/***************************************************************************
 *             GModelSpatialMap.cpp  -  Spatial map model class            *
 * ----------------------------------------------------------------------- *
 *  copyright (C) 2012 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 GModelSpatialMap.cpp
 * @brief Spatial map model class implementation
 * @author J. Knoedlseder
 */

/* __ Includes ___________________________________________________________ */
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include "GException.hpp"
#include "GTools.hpp"
#include "GModelSpatialMap.hpp"
#include "GModelSpatialRegistry.hpp"

/* __ Constants __________________________________________________________ */

/* __ Globals ____________________________________________________________ */
const GModelSpatialMap      g_spatial_map_seed;
const GModelSpatialRegistry g_spatial_map_registry(&g_spatial_map_seed);

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

/* __ Macros _____________________________________________________________ */

/* __ Coding definitions _________________________________________________ */

/* __ Debug definitions __________________________________________________ */
//#define G_DEBUG_CACHE              //!< Debug Monte Carlo Cache computation


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

/***********************************************************************//**
 * @brief Void constructor
 ***************************************************************************/
GModelSpatialMap::GModelSpatialMap(void) : GModelSpatial()
{
    // Initialise members
    init_members();

    // Return
    return;
}


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

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

    // Return
    return;
}


/***********************************************************************//**
 * @brief Filename constructor
 *
 * @param[in] filename Name of FITS file.
 *
 * Creates instance of spatial map model by loading a skymap from a FITS
 * file.
 ***************************************************************************/
GModelSpatialMap::GModelSpatialMap(const std::string& filename) : GModelSpatial()
{
    // Initialise members
    init_members();

    // Load skymap
    load_map(filename);

    // Return
    return;
}


/***********************************************************************//**
 * @brief Copy constructor
 *
 * @param[in] model Spatial map model.
 ***************************************************************************/
GModelSpatialMap::GModelSpatialMap(const GModelSpatialMap& model)
                                   : GModelSpatial(model)
{
    // Initialise members
    init_members();

    // Copy members
    copy_members(model);

    // Return
    return;
}


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

    // Return
    return;
}


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

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

        // Copy base class members
        this->GModelSpatial::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 GModelSpatialMap::clear(void)
{
    // Free class members (base and derived classes, derived class first)
    free_members();
    this->GModelSpatial::free_members();

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

    // Return
    return;
}


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


/***********************************************************************//**
 * @brief Return intensity of skymap
 *
 * @param[in] srcDir True photon arrival direction.
 *
 * Returns the intensity of the skymap at the specified sky direction
 * multiplied by the normalization factor. If the sky direction falls outside
 * the skymap, an intensity of 0 is returned.
 ***************************************************************************/
double GModelSpatialMap::eval(const GSkyDir& srcDir) const
{
    // Get skymap intensity
    double intensity = m_map(srcDir);

    // Return intensity times normalization factor
    return (intensity * m_value.real_value());
}


/***********************************************************************//**
 * @brief Return intensity of skymap and gradient
 *
 * @param[in] srcDir True photon arrival direction.
 *
 * Returns the intensity of the skymap at the specified sky direction
 * multiplied by the normalization factor. The method also sets the gradient
 * with respect to the normalization factor. If the sky direction falls
 * outside the skymap, an intensity of 0 is returned.
 ***************************************************************************/
double GModelSpatialMap::eval_gradients(const GSkyDir& srcDir) const
{
    // Get skymap intensity
    double intensity = m_map(srcDir);

    // Compute partial derivatives of the parameter values
    double g_value = (m_value.isfree()) ? intensity * m_value.scale() : 0.0;

    // Set gradient to 0 (circumvent const correctness)
    const_cast<GModelSpatialMap*>(this)->m_value.gradient(g_value);

    // Return intensity times normalization factor
    return (intensity * m_value.real_value());
}


