/***********************************************************************//**
 * @brief Return simulated list of events
 *
 * @param[in] obs Observation.
 * @param[in] ran Random number generator.
 * @return Pointer to list of simulated events (needs to be de-allocated by
 *         client)
 *
 * @exception GException::invalid_argument
 *            Specified observation is not a CTA observation.
 *
 * Draws a sample of events from the background model using a Monte
 * Carlo simulation. The region of interest, the energy boundaries and the
 * good time interval for the sampling will be extracted from the observation
 * argument that is passed to the method. The method also requires a random
 * number generator of type GRan which is passed by reference, hence the
 * state of the random number generator will be changed by the method.
 *
 * The method also applies a deadtime correction using a Monte Carlo process,
 * taking into account temporal deadtime variations. For this purpose, the
 * method makes use of the time dependent GObservation::deadc method.
 *
 * For each event in the returned event list, the sky direction, the nominal
 * coordinates (DETX and DETY), the energy and the time will be set.
 ***************************************************************************/
GCTAEventList* GCTAModelAeffBackground::mc(const GObservation& obs,
                                           GRan& ran) const
{
    // Initialise new event list
    GCTAEventList* list = new GCTAEventList;

    // Continue only if model is valid)
    if (valid_model()) {

        // Retrieve CTA observation
        const GCTAObservation* cta = dynamic_cast<const GCTAObservation*>(&obs);
        if (cta == NULL) {
            std::string msg = "Specified observation is not a CTA "
                              "observation.\n" + obs.print();
            throw GException::invalid_argument(G_MC, msg);
        }

        // Get pointer on CTA IRF response
        const GCTAResponseIrf* rsp =
              dynamic_cast<const GCTAResponseIrf*>(cta->response());
        if (rsp == NULL) {
            std::string msg = "Specified observation does not contain"
                              " an IRF response.\n" + obs.print();
            throw GException::invalid_argument(G_MC, msg);
        }

        // Retrieve CTA response and pointing
        const GCTAPointing& pnt = cta->pointing();

        // Get pointer to CTA effective area
        const GCTAAeff* aeff = rsp->aeff();
        if (aeff == NULL) {
            std::string msg = "Specified observation contains no effective area"
                              " information.\n" + obs.print();
            throw GException::invalid_argument(G_MC, msg);
        }

        // Retrieve event list to access the ROI, energy boundaries and GTIs
        const GCTAEventList* events =
              dynamic_cast<const GCTAEventList*>(obs.events());
        if (events == NULL) {
            std::string msg = "No CTA event list found in observation.\n" +
                              obs.print();
            throw GException::invalid_argument(G_MC, msg);
        }

        // Get simulation region
        const GCTARoi&  roi     = events->roi();
        const GEbounds& ebounds = events->ebounds();
        const GGti&     gti     = events->gti();

        // Get maximum offset value for simulations
        double max_theta     = pnt.dir().dist(roi.centre().dir()) +
                               roi.radius() * gammalib::deg2rad;
        double cos_max_theta = std::cos(max_theta);

        // Set simulation region for result event list
        list->roi(roi);
        list->ebounds(ebounds);
        list->gti(gti);

        // Set up spectral model to draw random energies from. Here we use
        // a fixed energy sampling for an instance of GModelSpectralNodes.
        // This is analogous to to the GCTAModelIrfBackground::mc method.
        // We make sure that only non-negative nodes get appended.
        GEbounds spectral_ebounds =
            GEbounds(m_n_mc_energies, ebounds.emin(), ebounds.emax(), true);
        GModelSpectralNodes spectral;
        for (int i = 0; i < spectral_ebounds.size(); ++i) {
            GEnergy energy    = spectral_ebounds.elogmean(i);
            double  intensity = aeff_integral(obs, energy.log10TeV());
            double  norm      = m_spectral->eval(energy, events->tstart());
            double  arg       = norm * intensity;
            if (arg > 0.0) {
                spectral.append(energy, arg);
            }
        }

        // Loop over all energy bins
        for (int ieng = 0; ieng < ebounds.size(); ++ieng) {

