GModelSpectralSmoothBrokenPlaw.hpp
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/***************************************************************************
* GModelSpectralSmoothBrokenPlaw.hpp *
* Smoothly broken power law spectrum class *
* ----------------------------------------------------------------------- *
* copyright (C) 2017 by Josh Cardenzana *
* ----------------------------------------------------------------------- *
* *
* 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 <http://www.gnu.org/licenses/>. *
* *
***************************************************************************/
/**
* @file GModelSpectralSmoothBrokenPlaw.hpp
* @brief Smoothly broken power law spectrum class definition
* @author Josh Cardenzana
*/
#ifndef GMODELSPECTRALSMOOTHBROKENPLAW_HPP
#define GMODELSPECTRALSMOOTHBROKENPLAW_HPP
/* __ Includes ___________________________________________________________ */
#include <string>
#include "GModelSpectral.hpp"
#include "GFunction.hpp"
#include "GModelPar.hpp"
#include "GEnergy.hpp"
#include "GModelSpectralBrokenPlaw.hpp"
/* __ Forward declarations _______________________________________________ */
class GRan;
class GTime;
class GXmlElement;
/***********************************************************************//**
* @class GModelSpectralSmoothBrokenPlaw
*
* @brief Smoothly broken power law spectral model class
*
* This class implements a smoothly broken power law spectrum. The model is
* defined by
*
* \f[
* S_{\rm E}(E | t) = k_0 \left( \frac{E}{E_0} \right)^{\gamma_1}
* \left[ 1 + \left( \frac{E}{E_b} \right)^{\frac{\gamma_1 - \gamma_2}{\beta}}
* \right]^{-\beta}
* \f]
*
* where
* - \f$k_0\f$ is the normalization or prefactor,
* - \f$\gamma_1\f$ is the spectral index before the break,
* - \f$\gamma_2\f$ is the spectral index after the break,
* - \f$E_0\f$ is the pivot energy,
* - \f$E_b\f$ is the break energy,
* - \f$\beta\f$ defines the break smoothness (larger = smoother transition)
*
* Notes:
* - The pivot energy should be set far away from the expected break energy
* value.
* - When the two indices are close together, the beta parameter becomes
* poorly constrained. Since the beta parameter also scales the indices, this
* can cause very large errors in the estimates of the various spectral
* parameters. In this case, consider fixing beta.
***************************************************************************/
class GModelSpectralSmoothBrokenPlaw : public GModelSpectral {
public:
// Constructors and destructors
GModelSpectralSmoothBrokenPlaw(void);
GModelSpectralSmoothBrokenPlaw(const std::string& type,
const std::string& prefactor,
const std::string& index1,
const std::string& pivot,
const std::string& index2,
const std::string& breakenergy,
const std::string& beta);
GModelSpectralSmoothBrokenPlaw(const double& prefactor,
const double& index1,
const GEnergy& pivot,
const double& index2,
const GEnergy& breakenergy,
const double& beta);
explicit GModelSpectralSmoothBrokenPlaw(const GXmlElement& xml);
GModelSpectralSmoothBrokenPlaw(const GModelSpectralSmoothBrokenPlaw& model);
virtual ~GModelSpectralSmoothBrokenPlaw(void);
// Operators
virtual GModelSpectralSmoothBrokenPlaw& operator=(const GModelSpectralSmoothBrokenPlaw& model);
// Implemented pure virtual methods
virtual void clear(void);
virtual GModelSpectralSmoothBrokenPlaw* clone(void) const;
virtual std::string classname(void) const;
virtual std::string type(void) const;
virtual double eval(const GEnergy& srcEng,
const GTime& srcTime = GTime(),
const bool& gradients = false) const;
virtual double flux(const GEnergy& emin,
const GEnergy& emax) const;
virtual double eflux(const GEnergy& emin,
const GEnergy& emax) const;
virtual GEnergy mc(const GEnergy& emin,
const GEnergy& emax,
const GTime& time,
GRan& ran) const;
virtual void read(const GXmlElement& xml);
virtual void write(GXmlElement& xml) const;
virtual std::string print(const GChatter& chatter = NORMAL) const;
// Other methods
double prefactor(void) const;
