LauArgusPdf.cc

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// Copyright University of Warwick 2006 - 2013.
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

// Authors:
// Thomas Latham
// John Back
// Paul Harrison

#include <iostream>
#include <vector>

#include "TMath.h"
#include "TSystem.h"

#include "LauArgusPdf.hh"
#include "LauConstants.hh"

ClassImp(LauArgusPdf)


LauArgusPdf::LauArgusPdf(const TString& theVarName, const std::vector<LauParameter*>& params, Double_t minAbscissa, Double_t maxAbscissa) :
        LauAbsPdf(theVarName, params, minAbscissa, maxAbscissa),
        xi_(0),
        m0_(0)
{
        // Constructor for the ARGUS PDF.
        //
        // The parameters in params are the shape, xi, and the end-point of the curve.
        // The last two arguments specify the range in which the PDF is defined, and the PDF
        // will be normalised w.r.t. these limits.

        xi_ = this->findParameter("xi");
        m0_ = this->findParameter("m0");

        if ((this->nParameters() != 2) || (xi_ == 0) || (m0_ == 0)) {
                std::cerr << "ERROR in LauArgusPdf constructor: LauArgusPdf requires 2 parameters: argus shape parameter, \"xi\", and end-point, \"m0\"." << std::endl;
                gSystem->Exit(EXIT_FAILURE);
        }

        // Cache the normalisation factor.
        this->calcNorm();
}

LauArgusPdf::~LauArgusPdf() 
{
        // Destructor
}

LauArgusPdf::LauArgusPdf(const LauArgusPdf& other) : LauAbsPdf(other.varName(), other.getParameters(), other.getMinAbscissa(), other.getMaxAbscissa())
{
        // Copy constructor
        this->setRandomFun(other.getRandomFun());
        this->calcNorm();
}

void LauArgusPdf::calcLikelihoodInfo(const LauAbscissas& abscissas)
{
        // Check that the given abscissa is within the allowed range
        if (!this->checkRange(abscissas)) {
                gSystem->Exit(EXIT_FAILURE);
        }

        // Get our abscissa
        Double_t abscissa = abscissas[0];

        // Get the up to date parameter values
        Double_t xi = xi_->value();
        Double_t m0 = m0_->value();

        // Calculate the value of the ARGUS function for the given value of the abscissa.
        Double_t x = abscissa/m0;

        Double_t term = 1.0 - x*x;
        if (term < 0.0) {term = 0.0;} // In case |x| > 1.0 (which should happen rarely).

        Double_t value = abscissa*TMath::Sqrt(term)*TMath::Exp(-xi*term);
        this->setUnNormPDFVal(value);

        // if the parameters are floating then we
        // need to recalculate the normalisation
        if (!this->cachePDF() && !this->withinNormCalc() && !this->withinGeneration()) {
                this->calcNorm();
        }
}

void LauArgusPdf::calcNorm() 
{
        // Calculate the PDF normalisation and cache it

        // Get the up to date parameter values
        Double_t xi = xi_->value();
        Double_t m0 = m0_->value();

        // Since the PDF is 0 above m0 by definition need to check whether m0 is within the range, above it or below it
        Double_t min = (this->getMinAbscissa() < m0) ? this->getMinAbscissa() : m0;
        Double_t max = (this->getMaxAbscissa() < m0) ? this->getMaxAbscissa() : m0;

        // Define variables equivalent to "term" in calcLikelihoodInfo above but at the min and max points
        Double_t termMin = 1.0 - (min/m0)*(min/m0);
        Double_t termMax = 1.0 - (max/m0)*(max/m0);

        // Calculate the various terms in the integrals
        Double_t norm1 = TMath::Sqrt(termMax)*TMath::Exp(-xi*termMax) - TMath::Sqrt(termMin)*TMath::Exp(-xi*termMin);
        Double_t norm2 = LauConstants::rootPi/(2.0*TMath::Sqrt(xi)) * ( TMath::Erf(TMath::Sqrt(xi*termMax)) - TMath::Erf(TMath::Sqrt(xi*termMin)) );

        // Combine them and set the normalisation
        Double_t norm = m0*m0*(norm1 - norm2)/(2.0*xi);

        this->setNorm(norm);
}

void LauArgusPdf::calcPDFHeight( const LauKinematics* /*kinematics*/ )
{
        if (this->heightUpToDate()) {
                return;
        }

        // Calculate the PDF height of the ARGUS function.
        // Get the up to date parameter values
        Double_t xi = xi_->value();
        Double_t m0 = m0_->value();

        // First make sure that the limits are not larger than the end-point.
        // (Btw, use the logarithmic derivative to derive this formula) 
        Double_t term = xi*xi + 1.0;
        Double_t x = TMath::Sqrt((TMath::Sqrt(term) - 1.0 + xi)/(2.0*xi));
        x = (x*m0 >= this->getMinAbscissa()) ? x*m0 : this->getMinAbscissa();

        LauAbscissas abscissa(1);
        abscissa[0] = x;
        this->calcLikelihoodInfo(abscissa);

        Double_t height = this->getUnNormLikelihood();
        this->setMaxHeight(height);
}