            // Compute the background rate in model within the energy
            // boundaries from spectral component (units: cts/s).
            // Note that the time here is ontime. Deadtime correction will
            // be done later.
            double rate = spectral.flux(ebounds.emin(ieng), ebounds.emax(ieng));

            // Debug option: dump rate
            #if defined(G_DUMP_MC)
            std::cout << "GCTAModelAeffBackground::mc(\"" << name() << "\": ";
            std::cout << "rate=" << rate << " cts/s)" << std::endl;
            #endif

            // If the rate is not positive then skip this energy bins
            if (rate <= 0.0) {
                continue;
            }

            // Loop over all good time intervals
            for (int itime = 0; itime < gti.size(); ++itime) {

                // Get Monte Carlo event arrival times from temporal model
                GTimes times = m_temporal->mc(rate,
                                              gti.tstart(itime),
                                              gti.tstop(itime),
                                              ran);

                // Get number of events
                int n_events = times.size();

                // Reserve space for events
                if (n_events > 0) {
                    list->reserve(n_events);
                }

                // Debug option: provide number of times and initialize
                // statisics
                #if defined(G_DUMP_MC)
                std::cout << " Interval " << itime;
                std::cout << " times=" << n_events << std::endl;
                int n_killed_by_deadtime = 0;
                int n_killed_by_roi      = 0;
                #endif

                // Loop over events
                for (int i = 0; i < n_events; ++i) {

                    // Apply deadtime correction
                    double deadc = obs.deadc(times[i]);
                    if (deadc < 1.0) {
                        if (ran.uniform() > deadc) {
                            #if defined(G_DUMP_MC)
                            n_killed_by_deadtime++;
                            #endif
                            continue;
                        }
                    }

                    // Get Monte Carlo event energy from spectral model
                    GEnergy energy = spectral.mc(ebounds.emin(ieng),
                                                 ebounds.emax(ieng),
                                                 times[i],
                                                 ran);

                    // Get maximum effective area for rejection method
                    double max_aeff = aeff->max(energy.log10TeV(), pnt.zenith(),
                                                pnt.azimuth(), false);

                    // Skip event if the maximum effective area is not positive
                    if (max_aeff <= 0.0) {
                        continue;
                    }

                    // Initialise randomised coordinates
                    double offset = 0.0;
                    double phi    = 0.0;

                    // Initialise acceptance fraction and counter of zeros for
                    // rejection method
                    double acceptance_fraction = 0.0;
                    int    zeros               = 0;

                    // Start rejection method loop
                    do {

                        // Throw random offset and azimuth angle in
                        // considered range
                        offset = std::acos(1.0 - ran.uniform() *
                                           (1.0 - cos_max_theta));
                        phi    = ran.uniform() * gammalib::twopi;

                        // Compute function value at this offset angle
                        double value = (*aeff)(energy.log10TeV(), offset, phi,
                                               pnt.zenith(), pnt.azimuth(),
                                               false);

                        // If the value is not positive then increment the
                        // zeros counter and fall through. The counter assures
                        // that this loop does not lock up.
                        if (value <= 0.0) {
                            zeros++;
                            continue;
                        }

                        // Value is non-zero so reset the zeros counter
                        zeros = 0;

                        // Compute acceptance fraction
                        acceptance_fraction = value / max_aeff;
			
                    } while ((ran.uniform() > acceptance_fraction) &&
                             (zeros < 1000));

                    // If the zeros counter is non-zero then the loop was
                    // exited due to exhaustion and the event is skipped
                    if (zeros > 0) {
                        continue;
                    }

                    // Convert CTA pointing direction in instrument system
                    GCTAInstDir mc_dir(pnt.dir());

                    // Rotate pointing direction by offset and azimuth angle
                    mc_dir.dir().rotate_deg(phi    * gammalib::rad2deg,
                                            offset * gammalib::rad2deg);

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

                    // Set DETX and DETY coordinates
                    mc_dir.detx(detx);
                    mc_dir.dety(dety);

                    // Allocate event
                    GCTAEventAtom event;

                    // Set event attributes
                    event.dir(mc_dir);
                    event.energy(energy);
                    event.time(times[i]);

