TrackUtil/TrackUtil-00-00-12/src/Lpav.cxx

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// -*- C++ -*-
//
// Package:     <package>
// Module:      Lpav
// 
// Description: <one line class summary>
//
// Implimentation:
//     <Notes on implimentation>
//
// Author:      KATAYAMA Nobuhiko
// Created:     Fri Feb  6 10:21:46 JST 1998
// $Id: Lpav.cxx,v 1.1.1.1 2008/06/16 02:10:31 max Exp $
 
// system include files
 
#include <cmath>
#include <iostream>
 
// user include files
#include "TrackUtil/Lpav.h"
 
//
// constants, enums and typedefs
//
 
extern "C" {
  float prob_ (float *, int*);
}
 
 
static double err_dis_inv(double x, double y, double w, double a, double b) {
  if (a==0 && b==0) {
    return w;
  } else {
    double f = x * b - y * a;
    double rsq = x*x+y*y;
    f *= f;
    return w*rsq/f;
  }
}
 
//
// static data member definitions
//
 
//
// constructors and destructor
//
Lpav::Lpav()
{
  clear();
}
 
// Lpav::Lpav( const Lpav& )
// {
// }
 
Lpav::~Lpav()
{
}
 
//
// assignment operators
//
// const Lpav& Lpav::operator=( const Lpav& )
// {
// }
 
//
// comparison operators
//
// bool Lpav::operator==( const Lpav& ) const
// {
// }
 
// bool Lpav::operator!=( const Lpav& ) const
// {
// }
 
//
// member functions
//
void Lpav::calculate_average(double xi, double yi, double wi) {
  if(m_wsum<=0) return;
  m_wsum_temp = m_wsum + wi;
  double rri(xi * xi + yi * yi);
  double wrri(wi * rri);
  double wsum_inv(1/m_wsum_temp);
  m_xav = (m_xsum + wi * xi) * wsum_inv;
  m_yav = (m_ysum + wi * yi) * wsum_inv;
  
  double xxav((m_xxsum + wi * xi * xi) * wsum_inv);
  double yyav((m_yysum + wi * yi * yi) * wsum_inv);
  double xyav((m_xysum + wi * xi * yi) * wsum_inv);
  double xrrav((m_xrrsum + xi * wrri) * wsum_inv);
  double yrrav((m_yrrsum + yi * wrri) * wsum_inv);
  double rrrrav((m_rrrrsum + wrri * rri) * wsum_inv);
 
  calculate_average_n(xxav, yyav, xyav, xrrav, yrrav, rrrrav);
  
}
 
void Lpav::calculate_average(void) {
  if(m_wsum<=0) return;
  m_wsum_temp = m_wsum;
  double wsum_inv(1/m_wsum_temp);
  m_xav = m_xsum * wsum_inv;
  m_yav = m_ysum * wsum_inv;
  
  double xxav(m_xxsum * wsum_inv);
  double yyav(m_yysum * wsum_inv);
  double xyav(m_xysum * wsum_inv);
  double xrrav(m_xrrsum * wsum_inv);
  double yrrav(m_yrrsum * wsum_inv);
  double rrrrav(m_rrrrsum * wsum_inv);
 
  calculate_average_n(xxav, yyav, xyav, xrrav, yrrav, rrrrav);
}
 
void Lpav::calculate_average_n(double xxav, double yyav, double xyav,
                 double xrrav, double yrrav, double rrrrav) {
  double xxav_p = xxav - m_xav * m_xav;
  double yyav_p = yyav - m_yav * m_yav;
  double xyav_p = xyav - m_xav * m_yav;
  double rrav_p = xxav_p + yyav_p;
  
