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userfcn.cc
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#include "userfcn.h"
#include <fstream>
static char gObjName[1024];
static int gObjNumber = 0;
static char * GetObjName() {sprintf(gObjName,"UserFcn%d",gObjNumber++); return gObjName;}
// About the TParameter class
TParameter::TParameter() {fStatus = eFree; fValue = 0;}
// About the TFitFunction class
TFitFunction::TFitFunction()
{
fNBins = 10;
fDegreeMax = 10;
fFitFcn = 0x0;
fPFitParameters = 0x0;
}
TFitFunction::~TFitFunction()
{
if( fFitFcn ) delete fFitFcn;
if( fPFitParameters ) delete [] fPFitParameters;
}
void TFitFunction::ComputeFitFunction()
{
fDataBins.clear();
fDataFit.clear();
if( fFitFcn == 0x0 )
{
cout << "TFitFunction::ComputeFitFunction: Impossible to compute fit function. Pointer not allocated." << endl;
return;
}
unsigned int mybins=1000;
fDataBins.resize(mybins,0.);
fDataFit.resize(mybins,0.);
double step = (fDataMax-fDataMin)/(mybins-1);
for(unsigned int i=0; i<mybins; i++)
{
fDataBins[i] = fDataMin+i*step;
fDataFit[i] = fFitFcn->EvalPar(&fDataBins[i],fPFitParameters);
}
string fn = fDataName+"distribution.txt";
ofstream outangdist(fn.c_str());
for( unsigned int i=0;i<mybins;i++ ) outangdist << fDataBins[i] << " " << fDataFit[i] << endl;
outangdist.close();
}
void TFitFunction::PlotDistribution() const
{
if( fExtension == "" ) return;
unsigned int size = fDataBins.size();
double* th = new double[size];
double* pth = new double[size];
for(unsigned int i=0; i<size; i++)
{
th[i] = fDataBins[i];
pth[i] = fDataFit[i];
}
string Xaxis = "#"+fDataName;
string Yaxis = "";
string save = fDataName+"Fit"+fExtension;
TCanvas* cAngle = new TCanvas(GetObjName(), fDataName.c_str(),700,700);
TGraphErrors* angle = new TGraphErrors(size, th, pth);
PlotXY(cAngle, angle, fDataMin, fDataMax, "", Xaxis, Yaxis);
angle->SetLineWidth(2);
angle->Draw("AL");
cAngle->Update();
cAngle->SaveAs(save.c_str());
delete [] th;
delete [] pth;
}
bool TFitFunction::Run()
{
string filename= "";
string xAxis = "#"+fDataName;
string name = "";
TH1F* Distribution = new TH1F(GetObjName(), name.c_str(), fNBins, fDataMin, fDataMax);
TCanvas * cDistribution = 0x0;
GetHisto(Distribution,fData);
if( fExtension != "" )
{
cDistribution = new TCanvas(GetObjName(), "Fit", 700, 700);
filename = fDataName+"RawDistribution"+fExtension;
DrawHisto(cDistribution,Distribution,xAxis,"",filename);
}
// Now let's fit the histogram !
