Fourvec_Constrainer.cc

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//
//
// File: src/Fourvec_Constrainer.cc
// Purpose: Do a kinematic fit for a set of 4-vectors, given a set
//          of mass constraints.
// Created: Jul, 2000, sss, based on run 1 mass analysis code.
//
// CMSSW File      : src/Fourvec_Constrainer.cc
// Original Author : Scott Stuart Snyder <snyder@bnl.gov> for D0
// Imported to CMSSW by Haryo Sumowidagdo <Suharyo.Sumowidagdo@cern.ch>
//


#include "TopQuarkAnalysis/TopHitFit/interface/Fourvec_Constrainer.h"
#include "TopQuarkAnalysis/TopHitFit/interface/Fourvec_Event.h"
#include "TopQuarkAnalysis/TopHitFit/interface/Pair_Table.h"
#include "TopQuarkAnalysis/TopHitFit/interface/Chisq_Constrainer.h"
#include "TopQuarkAnalysis/TopHitFit/interface/matutil.h"
#include "TopQuarkAnalysis/TopHitFit/interface/Defaults.h"
#include <cmath>
#include <iostream>


using std::sqrt;
using std::exp;
using std::cos;
using std::sin;
using std::ostream;
using std::vector;


namespace hitfit {


//*************************************************************************
// Argument handling.
//


Fourvec_Constrainer_Args::Fourvec_Constrainer_Args (const Defaults& defs)
//
// Purpose: Constructor.
//
// Inputs:
//   defs -        The Defaults instance from which to initialize.
//
  : _use_e (defs.get_bool ("use_e")),
    _e_com (defs.get_float ("e_com")),
    _ignore_met (defs.get_bool ("ignore_met")),
    _chisq_constrainer_args (defs)
{
}


bool Fourvec_Constrainer_Args::use_e () const
//
// Purpose: Return the use_e parameter.
//          See the header for documentation.
//
{
  return _use_e;
}


double Fourvec_Constrainer_Args::e_com () const
//
// Purpose: Return the e_com parameter.
//          See the header for documentation.
//
{
  return _e_com;
}


bool Fourvec_Constrainer_Args::ignore_met () const
//
// Purpose: Return the ignore_met parameter.
//          See the header for documentation.
//
{
  return _ignore_met;
}


const Chisq_Constrainer_Args&
Fourvec_Constrainer_Args::chisq_constrainer_args () const
//
// Purpose: Return the contained subobject parameters.
//
{
  return _chisq_constrainer_args;
}


//*************************************************************************
// Variable layout.
//
// We need to map the quantities we fit onto the vectors of well- and
// poorly-measured quantities.
//

//
// The well-measured variables consist of three variables for each
// object.  If we are using transverse momentum constraints,
// these fill be followed by the two cartesian components of kt.
//
// Each object is represented by three variables: the momentum (or 1/p
// if the muon flag was set), and the two spherical angles, phi and eta.
// Here is how they're ordered.
//
typedef enum {
  p_offs = 0,
  phi_offs = 1,
  eta_offs = 2
} Offsets;

typedef enum {
  x_offs = 0,
  y_offs = 1
} Kt_Offsets;

//
// If there is a neutrino, then it is at index 1 of the poorly-measured
// set (otherwise, that set is empty).
//
typedef enum {
  nu_z = 1
} Unmeasured_Variables;



namespace {


int obj_index (int i)
//
// Purpose: Return the starting variable index for object I.
//
// Inputs:
//   i -           The object index.
//
// Returns:
//   The index in the well-measured set of the first variable
//   for object I.
//
{
  return i*3 + 1;
}


} // unnamed namespace


//*************************************************************************
// Object management.
//


Fourvec_Constrainer::Fourvec_Constrainer (const Fourvec_Constrainer_Args& args)
//
// Purpose: Constructor.
//
// Inputs:
//   args -        The parameter settings for this instance.
//
  : _args (args)
{
}


void Fourvec_Constrainer::add_constraint (std::string s)
//
// Purpose: Specify an additional constraint S for the problem.
//          The format for S is described in the header.
//
// Inputs:
//   s -           The constraint to add.
//
{
  _constraints.push_back (Constraint (s));
}


void Fourvec_Constrainer::mass_constraint (std::string s)
//
// Purpose: Specify the combination of objects that will be returned by
//          constrain() as the mass.  The format of S is the same as for
//          normal constraints.  The LHS specifies the mass to calculate;
//          the RHS should be zero.
//          This should only be called once.
//
// Inputs:
//   s -           The constraint defining the mass.
//
{
  assert (_mass_constraint.size() == 0);
  _mass_constraint.push_back (Constraint (s));
}


std::ostream& operator<< (std::ostream& s, const Fourvec_Constrainer& c)
//
// Purpose: Print the object to S.
//
// Inputs:
//   s -           The stream to which to write.
//   c -           The object to write.
//
// Returns:
//   The stream S.
//
{
  s << "Constraints: (e_com = " << c._args.e_com() << ") ";
  if (c._args.use_e())
    s << "(E)";
  s << "\n";

  for (std::vector<Constraint>::size_type i=0; i < c._constraints.size(); i++)
    s << "  " << c._constraints[i] << "\n";

  if (c._mass_constraint.size() > 0) {
    s << "Mass constraint:\n";
    s << c._mass_constraint[0] << "\n";
  }
  return s;
}


