Functions.h

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#ifndef _un2_Functions_h_
#define _un2_Functions_h_

// OFFLINE
#include <utl/Math.h>
#include <vector>


namespace un2 {

  inline
  constexpr
  double
  Deg2Rad(const double deg)
  {
    return (M_PI/180)*deg;
  }


  inline
  constexpr
  double
  Rad2Deg(const double rad)
  {
    return (180/M_PI)*rad;
  }


  inline
  double
  Mean(const std::vector<double>& v)
  {
    return std::accumulate(v.begin(), v.end(), 0.) / v.size();
  }


  double
  StandardDeviation(const std::vector<double>& v, const double mean);


  double
  StandardDeviation(const std::vector<double>& v);


  // universality signal model paper 2016, ave engel roth schulz, eq. (12)
  double 
  ModifiedGH(
    /* x  */   const double DeltaX,
    /*p[0]*/   const double Sref,
    /*p[1]*/   const double lgE,
    /*p[2]*/   const double gamma,
    /*p[3]*/   const double DeltaX0,
    /*p[4]*/   const double DeltaXmax,
    /*p[5]*/   const double DeltaXref,
    /*p[6]*/   const double lambda0,
    /*p[7]*/   const double lambda1,
    /*p[8]*/   const double lambda2
  );


  inline
  constexpr
  double 
  Polynomial4(/* x */ const double x,
              /*p[0]*/ const double a0,
              /*p[1]*/ const double a1,
              /*p[2]*/ const double a2,
              /*p[3]*/ const double a3,
              /*p[4]*/ const double a4)
  {
    // f(x) = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + a_4 x^4
    return a0 + x * (a1 + x * (a2 + x * (a3 + x * a4)));
  }


  inline
  constexpr
  double 
  Exponential(/* x */ const double x,
              /*p[0]*/ const double a,
              /*p[1]*/ const double b,
              /*p[2]*/ const double c)
  {
    // f(x) = a \e^{b x} + c
    return a * exp(x / b) + c;
  }


  double
  NKG(
    /* x  */ const double r,
    /*p[0]*/ const double n,
    /*p[1]*/ const double rG, 
    /*p[2]*/ const double s
  );


  double
  ActivationFunctionBackground(
    const double f,
    const double fThrsh,
    const double cThrsh,
    const double bg
  );


  double
  AzimuthCorrectionFactor(const double theta,
                          const double psi,
                          const double r,
                          const double r0,
                          const double l);


  // this is NOT empiric
  double
  TwoFormAzimuthCorrectionFactor(const double theta,
                                 const double psi,
                                 const double M1, 
                                 const double M3);


  double
  Gaussian(const double x,
           const double mu,
           const double sigma);


  double
  SpikyFunction(const double x,
                const double sigma,
                const double delta,
                const std::vector<double>& nvec);


  double
  SpikyFunction(const double x,
                const std::vector<double>& sigmavec,
                const std::vector<double>& muvec,
                const std::vector<double>& nvec);


  double
  SignalStartTime(const double r,
                  const double psi,
                  const double theta,
                  const double DX,
                  const double Xvert = 883,
                  const double hs = 8380,
                  const double hs2 = 0.07);


  double
  SignalStartTimePlaneFront(const double r,
                            const double psi,
                            const double theta,
                            const double DX,
                            const double Xvert = 883,
                            const double hs = 8380,
                            const double hs2 = 0.07,
                            const double height = 1400.);


  double
  LogarithmOfRayleighPDF(const double x,
                         const double sigma);


  double
  LogarithmOfTruncatedGaussianPDF(const double x,
                                  const double mu,
                                  const double sigma);


  double
  LogNormalPDF(const double x,
               const double mu,
               const double sigma);


  double
  LogNormalCDF(const double x,
               const double mu,
               const double sigma);


  double
  LogNormalMuFromModeAndSigma(const double mode,
                              const double sigma,
                              const double ns_bin = 8.3333);


  double
  LogNormalMuFromExpAndStd(const double exp,
                           const double std,
                           const double ns_bin = 8.3333);


  double
  LogNormalSigmaFromExpAndStd(const double exp,
                              const double std,
                              const double ns_bin = 8.3333);


  double
  LogNormalTimeQuantileFromMuAndSigma(const double mu,
                                      const double sigma,
                                      const double quantile,
                                      const double ns_bin = 8.3333);


  double
  LogNormalMuFromTimeQuantileAndSigma(const double timeQuantile,
                                      const double quantile,
                                      const double sigma,
                                      const double ns_bin = 8.3333);


  double
  ErfInv(double x);


  double
  ErfcInv(const double x);


  double
  GammaPDF(const double x,
           const double mu,
           const double theta);


  double
  AnalyticDX(const double r,
             const double psi,
             const double theta,
             const double Xmax,
             const double Xvert = 883,
             const double hs = 8380,
             const double hs2 = 0.07,
             const double height = 1400);


  double
  AnalyticXmax(const double r,
               const double psi,
               const double theta,
               const double DX,
               const double Xvert = 883,
               const double hs = 8380,
               const double hs2 = 0.07,
               const double height = 1400);


  double
  AnalyticHeightFromDepth(const double depth,
                          const double theta,
                          const double xVertGround,
                          const double hs,
                          const double hs2);

  double
  BiasCorrectionXmax(const double sst,
                     const double lgE, 
                     const bool realEvent = false);

  double
  BiasCorrectionRmu(const double sst,
                    const double lgE, 
                    const bool realEvent = false);

  double
  GHGauss(const double r,
          const double psi,
          const double theta,
          const double Xmax,
          const double lambda);

  double
  avgXmax0(const double lgE, const bool realEvent);

  double
  avglnRmu0(const double lgE, const bool realEvent);

  double
  XmaxFromRmu(const double Rmu, const double lgE, const bool realEvent);

  double
  SigmaXmaxFromRmu(const double Rmu, const double lgE, const bool realEvent);

  double
  XmaxDistribution(const double Rmu, const double Xmax, const double lgE, const bool realEvent);

  double
  lnA(const double Rmu, const double Xmax, const double lgE, const bool realEvent);

}


#endif