GModelSpectralFunc.cpp

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/***************************************************************************
 *         GModelSpectralFunc.cpp - Spectral function model class          *
 * ----------------------------------------------------------------------- *
 *  copyright (C) 2010-2022 by Juergen Knoedlseder                         *
 * ----------------------------------------------------------------------- *
 *                                                                         *
 *  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 GModelSpectralFunc.cpp
 * @brief Spectral function model class implementation
 * @author Juergen Knoedlseder
 */

/* __ Includes ___________________________________________________________ */
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <cmath>
#include "GException.hpp"
#include "GTools.hpp"
#include "GCsv.hpp"
#include "GRan.hpp"
#include "GEnergies.hpp"
#include "GModelSpectralFunc.hpp"
#include "GModelSpectralRegistry.hpp"

/* __ Constants __________________________________________________________ */

/* __ Globals ____________________________________________________________ */
const GModelSpectralFunc     g_spectral_func_seed;
const GModelSpectralRegistry g_spectral_func_registry(&g_spectral_func_seed);

/* __ Method name definitions ____________________________________________ */
#define G_FLUX                 "GModelSpectralFunc::flux(GEnergy&, GEnergy&)"
#define G_EFLUX               "GModelSpectralFunc::eflux(GEnergy&, GEnergy&)"
#define G_MC      "GModelSpectralFunc::mc(GEnergy&, GEnergy&, GTime&, GRan&)"
#define G_READ                       "GModelSpectralFunc::read(GXmlElement&)"
#define G_WRITE                     "GModelSpectralFunc::write(GXmlElement&)"
#define G_APPEND              "GModelSpectralFunc::append(GEnergy&, double&)"
#define G_INSERT              "GModelSpectralFunc::insert(GEnergy&, double&)"
#define G_REMOVE                           "GModelSpectralFunc::remove(int&)"
#define G_ENERGY1                          "GModelSpectralFunc::energy(int&)"
#define G_ENERGY2                "GModelSpectralFunc::energy(int&, GEnergy&)"
#define G_INTENSITY1                    "GModelSpectralFunc::intensity(int&)"
#define G_INTENSITY2           "GModelSpectralFunc::intensity(int&, double&)"
#define G_LOAD_NODES             "GModelSpectralFunc::load_nodes(GFilename&)"

/* __ Macros _____________________________________________________________ */

/* __ Coding definitions _________________________________________________ */

/* __ Debug definitions __________________________________________________ */


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

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

    // Return
    return;
}


/***********************************************************************//**
 * @brief File constructor
 *
 * @param[in] filename File name of nodes.
 * @param[in] norm Normalization factor.
 *
 * Constructs spectral file function model from a list of nodes that is found
 * in the specified ASCII file. See the load_nodes() method for more
 * information about the expected structure of the file.
 ***************************************************************************/
GModelSpectralFunc::GModelSpectralFunc(const GFilename& filename,
                                       const double&    norm) :
                    GModelSpectral()
{
    // Initialise members
    init_members();

    // Load nodes
    load_nodes(filename);

    // Set normalization
    m_norm.value(norm);

    // Return
    return;
}


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

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

    // Return
    return;
}


/***********************************************************************//**
 * @brief Spectral model constructor
 *
 * @param[in] model Spectral model.
 * @param[in] energies File function node energies.
 *
 * Constructs a spectral file function model from any spectral model.
 * The file function normalisation will be set to unity.
 ***************************************************************************/
GModelSpectralFunc::GModelSpectralFunc(const GModelSpectral& model,
                                       const GEnergies&      energies) :
                    GModelSpectral()
{
    // Initialise members
    init_members();

    // Reserve space for file function nodes
    reserve(energies.size());

    // Append nodes for all energies
    for (int i = 0; i < energies.size(); ++i) {
        append(energies[i], model.eval(energies[i]));
    }

    // Return
    return;
}


/***********************************************************************//**
 * @brief Copy constructor
 *
 * @param[in] model File function model.
 ***************************************************************************/
GModelSpectralFunc::GModelSpectralFunc(const GModelSpectralFunc& model) :
                    GModelSpectral(model)
{
    // Initialise members
    init_members();

    // Copy members
    copy_members(model);

    // Return
    return;
}


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

    // Return
    return;
}


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

/***********************************************************************//**
 * @brief Assignment operator
 *
 * @param[in] model File function model.
 * @return File function model.
 ***************************************************************************/
GModelSpectralFunc& GModelSpectralFunc::operator=(const GModelSpectralFunc& 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 file function
***************************************************************************/
void GModelSpectralFunc::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 file function
***************************************************************************/
GModelSpectralFunc* GModelSpectralFunc::clone(void) const
{
    // Clone file function
    return new GModelSpectralFunc(*this);
}


