LauIsobarDynamics.cc

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// Copyright University of Warwick 2005 - 2013.
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

// Authors:
// Thomas Latham
// John Back
// Paul Harrison

#include <iostream>
#include <iomanip>
#include <fstream>

#include "TFile.h"
#include "TRandom.h"
#include "TSystem.h"

#include "LauAbsResonance.hh"
#include "LauBelleNR.hh"
#include "LauBelleSymNR.hh"
#include "LauConstants.hh"
#include "LauDaughters.hh"
#include "LauEffModel.hh"
#include "LauFitDataTree.hh"
#include "LauGounarisSakuraiRes.hh"
#include "LauIntegrals.hh"
#include "LauIsobarDynamics.hh"
#include "LauKinematics.hh"
#include "LauKMatrixPropagator.hh"
#include "LauKMatrixPropFactory.hh"
#include "LauKMatrixProdPole.hh"
#include "LauKMatrixProdSVP.hh"
#include "LauNRAmplitude.hh"
#include "LauPolNR.hh"
#include "LauPrint.hh"
#include "LauRandom.hh"
#include "LauRelBreitWignerRes.hh"
#include "LauResonanceMaker.hh"

ClassImp(LauIsobarDynamics)


// for Kpipi: only one scfFraction 2D histogram is needed
LauIsobarDynamics::LauIsobarDynamics(LauDaughters* daughters, LauEffModel* effModel, LauEffModel* scfFractionModel) :
        LauAbsDPDynamics(daughters, effModel, scfFractionModel),
        symmetricalDP_(kFALSE),
        integralsDone_(kFALSE),
        intFileName_("integ.dat"),
        m13BinWidth_(0.005),
        m23BinWidth_(0.005),
        m13Sq_(0.0),
        m23Sq_(0.0),
        mPrime_(0.0),
        thPrime_(0.0),
        eff_(1.0),
        scfFraction_(0.0),
        jacobian_(0.0),
        ASq_(0.0),
        evtLike_(0.0),
        iterationsMax_(100000),
        nSigGenLoop_(0),
        aSqMaxSet_(1.25),
        aSqMaxVar_(0.0),
        BelleNRAlpha_(0.0),
        LASSScatteringLength_(0.0),
        LASSEffectiveRange_(0.0),
        LASSResonanceMag_(0.0),
        LASSResonancePhase_(0.0),
        LASSBackgroundMag_(0.0),
        LASSBackgroundPhase_(0.0),
        LASSCutOff_(0.0),
        changeLASSScatteringLength_(kFALSE),
        changeLASSEffectiveRange_(kFALSE),
        changeLASSResonanceMag_(kFALSE),
        changeLASSResonancePhase_(kFALSE),
        changeLASSBackgroundMag_(kFALSE),
        changeLASSBackgroundPhase_(kFALSE),
        changeLASSCutOff_(kFALSE),
        FlatteParameterg1_(0.0),
        FlatteParameterg2_(0.0),
        changeFlatteParameterg1_(kFALSE),
        changeFlatteParameterg2_(kFALSE),
        resBarrierRadius_(4.0),
        parBarrierRadius_(4.0),
        barrierType_( LauAbsResonance::BWPrimeBarrier ),
        flipHelicity_(kTRUE)
{
        // Constructor for the isobar signal model
        if (daughters != 0) {
                symmetricalDP_ = daughters->gotSymmetricalDP();
                typDaug_.push_back(daughters->getTypeDaug1());
                typDaug_.push_back(daughters->getTypeDaug2());
                typDaug_.push_back(daughters->getTypeDaug3());
        }
        sigResonances_.clear();
        kMatrixPropagators_.clear();
        kMatrixPropSet_.clear();
}

// for Kspipi, we need a scfFraction 2D histogram for each tagging category. They are provided by the map.
// Also, we need to know the place that the tagging category of the current event occupies in the data structure inputFitTree
LauIsobarDynamics::LauIsobarDynamics(LauDaughters* daughters, LauEffModel* effModel, LauTagCatScfFractionModelMap scfFractionModel) :
        LauAbsDPDynamics(daughters, effModel, scfFractionModel),
        symmetricalDP_(kFALSE),
        integralsDone_(kFALSE),
        intFileName_("integ.dat"),
        m13BinWidth_(0.005),
        m23BinWidth_(0.005),
        m13Sq_(0.0),
        m23Sq_(0.0),
        mPrime_(0.0),
        thPrime_(0.0),
        eff_(0.0),
        scfFraction_(0.0),
        jacobian_(0.0),
        ASq_(0.0),
        evtLike_(0.0),
        iterationsMax_(100000),
        nSigGenLoop_(0),
        aSqMaxSet_(1.25),
        aSqMaxVar_(0.0),
        BelleNRAlpha_(0.0),
        LASSScatteringLength_(0.0),
        LASSEffectiveRange_(0.0),
        LASSResonanceMag_(0.0),
        LASSResonancePhase_(0.0),
        LASSBackgroundMag_(0.0),
        LASSBackgroundPhase_(0.0),
        LASSCutOff_(0.0),
        changeLASSScatteringLength_(kFALSE),
        changeLASSEffectiveRange_(kFALSE),
        changeLASSResonanceMag_(kFALSE),
        changeLASSResonancePhase_(kFALSE),
        changeLASSBackgroundMag_(kFALSE),
        changeLASSBackgroundPhase_(kFALSE),
        changeLASSCutOff_(kFALSE),
        FlatteParameterg1_(0.0),
        FlatteParameterg2_(0.0),
        changeFlatteParameterg1_(kFALSE),
        changeFlatteParameterg2_(kFALSE),
        resBarrierRadius_(4.0),
        parBarrierRadius_(4.0),
        barrierType_( LauAbsResonance::BWPrimeBarrier ),
        flipHelicity_(kTRUE)
{
        // Constructor for the isobar signal model
        if (daughters != 0) {
                symmetricalDP_ = daughters->gotSymmetricalDP();
                typDaug_.push_back(daughters->getTypeDaug1());
                typDaug_.push_back(daughters->getTypeDaug2());
                typDaug_.push_back(daughters->getTypeDaug3());
        }
        sigResonances_.clear();
        kMatrixPropagators_.clear();
        kMatrixPropSet_.clear();
}

LauIsobarDynamics::~LauIsobarDynamics()
{
}

void LauIsobarDynamics::initialise(const std::vector<LauComplex>& coeffs)
{
        // Check whether we have a valid set of integration constants for
        // the normalisation of the signal likelihood function.
        this->initialiseVectors();

        integralsDone_ = kFALSE;

        // Print summary of what we have so far to screen
        this->initSummary();

        if ( nAmp_ == 0 ) {
                std::cout << "INFO in LauIsobarDynamics::initialise : No contributions to DP model, not performing normalisation integrals." << std::endl;
        } else {

                // We need to calculate the normalisation constants for the
                // Dalitz plot generation/fitting.
                std::cout<<"INFO in LauIsobarDynamics::initialise : Starting special run to generate the integrals for normalising the PDF..."<<std::endl;
                this->calcDPNormalisation();

                // Write the integrals to a file (mainly for debugging purposes)
                this->writeIntegralsFile();
        }


        integralsDone_ = kTRUE;

        std::cout << std::setprecision(10);

        // Calculate and cache the relative normalisations of each resonance _dynamic_ amplitude
        // (e.g. Breit-Wigner contribution, not from the complex amplitude/phase) w.r.t. the
        // total DP amplitude. These are stored in fNorm_[i].
        // The normalisation uses fSqSum[i], which is calculated within the dynamics() function, 
        // which has already been called by the calcDPNomalisation() function above to create the 
        // normalisation integrals. 
        // fSqSum[i] is the event-by-event running total of the dynamical amplitude 
        // squared for a given resonance, i. We require that:
        // |fNorm_[i]|^2 * |fSqSum[i]|^2 = 1,
        // i.e. fNorm_[i] normalises each resonance contribution to give the same number of
        // events in the DP, accounting for the total DP area and the
        // dynamics of the resonance.

        std::cout<<"INFO in LauIsobarDynamics::initialise : Summary of the integrals:"<<std::endl;
        for (UInt_t i = 0; i < nAmp_; i++) {
                fNorm_[i] = 0.0;
                if (fSqSum_[i] > 0.0) {fNorm_[i] = TMath::Sqrt(1.0/(fSqSum_[i]));}
                std::cout<<" fNorm["<<i<<"] = "<<fNorm_[i]<<std::endl;
                std::cout<<" fSqSum["<<i<<"] = "<<fSqSum_[i]<<std::endl;
        }

        for (UInt_t i = 0; i < nAmp_; i++) {    
                for (UInt_t j = 0; j < nAmp_; j++) {
                        std::cout<<" fifjEffSum["<<i<<"]["<<j<<"] = "<<fifjEffSum_[i][j];
                }
                std::cout<<std::endl;
        }

        for (UInt_t i = 0; i < nAmp_; i++) {    
                for (UInt_t j = 0; j < nAmp_; j++) {
                        std::cout<<" fifjSum["<<i<<"]["<<j<<"] = "<<fifjSum_[i][j];
                }
                std::cout<<std::endl;
        }

        // Calculate the initial fit fractions (for later comparison with Toy MC, if required)
        this->updateCoeffs(coeffs);
        this->calcExtraInfo(kTRUE);
        for (UInt_t i = 0; i < nAmp_; i++) {
                for (UInt_t j = i; j < nAmp_; j++) {
                        std::cout<<"INFO in LauIsobarDynamics::initialise : Initial fit fraction for amplitude ("<<i<<","<<j<<") = "<<fitFrac_[i][j].genValue()<<std::endl;
                }
        }

        std::cout<<"INFO in LauIsobarDynamics::initialise : Initial efficiency = "<<meanDPEff_.initValue()<<std::endl;

        std::cout<<"INFO in LauIsobarDynamics::initialise : Initial DPRate = "<<DPRate_.initValue()<<std::endl;
}

void LauIsobarDynamics::initSummary()
{

        UInt_t i(0);
        TString nameP = daughters_->getNameParent();
        TString name1 = daughters_->getNameDaug1();
        TString name2 = daughters_->getNameDaug2();
        TString name3 = daughters_->getNameDaug3();

        std::cout<<"INFO in LauIsobarDynamics::initSummary : We are going to do a DP with "<<nameP<<" going to "<<name1<<" "<<name2<<" "<<name3<<std::endl;

        std::cout<<"                                       : For the following resonance combinations:"<<std::endl;

        std::cout<<"                                       : In tracks 2 and 3:"<<std::endl;
        for (i = 0; i < nAmp_; i++) {
                if (resPairAmp_[i] == 1) {
                        std::cout<<"                                       : "<<resTypAmp_[i]<<" to "<<name2<<", "<< name3<<std::endl;
                }
        }

        std::cout<<std::endl;

        std::cout<<"                                       : In tracks 1 and 3:"<<std::endl;
        for (i = 0; i < nAmp_; i++) {
                if (resPairAmp_[i] == 2) {
                        std::cout<<"                                       : "<<resTypAmp_[i]<<" to "<<name1<<", "<< name3<<std::endl;
                }
        }

        std::cout<<std::endl;

        std::cout<<"                                       : In tracks 1 and 2:"<<std::endl;
        for (i = 0; i < nAmp_; i++) {
                if (resPairAmp_[i] == 3) {
                        std::cout<<"                                       : "<<resTypAmp_[i]<<" to "<<name1<<", "<< name2<<std::endl;
                }
        }

        std::cout<<std::endl;

        for (i = 0; i < nAmp_; i++) {
                if (resPairAmp_[i] == 0) {
                        std::cout<<"                                       : and a non-resonant amplitude."<<std::endl;
                }
        }

        std::cout<<std::endl;
}

void LauIsobarDynamics::initialiseVectors()
{
        fSqSum_.clear();     fSqSum_.resize(nAmp_);
        fifjEffSum_.clear(); fifjEffSum_.resize(nAmp_);
        fifjSum_.clear();    fifjSum_.resize(nAmp_);
        ff_.clear();         ff_.resize(nAmp_);
        fNorm_.clear();      fNorm_.resize(nAmp_);
        fitFrac_.clear();    fitFrac_.resize(nAmp_);