                    // Append event to list if it falls in ROI
                    if (events->roi().contains(event)) {
                        list->append(event);
                    }
                    #if defined(G_DUMP_MC)
                    else {
                        n_killed_by_roi++;
                    }
                    #endif

                } // endfor: looped over all events

                // Debug option: provide  statisics
                #if defined(G_DUMP_MC)
                std::cout << " Killed by deadtime=";
                std::cout << n_killed_by_deadtime << std::endl;
                std::cout << " Killed by ROI=";
                std::cout << n_killed_by_roi << std::endl;
                #endif

            } // endfor: looped over all GTIs

        } // endfor: looped over all energy boundaries

    } // endif: model was valid

    // Return
    return list;
}
/***********************************************************************//**
 * @brief Return simulated list of events
 *
 * @param[in] obs Observation.
 * @param[in] ran Random number generator.
 * @return Pointer to list of simulated events (needs to be de-allocated by
 *         client)
 *
 * @exception GException::invalid_argument
 *            No CTA event list found in observation.
 *
 * Draws a sample of events from the background model using a Monte
 * Carlo simulation. The pointing information, the energy boundaries and the
 * good time interval for the sampling will be extracted from the observation
 * argument that is passed to the method. The method also requires a random
 * number generator of type GRan which is passed by reference, hence the
 * state of the random number generator will be changed by the method.
 *
 * The method also applies a deadtime correction using a Monte Carlo process,
 * taking into account temporal deadtime variations. For this purpose, the
 * method makes use of the time dependent GObservation::deadc method.
 ***************************************************************************/
GCTAEventList* GCTAModelBackground::mc(const GObservation& obs, GRan& ran) const
{
    // Initialise new event list
    GCTAEventList* list = new GCTAEventList;

    // Continue only if model is valid)
    if (valid_model()) {

        // Extract event list to access the ROI, energy boundaries and GTIs
        const GCTAEventList* events = dynamic_cast<const GCTAEventList*>(obs.events());
        if (events == NULL) {
            std::string msg = "No CTA event list found in observation.\n" +
                              obs.print();
            throw GException::invalid_argument(G_MC, msg);
        }

        // Get simulation region
        const GCTARoi&  roi     = events->roi();
        const GEbounds& ebounds = events->ebounds();
        const GGti&     gti     = events->gti();

        // Set simulation region for result event list
        list->roi(roi);
        list->ebounds(ebounds);
        list->gti(gti);

        // Loop over all energy boundaries
        for (int ieng = 0; ieng < ebounds.size(); ++ieng) {

            // Initialise de-allocation flag
            bool free_spectral = false;

            // Set pointer to spectral model
            GModelSpectral* spectral = m_spectral;

            // If the spectral model is a diffuse cube then create a node
            // function spectral model that is the product of the diffuse
            // cube node function and the spectral model evaluated at the
            // energies of the node function
            GModelSpatialDiffuseCube* cube =
                dynamic_cast<GModelSpatialDiffuseCube*>(m_spatial);
            if (cube != NULL) {

			   // Set MC simulation cone based on ROI
			   cube->set_mc_cone(roi.centre().dir(), roi.radius());

			   // Allocate node function to replace the spectral component
			   GModelSpectralNodes* nodes = new GModelSpectralNodes(cube->spectrum());
			   for (int i = 0; i < nodes->nodes(); ++i) {
				   GEnergy energy    = nodes->energy(i);
				   double  intensity = nodes->intensity(i);
				   double  norm      = m_spectral->eval(energy, events->tstart());
				   nodes->intensity(i, norm*intensity);
			   }

			   // Signal that node function needs to be de-allocated later
			   free_spectral = true;

			   // Set the spectral model pointer to the node function
			   spectral = nodes;

            } // endif: spatial model was a diffuse cube

            // Compute the background rate in model within the energy boundaries
            // from spectral component (units: cts/s).
            // Note that the time here is ontime. Deadtime correction will be done
            // later.
            double rate = spectral->flux(ebounds.emin(ieng), ebounds.emax(ieng));

