hist040_TH2Poly_europe.C

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/// \file
/// \ingroup tutorial_hist
/// \notebook -js
/// This tutorial illustrates how to create an histogram with polygonal
/// bins (TH2Poly), fill it and draw it. The initial data are stored
/// in TMultiGraphs. They represent the european countries.
/// The histogram filling is done according to a Mercator projection,
/// therefore the bin contains should be proportional to the real surface
/// of the countries.
///
/// The initial data have been downloaded from: http://www.maproom.psu.edu/dcw/
/// This database was developed in 1991/1992 and national boundaries reflect
/// political reality as of that time.
///
/// The script is shooting npoints (script argument) randomly over the Europe area.
/// The number of points inside the countries should be proportional to the country surface
/// The estimated surface is compared to the surfaces taken from wikipedia.
///
/// \macro_image
/// \macro_output
/// \macro_code
///
/// \date August 2020
/// \author Olivier Couet
 
void hist040_TH2Poly_europe(Int_t npoints = 500000)
{
   Int_t i, j;
   Double_t lon1 = -25;
   Double_t lon2 = 35;
   Double_t lat1 = 34;
   Double_t lat2 = 72;
   Double_t R = (lat2 - lat1) / (lon2 - lon1);
   Int_t W = 800;
   Int_t H = (Int_t)(R * 800);
   gStyle->SetStatX(0.28);
   gStyle->SetStatY(0.45);
   gStyle->SetStatW(0.15);
 
   // Canvas used to draw TH2Poly (the map)
   TCanvas *ce = new TCanvas("ce", "ce", 0, 0, W, H);
   ce->ToggleEventStatus();
   ce->SetGridx();
   ce->SetGridy();
 
   // Real surfaces taken from Wikipedia.
   const Int_t nx = 36;
   // see http://en.wikipedia.org/wiki/Area_and_population_of_European_countries
   const char *countries[nx] = {
      "france",      "spain",          "sweden",     "germany", "finland",   "norway",         "poland",     "italy",
      "yugoslavia",  "united_kingdom", "romania",    "belarus", "greece",    "czechoslovakia", "bulgaria",   "iceland",
      "hungary",     "portugal",       "austria",    "ireland", "lithuania", "latvia",         "estonia",    "denmark",
      "netherlands", "switzerland",    "moldova",    "belgium", "albania",   "cyprus",         "luxembourg", "andorra",
      "malta",       "liechtenstein",  "san_marino", "monaco"};
   Float_t surfaces[nx] = {547030, 505580, 449964, 357021, 338145, 324220, 312685, 301230, 255438,
                           244820, 237500, 207600, 131940, 127711, 110910, 103000, 93030,  89242,
                           83870,  70280,  65200,  64589,  45226,  43094,  41526,  41290,  33843,
                           30528,  28748,  9250,   2586,   468,    316,    160,    61,     2};
 
   TH1F *h = new TH1F("h", "Countries surfaces (in km^{2})", 3, 0, 3);
   for (i = 0; i < nx; i++)
      h->Fill(countries[i], surfaces[i]);
   h->LabelsDeflate();
 
   TFile::SetCacheFileDir(".");
   TFile *f;
   f = TFile::Open("http://root.cern/files/europe.root", "cacheread");
 
   if (!f) {
      printf("Cannot access europe.root. Is internet working ?\n");
      return;
   }
 
   TH2Poly *p =
      new TH2Poly("Europe", "Europe (bin contents are normalized to the surfaces in km^{2})", lon1, lon2, lat1, lat2);
   p->GetXaxis()->SetNdivisions(520);
   p->GetXaxis()->SetTitle("longitude");
   p->GetYaxis()->SetTitle("latitude");
 
   p->SetContour(100);
 
   TMultiGraph *mg;
   TKey *key;
   TIter nextkey(gDirectory->GetListOfKeys());
   while ((key = (TKey *)nextkey())) {
      TObject *obj = key->ReadObj();
      if (obj->InheritsFrom("TMultiGraph")) {
         mg = (TMultiGraph *)obj;
         p->AddBin(mg);
      }
   }
 
   TRandom r;
   Double_t longitude, latitude;
   Double_t x, y, pi4 = TMath::Pi() / 4, alpha = TMath::Pi() / 360;
 
   gBenchmark->Start("Partitioning");
   p->ChangePartition(100, 100);
   gBenchmark->Show("Partitioning");
 
   // Fill TH2Poly according to a Mercator projection.
   gBenchmark->Start("Filling");
   for (i = 0; i < npoints; i++) {
      longitude = r.Uniform(lon1, lon2);
      latitude = r.Uniform(lat1, lat2);
      x = longitude;
      y = 38 * TMath::Log(TMath::Tan(pi4 + alpha * latitude));
      p->Fill(x, y);
   }
   gBenchmark->Show("Filling");
 
   Int_t nbins = p->GetNumberOfBins();
   Double_t maximum = p->GetMaximum();
 
   // h2 contains the surfaces computed from TH2Poly.
   TH1F *h2 = (TH1F *)h->Clone("h2");
   h2->Reset();
   for (j = 0; j < nx; j++) {
      for (i = 0; i < nbins; i++) {
         if (strstr(countries[j], p->GetBinName(i + 1))) {
            h2->Fill(countries[j], p->GetBinContent(i + 1));
            h2->SetBinError(j, p->GetBinError(i + 1));
         }
      }
   }
 
   // Normalize the TH2Poly bin contents to the real surfaces.
   Double_t scale = surfaces[0] / maximum;
   for (i = 0; i < nbins; i++)
      p->SetBinContent(i + 1, scale * p->GetBinContent(i + 1));
 
   gStyle->SetOptStat(1111);
   p->Draw("COLZ");
 
   TCanvas *c1 = new TCanvas("c1", "c1", W + 10, 0, W - 20, H);
   c1->SetRightMargin(0.047);
 
   scale = h->GetMaximum() / h2->GetMaximum();
 
   h->SetStats(0);
   h->SetLineColor(kRed - 3);
   h->SetLineWidth(2);
   h->SetMarkerStyle(20);
   h->SetMarkerColor(kBlue);
   h->SetMarkerSize(0.8);
   h->Draw("LP");
   h->GetXaxis()->SetLabelFont(42);
   h->GetXaxis()->SetLabelSize(0.03);
   h->GetYaxis()->SetLabelFont(42);
 
   h2->Scale(scale);
   Double_t scale2 = TMath::Sqrt(scale);
   for (i = 0; i < nx; i++)
      h2->SetBinError(i + 1, scale2 * h2->GetBinError(i + 1));
   h2->Draw("E SAME");
   h2->SetMarkerStyle(20);
   h2->SetMarkerSize(0.8);
 
   TLegend *leg = new TLegend(0.5, 0.67, 0.92, 0.8, nullptr, "NDC");
   leg->SetTextFont(42);
   leg->SetTextSize(0.025);
   leg->AddEntry(h, "Real countries surfaces from Wikipedia (in km^{2})", "lp");
   leg->AddEntry(h2, "Countries surfaces from TH2Poly (with errors)", "lp");
   leg->Draw();
   leg->Draw();
 
   Double_t wikiSum = h->Integral();
   Double_t polySum = h2->Integral();
   Double_t error = TMath::Abs(wikiSum - polySum) / wikiSum;
   printf("THPoly Europe surface estimation error wrt wikipedia = %f per cent when using %d points\n", 100 * error,
          npoints);
}