source: git/display/Delphes3DGeometry.cc@ 7d790c1

/*
 *  Delphes: a framework for fast simulation of a generic collider experiment
 *  Copyright (C) 2012-2014  Universite catholique de Louvain (UCL), Belgium
 *
 *  This program is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */

#include <algorithm>
#include <cassert>
#include <map>
#include <set>
#include <sstream>
#include <utility>
#include <vector>

#include "TAxis.h"
#include "TF2.h"
#include "TFormula.h"
#include "TGeoArb8.h"
#include "TGeoCompositeShape.h"
#include "TGeoCone.h"
#include "TGeoManager.h"
#include "TGeoMatrix.h"
#include "TGeoMedium.h"
#include "TGeoNode.h"
#include "TGeoTube.h"
#include "TGeoVolume.h"
#include "TH1F.h"
#include "TMath.h"
#include "TString.h"

#include "display/Delphes3DGeometry.h"

#include "classes/DelphesClasses.h"
#include "external/ExRootAnalysis/ExRootConfReader.h"

using namespace std;

Delphes3DGeometry::Delphes3DGeometry(TGeoManager *geom, bool transp)
{

  //--- the geometry manager
  geom_ = geom == NULL ? gGeoManager : geom;
  //gGeoManager->DefaultColors();

  //--- define some materials
  TGeoMaterial *matVacuum = new TGeoMaterial("Vacuum", 0, 0, 0);
  TGeoMaterial *matAl = new TGeoMaterial("Al", 26.98, 13, 2.7); // placeholder
  if(transp)
  {
    matVacuum->SetTransparency(85);
    matAl->SetTransparency(85);
  }

  //--- define some media
  TGeoMedium *Vacuum = new TGeoMedium("Vacuum", 1, matVacuum);
  TGeoMedium *Al = new TGeoMedium("Root Material", 2, matAl);
  vacuum_ = Vacuum;
  tkmed_ = Vacuum; // placeholder
  calomed_ = Al; // placeholder
  mudetmed_ = Al; // placeholder

  // custom parameters
  contingency_ = 10.;
  calo_barrel_thickness_ = 50.;
  calo_endcap_thickness_ = 75.;
  muonSystem_thickn_ = 10.;

  // read these parameters from the Delphes Card (with default values)
  etaAxis_ = NULL;
  phiAxis_ = NULL;
  tk_radius_ = 120.;
  tk_length_ = 150.;
  tk_etamax_ = 3.0;
  tk_Bz_ = 1.;
  muonSystem_radius_ = 200.;
}

void Delphes3DGeometry::readFile(const char *configFile,
  const char *ParticlePropagator, const char *TrackingEfficiency,
  const char *MuonEfficiency, const char *Calorimeters)
{

  ExRootConfReader *confReader = new ExRootConfReader;
  confReader->ReadFile(configFile);

  tk_radius_ = confReader->GetDouble(Form("%s::Radius", ParticlePropagator), 1.0) * 100.; // tk_radius
  tk_length_ = confReader->GetDouble(Form("%s::HalfLength", ParticlePropagator), 3.0) * 100.; // tk_length
  tk_Bz_ = confReader->GetDouble("ParticlePropagator::Bz", 0.0); // tk_Bz

  TString buffer;
  const char *it;

  {
    TString tkEffFormula = confReader->GetString(Form("%s::EfficiencyFormula", TrackingEfficiency), "abs(eta)<3.0");
    tkEffFormula.ReplaceAll("pt", "x");
    tkEffFormula.ReplaceAll("eta", "y");
    tkEffFormula.ReplaceAll("phi", "0.");

    buffer.Clear();
    for(it = tkEffFormula.Data(); *it; ++it)
    {
      if(*it == ' ' || *it == '\t' || *it == '\r' || *it == '\n' || *it == '\\') continue;
      buffer.Append(*it);
    }