        LauComplex null(0.0, 0.0);

        for (UInt_t i = 0; i < nAmp_; i++) {

                fSqSum_[i] = 0.0; fNorm_[i] = 0.0;
                ff_[i] = null;
                fifjEffSum_[i].resize(nAmp_);
                fifjSum_[i].resize(nAmp_);
                fitFrac_[i].resize(nAmp_);

                for (UInt_t j = 0; j < nAmp_; j++) {
                        fifjEffSum_[i][j] = null;
                        fifjSum_[i][j] = null;
                        fitFrac_[i][j].valueAndRange(0.0, -100.0, 100.0);
                }
        }

        UInt_t nKMatrixProps = kMatrixPropagators_.size();
        extraParameters_.clear();
        extraParameters_.resize( nKMatrixProps );

        for ( UInt_t i = 0; i < nKMatrixProps; ++i ) {
                extraParameters_[i].valueAndRange(0.0, -100.0, 100.0);
        }
}


void LauIsobarDynamics::writeIntegralsFile()
{
        // Routine to end integration calculation for loglike normalisation.
        // This writes out the normalisation integral output into the file named
        // outputFileName.
        std::cout<<"INFO in LauIsobarDynamics::writeIntegralsFile : Writing integral output to integrals file "<<intFileName_.Data()<<std::endl;

        UInt_t i(0), j(0);
        std::ofstream getChar(intFileName_.Data());

        getChar << std::setprecision(10);

        // Write out daughter types (pi, pi0, K, K0s?)
        for (i = 0; i < 3; i++) {    
                getChar << typDaug_[i] << " ";
        }

        // Write out number of resonances in the Dalitz plot model
        getChar << nAmp_ << std::endl;

        // Write out the resonances
        for (i = 0; i < nAmp_; i++) {
                getChar << resTypAmp_[i] << " ";
        }

        getChar << std::endl;

        // Write out the resonance model types (BW, RelBW etc...)
        for (i = 0; i < nAmp_; i++) {
                LauAbsResonance* theResonance = sigResonances_[i];
                Int_t resModelInt = theResonance->getResonanceModel();
                getChar << resModelInt << " ";
        }

        getChar << std::endl;

        // Write out the track pairings for each resonance. This is specified
        // by the resPairAmpInt integer in the addResonance function.
        for (i = 0; i < nAmp_; i++) {
                getChar << resPairAmp_[i] << " ";
        }

        getChar << std::endl;

        // Write out the fSqSum = |ff|^2, where ff = resAmp()
        for (i = 0; i < nAmp_; i++) {
                getChar << fSqSum_[i] << " ";
        }

        getChar << std::endl;

        // Write out the f_i*f_j_conj*eff values = resAmp_i*resAmp_j_conj*eff.
        // Note that only the top half of the i*j "matrix" is required, as it
        // is symmetric w.r.t i, j.
        for (i = 0; i < nAmp_; i++) {
                for (j = i; j < nAmp_; j++) {
                        getChar << fifjEffSum_[i][j] << " ";
                }
        }

        getChar << std::endl;

        // Similar to fifjEffSum, but without the efficiency term included.
        for (i = 0; i < nAmp_; i++) {
                for (j = i; j < nAmp_; j++) {
                        getChar << fifjSum_[i][j] << " ";
                }
        }

        getChar << std::endl;

}

void LauIsobarDynamics::addResonance(const TString& resName, Int_t resPairAmpInt, const TString& resType, Double_t newMass, Double_t newWidth, Int_t newSpin)
{
        // Function to add a resonance in a Dalitz plot.
        // No check is made w.r.t flavour and charge conservation rules, and so
        // the user is responsible for checking the internal consistency of
        // their function statements with these laws. For example, the program
        // will not prevent the user from asking for a rho resonance in a K-pi
        // pair or a K* resonance in a pi-pi pair.
        // However, to assist the user, a summary of the resonant structure requested
        // by the user is printed before the program runs. It is important to check this
        // information when you first define your Dalitz plot model before doing
        // any fitting/generating.
        // Arguments are: resonance name, integer to specify the resonance track pairing
        // (1 => m_23, 2 => m_13, 3 => m_12), i.e. the bachelor track number.
        // The third argument resType specifies whether the resonance is a Breit-Wigner (BW)
        // Relativistic Breit-Wigner (RelBW) or Flatte distribution (Flatte), for example.

        LauAbsResonance *theResonance = 
                resonanceMaker_->getResonance(resName, resPairAmpInt, resType);

        if (theResonance == 0) {
                std::cerr<<"ERROR in LauIsobarDynamics::addResonance : Couldn't create the resonance \""<<resName<<"\""<<std::endl;
                return;
        }

        // Change resonance and lineshape parameters as required.
        if (newMass > 0.0 || newWidth > 0.0 || newSpin > -1) {
                theResonance->changeResonance(newMass, newWidth, newSpin);
        }

        // implement the helicity flip here
        if (flipHelicity_ && daughters_->getCharge(resPairAmpInt) == 0) {         
                if ( daughters_->getChargeParent() == 0 && daughters_->getTypeParent() > 0 ) {
                        theResonance->flipHelicity(kTRUE);
                }
        }

        TString resTypeName(resType);

        // Reset the Blatt-Weisskopf barrier factors as appropriate
        if (!resTypeName.CompareTo("RelBW")) {
                LauRelBreitWignerRes* theRBW = dynamic_cast<LauRelBreitWignerRes*>(theResonance);
                theRBW->setBarrierRadii(resBarrierRadius_, parBarrierRadius_, barrierType_);
        } else if (!resTypeName.CompareTo("GS")) {
                LauGounarisSakuraiRes* theGS = dynamic_cast<LauGounarisSakuraiRes*>(theResonance);
                theGS->setBarrierRadii(resBarrierRadius_, parBarrierRadius_, barrierType_);
        }

        if (changeLASSScatteringLength_ == kTRUE && resTypeName.BeginsWith("LASS") ) {
                theResonance->setResonanceParameter(LASSScatteringLength_, "a");
        }
        if (changeLASSEffectiveRange_ == kTRUE && resTypeName.BeginsWith("LASS") ) {
                theResonance->setResonanceParameter(LASSEffectiveRange_, "r");
        }
        if (changeLASSResonanceMag_ == kTRUE && !resTypeName.CompareTo("LASS") ) {
                theResonance->setResonanceParameter(LASSResonanceMag_, "R");
        }
        if (changeLASSResonancePhase_ == kTRUE && !resTypeName.CompareTo("LASS") ) {
                theResonance->setResonanceParameter(LASSResonancePhase_, "phiR");
        }
        if (changeLASSBackgroundMag_ == kTRUE && !resTypeName.CompareTo("LASS") ) {
                theResonance->setResonanceParameter(LASSBackgroundMag_, "B");
        }
        if (changeLASSBackgroundPhase_ == kTRUE && !resTypeName.CompareTo("LASS") ) {
                theResonance->setResonanceParameter(LASSBackgroundPhase_, "phiB");
        }
        if (changeLASSCutOff_ == kTRUE && resTypeName.BeginsWith("LASS") ) {
                theResonance->setResonanceParameter(LASSCutOff_, "cutOff");
        }

        if (changeFlatteParameterg1_ == kTRUE && !resTypeName.CompareTo("Flatte") ) {
                theResonance->setResonanceParameter(FlatteParameterg1_, "g1");
        }
        if (changeFlatteParameterg2_ == kTRUE && !resTypeName.CompareTo("Flatte") ) {
                theResonance->setResonanceParameter(FlatteParameterg2_, "g2");
        }

        TString resonanceName = theResonance->getResonanceName();

        if ( resonanceName.BeginsWith("BelleNR", TString::kExact) ) {
                LauBelleNR* belleNR = dynamic_cast<LauBelleNR*>(theResonance);
                if (belleNR != 0) {
                        belleNR->setAlpha(BelleNRAlpha_);
                } else {
                        std::cerr<<"ERROR in LauIsobarDynamics::addResonance : Belle non-resonant object is null"<<std::endl;
                }
        } else if ( resonanceName.BeginsWith("BelleSymNR", TString::kExact) ) {
                LauBelleSymNR* belleNR = dynamic_cast<LauBelleSymNR*>(theResonance);
                if (belleNR != 0) {
                        belleNR->initialise(symmetricalDP_, BelleNRAlpha_, resTypeName);
                } else {
                        std::cerr<<"ERROR in LauIsobarDynamics::addResonance : Symmetric Belle non-resonant object is null"<<std::endl;
                }

        } else if ( resonanceName.BeginsWith("PolNR", TString::kExact) ) {
                LauPolNR* polNR = dynamic_cast<LauPolNR*>(theResonance);
                Double_t omega = 0.5*(daughters_->getMassParent()+(1./3)*(daughters_->getMassDaug1()+daughters_->getMassDaug2()+daughters_->getMassDaug3()));
                if (polNR != 0) {
                  polNR->setOmega(omega);
                } else {
                        std::cerr<<"ERROR in LauIsobarDynamics::addResonance : Polynomial non-resonant object is null"<<std::endl;
                }
        }
        // Initialise the resonance model
        theResonance->initialise();

        // Set the resonance name and what track is the bachelor
        resTypAmp_.push_back(resonanceName);
        resIntAmp_.push_back(resonanceMaker_->resTypeInt(resonanceName));

        // Always force the non-resonant amplitude pair to have resPairAmp = 0
        // in case the user chooses the wrong number.
        if (    (resonanceName.BeginsWith("NonReson",   TString::kExact) == kTRUE) || 
                (resonanceName.BeginsWith("BelleSymNR", TString::kExact) == kTRUE) ||
                (resonanceName.BeginsWith("NRModel",    TString::kExact) == kTRUE)) {
                std::cout<<"INFO in LauIsobarDynamics::addResonance : Setting resPairAmp to 0 for "<<resonanceName<<" contribution."<<std::endl;
                resPairAmp_.push_back(0);
        } else {
                resPairAmp_.push_back(resPairAmpInt);
        }

        // Increment the number of resonance amplitudes we have so far
        ++nAmp_;

        // Finally, add the resonance object to the internal array
        sigResonances_.push_back(theResonance);

        std::cout<<"INFO in LauIsobarDynamics::addResonance : Successfully added resonance. Total number of resonances so far = "<<nAmp_<<std::endl;

}

void LauIsobarDynamics::defineKMatrixPropagator(const TString& propName, const TString& paramFileName, Int_t resPairAmpInt, 
                                                Int_t nChannels, Int_t nPoles, Int_t rowIndex)
{
        // Define the K-matrix propagator. The resPairAmpInt integer specifies which mass combination should be used
        // for the invariant mass-squared variable "s". The pole masses and coupling constants are defined in the
        // paramFileName parameter file. The number of channels and poles are defined by the nChannels and nPoles integers, respectively.
        // The integer rowIndex specifies which row of the propagator should be used when 
        // summing over all amplitude channels: S-wave will be the first row, so rowIndex = 1.

        if (rowIndex < 1) {
                std::cerr<<"Error in defineKMatrixPropagator: rowIndex must be > 0 but is equal to "<<rowIndex<<std::endl;
                return;
        }

        TString propagatorName(propName), parameterFile(paramFileName);

        LauKMatrixPropagator* thePropagator = LauKMatrixPropFactory::getInstance()->getPropagator(propagatorName, parameterFile,
                        resPairAmpInt, nChannels,
                        nPoles, rowIndex);
        kMatrixPropagators_[propagatorName] = thePropagator;

}

void LauIsobarDynamics::addKMatrixProdPole(const TString& poleName, const TString& propName, Int_t poleIndex)
{

        // Add a K-matrix production pole term, using the K-matrix propagator given by the propName.
        // Here, poleIndex is the integer specifying the pole number.