/***********************************************************************//**
 * @brief Evaluate function
 *
 * @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) = {\tt m\_norm} F(E)
 * \f]
 *
 * where
 * - \f${\tt m\_norm}\f$ is the normalization factor and
 * - \f${F(E)}\f$ is the spectral function.
 *
 * 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]
 ***************************************************************************/
double GModelSpectralFunc::eval(const GEnergy& srcEng,
                                const GTime&   srcTime,
                                const bool&    gradients) const
{
    // Interpolate function. This is done in log10-log10 space, but the
    // linear value is returned.
    double arg  = m_log_nodes.interpolate(srcEng.log10MeV(), m_log_values);
    double func = std::pow(10.0, arg);

    // Compute function value
    double value  = m_norm.value() * func;

    // Optionally compute gradients
    if (gradients) {

        // Compute partial derivatives of the parameter values
        double g_norm  = (m_norm.is_free())  ? m_norm.scale() * func : 0.0;

        // Set gradients
        m_norm.factor_gradient(g_norm);

    } // 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: GModelSpectralFunc::eval";
        std::cout << "(srcEng=" << srcEng;
        std::cout << ", srcTime=" << srcTime << "):";
        std::cout << " NaN/Inf encountered";
        std::cout << " (value=" << value;
        std::cout << ", norm=" << norm();
        std::cout << ", func=" << func;
        std::cout << ")" << std::endl;
    }
    #endif

    // Return
    return value;
}


/***********************************************************************//**
 * @brief Returns model photon flux between [emin, emax] (units: 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).
 ***************************************************************************/
double GModelSpectralFunc::flux(const GEnergy& emin, const GEnergy& emax) const
{
    // Initialise flux
    double flux = 0.0;

    // Compute only if integration range is valid
    if (emin < emax) {

        // Get energy range in MeV
        double e_min = emin.MeV();
        double e_max = emax.MeV();

        // Determine left node index for minimum energy
        m_lin_nodes.set_value(e_min);
        int inx_emin = m_lin_nodes.inx_left();

        // Determine left node index for maximum energy
        m_lin_nodes.set_value(e_max);
        int inx_emax = m_lin_nodes.inx_left();

        // If both energies are within the same nodes then simply
        // integrate over the energy interval using the appropriate power
        // law parameters
        if (inx_emin == inx_emax) {
            flux = m_prefactor[inx_emin] * 
                   gammalib::plaw_photon_flux(e_min,
                                              e_max, 
                                              m_epivot[inx_emin],
                                              m_gamma[inx_emin]);
        }

        // ... otherwise integrate over the nodes where emin and emax
        // resides and all the remaining nodes
        else {

            // If we are requested to extrapolate beyond first node,
            // the use the first nodes lower energy and upper energy
            // boundary for the initial integration.
            int i_start = (e_min < m_lin_nodes[0]) ? inx_emin : inx_emin+1;

            // Integrate from emin to the node boundary
            flux = m_prefactor[inx_emin] *
                   gammalib::plaw_photon_flux(e_min,
                                              m_lin_nodes[i_start],
                                              m_epivot[inx_emin],
                                              m_gamma[inx_emin]);

            // Integrate over all nodes between
            for (int i = i_start; i < inx_emax; ++i) {
                flux += m_flux[i];
            }

            // Integrate from node boundary to emax
            flux += m_prefactor[inx_emax] *
                    gammalib::plaw_photon_flux(m_lin_nodes[inx_emax],
                                               e_max,
                                               m_epivot[inx_emax],
                                               m_gamma[inx_emax]);

        } // endelse: emin and emax not between same nodes

        // Multiply flux by normalisation factor
        flux *= norm();

    } // endif: integration range was valid

    // Return
    return flux;
}


/***********************************************************************//**
 * @brief Returns model energy flux between [emin, emax] (units: 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).
 ***************************************************************************/
double GModelSpectralFunc::eflux(const GEnergy& emin, const GEnergy& emax) const
{
    // Initialise flux
    double eflux = 0.0;

    // Compute only if integration range is valid
    if (emin < emax) {

        // Get energy range in MeV
        double e_min = emin.MeV();
        double e_max = emax.MeV();

        // Determine left node index for minimum energy
        m_lin_nodes.set_value(e_min);
        int inx_emin = m_lin_nodes.inx_left();

        // Determine left node index for maximum energy
        m_lin_nodes.set_value(e_max);
        int inx_emax = m_lin_nodes.inx_left();

        // If both energies are within the same nodes then simply
        // integrate over the energy interval using the appropriate power
        // law parameters
        if (inx_emin == inx_emax) {
            eflux = m_prefactor[inx_emin] * 
                    gammalib::plaw_energy_flux(e_min,
                                               e_max, 
                                               m_epivot[inx_emin],
                                               m_gamma[inx_emin]) *
                                               gammalib::MeV2erg;
        }

        // ... otherwise integrate over the nodes where emin and emax
        // resides and all the remaining nodes
        else {