    TF2 *tkEffFunction = new TF2("tkEff", buffer, 0, 1000, -10, 10);
    TH1F etaHisto("eta", "eta", 100, 5., -5.);
    Double_t pt, eta;
    for(int i = 0; i < 1000; ++i)
    {
      tkEffFunction->GetRandom2(pt, eta);
      etaHisto.Fill(eta);
    }
    Int_t bin = -1;
    bin = etaHisto.FindFirstBinAbove(0.5);
    Double_t etamin = (bin > -1) ? etaHisto.GetBinLowEdge(bin) : -10.;
    bin = etaHisto.FindLastBinAbove(0.5);
    Double_t etamax = (bin > -1) ? etaHisto.GetBinLowEdge(bin + 1) : -10.;
    tk_etamax_ = TMath::Max(fabs(etamin), fabs(etamax)); // tk_etamax
    delete tkEffFunction;
  }

  {
    muondets_.push_back("muons");
    TString muonEffFormula = confReader->GetString(Form("%s::EfficiencyFormula", MuonEfficiency), "abs(eta)<2.0");
    muonEffFormula.ReplaceAll("pt", "x");
    muonEffFormula.ReplaceAll("eta", "y");
    muonEffFormula.ReplaceAll("phi", "0.");

    buffer.Clear();
    for(it = muonEffFormula.Data(); *it; ++it)
    {
      if(*it == ' ' || *it == '\t' || *it == '\r' || *it == '\n' || *it == '\\') continue;
      buffer.Append(*it);
    }

    TF2 *muEffFunction = new TF2("muEff", buffer, 0, 1000, -10, 10);
    TH1F etaHisto("eta2", "eta2", 100, 5., -5.);
    Double_t pt, eta;
    for(int i = 0; i < 1000; ++i)
    {
      muEffFunction->GetRandom2(pt, eta);
      etaHisto.Fill(eta);
    }
    Int_t bin = -1;
    bin = etaHisto.FindFirstBinAbove(0.5);
    Double_t etamin = (bin > -1) ? etaHisto.GetBinLowEdge(bin) : -10.;
    bin = etaHisto.FindLastBinAbove(0.5);
    Double_t etamax = (bin > -1) ? etaHisto.GetBinLowEdge(bin + 1) : -10.;
    muonSystem_etamax_["muons"] = TMath::Max(fabs(etamin), fabs(etamax)); // muonSystem_etamax
    delete muEffFunction;
  }

  std::string s(Calorimeters);
  std::replace(s.begin(), s.end(), ',', ' ');
  std::istringstream stream(s);
  std::string word;
  while(stream >> word) calorimeters_.push_back(word);

  caloBinning_.clear(); // calo binning
  for(std::vector<std::string>::const_iterator calo = calorimeters_.begin(); calo != calorimeters_.end(); ++calo)
  {
    set<pair<Double_t, Int_t> > caloBinning;
    ExRootConfParam paramEtaBins, paramPhiBins;
    ExRootConfParam param = confReader->GetParam(Form("%s::EtaPhiBins", calo->c_str()));
    Int_t size = param.GetSize();
    for(int i = 0; i < size / 2; ++i)
    {
      paramEtaBins = param[i * 2];
      paramPhiBins = param[i * 2 + 1];
      assert(paramEtaBins.GetSize() == 1);
      caloBinning.insert(std::make_pair(paramEtaBins[0].GetDouble(), paramPhiBins.GetSize() - 1));
    }
    caloBinning_[*calo] = caloBinning;
  }

  set<pair<Double_t, Int_t> > caloBinning = caloBinning_[*calorimeters_.begin()];
  Double_t *etaBins = new Double_t[caloBinning.size()]; // note that this is the eta binning of the first calo
  unsigned int ii = 0;
  for(set<pair<Double_t, Int_t> >::const_iterator itEtaSet = caloBinning.begin(); itEtaSet != caloBinning.end(); ++itEtaSet)
  {
    etaBins[ii++] = itEtaSet->first;
  }
  etaAxis_ = new TAxis(caloBinning.size() - 1, etaBins);
  phiAxis_ = new TAxis(72, -TMath::Pi(), TMath::Pi()); // note that this is fixed while #phibins could vary, also with eta, which doesn't seem possible in ROOT

  muonSystem_radius_ = tk_radius_ + contingency_ + (contingency_ + calo_barrel_thickness_) * calorimeters_.size() + muonSystem_thickn_;
  muonSystem_length_ = tk_length_ + contingency_ + (contingency_ + calo_endcap_thickness_) * calorimeters_.size() + muonSystem_thickn_;

