GModelSpectralGauss.cpp

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/***************************************************************************
 *         GModelSpectralGauss.cpp - Spectral Gaussian model class         *
 * ----------------------------------------------------------------------- *
 *  copyright (C) 2014-2021 by Christoph Deil & Ellis Owen                 *
 * ----------------------------------------------------------------------- *
 *                                                                         *
 *  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 GModelSpectralGauss.cpp
 * @brief Gaussian spectral model class implementation
 * @author Christoph Deil & Ellis Owen
 */

/* __ Includes ___________________________________________________________ */
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include "GException.hpp"
#include "GTools.hpp"
#include "GMath.hpp"
#include "GRan.hpp"
#include "GFunction.hpp"
#include "GIntegral.hpp"
#include "GModelSpectralGauss.hpp"
#include "GModelSpectralRegistry.hpp"

/* __ Constants __________________________________________________________ */

/* __ Globals ____________________________________________________________ */
const GModelSpectralGauss    g_spectral_gauss_seed;
const GModelSpectralRegistry g_spectral_gauss_registry(&g_spectral_gauss_seed);

/* __ Method name definitions ____________________________________________ */
#define G_FLUX                "GModelSpectralGauss::flux(GEnergy&, GEnergy&)"
#define G_EFLUX              "GModelSpectralGauss::eflux(GEnergy&, GEnergy&)"
#define G_MC             "GModelSpectralGauss::mc(GEnergy&, GEnergy&, GRan&)"
#define G_READ                      "GModelSpectralGauss::read(GXmlElement&)"
#define G_WRITE                    "GModelSpectralGauss::write(GXmlElement&)"

/* __ Macros _____________________________________________________________ */

/* __ Coding definitions _________________________________________________ */

/* __ Debug definitions __________________________________________________ */


/*==========================================================================
 =                                                                         =
 =                        Constructors/destructors                         =
 =                                                                         =
 ==========================================================================*/

/***********************************************************************//**
 * @brief Void constructor
 ***************************************************************************/
GModelSpectralGauss::GModelSpectralGauss(void) : GModelSpectral()
{
    // Initialise members
    init_members();

    // Return
    return;
}


/***********************************************************************//**
 * @brief XML constructor
 *
 * @param[in] xml XML element.
 *
 * Constructs constant spectral model by extracting information from an XML
 * element. See the read() method for more information about the expected
 * structure of the XML element.
 ***************************************************************************/
GModelSpectralGauss::GModelSpectralGauss(const GXmlElement& xml) :
                     GModelSpectral()
{
    // Initialise members
    init_members();

    // Read information from XML element
    read(xml);

    // Return
    return;
}


/***********************************************************************//**
 * @brief Constructor
 *
 * @param[in] norm Total flux under Gaussian (in ph/cm2/s).
 * @param[in] mean Mean energy.
 * @param[in] sigma Energy width.
 ***************************************************************************/
GModelSpectralGauss::GModelSpectralGauss(const double&  norm,
                                         const GEnergy& mean,
                                         const GEnergy& sigma) :
                     GModelSpectral()
{
    // Initialise members
    init_members();

    // Set parameters
    m_norm.value(norm);
    m_mean.value(mean.MeV());
    m_sigma.value(sigma.MeV());

    // Autoscale parameters
    autoscale();

    // Return
    return;
}


/***********************************************************************//**
 * @brief Copy constructor
 *
 * @param[in] model Spectral Gaussian model.
 ***************************************************************************/
GModelSpectralGauss::GModelSpectralGauss(const GModelSpectralGauss& model) :
                     GModelSpectral(model)
{
    // Initialise members
    init_members();

    // Copy members
    copy_members(model);

    // Return
    return;
}


/***********************************************************************//**
 * @brief Destructor
 ***************************************************************************/
GModelSpectralGauss::~GModelSpectralGauss(void)
{
    // Free members
    free_members();

    // Return
    return;
}


/*==========================================================================
 =                                                                         =
 =                                Operators                                =
 =                                                                         =
 ==========================================================================*/

/***********************************************************************//**
 * @brief Assignment operator
 *
 * @param[in] model Gauss spectral model.
 * @return Gauss spectral model.
 ***************************************************************************/
GModelSpectralGauss& GModelSpectralGauss::operator=(const GModelSpectralGauss& model)
{
    // Execute only if object is not identical
    if (this != &model) {

        // Copy base class members
        this->GModelSpectral::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 Gaussian spectral model
 ***************************************************************************/
void GModelSpectralGauss::clear(void)
{
    // Free class members (base and derived classes, derived class first)
    free_members();
    this->GModelSpectral::free_members();

    // Initialise members
    this->GModelSpectral::init_members();
    init_members();

