta_in);
double sin_theta_out = std::sin(m_theta_out);
double term1 = (f1(m_theta_out) - f1(m_theta_in)) * c2;
double term2 = f2(m_theta_out);
double term3 = f2(m_theta_in);
double denom = gammalib::twopi * (term1 + term2 - term3);
m_norm = (denom > 0.0) ? 1.0 / denom : 0.0;
m_x_in = sin_theta_in*sin_theta_in;
m_x_out = sin_theta_out * sin_theta_out;
}
} // endif: update required
// Compile option: Check for NaN/Inf
#if defined(G_NAN_CHECK)
if (gammalib::is_notanumber(m_norm) || gammalib::is_infinite(m_norm)) {
std::cout << "*** ERROR: GModelSpatialRadialShell::update:";
std::cout << " NaN/Inf encountered";
std::cout << " (m_norm=" << m_norm;
std::cout << ", radius=" << radius();
std::cout << ", width=" << width();
std::cout << ", m_theta_in=" << m_theta_in;
std::cout << ", m_theta_out=" << m_theta_out;
std::cout << ", term1=" << (f1(m_theta_out) - f1(m_theta_in)) * c2;
std::cout << ", term2=" << f2(m_theta_out);
std::cout << ", term3=" << f2(m_theta_in);
std::cout << ")" << std::endl;
}
#endif
// Return
return;
}
/***********************************************************************//**
* @brief Return function 1 value needed for precomputation
*
* Computes \f$f1(x) = \sqrt{1 - \cos 2 x}\f$.
***************************************************************************/
double GModelSpatialRadialShell::f1(double x)
{
// Compute value
double f1 = std::sqrt(1.0 - std::cos(2.0 * x));
// Return value
return f1;
}
/***********************************************************************//**
* @brief Return function 2 value needed for precomputation
*
* Compute
* \f[f2(x) = \frac{1+\cos 2x}{4}
* \ln \left( \frac{\sqrt{2} \cos x}{\sqrt{2} + \sqrt{ 1 - \cos 2 x}}
* \right)\f].
***************************************************************************/
double GModelSpatialRadialShell::f2(double x)
{
// Compute value
double t1 = (1.0 + std::cos(2.0*x)) / 4.0;
double t2 = gammalib::sqrt_two * std::cos(x);
double t3 = gammalib::sqrt_two + f1(x);
double f2 = t1 * std::log(t2 / t3);
// Return value
return f2;
}