unsigned int degree = 0;
unsigned int nPar = 0;
fChi2perNDF = fChi2Limit+1; // be sure that chi2perNDF > fChi2Limit
bool status = false;
cout << "Chi2/NDF max : " << fChi2Limit << endl;
int addpar = (fDegreeMax == 0) ? 0 : 1 ;
while( fChi2perNDF >= fChi2Limit )
{
nPar = degree+fNPars+addpar;
fFitFcn = new TF1(GetObjName(),fAngFitFunc,fDataMin,fDataMax,nPar);
for( unsigned int i = 0; i < fNPars;i++ ) // restore values
{
if( fParameters[i].fStatus == eFixed ) fFitFcn->FixParameter(i,fParameters[i].fValue);
else fFitFcn->SetParameter(i,fParameters[i].fValue);
}
fFitFcn->FixParameter(fNPars,degree);
{
double getParameter[nPar];
fFitFcn->GetParameters(getParameter);
}
if( fFitFcn->GetNumberFreeParameters() == 0 )
{
cout << "No free parameters ! Try increasing degree..." << endl;
delete fFitFcn;
fFitFcn = 0x0;
degree++;
if( ++degree > fDegreeMax )
{
status = false;
break;
}
continue;
}
string opts = "Q";
if( fExtension == "" ) opts += "N";
Distribution->Fit(fFitFcn,opts.c_str());
fChi2 = fFitFcn->GetChisquare();
fChi2perNDF = (fFitFcn->GetChisquare())/(fFitFcn->GetNDF());
cout << "Chi2/NDF = " << fChi2perNDF << endl;
if( fChi2perNDF >= fChi2Limit )
{
delete fFitFcn;
fFitFcn = 0x0;
if( ++degree > fDegreeMax )
{
status = false;
break;
}
}
else status = true;
}
if( !status )
{
cout << "Program Failed : Too much splines/poly used." << endl;
cout << "Fit failed. Returning." << endl;
return status;
}
if( fExtension != "" )
{
//Plot Histogram + Fit
Distribution->Draw("e1p");
fFitFcn->SetLineWidth(2);
fFitFcn->SetLineColor(kRed);
fFitFcn->Draw("same");
cDistribution->Update();
string filename = fDataName+"DistributionFitted"+fExtension;
cDistribution->SaveAs(filename.c_str());
}
// Fitted parameters (to be returned)
double getParameter[nPar];
fFitFcn->GetParameters(getParameter);
double error[nPar];
for( unsigned int i=0;i<nPar;i++ ) error[i] = fFitFcn->GetParError(i);
fFitParameters.resize(nPar);
fPFitParameters = new double[nPar];
fFitParametersErrors.resize(nPar);
for( unsigned int i=0;i<nPar;i++ )
{
fFitParameters[i] = getParameter[i];
fPFitParameters[i] = getParameter[i];
fFitParametersErrors[i] = error[i];
cout << "parameter " << i << " : " << fFitParameters[i] << " error : " << fFitParametersErrors[i] << endl;
}
ComputeFitFunction();
if( fExtension != "" ) PlotDistribution();
return status;
}
vector<double> spline_init(const vector<double>& x, const vector<double>& y)
{
unsigned int size = x.size();
vector<double> u(size-1), y2(size);
double sig, p;
// The so-called natural cubic spline has zero second derivative
// on one or both of its boudaries
y2[0] = u[0] = 0.;
// This is the decomposition loop of the tridiagonal algorithm
for( unsigned int i=1;i<size-1;i++ )
{
sig = (x[i]-x[i-1])/(x[i+1]-x[i-1]);
p = sig*y2[i-1]+2.;
y2[i] = (sig-1.)/p;
u[i] = (y[i+1]-y[i])/(x[i+1]-x[i])-(y[i]-y[i-1])/(x[i]-x[i-1]);
u[i] = (6.*u[i]/(x[i+1]-x[i-1])-sig*u[i-1])/p;
}
y2[size-1] = 0.;
// Back substitution loop of the tridiagonal algorithm
for( unsigned int i=size-2;i>0;i-- ) y2[i] = y2[i]*y2[i+1]+u[i];
return y2;
}
vector<double> spline_interp(const vector<double>& xa, const vector<double>& ya, const vector<double>& y2a, const vector<double>& x)