            // If we are requested to extrapolate beyond first node,
            // the use the first nodes lower energy and upper energy
            // boundary for the initial integration.
            int i_start = (e_min < m_lin_nodes[0]) ? inx_emin : inx_emin+1;

            // Integrate from emin to the node boundary
            eflux = m_prefactor[inx_emin] *
                    gammalib::plaw_energy_flux(e_min,
                                               m_lin_nodes[i_start],
                                               m_epivot[inx_emin],
                                               m_gamma[inx_emin]) *
                                               gammalib::MeV2erg;

            // Integrate over all nodes between
            for (int i = i_start; i < inx_emax; ++i) {
                eflux += m_eflux[i];
            }

            // Integrate from node boundary to emax
            eflux += m_prefactor[inx_emax] *
                     gammalib::plaw_energy_flux(m_lin_nodes[inx_emax],
                                                e_max,
                                                m_epivot[inx_emax],
                                                m_gamma[inx_emax]) *
                                                gammalib::MeV2erg;

        } // endelse: emin and emax not between same nodes

        // Multiply flux by normalisation factor
        eflux *= norm();

    } // endif: integration range was valid

    // Return flux
    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 broken power law
 * defined by the file function.
 ***************************************************************************/
GEnergy GModelSpectralFunc::mc(const GEnergy& emin,
                               const GEnergy& emax,
                               const GTime&   time,
                               GRan&          ran) const
{
    // Check energy interval
    gammalib::check_energy_interval(G_MC, emin, emax);

    // Allocate energy
    GEnergy energy;

    // Update cache
    mc_update(emin, emax);

    // Determine in which bin we reside
    int inx = 0;
    if (m_mc_cum.size() > 1) {
        double u = ran.uniform();
        for (inx = m_mc_cum.size()-1; inx > 0; --inx) {
            if (m_mc_cum[inx-1] <= u) {
                break;
            }
        }
    }

    // Get random energy for specific bin
    if (m_mc_exp[inx] != 0.0) {
        double e_min = m_mc_min[inx];
        double e_max = m_mc_max[inx];
        double u     = ran.uniform();
        double eng   = (u > 0.0) 
                        ? std::exp(std::log(u * (e_max - e_min) + e_min) / m_mc_exp[inx])
                        : 0.0;
        energy.MeV(eng);
    }
    else {
        double e_min = m_mc_min[inx];
        double e_max = m_mc_max[inx];
        double u     = ran.uniform();
        double eng   = std::exp(u * (e_max - e_min) + e_min);
        energy.MeV(eng);
    }

    // Return energy
    return energy;
}


/***********************************************************************//**
 * @brief Read model from XML element
 *
 * @param[in] xml XML element containing power law model information.
 *
 * Reads the spectral information from an XML element. The format of the XML
 * elements is
 *
 *     <spectrum type="FileFunction" file="..">
 *       <parameter name="Normalization" scale=".." value=".." min=".." max=".." free=".."/>
 *     </spectrum>
 ***************************************************************************/
void GModelSpectralFunc::read(const GXmlElement& xml)
{
    // Verify number of model parameters
    gammalib::xml_check_parnum(G_READ, xml, 1);

    // Get parameter
    const GXmlElement* norm = gammalib::xml_get_par(G_READ, xml, m_norm.name());

    // Read parameter
    m_norm.read(*norm);

    // Load nodes from file
    load_nodes(gammalib::xml_file_expand(xml, xml.attribute("file")));

    // 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="FileFunction" file="..">
 *       <parameter name="Normalization" scale=".." value=".." min=".." max=".." free=".."/>
 *     </spectrum>
 * 
 * Note that the function nodes will not be written since they will not be
 * altered by any method.
 ***************************************************************************/
void GModelSpectralFunc::write(GXmlElement& xml) const
{
    // Verify model type
    gammalib::xml_check_type(G_WRITE, xml, type());

    // Get or create parameter
    GXmlElement* norm = gammalib::xml_need_par(G_WRITE, xml, m_norm.name());

    // Write parameter
    m_norm.write(*norm);

    // Set file attribute
    xml.attribute("file", gammalib::xml_file_reduce(xml, m_filename));

    // Return
    return;
}


/***********************************************************************//**
 * @brief Append node to file function
 *
 * @param[in] energy Energy.
 * @param[in] intensity Intensity.
 *
 * @exception GException::invalid_argument
 *            Energy not larger than energy of last node or energy or
 *            intensity are not positive.
 *
 * Appends one node to the file function.
 ***************************************************************************/
void GModelSpectralFunc::append(const GEnergy& energy, const double& intensity)
{
    // Check that energy is larger than energy of last node
    if (nodes() > 0) {
        if (energy.MeV() <= m_lin_nodes[nodes()-1]) {
            GEnergy last(m_lin_nodes[nodes()-1], "MeV");
            std::string msg = "Specified energy "+energy.print()+" is not "
                              "larger than the energy "+last.print()+" of the "
                              "last node of the file function. Please append "
                              "nodes in increasing order of energy.";
            throw GException::invalid_argument(G_APPEND, msg);
        }
    }

