[[TOC]]


== Good weather Crab data ==

You want to create a file with good weather data with zenith distance smaller than 35° of Crab of the season 2017/18. The file should contain most of the image parameters with no cuts applied so that you can optimize cuts. Here is the query:

{{{#!Spoiler
{{{#!sql
SELECT
   Events.MeanX,
   Events.MeanY,
   Events.Width,
   Events.Length,
   Events.CosDelta,
   Events.SinDelta,
   Events.M3Long,
   Events.SlopeLong,
   Events.Leakage1,
   Events.NumIslands,
   Events.NumUsedPixels,
   Events.Size,
   Position.X,
   Position.Y
FROM
   Events
LEFT JOIN Position USING (FileId, EvtNumber)
LEFT JOIN RunInfo  USING (FileId)
WHERE
   fSourceKey=5
AND
   fRunTypeKey=1
AND
   FileId BETWEEN 170600000 AND 180500000
AND
   fZenithDistanceMax<35
AND
   fR750Cor>0.9*fR750Ref
}}}
}}}

You can run it, for example, with:

{{{
rootifysql --uri=fact:password@ihp-pc45.ethz.ch/factdata --out=crab2018.root
}}}

== Optimize Area-cut ==

Assume you have written a large data set of good-weather, low zenith-distance Crab data with the previous 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.

{{{#!Spoiler
{{{#!cpp
#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 (Observable) ==

{{{#!sql
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!)

{{{#!cpp
#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/sqrt(1-lx*lx)/(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");
}
}}}


== Optim Disp (Leakage==0) ==

{{{#!Spoiler
{{{#!cpp
#include <iostream>
#include <iomanip>

#include <TMath.h>
#include <TH2.h>
#include <TChain.h>
#include <TCanvas.h>

void optimdisp2()
{
    // 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 FileId, EvtNumber, X, Y, MeanX, MeanY, Width, Length, CosDelta, SinDelta,
        M3Long, SlopeLong, Leakage1, SlopeSpreadWeighted, Size,
        ConcCore, ConcCOG, NumIslands, NumUsedPixels, Zd;

    // Connect the variables to the cordesponding leaves
    c.SetBranchAddress("FileId", &FileId);
    c.SetBranchAddress("EvtNumber", &EvtNumber);
    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 -------------------

    TH2F hist("", "",
              26, 1.300-0.0025, 1.430-0.0025,
              20, 0.040-0.0025, 0.140-0.0025);

    for (float xi0=1.30; xi0<1.43; xi0+=0.005)
        for (float slope0=0.04; slope0<0.14; slope0+=0.005)
        {
            int cnt_on = 0;

            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;

                // The abberation correction does increase also Width and Length by 1.02

                bool cutq = NumIslands<3.5 && NumUsedPixels>5.5 && Leakage1==0;
                if (!cutq)
                    continue;

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

                int angle = 0;

                // -------------------- 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 = xi0 + slope0 *slope;

                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*disp + dist*dist - 2*disp*dist*sqrt(1-lx*lx);

                if (thetasq<0.024)
                    cnt_on++;
            }

            hist.Fill(xi0, slope0, cnt_on);

            cout << xi0 << " " << slope0 << " " << cnt_on << endl;
        }

    TCanvas *canv = new TCanvas;
    canv->SetTopMargin(0.01);

    hist.SetStats(kFALSE);
    hist.SetContour(100);
    hist.SetXTitle("Xi_{0} / deg");
    hist.SetYTitle("Slope_{0} #dot ns/deg^{2} ");
    hist.GetYaxis()->SetTitleOffset(1.2);
    hist.DrawCopy("colz cont2");

}
}}}
}}}

Results in

[[Image(Result.png)]]