  delete confReader;
}

TGeoVolume *Delphes3DGeometry::getDetector(bool withTowers)
{
  // compute the envelope
  Double_t system_radius = tk_radius_ + calo_barrel_thickness_ + 3 * contingency_;
  Double_t system_length = tk_length_ + contingency_ + (contingency_ + calo_endcap_thickness_) * calorimeters_.size() + contingency_;
  // the detector volume
  TGeoVolume *top = geom_->MakeBox("Delphes3DGeometry", vacuum_, system_radius, system_radius, system_length);
  // build the detector
  std::pair<Double_t, Double_t> limits = addTracker(top);
  Double_t radius = limits.first;
  Double_t length = limits.second;
  for(std::vector<std::string>::const_iterator calo = calorimeters_.begin(); calo != calorimeters_.end(); ++calo)
  {
    limits = addCalorimeter(top, calo->c_str(), radius, length, caloBinning_[*calo]);
    if(withTowers)
    {
      addCaloTowers(top, calo->c_str(), radius, length, caloBinning_[*calo]);
    }
    radius = limits.first;
    length = limits.second;
  }
  for(std::vector<std::string>::const_iterator muon = muondets_.begin(); muon != muondets_.end(); ++muon)
  {
    limits = addMuonDets(top, muon->c_str(), radius, length);
    radius = limits.first;
    length = limits.second;
  }
  // return the result
  return top;
}

std::pair<Double_t, Double_t> Delphes3DGeometry::addTracker(TGeoVolume *top)
{
  // tracker: a cylinder with two cones substracted
  new TGeoCone("forwardTkAcceptance", (tk_length_ / 2. + 0.05), 0., tk_radius_, (tk_length_)*2. * exp(-tk_etamax_) / (1 - exp(-2. * tk_etamax_)), tk_radius_);
  TGeoTranslation *tr1 = new TGeoTranslation("tkacc1", 0., 0., tk_length_ / 2.);
  tr1->RegisterYourself();
  TGeoRotation *negz = new TGeoRotation("tknegz", 0, 180, 0);
  negz->RegisterYourself();
  TGeoCombiTrans *tr2 = new TGeoCombiTrans("tkacc2", 0., 0., -tk_length_ / 2., negz);
  tr2->RegisterYourself();
  TGeoCompositeShape *tracker_cs = new TGeoCompositeShape("tracker_cs", "forwardTkAcceptance:tkacc1+forwardTkAcceptance:tkacc2");
  TGeoVolume *tracker = new TGeoVolume("tracker", tracker_cs, tkmed_);
  tracker->SetLineColor(kYellow);
  top->AddNode(tracker, 1);
  return std::make_pair(tk_radius_, tk_length_);
}

std::pair<Double_t, Double_t> Delphes3DGeometry::addCalorimeter(TGeoVolume *top, const char *name,
  Double_t innerBarrelRadius, Double_t innerBarrelLength, set<pair<Double_t, Int_t> > &caloBinning)
{
  // parameters derived from the inputs
  Double_t calo_endcap_etamax = TMath::Max(fabs(caloBinning.begin()->first), fabs(caloBinning.rbegin()->first));
  Double_t calo_barrel_innerRadius = innerBarrelRadius + contingency_;
  Double_t calo_barrel_length = innerBarrelLength + calo_barrel_thickness_;
  Double_t calo_endcap_etamin = -log(innerBarrelRadius / (2 * innerBarrelLength));
  Double_t calo_endcap_innerRadius1 = innerBarrelLength * 2. * exp(-calo_endcap_etamax) / (1 - exp(-2. * calo_endcap_etamax));
  Double_t calo_endcap_innerRadius2 = (innerBarrelLength + calo_endcap_thickness_) * 2. * exp(-calo_endcap_etamax) / (1 - exp(-2. * calo_endcap_etamax));
  Double_t calo_endcap_outerRadius1 = innerBarrelRadius;
  Double_t calo_endcap_outerRadius2 = innerBarrelRadius + calo_barrel_thickness_;
  Double_t calo_endcap_coneThickness = TMath::Min(calo_barrel_thickness_ * (1 - exp(-2. * calo_endcap_etamin)) / (2. * exp(-calo_endcap_etamin)), calo_endcap_thickness_);
  Double_t calo_endcap_diskThickness = TMath::Max(0., calo_endcap_thickness_ - calo_endcap_coneThickness);