//*************************************************************************
// Event packing and unpacking.
//


namespace {


void adjust_fourvecs (Fourvec_Event& ev,
                      bool use_e_flag)
//
// Purpose: For all objects in EV, adjust their 4-momenta
//          to have their requested masses.
//
// Inputs:
//   ev -          The event on which to operate.
//   use_e_flag -  If true, keep E and scale 3-momentum.
//                 If false, keep the 3-momentum and scale E.
//
{
  int nobjs = ev.nobjs ();
  for (int i=0; i < nobjs; i++) {
    const FE_Obj& obj = ev.obj (i);
    Fourvec p = obj.p;
    if (use_e_flag)
      adjust_p_for_mass (p, obj.mass);
    else
      adjust_e_for_mass (p, obj.mass);
    ev.set_obj_p (i, p);
  }
}


Fourvec get_p_eta_phi_vec (const Column_Vector& c,
                           int ndx,
                           const FE_Obj& obj,
                           bool use_e_flag)
//
// Purpose: Convert object NDX from its representation in the set
//          of well-measured variables C to a 4-vector.
//
// Inputs:
//   c -           The vector of well-measured variables.
//   ndx -         The index of the object in which we're interested.
//   obj -         The object from the Fourvec_Event.
//   use_e_flag -  If true, we're using E as the fit variable, otherwise p.
//
// Returns:
//   The object's 4-momentum.
//
{
  // Get the energy and momentum of the object.
  double e, p;

  if (use_e_flag) {
    // We're using E as a fit variable.  Get it directly.
    e = c(ndx + p_offs);

    // Take into account the muon case.
    if (obj.muon_p) e = 1/e;

    // Find the momentum given the energy.
    if (obj.mass == 0)
      p = e;
    else {
      double xx = e*e - obj.mass*obj.mass;
      if (xx >= 0)
    p = sqrt (xx);
      else
    p = 0;
    }
  }
  else {
    // We're using P as a fit variable.  Fetch it.
    p = c(ndx + p_offs);

    // Take into account the muon case.
    if (obj.muon_p) p = 1/p;

    // Find the energy given the momentum.
    e = (obj.mass == 0 ? p : sqrt (obj.mass*obj.mass + p*p));
  }

  // Get angular variables.
  double phi = c(ndx + phi_offs);
  double eta = c(ndx + eta_offs);
  if (fabs (eta) > 50) {
    // Protect against ridiculously large etas
    eta = eta > 0 ? 50 : -50;
  }
  double exp_eta = exp (eta);
  double iexp_eta = 1/exp_eta;
  double sin_theta = 2 / (exp_eta + iexp_eta);
  double cos_theta = (exp_eta - iexp_eta) / (exp_eta + iexp_eta);

  // Form the 4-momentum.
  return Fourvec (p * sin_theta * cos (phi),
                  p * sin_theta * sin (phi),
                  p * cos_theta,
                  e);
}


void set_p_eta_phi_vec (const FE_Obj& obj,
                        Column_Vector& c,
                        int ndx,
                        bool use_e_flag)
//
// Purpose: Initialize the variables in the well-measured set C describing
//          object NDX from its Fourvec_Event representation OBJ.
//
// Inputs:
//   obj -         The object from the Fourvec_Event.
//   c -           The vector of well-measured variables.
//   ndx -         The index of the object in which we're interested.
//   use_e_flag -  If true, we're using E as the fit variable, otherwise p.
//
//
{
  if (use_e_flag)
    c(ndx + p_offs) = obj.p.e();
  else
    c(ndx + p_offs) = obj.p.vect().mag();

  if (obj.muon_p) c(ndx + p_offs) = 1/c(ndx + p_offs);
  c(ndx + phi_offs) = obj.p.phi();
  c(ndx + eta_offs) = obj.p.pseudoRapidity();
}


Matrix error_matrix (double p_sig,
                     double phi_sig,
                     double eta_sig)
//
// Purpose: Set up the 3x3 error matrix for an object.
//
// Inputs:
//   p_sig -       The momentum uncertainty.
//   phi_sig -     The phi uncertainty.
//   eta_sig -     The eta uncertainty.
//
// Returns:
//   The object's error matrix.
//
{
  Matrix err (3, 3, 0);
  err(1+  p_offs, 1+  p_offs) = p_sig * p_sig;
  err(1+phi_offs, 1+phi_offs) = phi_sig * phi_sig;
  err(1+eta_offs, 1+eta_offs) = eta_sig * eta_sig;
  return err;
}


void pack_event (const Fourvec_Event& ev,
                 bool use_e_flag,
                 bool use_kt_flag,
                 Column_Vector& xm,
                 Column_Vector& ym,
                 Matrix& G_i,
                 Diagonal_Matrix& Y)
//
// Purpose: Take the information from a Fourvec_Event EV and pack
//          it into vectors of well- and poorly-measured variables.
//          Also set up the error matrices.
//
// Inputs:
//   ev -          The event to pack.
//   use_e_flag -  If true, we're using E as the fit variable, otherwise p.
//   use_kt_flag - True if we're to pack kt variables.
//
// Outputs:
//   xm -          Vector of well-measured variables.
//   ym -          Vector of poorly-measured variables.
//   G_i -         Error matrix for well-measured variables.
//   Y -           Inverse error matrix for poorly-measured variables.
//
{
  // Number of objects in the event.
  int nobjs = ev.nobjs ();

  int n_measured_vars = nobjs * 3;
  if (use_kt_flag)
    n_measured_vars += 2;

