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Reference Guide
th2polyEurope.C File Reference

Detailed Description

View in nbviewer Open in SWAN 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.

Partitioning: Real Time = 1.32 seconds Cpu Time = 1.31 seconds
Filling : Real Time = 4.10 seconds Cpu Time = 4.09 seconds
THPoly Europe surface estimation error wrt wikipedia = 1.260096 per cent when using 500000 points
void th2polyEurope(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->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 *f;
f = TFile::Open("http://root.cern.ch/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);
TKey *key;
TIter nextkey(gDirectory->GetListOfKeys());
while ((key = (TKey*)nextkey())) {
TObject *obj = key->ReadObj();
if (obj->InheritsFrom("TMultiGraph")) {
mg = (TMultiGraph*)obj;
p->AddBin(mg);
}
}
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));
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,NULL,"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);
}
#define f(i)
Definition: RSha256.hxx:104
#define h(i)
Definition: RSha256.hxx:106
int Int_t
Definition: RtypesCore.h:45
float Float_t
Definition: RtypesCore.h:57
double Double_t
Definition: RtypesCore.h:59
@ kRed
Definition: Rtypes.h:66
@ kBlue
Definition: Rtypes.h:66
R__EXTERN TBenchmark * gBenchmark
Definition: TBenchmark.h:59
#define gDirectory
Definition: TDirectory.h:348
winID h TVirtualViewer3D TVirtualGLPainter p
Option_t Option_t TPoint TPoint const char GetTextMagnitude GetFillStyle GetLineColor GetLineWidth GetMarkerStyle GetTextAlign GetTextColor GetTextSize void char Point_t Rectangle_t WindowAttributes_t Float_t r
R__EXTERN TStyle * gStyle
Definition: TStyle.h:414
virtual void SetMarkerStyle(Style_t mstyle=1)
Set the marker style.
Definition: TAttMarker.h:40
virtual void SetMarkerSize(Size_t msize=1)
Set the marker size.
Definition: TAttMarker.h:41
virtual void Start(const char *name)
Starts Benchmark with the specified name.
Definition: TBenchmark.cxx:172
virtual void Show(const char *name)
Stops Benchmark name and Prints results.
Definition: TBenchmark.cxx:155
The Canvas class.
Definition: TCanvas.h:23
virtual void ToggleEventStatus()
Toggle event statusbar.
Definition: TCanvas.cxx:2444
A ROOT file is a suite of consecutive data records (TKey instances) with a well defined format.
Definition: TFile.h:54
static Bool_t SetCacheFileDir(ROOT::Internal::TStringView cacheDir, Bool_t operateDisconnected=kTRUE, Bool_t forceCacheread=kFALSE)
Definition: TFile.h:326
static TFile * Open(const char *name, Option_t *option="", const char *ftitle="", Int_t compress=ROOT::RCompressionSetting::EDefaults::kUseCompiledDefault, Int_t netopt=0)
Create / open a file.
Definition: TFile.cxx:4019
1-D histogram with a float per channel (see TH1 documentation)}
Definition: TH1.h:574
void Reset(Option_t *option="") override
Reset.
Definition: TH1.cxx:9985
virtual Double_t GetBinError(Int_t bin) const
Return value of error associated to bin number bin.
Definition: TH1.cxx:8938
virtual Double_t GetMaximum(Double_t maxval=FLT_MAX) const
Return maximum value smaller than maxval of bins in the range, unless the value has been overridden b...
Definition: TH1.cxx:8420
virtual void SetBinError(Int_t bin, Double_t error)
Set the bin Error Note that this resets the bin eror option to be of Normal Type and for the non-empt...
Definition: TH1.cxx:9081
virtual Int_t Fill(Double_t x)
Increment bin with abscissa X by 1.
Definition: TH1.cxx:3348
void Draw(Option_t *option="") override
Draw this histogram with options.
Definition: TH1.cxx:3070
virtual Double_t Integral(Option_t *option="") const
Return integral of bin contents.
Definition: TH1.cxx:7860
virtual void Scale(Double_t c1=1, Option_t *option="")
Multiply this histogram by a constant c1.
Definition: TH1.cxx:6594
2D Histogram with Polygonal Bins
Definition: TH2Poly.h:66
Book space in a file, create I/O buffers, to fill them, (un)compress them.
Definition: TKey.h:28
virtual TObject * ReadObj()
To read a TObject* from the file.
Definition: TKey.cxx:750
This class displays a legend box (TPaveText) containing several legend entries.
Definition: TLegend.h:23
A TMultiGraph is a collection of TGraph (or derived) objects.
Definition: TMultiGraph.h:34
Mother of all ROOT objects.
Definition: TObject.h:37
virtual Bool_t InheritsFrom(const char *classname) const
Returns kTRUE if object inherits from class "classname".
Definition: TObject.cxx:445
virtual void Draw(Option_t *option="")
Default Draw method for all objects.
Definition: TObject.cxx:197
void SetGridx(Int_t value=1) override
Definition: TPad.h:327
void SetGridy(Int_t value=1) override
Definition: TPad.h:328
This is the base class for the ROOT Random number generators.
Definition: TRandom.h:27
void SetOptStat(Int_t stat=1)
The type of information printed in the histogram statistics box can be selected via the parameter mod...
Definition: TStyle.cxx:1590
void SetStatX(Float_t x=0)
Definition: TStyle.h:381
void SetStatW(Float_t w=0.19)
Definition: TStyle.h:383
void SetStatY(Float_t y=0)
Definition: TStyle.h:382
Double_t y[n]
Definition: legend1.C:17
return c1
Definition: legend1.C:41
Double_t x[n]
Definition: legend1.C:17
leg
Definition: legend1.C:34
#define H(x, y, z)
static constexpr double mg
Double_t Log(Double_t x)
Returns the natural logarithm of x.
Definition: TMath.h:753
Double_t Sqrt(Double_t x)
Returns the square root of x.
Definition: TMath.h:659
constexpr Double_t Pi()
Definition: TMath.h:37
Double_t Tan(Double_t)
Returns the tangent of an angle of x radians.
Definition: TMath.h:597
Short_t Abs(Short_t d)
Returns the absolute value of parameter Short_t d.
Definition: TMathBase.h:123
Author
Olivier Couet

Definition in file th2polyEurope.C.