FitMatrices.cxx

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/*
  Copyright (C) 2002-2024 CERN for the benefit of the ATLAS collaboration
*/
 
// class FitMatrices
//  Storage and manipulation of matrices during track fitting
//  (note the actual matrices are structs (FitMatrix.h) to give faster
//  execution)
//
//  Given matrix of measurement derivatives wrt fit parameters (DerivativeMatrix
//  DM) and vector of differences between measurements and fitted trajectory,
//  solve for:
//   parameter weight matrix = (covariance)-1 = DMtranspose.DM
//   parameter change        = (DMtranspose.DM)-1 * (DMtranspose.differences)
//
//  NOTE:
//  covariances, derivatives etc, use d0, z0, phi, cot(theta), qOverPt as first
//  5 parameters distinguish: full covariance with all parameters:
//          includes misalignments, scattering and energy loss
//               5*5 final covariance with possible external contribution
//               representing   leading material and field gradient effects
//
 
#include "TrkiPatFitterUtils/FitMatrices.h"
 
#include <iomanip>
#include <iostream>
 
#include "EventPrimitives/EventPrimitivesCovarianceHelpers.h"
#include "GaudiKernel/SystemOfUnits.h"
#include "TrkExUtils/TrackSurfaceIntersection.h"
#include "TrkiPatFitterUtils/FitMeasurement.h"
#include "TrkiPatFitterUtils/FitParameters.h"
 
#include "CxxUtils/inline_hints.h"
 
namespace Trk {
 
FitMatrices::FitMatrices(bool constrainedAlignmentEffects)
    : m_fitMatrix{},
      m_columnsDM(0),
      m_constrainedAlignmentEffects(constrainedAlignmentEffects),
      m_largePhiWeight(10000.),  // arbitrary - equiv to 10um
      m_matrixFromCLHEP(false),
      m_measurements(nullptr),
      m_numberDoF(0),
      m_numberDriftCircles(0),
      m_numberPerigee(5),
      m_parameters(nullptr),
      m_perigee(nullptr),
      m_perigeeDifference(Amg::MatrixX(1, m_numberPerigee)),
      m_perigeeWeight(nullptr),
      m_rowsDM(0),
      m_usePerigee(false){}
 
void FitMatrices::checkPointers(MsgStream& log) const {
  // debugging: check smart pointers
  for (int col = 0; col < m_columnsDM; ++col) {
    // firstRow
    for (int i = 0; i < m_firstRowForParameter[col]; ++i) {
      if (m_fitMatrix.derivative[i][col] != 0.)
        log << " col " << col << "   unexpected first nonzero DM element " << i
            << " / " << m_firstRowForParameter[col] << endmsg;
    }
    int j = m_firstRowForParameter[col];
    if (m_fitMatrix.derivative[j][col] == 0.)
      log << " col " << col << "   first nonzero DM element is zero! " << j
          << " / " << m_firstRowForParameter[col] << endmsg;
 
    // lastRow
    for (int i = m_lastRowForParameter[col]; i < m_rowsDM; ++i) {
      if (m_fitMatrix.derivative[i][col] != 0.)
        log << " col " << col << " unexpected last nonzero DM element " << i
            << " / " << m_lastRowForParameter[col] << endmsg;
    }
  }
}
 
double FitMatrices::chiSquaredChange(void) {
  std::cout << " unexpected :chiSquaredChange  " << std::endl;
  return 0.;
}
 
const Amg::MatrixX* FitMatrices::fullCovariance(void) {
  // return result if matrix already inverted
  if (m_covariance.size()!=0) {
    return &m_covariance;
  }
  m_covariance = Amg::MatrixX(m_columnsDM, m_columnsDM);
 
  // fix weighting    ???? shouldn't we just remove large phi weight?
  if (m_parameters->phiInstability()) {
    solveEquations();
  }
 
  // invert weight matrix
  Amg::MatrixX& covariance = m_covariance;
  // avoid singularity through ill-defined momentum   ???? again
  avoidMomentumSingularity();
 
  // neater - but gives small rounding-like diffs wrt matrix copy version
  // keep matrix copy for release 21 to avoid rounding changes at Tier0
  // covariance = (*m_weight).inverse();
 
