Fast Hough Transform Method Cvetan Cheshkov 11032004 ALICE

  • Slides: 24
Download presentation
Fast Hough Transform Method Cvetan Cheshkov 11/03/2004 ALICE offline week 1

Fast Hough Transform Method Cvetan Cheshkov 11/03/2004 ALICE offline week 1

Contents n n n Introduction Fast Hough Transform method Demo Results on timing, efficiency

Contents n n n Introduction Fast Hough Transform method Demo Results on timing, efficiency and resolution Concluding remarks and future plans 11/03/2004 ALICE offline week 2

HLT (high multiplicity case) Hough Transform TPC digits Local Peak finder Find, deconvolute and

HLT (high multiplicity case) Hough Transform TPC digits Local Peak finder Find, deconvolute and associate clusters Track fit n Hough Transform takes 1000 -2300 s in linear mode (dn/dy 3500; PIII 800 MHz) 11/03/2004 ALICE offline week 3

Hough Transform (HT) n n Each TPC digit is transformed into a curve in

Hough Transform (HT) n n Each TPC digit is transformed into a curve in the Hough parameter space corresponding to all possible tracks to which the digit could be associated: (x, y) (k=1/R, ) k – track curvature; - track emission angle The Hough approach: n n Assumes that the tracks are coming from (or close to) the primary vertex Neglects any energy losses and multiply scattering in the detector volume 11/03/2004 ALICE offline week 4

HLT implementation of HT n n n TPC data input is splitted in sectors,

HLT implementation of HT n n n TPC data input is splitted in sectors, r/o patches and slices (50 -100) Hough transform is performed on each of these slices separately (in parallel) The HT parameter space is binned and stored in histograms The histograms are summed over the patches Local peaks are identified by a peak finder and transmitted as track seeds to the cluster finder 11/03/2004 ALICE offline week 5

Improving HT n n Originally HT was done filling the digits charge Large amount

Improving HT n n Originally HT was done filling the digits charge Large amount of fakes in a high occupancy case Sophisticated peak finder Studying the HT performance it turned out that the performance can be improved by counting: digits charge #digits #clusters (TPC rows) 11/03/2004 ALICE offline week 6

“Counting Rows & Gaps” HT n n Naturally the studies lead to the idea

“Counting Rows & Gaps” HT n n Naturally the studies lead to the idea to count consecutive TPC rows Idea: Good track candidate must have not only some amount of digit’s charge, digits or rows along its trajectory, but also must occupy consecutive TPC rows Now the algorithm counts as #gaps between occupied rows Weight used to fill HT space: n n #rows/#gaps #rows (#gaps<N) 11/03/2004 ALICE offline week 7

Example Slice of 1 TPC sector n Corresponding HT space Central HIJING dn/dy=3500, 0.

Example Slice of 1 TPC sector n Corresponding HT space Central HIJING dn/dy=3500, 0. 2 T 11/03/2004 ALICE offline week 8

New Peak Finder (PF) n n n The improvement in the HT quality simpler

New Peak Finder (PF) n n n The improvement in the HT quality simpler PF The new PF looks for neighbor bins with the same weight Track parameters are extracted by averaging the peak edge points both in and 1/R (track curvature) directions track is guided by the cluster borders 11/03/2004 ALICE offline week 9

Comparison Standard HT New HT • New Hough seeds much more clear • It

Comparison Standard HT New HT • New Hough seeds much more clear • It seems that now the cluster fitter is the limiting factor (it is also the slowest part) 11/03/2004 ALICE offline week 10

Fast Hough Transform n n n Assuming ordered TPC digits (in time bins, padrows)

Fast Hough Transform n n n Assuming ordered TPC digits (in time bins, padrows) new algorithm offers big space for speeding up HT is monotonic along the padrows do it only for the first and last (in paw index direction) digits which belong to a cluster and fill a the corresponding ribbon in the HT space Stopping rules using already accumulated #gaps 11/03/2004 ALICE offline week 11

Fast Hough Transform n n By introducing the new HT and substituting sin and

Fast Hough Transform n n By introducing the new HT and substituting sin and cos by LUTs a factor of 10 in the speed 2300 s 230 s Which are the sources: LUTs - factor of 2 n HT algorithm – factor of 5 n n Additional factor of 2 Code improvement n #gaps stopping rule n Filter on the data (consistent with HT algorithm) n 11/03/2004 ALICE offline week 12