        // First, find the K-matrix propagator.
        KMPropMap::iterator mapIter = kMatrixPropagators_.find(propName);
        if (mapIter != kMatrixPropagators_.end()) {

                LauKMatrixPropagator* thePropagator = mapIter->second;

                // Make sure the pole index is valid
                Int_t nPoles = thePropagator->getNPoles();
                if (poleIndex < 1 || poleIndex > nPoles) {
                        std::cerr<<"ERROR in LauIsobarDynamics::addKMatrixProdPole : The pole index "<<poleIndex
                                <<" is not between 1 and "<<nPoles<<". Not adding production pole "<<poleName
                                <<" for K-matrix propagator "<<propName<<std::endl;
                        return;
                }

                // Now add the K-matrix production pole amplitude to the vector of LauAbsResonance pointers.
                Int_t resPairAmpInt = thePropagator->getResPairAmpInt();
                LauAbsResonance* prodPole = new LauKMatrixProdPole(poleName, poleIndex, resPairAmpInt, thePropagator, daughters_);

                resTypAmp_.push_back(poleName);
                resIntAmp_.push_back(0);
                resPairAmp_.push_back(resPairAmpInt);

                nAmp_++;
                sigResonances_.push_back(prodPole);

                // Also store the propName-poleName pair for calculating total fit fractions later on 
                // (avoiding the need to use dynamic casts to check which resonances are of the K-matrix type)
                kMatrixPropSet_[poleName] = propName;

                std::cout<<"INFO in LauIsobarDynamics::addKMatrixProdPole : Successfully added K-matrix production pole term. Total number of resonances so far = "<<nAmp_<<std::endl;

        } else {

                std::cerr<<"ERROR in LauIsobarDynamics::addKMatrixProdPole : The propagator of the name "<<propName
                        <<" could not be found for the production pole "<<poleName<<std::endl;

        }

}


void LauIsobarDynamics::addKMatrixProdSVP(const TString& SVPName, const TString& propName, Int_t channelIndex)
{

        // Add a K-matrix production "slowly-varying part" (SVP) term, using the K-matrix propagator 
        // given by the propName. Here, channelIndex is the integer specifying the channel number.

        // First, find the K-matrix propagator.
        KMPropMap::iterator mapIter = kMatrixPropagators_.find(propName);
        if (mapIter != kMatrixPropagators_.end()) {

                LauKMatrixPropagator* thePropagator = mapIter->second;

                // Make sure the channel index is valid
                Int_t nChannels = thePropagator->getNChannels();
                if (channelIndex < 1 || channelIndex > nChannels) {
                        std::cerr<<"ERROR in LauIsobarDynamics::addKMatrixProdSVP : The channel index "<<channelIndex
                                <<" is not between 1 and "<<nChannels<<". Not adding production slowly-varying part "<<SVPName
                                <<" for K-matrix propagator "<<propName<<std::endl;
                        return;
                }

                // Now add the K-matrix production SVP amplitude to the vector of LauAbsResonance pointers.
                Int_t resPairAmpInt = thePropagator->getResPairAmpInt();
                LauAbsResonance* prodSVP = new LauKMatrixProdSVP(SVPName, channelIndex, resPairAmpInt, thePropagator, daughters_);

                resTypAmp_.push_back(SVPName);
                resIntAmp_.push_back(0);
                resPairAmp_.push_back(resPairAmpInt);

                nAmp_++;
                sigResonances_.push_back(prodSVP);

                // Also store the SVPName-propName pair for calculating total fit fractions later on 
                // (avoiding the need to use dynamic casts to check which resonances are of the K-matrix type)
                kMatrixPropSet_[SVPName] = propName;

                std::cout<<"INFO in LauIsobarDynamics::addKMatrixProdSVP : Successfully added K-matrix production slowly-varying (SVP) term. Total number of resonances so far = "<<nAmp_<<std::endl;

        } else {

                std::cerr<<"ERROR in LauIsobarDynamics::addKMatrixProdSVP : The propagator of the name "<<propName
                         <<" could not be found for the production slowly-varying part "<<SVPName<<std::endl;

        }
}

LauAbsResonance* LauIsobarDynamics::findResonance(const TString& name)
{
        TString testName(name);
        testName.ToLower();
        LauAbsResonance* theResonance(0);

        for (std::vector<LauAbsResonance*>::iterator iter=sigResonances_.begin(); iter!=sigResonances_.end(); ++iter) {
                theResonance = (*iter);
                if (theResonance != 0) {
                        TString resString = theResonance->getResonanceName();
                        resString.ToLower();
                        if (resString.BeginsWith(testName, TString::kExact)) {
                                return theResonance;
                        }
                }
        }

        std::cerr<<"ERROR in LauIsobarDynamics::findResonance : Couldn't find resonance \""<<name<<"\" in the model."<<std::endl;
        return 0;
}

const LauAbsResonance* LauIsobarDynamics::findResonance(const TString& name) const
{
        TString testName(name);
        testName.ToLower();
        const LauAbsResonance* theResonance(0);

        for (std::vector<LauAbsResonance*>::const_iterator iter=sigResonances_.begin(); iter!=sigResonances_.end(); ++iter) {
                theResonance = (*iter);
                if (theResonance != 0) {
                        TString resString = theResonance->getResonanceName();
                        resString.ToLower();
                        if (resString.BeginsWith(testName, TString::kExact)) {
                                return theResonance;
                        }
                }
        }

        std::cerr<<"ERROR in LauIsobarDynamics::findResonance : Couldn't find resonance \""<<name<<"\" in the model."<<std::endl;
        return 0;
}

void LauIsobarDynamics::removeCharge(TString& string) const
{
        Ssiz_t index = string.Index("+");
        if (index != -1) {
                string.Remove(index,1);
        }
        index = string.Index("-");
        if (index != -1) {
                string.Remove(index,1);
        }
}

void LauIsobarDynamics::changeResonance(const TString& resName, Double_t newMass, Double_t newWidth, Int_t newSpin)
{
        // Change the mass, width or spin of a resonance.

        if (newMass > 0.0 || newWidth > 0.0 || newSpin > -1) {
                std::cerr<<"ERROR in LauIsobarDynamics::changeResonance : mass, width and spin parameters all out of range."<<std::endl;
                return;
        }

        LauAbsResonance* theRes = this->findResonance(resName);
        if (theRes != 0) {
                theRes->changeResonance(newMass, newWidth, newSpin);
        }

}

void LauIsobarDynamics::calcDPNormalisation()
{
        // Use Gauss-Legendre quadrature integration

        // Get the rectangle that encloses the DP
        Double_t minm13 = kinematics_->getm13Min();
        Double_t maxm13 = kinematics_->getm13Max();
        Double_t minm23 = kinematics_->getm23Min();
        Double_t maxm23 = kinematics_->getm23Max();
        Double_t minm12 = kinematics_->getm12Min();
        Double_t maxm12 = kinematics_->getm12Max();

        // Find out whether we have narrow resonances in the DP (defined here as width < 20 MeV).
        std::multimap<Double_t,Double_t> m13NarrowRes;
        std::multimap<Double_t,Double_t> m23NarrowRes;
        std::multimap<Double_t,Double_t> m12NarrowRes;
        for ( std::vector<LauAbsResonance*>::const_iterator iter = sigResonances_.begin(); iter != sigResonances_.end(); ++iter ) {
                Double_t width = (*iter)->getWidth();
                if ( width > 0.020 || width == 0.0 ) { continue; }
                Double_t mass = (*iter)->getMass();
                Int_t pair = (*iter)->getPairInt();
                TString name = (*iter)->getResonanceName();
                std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : Found narrow resonance: "<<name<<", mass = "<<mass<<", width = "<<width<<", pair int = "<<pair<<std::endl;
                if ( pair == 1 ) {
                        if ( mass < minm23 || mass > maxm23 ){ continue; }
                        m23NarrowRes.insert( std::make_pair(width,mass) );
                } else if ( pair == 2 ) {
                        if ( mass < minm13 || mass > maxm13 ){ continue; }
                        m13NarrowRes.insert( std::make_pair(width,mass) );
                } else if ( pair == 3 ) {
                        if ( mass < minm12 || mass > maxm12 ){ continue; }
                        m12NarrowRes.insert( std::make_pair(width,mass) );
                } else {
                        std::cerr<<"WARNING in LauIsobarDynamics::calcDPNormalisation : strange pair integer, "<<pair<<", for resonance \""<<(*iter)->getResonanceName()<<std::endl;
                }
        }

        // Find the narrowest resonance in each mass pairing
        const Bool_t e12 = m12NarrowRes.empty();
        const Bool_t e13 = m13NarrowRes.empty();
        const Bool_t e23 = m23NarrowRes.empty();
        //const UInt_t s12 = e12 ? 0 : m12NarrowRes.size();
        const UInt_t s13 = e13 ? 0 : m13NarrowRes.size();
        const UInt_t s23 = e23 ? 0 : m23NarrowRes.size();
        const Double_t w12 = e12 ? DBL_MAX : m12NarrowRes.begin()->first / 100.0;
        const Double_t w13 = e13 ? DBL_MAX : m13NarrowRes.begin()->first / 100.0;
        const Double_t w23 = e23 ? DBL_MAX : m23NarrowRes.begin()->first / 100.0;

        // Start off with default bin width (5 MeV)
        Double_t m13BinWidth = m13BinWidth_;
        Double_t m23BinWidth = m23BinWidth_;

