JanAlignmentAlgorithm Class Reference

Jan's alignment algorithm. More...

#include <JanAlignmentAlgorithm.h>

Inheritance diagram for JanAlignmentAlgorithm:

Classes
struct	DetStat
	structure holding statistical information for one detector More...
struct	ScatterPlot
	a scatter plot, with graph and histogram representations More...

Public Member Functions
void	analyze () override
	analyzes the data collected More...
void	begin (const CTPPSGeometry *geometryReal, const CTPPSGeometry *geometryMisaligned) override
	prepare for processing More...
void	end () override
	cleans up after processing More...
void	feed (const HitCollection &, const LocalTrackFit &) override
	process one track More...
std::string	getName () override
bool	hasErrorEstimate () override
	returns whether this algorithm is capable of estimating result uncertainties More...
	JanAlignmentAlgorithm ()
	dummy constructor (not to be used) More...
	JanAlignmentAlgorithm (const edm::ParameterSet &ps, AlignmentTask *_t)
	normal constructor More...
void	saveDiagnostics (TDirectory *) override
	saves diagnostic histograms/plots More...
unsigned int	solve (const std::vector< AlignmentConstraint > &, std::map< unsigned int, AlignmentResult > &results, TDirectory *dir) override
	~JanAlignmentAlgorithm () override
Public Member Functions inherited from AlignmentAlgorithm
	AlignmentAlgorithm ()
	dummy constructor (not to be used) More...
	AlignmentAlgorithm (const edm::ParameterSet &ps, AlignmentTask *_t)
	normal constructor More...
virtual	~AlignmentAlgorithm ()

Private Attributes
bool	buildDiagnosticPlots
	flag whether to build statistical plots More...
unsigned int	events
	event count More...
TVectorD	M
	final M vector More...
TVectorD *	Mc
TMatrixD	S
	final S matrix More...
TVectorD	S_eigVal
	eigen values of the S matrix More...
TMatrixD	S_eigVec
	matrix of S eigenvectors More...
TMatrixD **	Sc
std::vector< SingularMode >	singularModes
	a list of the singular modes of the S matrix More...
std::map< unsigned int, DetStat >	statistics
	statistical data collection More...
bool	stopOnSingularModes
	whether to stop when singular modes are identified More...
double	weakLimit
	normalized eigen value below which the (CS) eigen vectors are considered as weak More...

Additional Inherited Members
Protected Attributes inherited from AlignmentAlgorithm
double	singularLimit
	eigenvalues in (-singularLimit, singularLimit) are treated as singular More...
AlignmentTask *	task
	the tasked to be completed More...
unsigned int	verbosity

Detailed Description

Jan's alignment algorithm.

Definition at line 25 of file JanAlignmentAlgorithm.h.

Constructor & Destructor Documentation

JanAlignmentAlgorithm() [1/2]

JanAlignmentAlgorithm::JanAlignmentAlgorithm ( )

inline

dummy constructor (not to be used)

Definition at line 85 of file JanAlignmentAlgorithm.h.

JanAlignmentAlgorithm() [2/2]

JanAlignmentAlgorithm::JanAlignmentAlgorithm	(	const edm::ParameterSet &	ps,
		AlignmentTask *	_t
	)

normal constructor

Definition at line 27 of file JanAlignmentAlgorithm.cc.

    : AlignmentAlgorithm(ps, _t), Sc(nullptr), Mc(nullptr) {
  const ParameterSet &lps = ps.getParameterSet("JanAlignmentAlgorithm");
  weakLimit = lps.getParameter<double>("weakLimit");
  stopOnSingularModes = lps.getParameter<bool>("stopOnSingularModes");
  buildDiagnosticPlots = lps.getParameter<bool>("buildDiagnosticPlots");

References buildDiagnosticPlots, edm::ParameterSet::getParameter(), edm::ParameterSet::getParameterSet(), stopOnSingularModes, and weakLimit.

~JanAlignmentAlgorithm()

JanAlignmentAlgorithm::~JanAlignmentAlgorithm ( )

override

Definition at line 37 of file JanAlignmentAlgorithm.cc.

Member Function Documentation

analyze()

void JanAlignmentAlgorithm::analyze ( )

overridevirtual

analyzes the data collected

Implements AlignmentAlgorithm.

Definition at line 267 of file JanAlignmentAlgorithm.cc.