    // Return
    return;
}


/***********************************************************************//**
 * @brief Clone Gaussian spectral model
 *
 * @return Pointer to deep copy of Gaussian spectral model.
 ***************************************************************************/
GModelSpectralGauss* GModelSpectralGauss::clone(void) const
{
    // Clone Gaussian spectral model
    return new GModelSpectralGauss(*this);
}


/***********************************************************************//**
 * @brief Evaluate model value
 *
 * @param[in] srcEng True photon energy.
 * @param[in] srcTime True photon arrival time.
 * @param[in] gradients Compute gradients?
 * @return Model value (ph/cm2/s/MeV).
 *
 * Evaluates
 *
 * \f[
 * S_{\rm E}(E | t) = \frac{m\_norm}{\sqrt{2\pi}m\_sigma}
 *                    \exp(\frac{-(E-m\_mean)^2}{2 m\_sigma^2})
 * \f]
 *
 * where
 * - \f${\tt m\_norm}\f$ is the normalization,
 * - \f${\tt m\_mean}\f$ is the mean energy, and
 * - \f${\tt m\_sigma}\f$ is the energy width.
 *
 * If the @p gradients flag is true the method will also compute the
 * partial derivatives of the model with respect to the parameters using
 *
 * \f[
 *    \frac{\delta S_{\rm E}(E | t)}{\delta {\tt m\_norm}} =
 *      \frac{S_{\rm E}(E | t)}{{\tt m\_norm}}
 * \f]
 *
 * \f[
 *    \frac{\delta S_{\rm E}(E | t)}{\delta {\tt m\_mean}} =
 *      S_{\rm E}(E | t) \frac{E-m\_mean}{m\_sigma^2}
 * \f]
 *
 * \f[
 *    \frac{\delta S_{\rm E}(E | t)}{\delta {\tt m\_sigma}} =
 *      \frac{S_{\rm E}(E | t)}{{\tt m\_sigma}}
 *      \left( \frac{(E-m\_mean)^2}{m\_sigma^2} - 1 \right)
 * \f]
 ***************************************************************************/
double GModelSpectralGauss::eval(const GEnergy& srcEng,
                                 const GTime&   srcTime,
                                 const bool&    gradients) const
{
    // Get parameter values
    double energy = srcEng.MeV();
    double norm   = m_norm.value();
    double mean   = m_mean.value();
    double sigma  = m_sigma.value();

    // Compute function terms
    double delta  = energy - mean;
    double sigma2 = sigma * sigma;
    double term2  = (1.0 / sigma) * gammalib::inv_sqrt2pi;
    double term1  = norm * term2;
    double term3  = delta * delta / (2.0 * sigma2);
    double term4  = delta / sigma2;
    double term5  = (norm / sigma2) * gammalib::inv_sqrt2pi;
    double eterm3 = std::exp(-term3);

    // Compute function value
    double value = term1 * eterm3;

    // Optionally compute gradients
    if (gradients) {
    
        // Compute partial derivatives with respect to the parameter factor
        // values (partial differentials were determined analytically).
        double g_norm  = (m_norm.is_free())
                         ? term2 * eterm3 * m_norm.scale() : 0.0;
        double g_mean  = (m_mean.is_free())
                         ? value * term4 * m_mean.scale() : 0.0;
        double g_sigma = (m_sigma.is_free())
                         ? -term5 * eterm3 * (1.0 - (2.0 * term3)) * m_sigma.scale()
                         : 0.0;

        // Set gradients
        m_norm.factor_gradient(g_norm);
        m_mean.factor_gradient(g_mean);
        m_sigma.factor_gradient(g_sigma);

    } // endif: gradient computation was requested

    // Compile option: Check for NaN/Inf
    #if defined(G_NAN_CHECK)
    if (gammalib::is_notanumber(value) || gammalib::is_infinite(value)) {
        std::cout << "*** ERROR: GModelSpectralGauss::eval";
        std::cout << "(srcEng=" << srcEng;
        std::cout << ", srcTime=" << srcTime << "):";
        std::cout << " NaN/Inf encountered";
        std::cout << " (value=" << value;
        std::cout << ")" << std::endl;
    }
    #endif

    // Return
    return value;
}


/***********************************************************************//**
 * @brief Returns model photon flux between [emin, emax] (ph/cm2/s)
 *
 * @param[in] emin Minimum photon energy.
 * @param[in] emax Maximum photon energy.
 * @return Photon flux (ph/cm2/s).
 *
 * Computes
 *
 * \f[
 *    \int_{\tt emin}^{\tt emax} S_{\rm E}(E | t) dE
 * \f]
 *
 * where
 * - [@p emin, @p emax] is an energy interval, and
 * - \f$S_{\rm E}(E | t)\f$ is the spectral model (ph/cm2/s/MeV).
 * The integration is done analytically.
 ***************************************************************************/
double GModelSpectralGauss::flux(const GEnergy& emin,
                                 const GEnergy& emax) const
{
    // Initialise flux
    double flux = 0.0;
    