  // Clear the error matrix.
  G_i = Matrix (n_measured_vars, n_measured_vars, 0);

  // Loop over objects.
  for (int i=0; i<nobjs; i++) {
    const FE_Obj& obj = ev.obj (i);
    int this_index = obj_index (i);
    set_p_eta_phi_vec (obj, xm, this_index, use_e_flag);
    G_i.sub (this_index, this_index, error_matrix (obj.p_error,
                                                   obj.phi_error,
                                                   obj.eta_error));

  }

  if (use_kt_flag) {
    // Set up kt.
    int kt_ndx = obj_index (nobjs);
    xm (kt_ndx+x_offs) = ev.kt().x();
    xm (kt_ndx+y_offs) = ev.kt().y();

    // And its error matrix.
    G_i(kt_ndx+x_offs, kt_ndx+x_offs) = ev.kt_x_error() * ev.kt_x_error();
    G_i(kt_ndx+y_offs, kt_ndx+y_offs) = ev.kt_y_error() * ev.kt_y_error();
    G_i(kt_ndx+x_offs, kt_ndx+y_offs) = ev.kt_xy_covar();
    G_i(kt_ndx+y_offs, kt_ndx+x_offs) = ev.kt_xy_covar();
  }

  // Handle a neutrino.
  if (ev.has_neutrino()) {
    ym(nu_z) = ev.nu().z();
    Y = Diagonal_Matrix (1, 0);
  }
}


void unpack_event (Fourvec_Event& ev,
                   const Column_Vector& x,
                   const Column_Vector& y,
                   bool use_e_flag,
                   bool use_kt_flag)
//
// Purpose: Update the contents of EV from the variable sets X and Y.
//
// Inputs:
//   ev -          The event.
//   x -           Vector of well-measured variables.
//   use_e_flag -  If true, we're using E as the fit variable, otherwise p.
//   use_kt_flag - True if we're too unpack kt variables.
//
// Outputs:
//   ev -          The event after updating.
//
{
  // Do all the objects.
  Fourvec sum = Fourvec(0);
  for (int j=0; j<ev.nobjs(); j++) {
    const FE_Obj& obj = ev.obj (j);
    ev.set_obj_p (j, get_p_eta_phi_vec (x, obj_index (j), obj, use_e_flag));
    sum += obj.p;
  }


  if (use_kt_flag) {
    int kt_ndx = obj_index (ev.nobjs());
    Fourvec kt = Fourvec (x(kt_ndx+x_offs), x(kt_ndx+y_offs), 0, 0);
    Fourvec nu = kt - sum;
    if (ev.has_neutrino()) {
      nu.setPz (y(nu_z));
      adjust_e_for_mass (nu, 0);
      ev.set_nu_p (nu);
    }
    else {
      adjust_e_for_mass (nu, 0);
      ev.set_x_p (nu);
    }
  }
}


} // unnamed namespace


//*************************************************************************
// Constraint evaluation.
//


namespace {


double dot_and_gradient (const Fourvec& v1,
                         const Fourvec& v2,
                         bool use_e_flag,
                         double v1_x[3],
                         double v2_x[3],
                         bool& badflag)
//
// Purpose: Compute the dot product v1.v2 and its gradients wrt
//          p, phi, and theta of each 4-vector.
//
// Inputs:
//   v1 -          The first 4-vector in the dot product.
//   v2 -          The second 4-vector in the dot product.
//   use_e_flag -  If true, we're using E as the fit variable, otherwise p.
//
// Outputs:
//   v1_x -        Gradients of the dot product wrt v1's p, phi, theta.
//   v2_x -        Gradients of the dot product wrt v2's p, phi, theta.
//   badflag -     Set to true for the singular case (vectors vanish).
//
// Returns:
//   The dot product.
//
{
  // Calculate the dot product.
  double dot = v1 * v2;

  double p1 = v1.vect().mag();
  double p2 = v2.vect().mag();
  double e1 = v1.e();
  double e2 = v2.e();
  double pt1 = v1.vect().perp();
  double pt2 = v2.vect().perp();

  // Protect against the singular case.
  badflag = false;
  if (p1 == 0 || p2 == 0 || e1 == 0 || e2 == 0 || pt1 == 0 || pt2 == 0) {
    badflag = true;
    v1_x[p_offs] = v1_x[phi_offs] = v1_x[eta_offs] = 0;
    v2_x[p_offs] = v2_x[phi_offs] = v2_x[eta_offs] = 0;
    return false;
  }

