/***************************************************************************
 *       GCTAModelRadialGauss.cpp - Radial Gaussian CTA model class        *
 * ----------------------------------------------------------------------- *
 *  copyright (C) 2011-2016 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 GCTAModelRadialGauss.cpp
 * @brief Radial Gaussian model class implementation
 * @author Juergen Knoedlseder
 */

/* __ Includes ___________________________________________________________ */
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <cmath>
#include "GException.hpp"
#include "GTools.hpp"
#include "GMath.hpp"
#include "GIntegral.hpp"
#include "GCTAModelRadialGauss.hpp"
#include "GCTAModelRadialRegistry.hpp"

/* __ Constants __________________________________________________________ */

/* __ Globals ____________________________________________________________ */
const GCTAModelRadialGauss    g_cta_radial_gauss_seed;
const GCTAModelRadialRegistry g_cta_radial_gauss_registry(&g_cta_radial_gauss_seed);

/* __ Method name definitions ____________________________________________ */
#define G_READ                     "GCTAModelRadialGauss::read(GXmlElement&)"
#define G_WRITE                   "GCTAModelRadialGauss::write(GXmlElement&)"

/* __ Macros _____________________________________________________________ */

/* __ Coding definitions _________________________________________________ */
//#define G_DEBUG_MC                                     //!< Debug MC method

/* __ Debug definitions __________________________________________________ */


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

/***********************************************************************//**
 * @brief Void constructor
 ***************************************************************************/
GCTAModelRadialGauss::GCTAModelRadialGauss(void) : GCTAModelRadial()
{
    // Initialise members
    init_members();

    // Return
    return;
}


/***********************************************************************//**
 * @brief Constructor
 *
 * @param[in] sigma Gaussian width (degrees\f$^2\f$).
 ***************************************************************************/
GCTAModelRadialGauss::GCTAModelRadialGauss(const double& sigma) : GCTAModelRadial()
{
    // Initialise members
    init_members();

    // Assign sigma
    this->sigma(sigma);

    // Return
    return;
}


/***********************************************************************//**
 * @brief XML constructor
 *
 * @param[in] xml XML element.
 *
 * Creates instance of a radial Gaussian model by extracting information
 * from an XML element. See GCTAModelRadialGauss::read() for more information
 * about the expected structure of the XML element.
 ***************************************************************************/
GCTAModelRadialGauss::GCTAModelRadialGauss(const GXmlElement& xml) : GCTAModelRadial()
{
    // Initialise members
    init_members();

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

    // Return
    return;
}


/***********************************************************************//**
 * @brief Copy constructor
 *
 * @param[in] model Radial Gaussian model.
 ***************************************************************************/
GCTAModelRadialGauss::GCTAModelRadialGauss(const GCTAModelRadialGauss& model) :
                                           GCTAModelRadial(model)
{
    // Initialise members
    init_members();

    // Copy members
    copy_members(model);

    // Return
    return;
}


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

    // Return
    return;
}


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

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

        // Copy base class members
        this->GCTAModelRadial::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 instance
***************************************************************************/
void GCTAModelRadialGauss::clear(void)
{
    // Free class members (base and derived classes, derived class first)
    free_members();
    this->GCTAModelRadial::free_members();

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

    // Return
    return;
}


/***********************************************************************//**
 * @brief Clone instance
***************************************************************************/
GCTAModelRadialGauss* GCTAModelRadialGauss::clone(void) const
{
    return new GCTAModelRadialGauss(*this);
}


/***********************************************************************//**
 * @brief Evaluate function
 *
 * @param[in] offset Offset angle [degrees].
 * @param[in] gradients Compute gradients?
 * @return Function value
 *
 * Evaluates the Gaussian model for a given offset. The Gaussian model is
 * defined as
 * \f[f(\theta) = \exp \left(-\frac{1}{2}
 *                     \left( \frac{\theta^2}{\sigma} \right)^2 \right)\f]
 * where
 * \f$\theta\f$ is the offset angle (in degrees), and
 * \f$\sigma\f$ is the Gaussian width (in degrees\f$^2\f$).
 *
 * If the @p gradients flag is true the method will also compute the partial
 * derivatives of the parameters. The partial derivative of the Gaussian width
 * is given by
 * \f[\frac{df}{d\sigma_v} = f(\theta) \frac{\theta^4}{\sigma^3} \sigma_s\f]
 * where 
 * \f$\sigma_v\f$ is the value part, 
 * \f$\sigma_s\f$ is the scaling part, and 
 * \f$\sigma = \sigma_v \sigma_s\f$.
 *
 * Note that this method implements a function which is unity for
 * \f$\theta=0\f$.
 ***************************************************************************/
double GCTAModelRadialGauss::eval(const double& offset,
                                  const bool&   gradients) const
{
    // Compute value
    double arg   = offset * offset / sigma();
    double arg2  = arg * arg;
    double value = std::exp(-0.5 * arg2);