  // matrix copy version (legacy of older library which needed copy between
  // matrix packages)
  Amg::MatrixX weight(m_columnsDM, m_columnsDM);
  weight.selfadjointView<0x2>();
 
  // check if m_weights makes sense before inverting
  if (!Amg::hasPositiveDiagElems(m_weight)) {
    m_covariance.resize(0, 0);
    return nullptr;
  }
 
  weight = (m_weight).inverse();
  for (int row = 0; row != m_columnsDM; ++row) {
    for (int col = 0; col != m_columnsDM; ++col)
      covariance(row, col) = weight(col, row);
  }
 
  // back convert curved fits to Tracking units (MeV)
  if (m_parameters->fitMomentum()) {
    // transform to MeV
    double d4 = 1. / Gaudi::Units::TeV;
    for (int row = 0; row < m_columnsDM; ++row) {
      covariance(4, row) *= d4;
      covariance(row, 4) = covariance(4, row);
    }
    covariance(4, 4) *= d4;
 
    // transform units for fitted energy deposit (for now fit qOverP at calo
    // exit)
    if (m_parameters->fitEnergyDeposit()) {
      double d5 = 1. / Gaudi::Units::TeV;
      for (int row = 0; row < m_columnsDM; ++row) {
        covariance(5, row) *= d5;
        covariance(row, 5) = covariance(5, row);
      }
      covariance(5, 5) *= d5;
    }
  }
 
  // FIXME: errors underestimated on d0,z0 when large scatterer precedes precise
  // measurements final covariance starts with 5*5 representing perigee from
  // full covariance
  m_finalCovariance = Amg::MatrixX(5, 5);
  for (int i = 0; i != 5; ++i) {
    for (int j = 0; j != 5; ++j) {
      (m_finalCovariance)(i, j) = covariance(i, j);
    }
  }
 
  // return pointer to full covariance
  return &m_covariance;
}
 
double FitMatrices::perigeeChiSquared(void) {
  m_perigeeDifference = m_parameters->parameterDifference(*m_perigee);
  return (m_perigeeDifference * (*m_perigeeWeight) *
          m_perigeeDifference.transpose())(0, 0);
}
 
void FitMatrices::printDerivativeMatrix(void) {
  std::cout << "DerivativeMatrix:  rows * columns " << m_rowsDM << " * "
            << m_columnsDM << "  numberDoF " << m_numberDoF << std::endl;
 
  int firstCol = 0;
  int lastCol = 0;
  if (!m_measurements)
    return;
  std::vector<FitMeasurement*>::iterator m = m_measurements->begin();
  std::vector<FitMeasurement*> alignmentfm;
  FitMeasurement* fm = *m;
  bool singleRow = true;
 
  for (int row = 0; row < m_rowsDM; ++row) {
    // get corresponding FitMeasurement
    if (singleRow) {
      while (m != m_measurements->end() &&
             (!(**m).numberDoF() || (**m).isAlignment())) {
        if ((**m).isAlignment())
          alignmentfm.push_back(*m);
        ++m;
      }
      if (m != m_measurements->end()) {
        fm = *m;
      } else {
        fm = alignmentfm.back();
        alignmentfm.pop_back();
      }
 
      firstCol = fm->firstParameter();
      lastCol = fm->lastParameter() - 1;
      std::cout << std::endl << std::setiosflags(std::ios::fixed);
      if (fm->isPositionMeasurement()) {
        std::cout << "measurement";
      } else if (fm->isScatterer()) {
        std::cout << "scatterer  ";
      } else if (fm->isEnergyDeposit()) {
        std::cout << "energyDepos";
      } else if (fm->isAlignment()) {
        std::cout << "alignment  ";
      } else {
        std::cout << "   ??      ";
      }
      if (fm->is2Dimensional()) {
        singleRow = false;
      } else {
        if (m != m_measurements->end())
          ++m;
      }
      std::cout << " row " << std::setw(3) << row << " col  0     ";
    } else {
      if (m != m_measurements->end())
        ++m;
      singleRow = true;
      std::cout << std::endl
                << std::setiosflags(std::ios::fixed) << "            row "
                << std::setw(3) << row << " col  0     ";
    }
    for (int col = 0; col < m_columnsDM; ++col) {
      if (col < firstCol || col > lastCol)  // m_firstRowForParameter[row])
      {
        if (m_fitMatrix.derivative[row][col] == 0.) {
          std::cout << "            ";
        } else {
          // flag out-of-order
          std::cout << std::setiosflags(std::ios::scientific)
                    << std::setbase(10) << "<" << std::setw(10)
                    << m_fitMatrix.derivative[row][col] << ">";
        }
      } else {
        std::cout << std::setiosflags(std::ios::scientific) << std::setbase(10)
                  << std::setw(10) << m_fitMatrix.derivative[row][col] << "  ";
      }
 