        // Depending on how many narrow resonances we have and where they
        // are we adopt different approaches
        if ( e12 && e13 && e23 ) {
                // If we have no narrow resonances just integrate the whole
                // DP with the standard bin widths
                std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : No narrow resonances found, integrating over whole Dalitz plot..."<<std::endl;
                this->calcDPPartialIntegral(minm13, maxm13, minm23, maxm23, m13BinWidth, m23BinWidth);
        } else if ( ! e12 ) {
                // If we have a narrow resonance on the diagonal then we'll have to
                // just use a narrow bin width over the whole DP (1/10 of the width
                // of the narrowest resonance in any mass pair)
                m13BinWidth = m23BinWidth = 10.0*TMath::Min( w12, TMath::Min( w13, w23 ) );
                std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : One or more narrow resonances found in m12, integrating over whole Dalitz plot with bin width of "<<m13BinWidth<<" GeV/c2..."<<std::endl;
                this->calcDPPartialIntegral(minm13, maxm13, minm23, maxm23, m13BinWidth, m23BinWidth);
        } else if ( s13==1 && e23 ) {
                // We have a single narrow resonance in m13
                // Divide the plot into 3 regions: the resonance band and
                // the two areas either side.
                Double_t mass = m13NarrowRes.begin()->second;
                Double_t width = m13NarrowRes.begin()->first;
                Double_t resMin = mass - 5.0*width;
                Double_t resMax = mass + 5.0*width;
                // if the resonance is close to threshold just go from
                // threshold to resMax, otherwise treat threshold to resMin
                // as a separate region
                if ( resMin < (minm13+50.0*m13BinWidth_) ) {
                        std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : One narrow resonance found in m13, close to threshold, dividing Dalitz plot into two regions..."<<std::endl;
                        this->calcDPPartialIntegral(resMax, maxm13, minm23, maxm23, m13BinWidth, m23BinWidth);
                        m13BinWidth = w13;
                        this->calcDPPartialIntegral(minm13, resMax, minm23, maxm23, m13BinWidth, m23BinWidth);
                } else {
                        std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : One narrow resonance found in m13, dividing Dalitz plot into three regions..."<<std::endl;
                        this->calcDPPartialIntegral(minm13, resMin, minm23, maxm23, m13BinWidth, m23BinWidth);
                        this->calcDPPartialIntegral(resMax, maxm13, minm23, maxm23, m13BinWidth, m23BinWidth);
                        m13BinWidth = w13;
                        this->calcDPPartialIntegral(resMin, resMax, minm23, maxm23, m13BinWidth, m23BinWidth);
                }
        } else if ( s13==2 && e23 ) {
                // We have a two narrow resonances in m13
                // Divide the plot into 5 regions: the resonance bands,
                // the two areas either side and the area in between.
                std::multimap<Double_t,Double_t> massordered;
                for ( std::map<Double_t,Double_t>::const_iterator iter = m13NarrowRes.begin(); iter != m13NarrowRes.end(); ++iter ) {
                        massordered.insert( std::make_pair( iter->second, iter->first ) );
                }
                Double_t res1Mass = massordered.begin()->first;
                Double_t res1Width = massordered.begin()->second;
                Double_t res1Min = res1Mass - 5.0*res1Width;
                Double_t res1Max = res1Mass + 5.0*res1Width;
                Double_t res2Mass = (++(massordered.begin()))->first;
                Double_t res2Width = (++(massordered.begin()))->second;
                Double_t res2Min = res2Mass - 5.0*res2Width;
                Double_t res2Max = res2Mass + 5.0*res2Width;
                // if the resonance is close to threshold just go from
                // threshold to resMax, otherwise treat threshold to resMin
                // as a separate region
                if ( res1Min < (minm13+50.0*m13BinWidth_) ) {
                        if ( res1Max > res2Min ) {
                                std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : Two narrow resonances found in m13, both close to threshold, dividing Dalitz plot into two regions..."<<std::endl;
                                this->calcDPPartialIntegral(res2Max, maxm13, minm23, maxm23, m13BinWidth, m23BinWidth);
                                m13BinWidth = TMath::Min(res1Width,res2Width)/100.0;
                                this->calcDPPartialIntegral(minm13, res2Max, minm23, maxm23, m13BinWidth, m23BinWidth);
                        } else {
                                std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : Two narrow resonances found in m13, one close to threshold, dividing Dalitz plot into four regions..."<<std::endl;
                                this->calcDPPartialIntegral(res1Max, res2Min, minm23, maxm23, m13BinWidth, m23BinWidth);
                                this->calcDPPartialIntegral(res2Max, maxm13, minm23, maxm23, m13BinWidth, m23BinWidth);
                                m13BinWidth = res1Width/100.0;
                                this->calcDPPartialIntegral(minm13, res1Max, minm23, maxm23, m13BinWidth, m23BinWidth);
                                m13BinWidth = res2Width/100.0;
                                this->calcDPPartialIntegral(res2Min, res2Max, minm23, maxm23, m13BinWidth, m23BinWidth);
                        }
                } else {
                        if ( res1Max > res2Min ) {
                                std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : Two narrow resonances found close together in m13, dividing Dalitz plot into three regions..."<<std::endl;
                                this->calcDPPartialIntegral(minm13, res1Min, minm23, maxm23, m13BinWidth, m23BinWidth);
                                this->calcDPPartialIntegral(res2Max, maxm13, minm23, maxm23, m13BinWidth, m23BinWidth);
                                m13BinWidth = TMath::Min(res1Width,res2Width)/100.0;
                                this->calcDPPartialIntegral(res1Min, res2Max, minm23, maxm23, m13BinWidth, m23BinWidth);
                        } else {
                                std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : Two narrow resonances found in m13, dividing Dalitz plot into five regions..."<<std::endl;
                                this->calcDPPartialIntegral(minm13, res1Min, minm23, maxm23, m13BinWidth, m23BinWidth);
                                this->calcDPPartialIntegral(res1Max, res2Min, minm23, maxm23, m13BinWidth, m23BinWidth);
                                this->calcDPPartialIntegral(res2Max, maxm13, minm23, maxm23, m13BinWidth, m23BinWidth);
                                m13BinWidth = res1Width/100.0;
                                this->calcDPPartialIntegral(res1Min, res1Max, minm23, maxm23, m13BinWidth, m23BinWidth);
                                m13BinWidth = res2Width/100.0;
                                this->calcDPPartialIntegral(res2Min, res2Max, minm23, maxm23, m13BinWidth, m23BinWidth);
                        }
                }
        } else if ( s23==1 && e13 ) {
                // We have a single narrow resonance in m23
                // Divide the plot into 3 regions: the resonance band and
                // the two areas either side.
                Double_t mass = m23NarrowRes.begin()->second;
                Double_t width = m23NarrowRes.begin()->first;
                Double_t resMin = mass - 5.0*width;
                Double_t resMax = mass + 5.0*width;
                // if the resonance is close to threshold just go from
                // threshold to resMax, otherwise treat threshold to resMin
                // as a separate region
                if ( resMin < (minm23+50.0*m23BinWidth_) ) {
                        std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : One narrow resonance found in m23, close to threshold, dividing Dalitz plot into two regions..."<<std::endl;
                        this->calcDPPartialIntegral(minm13, maxm13, resMax, maxm23, m13BinWidth, m23BinWidth);
                        m23BinWidth = w23;
                        this->calcDPPartialIntegral(minm13, maxm13, minm23, resMax, m13BinWidth, m23BinWidth);
                } else {
                        std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : One narrow resonance found in m23, dividing Dalitz plot into three regions..."<<std::endl;
                        this->calcDPPartialIntegral(minm13, maxm13, minm23, resMin, m13BinWidth, m23BinWidth);
                        this->calcDPPartialIntegral(minm13, maxm13, resMax, maxm23, m13BinWidth, m23BinWidth);
                        m23BinWidth = w23;
                        this->calcDPPartialIntegral(minm13, maxm13, resMin, resMax, m13BinWidth, m23BinWidth);
                }
        } else if ( s23==2 && e13 ) {
                // We have a two narrow resonances in m23
                // Divide the plot into 5 regions: the resonance bands,
                // the two areas either side and the area in between.
                std::multimap<Double_t,Double_t> massordered;
                for ( std::map<Double_t,Double_t>::const_iterator iter = m23NarrowRes.begin(); iter != m23NarrowRes.end(); ++iter ) {
                        massordered.insert( std::make_pair( iter->second, iter->first ) );
                }
                Double_t res1Mass = massordered.begin()->first;
                Double_t res1Width = massordered.begin()->second;
                Double_t res1Min = res1Mass - 5.0*res1Width;
                Double_t res1Max = res1Mass + 5.0*res1Width;
                Double_t res2Mass = (++(massordered.begin()))->first;
                Double_t res2Width = (++(massordered.begin()))->second;
                Double_t res2Min = res2Mass - 5.0*res2Width;
                Double_t res2Max = res2Mass + 5.0*res2Width;
                // if the resonance is close to threshold just go from
                // threshold to resMax, otherwise treat threshold to resMin
                // as a separate region
                if ( res1Min < (minm23+50.0*m23BinWidth_) ) {
                        if ( res1Max > res2Min ) {
                                std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : Two narrow resonances found in m23, both close to threshold, dividing Dalitz plot into two regions..."<<std::endl;
                                this->calcDPPartialIntegral(minm13, maxm13, res2Max, maxm23, m13BinWidth, m23BinWidth);
                                m23BinWidth = TMath::Min(res1Width,res2Width)/100.0;
                                this->calcDPPartialIntegral(minm13, maxm13, minm23, res2Max, m13BinWidth, m23BinWidth);
                        } else {
                                std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : Two narrow resonances found in m23, one close to threshold, dividing Dalitz plot into four regions..."<<std::endl;
                                this->calcDPPartialIntegral(minm13, maxm13, res1Max, res2Min, m13BinWidth, m23BinWidth);
                                this->calcDPPartialIntegral(minm13, maxm13, res2Max, maxm23, m13BinWidth, m23BinWidth);
                                m23BinWidth = res1Width/100.0;
                                this->calcDPPartialIntegral(minm13, maxm13, minm23, res1Max, m13BinWidth, m23BinWidth);
                                m23BinWidth = res2Width/100.0;
                                this->calcDPPartialIntegral(minm13, maxm13, res2Min, res2Max, m13BinWidth, m23BinWidth);
                        }
                } else {
                        if ( res1Max > res2Min ) {
                                std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : Two narrow resonances found close together in m23, dividing Dalitz plot into three regions..."<<std::endl;
                                this->calcDPPartialIntegral(minm13, maxm13, minm23, res1Min, m13BinWidth, m23BinWidth);
                                this->calcDPPartialIntegral(minm13, maxm13, res2Max, maxm23, m13BinWidth, m23BinWidth);
                                m23BinWidth = TMath::Min(res1Width,res2Width)/100.0;
                                this->calcDPPartialIntegral(minm13, maxm13, res1Min, res2Max, m13BinWidth, m23BinWidth);
                        } else {
                                std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : Two narrow resonances found in m23, dividing Dalitz plot into five regions..."<<std::endl;
                                this->calcDPPartialIntegral(minm13, maxm13, minm23, res1Min, m13BinWidth, m23BinWidth);
                                this->calcDPPartialIntegral(minm13, maxm13, res1Max, res2Min, m13BinWidth, m23BinWidth);
                                this->calcDPPartialIntegral(minm13, maxm13, res2Max, maxm23, m13BinWidth, m23BinWidth);
                                m23BinWidth = res1Width/100.0;
                                this->calcDPPartialIntegral(minm13, maxm13, res1Min, res1Max, m13BinWidth, m23BinWidth);
                                m23BinWidth = res2Width/100.0;
                                this->calcDPPartialIntegral(minm13, maxm13, res2Min, res2Max, m13BinWidth, m23BinWidth);
                        }
                }
        } else if ( s13==1 && s23==1 ) {
                // We have a single narrow resonance in both m13 and m23
                // Divide the plot into 9 regions: the point where the
                // resonance bands cross, the four other parts of the bands
                // and the four remaining areas of the DP.
                Double_t mass23 = m23NarrowRes.begin()->second;
                Double_t width23 = m23NarrowRes.begin()->first;
                Double_t resMin23 = mass23 - 5.0*width23;
                Double_t resMax23 = mass23 + 5.0*width23;
                Double_t mass13 = m13NarrowRes.begin()->second;
                Double_t width13 = m13NarrowRes.begin()->first;
                Double_t resMin13 = mass13 - 5.0*width13;
                Double_t resMax13 = mass13 + 5.0*width13;
                // if either resonance is close to threshold just go from
                // threshold to resMax, otherwise treat threshold to resMin
                // as a separate region
                if ( resMin13 < (minm13+50.0*m13BinWidth_) && resMin23 < (minm23+50.0*m23BinWidth_) ) {
                        std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : One narrow resonance found in m13 and one in m23, both close to threshold, dividing Dalitz plot into four regions..."<<std::endl;
                        m13BinWidth = m13BinWidth_;