    // Check that energy is positive
    if (energy.MeV() <= 0.0) {
        std::string msg = "Specified energy "+energy.print()+" is  not "
                          "positive. Please append only nodes with positive "
                          "energies.";
        throw GException::invalid_argument(G_APPEND, msg);
    }

    // Check that intensity is positive
    if (intensity <= 0.0) {
        std::string msg = "Specified intensity "+gammalib::str(intensity)+" is "
                          "not positive. Please append only nodes with positive "
                          "intensities.";
        throw GException::invalid_argument(G_APPEND, msg);
    }

    // Append node
    m_lin_nodes.append(energy.MeV());
    m_log_nodes.append(energy.log10MeV());
    m_lin_values.push_back(intensity);
    m_log_values.push_back(std::log10(intensity));

    // Set pre-computation cache
    set_cache();

    // Return
    return;
}


/***********************************************************************//**
 * @brief Insert node into file function
 *
 * @param[in] energy Energy.
 * @param[in] intensity Intensity.
 *
 * @exception GException::invalid_argument
 *            Energy or intensity are not positive, or energy does already
 *            exist in file function.
 *
 * Inserts one node at the appropriate location into the file function.
 ***************************************************************************/
void GModelSpectralFunc::insert(const GEnergy& energy, const double& intensity)
{
    // Get energy in MeV
    double energy_MeV = energy.MeV();

    // Check that energy is positive
    if (energy_MeV <= 0.0) {
        std::string msg = "Specified energy "+energy.print()+" is  not "
                          "positive. Please append only nodes with positive "
                          "energies.";
        throw GException::invalid_argument(G_INSERT, msg);
    }

    // Check that intensity is positive
    if (intensity <= 0.0) {
        std::string msg = "Specified intensity "+gammalib::str(intensity)+" is "
                          "not positive. Please append only nodes with positive "
                          "intensities.";
        throw GException::invalid_argument(G_INSERT, msg);
    }

    // Find index before which the node should be inserted
    int index = 0;
    for (int i = 0; i < nodes(); ++i) {
        if (m_lin_nodes[i] == energy_MeV) {
            std::string msg = "A node with the specified energy "+
                              energy.print()+" exists already in the file "
                              "function. Please insert only nodes with "
                              "energies that do not yet exist.";
            throw GException::invalid_argument(G_INSERT, msg);
        }
        else if (m_lin_nodes[i] > energy_MeV) {
            break;
        }
        index++;
    }

    // Insert node
    m_lin_nodes.insert(index, energy_MeV);
    m_log_nodes.insert(index, energy.log10MeV());
    m_lin_values.insert(m_lin_values.begin()+index, intensity);
    m_log_values.insert(m_log_values.begin()+index, std::log10(intensity));

    // Set pre-computation cache
    set_cache();

    // Return
    return;
}


/***********************************************************************//**
 * @brief Remove node from file function
 *
 * @param[in] index Node index [0,...,nodes()-1].
 *
 * @exception GException::out_of_range
 *            Node index is out of range.
 *
 * Removes the node of specified @p index from the file function.
 ***************************************************************************/
void GModelSpectralFunc::remove(const int& index)
{
    // Compile option: raise exception if index is out of range
    #if defined(G_RANGE_CHECK)
    if (index < 0 || index >= nodes()) {
        throw GException::out_of_range(G_REMOVE, "Node index", index, nodes());
    }
    #endif

    // Delete node
    m_lin_nodes.remove(index);
    m_log_nodes.remove(index);
    m_lin_values.erase(m_lin_values.begin() + index);
    m_log_values.erase(m_log_values.begin() + index);

    // Set pre-computation cache
    set_cache();

    // Return
    return;
}


/***********************************************************************//**
 * @brief Append file function
 *
 * @param[in] filefct File function.
 *
 * Appends file function to the existing file function.
 ***************************************************************************/
void GModelSpectralFunc::extend(const GModelSpectralFunc& filefct)
{
    // Do nothing if file function is empty
    if (!filefct.is_empty()) {

        // Get file function size
        int num = filefct.nodes();

        // Reserve enough space
        reserve(nodes() + num);

        // Append all nodes
        for (int i = 0; i < num; ++i) {
            append(filefct.energy(i), filefct.intensity(i));
        }

    } // endif: file function was not empty

    // Set pre-computation cache
    set_cache();

    // Return
    return;
}


/***********************************************************************//**
 * @brief Return energy of node
 *
 * @param[in] index Node index [0,...,nodes()-1].
 *
 * @exception GException::out_of_range
 *            Node index is out of range.
 *
 * Returns the energy of node with specified @p index in the file function.
 ***************************************************************************/
GEnergy GModelSpectralFunc::energy(const int& index) const
{
    // Compile option: raise exception if index is out of range
    #if defined(G_RANGE_CHECK)
    if (index < 0 || index >= nodes()) {
        throw GException::out_of_range(G_ENERGY1, "Node index", index, nodes());
    }
    #endif