  // calorimeters: tube truncated in eta + cones
  new TGeoTube(Form("%s_barrel_cylinder", name), calo_barrel_innerRadius, calo_barrel_innerRadius + calo_barrel_thickness_, calo_barrel_length);
  new TGeoCone(Form("%s_endcap_cone", name), calo_endcap_coneThickness / 2., calo_endcap_innerRadius1, calo_endcap_outerRadius1, calo_endcap_innerRadius2, calo_endcap_outerRadius2);
  new TGeoTube(Form("%s_endcap_disk", name), calo_endcap_innerRadius2, tk_radius_ + calo_barrel_thickness_, calo_endcap_diskThickness / 2.);
  TGeoTranslation *tr1 = new TGeoTranslation(Form("%s_tr1", name), 0., 0., (calo_endcap_coneThickness + calo_endcap_diskThickness) / 2.);
  tr1->RegisterYourself();
  TGeoCompositeShape *calo_endcap_cs = new TGeoCompositeShape(Form("%s_endcap_cs", name), Form("%s_endcap_cone+%s_endcap_disk:%s_tr1", name, name, name));
  TGeoTranslation *trc1 = new TGeoTranslation(Form("%s_endcap1_position", name), 0., 0., innerBarrelLength + calo_endcap_coneThickness / 2.);
  trc1->RegisterYourself();
  TGeoRotation *negz = new TGeoRotation(Form("%s_negz", name), 0, 180, 0);
  TGeoCombiTrans *trc2 = new TGeoCombiTrans(Form("%s_endcap2_position", name), 0., 0., -(innerBarrelLength + calo_endcap_coneThickness / 2.), negz);
  trc2->RegisterYourself();
  TGeoTranslation *trc1c = new TGeoTranslation(Form("%s_endcap1_position_cont", name), 0., 0., innerBarrelLength + calo_endcap_coneThickness / 2. + contingency_);
  trc1c->RegisterYourself();
  TGeoCombiTrans *trc2c = new TGeoCombiTrans(Form("%s_endcap2_position_cont", name), 0., 0., -(innerBarrelLength + calo_endcap_coneThickness / 2.) - contingency_, negz);
  trc2c->RegisterYourself();
  TGeoVolume *calo_endcap = new TGeoVolume(Form("%s_endcap", name), calo_endcap_cs, calomed_);
  TGeoCompositeShape *calo_barrel_cs = new TGeoCompositeShape(Form("%s_barrel_cs", name),
    Form("%s_barrel_cylinder-%s_endcap_cs:%s_endcap1_position-%s_endcap_cs:%s_endcap2_position", name, name, name, name, name));
  TGeoVolume *calo_barrel = new TGeoVolume(Form("%s_barrel", name), calo_barrel_cs, calomed_);
  calo_endcap->SetLineColor(kViolet);
  calo_endcap->SetFillColor(kViolet);
  calo_barrel->SetLineColor(kRed);
  top->AddNode(calo_endcap, 1, trc1c);
  top->AddNode(calo_endcap, 2, trc2c);
  top->AddNode(calo_barrel, 1);
  return std::make_pair(calo_barrel_innerRadius + calo_barrel_thickness_, innerBarrelLength + calo_endcap_thickness_ + contingency_);
}