  // Calculate the gradients.
  v1_x[p_offs] = (dot - v1.m2() * e2 / e1) / p1;
  v2_x[p_offs] = (dot - v2.m2() * e1 / e2) / p2;

  if (use_e_flag) {
    v1_x[p_offs] *= e1 / p1;
    v2_x[p_offs] *= e2 / p2;
  }

  v1_x[phi_offs] = v1(1)*v2(0) - v1(0)*v2(1);
  v2_x[phi_offs] = -v1_x[phi_offs];

  double fac = v1(0)*v2(0) + v1(1)*v2(1);
  v1_x[eta_offs] = pt1*v2(2) - v1(2)/pt1 * fac;
  v2_x[eta_offs] = pt2*v1(2) - v2(2)/pt2 * fac;

  return dot;
}


void addin_obj_gradient (int constraint_no,
                         int sign,
                         int base_index,
                         const double grad[],
                         Matrix& Bx)
//
// Purpose: Tally up the dot product gradients for an object
//          into Bx.
//
// Inputs:
//   constraint_no-The number of the constraint.
//   base_index -  The index in the well-measured variable list
//                 of the first variable for this object.
//   sign -        The sign with which these gradients should be
//                 added into Bx, either +1 or -1.  (I.e., which
//                 side of the constraint equation.)
//   grad -        The gradients for this object, vs. p, phi, theta.
//   Bx -          The well-measured variable gradients.
//
// Outputs:
//   Bx -          The well-measured variable gradients, updated.
//
{
  Bx(base_index + p_offs,   constraint_no) += sign * grad[p_offs];
  Bx(base_index + phi_offs, constraint_no) += sign * grad[phi_offs];
  Bx(base_index + eta_offs, constraint_no) += sign * grad[eta_offs];
}


void addin_nu_gradient (int constraint_no,
                        int sign,
                        int kt_ndx,
                        const double grad[],
                        Matrix& Bx, Matrix& By)
//
// Purpose: Tally up the dot product gradients for a neutrino
//          into Bx and By.
//
// Inputs:
//   constraint_no-The number of the constraint.
//   sign -        The sign with which these gradients should be
//                 added into Bx, either +1 or -1.  (I.e., which
//                 side of the constraint equation.)
//   kt_ndx -      The index of the kt variables in the variables array.
//   grad -        The gradients for this object, vs. p, phi, theta.
//   Bx -          The well-measured variable gradients.
//   By -          The poorly-measured variable gradients.
//
// Outputs:
//   Bx -          The well-measured variable gradients, updated.
//   By -          The poorly-measured variable gradients, updated.
//
{
  Bx(kt_ndx+x_offs,constraint_no) += sign*grad[p_offs];  // Really p for now.
  Bx(kt_ndx+y_offs,constraint_no) += sign*grad[phi_offs];// Really phi for now.
  By(nu_z,         constraint_no) += sign*grad[eta_offs]; // Really theta ...
}


void addin_gradient (const Fourvec_Event& ev,
                     int constraint_no,
                     int sign,
                     int obj_no,
                     const double grad[],
                     Matrix& Bx,
                     Matrix& By)
//
// Purpose: Tally up the dot product gradients for an object (which may
//          or may not be a neutrino) into Bx and By.
//
// Inputs:
//   ev -          The event we're fitting.
//   constraint_no-The number of the constraint.
//   sign -        The sign with which these gradients should be
//                 added into Bx, either +1 or -1.  (I.e., which
//                 side of the constraint equation.)
//   obj_no -      The number of the object.
//   grad -        The gradients for this object, vs. p, phi, theta.
//   Bx -          The well-measured variable gradients.
//   By -          The poorly-measured variable gradients.
//
// Outputs:
//   Bx -          The well-measured variable gradients, updated.
//   By -          The poorly-measured variable gradients, updated.
//
{
  if (obj_no >= ev.nobjs()) {
    assert (obj_no == ev.nobjs());
    addin_nu_gradient (constraint_no, sign, obj_index (obj_no), grad, Bx, By);
  }
  else
    addin_obj_gradient (constraint_no, sign, obj_index (obj_no), grad, Bx);
}


void addin_gradients (const Fourvec_Event& ev,
                      int constraint_no,
                      int sign,
                      int i,
                      const double igrad[],
                      int j,
                      const double jgrad[],
                      Matrix& Bx,
                      Matrix& By)
//
// Purpose: Tally up the gradients from a single dot product into Bx and By.
//
// Inputs:
//   ev -          The event we're fitting.
//   constraint_no-The number of the constraint.
//   sign -        The sign with which these gradients should be
//                 added into Bx, either +1 or -1.  (I.e., which
//                 side of the constraint equation.)
//   i -           The number of the first object.
//   igrad -       The gradients for the first object, vs. p, phi, theta.
//   j -           The number of the second object.
//   jgrad -       The gradients for the second object, vs. p, phi, theta.
//   Bx -          The well-measured variable gradients.
//   By -          The poorly-measured variable gradients.
//
// Outputs:
//   Bx -          The well-measured variable gradients, updated.
//   By -          The poorly-measured variable gradients, updated.
//
{
  addin_gradient (ev, constraint_no, sign, i, igrad, Bx, By);
  addin_gradient (ev, constraint_no, sign, j, jgrad, Bx, By);
}