    // Set energy
    GEnergy energy;
    energy.MeV(m_lin_nodes[index]);

    // Return energy
    return energy;
}


/***********************************************************************//**
 * @brief Set energy of node
 *
 * @param[in] index Node index [0,...,nodes()-1].
 * @param[in] energy Energy.
 *
 * @exception GException::out_of_range
 *            Node index is out of range.
 * @exception GException::invalid_argument
 *            Specified energy is not larger than energy of preceeding node
 *            or not smaller than energy of following node.
 *
 * Sets the energy of node with specified @p index in the file function.
 ***************************************************************************/
void GModelSpectralFunc::energy(const int& index, const GEnergy& energy)
{
    // Compile option: raise exception if index is out of range
    #if defined(G_RANGE_CHECK)
    if (index < 0 || index >= nodes()) {
        throw GException::out_of_range(G_ENERGY2, "Node index", index, nodes());
    }
    #endif

    // Check that energy is larger than energy of precedent node
    if (index > 0) {
        if (energy.MeV() <= m_lin_nodes[index-1]) {
            GEnergy precedent(m_lin_nodes[index-1], "MeV");
            std::string msg = "Specified energy "+energy.print()+" is not "
                              "larger than energy "+precedent.print()+" of "
                              "precedent node. Please specify an energy that "
                              "is larger than "+precedent.print()+".";
            throw GException::invalid_argument(G_ENERGY2, msg);
        }
    }

    // Check that energy is smaller than energy of following node
    if (index < nodes()-1) {
        if (energy.MeV() >= m_lin_nodes[index+1]) {
            GEnergy following(m_lin_nodes[index+1], "MeV");
            std::string msg = "Specified energy "+energy.print()+" is not "
                              "smaller than energy "+following.print()+" of "
                              "following node. Please specify an energy that "
                              "is smaller than "+following.print()+".";
            throw GException::invalid_argument(G_ENERGY2, msg);
        }
    }

    // Set node
    m_lin_nodes[index] = energy.MeV();
    m_log_nodes[index] = energy.log10MeV();

    // Set pre-computation cache
    set_cache();

    // Return
    return;
}


/***********************************************************************//**
 * @brief Return intensity of node
 *
 * @param[in] index Node index [0,...,nodes()-1].
 * @return Intensity (ph/cm2/s/MeV).
 *
 * @exception GException::out_of_range
 *            Node index is out of range.
 *
 * Returns the intensity of node with specified @p index in the file function.
 ***************************************************************************/
double GModelSpectralFunc::intensity(const int& index) const
{
    // Compile option: raise exception if index is out of range
    #if defined(G_RANGE_CHECK)
    if (index < 0 || index >= nodes()) {
        throw GException::out_of_range(G_INTENSITY1, "Node index", index, nodes());
    }
    #endif

    // Return intensity
    return (m_lin_values[index]);
}


/***********************************************************************//**
 * @brief Set intensity of node
 *
 * @param[in] index Node index [0,...,nodes()-1].
 * @param[in] intensity Intensity (ph/cm2/s/MeV).
 *
 * @exception GException::out_of_range
 *            Node index is out of range.
 * @exception GException::invalid_argument
 *            Intensity is not positive.
 *
 * Sets the intensity of node with specified @p index in the file function.
 ***************************************************************************/
void GModelSpectralFunc::intensity(const int& index, const double& intensity)
{
    // Compile option: raise exception if index is out of range
    #if defined(G_RANGE_CHECK)
    if (index < 0 || index >= nodes()) {
        throw GException::out_of_range(G_INTENSITY2, "Node index", index, nodes());
    }
    #endif

    // Check that intensity is positive
    if (intensity <= 0.0) {
        std::string msg = "Specified intensity "+gammalib::str(intensity)+" is "
                          "not positive. Please set only positive intensities.";
        throw GException::invalid_argument(G_INTENSITY2, msg);
    }

    // Set intensity
    m_lin_values[index] = intensity;
    m_log_values[index] = std::log10(intensity);

    // Set pre-computation cache
    set_cache();

    // Return
    return;
}


/***********************************************************************//**
 * @brief Save file function in ASCII file
 *
 * @param[in] filename ASCII filename.
 * @param[in] clobber Overwrite existing file?
 *
 * Saves file function in ASCII file.
 ***************************************************************************/
void GModelSpectralFunc::save(const GFilename& filename, const bool& clobber) const
{
    // Allocate CSV file
    GCsv csv(nodes(), 2);

    // Fill CSV file
    for (int i = 0; i < nodes(); ++i) {
        csv(i,0) = gammalib::str(m_lin_nodes[i]);
        csv(i,1) = gammalib::str(m_lin_values[i]);
    }