    // Optionally compute partial derivatives
    if (gradients) {

        // Compute partial derivatives of the sigma parameter.
        double g_sigma = value * arg2 / sigma() * m_sigma.scale();

        // Set factor gradient
        m_sigma.factor_gradient(g_sigma);

    } // endif: computed partial derivatives

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

    // Return value
    return value;
}


/***********************************************************************//**
 * @brief Returns MC instrument direction
 *
 * @param[in] dir Pointing direction.
 * @param[in] ran Random number generator.
 *
 * Draws an arbitrary CTA instrument position from
 * \f[f(\theta) = \sin(\theta)
 *                \exp \left(-\frac{1}{2}\frac{\theta^4}{\sigma^2} \right)\f]
 * where
 * \f$\theta\f$ is the offset angle (in degrees), and
 * \f$\sigma\f$ is the Gaussian width (in degrees\f$^2\f$),
 * using the rejection method.
 *
 * @todo Method can be optimised by using a random deviate of sin instead
 *       of the uniform random deviate which leads to many unnecessary
 *       rejections.
 ***************************************************************************/
GCTAInstDir GCTAModelRadialGauss::mc(const GCTAInstDir& dir, GRan& ran) const
{
    // Simulate offset from photon arrival direction
    #if defined(G_DEBUG_MC)
    int    n_samples = 0;
    #endif
    double sigma_max = 4.0 * sqrt(sigma());
    double u_max     = sin(sigma_max * gammalib::deg2rad);
    double value     = 0.0;
    double u         = 1.0;
    double offset    = 0.0;
    do {
        offset      = ran.uniform() * sigma_max;
        double arg  = offset * offset / sigma();
        double arg2 = arg * arg;
        value       = sin(offset * gammalib::deg2rad) * exp(-0.5 * arg2);
        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
    GCTAInstDir mc_dir = dir;
    mc_dir.dir().rotate_deg(phi, offset);

    // Compute DETX and DETY coordinates
    double detx(0.0);
    double dety(0.0);
	if (offset > 0.0 ) {
		detx = offset*gammalib::deg2rad * std::cos(phi*gammalib::deg2rad);
		dety = offset*gammalib::deg2rad * std::sin(phi*gammalib::deg2rad);
	}
	mc_dir.detx(detx);
	mc_dir.dety(dety);

    // Return MC direction
    return mc_dir;
}


/***********************************************************************//**
 * @brief Returns integral over radial model (in steradians)
 *
 * Computes
 * \f[\Omega = 2 \pi \int_0^{\pi} \sin \theta f(\theta) d\theta\f]
 * where
 * \f[f(\theta) = \exp \left(-\frac{1}{2}
 *                     \left( \frac{\theta^2}{\sigma} \right)^2 \right)\f]
 * \f$\theta\f$ is the offset angle (in degrees), and
 * \f$\sigma\f$ is the Gaussian width (in degrees\f$^2\f$).
 *
 * The integration is performed numerically, and the upper integration bound
 * \f$\pi\f$
 * is set to
 * \f$\sqrt(10 \sigma)\f$
 * to reduce inaccuracies in the numerical integration.
 ***************************************************************************/
double GCTAModelRadialGauss::omega(void) const
{
    // Allocate integrand
    GCTAModelRadialGauss::integrand integrand(sigma() *
                                              gammalib::deg2rad * 
                                              gammalib::deg2rad);

    // Allocate intergal
    GIntegral integral(&integrand);

    // Set upper integration boundary
    double offset_max = sqrt(10.0*sigma()) * gammalib::deg2rad;
    if (offset_max > gammalib::pi) {
        offset_max = gammalib::pi;
    }

    // Perform numerical integration
    double omega = integral.romberg(0.0, offset_max) * gammalib::twopi;