  double a = std::fabs(xxav_p - yyav_p);
  double b = 4 * xyav_p * xyav_p;
  double asqpb = a * a + b;
  double rasqpb = std::sqrt(asqpb);
  double splus = 1 + a / rasqpb;
  double sminus = b / (asqpb*splus);
  splus = std::sqrt(0.5*splus);
  sminus = std::sqrt(0.5*sminus);
//C
//C== First require : SIGN(C**2 - S**2) = SIGN(XXAV - YYAV)
//C
  if ( xxav_p <= yyav_p ) {
    m_cosrot = sminus;
    m_sinrot = splus;
  } else {
    m_cosrot = splus;
    m_sinrot = sminus;
  }
//C
//C== Require : SIGN(S) = SIGN(XYAV)*SIGN(C) (Assuming SIGN(C) > 0)
//C
  if (xyav_p < 0) m_sinrot = - m_sinrot;
//*
//* We now have the smallest angle that guarantees <X**2> > <Y**2>
//*
//*  To get the SIGN of the charge right, the new X-AXIS must point
//*  outward from the orgin.  We are free to change signs of both
//*  COSROT and SINROT simultaneously to accomplish this.
//*
//*  Choose SIGN of C wisely to be able to get the sign of the charge
//*
  if ( m_cosrot*m_xav + m_sinrot*m_yav <= 0 ) {
    m_cosrot = - m_cosrot;
    m_sinrot = - m_sinrot;
  }
  m_rscale = std::sqrt(rrav_p);
  double cos2 = m_cosrot * m_cosrot;
  double sin2 = m_sinrot * m_sinrot;
  double cs2 = 2 * m_sinrot * m_cosrot;
  double rrav_p_inv(1/rrav_p);
  m_xxavp = (cos2 * xxav_p + cs2 * xyav_p + sin2 * yyav_p) * rrav_p_inv;
  m_yyavp = (cos2 * yyav_p - cs2 * xyav_p + sin2 * xxav_p) * rrav_p_inv;
  
  double xav2 = m_xav * m_xav;
  double yav2 = m_yav * m_yav;
  double xrrav_p = (xrrav - 2 * xxav * m_xav + xav2 * m_xav -
            2 * xyav * m_yav + m_xav * yav2) - m_xav * rrav_p;
  double yrrav_p = (yrrav - 2 * yyav * m_yav + yav2 * m_yav -
            2 * xyav * m_xav + m_yav * xav2) - m_yav * rrav_p;
  m_xrravp = (  m_cosrot * xrrav_p + m_sinrot * yrrav_p) * rrav_p_inv/m_rscale;
  m_yrravp = (- m_sinrot * xrrav_p + m_cosrot * yrrav_p) * rrav_p_inv/m_rscale;
  
  double rrav = xxav + yyav;
  double rrrrav_p = rrrrav
    - 2 * m_yav * yrrav - 2 * m_xav * xrrav
    + rrav * (xav2 + yav2)
    - 2 * m_xav * xrrav_p - xav2 * rrav_p 
    - 2 * m_yav * yrrav_p - yav2 * rrav_p;
  m_rrrravp = rrrrav_p * rrav_p_inv * rrav_p_inv;
  m_xyavp = 0;
}
  
void Lpav::calculate_average3(double xi, double yi, double wi) {
  if(m_wsum<=0) return;
  m_wsum_temp = m_wsum + wi;
  double wsum_inv(1/m_wsum_temp);
  double rri(xi * xi + yi * yi);
  m_xav = (m_xsum + wi * xi) * wsum_inv;
  m_yav = (m_ysum + wi * yi) * wsum_inv;
 
  m_rscale = 1;
  m_cosrot = 1;
  m_sinrot = 0;
  m_xxavp = (m_xxsum + wi * xi * xi) * wsum_inv;
  m_xyavp = (m_xysum + wi * xi * yi) * wsum_inv;
  m_yyavp = (m_yysum + wi * yi * yi) * wsum_inv;
  double wrri(wi * rri);
  m_xrravp = (m_xrrsum + xi * wrri) * wsum_inv;
  m_yrravp = (m_yrrsum + yi * wrri) * wsum_inv;
  m_rrrravp = (m_rrrrsum + rri * wrri) * wsum_inv;
}
 
void Lpav::calculate_average3(void) {
  if(m_wsum<=0) return;
  m_wsum_temp = m_wsum;
  double wsum_inv(1/m_wsum_temp);
  m_xav = m_xsum * wsum_inv;
  m_yav = m_ysum * wsum_inv;
 
  m_rscale = 1;
  m_cosrot = 1;
  m_sinrot = 0;
  m_xxavp = m_xxsum * wsum_inv;
  m_xyavp = m_xysum * wsum_inv;
  m_yyavp = m_yysum * wsum_inv;
  m_xrravp = m_xrrsum * wsum_inv;
  m_yrravp = m_yrrsum * wsum_inv;
  m_rrrravp = m_rrrrsum * wsum_inv;
}
 
