Lau2DHistDPPdf.cc

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// Copyright University of Warwick 2004 - 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 "TAxis.h"
#include "TH2.h"
#include "TRandom.h"

#include "Lau2DHistDPPdf.hh"
#include "LauKinematics.hh"
#include "LauRandom.hh"
#include "LauVetoes.hh"

ClassImp(Lau2DHistDPPdf)


Lau2DHistDPPdf::Lau2DHistDPPdf(const TH2* hist, LauKinematics* kinematics, const LauVetoes* vetoes,
                Bool_t useInterpolation, Bool_t fluctuateBins, Bool_t useUpperHalfOnly, Bool_t squareDP) :
        Lau2DAbsHistDPPdf(kinematics,vetoes,useUpperHalfOnly,squareDP),
        hist_(hist ? dynamic_cast<TH2*>(hist->Clone()) : 0),
        minX_(0.0), maxX_(0.0), minY_(0.0), maxY_(0.0), rangeX_(0.0), rangeY_(0.0), 
        binXWidth_(0.0), binYWidth_(0.0),
        invBinXWidth_(0.0), invBinYWidth_(0.0),
        nBinsX_(0), nBinsY_(0),
        norm_(0.0),
        useInterpolation_(useInterpolation)
{
        // For square Dalitz plots, the co-ordinates must be m', theta'
        // The input data to the fit is still in m13^2, m23^2 co-ords, and a
        // transformation is applied to go from one co-ordinate system to the
        // other.

        // Save various attributes of the histogram 
        // (axis ranges, number of bins, areas)
        if ( hist_ ) {
                TAxis* xAxis = hist_->GetXaxis();
                minX_ = xAxis->GetXmin();
                maxX_ = xAxis->GetXmax();

                TAxis* yAxis = hist_->GetYaxis();
                minY_ = yAxis->GetXmin();
                maxY_ = yAxis->GetXmax();

                nBinsX_ = hist_->GetNbinsX();
                nBinsY_ = hist_->GetNbinsY();
        } else {
                minX_ = getKinematics()->getm13SqMin();
                maxX_ = getKinematics()->getm13SqMax();

                minY_ = getKinematics()->getm23SqMin();
                maxY_ = getKinematics()->getm23SqMax();

                nBinsX_ = 1;
                nBinsY_ = 1;
        }

        rangeX_ = maxX_ - minX_;
        rangeY_ = maxY_ - minY_;
        if (nBinsX_ > 0) { binXWidth_ = TMath::Abs(rangeX_)/(nBinsX_*1.0); }
        if (nBinsY_ > 0) { binYWidth_ = TMath::Abs(rangeY_)/(nBinsY_*1.0); }
        if (binXWidth_ > 1e-10) { invBinXWidth_ = 1.0/binXWidth_; }
        if (binYWidth_ > 1e-10) { invBinYWidth_ = 1.0/binYWidth_; }

        // If the bins are to be fluctuated then do so now before
        // calculating anything that depends on the bin content.
        if (fluctuateBins) {
                this->doBinFluctuation(hist_);
        }

        // Calculate the PDF normalisation.
        this->calcHistNorm();

        // And check it is OK.
        this->checkNormalisation();

        // Also obtain the maximum height
        this->calcMaxHeight(hist_);
}

Lau2DHistDPPdf::~Lau2DHistDPPdf()
{
        // Destructor
        delete hist_; hist_ = 0;
}

void Lau2DHistDPPdf::calcHistNorm()
{
        // Calculate the histogram normalisation. We must integrate
        // over the allowed kinematic DP region.

        // Loop over the total x and y range to get the total area
        // under x and y. Just sum the contributions up using 1e-3 increments
        // of the range in x and y. Multiply the end result by dx and dy.

        const Double_t axisMin = TMath::Min( minX_, minY_ );
        const Double_t axisMax = TMath::Max( maxX_, maxY_ );
        const Double_t axisRange = axisMax - axisMin;

        const Double_t dx(1e-3 * axisRange);
        const Double_t dy(dx);

        Double_t area(0.0);

        Double_t x(axisMin + dx/2.0);
        while (x < axisMax) {
                Double_t y(axisMin + dy/2.0);
                while (y < axisMax) {   
                        area += this->interpolateXY(x,y);
                        y += dy;
                } // y while loop
                x += dx;
        } // x while loop

        norm_ = area*dx*dy;

        std::cout << "INFO in Lau2DHistDPPdf::calcHistNorm : Norm = " << norm_ << ", bX*bY = " << binXWidth_ << "*" << binYWidth_ << " = " << binXWidth_*binYWidth_ << std::endl;
}