/***********************************************************************//**
 * @brief Returns MC sky direction
 *
 * @param[in] ran Random number generator.
 *
 * @exception GException::feature_not_implemented
 *            Method not yet implemented
 *
 * This method returns a random sky direction according to the intensity
 * distribution of the model sky map. It makes use of a cache array that
 * contains the normalized cumulative flux values of the skymap. Using a
 * uniform random number, this cache array is scanned using a bi-section
 * method to determine the skymap pixel for which the position should be
 * returned. To avoid binning problems, the exact position within the pixel
 * is set by a uniform random number generator (neglecting thus pixel
 * distortions). The fractional skymap pixel is then converted into a sky
 * direction.
 ***************************************************************************/
GSkyDir GModelSpatialMap::mc(GRan& ran) const
{
    // Allocate sky direction
    GSkyDir dir;

    // Determine number of skymap pixels
    int npix = m_map.npix();

    // Continue only if there are skymap pixels
    if (npix > 0) {

        // Get uniform random number
        double u = ran.uniform();

        // Get pixel index according to random number. We use a bi-section
        // method to find the corresponding skymap pixel
        int low  = 0;
        int high = npix;
        while ((high - low) > 1) {
            int mid = (low+high) / 2;
            if (u < m_mc_cache[mid]) {
                high = mid;
            }
            else if (m_mc_cache[mid] <= u) {
                low = mid;
            }
        }

        // Convert 1D pixel index to 2D pixel index
        GSkyPixel pixel = m_map.pix2xy(low);

        // Randomize pixel
        pixel.x(pixel.x() + ran.uniform() - 0.5);
        pixel.y(pixel.y() + ran.uniform() - 0.5);

        // Get sky direction
        dir = m_map.xy2dir(pixel);

    } // endif: there were pixels in sky map
    
    // Return sky direction
    return dir;
}


/***********************************************************************//**
 * @brief Read model from XML element
 *
 * @param[in] xml XML element.
 *
 * @exception GException::model_invalid_parnum
 *            Invalid number of model parameters found in XML element.
 * @exception GException::model_invalid_parnames
 *            Invalid model parameter names found in XML element.
 *
 * Read the skymap information from an XML element. The XML element is
 * required to have 1 parameter named either "Normalization" or "Prefactor".
 ***************************************************************************/
void GModelSpatialMap::read(const GXmlElement& xml)
{
    // Verify that XML element has exactly 1 parameters
    if (xml.elements() != 1 || xml.elements("parameter") != 1) {
        throw GException::model_invalid_parnum(G_READ, xml,
              "Spatial map model requires exactly 1 parameter.");
    }

    // Get pointer on model parameter
    GXmlElement* par = static_cast<GXmlElement*>(xml.element("parameter", 0));

    // Get value
    if (par->attribute("name") == "Normalization" ||
        par->attribute("name") == "Prefactor") {
        m_value.read(*par);
    }
    else {
        throw GException::model_invalid_parnames(G_READ, xml,
              "Spatial map model requires either \"Prefactor\" or"
              " \"Normalization\" parameter.");
    }

    // Load skymap
    load_map(xml.attribute("file"));

    // 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 "SpatialMap"
 * @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 map cube information into an XML element. The XML element has to
 * be of type "MapCubeFunction" and will have 1 parameter leaf named either
 * "Value" or "Normalization" (default).
 ***************************************************************************/
void GModelSpatialMap::write(GXmlElement& xml) const
{
    // Set model type
    if (xml.attribute("type") == "") {
        xml.attribute("type", "SpatialMap");
    }

    // Set model filename
    xml.attribute("file", m_filename);

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

    // If XML element has 0 nodes then append parameter node. The name
    // of the node is "Prefactor" as this is the Fermi/LAT standard.
    // We thus assure that the XML files will be compatible with
    // Fermi/LAT.
    if (xml.elements() == 0) {
        xml.append(new GXmlElement("parameter name=\"Prefactor\""));
    }

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

    // Get pointer on model parameter
    GXmlElement* par = static_cast<GXmlElement*>(xml.element("parameter", 0));

    // Set or update parameter
    if (par->attribute("name") == "Normalization" ||
        par->attribute("name") == "Prefactor") {
        m_value.write(*par);
    }
    else {
        throw GException::model_invalid_parnames(G_WRITE, xml,
              "Spatial map model requires either \"Prefactor\" or"
              " \"Normalization\" parameter.");
    }