      if ((col + 1) % 12 == 0 && col + 1 < m_columnsDM)
        std::cout << std::endl
                  << std::setiosflags(std::ios::fixed)
                  << "                    col " << std::setw(3) << col + 1
                  << "    ";
    }
  }
  std::cout << std::endl;
}
 
void FitMatrices::printWeightMatrix(void) {
  std::cout << std::endl
            << "WeightMatrix:  symmetric with rank " << m_columnsDM;
 
  for (int row = 0; row < m_columnsDM; ++row) {
    std::cout << std::endl
              << std::setiosflags(std::ios::fixed) << " row " << std::setw(3)
              << row << " col  0     ";
    for (int col = 0; col <= row; ++col) {
      std::cout << std::setiosflags(std::ios::scientific) << std::setbase(10)
                << std::setw(10) << (m_weight)(row, col) << "  ";
 
      if ((col + 1) % 13 == 0 && col < row)
        std::cout << std::endl
                  << std::setiosflags(std::ios::fixed) << "         col "
                  << std::setw(3) << col + 1 << "    ";
    }
  }
  std::cout << std::endl;
}
 
void FitMatrices::refinePointers(void) {
  // remove leading and trailing zeroes from smart pointers
  for (int col = 0; col < m_columnsDM; ++col) {
    int i = m_firstRowForParameter[col];
    int j = m_lastRowForParameter[col];
    if (i < --j && m_fitMatrix.derivative[i][col] == 0. ) {
      while (i != j && m_fitMatrix.derivative[i][col] == 0.)
        ++i;
      m_firstRowForParameter[col] = i;
    }
    if (m_fitMatrix.derivative[j][col] == 0. && j > i) {
      while (j != i && m_fitMatrix.derivative[j][col] == 0.)
        --j;
      m_lastRowForParameter[col] = ++j;
    }
  }
}
 
void FitMatrices::releaseMemory(void) {
  m_derivativeMatrix.resize(0,0);
  m_weight.resize(0,0);
  m_weightedDifference.resize(0,0);
}
 
int FitMatrices::setDimensions(std::vector<FitMeasurement*>& measurements,
                               FitParameters* parameters) {
  // keep pointer for debug purposes
  m_measurements = &measurements;
 
  // only use perigee on request (from special fit types)
  m_usePerigee = false;
 
  // count rows, misalignments and scatterers from loop over FitMeasurements
  m_firstRowForParameter.clear();
  m_firstRowForParameter.reserve(128);
  m_lastRowForParameter.clear();
  m_lastRowForParameter.reserve(128);
  m_parameters = parameters;
  m_residuals = std::vector<double>(2 * measurements.size(), 0.);
  m_numberDriftCircles = 0;
  bool haveMeasurement = false;
  bool haveVertex = false;
  int numberAlignments = 0;
  int numberEnergyDeposits = 0;
  int numberParameters = 5;
  int numberScatterers = 0;
  int row = 0;
 
  // keep first row with measurements up to each number of parameters
  m_firstRowForParameter = std::vector<int>(numberParameters, -1);
  std::vector<FitMeasurement*>::iterator m = measurements.begin();
  if ((**m).isVertex()) {
    haveVertex = true;
    m_firstRowForParameter[row] = row;
 
    // set pointers into big matrix
    (**m).derivative(&m_fitMatrix.derivative[row][0]);
    (**m).residual(row + m_residuals.begin());
    ++row;
    if ((**m).is2Dimensional()) {
      m_firstRowForParameter[row] = row;
      (**m).derivative2(&m_fitMatrix.derivative[row][0]);
      ++row;
    }
    ++m;
  }
 