                        m23BinWidth = m23BinWidth_;
                        this->calcDPPartialIntegral(resMax13, maxm13, resMax23, maxm23, m13BinWidth, m23BinWidth);
                        m13BinWidth = m13BinWidth_;
                        m23BinWidth = w23;
                        this->calcDPPartialIntegral(resMax13, maxm13, minm23, resMax23, m13BinWidth, m23BinWidth);
                        m13BinWidth = w13;
                        m23BinWidth = m23BinWidth_;
                        this->calcDPPartialIntegral(minm13, resMax13, resMax23, maxm23, m13BinWidth, m23BinWidth);
                        m13BinWidth = w13;
                        m23BinWidth = w23;
                        this->calcDPPartialIntegral(minm13, resMax13, minm23, resMax23, m13BinWidth, m23BinWidth);
                } else if ( resMin13 < (minm13+50.0*m13BinWidth_) ) {
                        std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : One narrow resonance found in m13, close to threshold, and one in m23, not close to threshold, dividing Dalitz plot into six regions..."<<std::endl;
                        this->calcDPPartialIntegral(resMax13, maxm13, minm23, resMin23, m13BinWidth, m23BinWidth);
                        this->calcDPPartialIntegral(resMax13, maxm13, resMax23, maxm23, m13BinWidth, m23BinWidth);
                        m13BinWidth = m13BinWidth_;
                        m23BinWidth = w23;
                        this->calcDPPartialIntegral(resMax13, maxm13, resMin23, resMax23, m13BinWidth, m23BinWidth);
                        m13BinWidth = w13;
                        m23BinWidth = m23BinWidth_;
                        this->calcDPPartialIntegral(minm13, resMax13, minm23, resMin23, m13BinWidth, m23BinWidth);
                        this->calcDPPartialIntegral(minm13, resMax13, resMax23, maxm23, m13BinWidth, m23BinWidth);
                        m13BinWidth = w13;
                        m23BinWidth = w23;
                        this->calcDPPartialIntegral(minm13, resMax13, resMin23, resMax23, m13BinWidth, m23BinWidth);
                } else if ( resMin23 < (minm23+50.0*m23BinWidth_) ) {
                        std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : One narrow resonance found in m23, close to threshold, and one in m13, not close to threshold, dividing Dalitz plot into six regions..."<<std::endl;
                        this->calcDPPartialIntegral(minm13, resMin13, resMax23, maxm23, m13BinWidth, m23BinWidth);
                        this->calcDPPartialIntegral(resMax13, maxm13, resMax23, maxm23, m13BinWidth, m23BinWidth);
                        m13BinWidth = m13BinWidth_;
                        m23BinWidth = w23;
                        this->calcDPPartialIntegral(minm13, resMin13, minm23, resMax23, m13BinWidth, m23BinWidth);
                        this->calcDPPartialIntegral(resMax13, maxm13, minm23, resMax23, m13BinWidth, m23BinWidth);
                        m13BinWidth = w13;
                        m23BinWidth = m23BinWidth_;
                        this->calcDPPartialIntegral(resMin13, resMax13, resMax23, maxm23, m13BinWidth, m23BinWidth);
                        m13BinWidth = w13;
                        m23BinWidth = w23;
                        this->calcDPPartialIntegral(resMin13, resMax13, minm23, resMax23, m13BinWidth, m23BinWidth);
                } else {
                        std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : One narrow resonance found in both m13 and m23, neither close to threshold, dividing Dalitz plot into nine regions..."<<std::endl;
                        this->calcDPPartialIntegral(minm13, resMin13, minm23, resMin23, m13BinWidth, m23BinWidth);
                        this->calcDPPartialIntegral(minm13, resMin13, resMax23, maxm23, m13BinWidth, m23BinWidth);
                        this->calcDPPartialIntegral(resMax13, maxm13, minm23, resMin23, m13BinWidth, m23BinWidth);
                        this->calcDPPartialIntegral(resMax13, maxm13, resMax23, maxm23, m13BinWidth, m23BinWidth);
                        m13BinWidth = m13BinWidth_;
                        m23BinWidth = w23;
                        this->calcDPPartialIntegral(minm13, resMin13, resMin23, resMax23, m13BinWidth, m23BinWidth);
                        this->calcDPPartialIntegral(resMax13, maxm13, resMin23, resMax23, m13BinWidth, m23BinWidth);
                        m13BinWidth = w13;
                        m23BinWidth = m23BinWidth_;
                        this->calcDPPartialIntegral(resMin13, resMax13, minm23, resMin23, m13BinWidth, m23BinWidth);
                        this->calcDPPartialIntegral(resMin13, resMax13, resMax23, maxm23, m13BinWidth, m23BinWidth);
                        m13BinWidth = w13;
                        m23BinWidth = w23;
                        this->calcDPPartialIntegral(resMin13, resMax13, resMin23, resMax23, m13BinWidth, m23BinWidth);
                }
        } else if ( e23 && s13>1 ) {
                // We have multiple narrow resonances in m13 only.
                // Divide the plot into 2 regions: threshold to the most
                // massive of the narrow resonances, and the rest
                std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : Multiple narrow resonances found in m13, dividing Dalitz plot into two regions..."<<std::endl;
                Double_t mass = 0.0;
                Double_t width = 0.0;
                for ( std::map<Double_t,Double_t>::const_iterator iter = m13NarrowRes.begin(); iter != m13NarrowRes.end(); ++iter ) {
                        if ( mass < iter->second ) {
                                mass = iter->second;
                                width = iter->first;
                        }
                }
                Double_t resMax = mass + 5.0*width;
                this->calcDPPartialIntegral(resMax, maxm13, minm23, maxm23, m13BinWidth, m23BinWidth);
                m13BinWidth = w13;
                this->calcDPPartialIntegral(minm13, resMax, minm23, maxm23, m13BinWidth, m23BinWidth);
        } else if ( e13 && s23>1 ) {
                // We have multiple narrow resonances in m23 only.
                // Divide the plot into 2 regions: threshold to the most
                // massive of the narrow resonances, and the rest
                std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : Multiple narrow resonances found in m23, dividing Dalitz plot into two regions..."<<std::endl;
                Double_t mass = 0.0;
                Double_t width = 0.0;
                for ( std::map<Double_t,Double_t>::const_iterator iter = m23NarrowRes.begin(); iter != m23NarrowRes.end(); ++iter ) {
                        if ( mass < iter->second ) {
                                mass = iter->second;
                                width = iter->first;
                        }
                }
                Double_t resMax = mass + 5.0*width;
                this->calcDPPartialIntegral(minm13, maxm13, resMax, maxm23, m13BinWidth, m23BinWidth);
                m23BinWidth = w23;
                this->calcDPPartialIntegral(minm13, maxm13, minm23, resMax, m13BinWidth, m23BinWidth);
        } else if ( s13==1 && s23>1 ) {
                // We've got a single narrow resonance in m13 and multiple
                // narrow resonances in m23.  Divide the plot into 6 regions.
                Double_t mass23 = 0.0;
                Double_t width23 = 0.0;
                for ( std::map<Double_t,Double_t>::const_iterator iter = m23NarrowRes.begin(); iter != m23NarrowRes.end(); ++iter ) {
                        if ( mass23 < iter->second ) {
                                mass23 = iter->second;
                                width23 = iter->first;
                        }
                }
                Double_t resMax23 = mass23 + 5.0*width23;
                Double_t mass13 = m13NarrowRes.begin()->second;
                Double_t width13 = m13NarrowRes.begin()->first;
                Double_t resMin13 = mass13 - 5.0*width13;
                Double_t resMax13 = mass13 + 5.0*width13;
                // if the m13 resonance is close to threshold just go from
                // threshold to resMax, otherwise treat threshold to resMin
                // as a separate region
                if ( resMin13 < (minm13+50.0*m13BinWidth_) ) {
                        std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : Multiple narrow resonances found in m23 and one in m13, close to threshold, dividing Dalitz plot into four regions..."<<std::endl;
                        m13BinWidth = m13BinWidth_;
                        m23BinWidth = m23BinWidth_;
                        this->calcDPPartialIntegral(resMax13, maxm13, resMax23, maxm23, m13BinWidth, m23BinWidth);
                        m13BinWidth = m13BinWidth_;
                        m23BinWidth = w23;
                        this->calcDPPartialIntegral(resMax13, maxm13, minm23, resMax23, m13BinWidth, m23BinWidth);
                        m13BinWidth = w13;
                        m23BinWidth = m23BinWidth_;
                        this->calcDPPartialIntegral(minm13, resMax13, resMax23, maxm23, m13BinWidth, m23BinWidth);
                        m13BinWidth = w13;
                        m23BinWidth = w23;
                        this->calcDPPartialIntegral(minm13, resMax13, minm23, resMax23, m13BinWidth, m23BinWidth);
                } else {
                        std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : Multiple narrow resonances found in m23 and one in m13, not close to threshold, dividing Dalitz plot into six regions..."<<std::endl;
                        m13BinWidth = m13BinWidth_;
                        m23BinWidth = m23BinWidth_;
                        this->calcDPPartialIntegral(minm13, resMin13, resMax23, maxm23, m13BinWidth, m23BinWidth);
                        this->calcDPPartialIntegral(resMax13, maxm13, resMax23, maxm23, m13BinWidth, m23BinWidth);
                        m13BinWidth = m13BinWidth_;
                        m23BinWidth = w23;
                        this->calcDPPartialIntegral(minm13, resMin13, minm23, resMax23, m13BinWidth, m23BinWidth);
                        this->calcDPPartialIntegral(resMax13, maxm13, minm23, resMax23, m13BinWidth, m23BinWidth);
                        m13BinWidth = w13;
                        m23BinWidth = m23BinWidth_;
                        this->calcDPPartialIntegral(resMin13, resMax13, resMax23, maxm23, m13BinWidth, m23BinWidth);
                        m13BinWidth = w13;
                        m23BinWidth = w23;
                        this->calcDPPartialIntegral(resMin13, resMax13, minm23, resMax23, m13BinWidth, m23BinWidth);
                }
        } else if ( s13>1 && s23==1 ) {
                // We've got a single narrow resonance in m23 and multiple
                // narrow resonances in m13.  Divide the plot into 6 regions.
                Double_t mass13 = 0.0;
                Double_t width13 = 0.0;
                for ( std::map<Double_t,Double_t>::const_iterator iter = m13NarrowRes.begin(); iter != m13NarrowRes.end(); ++iter ) {
                        if ( mass13 < iter->second ) {
                                mass13 = iter->second;
                                width13 = iter->first;
                        }
                }
                Double_t resMax13 = mass13 + 5.0*width13;
                Double_t mass23 = m23NarrowRes.begin()->second;
                Double_t width23 = m23NarrowRes.begin()->first;
                Double_t resMin23 = mass23 - 5.0*width23;
                Double_t resMax23 = mass23 + 5.0*width23;
                // if the m23 resonance is close to threshold just go from
                // threshold to resMax, otherwise treat threshold to resMin
                // as a separate region
                if ( resMin23 < (minm23+50.0*m23BinWidth_) ) {
                        std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : Multiple narrow resonances found in m13 and one in m23, close to threshold, dividing Dalitz plot into four regions..."<<std::endl;
                        m13BinWidth = m13BinWidth_;
                        m23BinWidth = m23BinWidth_;
                        this->calcDPPartialIntegral(resMax13, maxm13, resMax23, maxm23, m13BinWidth, m23BinWidth);
                        m13BinWidth = m13BinWidth_;
                        m23BinWidth = w23;
                        this->calcDPPartialIntegral(resMax13, maxm13, minm23, resMax23, m13BinWidth, m23BinWidth);
                        m13BinWidth = w13;
                        m23BinWidth = m23BinWidth_;
                        this->calcDPPartialIntegral(minm13, resMax13, resMax23, maxm23, m13BinWidth, m23BinWidth);
                        m13BinWidth = w13;
                        m23BinWidth = w23;
                        this->calcDPPartialIntegral(minm13, resMax13, minm23, resMax23, m13BinWidth, m23BinWidth);
                } else {
                        std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : Multiple narrow resonances found in m13 and one in m23, not close to threshold, dividing Dalitz plot into six regions..."<<std::endl;
                        this->calcDPPartialIntegral(resMax13, maxm13, minm23, resMin23, m13BinWidth, m23BinWidth);
                        this->calcDPPartialIntegral(resMax13, maxm13, resMax23, maxm23, m13BinWidth, m23BinWidth);
                        m13BinWidth = m13BinWidth_;
                        m23BinWidth = w23;
                        this->calcDPPartialIntegral(resMax13, maxm13, resMin23, resMax23, m13BinWidth, m23BinWidth);
                        m13BinWidth = w13;
                        m23BinWidth = m23BinWidth_;
                        this->calcDPPartialIntegral(minm13, resMax13, minm23, resMin23, m13BinWidth, m23BinWidth);
                        this->calcDPPartialIntegral(minm13, resMax13, resMax23, maxm23, m13BinWidth, m23BinWidth);
                        m13BinWidth = w13;
                        m23BinWidth = w23;
                        this->calcDPPartialIntegral(minm13, resMax13, resMin23, resMax23, m13BinWidth, m23BinWidth);
                }
        } else {
                // We've got multiple narrow resonances in both m13 and m23.
                // Divide the plot into 4 regions.
                std::cout<<"INFO in LauIsobarDynamics::calcDPNormalisation : Multiple narrow resonances found in both m13 and m23, dividing Dalitz plot into four regions..."<<std::endl;
                Double_t mass13 = 0.0;
                Double_t width13 = 0.0;
                for ( std::map<Double_t,Double_t>::const_iterator iter = m13NarrowRes.begin(); iter != m13NarrowRes.end(); ++iter ) {
                        if ( mass13 < iter->second ) {
                                mass13 = iter->second;
                                width13 = iter->first;
                        }
                }
                Double_t resMax13 = mass13 + 5.0*width13;