== Optim Disp (Leakage>0) ==

{{{#!Spoiler
{{{#!cpp
#include <iostream>
#include <iomanip>

#include <TMath.h>
#include <TH2.h>
#include <TChain.h>
#include <TCanvas.h>

void optimdisp3()
{
    // 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 FileId, EvtNumber, X, Y, MeanX, MeanY, Width, Length, CosDelta, SinDelta,
        M3Long, SlopeLong, Leakage1, SlopeSpreadWeighted, Size,
        ConcCore, ConcCOG, NumIslands, NumUsedPixels, Zd;

    // Connect the variables to the cordesponding leaves
    c.SetBranchAddress("FileId", &FileId);
    c.SetBranchAddress("EvtNumber", &EvtNumber);
    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("SlopeSpreadWeighted", &SlopeSpreadWeighted);
    c.SetBranchAddress("Size", &Size);
    c.SetBranchAddress("Zd", &Zd);
    //c.SetBranchAddress("ConcCOG", &ConcCOG);
    //c.SetBranchAddress("ConcCore", &ConcCore);

    // Set some constants (they could be included in the database
    // in the future)
    double mm2deg = +0.0117193246260285378;
    //double abberation = 1.02;

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

    TH2F hist("", "",
              32, 0.800-0.0250, 2.400-0.0250,
              60, 3.000-0.0250, 6.000-0.0250);


    for (float l0=0.8; l0<2.4; l0+=0.05)
        for (float l1=3; l1<6; l1+=0.05)
        {
            int cnt_on = 0;

            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;

                // The abberation correction does increase also Width and Length by 1.02

                bool cutq = NumIslands<3.5 && NumUsedPixels>5.5 && Leakage1>0;
                if (!cutq)
                    continue;

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

                int angle = 0;

                // -------------------- 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 = 1.36 + 0.085*slope + l0 *(1-1/(1+l1*Leakage1));

                // Optim: 1.36 + 0.085

                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*disp + dist*dist - 2*disp*dist*sqrt(1-lx*lx);

                if (thetasq<0.024)
                    cnt_on++;
            }

            hist.Fill(l0, l1, cnt_on);

            cout << l0 << " " << l1 << " " << cnt_on << endl;
        }

    TCanvas *canv = new TCanvas;
    canv->SetTopMargin(0.01);

    hist.SetStats(kFALSE);
    hist.SetContour(100);
    hist.SetXTitle("L_{0} / deg");
    hist.SetYTitle("L_{1} / deg");
    hist.GetYaxis()->SetTitleOffset(1.2);
    hist.DrawCopy("colz cont2");

}
}}}
}}}

Results in

[[Image(Result2.png)]]

== Optimize Disp (on Crab Data) ==

This is the same analysis using the Excess-Error on Crab Data.

{{{#!Spoiler
{{{#!cpp
#include <iostream>
#include <iomanip>

#include <TMath.h>
#include <TH2.h>
#include <TChain.h>
#include <TCanvas.h>
#include <TGraph.h>
#include <TStopwatch.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);
}

Double_t Error(Double_t s, Double_t b, Double_t alpha=0.2)
{
    const Double_t sN = s + alpha*alpha*b;

    const Double_t error = sN<0 ? 0 : TMath::Sqrt(sN);
    if (error==0)
        return 0;

    const Double_t Ns = s - alpha*b;

    return Ns<0 ? 0 : Ns/error;
}


double ganymed2(double xi0, double slope0)
{
    // 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("crab-data-only.root");

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

    // Connect the variables to the cordesponding leaves
    c.SetBranchAddress("FileId", &FileId);
    c.SetBranchAddress("EvtNumber", &EvtNumber);
    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("SlopeSpreadWeighted", &SlopeSpreadWeighted);
    c.SetBranchAddress("Size", &Size);
    //c.SetBranchAddress("ConcCOG", &ConcCOG);
    //c.SetBranchAddress("ConcCore", &ConcCore);

    // Set some constants (they could be included in the database
    // in the future)
    double mm2deg = +0.0117193246260285378;
    //double abberation = 1.02;

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

    // Create a histogram for on- and off-data
    TH1F hon("on",   "", 55, 0, 1);
    TH1F hoff("off", "", 55, 0, 1);

    long cnt_on  = 0;
    long cnt_off = 0;