    // Save CSV file
    csv.save(filename, " ", clobber);

    // Store filename
    m_filename = filename;

    // Return
    return;
}


/***********************************************************************//**
 * @brief Print file function information
 *
 * @param[in] chatter Chattiness.
 * @return String containing file function information.
 ***************************************************************************/
std::string GModelSpectralFunc::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("=== GModelSpectralFunc ===");

        // Append information
        result.append("\n"+gammalib::parformat("Function file"));
        result.append(m_filename.url());
        result.append("\n"+gammalib::parformat("Number of nodes"));
        result.append(gammalib::str(nodes()));
        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));
        }

        // Append node information
        for (int i = 0; i < m_prefactor.size(); ++i) {
            result.append("\n"+gammalib::parformat("Node "+gammalib::str(i+1)));
            result.append("Epivot="+gammalib::str(m_epivot[i]));
            result.append(" Prefactor="+gammalib::str(m_prefactor[i]));
            result.append(" Gamma="+gammalib::str(m_gamma[i]));
            result.append(" Flux="+gammalib::str(m_flux[i]));
            result.append(" EFlux="+gammalib::str(m_eflux[i]));
        }

    } // endif: chatter was not silent

    // Return result
    return result;
}


/*==========================================================================
 =                                                                         =
 =                             Private methods                             =
 =                                                                         =
 ==========================================================================*/

/***********************************************************************//**
 * @brief Initialise class members
 ***************************************************************************/
void GModelSpectralFunc::init_members(void)
{
    // Initialise powerlaw normalisation
    m_norm.clear();
    m_norm.name("Normalization");
    m_norm.scale(1.0);
    m_norm.value(1.0);
    m_norm.range(0.0,1000.0);
    m_norm.free();
    m_norm.gradient(0.0);
    m_norm.has_grad(true);

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

    // Initialise members
    m_lin_nodes.clear();
    m_log_nodes.clear();
    m_lin_values.clear();
    m_log_values.clear();
    m_filename.clear();

    // Initialise flux cache
    m_prefactor.clear();
    m_gamma.clear();
    m_epivot.clear();
    m_flux.clear();
    m_eflux.clear();

    // Initialise MC cache
    m_mc_emin.clear();
    m_mc_emax.clear();
    m_mc_cum.clear();
    m_mc_min.clear();
    m_mc_max.clear();
    m_mc_exp.clear();

    // Return
    return;
}


/***********************************************************************//**
 * @brief Copy class members
 *
 * @param[in] model Spectral function model.
 ***************************************************************************/
void GModelSpectralFunc::copy_members(const GModelSpectralFunc& model)
{
    // Copy members
    m_norm       = model.m_norm;
    m_lin_nodes  = model.m_lin_nodes;
    m_log_nodes  = model.m_log_nodes;
    m_lin_values = model.m_lin_values;
    m_log_values = model.m_log_values;
    m_filename   = model.m_filename;

    // Copy flux cache
    m_prefactor  = model.m_prefactor;
    m_gamma      = model.m_gamma;
    m_epivot     = model.m_epivot;
    m_flux       = model.m_flux;
    m_eflux      = model.m_eflux;

    // Copy MC cache
    m_mc_emin    = model.m_mc_emin;
    m_mc_emax    = model.m_mc_emax;
    m_mc_cum     = model.m_mc_cum;
    m_mc_min     = model.m_mc_min;
    m_mc_max     = model.m_mc_max;
    m_mc_exp     = model.m_mc_exp;

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

    // Return
    return;
}


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


/***********************************************************************//**
 * @brief Load nodes from file
 *
 * @param[in] filename File name.
 *
 * @exception GException::invalid_argument
 *            Empty @p filename specified.
 *            GException::invalid_value
 *            Invalid file function ASCII file.
 *
 * The file function is stored as a column separated value table (CSV) in an
 * ASCII file with (at least) 2 columns. The first column specifies the
 * energy in MeV while the second column specifies the intensity at this
 * energy in units of ph/cm2/s/MeV.
 *
 * The node energies and values will be stored both linearly and as log10.
 * The log10 storing requires that node energies and node values are
 * positive. Also, at least 2 nodes and 2 columns are required in the file
 * function.
 ***************************************************************************/
void GModelSpectralFunc::load_nodes(const GFilename& filename)
{
    // Clear nodes and values
    m_lin_nodes.clear();
    m_log_nodes.clear();
    m_lin_values.clear();
    m_log_values.clear();

    // Throw an exception if the filename is empty
    if (filename.is_empty()) {
        std::string msg = "Empty file function ASCII file name specified. "
                          "Please specify a valid file function ASCII file "
                          "name.";
        throw GException::invalid_argument(G_LOAD_NODES, msg);
    }

    // Set filename
    m_filename = filename;

    // Load file
    GCsv csv = GCsv(filename.url());

