source: trunk/CLHEP/src/SpaceVectorP.cc

// -*- C++ -*-
// ---------------------------------------------------------------------------
//
// This file is a part of the CLHEP - a Class Library for High Energy Physics.
//
// SpaceVector
//
// This is the implementation of the subset of those methods of the Hep3Vector 
// class which originated from the ZOOM SpaceVector class *and* which involve
// intrinsic properties or propeties relative to a second vector.
//

#ifdef GNUPRAGMA
#pragma implementation
#endif

#include "CLHEP/Vector/defs.h"
#include "CLHEP/Vector/ThreeVector.h"
#include "CLHEP/Vector/ZMxpv.h"

#include <cmath>

namespace CLHEP  {

//-********************************
//              - 5 -
// Intrinsic properties of a vector
// and properties relative to a direction
//
//-********************************

double Hep3Vector::beta() const {
  double b = sqrt(mag2());
  if (b >= 1) {
    ZMthrowA (ZMxpvTachyonic(
      "Beta taken for Hep3Vector of at least unit length"));
  }
  return b;
}

double Hep3Vector::gamma() const {
  double beta = sqrt(mag2());
  if (beta == 1) {
    ZMthrowA (ZMxpvTachyonic(
      "Gamma taken for Hep3Vector of unit magnitude -- infinite result"));
  }
  if (beta > 1) {
    ZMthrowA (ZMxpvTachyonic(
      "Gamma taken for Hep3Vector of more than unit magnitude -- "
      "the sqrt function would return NAN" ));
  }
  return 1/sqrt(1-beta*beta);
}

double Hep3Vector::rapidity() const {
  if (fabs(dz) == 1) {
    ZMthrowC (ZMxpvTachyonic(
      "Rapidity in Z direction taken for Hep3Vector with |Z| = 1 -- \n"
      "the log should return infinity"));
  }
  if (fabs(dz) > 1) {
    ZMthrowA (ZMxpvTachyonic(
      "Rapidity in Z direction taken for Hep3Vector with |Z| > 1 -- \n"
      "the log would return a NAN" ));
  }
  // Want inverse tanh(dz):
  return (.5 * log((1+dz)/(1-dz)) );
}

double Hep3Vector::coLinearRapidity() const {
  double b = beta();
  if (b == 1) {
    ZMthrowA (ZMxpvTachyonic(
      "Co-linear Rapidity taken for Hep3Vector of unit length -- "
      "the log should return infinity"));
  }
  if (b > 1) {
    ZMthrowA (ZMxpvTachyonic(
      "Co-linear Rapidity taken for Hep3Vector of more than unit length -- "
      "the log would return a NAN" ));
  }
  // Want inverse tanh(b):
  return (.5 * log((1+b)/(1-b)) );
}

//-***********************************************
// Other properties relative to a reference vector
//-***********************************************

Hep3Vector Hep3Vector::project (const Hep3Vector & v2) const {
  double mag2v2 = v2.mag2();
  if (mag2v2 == 0) {
    ZMthrowA (ZMxpvZeroVector(
      "Attempt to take projection of vector against zero reference vector "));
    return project();
  }
  return ( v2 * (dot(v2)/mag2v2) );
}

double Hep3Vector::rapidity(const Hep3Vector & v2) const {
  double vmag = v2.mag();
  if ( vmag == 0 ) {
    ZMthrowA (ZMxpvZeroVector(
      "Rapidity taken with respect to zero vector" ));
    return 0;    
  }
  double z = dot(v2)/vmag;
  if (fabs(z) >= 1) {
    ZMthrowA (ZMxpvTachyonic(
      "Rapidity taken for too large a Hep3Vector "
      "-- would return infinity or NAN"));
  }
  // Want inverse tanh(z):
  return (.5 * log((1+z)/(1-z)) );
}

double Hep3Vector::eta(const Hep3Vector & v2) const {
  // Defined as    -log ( tan ( .5* theta(u) ) );
  //
  // Quicker is to use cosTheta:
  // tan (theta/2) = sin(theta)/(1 + cos(theta))

  double r   = getR();
  double v2r = v2.mag();
  if ( (r == 0) || (v2r == 0) ) {
    ZMthrowA (ZMxpvAmbiguousAngle(
      "Cannot find pseudorapidity of a zero vector relative to a vector"));
    return 0.;
  }
  double c  = dot(v2)/(r*v2r);
  if ( c >= 1 ) {
    c = 1;      //-| We don't want to return NAN because of roundoff
    ZMthrowC (ZMxpvInfinity(
      "Pseudorapidity of vector relative to parallel vector -- "
      "will give infinite result"));
                            // We can just go on; tangent will be 0, so
                            // log (tangent) will be -INFINITY, so result
                            // will be +INFINITY.
  }
  if ( c <= -1 ) {
    ZMthrowC (ZMxpvInfinity(
      "Pseudorapidity of vector relative to anti-parallel vector -- "
      "will give negative infinite result"));
                        //-| We don't want to return NAN because of roundoff
    return ( negativeInfinity() );
                            //  If we just went on, the tangent would be NAN
                            //  so return would be NAN.  But the proper limit
                            // of tan is +Infinity, so the return should be
                            // -INFINITY.
  }

  double tangent = sqrt (1-c*c) / ( 1 + c );
  return (- log (tangent));

} /* eta (u) */


}  // namespace CLHEP