                                    {
  if (verbosity > 2)
    printf("\n>> JanAlignmentAlgorithm::Analyze\n");
 
  // calculate full dimension
  unsigned int dim = 0;
  for (unsigned int i = 0; i < task->quantityClasses.size(); i++)
    dim += Mc[i].GetNrows();
 
  if (verbosity > 2) {
    printf("\tsensors: %u\n", task->geometry.getNumberOfDetectors());
    printf("\tfull dimension: %u\n", dim);
    printf("\tquantity classes: %lu\n", task->quantityClasses.size());
  }
 
  // build full M
  M.ResizeTo(dim);
  unsigned int offset = 0;
  for (unsigned int i = 0; i < task->quantityClasses.size(); i++) {
    M.SetSub(offset, Mc[i]);
    offset += Mc[i].GetNrows();
  }
 
  // build full S
  S.ResizeTo(dim, dim);
  unsigned int r_offset = 0, c_offset = 0;
  for (unsigned int i = 0; i < task->quantityClasses.size(); i++) {
    c_offset = 0;
    unsigned int r_size = 0, c_size = 0;
    for (unsigned int j = 0; j < task->quantityClasses.size(); j++) {
      r_size = Sc[i][j].GetNrows();
      c_size = Sc[i][j].GetNcols();
 
      if (r_size < 1 || c_size < 1)
        continue;
 
      TMatrixDSub(S, r_offset, r_offset + r_size - 1, c_offset, c_offset + c_size - 1) = Sc[i][j];
      c_offset += c_size;
    }
    r_offset += r_size;
  }
 
  // analyze symmetricity
  if (verbosity >= 3) {
    double maxDiff = 0., maxElem = 0.;
    for (unsigned int i = 0; i < dim; i++) {
      for (unsigned int j = 0; j < dim; j++) {
        double diff = S[i][j] - S[j][i];
        if (fabs(diff) > maxDiff)
          maxDiff = diff;
        if (S[i][j] > maxElem)
          maxElem = S[i][j];
      }
    }
 
    printf("\n* S matrix:\n\tdimension = %i\n\tmaximum asymmetry: %E\t(ratio to maximum element %E)\n",
           dim,
           maxDiff,
           maxDiff / maxElem);
  }
 
  // make a symmetric copy
  TMatrixDSym S_sym(dim);
  for (unsigned int j = 0; j < dim; j++) {
    for (unsigned int i = 0; i < dim; i++) {
      S_sym[i][j] = S[i][j];
    }
  }
 
  // eigen analysis of S
  TMatrixDSymEigen S_eig(S_sym);
  const TVectorD &S_eigVal_temp = S_eig.GetEigenValues();
  S_eigVal.ResizeTo(S_eigVal_temp.GetNrows());
  S_eigVal = S_eigVal_temp;
  const TMatrixD &S_eigVec_temp = S_eig.GetEigenVectors();
  S_eigVec.ResizeTo(S_eigVec_temp);
  S_eigVec = S_eigVec_temp;
 
  // identify singular modes
  for (int i = 0; i < S_eigVal.GetNrows(); i++) {
    double nev = S_eigVal[i] / events;
    if (fabs(nev) < singularLimit) {
      SingularMode sM{S_eigVal[i], TMatrixDColumn(S_eigVec, i), i};
      singularModes.push_back(sM);
    }
  }
 
#if DEBUG
  // print singular vectors
  if (singularModes.size() > 0) {
    printf("\n* S singular modes\n   | ");
    for (unsigned int i = 0; i < singularModes.size(); i++)
      printf("%+10.3E   ", singularModes[i].val);
    printf("\n-- | ");
 
    for (unsigned int i = 0; i < singularModes.size(); i++)
      printf("----------   ");
    printf("\n");
 
    for (unsigned int j = 0; j < dim; j++) {
      printf("%2u | ", j);
      for (unsigned int i = 0; i < singularModes.size(); i++) {
        printf("%+10.3E   ", singularModes[i].vec[j]);
      }
      printf("\n");
    }
  } else
    printf("\n* S has no singular modes\n");
#endif

References change_name::diff, events, AlignmentTask::geometry, AlignmentGeometry::getNumberOfDetectors(), mps_fire::i, dqmiolumiharvest::j, M, reco::castor::maxDiff(), Mc, hltrates_dqm_sourceclient-live_cfg::offset, AlignmentTask::quantityClasses, S_eigVal, S_eigVec, Sc, AlignmentAlgorithm::singularLimit, singularModes, AlignmentAlgorithm::task, heppy_batch::val, and AlignmentAlgorithm::verbosity.

begin()

void JanAlignmentAlgorithm::begin ( const CTPPSGeometry *  geometryReal, const CTPPSGeometry *  geometryMisaligned  )

overridevirtual

prepare for processing

Implements AlignmentAlgorithm.

Definition at line 41 of file JanAlignmentAlgorithm.cc.