    // Compute only if integration range is valid
    if (emin < emax) {

        // Precomputations
        double energy_min = emin.MeV();
        double energy_max = emax.MeV();
        double norm       = m_norm.value();
        double mean       = m_mean.value();
        double sigma      = m_sigma.value();
        double zmin       = (energy_min - mean) / sigma;
        double zmax       = (energy_max - mean) / sigma;

        // Compute flux for a constant model
        flux = norm * gammalib::gauss_integral(zmin, zmax);
    
    } // endif: integration range was valid

    // Return
    return flux;
}


/***********************************************************************//**
 * @brief Returns model energy flux between [emin, emax] (erg/cm2/s)
 *
 * @param[in] emin Minimum photon energy.
 * @param[in] emax Maximum photon energy.
 * @return Energy flux (erg/cm2/s).
 *
 * Computes
 *
 * \f[
 *    \int_{\tt emin}^{\tt emax} S_{\rm E}(E | t) E \, dE
 * \f]
 *
 * where
 * - [@p emin, @p emax] is an energy interval, and
 * - \f$S_{\rm E}(E | t)\f$ is the spectral model (ph/cm2/s/MeV).
 * The integration is done analytically.
 ***************************************************************************/
double GModelSpectralGauss::eflux(const GEnergy& emin,
                                  const GEnergy& emax) const
{
    // Initialise flux
    double eflux = 0.0;
    
    // Compute only if integration range is valid
    if (emin < emax) {

        // Setup integration kernel
        eflux_kernel integrand(m_norm.value(),  m_mean.value(),
                               m_sigma.value());
        GIntegral integral(&integrand);

        // Get integration boundaries in MeV
        double e_min = emin.MeV();
        double e_max = emax.MeV();

        // Perform integration
        eflux = integral.romberg(e_min, e_max);

        // Convert from MeV/cm2/s to erg/cm2/s
        eflux *= gammalib::MeV2erg;
    
    } // endif: integration range was valid

    // Return
    return eflux;
}


/***********************************************************************//**
 * @brief Returns MC energy between [emin, emax]
 *
 * @param[in] emin Minimum photon energy.
 * @param[in] emax Maximum photon energy.
 * @param[in] time True photon arrival time.
 * @param[in,out] ran Random number generator.
 * @return Energy.
 *
 * @exception GException::erange_invalid
 *            Energy range is invalid (emin < emax required).
 *
 * Returns Monte Carlo energy by randomly drawing from a constant between
 * the minimum and maximum photon energy.
 *
 * Method Used: Box-Muller transform, outlined here:
 * http://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform
 *
 * Code from: http://www.design.caltech.edu/erik/Misc/Gaussian.html
 ***************************************************************************/
GEnergy GModelSpectralGauss::mc(const GEnergy& emin,
                                const GEnergy& emax,
                                const GTime&   time,
                                GRan&          ran) const
{
    // Check energy interval
    gammalib::check_energy_interval(G_MC, emin, emax);

    // Get energy boundaries in MeV
    double xmax = emax.MeV();
    double xmin = emin.MeV();

    // Initialize return energy
    double energy = 0.0;

    // Sample until we find a value within the requested energy range
    do {

        // Compute random value
        double val = ran.normal();

        // Scale to specified width and shift by mean value
        energy = m_sigma.value() * val + m_mean.value();

    } while (energy < xmin || energy > xmax);


    // Return energy
    return GEnergy(energy, "MeV");
}


/***********************************************************************//**
 * @brief Read model from XML element
 *
 * @param[in] xml XML element containing Gaussian model information.
 *
 * Read the spectral Gaussian information from an XML element.
 * The format of the XML elements is:
 *
 *     <spectrum type="Gaussian">
 *       <parameter name="Normalization" scale=".." value=".." min=".." max=".." free=".."/>
 *       <parameter name="Mean"          scale=".." value=".." min=".." max=".." free=".."/>
 *       <parameter name="Sigma"         scale=".." value=".." min=".." max=".." free=".."/>
 *     </spectrum>
 *
 ***************************************************************************/
void GModelSpectralGauss::read(const GXmlElement& xml)
{
    // Verify number of model parameters
    gammalib::xml_check_parnum(G_READ, xml, 3);