Double_t Lau2DHistDPPdf::getBinHistValue(Int_t xBinNo, Int_t yBinNo) const
{
        if (xBinNo < 0) {
                xBinNo = 0;
        } else if (xBinNo >= nBinsX_) {
                return 0.0;
        }

        if (yBinNo < 0) {
                yBinNo = 0;
        } else if (yBinNo >= nBinsY_) {
                return 0.0;
        }

        if ( hist_ == 0 ) {
                return 1.0;
        }

        Double_t value = hist_->GetBinContent(xBinNo+1, yBinNo+1);
        return value;
}

Double_t Lau2DHistDPPdf::interpolateXYNorm(Double_t x, Double_t y) const
{
        // Get the normalised interpolated value.
        Double_t value = this->interpolateXY(x,y);
        return value/norm_;

}

Double_t Lau2DHistDPPdf::interpolateXY(Double_t x, Double_t y) const
{
        // This function returns the interpolated value of the histogram function
        // for the given values of x and y by finding the adjacent bins and extrapolating
        // using weights based on the inverse distance of the point from the adajcent
        // bin centres.
        // Here, x = m13^2, y = m23^2, or m', theta' for square DP co-ordinates

        // If we're only using one half then flip co-ordinates
        // appropriately for conventional or square DP
        getUpperHalf(x,y);

        // First ask whether the point is inside the kinematic region.
        if (withinDPBoundaries(x,y) == kFALSE) {return 0.0;}

        // Update the kinematics to the position of interest.
        updateKinematics(x,y);

        // Check that we're not inside a veto
        Bool_t vetoOK(kTRUE);
        if (getVetoes()) {
                vetoOK = getVetoes()->passVeto(getKinematics());
        }
        if (vetoOK == kFALSE) {return 0.0;}

        // Find the 2D histogram bin for x and y
        Int_t i = TMath::FloorNint((x - minX_)*invBinXWidth_);
        Int_t j = TMath::FloorNint((y - minY_)*invBinYWidth_);

        if (i >= nBinsX_) {i = nBinsX_ - 1;}
        if (j >= nBinsY_) {j = nBinsY_ - 1;}

        // Ask whether we want to do the interpolation, since this method is
        // not reliable for low statistics histograms.
        if (useInterpolation_ == kFALSE) {
                return this->getBinHistValue(i,j);
        }

        // Find the bin centres (actual co-ordinate positions, not histogram indices)
        Double_t cbinx = (i+0.5)*binXWidth_ + minX_;
        Double_t cbiny = (j+0.5)*binYWidth_ + minY_;

        // If bin centres are outside kinematic region, do not extrapolate
        if (withinDPBoundaries(cbinx, cbiny) == kFALSE) {
                return this->getBinHistValue(i,j);
        }

        // Find the adjacent bins
        Double_t deltax = x - cbinx;
        Double_t deltay = y - cbiny;

        Int_t i_adj(0), j_adj(0);
        if (deltax > 0.0) {
                i_adj = i + 1;
        } else {
                i_adj = i - 1;
        }
        if (deltay > 0.0) {
                j_adj = j + 1;
        } else {
                j_adj = j - 1;
        }

        Bool_t isXBoundary(kFALSE), isYBoundary(kFALSE);

        Double_t value(0.0);

        if (i_adj >= nBinsX_ || i_adj < 0) {isYBoundary = kTRUE;}
        if (j_adj >= nBinsY_ || j_adj < 0) {isXBoundary = kTRUE;}

        // In the corners, do no interpolation. Use entry in bin (i,j)
        if (isXBoundary == kTRUE && isYBoundary == kTRUE) {

                value = this->getBinHistValue(i,j);

        } else if (isXBoundary == kTRUE && isYBoundary == kFALSE) {

                // Find the adjacent x bin centre
                Double_t cbinx_adj = Double_t(i_adj+0.5)*binXWidth_ + minX_;

                if (withinDPBoundaries(cbinx_adj, y) == kFALSE) {

                        // The adjacent bin is outside the DP range. Don't extrapolate.
                        value = this->getBinHistValue(i,j);