  // allocate rows to fitted measurements (DoF > 0)
  for (; m != measurements.end(); ++m) {
    if (!(**m).numberDoF())
      continue;
 
    // alignment rows come after scattering
    if ((**m).isAlignment())
      continue;
 
    // identify leading material
    if (!haveMeasurement) {
      if ((**m).isPositionMeasurement()) {
        haveMeasurement = true;
        for (int i = 0; i < numberParameters; ++i)
          if (m_firstRowForParameter[i] < 0)
            m_firstRowForParameter[i] = row;
      } else if (!haveVertex && (**m).isScatterer()) {
        (**m).numberDoF(0);
        continue;
      } else {
        // row  += (**m).numberDoF();
      }
    }
 
    // only allocate rows to fitted measurements (DoF > 0)
    // if (! (**m).numberDoF()) continue;
    if ((**m).isDrift())
      ++m_numberDriftCircles;
 
    // fit energyDeposit unless momentum fixed or near infinite
    if ((**m).isEnergyDeposit()) {
      //        if (! m_parameters->fitMomentum() ||
      // m_parameters->extremeMomentum())
      if (!m_parameters->fitMomentum()) {
        (**m).numberDoF(0);
        continue;
      } else {
        if (m_firstRowForParameter.back() < 0)
          m_firstRowForParameter.back() = row;
 
        // m_firstRowForParameter[numberParameters-1] = row;
        m_firstRowForParameter.push_back(row);
        m_parameters->fitEnergyDeposit((**m).minEnergyDeposit());
        ++numberEnergyDeposits;
        ++numberParameters;
      }
    }
    if ((**m).isScatterer())
      ++numberScatterers;
 
    // set pointers into big matrix
    (**m).derivative(&m_fitMatrix.derivative[row][0]);
    (**m).residual(row + m_residuals.begin());
    ++row;
    if ((**m).is2Dimensional()) {
      (**m).derivative2(&m_fitMatrix.derivative[row][0]);
      ++row;
    }
  }
 
  // second loop puts alignment rows at bottom of matrix
  for (m = measurements.begin(); m != measurements.end(); ++m) {
    if (!(**m).isAlignment())
      continue;
    ++numberAlignments;
 
    // set pointers into big matrix
    (**m).derivative(&m_fitMatrix.derivative[row][0]);
    (**m).residual(row + m_residuals.begin());
    ++row;
    if ((**m).is2Dimensional()) {
      (**m).derivative2(&m_fitMatrix.derivative[row][0]);
      ++row;
    }
  }
 
  // keep first row with measurements up to each number of parameters
  parameters->numberAlignments(numberAlignments);
  parameters->numberScatterers(numberScatterers);
  bool afterCalo = false;
  int lastRow = 0;
  m_rowsDM = 0;
  for (m = measurements.begin(); m != measurements.end(); ++m) {
    if ((**m).numberDoF()) {
      if ((**m).isEnergyDeposit()) {
        afterCalo = true;
        // m_lastRowForParameter[4] = m_firstRowForParameter[5] + 1;
      } else if ((**m).isScatterer()) {
        m_firstRowForParameter.push_back(m_rowsDM);
        m_firstRowForParameter.push_back(++m_rowsDM);
        (**m).lastParameter(m_firstRowForParameter.size(), afterCalo);
        parameters->addScatterer((**m).scattererPhi(), (**m).scattererTheta());
        lastRow = ++m_rowsDM;
        continue;
      } else if ((**m).isAlignment()) {
        // defer alignment
        continue;
      }
      m_rowsDM += (**m).numberDoF();
      lastRow = m_rowsDM;
    }
    (**m).lastParameter(m_firstRowForParameter.size(), afterCalo);
  }
 
  numberParameters = m_firstRowForParameter.size();
  m_lastRowForParameter = std::vector<int>(numberParameters, lastRow);
  if (afterCalo)
    m_lastRowForParameter[4] = m_firstRowForParameter[5] + 1;
 
