//************************************************
// Author: Federica Lionetto
// Created on: 07/05/2016
//************************************************

// Header guard.
#ifndef __LANDAU_C_INCLUDED__
#define __LANDAU_C_INCLUDED__

//-----------------------------------------------------------------------
//
// Convoluted Landau and Gaussian Fitting Function
//         (using ROOT's Landau and Gauss functions)
//
//  Based on a Fortran code by R.Fruehwirth (fruhwirth@hephy.oeaw.ac.at)
//  Adapted for C++/ROOT by H.Pernegger (Heinz.Pernegger@cern.ch) and
//   Markus Friedl (Markus.Friedl@cern.ch)
//
//  to execute this example, do:
//  root > .x langaus.C
// or
//  root > .x langaus.C++
//
//-----------------------------------------------------------------------

Double_t langaufun(Double_t *x, Double_t *par) {

    //Fit parameters:
    //par[0]=Width (scale) parameter of Landau density
    //par[1]=Most Probable (MP, location) parameter of Landau density
    //par[2]=Total area (integral -inf to inf, normalization constant)
    //par[3]=Width (sigma) of convoluted Gaussian function
    //
    //In the Landau distribution (represented by the CERNLIB approximation),
    //the maximum is located at x=-0.22278298 with the location parameter=0.
    //This shift is corrected within this function, so that the actual
    //maximum is identical to the MP parameter.

    // Numeric constants
    Double_t invsq2pi = 0.3989422804014;   // (2 pi)^(-1/2)
    Double_t mpshift  = -0.22278298;       // Landau maximum location

    // Control constants
    Double_t np = 100.0;      // number of convolution steps
    Double_t sc =   5.0;      // convolution extends to +-sc Gaussian sigmas

    // Variables
    Double_t xx;
    Double_t mpc;
    Double_t fland;
    Double_t sum = 0.0;
    Double_t xlow,xupp;
    Double_t step;
    Double_t i;


    // MP shift correction
    mpc = par[1] - mpshift * par[0];

    // Range of convolution integral
    xlow = x[0] - sc * par[3];
    xupp = x[0] + sc * par[3];

    step = (xupp-xlow) / np;

    // Convolution integral of Landau and Gaussian by sum
    for(i=1.0; i<=np/2; i++) {
        xx = xlow + (i-.5) * step;
        fland = TMath::Landau(xx,mpc,par[0]) / par[0];
        sum += fland * TMath::Gaus(x[0],xx,par[3]);

        xx = xupp - (i-.5) * step;
        fland = TMath::Landau(xx,mpc,par[0]) / par[0];
        sum += fland * TMath::Gaus(x[0],xx,par[3]);
    }

    return (par[2] * step * sum * invsq2pi / par[3]);
}



TF1 *langaufit(TH1F *his, Double_t *fitrange, Double_t *startvalues, Double_t *parlimitslo, Double_t *parlimitshi, Double_t *fitparams, Double_t *fiterrors, Double_t *ChiSqr, Int_t *NDF)
{
    // Once again, here are the Landau * Gaussian parameters:
    //   par[0]=Width (scale) parameter of Landau density
    //   par[1]=Most Probable (MP, location) parameter of Landau density
    //   par[2]=Total area (integral -inf to inf, normalization constant)
    //   par[3]=Width (sigma) of convoluted Gaussian function
    //
    // Variables for langaufit call:
    //   his             histogram to fit
    //   fitrange[2]     lo and hi boundaries of fit range
    //   startvalues[4]  reasonable start values for the fit
    //   parlimitslo[4]  lower parameter limits
    //   parlimitshi[4]  upper parameter limits
    //   fitparams[4]    returns the final fit parameters
    //   fiterrors[4]    returns the final fit errors
    //   ChiSqr          returns the chi square
    //   NDF             returns ndf

    Int_t i;
    Char_t FunName[100];

    sprintf(FunName,"Fitfcn_%s",his->GetName());

    TF1 *ffitold = (TF1*)gROOT->GetListOfFunctions()->FindObject(FunName);
    if (ffitold) delete ffitold;

    TF1 *ffit = new TF1(FunName,langaufun,fitrange[0],fitrange[1],4);
    ffit->SetParameters(startvalues);
    ffit->SetParNames("Width","MP","Area","GSigma");

    for (i=0; i<4; i++) {
        ffit->SetParLimits(i, parlimitslo[i], parlimitshi[i]);
    }

    his->Fit(FunName,"RB0");   // fit within specified range, use ParLimits, do not plot

    ffit->GetParameters(fitparams);    // obtain fit parameters
    for (i=0; i<4; i++) {
        fiterrors[i] = ffit->GetParError(i);     // obtain fit parameter errors
    }
    ChiSqr[0] = ffit->GetChisquare();  // obtain chi^2
    NDF[0] = ffit->GetNDF();           // obtain ndf

    return (ffit);              // return fit function

}



Int_t langaupro(Double_t *params, Double_t &maxx, Double_t &FWHM) {

    // Seaches for the location (x value) at the maximum of the
    // Landau-Gaussian convolute and its full width at half-maximum.
    //
    // The search is probably not very efficient, but it's a first try.

    Double_t p,x,fy,fxr,fxl;
    Double_t step;
    Double_t l,lold;
    Int_t i = 0;
    Int_t MAXCALLS = 10000;


    // Search for maximum

    p = params[1] - 0.1 * params[0];
    step = 0.05 * params[0];
    lold = -2.0;
    l    = -1.0;


    while ( (l != lold) && (i < MAXCALLS) ) {
        i++;

        lold = l;
        x = p + step;
        l = langaufun(&x,params);

        if (l < lold)
            step = -step/10;

        p += step;
    }

    if (i == MAXCALLS)
        return (-1);

    maxx = x;

    fy = l/2;


    // Search for right x location of fy

    p = maxx + params[0];
    step = params[0];
    lold = -2.0;
    l    = -1e300;
    i    = 0;


    while ( (l != lold) && (i < MAXCALLS) ) {
        i++;

        lold = l;
        x = p + step;
        l = TMath::Abs(langaufun(&x,params) - fy);

        if (l > lold)
            step = -step/10;

        p += step;
    }

    if (i == MAXCALLS)
        return (-2);

    fxr = x;


    // Search for left x location of fy

    p = maxx - 0.5 * params[0];
    step = -params[0];
    lold = -2.0;
    l    = -1e300;
    i    = 0;

    while ( (l != lold) && (i < MAXCALLS) ) {
        i++;

        lold = l;
        x = p + step;
        l = TMath::Abs(langaufun(&x,params) - fy);

        if (l > lold)
            step = -step/10;

        p += step;
    }

    if (i == MAXCALLS)
        return (-3);


    fxl = x;

    FWHM = fxr - fxl;
    return (0);
}

#endif