std::pair<Double_t, Double_t> Delphes3DGeometry::addMuonDets(TGeoVolume *top, const char *name, Double_t innerBarrelRadius, Double_t innerBarrelLength)
{
  // muon system: tube + disks
  Double_t muonSystem_radius = innerBarrelRadius + contingency_;
  Double_t muonSystem_length = innerBarrelLength + contingency_;
  Double_t muonSystem_rmin = muonSystem_length * 2. * exp(-muonSystem_etamax_[name]) / (1 - exp(-2. * muonSystem_etamax_[name]));
  TGeoVolume *muon_barrel = geom_->MakeTube(Form("%s_barrel", name), mudetmed_, muonSystem_radius, muonSystem_radius + muonSystem_thickn_, muonSystem_length);
  muon_barrel->SetLineColor(kBlue);
  top->AddNode(muon_barrel, 1);
  TGeoVolume *muon_endcap = geom_->MakeTube(Form("%s_endcap", name), mudetmed_, muonSystem_rmin, muonSystem_radius + muonSystem_thickn_, muonSystem_thickn_ / 2.);
  muon_endcap->SetLineColor(kBlue);
  TGeoTranslation *trm1 = new TGeoTranslation(Form("%sEndcap1_position", name), 0., 0., muonSystem_length);
  trm1->RegisterYourself();
  TGeoTranslation *trm2 = new TGeoTranslation(Form("%sEndcap2_position", name), 0., 0., -muonSystem_length);
  trm1->RegisterYourself();
  top->AddNode(muon_endcap, 1, trm1);
  top->AddNode(muon_endcap, 2, trm2);
  return std::make_pair(muonSystem_radius, muonSystem_length);
}

void Delphes3DGeometry::addCaloTowers(TGeoVolume *top, const char *name,
  Double_t innerBarrelRadius, Double_t innerBarrelLength, set<pair<Double_t, Int_t> > &caloBinning)
{

  TGeoVolume *calo_endcap = top->GetNode(Form("%s_endcap_1", name))->GetVolume();
  TGeoVolume *calo_barrel = top->GetNode(Form("%s_barrel_1", name))->GetVolume();
  Double_t calo_endcap_etamin = -log(innerBarrelRadius / (2 * innerBarrelLength));
  Double_t calo_endcap_coneThickness = TMath::Min(calo_barrel_thickness_ * (1 - exp(-2. * calo_endcap_etamin)) / (2. * exp(-calo_endcap_etamin)), calo_endcap_thickness_);