            // Debug option: dump rate
            #if defined(G_DUMP_MC)
            std::cout << "GCTAModelBackground::mc(\"" << name() << "\": ";
            std::cout << "rate=" << rate << " cts/s)" << std::endl;
            #endif

            // Loop over all good time intervals
            for (int itime = 0; itime < gti.size(); ++itime) {

                // Get Monte Carlo event arrival times from temporal model
                GTimes times = m_temporal->mc(rate,
                                              gti.tstart(itime),
                                              gti.tstop(itime),
                                              ran);

                // Get number of events
                int n_events = times.size();

                // Reserve space for events
                if (n_events > 0) {
                    list->reserve(n_events);
                }

                // Loop over events
                for (int i = 0; i < n_events; ++i) {

                    // Apply deadtime correction
                    double deadc = obs.deadc(times[i]);
                    if (deadc < 1.0) {
                        if (ran.uniform() > deadc) {
                            continue;
                        }
                    }

                    // Get Monte Carlo event energy from spectral model
                    GEnergy energy = spectral->mc(ebounds.emin(ieng),
                                                  ebounds.emax(ieng),
                                                  times[i],
                                                  ran);

                    // Get Monte Carlo event direction from spatial model
                    GSkyDir dir = spatial()->mc(energy, times[i], ran);

                    // Allocate event
                    GCTAEventAtom event;

                    // Set event attributes
                    event.dir(GCTAInstDir(dir));
                    event.energy(energy);
                    event.time(times[i]);

                    // Append event to list if it falls in ROI
                    if (events->roi().contains(event)) {
                        list->append(event);
                    }

                } // endfor: looped over all events

            } // endfor: looped over all GTIs

            // Free spectral model if required
            if (free_spectral) delete spectral;

        } // endfor: looped over all energy boundaries

    } // endif: model was valid

    // Return
    return list;
}
/***********************************************************************//**
 * @brief Return simulated list of events
 *
 * @param[in] obs Observation.
 * @param[in] ran Random number generator.
 * @return Pointer to list of simulated events (needs to be de-allocated by
 *         client)
 *
 * @exception GException::invalid_argument
 *            Specified observation is not a CTA observation.
 *
 * Draws a sample of events from the background model using a Monte
 * Carlo simulation. The region of interest, the energy boundaries and the
 * good time interval for the sampling will be extracted from the observation
 * argument that is passed to the method. The method also requires a random
 * number generator of type GRan which is passed by reference, hence the
 * state of the random number generator will be changed by the method.
 *
 * The method also applies a deadtime correction using a Monte Carlo process,
 * taking into account temporal deadtime variations. For this purpose, the
 * method makes use of the time dependent GObservation::deadc method.
 *
 * For each event in the returned event list, the sky direction, the nominal
 * coordinates (DETX and DETY), the energy and the time will be set.
 ***************************************************************************/
GCTAEventList* GCTAModelIrfBackground::mc(const GObservation& obs, GRan& ran) const
{
    // Initialise new event list
    GCTAEventList* list = new GCTAEventList;

    // Continue only if model is valid)
    if (valid_model()) {

        // Retrieve CTA observation
        const GCTAObservation* cta = dynamic_cast<const GCTAObservation*>(&obs);
        if (cta == NULL) {
            std::string msg = "Specified observation is not a CTA observation.\n" +
                              obs.print();
            throw GException::invalid_argument(G_MC, msg);
        }

        // Get pointer on CTA IRF response
        const GCTAResponseIrf* rsp = dynamic_cast<const GCTAResponseIrf*>(cta->response());
        if (rsp == NULL) {
            std::string msg = "Specified observation does not contain"
                              " an IRF response.\n" + obs.print();
            throw GException::invalid_argument(G_MC, msg);
        }

        // Retrieve CTA response and pointing
        const GCTAPointing& pnt = cta->pointing();

        // Get pointer to CTA background
        const GCTABackground* bgd = rsp->background();
        if (bgd == NULL) {
            std::string msg = "Specified observation contains no background"
                              " information.\n" + obs.print();
            throw GException::invalid_argument(G_MC, msg);
        }