 
//
// const member functions
//
 
//
// static member functions
//
        
 
std::ostream &operator<<(std::ostream &o, const Lpav &a) {
//  o << "wsum=" << a.m_wsum << " xsum=" << a.m_xsum << " ysum=" << a.m_ysum 
//  << " xxsum=" << a.m_xxsum << " xysum=" << a.m_xysum
//  << " yysum=" << a.m_yysum 
//  << " xrrsum=" << a.m_xrrsum << " yrrsum=" << a.m_yrrsum
//  << " rrrrsum=" << a.m_rrrrsum;
//  o << " rscale=" << a.m_rscale
//  << " xxavp=" << a.m_xxavp << " yyavp=" << a.m_yyavp
//  << " xrravp=" << a.m_xrravp << " yrravp=" << a.m_yrravp
//  << " rrrravp=" << a.m_rrrravp << " cosrot=" << a.m_cosrot
//  << " sinrot=" << a.m_sinrot
//  << endl;
  o << " nc=" << a.m_nc << " chisq=" << a.m_chisq << " " << (Lpar&) a;
  return o;
}
 
double Lpav::solve_lambda(void) {
  if (m_rscale<=0) return -1;
  double xrrxrr = m_xrravp * m_xrravp;
  double yrryrr = m_yrravp * m_yrravp;
  double rrrrm1 = m_rrrravp - 1;
  double xxyy = m_xxavp * m_yyavp;
 
  double c0 =       rrrrm1 * xxyy - xrrxrr * m_yyavp - yrryrr * m_xxavp;
  double c1 =     - rrrrm1        + xrrxrr        + yrryrr        - 4 * xxyy;
  double c2 =   4 + rrrrm1                                        - 4 * xxyy;
  double c4 = - 4;  
//
//C     COEFFICIENTS OF THE DERIVATIVE - USED IN NEWTON-RAPHSON ITERATIONS
//
  double c2d = 2 * c2;
  double c4d = 4 * c4;
//
  double lambda = 0;
  
  double chiscl = m_wsum_temp * m_rscale * m_rscale;
  double dlamax = 0.001 / chiscl;
  const int ntry = 5;
  int itry = 0;
  double dlambda = dlamax;
  while ( itry<ntry && std::fabs(dlambda) >= dlamax) {
    double cpoly = c0 + lambda * ( c1 + lambda *
                   ( c2 + lambda * lambda * c4));
    double dcpoly = c1 + lambda * ( c2d + lambda * lambda * c4d);
    dlambda = - cpoly / dcpoly;
    lambda += dlambda;
    itry ++;
  }
  lambda = lambda<0 ? 0 : lambda;
  return lambda;
}
 
double Lpav::solve_lambda3(void) {
  if (m_rscale<=0) return -1;
  double xrrxrr = m_xrravp * m_xrravp;
  double yrryrr = m_yrravp * m_yrravp;
  double rrrrm1 = m_rrrravp - 1;
  double xxyy = m_xxavp * m_yyavp;
 
  double a = m_rrrravp;
  double b = xrrxrr + yrryrr - m_rrrravp * (m_xxavp + m_yyavp);
  double c = m_rrrravp * m_xxavp * m_yyavp
    - m_yyavp * xrrxrr - m_xxavp * yrryrr
    + 2 * m_xyavp * m_xrravp * m_yrravp - m_rrrravp * m_xyavp * m_xyavp;
  if (c>=0 && b<=0) {
    return (-b-std::sqrt(b*b-4*a*c))/2/a;
  } else if (c>=0 && b>0) {
    std::cerr << " returning " <<-1<<std::endl; 
    return -1;
  } else if (c<0) {
    return (-b+std::sqrt(b*b-4*a*c))/2/a;
  }
  return -1;
}
 