  // following loop puts any alignment info into the final rows
  if (numberAlignments) {
    row = 0;
    unsigned alignmentParameter = 0;
    int firstAlignmentRow = 0;
    int firstAlignment2Row = 0;
    for (m = measurements.begin(); m != measurements.end(); ++m) {
      if ((**m).alignmentParameter()) {
        if ((**m).alignmentParameter() > alignmentParameter) {
          if (!firstAlignmentRow)
            firstAlignmentRow = row;
        }
        if ((**m).alignmentParameter2()) {
          if (!firstAlignment2Row)
            firstAlignment2Row = row;
        }
      }
      if (!(**m).numberDoF())
        continue;
      if (!(**m).isAlignment()) {
        row += (**m).numberDoF();
        continue;
      }
 
      parameters->addAlignment(m_constrainedAlignmentEffects,
                               (**m).alignmentAngle(), (**m).alignmentOffset());
      m_firstRowForParameter.push_back(firstAlignmentRow);
      m_firstRowForParameter.push_back(firstAlignmentRow);
      m_lastRowForParameter.push_back(++m_rowsDM);
      m_lastRowForParameter.push_back(++m_rowsDM);
      (**m).firstParameter(numberParameters);
      numberParameters += 2;
      alignmentParameter = parameters->numberAlignments();
      (**m).alignmentParameter(alignmentParameter);
      (**m).lastParameter(numberParameters, afterCalo);
      // m_rowsDM       +=  (**m).numberDoF();
 
      // some bug to fix here...
      // firstAlignmentRow  =  firstAlignment2Row;
      // firstAlignment2Row =  0;
    }
  }
 
  // initialize number of parameters (including alignments and scatterers)
  numberParameters = m_firstRowForParameter.size();
  parameters->numberParameters(numberParameters);
 
  // and degrees of freedom
  m_numberDoF = m_rowsDM - numberParameters;
 
  // make some checks: return fitCode in case of problem
  int fitCode = 0;
  // if (row > mxmeas)          fitCode = 2;    // too many measurements for
  // fit matrix size
  if (2 * measurements.size() > mxmeas)
    fitCode = 2;  // too many measurements for fit matrix size
  if (numberParameters > mxparam)
    fitCode = 3;  // too many parameters for fit matrix size
  if (m_numberDoF < 0)
    fitCode = 4;  // unconstrained fit: negative numberDoF
  if (numberEnergyDeposits > 1)
    fitCode = 12;  // too many EnergyDeposit parameters
  if (fitCode)
    return fitCode;
 
  // reserve derivatives for jacobian propagation to 'non-measurements'
  row = m_rowsDM;
  for (m = measurements.begin(); m != measurements.end(); ++m) {
    if (!(**m).isPositionMeasurement() || (**m).numberDoF() > 1)
      continue;
    if (!(**m).numberDoF()) {
      for (int i = 0; i != numberParameters; ++i)
        m_fitMatrix.derivative[row][i] = 0.;
      (**m).derivative(&m_fitMatrix.derivative[row][0]);
      (**m).residual(row + m_residuals.begin());
      ++row;
    }
    for (int i = 0; i != numberParameters; ++i)
      m_fitMatrix.derivative[row][i] = 0.;
    (**m).derivative2(&m_fitMatrix.derivative[row][0]);
    ++row;
  }
 
  // update partitioning of fit matrices
  for (int row = 0; row < m_rowsDM; ++row) {
    for (int param = 0; param < numberParameters; ++param) {
      m_fitMatrix.derivative[row][param] = 0.;
    }
  }
 
  // fix degrees of freedom for external customers
  if (!m_parameters->fitMomentum())
    ++m_numberDoF;
 
  // we don't have any fit results yet
  m_covariance.resize(0,0);
  m_finalCovariance.resize(0,0);
 
  // reallocate to get correct matrix sizes
  if (m_derivativeMatrix.size() == 0 || m_weight.size() == 0 ||
      numberParameters != m_columnsDM) {
    m_columnsDM = numberParameters;
    m_derivativeMatrix = Amg::MatrixX(m_rowsDM, m_columnsDM);
    m_weight = Amg::MatrixX(m_columnsDM, m_columnsDM);
    // isn't this faster?  indicating that we have a symmetric matrix <0x2> =
    // <Upper> any gain seems to be negated by additional for loop copies to
    // recover full cov matrix introduces some rounding differences - keep for
    // release 21 to respect strict Tier0 policy
    (m_weight).selfadjointView<0x2>();
    m_weightedDifference = Amg::VectorX(m_columnsDM);
  }
 
