Optimize Area-cut

Assume you have written a large data set of good-weather, low zenith-distance Crab data with the following query to a file. The following will give you a few example of how you can make use of that in your analysis. To speed up things or decrease the file size (715MB), you might want to add additional cuts depending on your analysis. If you want to apply a Theta-square cut, please refer to DatabaseBasedAnalysis#Dataretrieval.

SELECT
   MeanX,
   MeanY,
   Width,
   Length,
   CosDelta,
   SinDelta,
   M3Long,
   SlopeLong,
   Leakage1,
   NumIslands,
   NumUsedPixels,
   Size,
   X,
   Y
FROM
   Events
LEFT JOIN Position USING (FileId, EvtNumber)
LEFT JOIN RunInfo  USING (FileId)
WHERE
   fSourceKey=5
AND
   fRunTypeKey=1
AND
   FileId BETWEEN 170800000 AND 180800000
AND
   fZenithDistanceMax<35
AND
   fR750Cor>0.9*fR750Ref

#include <iostream>
#include <iomanip>

#include <TMath.h>
#include <TH1.h>
#include <TH2.h>
#include <TProfile.h>
#include <TChain.h>
#include <TGraph.h>
#include <TCanvas.h>

Double_t LiMa(Double_t s, Double_t b, Double_t alpha=0.2)
{
    const Double_t sum = s+b;

    if (s<0 || b<0 || alpha<=0)
        return -1;

    const Double_t l = s==0 ? 0 : s*TMath::Log(s/sum*(alpha+1)/alpha);
    const Double_t m = b==0 ? 0 : b*TMath::Log(b/sum*(alpha+1)      );

    return l+m<0 ? 0 : TMath::Sqrt((l+m)*2);
}

void optimarea()
{
    // Create chain for the tree Result
    // This is just easier than using TFile/TTree
    TChain c("Result");

    // Add the input file to the
    c.AddFile("crab2018.root");

    // Define variables for all leaves to be accessed
    // By definition rootifysql writes only doubles
    double X, Y, MeanX, MeanY, Width, Length, CosDelta, SinDelta,
        M3Long, SlopeLong, Leakage1, Size,
        ConcCore, ConcCOG, NumIslands, NumUsedPixels, Zd;

    // Connect the variables to the cordesponding leaves
    c.SetBranchAddress("X", &X);
    c.SetBranchAddress("Y", &Y);
    c.SetBranchAddress("MeanX", &MeanX);
    c.SetBranchAddress("MeanY", &MeanY);
    c.SetBranchAddress("Width", &Width);
    c.SetBranchAddress("Length", &Length);
    c.SetBranchAddress("CosDelta", &CosDelta);
    c.SetBranchAddress("SinDelta", &SinDelta);
    c.SetBranchAddress("M3Long", &M3Long);
    c.SetBranchAddress("SlopeLong", &SlopeLong);
    c.SetBranchAddress("Leakage1", &Leakage1);
    c.SetBranchAddress("NumIslands", &NumIslands);
    c.SetBranchAddress("NumUsedPixels", &NumUsedPixels);
    c.SetBranchAddress("Size", &Size);

    // Set some constants (they could be included in the database
    // in the future)
    double mm2deg = +0.0117193246260285378;

    // -------------------- Source dependent parameter calculation -------------------

    // Create a histogram for on- and off-data
    TH1F hold("old",  "", 100, 0, 1);
    TH1F hnew("onew", "", 100, 0, 1);

    TH2F h2area_on( "H_AvsS_on",   "", 24, 1.5, 4.5, 200, -2, 0);
    TH2F h2area_of( "H_AvsS_of",   "", 24, 1.5, 4.5, 200, -2, 0);
    TH2F h2area_sig("H_AvsS_sig",  "", 24, 1.5, 4.5, 200, -2, 0);

    // Loop over all events
    for (int i=0; i<c.GetEntries(); i++)
    {
        // read the i-th event from the file
        c.GetEntry(i);

        // First calculate all cuts to speedup the analysis
        double area = TMath::Pi()*Width*Length;

        bool cutq = NumIslands<3.5 && NumUsedPixels>5.5 && Leakage1<0.1;
        if (!cutq)
            continue;

        // Loop over all wobble positions in the camera
        for (int angle=0; angle<360; angle+=60)
        {

        // -------------------- Source dependent parameter calculation -------------------

            double cr = cos(angle*TMath::DegToRad());
            double sr = sin(angle*TMath::DegToRad());

            double px = cr*X-sr*Y;
            double py = cr*Y+sr*X;

            double dx = MeanX - px*1.02;
            double dy = MeanY - py*1.02;

            double norm = sqrt(dx*dx + dy*dy);
            double dist = norm*mm2deg;

            double lx = min(max((CosDelta*dy - SinDelta*dx)/norm, -1.), 1.);
            double ly = min(max((CosDelta*dx + SinDelta*dy)/norm, -1.), 1.);

            double alpha = asin(lx);
            double sgn   = TMath::Sign(1., ly);