void add_mass_terms (const Fourvec_Event& ev,
                     const vector<Constraint>& constraints,
                     Row_Vector& F)
//
// Purpose: Add the m^2 terms into the constraint values.
//
// Inputs:
//   ev -          The event we're fitting.
//   constraints - The list of constraints.
//   F -           Vector of constraint values.
//
// Outputs:
//   F -           Vector of constraint values, updated.
//
{
  for (std::vector<Constraint>::size_type i=0; i<constraints.size(); i++)
    F(i+1) += constraints[i].sum_mass_terms (ev);
}


bool calculate_mass_constraints (const Fourvec_Event& ev,
                                 const Pair_Table& pt,
                                 const vector<Constraint>& constraints,
                                 bool use_e_flag,
                                 Row_Vector& F,
                                 Matrix& Bx,
                                 Matrix& By)
//
// Purpose: Calculate the mass constraints and gradients.
//          Note: At this stage, the gradients are calculated not
//                quite with respect to the fit variables; instead, for
//                all objects (including the neutrino) we calculate
//                the gradients with respect to p, phi, theta.  They'll
//                be converted via appropriate Jacobian transformations
//                later.
//
// Inputs:
//   ev -          The event we're fitting.
//   pt -          Table of cached pair assignments.
//   constraints - The list of constraints.
//   use_e_flag -  If true, we're using E as the fit variable, otherwise p.
//
// Outputs:
//   (nb. these should be passed in correctly dimensioned.)
//   F -           Vector of constraint values.
//   Bx -          The well-measured variable gradients.
//   By -          The poorly-measured variable gradients.
//
{
  int npairs = pt.npairs ();
  for (int p=0; p < npairs; p++) {
    const Objpair& objpair = pt.get_pair (p);
    int i = objpair.i();
    int j = objpair.j();
    double igrad[3], jgrad[3];
    bool badflag = false;
    double dot = dot_and_gradient (ev.obj (i).p,
                                   ev.obj (j).p,
                                   use_e_flag,
                                   igrad,
                                   jgrad,
                                   badflag);
    if (badflag)
      return false;

    for (std::vector<Constraint>::size_type k=0; k < constraints.size(); k++)
      if (objpair.for_constraint (k)) {
    F(k+1) += objpair.for_constraint (k) * dot;
    addin_gradients (ev, k+1, objpair.for_constraint (k),
             i, igrad, j, jgrad, Bx, By);
      }

  }

  add_mass_terms (ev, constraints, F);
  return true;
}


void add_nuterm (unsigned ndx,
                 const Fourvec& v,
                 Matrix& Bx,
                 bool use_e_flag,
                 int kt_ndx)
//
// Purpose: Carry out the Jacobian transformation for
//          (p_nu^x,p_nu_y) -> (kt^x, kt_y) for a given object.
//
// Inputs:
//   ndx -         Index of the object for which to transform gradients.
//   v -           The object's 4-momentum.
//   Bx -          The well-measured variable gradients.
//   use_e_flag -  If true, we're using E as the fit variable, otherwise p.
//   kt_ndx -      The index of the kt variables in the variables array.
//
// Outputs:
//   Bx -          The well-measured variable gradients, updated.
//
{
  double px = v.px();
  double py = v.py();
  double cot_theta = v.pz() / v.vect().perp();

  for (int j=1; j<=Bx.num_col(); j++) {
    double dxnu = Bx(kt_ndx+x_offs, j);
    double dynu = Bx(kt_ndx+y_offs, j);

    if (dxnu != 0 || dynu != 0) {
      double fac = 1 / v.vect().mag();
      if (use_e_flag)
    fac = v.e() * fac * fac;
      Bx(ndx +   p_offs, j) -= (px*dxnu + py*dynu) * fac;
      Bx(ndx + phi_offs, j) +=  py*dxnu - px*dynu;
      Bx(ndx + eta_offs, j) -= (px*dxnu + py*dynu) * cot_theta;
    }
  }
}


void convert_neutrino (const Fourvec_Event& ev,
                       bool use_e_flag,
                       Matrix& Bx,
                       Matrix& By)
//
// Purpose: Carry out the Jacobian transformations the neutrino.
//          First, convert from spherical (p, phi, theta) coordinates
//          to rectangular (x, y, z).  Then convert from neutrino pt
//          components to kt components.
//
// Inputs:
//   ev -          The event we're fitting.
//   use_e_flag -  If true, we're using E as the fit variable, otherwise p.
//   Bx -          The well-measured variable gradients.
//   By -          The poorly-measured variable gradients.
//
// Outputs:
//   Bx -          The well-measured variable gradients, updated.
//   By -          The poorly-measured variable gradients, updated.
//
{
  int nconstraints = Bx.num_col ();

  const Fourvec& nu = ev.nu ();