double index1(void) const;
double index2(void) const;
GEnergy pivot(void) const;
GEnergy breakenergy(void) const;
double beta(void) const;
void prefactor(const double& prefactor);
void index1(const double& index1);
void index2(const double& index2);
void pivot(const GEnergy& pivot);
void breakenergy(const GEnergy& breakenergy);
void beta(const double& beta);
protected:
// Protected methods
void init_members(void);
void copy_members(const GModelSpectralSmoothBrokenPlaw& model);
void free_members(void);
void update_eval_cache(const GEnergy& energy) const;
void update_mc_cache(void) const;
// Class to determine the integral photon flux
class flux_kern : public GFunction {
public:
// Constructor
flux_kern(const double& prefactor,
const double& index1,
const GEnergy& pivot,
const double& index2,
const GEnergy& breakenergy,
const double& beta) :
m_prefactor(prefactor),
m_index1(index1),
m_index2(index2),
m_pivot(pivot),
m_breakenergy(breakenergy),
m_beta(beta) {};
// Evaluation method
double eval(const double& energy) {
double epivot = energy / m_pivot.MeV();
double ebreak = energy / m_breakenergy.MeV();
return m_prefactor * std::pow(epivot, m_index1) *
std::pow(1.0 + std::pow(ebreak,(m_index1-m_index2)/m_beta),-m_beta);
}
// Members
protected:
double m_prefactor; //!< Normalization
double m_index1; //!< Spectral index1
double m_index2; //!< Spectral index2
GEnergy m_pivot; //!< Pivot energy
GEnergy m_breakenergy; //!< Break energy
double m_beta; //!< Break smoothness parameter
};
// Class to determine the integral energy flux, derivation of flux_kern
class eflux_kern : public flux_kern {
public:
// Constructor
eflux_kern(const double& prefactor,
const double& index1,
const GEnergy& pivot,
const double& index2,
const GEnergy& breakenergy,
const double& beta):
flux_kern(prefactor, index1, pivot, index2, breakenergy, beta)
{};
// Evaluation method
double eval(const double& energy) {
return energy * flux_kern::eval(energy);
}
};
// Protected members
std::string m_type; //!< Model type
GModelPar m_norm; //!< Normalization factor
GModelPar m_index1; //!< Spectral index1
GModelPar m_index2; //!< Spectral index2
GModelPar m_pivot; //!< Pivot energy
GModelPar m_breakenergy; //!< Energy of spectral break
GModelPar m_beta; //!< Break smoothness
// Cached members used for pre-computations
mutable GEnergy m_last_energy; //!< Last energy value
mutable double m_last_index1; //!< Last index1 parameter
mutable double m_last_index2; //!< Last index2 parameter
mutable double m_last_pivot; //!< Last pivot parameter
mutable double m_last_breakenergy; //!< Last breakenergy parameter
mutable double m_last_beta; //!< Last beta parameter
mutable double m_last_epivot_norm; //!< Last E/Epivot value
mutable double m_last_ebreak_norm; //!< Last E/Ebreakenergy value
mutable double m_last_log_epivot_norm; //!< Last ln(E/Epivot) value
mutable double m_last_log_ebreak_norm; //!< Last ln(E/Ebreakenergy) value
mutable double m_last_epivot_pow; //!< Last pow(E/Epivot,index1) value
mutable double m_last_ebreak_pow; //!< Last pow(E/Ebreakenergy,(index1-index2)/beta)
// Cached members for Monte-Carlo simulations
mutable double m_mc_prefactor; //!< Last pre factor
mutable double m_mc_index1; //!< Last first index
mutable double m_mc_index2; //!< Last second index
mutable double m_mc_pivot; //!< Last pivot energy
mutable double m_mc_breakenergy; //!< Last break energy
mutable GModelSpectralBrokenPlaw m_mc_brokenplaw; //!< Broken power plaw
};
/***********************************************************************//**
* @brief Return class name
*
* @return String containing the class name ("GModelSpectralSmoothBrokenPlaw").
***************************************************************************/
inline
std::string GModelSpectralSmoothBrokenPlaw::classname(void) const
{
return ("GModelSpectralSmoothBrokenPlaw");
}
/***********************************************************************//**
* @brief Return model type
*
* @return "SmoothBrokenPowerLaw".