                                                                                                            {
  // initialize M and S components
  Mc = new TVectorD[task->quantityClasses.size()];
  Sc = new TMatrixD *[task->quantityClasses.size()];
  for (unsigned int i = 0; i < task->quantityClasses.size(); i++) {
    unsigned int rows = task->quantitiesOfClass(task->quantityClasses[i]);
 
    Mc[i].ResizeTo(rows);
    Mc[i].Zero();
 
    Sc[i] = new TMatrixD[task->quantityClasses.size()];
    for (unsigned int j = 0; j < task->quantityClasses.size(); j++) {
      unsigned int cols = task->quantitiesOfClass(task->quantityClasses[j]);
      Sc[i][j].ResizeTo(rows, cols);
      Sc[i][j].Zero();
    }
  }
 
  // prepare statistics plots
  if (buildDiagnosticPlots) {
    for (const auto &it : task->geometry.getSensorMap()) {
      unsigned int id = it.first;
      char buf[50];
      DetStat s;
 
      sprintf(buf, "%u: m distribution", id);
      s.m_dist = new TH1D(buf, ";u or v   (mm)", 100, -25., 25.);
 
      sprintf(buf, "%u: R distribution", id);
      s.R_dist = new TH1D(buf, ";R   (mm)", 500, -0.5, 0.5);
 
      for (unsigned int c = 0; c < task->quantityClasses.size(); c++) {
        sprintf(buf, "%u: coef, %s", id, task->quantityClassTag(task->quantityClasses[c]).c_str());
        s.coefHist.push_back(new TH1D(buf, ";coefficient", 100, -2., +2.));
 
        sprintf(buf, "%u: R vs. coef, %s", id, task->quantityClassTag(task->quantityClasses[c]).c_str());
        TGraph *g = new TGraph();
        g->SetName(buf);
        g->SetTitle(";coefficient;residual   (mm)");
        s.resVsCoef.push_back(g);
      }
 
      statistics[id] = s;
    }
  }
 
  events = 0;

References visDQMUpload::buf, buildDiagnosticPlots, HltBtagPostValidation_cff::c, events, g, AlignmentTask::geometry, AlignmentGeometry::getSensorMap(), mps_fire::i, triggerObjects_cff::id, dqmiolumiharvest::j, Mc, AlignmentTask::quantitiesOfClass(), AlignmentTask::quantityClasses, AlignmentTask::quantityClassTag(), postprocess-scan-build::rows, alignCSCRings::s, Sc, statistics, and AlignmentAlgorithm::task.

end()

void JanAlignmentAlgorithm::end ( )

overridevirtual

cleans up after processing

Implements AlignmentAlgorithm.

Definition at line 706 of file JanAlignmentAlgorithm.cc.

                                {
  delete[] Mc;
 
  for (unsigned int i = 0; i < task->quantityClasses.size(); i++) {
    delete[] Sc[i];
  }
  delete[] Sc;

References mps_fire::i, Mc, AlignmentTask::quantityClasses, Sc, and AlignmentAlgorithm::task.

Referenced by Types.LuminosityBlockRange::cppID(), and Types.EventRange::cppID().

feed()

void JanAlignmentAlgorithm::feed ( const HitCollection &  , const LocalTrackFit &    )

overridevirtual

process one track

Implements AlignmentAlgorithm.

Definition at line 92 of file JanAlignmentAlgorithm.cc.

                                                                                              {
  if (verbosity > 9)
    printf("\n>> JanAlignmentAlgorithm::Feed\n");
 
  events++;
 
  // prepare fit - make z0 compatible
  double hax = trackFit.ax;
  double hay = trackFit.ay;
  double hbx = trackFit.bx + trackFit.ax * (task->geometry.z0 - trackFit.z0);
  double hby = trackFit.by + trackFit.ay * (task->geometry.z0 - trackFit.z0);
 
  // prepare Gamma matrices (full of zeros)
  TMatrixD *Ga = new TMatrixD[task->quantityClasses.size()];
  for (unsigned int i = 0; i < task->quantityClasses.size(); i++) {
    Ga[i].ResizeTo(selection.size(), Mc[i].GetNrows());
    Ga[i].Zero();
  }
 
  TMatrixD A(selection.size(), 4);
  TMatrixD Vi(selection.size(), selection.size());
  TVectorD m(selection.size());
 
  set<unsigned int> rpSet;
  if (buildDiagnosticPlots) {
    for (const auto &hit : selection) {
      CTPPSDetId detId(hit.id);
      const unsigned int rpDecId = 100 * detId.arm() + 10 * detId.station() + detId.rp();
      rpSet.insert(rpDecId);
    }
  }
 
  // fill fit matrix and Gamma matrices
  unsigned int j = 0;
 
  for (HitCollection::const_iterator hit = selection.begin(); hit != selection.end(); ++hit, ++j) {
    unsigned int id = hit->id;
 
    const DetGeometry &d = task->geometry.get(id);
    const auto &dirData = d.getDirectionData(hit->dirIdx);
 