double Lpav::calculate_lpar(void) {
  double lambda = solve_lambda();
// changed on Oct-13-93
//  if (lambda<=0) return -1;
  if (lambda<0) return -1;
  double h11 = m_xxavp - lambda;
  double h22 = m_yyavp - lambda;
  if (h11==0.0) return -1;
  double h14 = m_xrravp;
  double h24 = m_yrravp;
  double h34 = 1 + 2 * lambda;
  double rootsq = (h14*h14/h11/h11) + 4 * h34;
  if ( std::fabs(h22) > std::fabs(h24) ) {
    if(h22==0.0) return -1;
    double ratio = h24/h22;
    rootsq += ratio * ratio ;
    m_kappa = 1/std::sqrt(rootsq);
    m_beta = - ratio * m_kappa;
  } else {
    if(h24==0.0) return -1;
    double ratio = h22 / h24;
    rootsq = 1 + ratio * ratio * rootsq;
    m_beta = 1 / std::sqrt(rootsq);
    m_beta = h24>0 ? -m_beta : m_beta;
    m_kappa = -ratio * m_beta;
  }
  m_alpha = - (h14/h11)*m_kappa;
  m_gamma = - h34 * m_kappa;
//    if (lambda<0.0001) {
//      cout << " lambda=" << lambda << " h34=" << h34
//  << " rootsq=" << rootsq << " h22=" << h22
//    << " h11=" << h11 << " h14=" << h14 << " h24=" << h24 <<
//      " " << *this << endl;
//    }
//
//C     TRANSFORM THESE INTO THE LAB COORDINATE SYSTEM
//
//C     FIRST GET KAPPA  AND GAMMA  BACK TO REAL DIMENSIONS
//
  scale(m_rscale);
//
//C     NEXT ROTATE ALPHA  AND BETA
//
  rotate(m_cosrot, -m_sinrot);
//
//C     THEN TRANSLATE BY (XAV,YAV)
//
  move(-m_xav, -m_yav);
  if (m_yrravp < 0) neg();
  if (lambda>=0) m_chisq = lambda * m_wsum_temp * m_rscale * m_rscale;
  return lambda;
}
 
double Lpav::calculate_lpar3(void) {
  double lambda = solve_lambda3();
// changed on Oct-13-93
//  if (lambda<=0) return -1;
  if (lambda<0) return -1;
  double h11 = m_xxavp - lambda;
  double h22 = m_yyavp - lambda;
  double h14 = m_xrravp;
  double h24 = m_yrravp;
  m_gamma = 0;
  double h12 = m_xyavp;
  double det = h11*h22-h12*h12;
  if (det!=0) {
    double r1 = (h14*h22-h24*h12)/(det);
    double r2 = (h24*h11-h14*h12)/(det);
    double kinvsq = r1*r1 + r2*r2;
    m_kappa = std::sqrt(1/kinvsq);
    if(h11!=0) m_alpha = -m_kappa * r1;
    else m_alpha = 1;
    if(h22!=0) m_beta = -m_kappa * r2;
    else m_beta = 1;
  } else {
    m_kappa = 0;
    if (h11!=0 && h22!=0) {
      m_beta = 1/std::sqrt(1+h12*h12/h11/h11);
      m_alpha = std::sqrt(1-m_beta*m_beta);
    } else if (h11!=0) {
      m_beta = 1;
      m_alpha = 0;
    } else {
      m_beta = 0;
      m_alpha = 1;
    }
  }
  if((m_alpha*m_xav + m_beta*m_yav) *
     (m_beta*m_xav - m_alpha*m_yav)<0) neg();
//    if (std::fabs(m_alpha)<0.01 && std::fabs(m_beta)<0.01) {
//      cout << " lambda=" << lambda << " " << *this << endl;
//    }
  if (lambda>=0) m_chisq = lambda * m_wsum_temp * m_rscale * m_rscale;
  return lambda;
}
 