{
vector<double> y(x.size(),0.);
unsigned int k, klow, khigh;
float h, b, a;
klow = 0;
khigh = xa.size()-1;
for( unsigned int i=0;i<x.size();i++ )
{
while( khigh-klow>1 )
{
k = (khigh+klow) >> 1;
if(xa[k]>x[i]) khigh = k;
else klow = k;
}
h = xa[khigh]-xa[klow];
if( h == 0. )
{
cout << "Bad xa input to routine spline_interp" << endl;
return y;
}
a = (xa[khigh]-x[i])/h;
b = (x[i]-xa[klow])/h;
y[i] = a*ya[klow]+b*ya[khigh]+((a*a*a-a)*y2a[klow]+(b*b*b-b)*y2a[khigh])*(h*h)/6.0;
}
return y;
}
vector<double> linear_interp(const vector<double>& x, const vector<double>& y, const vector<double>& u)
{
unsigned int size = u.size();
unsigned int xsize = x.size();
vector<double> v(size);
unsigned int k, klow, khigh;
for( unsigned int i=0;i<size;i++ )
{
klow = 0;
khigh = xsize-1;
while(khigh-klow>1)
{
k = (khigh+klow)/2.;
if( x[k]>u[i] ) khigh = k;
else klow = k;
}
v[i] = y[klow]+((y[klow]-y[khigh])/(x[klow]-x[khigh]))*(u[i]-x[klow]);
}
return v;
}
double linear_interp(const vector<double>& x, const vector<double>& y, double u)
{
vector<double> v(1);
vector<double> uu(1);
uu[0] = u;
v = linear_interp(x,y,uu);
return v[0];
}
double splineFunction(double* t, double* par)
{
// par[0] : tMin
// par[1] : tMax
// par[2] : number of spline
// par[3+i] : coeff. deg i
static double xmin = par[0];
static double xmax = par[1];
static unsigned int nbspl = (unsigned int)par[2]+100; // be sure that at first call, nbspl != newnbspl
double nxmin = par[0];
double nxmax = par[1];
unsigned int newnbspl = (unsigned int)par[2];
if( newnbspl == 1 ) return 1;
static vector<double> xspl(newnbspl);
bool splinit = false;
if( newnbspl != nbspl || nxmin != xmin || nxmax != xmax )
{
xmin = nxmin;
xmax = nxmax;
nbspl = newnbspl;
splinit = true;
xspl.resize(nbspl);
for( unsigned int i = 0;i < nbspl;i++ ) xspl[i] = xmin+i*(xmax-xmin)/(nbspl-1.);
}
// We create a base of spline function
vector<double> fcsplines(nbspl);
static vector< vector<double> > vy2;
static vector< vector<double> > vyspl;
if( splinit )
{
vy2.resize(nbspl);
vyspl.resize(nbspl);
for( unsigned int i = 0;i < nbspl;i++ )
{
vector<double> yspl(nbspl,0);
yspl[i] = 1.;
vyspl[i] = yspl;
vy2[i] = spline_init(xspl,yspl);
}
}
vector<double> tt(1,t[0]);
for( unsigned int i = 0;i < nbspl;i++ )
{
vector<double> tmp = spline_interp(xspl,vyspl[i],vy2[i],tt);
fcsplines[i] = tmp[0];
}
// Linear combination of the spline function of the base
double value = 0;
for( unsigned int i = 0;i<nbspl;i++ ) value += par[3+i]*fcsplines[i];
return value;
}
double polyFunction(double* t, double* par)
{
// t[0] : theta
// par[0] : tMin
// par[1] : tMax
// par[2] : polynom degree
// par[3+i] : coeff. deg i
unsigned int degree = (unsigned int)par[2];
double value = 0.;
for(unsigned int i = 0; i < degree; i++) value = value+par[3+i]*pow(t[0],i*1.);
return value;
}
double geoFunction(double* t, double *par)
{
// t[0] = theta
return cos(t[0]*DTOR)*sin(t[0]*DTOR);
}
double fdFunction(double* t, double* par)
{
// t[0] : theta
// par[0] : FD cutoff
// par[1] : FD width
double arg = (t[0]-par[0])/par[1];
return 1./(1.+exp(arg));
}
double fdsplFunction(double* t, double *par)
{
double val;
if(*t < par[2] || *t > par[3])
{