    A(j, 0) = hit->z * dirData.dx;
    A(j, 1) = dirData.dx;
    A(j, 2) = hit->z * dirData.dy;
    A(j, 3) = dirData.dy;
 
    m(j) = hit->position + dirData.s - (hit->z - d.z) * dirData.dz;  // in mm
 
    Vi(j, j) = 1. / hit->sigma / hit->sigma;
 
    double C = dirData.dx, S = dirData.dy;
 
    double hx = hax * hit->z + hbx;  // in mm
    double hy = hay * hit->z + hby;
    double R = m(j) - (hx * C + hy * S);  // (standard) residual
 
    if (buildDiagnosticPlots) {
      statistics[id].m_dist->Fill(m(j));
      statistics[id].R_dist->Fill(R);
    }
 
    for (unsigned int i = 0; i < task->quantityClasses.size(); i++) {
      // check compatibility
      signed int matrixIndex = task->getMeasurementIndex(task->quantityClasses[i], hit->id, hit->dirIdx);
      if (matrixIndex < 0)
        continue;
 
      matrixIndex = task->getQuantityIndex(task->quantityClasses[i], hit->id);
 
      switch (task->quantityClasses[i]) {
        case AlignmentTask::qcShR1:
          Ga[i][j][matrixIndex] = -1.;
          break;
 
        case AlignmentTask::qcShR2:
          Ga[i][j][matrixIndex] = -1.;
          break;
 
        case AlignmentTask::qcShZ:
          Ga[i][j][matrixIndex] = hax * C + hay * S;
          break;
 
        case AlignmentTask::qcRotZ:
          Ga[i][j][matrixIndex] = (hax * hit->z + hbx - d.sx) * (-S) + (hay * hit->z + hby - d.sy) * C;
          break;
      }
 
      if (buildDiagnosticPlots) {
        double c = Ga[i][j][matrixIndex];
        DetStat &s = statistics[id];
        s.coefHist[i]->Fill(c);
        s.resVsCoef[i]->SetPoint(s.resVsCoef[i]->GetN(), c, R);
 
        if (task->quantityClasses[i] == AlignmentTask::qcRotZ) {
          map<set<unsigned int>, ScatterPlot>::iterator hit = s.resVsCoefRot_perRPSet.find(rpSet);
          if (hit == s.resVsCoefRot_perRPSet.end()) {
            ScatterPlot sp;
            sp.g = new TGraph();
            sp.h = new TH2D("", "", 40, -20., +20., 60, -0.15, +0.15);
            hit = s.resVsCoefRot_perRPSet.insert(pair<set<unsigned int>, ScatterPlot>(rpSet, sp)).first;
          }
          hit->second.g->SetPoint(hit->second.g->GetN(), c, R);
          hit->second.h->Fill(c, R);
        }
      }
    }
  }
 
  // sigma matrix
  TMatrixD AT(TMatrixD::kTransposed, A);
  TMatrixD ATViA(4, 4);
  ATViA = AT * Vi * A;
  TMatrixD ATViAI(ATViA);
  ATViAI = ATViA.Invert();
  TMatrixD sigma(Vi);
  sigma -= Vi * A * ATViAI * AT * Vi;
 
  // traspose Gamma matrices
  TMatrixD *GaT = new TMatrixD[task->quantityClasses.size()];
  for (unsigned int i = 0; i < task->quantityClasses.size(); i++) {
    GaT[i].ResizeTo(Mc[i].GetNrows(), selection.size());
    GaT[i].Transpose(Ga[i]);
  }
 
  // normalized residuals
  TVectorD r(selection.size());
  r = sigma * m;
 
  // increment M
  for (unsigned int i = 0; i < task->quantityClasses.size(); i++) {
    if (Mc[i].GetNrows() < 1)
      continue;
 
    Mc[i] += GaT[i] * r;
  }
 
  // increment S
  for (unsigned int i = 0; i < task->quantityClasses.size(); i++) {
    for (unsigned int j = 0; j < task->quantityClasses.size(); j++) {
      if (Sc[i][j].GetNrows() < 1 || Sc[i][j].GetNcols() < 1)
        continue;
 
      Sc[i][j] += GaT[i] * sigma * Ga[j];
    }
  }
 
#ifdef DEBUG
  printf("* checking normalized residuals, selection.size = %u\n", selection.size());
  r.Print();
 
  for (unsigned int i = 0; i < task->quantityClasses.size(); i++) {
    printf("- class %u\n", i);
    TVectorD t(Mc[i].GetNrows());
    for (int j = 0; j < t.GetNrows(); j++)
      t[j] = 1.;
    t.Print();
 
    Ga[i].Print();
 
    TVectorD tt(selection.size());
    tt = sigma * Ga[i] * t;
 
    double ttn = sqrt(tt.Norm2Sqr());
    printf("|tt| = %E\n", ttn);
    if (ttn > 1E-8)
      tt.Print();
  }
#endif
 
  delete[] Ga;
  delete[] GaT;