*
* Returns the type of the spectral smoothly broken power law model.
***************************************************************************/
inline
std::string GModelSpectralSmoothBrokenPlaw::type(void) const
{
return (m_type);
}
/***********************************************************************//**
* @brief Return pre factor
*
* @return Pre factor (ph/cm2/s/MeV).
*
* Returns the pre factor.
***************************************************************************/
inline
double GModelSpectralSmoothBrokenPlaw::prefactor(void) const
{
return (m_norm.value());
}
/***********************************************************************//**
* @brief Set pre factor
*
* @param[in] prefactor Pre factor (ph/cm2/s/MeV).
*
* Sets the pre factor.
***************************************************************************/
inline
void GModelSpectralSmoothBrokenPlaw::prefactor(const double& prefactor)
{
m_norm.value(prefactor);
return;
}
/***********************************************************************//**
* @brief Return smoothly broken power law index1
*
* @return Power law index1.
*
* Returns the power law index1.
***************************************************************************/
inline
double GModelSpectralSmoothBrokenPlaw::index1(void) const
{
return (m_index1.value());
}
/***********************************************************************//**
* @brief Set smoothly broken power law index1
*
* @param[in] index1 Power law index1.
*
* Sets the power law index1.
***************************************************************************/
inline
void GModelSpectralSmoothBrokenPlaw::index1(const double& index1)
{
m_index1.value(index1);
return;
}
/***********************************************************************//**
* @brief Return smoothly broken power law index2
*
* @return Power law index2.
*
* Returns the power law index2.
***************************************************************************/
inline
double GModelSpectralSmoothBrokenPlaw::index2(void) const
{
return (m_index2.value());
}
/***********************************************************************//**
* @brief Set smoothly broken power law index2
*
* @param[in] index2 Power law index2.
*
* Sets the power law index2.
***************************************************************************/
inline
void GModelSpectralSmoothBrokenPlaw::index2(const double& index2)
{
m_index2.value(index2);
return;
}
/***********************************************************************//**
* @brief Return pivot energy
*
* @return Smoothly broken power law pivot energy.
*
* Returns the smoothly broken power law scale energy.
***************************************************************************/
inline
GEnergy GModelSpectralSmoothBrokenPlaw::pivot(void) const
{
GEnergy energy;
energy.MeV(m_pivot.value());
return energy;
}
/***********************************************************************//**
* @brief Set pivot energy
*
* @param[in] pivot Smoothly broken power law pivot energy.
*
* Sets the smoothly broken power law pivot energy.
***************************************************************************/
inline
void GModelSpectralSmoothBrokenPlaw::pivot(const GEnergy& pivot)
{
m_pivot.value(pivot.MeV());
return;
}
/***********************************************************************//**
* @brief Return breakenergy energy
*
* @return breakenergy energy.
*
* Returns the breakenergy energy.
***************************************************************************/
inline
GEnergy GModelSpectralSmoothBrokenPlaw::breakenergy(void) const
{
GEnergy energy;
energy.MeV(m_breakenergy.value());
return energy;
}
/***********************************************************************//**
* @brief Set breakenergy energy
*
* @param[in] breakenergy break energy.
*
* Sets the "breakenergy" energy.
***************************************************************************/
inline
void GModelSpectralSmoothBrokenPlaw::breakenergy(const GEnergy& breakenergy)
{
m_breakenergy.value(breakenergy.MeV());
return;
}
/***********************************************************************//**
* @brief Returns break smoothness parameter beta
*
* @return break smoothness parameter.
*
* Returns the break smoothness parameter 'beta'.
***************************************************************************/
inline
double GModelSpectralSmoothBrokenPlaw::beta(void) const
{
return (m_beta.value());
}
/***********************************************************************//**
* @brief Set break smoothness
*
* @param[in] beta break smoothness parameter.
*
* Sets the beta break smoothness parameter.
***************************************************************************/
inline
void GModelSpectralSmoothBrokenPlaw::beta(const double& beta)
{
m_beta.value(beta);
return;
}
#endif /* GMODELSPECTRALSMOOTHBROKENPLAW_HPP */