        // Retrieve event list to access the ROI, energy boundaries and GTIs
        const GCTAEventList* events = dynamic_cast<const GCTAEventList*>(obs.events());
        if (events == NULL) {
            std::string msg = "No CTA event list found in observation.\n" +
                              obs.print();
            throw GException::invalid_argument(G_MC, msg);
        }

        // Get simulation region
        const GCTARoi&  roi     = events->roi();
        const GEbounds& ebounds = events->ebounds();
        const GGti&     gti     = events->gti();

        // Set simulation region for result event list
        list->roi(roi);
        list->ebounds(ebounds);
        list->gti(gti);

        // Create a spectral model that combines the information from the
        // background information and the spectrum provided by the model
        GModelSpectralNodes spectral(bgd->spectrum());
        for (int i = 0; i < spectral.nodes(); ++i) {
            GEnergy energy    = spectral.energy(i);
            double  intensity = spectral.intensity(i);
            double  norm      = m_spectral->eval(energy, events->tstart());
            spectral.intensity(i, norm*intensity);
        }

        // Loop over all energy boundaries
        for (int ieng = 0; ieng < ebounds.size(); ++ieng) {

            // Compute the background rate in model within the energy
            // boundaries from spectral component (units: cts/s).
            // Note that the time here is ontime. Deadtime correction will
            // be done later.
            double rate = spectral.flux(ebounds.emin(ieng), ebounds.emax(ieng));

            // Debug option: dump rate
#if defined(G_DUMP_MC)
            std::cout << "GCTAModelIrfBackground::mc(\"" << name() << "\": ";
            std::cout << "rate=" << rate << " cts/s)" << std::endl;
#endif

            // Loop over all good time intervals
            for (int itime = 0; itime < gti.size(); ++itime) {

                // Get Monte Carlo event arrival times from temporal model
                GTimes times = m_temporal->mc(rate,
                                              gti.tstart(itime),
                                              gti.tstop(itime),
                                              ran);

                // Get number of events
                int n_events = times.size();

                // Reserve space for events
                if (n_events > 0) {
                    list->reserve(n_events);
                }

                // Debug option: provide number of times and initialize
                // statisics
#if defined(G_DUMP_MC)
                std::cout << " Interval " << itime;
                std::cout << " times=" << n_events << std::endl;
                int n_killed_by_deadtime = 0;
                int n_killed_by_roi      = 0;
#endif

                // Loop over events
                for (int i = 0; i < n_events; ++i) {

                    // Apply deadtime correction
                    double deadc = obs.deadc(times[i]);
                    if (deadc < 1.0) {
                        if (ran.uniform() > deadc) {
#if defined(G_DUMP_MC)
                            n_killed_by_deadtime++;
#endif
                            continue;
                        }
                    }

                    // Get Monte Carlo event energy from spectral model
                    GEnergy energy = spectral.mc(ebounds.emin(ieng),
                                                 ebounds.emax(ieng),
                                                 times[i],
                                                 ran);

                    // Get Monte Carlo event direction from spatial model.
                    // This only will set the DETX and DETY coordinates.
                    GCTAInstDir instdir = bgd->mc(energy, times[i], ran);

                    // Derive sky direction from instrument coordinates
                    GSkyDir skydir = pnt.skydir(instdir);

                    // Set sky direction in GCTAInstDir object
                    instdir.dir(skydir);

                    // Allocate event
                    GCTAEventAtom event;

                    // Set event attributes
                    event.dir(instdir);
                    event.energy(energy);
                    event.time(times[i]);

                    // Append event to list if it falls in ROI
                    if (events->roi().contains(event)) {
                        list->append(event);
                    }
#if defined(G_DUMP_MC)
                    else {
                        n_killed_by_roi++;
                    }
#endif

                } // endfor: looped over all events

                // Debug option: provide  statisics
#if defined(G_DUMP_MC)
                std::cout << " Killed by deadtime=";
                std::cout << n_killed_by_deadtime << std::endl;
                std::cout << " Killed by ROI=";
                std::cout << n_killed_by_roi << std::endl;
#endif

            } // endfor: looped over all GTIs

        } // endfor: looped over all energy boundaries

    } // endif: model was valid

    // Return
    return list;
}