References MaterialEffects_cfi::A, CTPPSDetId::arm(), LocalTrackFit::ax, LocalTrackFit::ay, buildDiagnosticPlots, LocalTrackFit::bx, LocalTrackFit::by, HltBtagPostValidation_cff::c, gen::C, ztail::d, events, JanAlignmentAlgorithm::ScatterPlot::g, AlignmentTask::geometry, AlignmentGeometry::get(), AlignmentTask::getMeasurementIndex(), AlignmentTask::getQuantityIndex(), JanAlignmentAlgorithm::ScatterPlot::h, mps_fire::i, triggerObjects_cff::id, hit::id, dqmiolumiharvest::j, visualization-live-secondInstance_cfg::m, Mc, AlignmentTask::qcRotZ, AlignmentTask::qcShR1, AlignmentTask::qcShR2, AlignmentTask::qcShZ, AlignmentTask::quantityClasses, dttmaxenums::R, alignCSCRings::r, CTPPSDetId::rp(), S, alignCSCRings::s, Sc, corrVsCorr::selection, mathSSE::sqrt(), CTPPSDetId::station(), statistics, submitPVValidationJobs::t, AlignmentAlgorithm::task, groupFilesInBlocks::tt, AlignmentAlgorithm::verbosity, hit::z, LocalTrackFit::z0, and AlignmentGeometry::z0.

Referenced by Page1Parser.Page1Parser::_Parse().

getName()

std::string JanAlignmentAlgorithm::getName ( )

inlineoverridevirtual

Reimplemented from AlignmentAlgorithm.

Definition at line 92 of file JanAlignmentAlgorithm.h.

{ return true; }

Referenced by plotting.Plot::draw().

hasErrorEstimate()

bool JanAlignmentAlgorithm::hasErrorEstimate ( )

inlineoverridevirtual

returns whether this algorithm is capable of estimating result uncertainties

Implements AlignmentAlgorithm.

Definition at line 94 of file JanAlignmentAlgorithm.h.

saveDiagnostics()

void JanAlignmentAlgorithm::saveDiagnostics ( TDirectory *  )

overridevirtual

saves diagnostic histograms/plots

Implements AlignmentAlgorithm.

Definition at line 717 of file JanAlignmentAlgorithm.cc.

                                                           {
  if (!buildDiagnosticPlots)
    return;
 
  for (map<unsigned int, DetStat>::iterator it = statistics.begin(); it != statistics.end(); ++it) {
    char buf[50];
    sprintf(buf, "%u", it->first);
    gDirectory = dir->mkdir(buf);
 
    it->second.m_dist->Write();
    it->second.R_dist->Write();
 
    for (unsigned int c = 0; c < task->quantityClasses.size(); c++) {
      it->second.coefHist[c]->Write();
      it->second.resVsCoef[c]->Write();
    }
 
    gDirectory = gDirectory->mkdir("R vs. rot. coef, per RP set");
    TCanvas *c = new TCanvas;
    c->SetName("R vs. rot. coef, overlapped");
    TH2D *frame = new TH2D("frame", "frame", 100, -20., +20., 100, -0.15, +0.15);
    frame->Draw();
    unsigned int idx = 0;
    for (map<set<unsigned int>, ScatterPlot>::iterator iit = it->second.resVsCoefRot_perRPSet.begin();
         iit != it->second.resVsCoefRot_perRPSet.end();
         ++iit, ++idx) {
      string label;
      bool first = true;
      for (set<unsigned int>::iterator sit = iit->first.begin(); sit != iit->first.end(); ++sit) {
        char buf[50];
        sprintf(buf, "%u", *sit);
 
        if (first) {
          label = buf;
          first = false;
        } else {
          label = label + ", " + buf;
        }
      }
 
      iit->second.g->SetTitle(";rotation coefficient   (mm);residual   (mm)");
      iit->second.g->SetMarkerColor(idx + 1);
      iit->second.g->SetName(label.c_str());
      iit->second.g->Draw((idx == 0) ? "p" : "p");
      iit->second.g->Write();
 
      iit->second.h->SetName((label + " (hist)").c_str());
      iit->second.h->SetTitle(";rotation coefficient   (mm);residual   (mm)");
      iit->second.h->Write();
    }
 
    gDirectory->cd("..");
    c->Write();
  }

References visDQMUpload::buf, buildDiagnosticPlots, HltBtagPostValidation_cff::c, DeadROC_duringRun::dir, dqmdumpme::first, amptDefault_cfi::frame, heavyIonCSV_trainingSettings::idx, label, genParticles_cff::map, AlignmentTask::quantityClasses, statistics, and AlignmentAlgorithm::task.

solve()

unsigned int JanAlignmentAlgorithm::solve ( const std::vector< AlignmentConstraint > &  , std::map< unsigned int, AlignmentResult > &  results, TDirectory *  dir  )

overridevirtual

solves the alignment problem with the given constraints

Parameters

dir	a directory (in StraightTrackAlignment::taskDataFileName) where intermediate results can be stored

Implements AlignmentAlgorithm.

Definition at line 380 of file JanAlignmentAlgorithm.cc.