    // Check if there are at least 2 nodes
    if (csv.nrows() < 2) {
        std::string msg = "File function ASCII file \""+filename.url()+
                          "\" contains "+gammalib::str(csv.nrows())+
                          " rows but at least 2 rows are required. Please "
                          "specify a file function ASCII file with at "
                          "least two rows.";
        throw GException::invalid_value(G_LOAD_NODES, msg);
    }

    // Check if there are at least 2 columns
    if (csv.ncols() < 2) {
        std::string msg = "File function ASCII file \""+filename.url()+
                          "\" contains "+gammalib::str(csv.ncols())+
                          " columns but at least 2 columns are required. "
                          "Please specify a file function ASCII file with "
                          "at least two columns.";
        throw GException::invalid_value(G_LOAD_NODES, msg);
    }

    // Setup nodes
    double last_energy = 0.0;
    for (int i = 0; i < csv.nrows(); ++i) {

        // Get log10 of node energy and value. Make sure they are valid.
        double log10energy;
        double log10value;
        if (csv.real(i,0) > 0.0) {
            log10energy = std::log10(csv.real(i,0));
        }
        else {
            std::string msg = "Non-positive energy "+
                              gammalib::str(csv.real(i,0))+" encountered "
                              "in row "+gammalib::str(i)+" of file "
                              "function ASCII file. Please specify only "
                              "positive energies in file function.";
            throw GException::invalid_value(G_LOAD_NODES, msg);
        }
        if (csv.real(i,1) > 0.0) {
            log10value = std::log10(csv.real(i,1));
        }
        else {
            std::string msg = "Non-positive intensity "+
                              gammalib::str(csv.real(i,1))+" encountered "
                              "in row "+gammalib::str(i)+" of file "
                              "function ASCII file. Please specify only "
                              "positive intensities in file function.";
            throw GException::invalid_value(G_LOAD_NODES, msg);
        }

        // Make sure that energies are increasing
        if (csv.real(i,0) <= last_energy) {
            std::string msg = "Energy "+gammalib::str(csv.real(i,0))+
                              "in row "+gammalib::str(i)+" of file "
                              "function ASCII file is equal or smaller "
                              "than preceding energy "+
                              gammalib::str(last_energy)+". Please specify "
                              "monotonically increasing energies in the "
                              "file function ASCII file.";
            throw GException::invalid_value(G_LOAD_NODES, msg);
        }

        // Append log10 of node energy and value
        m_lin_nodes.append(csv.real(i,0));
        m_log_nodes.append(log10energy);
        m_lin_values.push_back(csv.real(i,1));
        m_log_values.push_back(log10value);

        // Store last energy for monotonically increasing check
        last_energy = csv.real(i,0);

    } // endfor: looped over nodes

    // Set pre-computation cache
    set_cache();

    // Return
    return;
}


/***********************************************************************//**
 * @brief Set pre-computation cache
 ***************************************************************************/
void GModelSpectralFunc::set_cache(void) const
{
    // Clear any existing values
    m_prefactor.clear();
    m_gamma.clear();
    m_epivot.clear();
    m_flux.clear();
    m_eflux.clear();

    // Loop over all nodes-1
    for (int i = 0; i < nodes()-1; ++i) {

        // Get energies and function values
        double emin = m_lin_nodes[i];
        double emax = m_lin_nodes[i+1];
        double fmin = m_lin_values[i];
        double fmax = m_lin_values[i+1];

        // Compute pivot energy (MeV). We use here the geometric mean of
        // the node boundaries.
        double epivot = std::sqrt(emin*emax);

        // Compute spectral index
        double gamma = std::log(fmin/fmax) / std::log(emin/emax);

        // Compute power law normalisation
        double prefactor = fmin / std::pow(emin/epivot, gamma);

        // Compute photon flux between nodes
        double flux = prefactor *
                      gammalib::plaw_photon_flux(emin, emax, epivot, gamma);

        // Compute energy flux between nodes
        double eflux = prefactor *
                       gammalib::plaw_energy_flux(emin, emax, epivot, gamma);

        // Convert energy flux from MeV/cm2/s to erg/cm2/s
        eflux *= gammalib::MeV2erg;

        // Push back values on pre-computation cache
        m_prefactor.push_back(prefactor);
        m_gamma.push_back(gamma);
        m_epivot.push_back(epivot);
        m_flux.push_back(flux);
        m_eflux.push_back(eflux);

    } // endfor: looped over all nodes

    // Return
    return;
}


/***********************************************************************//**
 * @brief Set MC pre-computation cache
 *
 * @param[in] emin Minimum energy.
 * @param[in] emax Maximum energy.
 *
 * This method sets up an array of indices and the cumulative distribution
 * function needed for MC simulations.
 ***************************************************************************/
void GModelSpectralFunc::mc_update(const GEnergy& emin,
                                   const GEnergy& emax) const
{
    // Check if we need to update the cache
    if (emin != m_mc_emin || emax != m_mc_emax) {

