A clustering algorithm for a generalised calorimeter

1
A clustering algorithm for a generalised
calorimeter

• Chris Ainsley
• University of Cambridge
• ltainsley_at_hep.phy.cam.ac.ukgt

LC Simulation Workshop 9-10 December 2004, DESY,
Germany
2
Order of service

• Layer-by-layer approach to clustering.
• Separation of nearby charged/neutral clusters.
• Application to a generalised calorimeter.
• Clustering a Z event in the full CALICE
  calorimeter.
• Coding in the LCIO framework.
• Summary.

3
Layer-by-layer clustering the algorithm

• Form clusters by tracking closely-related hits
  (gt 1/3 mip) layer-by-layer through
  calorimeter
• for a given hit j in a given layer l, minimize
  the distance d w.r.t all hits k in layer l-1
• if d lt dist_max_ecal (Ecal) or dist_max_hcal
  (Hcal) for minimum d, assign hit j to same
  cluster as hit k which yields minimum
• if not, repeat with all hits in layer l-2, then,
  if necessary, layer l-3, etc., right through to
  first layer of Ecal
• after iterating over all hits j, seed new
  clusters with those still unassigned, grouping
  those within prox_seed_max into same seed
• if in Ecal, calculate weighted centre of each
  clusters hits in layer l (weight by energy
  (analogue) or density (digital)) and assign a
  direction cosine to each hit along the line
  joining its clusters centre in the seed layer
  (or (0,0,0) if its a seed) to its clusters
  centre in layer l
• if in Hcal, assign a direction cosine to each hit
  along the line from the hit to which each is
  linked (or (0,0,0) if its a seed) to the hit
  itself
• try to recover backward-spiralling track-like,
  and low multiplicity halo, cluster fragments
  

4
5 GeV ?? event at 3 cm separation
Reconstructed clusters
True particle clusters

• Cell-size 11 cm2 (Si/W Ecal RPC Hcal).
• dist_max_ecal 2.0 cm dist_max_hcal 3.0
  cm.
• 98 of event energy maps black ? black (?)
  and red ? red (?) .

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Same event, different clustering cuts
Reconstructed clusters
True particle clusters

• dist_max_ecal 3.0 cm dist_max_hcal 1.0
  cm.
• Now 78 of event energy maps black ? red (?)
  and red ? black (?) .
• 22 confusion.

6
Layer-by-layer clustering in a generalised
detector

• Approach requires layer index to vary smoothly
  e.g. in TESLA detector, index changes abruptly
• at stave boundaries in Ecal barrel (layers
  overlap at 45)
• at barrel/endcap boundaries in Ecal Hcal
  (layers overlap at 90).
• To apply layer-by-layer clustering, need a scheme
  to overcome this.
• Achieved by replacing layer index with
  pseudolayer index in regions where layer index
  discontinuities occur.
• Same-pseudolayer indexed hits defined by closed
  shells of octagonal prisms coaxial with z-axis.
• Simple extension to cope with any arbitrary
  n-fold rotationally-symmetric, layered
  calorimeter octagonal prisms ? n-polygonal
  prisms.
• Locations/orientations of shells automatically
  set by locations/orientations of real, physical,
  sensitive layers.
• Just takes n and layer-spacings in barrel and
  endcaps as input.

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How the generalised detector shapes up
Transverse section
Longitudinal section

• Solid blue lines aligned along real, physical,
  sensitive layers.
• Dot-dashed magenta lines bound shell
  containing hits with same pseudolayer index, l.
• Pseudostaves automatically encoded by
  specifying n, f1 and Rl and Zl (? l).

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91 GeV Z ? u,d,s jets event
Reconstructed clusters
True particle clusters

• Reconstruction in full detector (Si/W Ecal
  RPC Hcal).
• dist_max_ecal 2.0 cm dist_max_hcal 3.0
  cm.
• Good 11 correspondence between reconstructed
  and true clusters (5 highest energy clusters
  shown).

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Clustering in LCIO a modular approach

• Modules to do the reconstruction
• CalorimeterConfig.cc
• ? (re)defines calorimeter layer positions
• HitToCell.cc
• ? merges same-cell hits
• CellToStore.cc
• ? stores cells above energy threshold
• StoreCalibration.cc
• ? calibrates the stored cell energies
• StoreToStoreOrdered.cc
• ? ranks stored cells by weight in each
  pseudolayer (in preparation for clustering)
• StoreOrderedToCluster1.cc
• ? does the coarse cluster reconstruction
• Cluster1ToCluster2.cc
• ? attempts matching of backward-spiralling
  track-like cluster fragments onto
  forward-propagating parent clusters
• Cluster2ToCluster3.cc
• ? attempts to reunite low multiplicity halo
  cluster fragments with parent clusters.