                                                           {
  if (verbosity)
    printf(">> JanAlignmentAlgorithm::Solve\n");
 
  results.clear();
 
  // build C matrix
  unsigned int dim = S.GetNrows();
  TMatrixD C(dim, constraints.size());
  TMatrixD C2(dim, constraints.size());
  for (unsigned int i = 0; i < constraints.size(); i++) {
    unsigned int offset = 0;
    for (auto &quantityClass : task->quantityClasses) {
      const TVectorD &cv = constraints[i].coef.find(quantityClass)->second;
      for (int k = 0; k < cv.GetNrows(); k++) {
        C[offset][i] = events * cv[k];
        C2[offset][i] = events * cv[k] * 1E3;
        offset++;
      }
    }
  }
 
#ifdef DEBUG
  printf("\n* constraint matrix\n");
  Print(C);
#endif
 
  // build E matrix (singular vectors of S as its columns)
  TMatrixD E(S.GetNrows(), singularModes.size());
  for (unsigned int i = 0; i < singularModes.size(); i++)
    for (int j = 0; j < S.GetNrows(); j++)
      E(j, i) = singularModes[i].vec[j];
 
  // build CS matrix
  TMatrixDSym CS(dim + constraints.size());
  TMatrixDSym CS2(dim + constraints.size());
  CS.Zero();
  CS2.Zero();
  for (unsigned int j = 0; j < dim; j++) {
    for (unsigned int i = 0; i < dim; i++) {
      CS[i][j] = S[i][j];
      CS2[i][j] = S[i][j];
    }
  }
 
  for (unsigned int i = 0; i < constraints.size(); i++) {
    for (unsigned int j = 0; j < dim; j++) {
      CS[j][dim + i] = CS[dim + i][j] = C(j, i);
      CS2[j][dim + i] = CS2[dim + i][j] = C2(j, i);
    }
  }
 
  // eigen analysis of CS matrix
  TMatrixDSymEigen CS_eig(CS);
  TVectorD CS_eigVal = CS_eig.GetEigenValues();
  TMatrixD CS_eigVec = CS_eig.GetEigenVectors();
 
  // check regularity of CS matrix
  if (verbosity >= 2) {
    printf("\n* eigen values of CS and S matrices (events = %u)\n", events);
    printf("   #          CS    norm. CS               S     norm. S\n");
  }
 
  unsigned int singularModeCount = 0;
  vector<unsigned int> weakModeIdx;
  for (int i = 0; i < CS_eigVal.GetNrows(); i++) {
    const double CS_nev = CS_eigVal[i] / events;
 
    if (fabs(CS_nev) < singularLimit)
      singularModeCount++;
 
    if (verbosity >= 2) {
      printf("%4i%+12.2E%+12.2E", i, CS_eigVal[i], CS_nev);
      if (fabs(CS_nev) < singularLimit) {
        singularModeCount++;
        printf(" (S)");
      } else {
        if (fabs(CS_nev) < weakLimit) {
          weakModeIdx.push_back(i);
          printf(" (W)");
        } else {
          printf("    ");
        }
      }
 
      if (i < S_eigVal.GetNrows()) {
        double S_nev = S_eigVal[i] / events;
        printf("%+12.2E%+12.2E", S_eigVal[i], S_nev);
        if (fabs(S_nev) < singularLimit)
          printf(" (S)");
        else if (fabs(S_nev) < weakLimit)
          printf(" (W)");
      }
 
      printf("\n");
    }
  }
 
  if (verbosity >= 2) {
    // print weak vectors
    if (!weakModeIdx.empty()) {
      unsigned int columns = 10;
      unsigned int first = 0;
 
      while (first < weakModeIdx.size()) {
        unsigned int last = first + columns;
        if (last >= weakModeIdx.size())
          last = weakModeIdx.size();
 
        printf("\n* CS weak modes\n    | ");
        for (unsigned int i = first; i < last; i++)
          printf("%+10.3E   ", CS_eigVal[weakModeIdx[i]]);
        printf("\n--- | ");
 
        for (unsigned int i = first; i < last; i++)
          printf("----------   ");
        printf("\n");
 
        // determine maximum elements
        vector<double> maxs;
        for (unsigned int i = first; i < last; i++) {
          double max = 0;
          for (unsigned int j = 0; j < dim + constraints.size(); j++) {
            double v = fabs(CS_eigVec(weakModeIdx[i], j));
            if (v > max)
              max = v;
          }
          maxs.push_back(max);
        }
 
        for (unsigned int j = 0; j < dim + constraints.size(); j++) {
          printf("%3u | ", j);
          for (unsigned int i = first; i < last; i++) {
            double v = CS_eigVec(weakModeIdx[i], j);
            if (fabs(v) / maxs[i - first] > 1E-3)
              printf("%+10.3E   ", v);
            else
              printf("         .   ");
          }
          printf("\n");
        }
 
        first = last;
      }
    } else
      printf("\n* CS has no weak modes\n");
  }
 
  // check the regularity of C^T E
  if (verbosity >= 2) {
    if (E.GetNcols() == C.GetNcols()) {
      TMatrixD CTE(C, TMatrixD::kTransposeMult, E);
      print(CTE, "* CTE matrix:");
      const double &det = CTE.Determinant();
      printf(
          "\n* det(CTE) = %E, max(CTE) = %E, det(CTE)/max(CTE) = %E\n\tmax(C) = %E, max(E) = %E, "
          "det(CTE)/max(C)/max(E) = %E\n",
          det,
          CTE.Max(),
          det / CTE.Max(),
          C.Max(),
          E.Max(),
          det / C.Max() / E.Max());
    } else {
      printf(">> JanAlignmentAlgorithm::Solve > WARNING: C matrix has %u, while E matrix %u columns.\n",
             C.GetNcols(),
             E.GetNcols());
    }
  }
 