    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;
        if (!cutq)
            continue;

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

        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;

            //                   blau             rot
            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 = xi0 + slope0  *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*disp + dist*dist - 2*disp*dist*cos(alpha))*mm2deg*mm2deg;
            double thetasq = disp*disp + dist*dist - 2*disp*dist*sqrt(1-lx*lx);

            // Fill the on- and off-histograms
            if (thetasq<0.024)
                angle==0 ? cnt_on++ : cnt_off++;
        }
    }

    cout << cnt_on << "\t" << cnt_off << "\t" << cnt_on-cnt_off*0.2 << endl;
    return Error(cnt_on, cnt_off);
}


void ganymed_optimdisp()
{
    TH2F hist("", "",
              21, 1.200-0.0050, 1.410-0.0050,
              13, 0.010-0.0025, 0.140-0.0025);

    for (float xi0=1.20; xi0<1.41; xi0+=0.01)
        for (float slope0=0.01; slope0<0.14; slope0+=0.01)
        {
            cout << xi0 << "\t" << slope0 << "\t";
            hist.Fill(xi0, slope0, ganymed2(xi0, slope0));
        }

    TCanvas *canv = new TCanvas;
    canv->SetTopMargin(0.01);

    hist.SetStats(kFALSE);
    hist.SetContour(100);
    hist.SetXTitle("Xi_{0} / deg");
    hist.SetYTitle("Slope_{0} #dot ns/deg^{2} ");
    hist.GetYaxis()->SetTitleOffset(1.2);
    hist.DrawCopy("colz cont2");
}
}}}
}}}

Which gives the following result

[[Image(Result4.png)]]



== Energy Optimization == 

{{{#!cpp
#include <iostream>
#include <iomanip>

#include <TMath.h>
#include <TF1.h>
#include <TH1.h>
#include <TH2.h>
#include <TProfile.h>
#include <TChain.h>
#include <TGraph.h>
#include <TCanvas.h>
#include <TStopwatch.h>

void optimenergy()
{
    // 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, SlopeSpreadWeighted, Size,
        ConcCore, ConcCOG, NumIslands, NumUsedPixels, Zd, Energy;

    // Connect the variables to the cordesponding leaves
    //c.SetBranchAddress("FileId", &FileId);
    //c.SetBranchAddress("EvtNumber", &EvtNumber);
    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);
    c.SetBranchAddress("Energy", &Energy);

    // Set some constants (they could be included in the database
    // in the future)
    double mm2deg = +0.0117193246260285378;
    //double abberation = 1.02;

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

    TH2F h2svse ("H_SvsE",      "", 26*3, 2.2, 4.8, 3*30, 1.3, 4.3);
    TH2F h2est  ("H_EstVsMC",   "", 26*3, 2.2, 4.8, 26*3, 2.2, 4.8);
    TH2F h2bias ("H_BiasLog",   "", 26*3, 2.2, 4.8, 100, -1, 1);
    TH2F h2lin  ("H_BiasLin",   "", 26*3, 2.2, 4.8, 100, -1, 2);

    TH2F h2size ("H_ResSize",   "", 26*3, 2.2, 4.8, 100, -1, 1);
    TH2F h2dist ("H_ResDist",   "", 50,  0, 2.5,    100, -1, 1);
    TH2F h2slope("H_ResSlope",  "", 50, -10, 10,    100, -1, 1);
    TH2F h2zd   ("H_ResZd",     "", 90, 0,   90,    100, -1, 1);

    h2svse.SetStats(kFALSE);
    h2bias.SetStats(kFALSE);
    h2lin.SetStats(kFALSE);
    h2est.SetStats(kFALSE);
    h2size.SetStats(kFALSE);
    h2dist.SetStats(kFALSE);
    h2slope.SetStats(kFALSE);
    h2zd.SetStats(kFALSE);