  // convert neutrino from polar coordinates to rectangular.
  double pnu2  = nu.vect().mag2();  double pnu = sqrt (pnu2);
  double ptnu2 = nu.vect().perp2(); double ptnu = sqrt (ptnu2);

  // Doesn't matter whether we use E or P here, since nu is massless.

  double thfac = nu.z()/pnu2/ptnu;
  double fac[3][3];
  fac[0][0] = nu(0)/pnu;     fac[0][1] = nu(1)/pnu;     fac[0][2] = nu(2)/pnu;
  fac[1][0] = - nu(1)/ptnu2; fac[1][1] =   nu(0)/ptnu2; fac[1][2] = 0;
  fac[2][0] = nu(0)*thfac;   fac[2][1] = nu(1)*thfac;   fac[2][2] = -ptnu/pnu2;

  int kt_ndx = obj_index (ev.nobjs());
  for (int j=1; j<=nconstraints; j++) {
    double tmp1 = fac[0][0]*Bx(kt_ndx+x_offs,j) +
                  fac[1][0]*Bx(kt_ndx+y_offs,j) +
                  fac[2][0]*By(nu_z,j);
    Bx(kt_ndx+y_offs,j) = fac[0][1]*Bx(kt_ndx+x_offs,j) +
                          fac[1][1]*Bx(kt_ndx+y_offs,j) +
                          fac[2][1]*By(nu_z,j);
    By(nu_z,j) = fac[0][2]*Bx(kt_ndx+x_offs,j) + fac[2][2]*By(nu_z,j);

    Bx(kt_ndx+x_offs,j) = tmp1;
  }

  // Add nu terms.
  for (int j=0; j<ev.nobjs(); j++) {
    add_nuterm (obj_index (j), ev.obj(j).p, Bx, use_e_flag, kt_ndx);
  }
}


void calculate_kt_constraints (const Fourvec_Event& ev,
                               bool use_e_flag,
                               Row_Vector& F,
                               Matrix& Bx)
//
// Purpose: Calculate the overall kt constraints (kt = 0) for the case
//          where there is no neutrino.
//
// Inputs:
//   ev -          The event we're fitting.
//   use_e_flag -  If true, we're using E as the fit variable, otherwise p.
//   F -           Vector of constraint values.
//   Bx -          The well-measured variable gradients.
//
// Outputs:
//   F -           Vector of constraint values, updated.
//   Bx -          The well-measured variable gradients, updated.
//
{
  Fourvec tmp = Fourvec(0);
  int base = F.num_col() - 2;
  int nobjs = ev.nobjs();
  for (int j=0; j<nobjs; j++) {
    const Fourvec& obj = ev.obj (j).p;
    tmp += obj;

    int ndx = obj_index (j);
    double p = obj.vect().mag();
    double cot_theta = obj.z() / obj.vect().perp();

    Bx(ndx +   p_offs, base+1) = obj(0) / p;
    Bx(ndx + phi_offs, base+1) = -obj(1);
    Bx(ndx + eta_offs, base+1) = obj(0) * cot_theta;

    Bx(ndx +   p_offs, base+2) = obj(1) / p;
    Bx(ndx + phi_offs, base+2) = obj(0);
    Bx(ndx + eta_offs, base+2) = obj(1) * cot_theta;

    if (use_e_flag) {
      Bx(ndx +   p_offs, base+1) *= obj.e() / p;
      Bx(ndx +   p_offs, base+2) *= obj.e() / p;
    }
  }

  int kt_ndx = obj_index (nobjs);
  Bx(kt_ndx+x_offs, base+1) = -1;
  Bx(kt_ndx+y_offs, base+2) = -1;

  F(base+1) = tmp(0) - ev.kt().x ();
  F(base+2) = tmp(1) - ev.kt().y ();
}


void ddtheta_to_ddeta (int i, double cos_theta, Matrix& Bx)
//
// Purpose: Do the Jacobian transformation from theta -> eta
//          for a single object.
//
// Inputs:
//   i -           The index of the object.
//   cos_theta -   cos(theta) for the object.
//   Bx -          The well-measured variable gradients.
//
// Outputs:
//   Bx -          The well-measured variable gradients, updated.
//
{
  double sin_theta = sqrt (1 - cos_theta * cos_theta);
  for (int j=1; j<=Bx.num_col(); j++)
    Bx(i,j) *= - sin_theta;   /* \sin\theta = 1 / \cosh\eta */
}


} // unnamed namespace


class Fourvec_Constraint_Calculator
  : public Constraint_Calculator
//
// Purpose: Constraint evaluator.
//
{
public:
  // Constructor, destructor.
  Fourvec_Constraint_Calculator (Fourvec_Event& ev,
                                 const vector<Constraint>& constraints,
                                 const Fourvec_Constrainer_Args& args);
  virtual ~Fourvec_Constraint_Calculator () {}