    // Get parameters
    const GXmlElement* norm  = gammalib::xml_get_par(G_READ, xml, m_norm.name());
    const GXmlElement* mean  = gammalib::xml_get_par(G_READ, xml, m_mean.name());
    const GXmlElement* sigma = gammalib::xml_get_par(G_READ, xml, m_sigma.name());

    // Read parameters
    m_norm.read(*norm);
    m_mean.read(*mean);
    m_sigma.read(*sigma);

    // Return
    return;
}


/***********************************************************************//**
 * @brief Write model into XML element
 *
 * @param[in] xml XML element into which model information is written.
 *
 * Writes the spectral information into an XML element. The format of the XML
 * element is
 *
 *     <spectrum type="Gaussian">
 *       <parameter name="Normalization" scale=".." value=".." min=".." max=".." free=".."/>
 *       <parameter name="Mean"          scale=".." value=".." min=".." max=".." free=".."/>
 *       <parameter name="Sigma"         scale=".." value=".." min=".." max=".." free=".."/>
 *     </spectrum>
 ***************************************************************************/
void GModelSpectralGauss::write(GXmlElement& xml) const
{
    // Verify model type
    gammalib::xml_check_type(G_WRITE, xml, type());

    // Get XML parameters
    GXmlElement* norm  = gammalib::xml_need_par(G_WRITE, xml, m_norm.name());
    GXmlElement* mean  = gammalib::xml_need_par(G_WRITE, xml, m_mean.name());
    GXmlElement* sigma = gammalib::xml_need_par(G_WRITE, xml, m_sigma.name());

    // Write parameters
    m_norm.write(*norm);
    m_mean.write(*mean);
    m_sigma.write(*sigma);

    // Return
    return;
}


/***********************************************************************//**
 * @brief Print spectral model information
 *
 * @param[in] chatter Chattiness (defaults to NORMAL).
 * @return String containing spectral model information.
 ***************************************************************************/
std::string GModelSpectralGauss::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("=== GModelSpectralGauss ===");

        // Append model content
        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 GModelSpectralGauss::init_members(void)
{
    // Initialise normalisation
    m_norm.clear();
    m_norm.name("Normalization");
    m_norm.unit("ph/cm2/s");
    m_norm.scale(1.0);
    m_norm.value(1.0);          // default: 1.0
    m_norm.min(0.0);            // min:     0.0
    m_norm.free();
    m_norm.gradient(0.0);
    m_norm.has_grad(false);

    // Initialise mean energy
    m_mean.clear();
    m_mean.name("Mean");
    m_mean.unit("MeV");
    m_mean.scale(1.0);
    m_mean.value(1000.0);       // default: 1000.0
    m_mean.min(0.001);          // min:     0.001  MeV
    m_mean.free();
    m_mean.gradient(0.0);
    m_mean.has_grad(false);

    // Initialise energy width
    m_sigma.clear();
    m_sigma.name("Sigma");
    m_sigma.unit("MeV");
    m_sigma.scale(1.0);
    m_sigma.value(100.0);       // default: 100.0 MeV
    m_sigma.min(0.0001);        // min:     0.1 keV
    m_sigma.free();
    m_sigma.gradient(0.0);
    m_sigma.has_grad(false);

    // Set parameter pointer(s)
    m_pars.clear();
    m_pars.push_back(&m_norm);
    m_pars.push_back(&m_mean);
    m_pars.push_back(&m_sigma);

    // Return
    return;
}


/***********************************************************************//**
 * @brief Copy class members
 *
 * @param[in] model Spectral constant model.
 ***************************************************************************/
void GModelSpectralGauss::copy_members(const GModelSpectralGauss& model)
{
    // Copy members
    m_norm  = model.m_norm;
    m_mean  = model.m_mean;
    m_sigma = model.m_sigma;

    // Set parameter pointer(s)
    m_pars.clear();
    m_pars.push_back(&m_norm);
    m_pars.push_back(&m_mean);
    m_pars.push_back(&m_sigma);

    // Return
    return;
}


/***********************************************************************//**
 * @brief Delete class members
 ***************************************************************************/
void GModelSpectralGauss::free_members(void)
{
    // Return
    return;
}

/***********************************************************************//**
 * @brief Kernel for energy flux integration
 *
 * @param[in] energy Energy (MeV).
 ***************************************************************************/
double GModelSpectralGauss::eflux_kernel::eval(const double& energy)
{
    // Evaluate function value
    double delta = energy - m_mean;
    double term1 = (m_norm / m_sigma) * gammalib::inv_sqrt2pi;
    double term2 = delta * delta / (2.0 * m_sigma * m_sigma);
    double value = term1 * std::exp(- term2);

    // Return value
    return value;
}