double Lpav::fit(double x, double y, double w) {
  if (m_nc<=3) return -1;
  m_chisq = -1;
  double q;
  if (m_nc<4) {
    calculate_average3(x,y,w);
    double q = calculate_lpar3();
    if (q>0) m_chisq = q * m_wsum_temp * m_rscale * m_rscale;
  } else {
    calculate_average(x,y,w);
    q = calculate_lpar();
    if (q>0) m_chisq = q * m_wsum_temp * m_rscale * m_rscale;
  }
  return m_chisq;
}
 
double Lpav::fit(void) {
  if (m_nc<=3) return -1;
  m_chisq = -1;
  double q;
  if (m_nc<4) {
    calculate_average3();
    q = calculate_lpar3();
    if (q>0) m_chisq = q * m_wsum_temp * m_rscale * m_rscale;
  } else {
    calculate_average();
    q = calculate_lpar();
    if (q>0) m_chisq = q * m_wsum_temp * m_rscale * m_rscale;
  }
  return m_chisq;
}
 
HepSymMatrix Lpav::cov(int inv) const
#ifdef BELLE_OPTIMIZED_RETURN
return vret(4);
{
#else
{
  HepSymMatrix vret(4);
#endif
  vret(1,1) = m_xxsum;
  vret(2,1) = m_xysum;
  vret(2,2) = m_yysum;
  vret(3,1) = m_xsum;
  vret(3,2) = m_ysum;
  vret(3,3) = m_wsum;
  vret(4,1) = m_xrrsum;
  vret(4,2) = m_yrrsum;
  vret(4,3) = m_xxsum + m_yysum;
  vret(4,4) = m_rrrrsum;
  if(inv==0) {
//    int i=vret.Inv();
    int i;
    vret.invert(i);
    if (i!=0) {
      std::cerr << "Lpav::cov:could not invert nc=" << m_nc << vret;
#ifdef HAVE_EXCEPTION
      THROW(Lpav::cov,Singular);
#endif
    }
  }
  return vret;
}
 
HepSymMatrix Lpav::cov_c(int inv) const
#ifdef BELLE_OPTIMIZED_RETURN
return vret(3);
{
#else
{
  HepSymMatrix vret(3);
#endif
#ifdef HAVE_EXCEPTION
  try {
#endif
    vret = cov(1).similarity(dldc());
#ifdef HAVE_EXCEPTION
  }
  catch (Lpav::Singular) {
    THROW(Lpav::cov_c1,Singular_c);
  }
#endif
  if(inv==0) {
//    int i = vret.Inv();
    int i;
    vret.invert(i);
    if (i!=0) {
      std::cerr << "Lpav::cov_c:could not invert " << vret;
#ifdef HAVE_EXCEPTION
      THROW(Lpav::cov_c2,Singular_c);
#endif
    }
  }
  return vret;
}
 
int Lpav::extrapolate(double r, double&phi, double &dphi) const {
  double x, y;
  if (m_chisq<0) return -1;
  if (xy(r, x, y)!=0) return -1;
  phi = std::atan2(y,x);
  if (phi<0) phi += (2*M_PI);
  HepVector v(4);
  v(1) = x;
  v(2) = y;
  v(3) = 1;
  v(4) = r * r;
//  HepSymMatrix l = cov().similarityT(v);
#ifdef HAVE_EXCEPTION
  try {
#endif
//     HepSymMatrix l = cov().similarity(v.T());
//     //  cout << "delta d^2=" << l(1,1);
//     if (l(1,1)>0) {
    double l = cov().similarity(v);
    if(l>0) {
      double ls = std::sqrt(l);
      dphi = ls / r;
      //    cout << " delta d=" << ls << " dphi=" << dphi;
    }
#ifdef HAVE_EXCEPTION
  }
  catch (Lpav::Singular) {
    return -1;
  }
#endif
//  cout << endl;
  return 0;
}
 
double Lpav::similarity(double x, double y) const {
  if (m_nc<=3) return -1;
  HepVector v(4);
  v(1) = x;
  v(2) = y;
  v(3) = 1;
  v(4) = x * x + y * y;
  double l;
#ifdef HAVE_EXCEPTION
  try {
#endif
    l = cov().similarity(v);
#ifdef HAVE_EXCEPTION
  }
  catch (Lpav::Singular) {
    return -1;
  }
#endif
  return l;
}
 
