1. A clustering algorithm for a generalised calorimeter
Chris Ainsley
University of Cambridge
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.
Chris Ainsley
LC Simulation Workshop
9-10 December 2004, DESY, Germany

3. Layer-by-layer clustering: the algorithm
Form clusters by tracking closely-related hits (> 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 < 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 cluster’s hits in layer l (weight by energy (analogue) or density (digital)) and assign a direction cosine to each hit along the line joining its cluster’s centre in the seed layer (or (0,0,0) if it’s a seed) to its cluster’s 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 it’s a seed) to the hit itself;
try to recover backward-spiralling track-like, and low multiplicity ‘halo’, cluster fragments …
Chris Ainsley
LC Simulation Workshop
9-10 December 2004, DESY, Germany

4. 5 GeV + event at 3 cm separation
Reconstructed clusters
True particle clusters
Cell-size = 1×1 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 () .
Chris Ainsley
LC Simulation Workshop
9-10 December 2004, DESY, Germany

5. 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”.
Chris Ainsley
LC Simulation Workshop
9-10 December 2004, DESY, Germany

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.
Chris Ainsley
LC Simulation Workshop
9-10 December 2004, DESY, Germany

7. 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).
Chris Ainsley
LC Simulation Workshop
9-10 December 2004, DESY, Germany

8. Reconstructed clusters True particle clusters
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 1:1 correspondence between reconstructed and true clusters (5 highest energy clusters shown).
Chris Ainsley
LC Simulation Workshop
9-10 December 2004, DESY, Germany

9. 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.
Chris Ainsley
LC Simulation Workshop
9-10 December 2004, DESY, Germany

10. 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.cc.
To apply algorithm to new detector designs, just need to modify these two files.
Let’s see how …
Chris Ainsley
LC Simulation Workshop
9-10 December 2004, DESY, Germany

11. 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” => Si/W Ecal
// “maps” => MAPS Ecal
Set the Hcal type:
const string hcal = “rpc”;
// “rpc” => Fe/RPC Hcal
// “scint” => Fe/scintillator Hcal
Set the mode of operation:
const string mode = “a/d”;
// “a/a” => analogue Ecal / analogue Hcal
// “a/d” => analogue Ecal / digital Hcal
// “d/a” => digital Ecal / analogue Hcal
// “d/d” => digital Ecal / digital Hcal
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
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
Chris Ainsley
LC Simulation Workshop
9-10 December 2004, DESY, Germany

12. 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(LCIO::LCFLOATVEC);
LCCollectionVec* siteOfZLayerVec = new
// Fill the collections with their positions
for (int l=0; l<=1+nlayers_ecal+nlayers_hcal; l++) {
LCFloatVec* siteOfRLayer = new LCFloatVec;
LCFloatVec* siteOfZLayer = new LCFloatVec;
if (l<=30) { // layers 1-30 (Ecal) + layer 0
siteOfRLayer->push_back( (3.9* l));
siteOfZLayer->push_back( (3.9* l)); }
else if (l >30 && l<=nlayers_ecal) { // (Ecal)
siteOfRLayer->push_back( (6.7* (l -30)));
siteOfZLayer->push_back( (6.7* (l -30)));
else { // layers (Hcal) + layer 81
siteOfRLayer->push_back( (24.5* (l -41)));
siteOfZLayer->push_back( (24.5* (l -41))); }
siteOfRLayerVec->push_back(siteOfRLayer);
siteOfZLayerVec->push_back(siteOfZLayer);
// And save the collections
evt->addCollection(siteOfRLayerVec,"site_rlayers");
evt->addCollection(siteOfZLayerVec, "site_zlayers");
Chris Ainsley
LC Simulation Workshop
9-10 December 2004, DESY, Germany

13. Summary & outlook
R&D 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.
Chris Ainsley
LC Simulation Workshop
9-10 December 2004, DESY, Germany

14. That’s all folks… The end Chris Ainsley
LC Simulation Workshop
9-10 December 2004, DESY, Germany

15. Cluster-tracking between pseudolayers
From the pseudobarrel
From the pseudoendcap
Chris Ainsley
LC Simulation Workshop
9-10 December 2004, DESY, Germany