            // ------------------------------- Application ----------------------------------

            double m3l   = M3Long*sgn*mm2deg;
            double slope = SlopeLong*sgn/mm2deg;

            // --------------------------------- Analysis -----------------------------------

            double xi = 1.340   + 0.0755  *slope + 1.67972 *(1-1/(1+4.86232*Leakage1));

            double sign1 = m3l+0.07;
            double sign2 = (dist-0.5)*7.2-slope;

            double disp  = (sign1<0 || sign2<0 ? -xi : xi)*(1-Width/Length);

            double thetasq = disp_old*disp_old + dist*dist - 2*disp_old*dist*sqrt(1-lx*lx);

            if (thetasq>0.024)
                continue;

            if (angle==0)
                h2area_on.Fill(log10(Size), log10(area*mm2deg*mm2deg));
            else
                h2area_of.Fill(log10(Size), log10(area*mm2deg*mm2deg));
        }
    }

    for (int x=1; x<=h2area_sig.GetNbinsX(); x++)
        for (int y=1; y<=h2area_sig.GetNbinsY(); y++)
        {
            double on = h2area_on.Integral(x, x, 1, y);
            double of = h2area_of.Integral(x, x, 1, y);

            h2area_sig.SetBinContent(x, y, LiMa(on, of));
        }

    TGraph gmax;
    for (int x=1; x<=h2area_sig.GetNbinsX(); x++)
    {
        TH1D *p = h2area_sig.ProjectionY("_py", x, x);
        double max = p->GetXaxis()->GetBinCenter(p->GetMaximumBin());
        delete p;

        gmax.SetPoint(gmax.GetN(),
                      h2area_sig.GetXaxis()->GetBinCenter(x),
                      max);
    }

    h2area_on.SetStats(kFALSE);
    h2area_of.SetStats(kFALSE);
    h2area_sig.SetStats(kFALSE);

    TCanvas *canv = new TCanvas;
    canv->Divide(2,2);

    canv->cd(1);
    h2area_on.DrawCopy("colz");
    gmax.DrawClone("*");

    canv->cd(2);
    h2area_sig.DrawCopy("colz");
    gmax.DrawClone("*");

    canv->cd(3);
    h2area_of.DrawCopy("colz");
    gmax.DrawClone("*");

    canv->cd(4);
}

Don't forget that this only gives you the best significance per bin in Size. To get the best detection significance, you will have to introduce an additional Size-cut.

Optimize Disp

SELECT
   MeanX,
   MeanY,
   Width,
   Length,
   CosDelta,
   SinDelta,
   M3Long,
   SlopeLong,
   Leakage1,
   NumIslands,
   NumUsedPixels,
   Size,
   X,
   Y
FROM
   EventsMC
LEFT JOIN 
   PositionMC USING (FileId, EvtNumber)
WHER
   /* ... do some data selection here ... */

The following root-macro (to be compiled!)

#include <iostream>
#include <iomanip>

#include <TMath.h>
#include <TH1.h>
#include <TH2.h>
#include <TProfile.h>
#include <TChain.h>
#include <TGraph.h>
#include <TCanvas.h>

void optimdisp()
{
    // Create chain for the tree Result
    // This is just easier than using TFile/TTree
    TChain c("Result");

    // Add the input file to the
    c.AddFile("simulation.root");

    // Define variables for all leaves to be accessed
    // By definition rootifysql writes only doubles
    double X, Y, MeanX, MeanY, Width, Length, CosDelta, SinDelta,  M3Long, SlopeLong, 
       Leakage1, Size, ConcCore, ConcCOG, NumIslands, NumUsedPixels, Zd;

    // Connect the variables to the cordesponding leaves
    c.SetBranchAddress("X", &X);
    c.SetBranchAddress("Y", &Y);
    c.SetBranchAddress("MeanX", &MeanX);
    c.SetBranchAddress("MeanY", &MeanY);
    c.SetBranchAddress("Width", &Width);
    c.SetBranchAddress("Length", &Length);
    c.SetBranchAddress("CosDelta", &CosDelta);
    c.SetBranchAddress("SinDelta", &SinDelta);
    c.SetBranchAddress("M3Long", &M3Long);
    c.SetBranchAddress("SlopeLong", &SlopeLong);
    c.SetBranchAddress("Leakage1", &Leakage1);
    c.SetBranchAddress("NumIslands", &NumIslands);
    c.SetBranchAddress("NumUsedPixels", &NumUsedPixels);
    c.SetBranchAddress("Size", &Size);
    c.SetBranchAddress("Zd", &Zd);

    // Set some constants (they could be included in the database
    // in the future)
    double mm2deg = +0.0117193246260285378;

    // -------------------- Source dependent parameter calculation -------------------