  // Evaluate constraints at the point described by X and Y (well-measured
  // and poorly-measured variables, respectively).  The results should
  // be stored in F.  BX and BY should be set to the gradients of F with
  // respect to X and Y, respectively.
  //
  // Return true if the point X, Y is accepted.
  // Return false if it is rejected (i.e., in an unphysical region).
  // The constraints need not be evaluated in that case.
  virtual bool eval (const Column_Vector& x,
                     const Column_Vector& y,
                     Row_Vector& F,
                     Matrix& Bx,
                     Matrix& By) override;


  // Calculate the constraint functions and gradients.
  bool calculate_constraints (Row_Vector& F,
                              Matrix& Bx,
                              Matrix& By) const;

private:
  // The event we're fitting.
  Fourvec_Event& _ev;

  // Vector of constraints.
  const vector<Constraint>& _constraints;

  // Argument values.
  const Fourvec_Constrainer_Args& _args;

  // The pair table.
  Pair_Table _pt;
};


Fourvec_Constraint_Calculator::Fourvec_Constraint_Calculator
  (Fourvec_Event& ev,
   const vector<Constraint>& constraints,
   const Fourvec_Constrainer_Args& args)
//
// Purpose: Constructor.
//
// Inputs:
//   ev -          The event we're fitting.
//   constraints - The list of constraints.
//   args -        The parameter settings.
//
//
  : Constraint_Calculator (constraints.size() +
                           ((ev.has_neutrino() || args.ignore_met()) ? 0 : 2)),
    _ev (ev),
    _constraints (constraints),
    _args (args),
    _pt (constraints, ev)

{
}


bool
Fourvec_Constraint_Calculator::calculate_constraints (Row_Vector& F,
                                                      Matrix& Bx,
                                                      Matrix& By) const
//
// Purpose: Calculate the constraint functions and gradients.
//
// Outputs:
//   F -           Vector of constraint values.
//   Bx -          The well-measured variable gradients.
//   By -          The poorly-measured variable gradients.
//
{
  // Clear the matrices.
  Bx = Matrix (Bx.num_row(), Bx.num_col(), 0);
  By = Matrix (By.num_row(), By.num_col(), 0);
  F = Row_Vector (F.num_col(), 0);

  const double p_eps = 1e-10;

  if (_ev.has_neutrino() && _ev.nu().z() > _args.e_com()) {
    return false;
  }

  int nobjs = _ev.nobjs ();

  // Reject the point if any of the momenta get too small.
  for (int j=0; j<nobjs; j++) {
    if (_ev.obj(j).p.perp() <= p_eps || _ev.obj(j).p.e() <= p_eps) {
      return false;
    }
  }

  if (! calculate_mass_constraints (_ev, _pt, _constraints, _args.use_e(),
                                    F, Bx, By))
    return false;

  if (_ev.has_neutrino())
    convert_neutrino (_ev, _args.use_e(), Bx, By);
  else if (!_args.ignore_met())
  {
    /* kt constraints */
    calculate_kt_constraints (_ev, _args.use_e(), F, Bx);
  }

  /* convert d/dtheta to d/deta */
  for (int j=0; j<nobjs; j++) {
    ddtheta_to_ddeta (obj_index (j) + eta_offs,
                      _ev.obj(j).p.cosTheta(),
                      Bx);
  }

  /* handle muons */
  for (int j=0; j<nobjs; j++) {
    const FE_Obj& obj = _ev.obj (j);
    if (obj.muon_p) {
      // Again, E vs. P doesn't matter here since we assume muons to be massless.
      double pmu2 = obj.p.vect().mag2();
      int ndx = obj_index (j) + p_offs;
      for (int k=1; k<=Bx.num_col(); k++)
    Bx(ndx, k) = - Bx(ndx, k) * pmu2;
    }
  }

  return true;
}


bool Fourvec_Constraint_Calculator::eval (const Column_Vector& x,
                                          const Column_Vector& y,
                                          Row_Vector& F,
                                          Matrix& Bx,
                                          Matrix& By)
//
// Purpose: Evaluate constraints at the point described by X and Y
//          (well-measured and poorly-measured variables, respectively).
//          The results should be stored in F.  BX and BY should be set
//          to the gradients of F with respect to X and Y, respectively.
//
// Inputs:
//   x -           Vector of well-measured variables.
//   y -           Vector of poorly-measured variables.
//
// Outputs:
//   F -           Vector of constraint values.
//   Bx -          The well-measured variable gradients.
//   By -          The poorly-measured variable gradients.
//
{
  int nobjs = _ev.nobjs();

  const double p_eps = 1e-10;
  const double eta_max = 10;