• Additional module to access MC truth
• StoreOrderedToMCParticle.cc
• ? forms the true clusters.
• Plotting modules
• ClusterToClusterOrdered.cc
• ? ranks reconstructed clusters by energy in
  each pseudostave (in preparation for plotting)
• PlotRecoClusters.cc
• ? plots reconstructed clusters
  colour-correlated with energy-rank in
  pseudostave
• MCParticleToMCParticleOrdered.cc
• ? ranks true clusters by energy in each
  pseudostave (in preparation for plotting)
• PlotTrueClusters.cc
• ? plots true clusters colour-correlated with
  energy-rank in pseudostave
• PlotPerformance.cc
• ? plots the distribution of energy between true
  and reconstructed clusters.

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Modifying the detector

• Given detector configuration, clustering governed
  by global constants set in header file
  LCIOFrameSteer.h ? tweaks go in here.
• Layer positions fed in through CalorimeterConfig.c
  c.
• To apply algorithm to new detector designs, just
  need to modify these two files.
• Lets see how

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Snippets of code from LCIOFrameSteer.h

• Set the detector parameters
• const int nlayers_ecal 40
• // number of Ecal (pseudo)layers
• const int nlayers_hcal 40
• // number of Hcal (pseudo)layers
• const int npseudostaves_barrel 8
• // degree of rotational symmetry of barrel
• const double phi_1 M_PI/2.
• // azimuthal angle of first barrel (pseudo)stave
• Set the Ecal type
• const string ecal siw
• // siw gt Si/W Ecal
• // maps gt MAPS Ecal
• Set the Hcal type
• const string hcal rpc
• // rpc gt Fe/RPC Hcal
• // scint gt Fe/scintillator Hcal
• Set the mode of operation
• const string mode a/d

• Set the clustering cuts
• const double dist_max_ecal 20.0 // mm
• // maximum d for cluster continuity across
  Ecal
• // layers
• const double dist_max_hcal 30.0 // mm
• // maximum d for cluster continuity across
  Hcal
• // layers
• const double prox_seed_max 20.0 // mm
• // maximum radius of new cluster seed
• const double prox_merge_max 20.0 // mm
• // maximum proximity for backward-spiralling
  track-
• // matching
• const double cos_gamma_max 0.25
• // minimum angle between direction cosines for
• // backward-spiralling track-matching
• const int cluster_size_min 10
• // maximum cluster size to be considered halo
• const double tan_beta_max 6.0
• // maximum angle for halo recovery

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Snippets of code from CalorimeterConfig.cc

• Set the layer positions in the r- and
  z-directions
• (e.g. TESLA TDR design)
• // Create collections for the r and z layers
• LCCollectionVec siteOfRLayerVec new
• LCCollectionVec(LCIOLCFLOATVEC)
• LCCollectionVec siteOfZLayerVec new
• LCCollectionVec(LCIOLCFLOATVEC)
• // Fill the collections with their positions
• for (int l0 llt1nlayers_ecalnlayers_hcal
  l)
• LCFloatVec siteOfRLayer new LCFloatVec
• LCFloatVec siteOfZLayer new LCFloatVec
• if (llt30) // layers 1-30 (Ecal) layer 0
• siteOfRLayer-gtpush_back(1698.85(3.9
  l))
• siteOfZLayer-gtpush_back(2831.10(3.9
  l))
• else if (l gt30 lltnlayers_ecal) //
  31-40 (Ecal)
• siteOfRLayer-gtpush_back(1815.85(6.7 (l
  -30)))

• else // layers 41-80 (Hcal) layer 81
• siteOfRLayer-gtpush_back(1931.25(24.5 (l
  -41)))
• siteOfZLayer-gtpush_back(3039.25(24.5 (l
  -41)))
• siteOfRLayerVec-gtpush_back(siteOfRLayer)
• siteOfZLayerVec-gtpush_back(siteOfZLayer)
• // And save the collections
• evt-gtaddCollection(siteOfRLayerVec,"site_rlayers"
  )
• evt-gtaddCollection(siteOfZLayerVec,
  "site_zlayers")

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Summary outlook

• RD on clustering algorithm for generalised
  calorimeter on-going.
• Approach utilizes the high granularity of the
  calorimeter cells to track clusters
  (pseudo)layer-by-(pseudo)layer.
• Pseudolayer concept ? flexibility to cope with
  alternative layered geometries without having to
  recode algorithm itself.
• Applicable to any (likely) detector design
  comprising an n-fold rotationally symmetric
  barrel closed by endcaps ? just to specify need n
  and layer-spacings.
• Written in C LCIO (v1.3) compliant
  modularised ? input parameters kept distinct from
  reconstruction.
• Will aim to make code publicly available soon.

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The end

• Thats all folks

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Cluster-tracking between pseudolayers
From the pseudobarrel
From the pseudoendcap