    // Create a histogram for on- and off-data
    TH1F hold("old",  "", 100, 0, 1);
    TH1F hnew("onew", "", 100, 0, 1);

    TH2F     h2slope("H_VsSlope",   "", 75, -8,     7,    100, -2.5, 1.5);
    TProfile p2slope("P_VsSlope",   "", 75, -8,     7);
    TH2F     h2leak( "H_VsLeakage", "", 75,  0,     0.15, 100, -2.5, 1.5);
    TH2F     h2m3l(  "H_M3long",    "", 75, -0.2,   0.6,  100, -2.5, 1.5);
    TH2F     h2zd(   "H_Zd",        "", 30, 30,    60,    100, -2.5, 1.5);
    TH2F     h2ni(   "H_NumIsl",    "", 10,  0.5,  10.5,  100, -2.5, 1.5);
    TH2F     h2np(   "H_NumPix",    "", 10,  0.5, 100.5,  100, -2.5, 1.5);
    TH2F     h2size( "H_Size",      "", 30,  1.5,   4.5,  100, -2.5, 1.5);

    // Loop over all events
    for (int i=0; i<c.GetEntries(); i++)
    {
        // read the i-th event from the file
        c.GetEntry(i);

        // First calculate all cuts to speedup the analysis
        double area = TMath::Pi()*Width*Length;

        bool cutq = NumIslands<3.5 && NumUsedPixels>5.5 && Leakage1<0.1;
        if (!cutq)
            continue;

        bool cut0 = area < log10(Size)*898-1535;
        if (!cut0)
            continue;

        // -------------------- Source dependent parameter calculation -------------------

        int angle = 0;

        double cr = cos(angle*TMath::DegToRad());
        double sr = sin(angle*TMath::DegToRad());

        double px = cr*X-sr*Y;
        double py = cr*Y+sr*X;

        double dx = MeanX - px*1.02;
        double dy = MeanY - py*1.02;

        double norm = sqrt(dx*dx + dy*dy);
        double dist = norm*mm2deg;

        double lx = min(max((CosDelta*dy - SinDelta*dx)/norm, -1.), 1.);
        double ly = min(max((CosDelta*dx + SinDelta*dy)/norm, -1.), 1.);

        double alpha = asin(lx);
        double sgn   = TMath::Sign(1., ly);

        // ------------------------------- Application ----------------------------------

        double m3l   = M3Long*sgn*mm2deg;
        double slope = SlopeLong*sgn/mm2deg;

        // --------------------------------- Analysis -----------------------------------

        //double xi = 1.34723 + 0.15214 *slope + 0.970704*(1-1/(1+8.89826*Leakage1));
        double xi_old = 1.39252 + 0.154247*slope + 1.67972 *(1-1/(1+4.86232*Leakage1));
        double xi_new = 1.340   + 0.0755  *slope + 1.67972 *(1-1/(1+4.86232*Leakage1));

        double sign1 = m3l+0.07;
        double sign2 = (dist-0.5)*7.2-slope;

        double disp_old  = (sign1<0 || sign2<0 ? -xi_old : xi_old)*(1-Width/Length);
        double disp_new  = (sign1<0 || sign2<0 ? -xi_new : xi_new)*(1-Width/Length);

        double thetasq_old = disp_old*disp_old + dist*dist - 2*disp_old*dist*sqrt(1-lx*lx);
        double thetasq_new = disp_new*disp_new + dist*dist - 2*disp_new*dist*sqrt(1-lx*lx);

        // Fill the on- and off-histograms
        hold.Fill(thetasq_old);
        hnew.Fill(thetasq_new);

        double residual = xi_new-dist/(1-Width/Length);

        h2slope.Fill(slope,        residual);
        p2slope.Fill(slope,        residual);

        h2leak.Fill(Leakage1,      residual);
        h2m3l.Fill( m3l,           residual);
        h2zd.Fill(  Zd,            residual);
        h2ni.Fill(  NumIslands,    residual);
        h2np.Fill(  NumUsedPixels, residual);
        h2size.Fill(log10(Size),   residual);
    }

    TCanvas *canv = new TCanvas;
    canv->Divide(2,2);

    canv->cd(1);
    gPad->SetGridy();
    h2slope.DrawCopy("colz");
    p2slope.DrawCopy("same");

    canv->cd(2);
    gPad->SetGridy();
    h2leak.DrawCopy("colz");

    canv->cd(3);
    gPad->SetGridy();
    //h2m3l.DrawCopy("colz");
    h2zd.DrawCopy("colz");
    //h2ni.DrawCopy("colz");
    //h2np.DrawCopy("colz");
    //h2size.DrawCopy("colz");

    canv->cd(4);
    // Plot the result
    hold.SetLineColor(kRed);
    hnew.SetMinimum(0);
    hnew.DrawCopy();
    hold.DrawCopy("same");
}