                } else {

                        Double_t dx0 = TMath::Abs(x - cbinx);
                        Double_t dx1 = TMath::Abs(cbinx_adj - x);
                        Double_t inter_denom = dx0 + dx1;

                        Double_t value1 = this->getBinHistValue(i,j);
                        Double_t value2 = this->getBinHistValue(i_adj,j);

                        value = (value1*dx1 + value2*dx0)/inter_denom;

                }

        } else if (isYBoundary == kTRUE && isXBoundary == kFALSE) {

                // Find the adjacent y bin centre
                Double_t cbiny_adj = Double_t(j_adj+0.5)*binYWidth_ + minY_;

                if (withinDPBoundaries(x, cbiny_adj) == kFALSE) {

                        // The adjacent bin is outside the DP range. Don't extrapolate.
                        value = this->getBinHistValue(i,j);

                } else {

                        Double_t dy0 = TMath::Abs(y - cbiny);
                        Double_t dy1 = TMath::Abs(cbiny_adj - y);
                        Double_t inter_denom = dy0 + dy1;

                        Double_t value1 = this->getBinHistValue(i,j);
                        Double_t value2 = this->getBinHistValue(i,j_adj);

                        value = (value1*dy1 + value2*dy0)/inter_denom;

                }

        } else {

                // 2D linear interpolation using inverse distance as weights.
                // Find the adjacent x and y bin centres
                Double_t cbinx_adj = Double_t(i_adj+0.5)*binXWidth_ + minX_;
                Double_t cbiny_adj = Double_t(j_adj+0.5)*binYWidth_ + minY_;

                if (withinDPBoundaries(cbinx_adj, cbiny_adj) == kFALSE) {

                        // The adjacent bin is outside the DP range. Don't extrapolate.
                        value = this->getBinHistValue(i,j);

                } else {

                        Double_t dx0 = TMath::Abs(x - cbinx);
                        Double_t dx1 = TMath::Abs(cbinx_adj - x);
                        Double_t dy0 = TMath::Abs(y - cbiny);
                        Double_t dy1 = TMath::Abs(cbiny_adj - y);

                        Double_t inter_denom = (dx0 + dx1)*(dy0 + dy1);

                        Double_t value1 = this->getBinHistValue(i,j);
                        Double_t value2 = this->getBinHistValue(i_adj,j);
                        Double_t value3 = this->getBinHistValue(i,j_adj);
                        Double_t value4 = this->getBinHistValue(i_adj,j_adj);

                        value = value1*dx1*dy1 + value2*dx0*dy1 + value3*dx1*dy0 + value4*dx0*dy0;
                        value /= inter_denom;
                }

        }

        return value;

}

void Lau2DHistDPPdf::checkNormalisation()
{
        // Loop over the total x and y range to get the total area
        // under x and y. Just sum the contributions up using 1e-3 increments
        // of the range in x and y. Multiply the end result by dx and dy.

        const Double_t axisMin = TMath::Min( minX_, minY_ );
        const Double_t axisMax = TMath::Max( maxX_, maxY_ );
        const Double_t axisRange = axisMax - axisMin;

        const Double_t dx(1e-3 * axisRange);
        const Double_t dy(dx);

        Double_t area(0.0);
        Double_t areaNoNorm(0.0);

        // Preserve the value of a variable we change temporarily
        Bool_t interpolate = useInterpolation_;

        Double_t x(axisMin + dx/2.0);
        while (x < axisMax) {
                Double_t y(axisMin + dy/2.0);
                while (y < axisMax) {   
                        area += this->interpolateXYNorm(x,y);
                        useInterpolation_ = kFALSE;
                        areaNoNorm += this->interpolateXY(x,y);
                        useInterpolation_ = kTRUE;
                        y += dy;
                } // y while loop
                x += dx;
        } // x while loop
        Double_t norm = area*dx*dy;

        useInterpolation_ = interpolate; //Restore old value

        std::cout << "INFO in Lau2DHistDPPdf::checkNormalisation : Area = " << area << ", dx = " << dx << ", dy = " << dy << ", dx*dy = " << dx*dy << std::endl;
        std::cout << "                                           : Area with no norm = " << areaNoNorm << "*dx*dy = " << areaNoNorm*dx*dy << std::endl;
        std::cout << "                                           : The total area of the normalised histogram PDF is " << norm << std::endl;
}