    // Return integral
    return omega;
}


/***********************************************************************//**
 * @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_parvalue
 *            Non-positive parameter value found.
 * @exception GException::model_invalid_parlimit
 *            Missing or non-positive minimum parameter boundary.
 * @exception GException::model_invalid_parnames
 *            Invalid model parameter names found in XML element.
 *
 * Read the Gaussian radial model information from an XML element. The XML
 * element is required to have one parameter named "Sigma". 
 ***************************************************************************/
void GCTAModelRadialGauss::read(const GXmlElement& xml)
{
    // Verify that XML element has exactly 1 parameter
    if (xml.elements() != 1 || xml.elements("parameter") != 1) {
        throw GException::model_invalid_parnum(G_READ, xml,
              "Radial Gaussian model requires exactly 1 parameter.");
    }

    // Extract model parameters
    int  npar[]   = {0};
    for (int i = 0; i < 1; ++i) {

        // Get parameter element
        const GXmlElement* par = xml.element("parameter", i);

        // Handle Sigma
        if (par->attribute("name") == "Sigma") {
            
            // Read parameter
            m_sigma.read(*par);
            
            // Check parameter
            if (m_sigma.value() <= 0.0) {
                throw GException::model_invalid_parvalue(G_READ, xml,
                      "\"Sigma\" parameter is required to be positive.");
            }
            if (!m_sigma.has_min() || m_sigma.min() <= 0.0) {
                throw GException::model_invalid_parlimit(G_READ, xml,
                      "\"Sigma\" parameter requires positive minimum boundary.");
            }
            
            // Increment parameter counter
            npar[0]++;
        }

    } // endfor: looped over all parameters

    // Verify that all parameters were found
    if (npar[0] != 1) {
        throw GException::model_invalid_parnames(G_READ, xml,
              "Radial Gaussian model requires \"Sigma\" parameter.");
    }

    // Return
    return;
}


/***********************************************************************//**
 * @brief Write model into XML element
 *
 * @param[in] xml XML element.
 *
 * @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.
 *
 * Write the Gaussian radial model information into an XML element. The XML
 * element will have one parameter leaf named "Sigma".
 ***************************************************************************/
void GCTAModelRadialGauss::write(GXmlElement& xml) const
{
    // Set model type
    if (xml.attribute("type") == "") {
        xml.attribute("type", type());
    }

    // Verify model type
    if (xml.attribute("type") != type()) {
        throw GException::model_invalid_spatial(G_WRITE, xml.attribute("type"),
              "Radial Gaussian model is not of type \""+type()+"\".");
    }

    // If XML element has 0 nodes then append 1 parameter node
    if (xml.elements() == 0) {
        xml.append(GXmlElement("parameter name=\"Sigma\""));
    }

    // Verify that XML element has exactly 1 parameter
    if (xml.elements() != 1 || xml.elements("parameter") != 1) {
        throw GException::model_invalid_parnum(G_WRITE, xml,
              "Radial Gaussian model requires exactly 1 parameter.");
    }

    // Set or update model parameter attributes
    int npar[] = {0};
    for (int i = 0; i < 1; ++i) {

        // Get parameter element
        GXmlElement* par = xml.element("parameter", i);

        // Handle sigma
        if (par->attribute("name") == "Sigma") {
            m_sigma.write(*par);
            npar[0]++;
        }

    } // endfor: looped over all parameters

    // Check of all required parameters are present
    if (npar[0] != 1) {
        throw GException::model_invalid_parnames(G_WRITE, xml,
              "Radial Gaussian model requires \"Sigma\" parameter.");
    }

    // Return
    return;
}


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

        // Append information
        result.append("\n"+gammalib::parformat("Number of parameters") +
                      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 GCTAModelRadialGauss::init_members(void)
{
    // Initialise Gaussian sigma
    m_sigma.clear();
    m_sigma.name("Sigma");
    m_sigma.unit("deg2");
    m_sigma.value(7.71728e-8); // (1 arcsec)^2
    m_sigma.min(7.71728e-8);   // (1 arcsec)^2
    m_sigma.free();
    m_sigma.scale(1.0);
    m_sigma.gradient(0.0);
    m_sigma.has_grad(true);

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

    // Return
    return;
}


/***********************************************************************//**
 * @brief Copy class members
 *
 * @param[in] model Radial Gaussian model.
 ***************************************************************************/
void GCTAModelRadialGauss::copy_members(const GCTAModelRadialGauss& model)
{
    // Copy members
    m_sigma = model.m_sigma;

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

    // Return
    return;
}


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