  // stop if CS is singular
  if (singularModeCount > 0 && stopOnSingularModes) {
    LogError("PPS") << "\n>> JanAlignmentAlgorithm::Solve > ERROR: There are " << singularModeCount
                    << " singular modes in CS matrix. Stopping.";
    return 1;
  }
 
  // build MV vector
  TVectorD MV(dim + constraints.size());
  for (unsigned int i = 0; i < dim; i++)
    MV[i] = M[i];
  for (unsigned int i = 0; i < constraints.size(); i++)
    MV[dim + i] = events * constraints[i].val;
 
  // perform inversion and solution
  TMatrixD CSI(TMatrixD::kInverted, CS);
  TMatrixD CS2I(TMatrixD::kInverted, CS2);
  TVectorD AL(MV);
  AL = CSI * MV;
 
  // evaluate error matrix
  TMatrixD S0(S);  // new parts full of zeros
  S0.ResizeTo(dim + constraints.size(), dim + constraints.size());
  TMatrixD EM(CS);
  EM = CSI * S0 * CSI;
 
  TMatrixD EM2(CS2);
  EM2 = CS2I * S0 * CS2I;
 
  TMatrixD EMdiff(EM2 - EM);
 
  if (verbosity >= 3) {
    double max1 = -1., max2 = -1., maxDiff = -1.;
    for (int i = 0; i < EMdiff.GetNrows(); i++) {
      for (int j = 0; j < EMdiff.GetNcols(); j++) {
        if (maxDiff < fabs(EMdiff(i, j)))
          maxDiff = fabs(EMdiff(i, j));
 
        if (max1 < fabs(EM(i, j)))
          max1 = fabs(EM(i, j));
 
        if (max2 < fabs(EM2(i, j)))
          max2 = fabs(EM2(i, j));
      }
    }
 
    printf("EM max = %E, EM2 max = %E, EM2 - EM max = %E\n", max1, max2, maxDiff);
  }
 
  // tests
  TMatrixD &U = CS_eigVec;
  TMatrixD UT(TMatrixD::kTransposed, U);
  //TMatrixD CSEi(CS);
  //CSEi = UT * CS * U;
  //Print(CSEi, "CSEi");
 
  TMatrixD EMEi(EM);
  EMEi = UT * EM * U;
  //Print(EMEi, "*EMEi");
 
  if (verbosity >= 3) {
    double max = -1.;
    for (int i = 0; i < EMEi.GetNrows(); i++) {
      for (int j = 0; j < EMEi.GetNcols(); j++) {
        if (max < EMEi(i, j))
          max = EMEi(i, j);
      }
    }
 
    printf("max = %E\n", max);
  }
 
  // print lambda values
  if (verbosity >= 3) {
    printf("\n* Lambda (from the contribution of singular modes to MV)\n");
    for (unsigned int i = 0; i < constraints.size(); i++) {
      printf("\t%u (%25s)\t%+10.1E +- %10.1E\n",
             i,
             constraints[i].name.c_str(),
             AL[dim + i] * 1E3,
             sqrt(EM[i + dim][i + dim]) * 1E3);
    }
  }
 
  // fill results
  unsigned int offset = 0;
  vector<unsigned int> offsets;
  for (unsigned int i = 0; i < task->quantityClasses.size(); i++) {
    offsets.push_back(offset);
    offset += Mc[i].GetNrows();
  }
 
  for (const auto &dit : task->geometry.getSensorMap()) {
    AlignmentResult r;
 
    for (unsigned int i = 0; i < task->quantityClasses.size(); i++) {
      signed idx = task->getQuantityIndex(task->quantityClasses[i], dit.first);
      if (idx < 0)
        continue;
 
      unsigned int fi = offsets[i] + idx;
      double v = AL[fi];
      double e = sqrt(EM[fi][fi]);
      switch (task->quantityClasses[i]) {
        case AlignmentTask::qcShR1:
          r.setShR1(v);
          r.setShR1Unc(e);
          break;
        case AlignmentTask::qcShR2:
          r.setShR2(v);
          r.setShR2Unc(e);
          break;
        case AlignmentTask::qcShZ:
          r.setShZ(v);
          r.setShZUnc(e);
          break;
        case AlignmentTask::qcRotZ:
          r.setRotZ(v);
          r.setRotZUnc(e);
          break;
      }
    }
 
    results[dit.first] = r;
  }
 
  // save matrices, eigen data, ...
  if (dir) {
    dir->cd();
 