    // Return
    return;
}


/***********************************************************************//**
 * @brief Print map cube information
 ***************************************************************************/
std::string GModelSpatialMap::print(void) const
{
    // Initialise result string
    std::string result;

    // Append header
    result.append("=== GModelSpatialMap ===");
    result.append("\n"+parformat("Sky map file")+m_filename);
    result.append("\n"+parformat("Number of parameters")+str(size()));
    for (int i = 0; i < size(); ++i) {
        result.append("\n"+m_pars[i]->print());
    }

    // Return result
    return result;
}


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

/***********************************************************************//**
 * @brief Initialise class members
 ***************************************************************************/
void GModelSpatialMap::init_members(void)
{
    // Initialise Value
    m_value.clear();
    m_value.name("Prefactor");
    m_value.value(1.0);
    m_value.scale(1.0);
    m_value.range(0.001, 1000.0);
    m_value.gradient(0.0);
    m_value.fix();
    m_value.hasgrad(true);

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

    // Initialise other members
    m_map.clear();
    m_filename.clear();
    m_mc_cache.clear();

    // Return
    return;
}


/***********************************************************************//**
 * @brief Copy class members
 *
 * @param[in] model Spatial map cube model.
 ***************************************************************************/
void GModelSpatialMap::copy_members(const GModelSpatialMap& model)
{
    // Copy members
    m_value    = model.m_value;
    m_map      = model.m_map;
    m_filename = model.m_filename;
    m_mc_cache = model.m_mc_cache;

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

    // Return
    return;
}


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


/***********************************************************************//**
 * @brief Load skymap into the model class
 *
 * Loads skymap into the model class. After loading, the map is normalized
 * so that the total flux in the map amounts to 1 ph/cm2/s. Negative skymap
 * pixels are set to zero intensity.
 *
 * The method also initialises a cache for Monte Carlo sampling of the
 * skymap. This Monte Carlo cache consists of a linear array that maps a
 * value between 0 and 1 into the skymap pixel.
 ***************************************************************************/
void GModelSpatialMap::load_map(const std::string& filename)
{
    // Initialise skymap and cache
    m_map.clear();
    m_mc_cache.clear();

    // Store filename of skymap (for XML writing). Note that we do not
    // expand any environment variable at this level, so that if we write
    // back the XML element we write the filepath with the environment
    // variable
    m_filename = filename;

    // Load skymap
    m_map.load(expand_env(m_filename));

    // Determine number of skymap pixels
    int npix = m_map.npix();

    // Continue only if there are skymap pixels
    if (npix > 0) {

        // Reserve space for all pixels in cache
        m_mc_cache.reserve(npix+1);

        // Set first cache value to 0
        m_mc_cache.push_back(0.0);

        // Initialise cache with cumulative pixel fluxes and compute total
        // flux in skymap for normalization. Negative pixels are set to
        // zero intensity in the skymap.
        double sum = 0.0;
        for (int i = 0; i < npix; ++i) {
            double flux = m_map(i) * m_map.omega(i);
            if (flux < 0.0) {
                m_map(i) = 0.0;
                flux     = 0.0;
            }
            sum += flux;
            m_mc_cache.push_back(sum);
        }

        // Normalize skymap and pixel fluxes in the cache so that the values
        // in the cache run from 0 to 1
        if (sum > 0.0) {
            for (int i = 0; i < npix; ++i) {
                m_map(i)      /= sum;
                m_mc_cache[i] /= sum;
            }
        }
        
        // Make sure that last pixel in the cache is >1
        m_mc_cache[npix] = 1.0001;

        // Dump cache values for debugging
        #if defined(G_DEBUG_CACHE)
        for (int i = 0; i < npix+1; ++i) {
            std::cout << "i=" << i;
            std::cout << " c=" << m_mc_cache[i] << std::endl;
        }
        #endif
        
    } // endif: there were skymap pixels

    // Return
    return;
}


/*==========================================================================
 =                                                                         =
 =                                Friends                                  =
 =                                                                         =
 ==========================================================================*/