void Lpav::add(double xi, double yi, double w, double a, double b) {
  register double wi = err_dis_inv(xi, yi, w, a, b);
  add(xi, yi, wi);
}
 
void Lpav::add_point(register double xi, register double yi,
             register double wi) {
  m_wsum += wi;
  m_xsum += wi * xi;
  m_ysum += wi * yi;
  m_xxsum += wi * xi * xi;
  m_yysum += wi * yi * yi;
  m_xysum += wi * xi * yi;
  register double rri = ( xi * xi + yi * yi );
  register double wrri = wi * rri;
  m_xrrsum += wrri * xi;
  m_yrrsum += wrri * yi;
  m_rrrrsum += wrri * rri;
  m_nc += 1;
}
 
void Lpav::add_point_frac(double xi, double yi, double w, double a) {
  register double wi = w * a;
  m_wsum += wi;
  m_xsum += wi * xi;
  m_ysum += wi * yi;
  m_xxsum += wi * xi * xi;
  m_yysum += wi * yi * yi;
  m_xysum += wi * xi * yi;
  register double rri = ( xi * xi + yi * yi );
  register double wrri = wi * rri;
  m_xrrsum += wrri * xi;
  m_yrrsum += wrri * yi;
  m_rrrrsum += wrri * rri;
  m_nc += a;
}
 
void Lpav::sub(double xi, double yi, double w, double a, double b) {
  register double wi = err_dis_inv(xi, yi, w, a, b);
  m_wsum -= wi;
  m_xsum -= wi * xi;
  m_ysum -= wi * yi;
  m_xxsum -= wi * xi * xi;
  m_yysum -= wi * yi * yi;
  m_xysum -= wi * xi * yi;
  register double rri = ( xi * xi + yi * yi );
  register double wrri = wi * rri;
  m_xrrsum -= wrri * xi;
  m_yrrsum -= wrri * yi;
  m_rrrrsum -= wrri * rri;
  m_nc -= 1;
}
 
const Lpav & Lpav::operator+=(const Lpav &la1) {
  m_wsum += la1.m_wsum;
  m_xsum += la1.m_xsum;
  m_ysum += la1.m_ysum;
  m_xxsum += la1.m_xxsum;
  m_yysum += la1.m_yysum;
  m_xysum += la1.m_xysum;
  m_xrrsum += la1.m_xrrsum;
  m_yrrsum += la1.m_yrrsum;
  m_rrrrsum += la1.m_rrrrsum;
  m_nc += la1.m_nc;
  return *this;
}
 
Lpav operator+(const Lpav &la1, const Lpav &la2)
#ifdef BELLE_OPTIMIZED_RETURN
return la;
{
#else
{
  Lpav la;
#endif
  la.m_wsum = la1.m_wsum + la2.m_wsum;
  la.m_xsum = la1.m_xsum + la2.m_xsum;
  la.m_ysum = la1.m_ysum + la2.m_ysum;
  la.m_xxsum = la1.m_xxsum + la2.m_xxsum;
  la.m_yysum = la1.m_yysum + la2.m_yysum;
  la.m_xysum = la1.m_xysum + la2.m_xysum;
  la.m_xrrsum = la1.m_xrrsum + la2.m_xrrsum;
  la.m_yrrsum = la1.m_yrrsum + la2.m_yrrsum;
  la.m_rrrrsum = la1.m_rrrrsum + la2.m_rrrrsum;
  la.m_nc = la1.m_nc + la2.m_nc;
  return la;
}
 
double Lpav::prob() const {
  if (m_nc<=3) return 0;
  if (m_chisq<0) return 0;
  float c = m_chisq;
  int nci = (int)m_nc - 3;
  double p = (double) prob_(&c, &nci);
  return p;
}
 
double Lpav::chi_deg() const {
  if (m_nc<=3) return -1;
  else return m_chisq/(m_nc-3);
}
 
double Lpav::delta_chisq(double x, double y, double w) const {
  double sim = similarity(x,y);
  if(sim<0) return -1;
  double d = d0(x,y);
  double delta = std::sqrt(d) * w / (1 + sim * w);
  return delta;
}