  // calo towers in the barrel
  Double_t vertices[16] = {0., 0., 0., 0., 0., 0., 0., 0.}; // summit of the pyramid
  Double_t R = tk_radius_ + contingency_ + (contingency_ + calo_barrel_thickness_) * calorimeters_.size(); // radius of the muons system = height of the pyramid
  Int_t nEtaBins = caloBinning.size();
  // this rotation is to make the tower point "up"
  TGeoRotation *initTowerRot = new TGeoRotation(Form("%s_initTowerRot", name), 0., 90., 0.);
  TGeoCombiTrans *initTower = new TGeoCombiTrans(Form("%s_initTower", name), 0., -R / 2., 0., initTowerRot);
  initTower->RegisterYourself();
  // eta bins... we build one pyramid per eta slice and then translate it nphi times.
  // phi bins represented by rotations around z
  Double_t *y = new Double_t[nEtaBins];
  Double_t *dx = new Double_t[nEtaBins];
  Int_t *nphi = new Int_t[nEtaBins];
  Int_t etaslice = 0;
  std::map<std::pair<int, int>, TGeoRotation *> phirotations;
  for(set<pair<Double_t, Int_t> >::const_iterator bin = caloBinning.begin(); bin != caloBinning.end(); ++bin)
  {
    if(abs(bin->first) > calo_endcap_etamin) continue; // only in the barrel
    nphi[etaslice] = bin->second;
    y[etaslice] = 0.5 * R * (1 - exp(-2 * bin->first)) / exp(-bin->first);
    Double_t phiRotationAngle = 360. / nphi[etaslice];
    dx[etaslice] = R * tan(TMath::Pi() * phiRotationAngle / 360.);
    for(int phislice = 0; phislice < nphi[etaslice]; ++phislice)
    {
      phirotations[make_pair(etaslice, phislice)] = new TGeoRotation(Form("%s_phi%d_%d", name, etaslice, phislice), phiRotationAngle * phislice, 0., 0.);
      phirotations[make_pair(etaslice, phislice)]->RegisterYourself();
    }
    ++etaslice;
  }
  nEtaBins = etaslice;
  for(int i = 0; i < nEtaBins - 1; ++i)
  { // loop on the eta slices
    vertices[8] = -dx[i];
    vertices[9] = y[i];
    vertices[10] = -dx[i];
    vertices[11] = y[i + 1];
    vertices[12] = dx[i];
    vertices[13] = y[i + 1];
    vertices[14] = dx[i];
    vertices[15] = y[i];
    new TGeoArb8(Form("%s_tower%d", name, i), R / 2., vertices); // tower in the proper eta slice, at phi=0
    // intersection between the tower and the calo_barrel
    TGeoCompositeShape *finaltower_cs = new TGeoCompositeShape(Form("%s_ftower%d_cs", name, i), Form("%s_tower%d:%s_initTower*%s_barrel_cs", name, i, name, name));
    TGeoVolume *finaltower = new TGeoVolume(Form("%s_ftower%d", name, i), finaltower_cs, calomed_);
    finaltower->SetLineColor(kRed);
    for(int j = 0; j < nphi[i]; ++j)
    { // loop on the phi slices
      calo_barrel->AddNode(finaltower, j, phirotations[make_pair(i, j)]);
    }
  }
  delete[] y;
  delete[] dx;
  delete[] nphi;
  //the towers in the forward region
  R = tk_length_ + contingency_ + (contingency_ + calo_endcap_thickness_) * calorimeters_.size(); // Z of the muons system = height of the pyramid
  nEtaBins = caloBinning.size();
  // translation to bring the origin of the tower to (0,0,0) (well, not really as the endcap is not yet in place)
  TGeoTranslation *towerdz = new TGeoTranslation(Form("%s_towerdz", name), 0., 0., R / 2. - (innerBarrelLength + calo_endcap_coneThickness / 2.));
  towerdz->RegisterYourself();
  // eta bins... we build one pyramid per eta slice and then translate it nphi times.
  Double_t *r = new Double_t[nEtaBins];
  nphi = new Int_t[nEtaBins];
  etaslice = 0;
  phirotations.clear();
  for(set<pair<Double_t, Int_t> >::const_iterator bin = caloBinning.begin(); bin != caloBinning.end(); ++bin)
  {
    if(bin->first < calo_endcap_etamin) continue; // only in the + endcap
    r[etaslice] = R * 2 * exp(-bin->first) / (1 - exp(-2 * bin->first));
    nphi[etaslice] = bin->second;
    Double_t phiRotationAngle = 360. / nphi[etaslice];
    for(int phislice = 0; phislice < nphi[etaslice]; ++phislice)
    {
      phirotations[make_pair(etaslice, phislice)] = new TGeoRotation(Form("%s_forward_phi%d_%d", name, etaslice, phislice), phiRotationAngle * phislice, 0., 0.);
      phirotations[make_pair(etaslice, phislice)]->RegisterYourself();
    }
    ++etaslice;
  }
  nEtaBins = etaslice;
  for(int i = 0; i < nEtaBins - 1; ++i)
  { // loop on the eta slices
    vertices[8] = -r[i + 1] * sin(TMath::Pi() / nphi[i]);
    vertices[9] = r[i + 1] * cos(TMath::Pi() / nphi[i]);
    vertices[10] = -r[i] * sin(TMath::Pi() / nphi[i]);
    vertices[11] = r[i] * cos(TMath::Pi() / nphi[i]);
    vertices[12] = r[i] * sin(TMath::Pi() / nphi[i]);
    vertices[13] = r[i] * cos(TMath::Pi() / nphi[i]);
    vertices[14] = r[i + 1] * sin(TMath::Pi() / nphi[i]);
    vertices[15] = r[i + 1] * cos(TMath::Pi() / nphi[i]);
    new TGeoArb8(Form("%sfwdtower%d", name, i), R / 2., vertices); // tower in the proper eta slice, at phi=0
    // intersection between the tower and the calo_endcap
    TGeoCompositeShape *finalfwdtower_cs = new TGeoCompositeShape(Form("%sffwdtower%d_cs", name, i), Form("%sfwdtower%d:%s_towerdz*%s_endcap_cs", name, i, name, name));
    TGeoVolume *finalfwdtower = new TGeoVolume(Form("%sffwdtower%d", name, i), finalfwdtower_cs, calomed_);
    finalfwdtower->SetLineColor(kViolet);
    for(int j = 0; j < nphi[i]; ++j)
    { // loop on the phi slices
      calo_endcap->AddNode(finalfwdtower, j, phirotations[make_pair(i, j)]);
    }
  }
  delete[] r;
  delete[] nphi;
}