  // Give up if we've gone into an obviously unphysical region.
  for (int j=0; j<nobjs; j++)
    if (x(obj_index (j) + p_offs) < p_eps ||
        fabs(x(obj_index (j) + eta_offs)) > eta_max) {
      return false;
    }

  unpack_event (_ev, x, y, _args.use_e(),
                _ev.has_neutrino() || !_args.ignore_met());

  return calculate_constraints (F, Bx, By);
}


//*************************************************************************
// Mass calculation.
//


namespace {


double calculate_sigm (const Matrix& Q,
                       const Matrix& R,
                       const Matrix& S,
                       const Column_Vector& Bx,
                       const Column_Vector& By)
//
// Purpose: Do error propagation to find the uncertainty in the final mass.
//
// Inputs:
//   Q -           The final error matrix for the well-measured variables.
//   R -           The final error matrix for the poorly-measured variables.
//   S -           The final cross error matrix for the two sets of variables.
//   Bx -          The well-measured variable gradients.
//   By -          The poorly-measured variable gradients.
//
{
  double sig2 = scalar (Bx.T() * Q * Bx);

  if (By.num_row() > 0) {
    sig2 += scalar (By.T() * R * By);
    sig2 += 2 * scalar (Bx.T() * S * By);
  }

  assert (sig2 >= 0);
  return sqrt (sig2);
}


void calculate_mass (Fourvec_Event& ev,
                     const vector<Constraint>& mass_constraint,
                     const Fourvec_Constrainer_Args& args,
                     double chisq,
                     const Matrix& Q,
                     const Matrix& R,
                     const Matrix& S,
                     double& m,
                     double& sigm)
//
// Purpose: Calculate the final requested mass and its uncertainty.
//
// Inputs:
//   ev -          The event we're fitting.
//   mass_constraint- The description of the mass we're to calculate.
//   args -        Parameter settings.
//   chisq -       The chisq from the fit.
//   Q -           The final error matrix for the well-measured variables.
//   R -           The final error matrix for the poorly-measured variables.
//   S -           The final cross error matrix for the two sets of variables.
//
// Outputs:
//   m -           The mass.
//   sigm -        Its uncertainty.
//
{
  // Don't do anything if the mass wasn't specified.
  if (mass_constraint.size () == 0) {
    m = 0;
    sigm = 0;
    return;
  }

  // Do the constraint calculation.
  int n_measured_vars = ev.nobjs()*3 + 2;
  int n_unmeasured_vars = 0;
  if (ev.has_neutrino ()) n_unmeasured_vars = 1;

  Row_Vector F(1);
  Matrix Bx (n_measured_vars, 1);
  Matrix By (n_unmeasured_vars, 1);

  Fourvec_Constraint_Calculator cc (ev, mass_constraint, args);
  cc.calculate_constraints (F, Bx, By);

  // Calculate the mass.
  //assert (F(1) >= 0);
  if (F(1) >= 0.)
    m = sqrt (F(1) * 2);
  else {
    m = 0.;
    chisq = -100.;
  }

  // And the uncertainty.
  // We can only do this if the fit converged.
  if (chisq < 0)
    sigm = 0;
  else {
    //assert (F(1) > 0);
    Bx = Bx / (m);
    By = By / (m);

    sigm = calculate_sigm (Q, R, S, Bx, By);
  }
}


} // unnamed namespace


double Fourvec_Constrainer::constrain (Fourvec_Event& ev,
                                       double& m,
                                       double& sigm,
                                       Column_Vector& pullx,
                                       Column_Vector& pully)
//
// Purpose: Do a constrained fit for EV.  Returns the requested mass and
//          its error in M and SIGM, and the pull quantities in PULLX and
//          PULLY.  Returns the chisq; this will be < 0 if the fit failed
//          to converge.
//
// Inputs:
//   ev -          The event we're fitting.
//
// Outputs:
//   ev -          The fitted event.
//   m -           Requested invariant mass.
//   sigm -        Uncertainty on m.
//   pullx -       Pull quantities for well-measured variables.
//   pully -       Pull quantities for poorly-measured variables.
//
// Returns:
//   The fit chisq, or < 0 if the fit didn't converge.
//
{
  adjust_fourvecs (ev, _args.use_e ());

  bool use_kt = ev.has_neutrino() || !_args.ignore_met();
  int nobjs = ev.nobjs ();
  int n_measured_vars = nobjs * 3;
  int n_unmeasured_vars = 0;
  int n_constraints = _constraints.size ();

  if (use_kt) {
    n_measured_vars += 2;

    if (ev.has_neutrino ())
      n_unmeasured_vars = 1;
    else
      n_constraints += 2;
  }

  Matrix G_i (n_measured_vars, n_measured_vars);
  Diagonal_Matrix Y (n_unmeasured_vars);
  Column_Vector x (n_measured_vars);
  Column_Vector y (n_unmeasured_vars);
  pack_event (ev, _args.use_e(), use_kt, x, y, G_i, Y);

  Column_Vector xm = x;
  Column_Vector ym = y;

  // ??? Should allow for using a different underlying fitter here.
  Chisq_Constrainer fitter (_args.chisq_constrainer_args());

  Fourvec_Constraint_Calculator cc (ev, _constraints, _args);

  Matrix Q;
  Matrix R;
  Matrix S;
  double chisq = fitter.fit (cc,
                             xm, x, ym, y, G_i, Y,
                             pullx, pully,
                             Q, R, S);

  unpack_event (ev, x, y, _args.use_e (), use_kt);

  calculate_mass (ev, _mass_constraint, _args, chisq, Q, R, S, m, sigm);

  return chisq;
}


} // namespace hitfit