        // Store new energy interval
        m_mc_emin = emin;
        m_mc_emax = emax;

        // Initialise cache
        m_mc_cum.clear();
        m_mc_min.clear();
        m_mc_max.clear();
        m_mc_exp.clear();

        // Get energy range in MeV
        double e_min = emin.MeV();
        double e_max = emax.MeV();

        // Continue only if e_max > e_min
        if (e_max > e_min) {

            // Allocate flux
            double flux;

            // Determine left node index for minimum energy
            m_lin_nodes.set_value(e_min);
            int inx_emin = m_lin_nodes.inx_left();

            // Determine left node index for maximum energy
            m_lin_nodes.set_value(e_max);
            int inx_emax = m_lin_nodes.inx_left();

            // If both energies are within the same node then just
            // add this one node on the stack
            if (inx_emin == inx_emax) {
                flux = m_prefactor[inx_emin] * 
                       gammalib::plaw_photon_flux(e_min,
                                                  e_max, 
                                                  m_epivot[inx_emin],
                                                  m_gamma[inx_emin]);
                m_mc_cum.push_back(flux);
                m_mc_min.push_back(e_min);
                m_mc_max.push_back(e_max);
                m_mc_exp.push_back(m_gamma[inx_emin]);
            }

            // ... otherwise integrate over the nodes where emin and emax
            // resides and all the remaining nodes
            else {

                // If we are requested to extrapolate beyond first node,
                // the use the first nodes lower energy and upper energy
                // boundary for the initial integration.
                int i_start = (e_min < m_lin_nodes[0]) ? inx_emin : inx_emin+1;

                // Add emin to the node boundary
                flux = m_prefactor[inx_emin] *
                       gammalib::plaw_photon_flux(e_min,
                                                  m_lin_nodes[i_start],
                                                  m_epivot[inx_emin],
                                                  m_gamma[inx_emin]);
                m_mc_cum.push_back(flux);
                m_mc_min.push_back(e_min);
                m_mc_max.push_back(m_lin_nodes[i_start]);
                m_mc_exp.push_back(m_gamma[inx_emin]);

                // Add all nodes between
                for (int i = i_start; i < inx_emax; ++i) {
                    flux = m_flux[i];
                    m_mc_cum.push_back(flux);
                    m_mc_min.push_back(m_lin_nodes[i]);
                    m_mc_max.push_back(m_lin_nodes[i+1]);
                    m_mc_exp.push_back(m_gamma[i]);
                }

                // Add node boundary to emax
                flux = m_prefactor[inx_emax] *
                       gammalib::plaw_photon_flux(m_lin_nodes[inx_emax],
                                                  e_max,
                                                  m_epivot[inx_emax],
                                                  m_gamma[inx_emax]);
                m_mc_cum.push_back(flux);
                m_mc_min.push_back(m_lin_nodes[inx_emax]);
                m_mc_max.push_back(e_max);
                m_mc_exp.push_back(m_gamma[inx_emax]);

            } // endelse: emin and emax not between same nodes

            // Build cumulative distribution
            for (int i = 1; i < m_mc_cum.size(); ++i) {
                m_mc_cum[i] += m_mc_cum[i-1];
            }
            double norm = m_mc_cum[m_mc_cum.size()-1];
            if (norm > 0.0) {
                for (int i = 0; i < m_mc_cum.size(); ++i) {
                    m_mc_cum[i] /= norm;
                }
            }

            // Set MC values
            for (int i = 0; i < m_mc_cum.size(); ++i) {

                // Compute exponent
                double exponent = m_mc_exp[i] + 1.0;

                // Exponent dependend computation
                if (std::abs(exponent) > 1.0e-11) {

                    // If the exponent is too small then use lower energy
                    // boundary
                    if (exponent < -50.0) {
                        m_mc_exp[i] = 0.0;
                        m_mc_min[i] = std::log(m_mc_min[i]);
                        m_mc_max[i] = m_mc_min[i];
                    }

                    // ... otherwise if exponent is too large then use
                    // upper energy boundary
                    else if (exponent > +50.0) {
                        m_mc_exp[i] = 0.0;
                        m_mc_min[i] = std::log(m_mc_max[i]);
                        m_mc_max[i] = m_mc_min[i];
                    }

                    // ... otherwise use transformation formula
                    else {
                        m_mc_exp[i] = exponent;
                        m_mc_min[i] = std::pow(m_mc_min[i], exponent);
                        m_mc_max[i] = std::pow(m_mc_max[i], exponent);
                    }
                }
                else {
                    m_mc_exp[i] = 0.0;
                    m_mc_min[i] = std::log(m_mc_min[i]);
                    m_mc_max[i] = std::log(m_mc_max[i]);
                }

            } // endfor: set MC values

        } // endif: e_max > e_min

    } // endif: Update was required

    // Return
    return;
}