                Double_t mass23 = 0.0;
                Double_t width23 = 0.0;
                for ( std::map<Double_t,Double_t>::const_iterator iter = m23NarrowRes.begin(); iter != m23NarrowRes.end(); ++iter ) {
                        if ( mass23 < iter->second ) {
                                mass23 = iter->second;
                                width23 = iter->first;
                        }
                }
                Double_t resMax23 = mass23 + 5.0*width23;

                m13BinWidth = m13BinWidth_;
                m23BinWidth = m23BinWidth_;
                this->calcDPPartialIntegral(resMax13, maxm13, resMax23, maxm23, m13BinWidth, m23BinWidth);
                m13BinWidth = m13BinWidth_;
                m23BinWidth = w23;
                this->calcDPPartialIntegral(resMax13, maxm13, minm23, resMax23, m13BinWidth, m23BinWidth);
                m13BinWidth = w13;
                m23BinWidth = m23BinWidth_;
                this->calcDPPartialIntegral(minm13, resMax13, resMax23, maxm23, m13BinWidth, m23BinWidth);
                m13BinWidth = w13;
                m23BinWidth = w23;
                this->calcDPPartialIntegral(minm13, resMax13, minm23, resMax23, m13BinWidth, m23BinWidth);
        }
}

void LauIsobarDynamics::setIntegralBinWidths(Double_t m13BinWidth, Double_t m23BinWidth)
{
        // Specify whether we're going to use Gauss-Legendre integration to calculate the normalisation
        // integrals, and the bin widths we require for the m13 and m23 axes. Note that the integration
        // is done over m13, m23 space, with the appropriate Jacobian applied, and not m13^2, m23^2 space.
        // The default bin widths in m13 and m23 space are 5 MeV.

        m13BinWidth_ = m13BinWidth;
        m23BinWidth_ = m23BinWidth;
}

void LauIsobarDynamics::calcDPPartialIntegral(Double_t minm13, Double_t maxm13, Double_t minm23, Double_t maxm23, 
                Double_t m13BinWidth, Double_t m23BinWidth)
{
        // Calculate the total DP area, as well as finding the normalisation terms for
        // the signal resonances

        Int_t i(0), j(0);
        Double_t precision(1e-6);

        Double_t meanm13 = 0.5*(minm13 + maxm13);
        Double_t rangem13 = maxm13 - minm13;
        Double_t halfRangem13 = 0.5*rangem13;

        Double_t meanm23 = 0.5*(minm23 + maxm23);
        Double_t rangem23 = maxm23 - minm23;
        Double_t halfRangem23 = 0.5*rangem23;

        Double_t intFactor = halfRangem13*halfRangem23;

        // Choose smallest of mass ranges to set number of bins, given specified bin width
        Int_t nm13Points = static_cast<Int_t>((rangem13/m13BinWidth));
        Int_t nm23Points = static_cast<Int_t>((rangem23/m23BinWidth));

        // Avoid integral if we have no points in either x or y space
        if (nm13Points == 0 || nm23Points == 0) {return;}

        std::cout<<"INFO in LauIsobarDynamics::calcDPPartialIntegral : nm13Points = "<<nm13Points<<", nm23Points = "<<nm23Points<<std::endl;
        std::cout<<"                                                 : m13BinWidth = "<<m13BinWidth<<", m23BinWidth = "<<m23BinWidth<<std::endl;
        std::cout<<"                                                 : Integrating over m13 = "<<minm13<<" to "<<maxm13<<", m23 = "<<minm23<<" to "<<maxm23<<std::endl;

        LauIntegrals DPIntegrals(precision);
        std::vector<Double_t> m13Weights, m23Weights;
        std::vector<Double_t> m13Abscissas, m23Abscissas;

        DPIntegrals.calcGaussLegendreWeights(nm13Points, m13Abscissas, m13Weights);
        DPIntegrals.calcGaussLegendreWeights(nm23Points, m23Abscissas, m23Weights);

        Int_t nm13Weights = static_cast<Int_t>(m13Weights.size());
        Int_t nm23Weights = static_cast<Int_t>(m23Weights.size());

        //std::cout<<"                                                 : nm13Weights = "<<nm13Weights<<", nm23Weights = "<<nm23Weights<<std::endl;
        // Print out abscissas and weights for the integration
        Double_t totm13Weight(0.0), totm23Weight(0.0);
        for (i = 0; i < nm13Weights; i++) {
                totm13Weight += m13Weights[i];
        }
        for (i = 0; i < nm23Weights; i++) {
                totm23Weight += m23Weights[i];
        }
        std::cout<<"                                                 : totm13Weight = "<<totm13Weight<<", totm23Weight = "<<totm23Weight<<std::endl;

        std::vector<Double_t> m13(nm13Weights), m23(nm23Weights);
        std::vector<Double_t> m13Sq(nm13Weights), m23Sq(nm23Weights);

        // Use same number of abscissas for x and y co-ordinates
        Int_t m = (nm13Weights + 1)/2;
        for (i = 0; i < m; i++) {

                Int_t ii = nm13Weights - 1 - i; // symmetric i index

                Double_t dm13 = halfRangem13*m13Abscissas[i];
                Double_t m13Val = meanm13 - dm13;
                m13[i] = m13Val;
                m13Sq[i] = m13Val*m13Val;

                m13Val = meanm13 + dm13;
                m13[ii] = m13Val;
                m13Sq[ii] = m13Val*m13Val;

        }

        m = (nm23Weights +1)/2;
        for (i = 0; i < m; i++) {

                Int_t ii = nm23Weights - 1 - i; // symmetric i index

                Double_t dm23 = halfRangem23*m23Abscissas[i];
                Double_t m23Val = meanm23 - dm23;
                m23[i] = m23Val;
                m23Sq[i] = m23Val*m23Val;
                m23Val = meanm23 + dm23;
                m23[ii] = m23Val;
                m23Sq[ii] = m23Val*m23Val;
        }

        // Now compute the integral
        Double_t dpArea(0.0);
        for (i = 0; i < nm13Weights; i++) {

                for (j = 0; j < nm23Weights; j++) {

                        Double_t weight = m13Weights[i]*m23Weights[j];
                        Double_t Jacobian = 4.0*m13[i]*m23[j];
                        weight *= (Jacobian*intFactor);

                        // Calculate the integral contributions for each resonance.
                        // Only resonances within the DP area contribute.
                        // This also calculates the total DP area as a check.
                        Bool_t withinDP = kinematics_->withinDPLimits(m13Sq[i], m23Sq[j]);
                        if (withinDP == kTRUE) {

                                kinematics_->updateKinematics(m13Sq[i], m23Sq[j]);
                                this->dynamics(kFALSE, weight);
                                // Increment total DP area
                                dpArea += weight;

                        }

                } // j weights loop
        } // i weights loop

        // Print out DP area to check whether we have a sensible output
        std::cout<<"                                                 : dpArea = "<<dpArea<<std::endl;

}

void LauIsobarDynamics::dynamics(Bool_t cacheResData, Double_t weight, Bool_t useEff)
{
        // Routine that calculates the Dalitz plot amplitude, incorporating
        // resonance dynamics (using resAmp()) and any interference between them.
        // Used by the fit() and sigGen() functions.