  // this should never happen
  if (m_derivativeMatrix.size()==0)
    fitCode = 13;
 
  return fitCode;
}
 
// We compile this package with optimization, even in debug builds; otherwise,
// the heavy use of Eigen makes it too slow.  However, from here we may call
// to out-of-line Eigen code that is linked from other DSOs; in that case,
// it would not be optimized.  Avoid this by forcing all Eigen code
// to be inlined here if possible.
ATH_FLATTEN
    bool
    FitMatrices::solveEquations(void) {
  // use Eigen Matrix multiplication ATR-15723
  // note: fitMatrix (struct) is row-major whereas Eigen prefers column-major
  // storage
  //       hence the loops are nested to optimise row-major and to form the
  //       Eigen transpose
  Amg::MatrixX& weight = m_weight;
  Amg::VectorX& weightedDifference = m_weightedDifference;
  Amg::MatrixX fitMatrixDerivativeT(m_columnsDM, m_rowsDM);
  Amg::MatrixX residuals(m_rowsDM, 1);
  for (int row = 0; row < m_rowsDM; ++row) {
    residuals(row, 0) = (m_residuals)[row];
    for (int col = 0; col < m_columnsDM; ++col) {
      fitMatrixDerivativeT(col, row) = m_fitMatrix.derivative[row][col];
    }
  }
  weight = fitMatrixDerivativeT * fitMatrixDerivativeT.transpose();
  weightedDifference = fitMatrixDerivativeT * residuals;
 
  // stabilize fits with badly determined phi
  if (m_parameters->phiInstability())
    weight(0, 0) += m_largePhiWeight;
 
  // avoid some possible singularities in matrix inversion
  avoidMomentumSingularity();
 
  // solve is faster than inverse: wait for explicit request for covariance
  // before inversion
  m_weightedDifference =
      weight.colPivHouseholderQr().solve(weightedDifference);
 
  m_parameters->update(m_weightedDifference);
  return true;
}
 
void FitMatrices::usePerigee(const FitMeasurement& measurement) {
  m_perigee = &(measurement.perigee());
  m_perigeeWeight = &(measurement.perigeeWeight());
  // TODO: needs eigen equiv !!
  if (m_matrixFromCLHEP) {
    m_usePerigee = true;
  }
}
 
void FitMatrices::addPerigeeMeasurement(void) {
  // TODO: needs eigen equiv !!
  // const Amg::MatrixX&    perigeeWeight       = *m_perigeeWeight;
  // Amg::MatrixX&  weight          = *m_weightCLHEP;
  // AmgVectorX&        weightedDifference  = *m_weightedDifferenceCLHEP;
  // AmgVectorX     diff_vector     =
  // perigeeWeight*m_perigeeDifference.T(); for (int row = 0; row <
  // m_numberPerigee; ++row)
  // {
  //    weightedDifference[row] += diff_vector[row];
  //    for (int col = 0; col <= row; ++col) weight[row][col] +=
  // perigeeWeight[row][col];
  // }
}
 
void FitMatrices::avoidMomentumSingularity(void) {
  // fix momentum if line-fit or fit attempted with negligible field integral
  Amg::MatrixX& weight = m_weight;
  if (m_parameters->fitEnergyDeposit() &&
      weight(5, 5) < 1. / Gaudi::Units::TeV) {
    for (int i = 0; i != m_columnsDM; ++i) {
      weight(i, 5) = 0.;
      weight(5, i) = 0.;
    }
    weight(5, 5) += 1. / Gaudi::Units::TeV;
  }
  if (!m_parameters->fitMomentum() || weight(4, 4) < 1. / Gaudi::Units::TeV) {
    m_parameters->fitMomentum(false);
    for (int i = 0; i != m_columnsDM; ++i) {
      weight(i, 4) = 0.;
      weight(4, i) = 0.;
    }
    weight(4, 4) += 1. / Gaudi::Units::TeV;
  }
}
 
}  // namespace Trk