    // Loop over all events
    TStopwatch clock;
        // Loop over all wobble positions in the camera
    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;

        // The abberation correction does increase also Width and Length by 1.02

        int angle = 0;

        // -------------------- 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*1.022;
        double dy = MeanY - py*1.022;

        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 = 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*disp + dist*dist - 2*disp*dist*sqrt(1-lx*lx);

        if (thetasq<0.024)
            continue;

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

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

        h2svse.Fill(log10(Energy), log10(Size));

        double step = 0.8;
        double dd = dist<step ? -(dist-step)*0.4 : (dist-step)*0.65;

        double energy = pow(10, 0.33 + log10(Size)/1.1 + Zd*0.02 + dd + slope*0.01);

        h2est.Fill(log10(Energy),   log10(energy));
        h2bias.Fill(log10(energy), log10(energy)-log10(Energy));
        h2lin.Fill(log10(energy),  (energy-Energy)/Energy);

        h2size.Fill (log10(Size), log10(energy)-log10(Energy));
        h2dist.Fill (dist,        log10(energy)-log10(Energy));
        h2slope.Fill(slope,       log10(energy)-log10(Energy));
        h2zd.Fill(   Zd,          log10(energy)-log10(Energy));
    }

    clock.Print();

    TF1 fx("f", "x", -100, 100);
    TF1 f0("f", "0", -100, 100);

    TCanvas *canv = new TCanvas("Canvas", "Energy estimation", 800, 900);
    canv->Divide(2,4);

    canv->cd(1);
    gPad->SetGridy();
    h2size.DrawCopy("colz");
    f0.DrawCopy("same");

    canv->cd(3);
    gPad->SetGridy();
    h2dist.DrawCopy("colz");
    f0.DrawCopy("same");

    canv->cd(5);
    gPad->SetGridy();
    h2slope.DrawCopy("colz");
    f0.DrawCopy("same");

    canv->cd(7);
    gPad->SetGridy();
    h2zd.DrawCopy("colz");
    f0.DrawCopy("same");

    canv->cd(2);
    gPad->SetGridy();
    h2svse.DrawCopy("colz");
    fx.DrawCopy("same");

    canv->cd(4);
    gPad->SetGridy();
    h2est.DrawCopy("colz");
    fx.DrawCopy("same");

    canv->cd(6);
    gPad->SetGridy();
    h2bias.DrawCopy("colz");
    f0.DrawCopy("same");


    canv->cd(8);

    TGraph grlin;
    TGraph grlog;

    for (int x=1; x<h2bias.GetNbinsX(); x++)
    {
        TH1D *p = h2bias.ProjectionY("_py", x, x);
        if (p->GetRMS()>0)
            grlog.SetPoint(grlog.GetN(), h2bias.GetXaxis()->GetBinCenter(x), pow(10, p->GetRMS())-1);
        delete p;

        p = h2lin.ProjectionY("_py", x, x);
        if (p->GetRMS()>0)
            grlin.SetPoint(grlin.GetN(), h2lin.GetXaxis()->GetBinCenter(x), p->GetRMS());
        delete p;
    }

    grlog.SetMarkerColor(kBlue);
    grlin.SetMinimum(0);
    grlin.DrawClone("A*");
    grlog.DrawClone("*");
}
}}}

== Day-by-day light-curve ==

{{{#!sql
WITH Table8 AS
(
    WITH Table7 AS
    (
        WITH Table6 AS
        (
            WITH Table5 AS
            ( 
                WITH Table4 AS
                (
                    WITH Table3 AS
                    (
                        WITH Table2 AS
                        (
                            WITH Table1 AS
                            (
                                WITH Table0 AS
                                (
                                    SELECT -- 0
                                        FileId,
                                        Weight,
                                        Size,
                                        NumUsedPixels,
                                        NumIslands,
                                        Leakage1,
                                        MeanX,
                                        MeanY,
                                        CosDelta,
                                        SinDelta,
                                        M3Long,
                                        SlopeLong,
                                        Width/Length      AS WdivL,
                                        PI()*Width*Length AS Area,
                                        cosa*X - sina*Y   AS PX,
                                        cosa*Y + sina*X   AS PY
                                    FROM RunInfo
                                    LEFT JOIN Events   USING (FileId)
                                    LEFT JOIN Position USING (FileId, EvtNumber)
                                    CROSS JOIN Wobble
                                    WHERE
                                        fSourceKey=5
                                    AND
                                        fRunTypeKey=1
                                    AND
                                        fR750Cor>0.9e0*fR750Ref
                                    AND
                                        NumUsedPixels>5.5
                                    AND
                                        NumIslands<3.5
                                    AND
                                        Leakage1<0.1

