benford.C

#include "Rtypes.h"
#include "TH1F.h"
#include "TF1.h"
 
#include "tkmanager.h"
#include "tkstring.h"
#include "tkunit.h"
#include "TStyle.h"
#include "TMath.h"
#include "TROOT.h"
#include "TCanvas.h"
 
using namespace tkn;
 
int first_digit(double value);
TH1* benford_level(std::function<double(shared_ptr<tklevel>)>const& eval, tkstring name="");
 
void benford()
{
    gROOT->SetStyle("tkn-histo");
 
    TF1 benford_law("Benford law","100*TMath::Log10(1+1/x)",0.5,9.5);
    benford_law.SetTitle("P(n) = log_{10}(1+1/n)      ");
    benford_law.SetMarkerStyle(0);
    benford_law.SetMarkerColor(benford_law.GetLineColor());
    benford_law.SetLineStyle(9);
 
    auto *cc = new TCanvas("benford","Benford's law on lifetimes",1800,500);
    cc->Divide(3,1);
 
    auto histo = benford_level([](auto lvl) {return lvl->get_lifetime(tkunit_manager::units_keys::s);},
    "lifetime (in s)");
 
    cc->cd(1);
    histo->Draw("");
    benford_law.DrawClone("same");
    cc->cd(1)->BuildLegend(0.332776,0.779412,0.934783,0.936975);
 
    histo = benford_level([](auto lvl) {return lvl->get_lifetime(tkunit_manager::units_keys::keV);},
    "lifetime (in keV)");
 
    cc->cd(2);
    histo->Draw("");
    benford_law.DrawClone("same");
    cc->cd(2)->BuildLegend(0.332776,0.779412,0.934783,0.936975);
 
    histo = benford_level([](auto lvl) {if(!lvl->get_lifetime_measure()) return 0.; return lvl->get_lifetime_measure()->get_error(tkunit_manager::units_keys::keV);},
    "lifetime error (in keV)");
 
    cc->cd(3);
    histo->Draw("");
    benford_law.DrawClone("same");
    cc->cd(3)->BuildLegend(0.332776,0.779412,0.934783,0.936975);
    cc->SaveAs("benford.png");
}
 
TH1* benford_level(std::function<double(shared_ptr<tklevel>)>const& eval, tkstring name)
{
    glog.set_warnings(false);
 
    auto histo = new TH1F("digit",name.data(),9,.5,9.5);
    histo->SetName(name.remove_all(" ").data());
    histo->GetXaxis()->SetTitle("first digit (n)");
    histo->GetXaxis()->SetNdivisions(10);
    histo->GetYaxis()->SetTitle("P(n) (in %)");
 
    for(const auto &nuc : gmanager->get_nuclei()) {
        auto levelscheme = nuc->get_level_scheme();
        for(const auto &lvl : nuc->get_level_scheme()->get_levels()) {
            int fd = first_digit(eval(lvl));
            if(fd>0) histo->Fill(fd);
        }
    }
    histo->Sumw2();
    histo->Scale(100./histo->Integral());
 
    return histo;
}
 
int first_digit(double value)
{
    if(value<=0.) return 0;
    tkstring tmp = tkstring::form("%e",value);
    return tmp.substr(0,1).atoi();
}