        UInt_t i(0), j(0);

        // Reset the total amplitude to zero
        totAmp_.zero();

        // Loop over the number of resonance amplitudes defined in the model
        // Have we already calculated this for this event (during fit?)
        // Or do we have a resonance that has varying pole mass/width/other factors?
        if (cacheResData == kFALSE) {

                for (i = 0; i < nAmp_; i++) {

                        // Calculate the dynamics for this resonance, using the resAmp function.
                        ff_[i] = resAmp(i);

                        //std::cout<<"ff_["<<i<<"] = "<<ff_[i]<<std::endl;

                        // If we have a symmetrical Dalitz plot, flip the m_13^2 and m_23^2
                        // variables, recalculate the dynamics, and average both contributions.
                        // Although, the factor of 0.5 cancels out with the fact that
                        // the resonance appears on both sides of the Dalitz plot.
                        if (symmetricalDP_ == kTRUE) { // was tieSg_ == 12
                                kinematics_->flipAndUpdateKinematics();
                                ff_[i] += resAmp(i);
                                // Flip the m_13^2 and m_23^2 variables back to their original values
                                kinematics_->flipAndUpdateKinematics();
                        }

                } // Loop over amplitudes

                // If we haven't cached the data, then we need to find out the efficiency.
                eff_ = this->retrieveEfficiency();

        } // Already cached data?

        if (integralsDone_ == kTRUE) {

                // Loop over all signal amplitudes
                LauComplex ATerm;
                for (i = 0; i < nAmp_; i++) {  

                        // Get the partial complex amplitude - (mag, phase)*(resonance dynamics)
                        ATerm = Amp_[i]*ff_[i];
                        // Scale this contribution by its relative normalisation w.r.t. the whole dynamics
                        ATerm.rescale(fNorm_[i]);

                        // Add this partial amplitude to the sum
                        //std::cout<<"For i = "<<i<<", ATerm = "<<ATerm<<", Amp = "<<Amp_[i]<<", ff = "<<ff_[i]<<std::endl;
                        totAmp_ += ATerm;

                } // Loop over amplitudes

                // |Sum of partial amplitudes|^2
                ASq_ = totAmp_.abs2();

                // Apply the efficiency correction for this event.
                // Multiply the amplitude squared sum by the DP efficiency
                if ( useEff ) {
                        ASq_ *= eff_;
                }

        } else {  // integrals not done

                // Find the efficiency correction to be applied for this event.
                eff_ = this->retrieveEfficiency();

                Double_t effWeight = eff_*weight;

                // Need this for integrals for normalisation of likelihood function.
                LauComplex fifjEffSumTerm;
                LauComplex fifjSumTerm;
                for (i = 0; i < nAmp_; i++) {

                        // Add the dynamical amplitude squared for this resonance.
                        Double_t fSqVal = ff_[i].abs2();
                        fSqSum_[i] += fSqVal*weight;

                        for (j = i; j < nAmp_; j++) {

                                fifjEffSumTerm = fifjSumTerm = ff_[i]*ff_[j].conj();

                                fifjEffSumTerm.rescale(effWeight);
                                fifjEffSum_[i][j] += fifjEffSumTerm;

                                fifjSumTerm.rescale(weight);
                                fifjSum_[i][j] += fifjSumTerm;
                        }
                }
        }
}

LauComplex LauIsobarDynamics::resAmp(Int_t index) 
{  
        // Routine to calculate the resonance dynamics (amplitude) 
        // using the appropriate Breit-Wigner/Form Factors. 
        // Called by the dynamics() function.

        // Get the signal resonance from the stored vector
        LauAbsResonance* sigResonance = sigResonances_[index];

        if (sigResonance == 0) {
                std::cout<<"ERROR in LauIsobarDynamics::resAmp : Couldn't retrieve resonance with index = "<<index<<std::endl;
                return LauComplex(0.0, 0.0);
        }

        // Get the integer index of the resonance.
        Int_t resInt = resIntAmp_[index];  

        LauComplex resAmplitude(0.0, 0.0);

        if (resInt < 0 || resInt >= static_cast<Int_t>(this->getnDefinedResonances())) {

                std::cout<<"ERROR in LauIsobarDynamics::resAmp : Probably bad resonance name."<<std::endl;
                resAmplitude = LauComplex(0.0, 0.0);

        } else {

                resAmplitude = sigResonance->amplitude(kinematics_);

        }

        return resAmplitude;
}

void LauIsobarDynamics::setFFTerm(UInt_t index, Double_t realPart, Double_t imagPart) 
{  
        // Function to set the internal ff = resAmp() term.  
        if ( index >= nAmp_ ) {
                std::cerr<<"ERROR in LauIsobarDynamics::setFFTerm : index = "<<index<<" is not within the range 0 and "<<nAmp_-1<<". Bailing out."<<std::endl;
                return;
        }

        ff_[index].setRealImagPart( realPart, imagPart );
}

void LauIsobarDynamics::calcExtraInfo(Bool_t init)
{
        // This method calculates the fit fractions, mean efficiency and total DP rate

        Double_t fifjEffTot(0.0), fifjTot(0.0);
        UInt_t i, j;
        for (i = 0; i < nAmp_; i++) {

                // Calculate the diagonal terms
                TString name = "A"; name += i; name += "Sq_FitFrac";
                fitFrac_[i][i].name(name);

                Double_t fifjSumReal = fifjSum_[i][i].re();
                Double_t sumTerm = Amp_[i].abs2()*fifjSumReal*fNorm_[i]*fNorm_[i];
                fifjTot += sumTerm;

                Double_t fifjEffSumReal = fifjEffSum_[i][i].re();
                Double_t sumEffTerm = Amp_[i].abs2()*fifjEffSumReal*fNorm_[i]*fNorm_[i];
                fifjEffTot += sumEffTerm;

                fitFrac_[i][i] = sumTerm;
        }

        for (i = 0; i < nAmp_; i++) {
                for (j = i+1; j < nAmp_; j++) {
                        // Calculate the cross-terms
                        TString name = "A"; name += i; name += "A"; name += j; name += "_FitFrac";
                        fitFrac_[i][j].name(name);

                        LauComplex AmpjConj = Amp_[j].conj();
                        LauComplex AmpTerm = Amp_[i]*AmpjConj;

                        Double_t crossTerm = 2.0*(AmpTerm*fifjSum_[i][j]).re()*fNorm_[i]*fNorm_[j];
                        fifjTot += crossTerm;

                        Double_t crossEffTerm = 2.0*(AmpTerm*fifjEffSum_[i][j]).re()*fNorm_[i]*fNorm_[j];
                        fifjEffTot += crossEffTerm;

                        fitFrac_[i][j] = crossTerm;
                }
        }

        if (TMath::Abs(fifjTot) > 1e-10) {
                meanDPEff_ = fifjEffTot/fifjTot;
                if (init) {
                        meanDPEff_.genValue( meanDPEff_.value() );
                        meanDPEff_.initValue( meanDPEff_.value() );
                }
        }
        DPRate_ = fifjTot;
        if (init) {
                DPRate_.genValue( DPRate_.value() );
                DPRate_.initValue( DPRate_.value() );
        }

        // Now divide the fitFraction sums by the overall integral
        for (i = 0; i < nAmp_; i++) {
                for (j = i; j < nAmp_; j++) {
                        // Get the actual fractions by dividing by the total DP rate
                        fitFrac_[i][j] /= fifjTot;
                        if (init) {
                                fitFrac_[i][j].genValue( fitFrac_[i][j].value() );
                                fitFrac_[i][j].initValue( fitFrac_[i][j].value() );
                        }
                }
        }

        // Work out total fit fraction over all K-matrix components (for each propagator)
        KMPropMap::iterator mapIter;
        Int_t propInt(0);

        for (mapIter = kMatrixPropagators_.begin(); mapIter != kMatrixPropagators_.end(); ++mapIter) {

                LauKMatrixPropagator* thePropagator = mapIter->second;

                TString propName = thePropagator->getName();

                // Now loop over all resonances and find those which are K-matrix components for this propagator
                Double_t kMatrixTotFitFrac(0.0);

                for (i = 0; i < nAmp_; i++) {
            
                        Bool_t gotKMRes1 = this->gotKMatrixMatch(i, propName);
                        if (gotKMRes1 == kFALSE) {continue;}

                        Double_t fifjSumReal = fifjSum_[i][i].re();
                        Double_t sumTerm = Amp_[i].abs2()*fifjSumReal*fNorm_[i]*fNorm_[i];

                        //Double_t fifjEffSumReal = fifjEffSum_[i][i].re();
                        //Double_t sumEffTerm = Amp_[i].abs2()*fifjEffSumReal*fNorm_[i]*fNorm_[i];

                        kMatrixTotFitFrac += sumTerm;
                        
                        for (j = i+1; j < nAmp_; j++) {

                                Bool_t gotKMRes2 = this->gotKMatrixMatch(j, propName);
                                if (gotKMRes2 == kFALSE) {continue;}

                                LauComplex AmpjConj = Amp_[j].conj();
                                LauComplex AmpTerm = Amp_[i]*AmpjConj;

                                Double_t crossTerm = 2.0*(AmpTerm*fifjSum_[i][j]).re()*fNorm_[i]*fNorm_[j];
                                //Double_t crossEffTerm = 2.0*(AmpTerm*fifjEffSum_[i][j]).re()*fNorm_[i]*fNorm_[j];

                                kMatrixTotFitFrac += crossTerm;       
                                
                        }
                        
                }
          
                kMatrixTotFitFrac /= fifjTot;

                TString parName("KMatrixTotFF_"); parName += propInt;
                extraParameters_[propInt].name( parName );
                extraParameters_[propInt] =  kMatrixTotFitFrac;
                if (init) {
                        extraParameters_[propInt].genValue(kMatrixTotFitFrac);
                        extraParameters_[propInt].initValue(kMatrixTotFitFrac);
                }

                std::cout<<"INFO in LauIsobarDynamics::calcExtraInfo : Total K-matrix fit fraction for propagator "<<propName<<" is "<<kMatrixTotFitFrac<<std::endl;
                
                ++propInt;

        }
        

}

Bool_t LauIsobarDynamics::gotKMatrixMatch(UInt_t resAmpInt, const TString& propName) const
{

        Bool_t gotMatch(kFALSE);
            
        if (resAmpInt >= nAmp_) {return kFALSE;}

        const LauAbsResonance* theResonance = sigResonances_[resAmpInt];
            
        if (theResonance == 0) {return kFALSE;}

        Int_t resModelInt = theResonance->getResonanceModel();

        if (resModelInt == LauAbsResonance::KMatrix) {
    
                TString resName = theResonance->getResonanceName();
    
                KMStringMap::const_iterator kMPropSetIter = kMatrixPropSet_.find(resName);

                if (kMPropSetIter != kMatrixPropSet_.end()) {
                        TString kmPropString = kMPropSetIter->second;
                        if (kmPropString == propName) {gotMatch = kTRUE;}
                }
                
        }

        return gotMatch;

}

Double_t LauIsobarDynamics::calcSigDPNorm()
{
        // Calculate the normalisation for the log-likelihood function.
        DPNorm_ = 0.0;

        for (UInt_t i = 0; i < nAmp_; i++) {
                // fifjEffSum is the contribution from the term involving the resonance
                // dynamics (f_i for resonance i) and the efficiency term.
                Double_t fifjEffSumReal = fifjEffSum_[i][i].re();
                // We need to normalise this contribution w.r.t. the complete dynamics in the DP.
                // Hence we scale by the fNorm_i factor (squared), which is calculated by the
                // initialise() function, when the normalisation integrals are calculated and cached. 
                // We also include the complex amplitude squared to get the total normalisation
                // contribution from this resonance.
                DPNorm_ += Amp_[i].abs2()*fifjEffSumReal*fNorm_[i]*fNorm_[i];
        }

        // We now come to the cross-terms (between resonances i and j) in the normalisation.
        for (UInt_t i = 0; i < nAmp_; i++) {
                for (UInt_t j = i+1; j < nAmp_; j++) {
                        LauComplex AmpjConj = Amp_[j].conj();
                        LauComplex AmpTerm = Amp_[i]*AmpjConj;
                        // Again, fifjEffSum is the contribution from the term involving the resonance
                        // dynamics (f_i*f_j_conjugate) and the efficiency cross term.
                        // Also include the relative normalisation between these two resonances w.r.t. the
                        // total DP dynamical structure (fNorm_i and fNorm_j) and the complex
                        // amplitude squared (mag,phase) part.
                        DPNorm_ += 2.0*(AmpTerm*fifjEffSum_[i][j]).re()*fNorm_[i]*fNorm_[j];
                }
        }

        return DPNorm_;
}

Bool_t LauIsobarDynamics::generate()
{
        // Routine to generate a signal event according to the Dalitz plot
        // model we have defined.

        nSigGenLoop_ = 0;
        Bool_t generatedSig(kFALSE);

        while (generatedSig == kFALSE && nSigGenLoop_ < iterationsMax_) {

                // Generates uniform DP phase-space distribution
                Double_t m13Sq(0.0), m23Sq(0.0);
                kinematics_->genFlatPhaseSpace(m13Sq, m23Sq);   

                // If we're in a symmetrical DP then we should only generate events in one half
                if ( symmetricalDP_ && m13Sq > m23Sq ) {
                        Double_t tmpSq = m13Sq;
                        m13Sq = m23Sq;
                        m23Sq = tmpSq;
                }

                // calculates the amplitudes and total amplitude for the given DP point
                this->calcLikelihoodInfo(m13Sq, m23Sq);

                if (integralsDone_ == kTRUE) {

                        // No need for efficiency correction here. It is already done in 
                        // the dynamics() function (unlike the Fortran version).

