eflowCellIntegrator.h

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/*
  Copyright (C) 2002-2023 CERN for the benefit of the ATLAS collaboration
*/
 
/*
 * eflowCellIntegration.h
 *
 *  Created on: 12.08.2013
 *      Author: tlodd
 */
 
#ifndef EFLOWCELLINTEGRATION_H_
#define EFLOWCELLINTEGRATION_H_
 
#include <stdexcept>
#include <iostream>
 
#include <math.h>
 
#include "eflowRec/eflowUtil.h"
#include "eflowRec/eflowLookupExp.h"
#include "eflowRec/LegendreWeights.h"

enum Exp_t {stdExp = 0, lookupExp};

template <class IntegrandType>
class eflowRecursiveGaussLegendreIntegrator {
public:
  eflowRecursiveGaussLegendreIntegrator(IntegrandType* integrand, double error) :
    m_integrand(integrand), m_error(error), m_depth(1) {
    assert(m_integrand);
  }
  virtual ~eflowRecursiveGaussLegendreIntegrator() { }
 
  virtual double integrate(const eflowRange& range) {
    /* Try a 5th and 6th order Gauss-Legendre quadrature */
    double I5 = DoGaussLegendreIntegration(range, 5);
    double I6 = DoGaussLegendreIntegration(range, 6);
 
    /* If results agree within m_error threshold, return the mean... */
    double Imean = (I5 + I6) / 2.0;
    if (fabs(I5 - I6) / Imean <= m_error) {
      return Imean;
    } else {
      /* ...else recursively part up the integration into n subRanges */
      return RecurseIntegration(range, 2);
    }
  }
 
  double getError() const {return m_error;}
 
private:
 
  double DoGaussLegendreIntegration(const eflowRange& range, int nOrder){
    /* Perform nth order Gauss-Legendre quadrature, see
     * http://en.wikipedia.org/wiki/Gaussian_quadrature#Gauss.E2.80.93Legendre_quadrature */
 
    /* Array offset for legendre weights/roots */
    int j = nOrder * (nOrder - 1) / 2;
    const double* roots   = legendreRoots   + j;
    const double* weights = legendreWeights + j;
 
    double rangeCenter    = range.getCenter();
    double rangeHalfWidth = range.getWidth()/2;
 
    double I = 0.0;
    double x;
    if(m_integrand){
      for (int i = 0; i < nOrder; i++) {
    x = rangeCenter + roots[i] * rangeHalfWidth;
    I += weights[i] * m_integrand->evaluate(x);
      }
    }
    else{
      std::cerr << "eflowCellIntergrator::DoGaussLegendreIntegration ERROR : Invalid pointer to IntegrandType and cannot perform integration" << std::endl;
    }
    if (I < 0. || rangeHalfWidth < 0.) std::cerr << "eflowCellIntergrator::DoGaussLegendreIntegration WARNING: I = " << I << "\trange = " << range.print() << std::endl;
 
    return I * rangeHalfWidth;
  }
 
  double RecurseIntegration(const eflowRange& range, int nSubRanges){
    m_depth++;
    /* Part up integration range in n subRanges */
    double subRangeWidth = range.getWidth() / nSubRanges;
    eflowRange subRange(range.getMin(), range.getMin() + subRangeWidth);
 
    /* Loop over subranges */
    double Integral(0.0);
    for (int i = 0; i < nSubRanges; i++) {
      Integral += integrate(subRange);
      subRange.shift(subRangeWidth);
    }
    m_depth--;
 
    return Integral;
  }
 
  IntegrandType* m_integrand;
  double m_error;
  int m_depth;
};

template <Exp_t expType> class eflowCellIntegrand {
public:
  eflowCellIntegrand(double sigma): m_lookupExp(eflowLookupExp::getInstance()),
  m_oneOverTwoSigmaSq(1 / (2 * sigma * sigma)), m_norm(m_oneOverTwoSigmaSq / M_PI), m_etaSq(NAN) { }
  ~eflowCellIntegrand() { }
 
  inline void setEtaSq(double xSq) { m_etaSq = xSq; }
 
  inline double evaluateStdExp(double rSq) const { return m_norm * exp(-rSq * m_oneOverTwoSigmaSq); }
  inline double evaluateLookupExp(double rSq) const { return m_lookupExp->evaluate(rSq * m_oneOverTwoSigmaSq)*m_norm; }

  inline double evaluate(double y);
 
private:
  const eflowLookupExp* m_lookupExp;
  double m_oneOverTwoSigmaSq;
  double m_norm;
  double m_etaSq;
};
template<> inline double eflowCellIntegrand<stdExp>::evaluate(double phi) { return evaluateStdExp(m_etaSq+phi*phi); }
template<> inline double eflowCellIntegrand<lookupExp>::evaluate(double phi) { return evaluateLookupExp(m_etaSq+phi*phi); }

template <int expType> class eflowCellIntegrator {
public:
  eflowCellIntegrator(double stdDev, double error) : m_integrand2D(std::make_unique<eflowCellIntegrand<(Exp_t)expType> >(stdDev)), m_outerIntegrator(this, error), m_innerIntegrator(m_integrand2D.get(), error) { }
  eflowCellIntegrator(const eflowCellIntegrator& original) : m_integrand2D(std::make_unique<eflowCellIntegrand<(Exp_t)expType> >(*(original.m_integrand2D.get()))), m_outerIntegrator(this, original.m_outerIntegrator.getError()), m_innerIntegrator( m_integrand2D.get(), original.m_innerIntegrator.getError()),
    m_rangePhi (original.m_rangePhi)
  {
  }
  eflowCellIntegrator&  operator=(const eflowCellIntegrator& original){
    m_integrand2D(std::make_unique<eflowCellIntegrand<(Exp_t)expType> >(*(original.m_integrand2D.get())));
    m_outerIntegrator(this, original.m_outerIntegrator.getError());
    m_innerIntegrator( m_integrand2D.get(), original.m_innerIntegrator.getError());
    m_rangePhi = original.m_rangePhi;
  }
  ~eflowCellIntegrator() {}

  inline double integrate(const eflowRange& etaRange, const eflowRange& phiRange) {
    /* Store the phi range for the inner integration */
    m_rangePhi = phiRange;
    /* Invoke the outer integration */
    return m_outerIntegrator.integrate(etaRange);
  }

  inline double evaluate(double eta) {
    /* Set the eta (square) value for the inner integration */
    m_integrand2D->setEtaSq(eta*eta);
    /* Perform the inner (i.e. phi) integration (will invoke the evaluate() method on m_innerIntegrator) */
    return m_innerIntegrator.integrate(m_rangePhi);
  }
 
private:
  std::unique_ptr<eflowCellIntegrand<(Exp_t)expType> > m_integrand2D;
  eflowRecursiveGaussLegendreIntegrator<eflowCellIntegrator<expType>  > m_outerIntegrator;
  eflowRecursiveGaussLegendreIntegrator<eflowCellIntegrand<(Exp_t)expType> > m_innerIntegrator;
  eflowRange m_rangePhi;
};
 
 
#endif /* EFLOWCELLINTEGRATION_H_ */