TF1::RejectPoint();
val = 0;
}
else val = fdFunction(t,par)*geoFunction(t)*splineFunction(t,&par[2]);
return val;
}
double fdpolyFunction(double* t, double* par)
{
double val;
if(*t < par[2] || *t > par[3]) val = 0;
else val = fdFunction(t,par)*geoFunction(t)*polyFunction(t,&par[2]);
return val;
}
double geosplFunction(double* t, double* par)
{
double val;
if(*t < par[2] || *t > par[3]) val = 0;
else val = geoFunction(t)*splineFunction(t,&par[2]);
return val;
}
double geopolyFunction(double* t, double* par)
{
double val;
if(*t < par[2] || *t > par[3]) val = 0;
else val = geoFunction(t)*polyFunction(t,&par[2]);
return val;
}
double scintillatorFunction(double *t, double *par)
{
// polysfd works very well
// par[0] : FD cutoff
// par[1] : FD width
// par[2] : thetamin
// par[3] : thetamax
double val;
if(*t < par[2] || *t > par[3]) val = 0;
else val = fdsplFunction(t,par)*cos(*t*DTOR);
return val;
}
double GaussFunction(double *t, double *par)
{
double arg = (t[0]-par[2])*DTOR/par[3];
return par[0]+par[1]*exp(-arg*arg/2.);
}
double AugerPhiFunction(double *t, double *par)
{
return par[0]*(1+par[1]*cos(t[0]*DTOR*1));
}
double ModPhiThetaLaw(double *t, double *par)
{
// force small zenith angle to 0 correction
return par[0]*t[0]*exp(t[0]/par[1]);
}
double PoissonFluctuation(double mean, double value)
{
double probability = 0.;
double valueTmp = 0;
while(valueTmp <= value)
{
probability += TMath::PoissonI(valueTmp, mean);
valueTmp++;
}
return(1.0 - probability);
}
double Binomial(int NTot, int k, double p)
{
double CkN = TMath::Binomial(NTot, k);
return ( CkN * pow( p, 1.*k ) * pow( 1.-p, 1.*(NTot-k) ) );
}
double bigP(int NTot, int k, double p)
{
double P = 0.;
for(int j = k; j <= NTot; j++) P += Binomial(NTot, j, p);
return P;
}
double OneSigmaOpeningAngle(double theta, double dTheta, double dPhi)
{
return ( sqrt( dTheta*dTheta + sin(theta*DTOR)*sin(theta*DTOR)*dPhi*dPhi) * 1/sqrt(2.0) );
}
double integrate_nc5(const vector<double> & x, const vector<double> & y)
{
// This is a five points Newton-Cotes (Bode's formula) integrator
// See NumRec for details
// We assume that the data is regularly gridded
unsigned int npts = x.size();
double h = x[1]-x[0];
vector<unsigned int> ii;
unsigned int nbii = (unsigned int)floor((npts-1.)/4);
unsigned int rest = (npts-1)-nbii*4;
unsigned int nbii2;
if(rest == 1 || rest == 2) nbii2 = nbii-1;
else nbii2 = nbii;
ii.resize(nbii2);
for(unsigned int i=0; i<nbii2; i++) ii[i] = (i+1)*4;
double integral = 0;
for(unsigned int i=0; i<nbii2; i++)
{
integral += 2.*h*(7.*(y[ii[i]-4]+y[ii[i]])+32.*(y[ii[i]-3]+y[ii[i]-1])+12.*y[ii[i]-2])/45.;
}
if( rest+1 == 2 )
{
// decoupage 4-3
unsigned int shift = npts-2;
// 4 points
integral += 3*h*(y[shift-4]+3*y[shift-3]+3*y[shift-2]+y[shift-1])/8.;
// 3 points
integral += h*(y[npts-3]+4*y[npts-2]+y[npts-1])/3.;
}
else if( rest+1 == 3 )
{
// decoupage 4-4
unsigned int shift = npts-3;
// 4 points
integral += 3*h*(y[shift-4]+3*y[shift-3]+3*y[shift-2]+y[shift-1])/8.;
// 3 points
shift = npts;
integral += 3*h*(y[shift-4]+3*y[shift-3]+3*y[shift-2]+y[shift-1])/8.;
}
else if(rest+1 == 4)
{
integral += 3*h*(y[npts-4]+3*y[npts-3]+3*y[npts-2]+y[npts-1])/8.;
}
return integral;
}