                        // Very important line to avoid bias in MC generation for the accept/reject method.
                        // Make sure that the total amplitude squared is below some number, given
                        // by aSqMaxSet_. If it is, then the event is valid.
                        // Otherwise, go through another toy MC loop until we can generate the event
                        // OK, or until we reach the maximum iteration limit.

                        Double_t randNo = LauRandom::randomFun()->Rndm();

                        if (randNo > ASq_/aSqMaxSet_) {
                                nSigGenLoop_++;
                        } else {
                                generatedSig = kTRUE;
                                nSigGenLoop_ = 0;
                                if (ASq_ > aSqMaxVar_) {aSqMaxVar_ = ASq_;}
                        }

                } else {
                        // For toy MC numerical integration only
                        generatedSig = kTRUE;
                }
        } // while loop

        Bool_t sigGenOK(kTRUE);
        if (GenOK != this->checkToyMC(kFALSE,kFALSE)) {
                sigGenOK = kFALSE;
        }

        return sigGenOK;
}

LauAbsDPDynamics::ToyMCStatus LauIsobarDynamics::checkToyMC(Bool_t printErrorMessages, Bool_t printInfoMessages)
{
        // Check whether we have generated the toy MC OK.
        ToyMCStatus ok(GenOK);

        if (nSigGenLoop_ >= iterationsMax_) {
                if (printErrorMessages) {
                        std::cerr<<"WARNING in LauIsobarDynamics::checkToyMC : More than "<<iterationsMax_<<" iterations required."<<std::endl;
                        std::cerr<<"                                         : Try to decrease the maximum allowed value of the total amplitude squared using the "
                                 <<"LauIsobarDynamics::setASqMaxValue(Double_t) function and re-run."<<std::endl;
                        std::cerr<<"                                         : This needs to be, perhaps significantly, less than "<<aSqMaxSet_<<std::endl;
                        std::cerr<<"                                         : Maximum value of ASq so far = "<<aSqMaxVar_<<std::endl;
                }
                aSqMaxSet_ = 1.01 * aSqMaxVar_;
                std::cout<<"INFO in LauIsobarDynamics::checkToyMC : |A|^2 max reset to "<<aSqMaxSet_<<std::endl;
                ok = MaxIterError;
        } else if (aSqMaxVar_ > aSqMaxSet_) {
                if (printErrorMessages) {
                        std::cerr<<"WARNING in LauIsobarDynamics::checkToyMC : aSqMaxSet_ was set to "<<aSqMaxSet_<<" but actual aSqMax was "<<aSqMaxVar_<<std::endl;
                        std::cerr<<"                                         : Run was invalid, as any generated MC will be biased, according to the accept/reject method!"<<std::endl;
                        std::cerr<<"                                         : Please set aSqMaxSet >= "<<aSqMaxVar_<<" using the LauIsobarDynamics::setASqMaxValue(Double_t) function and re-run."<<std::endl;
                }
                aSqMaxSet_ = 1.01 * aSqMaxVar_;
                std::cout<<"INFO in LauIsobarDynamics::checkToyMC : |A|^2 max reset to "<<aSqMaxSet_<<std::endl;
                ok = ASqMaxError;
        } else if (printInfoMessages) {
                std::cout<<"INFO in LauIsobarDynamics::checkToyMC : aSqMaxSet = "<<aSqMaxSet_<<" and aSqMaxVar = "<<aSqMaxVar_<<std::endl;
        }

        return ok;
}

void LauIsobarDynamics::setDataEventNo(UInt_t iEvt)
{
        this->LauAbsDPDynamics::setDataEventNo(iEvt);
        m13Sq_ = currentEvent_->retrievem13Sq();
        m23Sq_ = currentEvent_->retrievem23Sq();
        mPrime_ = currentEvent_->retrievemPrime();
        thPrime_ = currentEvent_->retrievethPrime();
        eff_ = currentEvent_->retrieveEff();
        scfFraction_ = currentEvent_->retrieveScfFraction();    // These two are necessary, even though the dynamics don't actually use scfFraction_ or jacobian_,
        jacobian_ = currentEvent_->retrieveJacobian();          // since this is at the heart of the caching mechanism.
}

void LauIsobarDynamics::calcLikelihoodInfo(UInt_t iEvt)
{
        // Calculate the likelihood and associated info
        // for the given event using cached information
        evtLike_ = 0.0;

        // retrieve the cached dynamics from the tree:
        // realAmp, imagAmp for each resonance plus efficiency, scf fraction and jacobian
        this->setDataEventNo(iEvt);

        // use realAmp and imagAmp to create the resonance amplitudes
        for (UInt_t i = 0; i < nAmp_; i++) {
                this->setFFTerm(i, currentEvent_->retrieveRealAmp()[i], currentEvent_->retrieveImagAmp()[i]);
        }

        // Update the dynamics - calculates totAmp_ and then ASq_ = totAmp_.abs2() * eff_
        // All calculated using cached information on the individual amplitudes and efficiency.
        this->dynamics(kTRUE, 1.0);  

        // Calculate the normalised matrix element squared value
        if (DPNorm_ > 1e-10) {
                evtLike_ = ASq_/DPNorm_;
        }
}

void LauIsobarDynamics::calcLikelihoodInfo(Double_t m13Sq, Double_t m23Sq)
{
        this->calcLikelihoodInfo(m13Sq, m23Sq, -1);
}

void LauIsobarDynamics::calcLikelihoodInfo(Double_t m13Sq, Double_t m23Sq, Int_t tagCat)
{
        // Calculate the likelihood and associated info
        // for the given point in the Dalitz plot
        // Also retrieves the SCF fraction in the bin where the event lies (done
        // here to cache it along with the the rest of the DP quantities, like eff)
        // The jacobian for the square DP is calculated here for the same reason.
        evtLike_ = 0.0;

        // update the kinematics for the specified DP point
        kinematics_->updateKinematics(m13Sq, m23Sq);

        // calculate the jacobian and the scfFraction to cache them later
        scfFraction_ = this->retrieveScfFraction(tagCat);
        if (kinematics_->squareDP() == kTRUE) {
                // If cacheResData == kFALSE, updateKinematics has been called before dynamics(). Then get Jacobian.
                jacobian_ = kinematics_->calcSqDPJacobian();
        }

        // calculates the ff_ terms and retrieves eff_ from the efficiency model
        // then calculates totAmp_ and finally ASq_ = totAmp_.abs2() * eff_
        this->dynamics(kFALSE, 1.0);

        // Calculate the normalised matrix element squared value
        if (DPNorm_ > 1e-10) {
                evtLike_ = ASq_/DPNorm_;
        }
}

void LauIsobarDynamics::fillDataTree(const LauFitDataTree& inputFitTree) 
{
        // In LauFitDataTree, the first two variables should always be m13^2 and m23^2.
        // Other variables follow thus: charge/flavour tag prob, etc.

        UInt_t nBranches = inputFitTree.nBranches();

        if (nBranches < 2) {
                std::cout<<"ERROR in LauIsobarDynamics::fillDataTree : Expecting at least 2 variables "
                        <<"in input data tree, but there are "<<nBranches<<"! Make sure you have "
                        <<"the right number of variables in your input data file!"<<std::endl;
                gSystem->Exit(-1);
        }

        // Data structure that will cache the variables required to 
        // calculate the signal likelihood for this experiment
        for ( std::vector<LauCacheData*>::iterator iter = data_.begin(); iter != data_.end(); ++iter ) {
                delete (*iter);
        }
        data_.clear();

        Double_t m13Sq(0.0), m23Sq(0.0);
        Double_t mPrime(0.0), thPrime(0.0);
        Int_t tagCat(-1);
        std::vector<Double_t> realAmp(nAmp_), imagAmp(nAmp_);
        Double_t eff(0.0), scfFraction(0.0), jacobian(0.0);

        UInt_t nEvents = inputFitTree.nEvents() + inputFitTree.nFakeEvents();

        data_.reserve(nEvents);

        for (UInt_t iEvt = 0; iEvt < nEvents; iEvt++) {

                const LauFitData& dataValues = inputFitTree.getData(iEvt);
                LauFitData::const_iterator iter = dataValues.find("m13Sq");
                m13Sq = iter->second;
                iter = dataValues.find("m23Sq");
                m23Sq = iter->second;

                // is there more than one tagging category?
                // if so then we need to know the category from the data
                if (scfFractionModel_.size()>1) {
                        iter = dataValues.find("tagCat");
                        tagCat = static_cast<Int_t>(iter->second);
                }

                // calculates the amplitudes and total amplitude for the given DP point
                // tagging category not needed by dynamics, but to find out the scfFraction
                this->calcLikelihoodInfo(m13Sq, m23Sq, tagCat);

                // extract the real and imaginary parts of the ff_ terms for storage
                for (UInt_t i = 0; i < nAmp_; i++) {
                        realAmp[i] = ff_[i].re();
                        imagAmp[i] = ff_[i].im();
                }

                if ( kinematics_->squareDP() ) {
                        mPrime = kinematics_->getmPrime();
                        thPrime = kinematics_->getThetaPrime();
                }

                eff = this->getEvtEff();
                scfFraction = this->getEvtScfFraction();
                jacobian = this->getEvtJacobian();

                // store the data for each event in the list
                data_.push_back( new LauCacheData() );
                data_[iEvt]->storem13Sq(m13Sq);
                data_[iEvt]->storem23Sq(m23Sq);
                data_[iEvt]->storemPrime(mPrime);
                data_[iEvt]->storethPrime(thPrime);
                data_[iEvt]->storeEff(eff);
                data_[iEvt]->storeScfFraction(scfFraction);
                data_[iEvt]->storeJacobian(jacobian);
                data_[iEvt]->storeRealAmp(realAmp);
                data_[iEvt]->storeImagAmp(imagAmp);
        }
}

Bool_t LauIsobarDynamics::gotReweightedEvent()
{
        // Select the event (kinematics_) using an accept/reject method based on the
        // ratio of the current value of ASq to the maximal value.
        Bool_t accepted(kFALSE);

        this->dynamics(kFALSE, 1.0, kFALSE);

        // Compare the ASq value with the maximal value (set by the user)
        if (LauRandom::randomFun()->Rndm() < ASq_/aSqMaxSet_) {
                accepted = kTRUE;
        }

        if (ASq_ > aSqMaxVar_) {aSqMaxVar_ = ASq_;}

        return accepted;
}

Double_t LauIsobarDynamics::getEventWeight()
{
        // calculate the dynamics from the current kinematics
        this->dynamics(kFALSE, 1.0, kFALSE);

        if (ASq_ > aSqMaxVar_) {aSqMaxVar_ = ASq_;}

        // return the event weight = the value of the squared amplitude divided
        // by the user-defined ceiling
        return ASq_ / aSqMaxSet_;
}