                                ) -- AS Table0

                                SELECT -- 1
                                    FileId, Weight, CosDelta, SinDelta, M3Long, SlopeLong, Leakage1, WdivL,
                                    MeanX - PX*1.02e0 AS DX,
                                    MeanY - PY*1.02e0 AS DY
                                FROM
                                    Table0
                                WHERE
                                    Area < LOG10(Size)*898-1535

                            ) -- AS Table1

                            SELECT -- 2
                                FileId, Weight, CosDelta, SinDelta, DX, DY, M3Long, SlopeLong, Leakage1, WdivL,
                                SQRT(DX*DX + DY*DY) AS Norm
                            FROM
                                Table1

                        ) -- AS Table2

                        SELECT -- 3
                            FileId, Weight, M3Long, SlopeLong, Leakage1, WdivL, Norm,
                            LEAST(GREATEST((CosDelta*DY - SinDelta*DX)/Norm, -1), 1) AS LX,
                            SIGN(CosDelta*DX + SinDelta*DY) AS Sign
                        FROM
                            Table2

                    ) -- AS Table3

                    SELECT -- 4
                        FileId, Weight, Leakage1, WdivL, LX,
                        Norm          *0.0117193246260285378e0 AS Dist,
                        M3Long   *Sign*0.0117193246260285378e0 AS M3L,
                        SlopeLong*Sign/0.0117193246260285378e0 AS Slope
                    FROM
                        Table3

                ) -- AS Table4

                SELECT -- 5
                    FileId, Weight, WdivL, Dist, LX, M3L, Slope,
--                    1.39252e0 + 0.154247e0*Slope + 1.67972e0*(1-1/(1+4.86232e0*Leakage1)) AS Xi
                    1.34e0 + 0.0755e0*Slope + 1.67972e0*(1-1/(1+4.86232e0*Leakage1)) AS Xi
                FROM
                    Table4

            ) -- AS Table5

            SELECT -- 6
                FileId, Weight, Dist, LX,
                IF (M3L<-0.07 || (Dist-0.5e0)*7.2e0-Slope<0, -Xi, Xi) * (1-WdivL) AS Disp
            FROM
                Table5

        ) -- AS Table6

        SELECT -- 7
            FileId, Weight,                         -- cos(alpha) = sqrt(1-lx^2)
            (Disp*Disp + Dist*Dist - 2*Disp*Dist*SQRT(1-LX*LX)) AS ThetaSq
        FROM
            Table6

    ) -- AS Table8

    SELECT -- 9
        FileId,
        COUNT(*)                       AS `Count`,
        COUNT(IF(Weight>0, 1, NULL))   AS `Signal`,
        COUNT(IF(Weight<0, 1, NULL))/5 AS `Background`
    FROM
        Table7
    WHERE
        ThetaSq<0.024336
    GROUP BY
        FileId

) -- AS Table8

SELECT -- 9
    FileId,
    20000000+FLOOR(FileId/1000)  AS fNight,
    FileId%1000                  AS fRunID,
    `Count`                      AS fNumRuns,
    `Signal`                     AS fNumSigEvts,
    `Background`                 AS fNumBgEvts,
    `Signal` - `Background`      AS fNumExcEvts
FROM
    Table8
}}}

Note that this query can easily run 30min or more!