    S.Write("S");
    S_eigVal.Write("S_eigen_values");
    S_eigVec.Write("S_eigen_vectors");
 
    E.Write("E");
    C.Write("C");
 
    CS.Write("CS");
    CS_eigVal.Write("CS_eigen_values");
    CS_eigVec.Write("CS_eigen_vectors");
 
    MV.Write("MV");
    AL.Write("AL");
 
    S0.Write("S0");
    EM.Write("EM");
  }
 
  // success
  return 0;

References gen::C, mps_check::columns, createBeamHaloJobs::constraints, cuy::cv, DeadROC_duringRun::dir, MillePedeFileConverter_cfg::e, events, dqmdumpme::first, AlignmentTask::geometry, AlignmentTask::getQuantityIndex(), AlignmentGeometry::getSensorMap(), mps_fire::i, heavyIonCSV_trainingSettings::idx, dqmiolumiharvest::j, dqmdumpme::k, dqmdumpme::last, M, SiStripPI::max, reco::castor::maxDiff(), Mc, Skims_PA_cff::name, hltrates_dqm_sourceclient-live_cfg::offset, unpackBuffers-CaloStage1::offsets, print(), AlignmentTask::qcRotZ, AlignmentTask::qcShR1, AlignmentTask::qcShR2, AlignmentTask::qcShZ, AlignmentTask::quantityClasses, alignCSCRings::r, bookConverter::results, S_eigVal, S_eigVec, AlignmentAlgorithm::singularLimit, singularModes, mathSSE::sqrt(), stopOnSingularModes, AlignmentAlgorithm::task, mitigatedMETSequence_cff::U, findQualityFiles::v, heppy_batch::val, AlignmentAlgorithm::verbosity, and weakLimit.

Member Data Documentation

buildDiagnosticPlots

bool JanAlignmentAlgorithm::buildDiagnosticPlots

private

flag whether to build statistical plots

Definition at line 81 of file JanAlignmentAlgorithm.h.

Referenced by begin(), feed(), JanAlignmentAlgorithm(), and saveDiagnostics().

events

unsigned int JanAlignmentAlgorithm::events

private

event count

Definition at line 75 of file JanAlignmentAlgorithm.h.

Referenced by eventsfwlite.Events::__getattr__(), eventsfwlite.Events::__getitem__(), eventsfwlite.Events::__len__(), analyze(), begin(), feed(), looper.Looper::loop(), looper.Looper::process(), and solve().

M

TVectorD JanAlignmentAlgorithm::M

private

final M vector

Definition at line 57 of file JanAlignmentAlgorithm.h.

Referenced by analyze(), and solve().

Mc

TVectorD* JanAlignmentAlgorithm::Mc

private

M vector components indeces correspond to the qClToOpt list

Definition at line 51 of file JanAlignmentAlgorithm.h.

Referenced by analyze(), begin(), end(), feed(), and solve().

S

TMatrixD JanAlignmentAlgorithm::S

private

final S matrix

Definition at line 54 of file JanAlignmentAlgorithm.h.

Referenced by feed().

S_eigVal

TVectorD JanAlignmentAlgorithm::S_eigVal

private

eigen values of the S matrix

Definition at line 60 of file JanAlignmentAlgorithm.h.

Referenced by analyze(), and solve().

S_eigVec

TMatrixD JanAlignmentAlgorithm::S_eigVec

private

matrix of S eigenvectors

Definition at line 63 of file JanAlignmentAlgorithm.h.

Referenced by analyze(), and solve().

Sc

TMatrixD** JanAlignmentAlgorithm::Sc

private

S matrix components indeces correspond to the qClToOpt list

Definition at line 47 of file JanAlignmentAlgorithm.h.

Referenced by analyze(), begin(), end(), and feed().

singularModes

std::vector<SingularMode> JanAlignmentAlgorithm::singularModes

private

a list of the singular modes of the S matrix

Definition at line 66 of file JanAlignmentAlgorithm.h.

Referenced by analyze(), and solve().

statistics

std::map<unsigned int, DetStat> JanAlignmentAlgorithm::statistics

private

statistical data collection

Definition at line 78 of file JanAlignmentAlgorithm.h.

Referenced by begin(), feed(), and saveDiagnostics().

stopOnSingularModes

bool JanAlignmentAlgorithm::stopOnSingularModes

private

whether to stop when singular modes are identified

Definition at line 69 of file JanAlignmentAlgorithm.h.

Referenced by JanAlignmentAlgorithm(), and solve().

weakLimit

double JanAlignmentAlgorithm::weakLimit

private

normalized eigen value below which the (CS) eigen vectors are considered as weak

Definition at line 72 of file JanAlignmentAlgorithm.h.

Referenced by JanAlignmentAlgorithm(), and solve().