JanAlignmentAlgorithm.cc

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/****************************************************************************
* Authors: 
*  Jan Kašpar (jan.kaspar@gmail.com) 
****************************************************************************/

#include "FWCore/MessageLogger/interface/MessageLogger.h"
#include "FWCore/ParameterSet/interface/ParameterSet.h"

#include "CalibPPS/AlignmentRelative/interface/JanAlignmentAlgorithm.h"
#include "CalibPPS/AlignmentRelative/interface/AlignmentTask.h"
#include "CalibPPS/AlignmentRelative/interface/Utilities.h"

#include "TMatrixDSymEigen.h"
#include "TDecompSVD.h"
#include "TFile.h"
#include "TCanvas.h"
#include "TH2D.h"

#include <cmath>

//#define DEBUG 1

using namespace std;
using namespace edm;

//----------------------------------------------------------------------------------------------------

JanAlignmentAlgorithm::JanAlignmentAlgorithm(const ParameterSet &ps, AlignmentTask *_t)
    : 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");
}

//----------------------------------------------------------------------------------------------------

JanAlignmentAlgorithm::~JanAlignmentAlgorithm() {}

//----------------------------------------------------------------------------------------------------

void JanAlignmentAlgorithm::begin(const CTPPSGeometry *geometryReal, const CTPPSGeometry *geometryMisaligned) {
  // 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;
}

//----------------------------------------------------------------------------------------------------

void JanAlignmentAlgorithm::feed(const HitCollection &selection, const LocalTrackFit &trackFit) {
  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;
}

//----------------------------------------------------------------------------------------------------

void JanAlignmentAlgorithm::analyze() {
  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
}

//----------------------------------------------------------------------------------------------------

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

//----------------------------------------------------------------------------------------------------

void JanAlignmentAlgorithm::end() {
  delete[] Mc;

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

//----------------------------------------------------------------------------------------------------

void JanAlignmentAlgorithm::saveDiagnostics(TDirectory *dir) {
  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();
  }
}