Demo! n n n Demo with central HIJING event (dn/dy=3500) on one of the

Demo! n n n Demo with central HIJING event (dn/dy=3500) on one of the GDCs (oplapro machines) used in the Computing DC The event is stored as DATE formatted file and is processed by a stand-alone exe (see Thomas’ talk) Oplapro – Itanium II; 1. 5 GHz; 4 Mb L 3 cache 11/03/2004 ALICE offline week 13

Timings dn/dy=2000 dn/dy=4000 dn/dy=8000 0. 4 T 0. 5 T 14 s 23 s

Timings dn/dy=2000 dn/dy=4000 dn/dy=8000 0. 4 T 0. 5 T 14 s 23 s 39 s 38 s 64 s/patch 106 s/patch 179 s/patch 177 s/patch dn/dy=4000 dn/dy=8000 0. 2 T 23 s 38 s 108 s/patch 178 s/patch 11/03/2004 HT space size: (75 in )x(140 in 1/R)x(100 in ) Time consumption is: • strictly proportional to the HT space size • roughly proportional to the event multiplicity ALICE offline week 14

Performance n n Try to run Hough stand-alone (without a consecutive cluster fitter and

Performance n n Try to run Hough stand-alone (without a consecutive cluster fitter and etc) The method requires new definitions in order to determine the performance: n n No clusters associated assign only 1 MC label to each track High occupancy (and therefore overlapping clusters) in general does not affect the track parameters, but cause appearance of “ghosts” fakes tracks ghost tracks If more than 1 track with the same MC label, take randomly one as good and second as ghost Good tracks – primaries from offline comparison 11/03/2004 ALICE offline week 15

Performance /Efficiencies/ Parameterized HIJING dn/dy=8000 B=0. 2 T 11/03/2004 B=0. 4 T ALICE offline

Performance /Efficiencies/ Parameterized HIJING dn/dy=8000 B=0. 2 T 11/03/2004 B=0. 4 T ALICE offline week B=0. 5 T 16

Performance /Efficiencies/ dn/dy=4000 B=0. 2 T 11/03/2004 dn/dy=2000 B=0. 4 T ALICE offline week

Performance /Efficiencies/ dn/dy=4000 B=0. 2 T 11/03/2004 dn/dy=2000 B=0. 4 T ALICE offline week B=0. 4 T 17

Performance /Efficiency/ n Summary: The efficiency is almost unaffected by the event multiplicity!! n

Performance /Efficiency/ n Summary: The efficiency is almost unaffected by the event multiplicity!! n About ½ of the ghosts are coming from the high occupancy n 11/03/2004 ALICE offline week 18

Performance /Resolution/ Parameterized HIJING dn/dy=4000, 0. 4 T Pt/Pt(%)=0. 7+2. 7 x. Pt =6.

Performance /Resolution/ Parameterized HIJING dn/dy=4000, 0. 4 T Pt/Pt(%)=0. 7+2. 7 x. Pt =6. 3 x 10 -3 11/03/2004 =7. 2 mrad ALICE offline week 19

Performance /Resolution/ n Summary: The relative Pt resolution rises linearly with Pt consistent with

Performance /Resolution/ n Summary: The relative Pt resolution rises linearly with Pt consistent with the expectations from HT binning! n It is almost proportional to 1/B n The resolution on eta, psi and Pt (high Pt tracks) increase by <10% when dn/dy goes from 2000 to 8000 (the effect is due mostly to ghosts) n At low Pt one can see clearly the effect of ghosts n 11/03/2004 ALICE offline week 20

Known problems n The Peak Finder has certain problems with the cut on the

Known problems n The Peak Finder has certain problems with the cut on the peaks size The main source of inefficiencies We need cut which depends on the position inside Hough space n Special treatment of tracks crossing 2 sectors They give significant contribution to the #ghosts Need in a proper global (between eta slices and sectors) track merger! 11/03/2004 ALICE offline week 21

Concluding remarks n n n The new Hough method shows reasonable performance and is

Concluding remarks n n n The new Hough method shows reasonable performance and is much faster! Needs some further optimization and evaluation The answer about its applicability can be given only by trying some real physics trigger algorithms (hopefully using PDC’ 04 data) 11/03/2004 ALICE offline week 22

Concluding remarks n Impact on physics cases: n Jet finder n n n The

Concluding remarks n Impact on physics cases: n Jet finder n n n The efficiency for Pt above 2 -2. 5 Ge. V is high The ghosts almost disappear at 2. 5 Ge. V The eta and psi resolutions are pretty good for any cone jet-finder sizes (0. 1, 0. 2, …) The Pt resolution for high Pt tracks does not explode Open charm track filter n n 11/03/2004 The efficiency between 0. 5 and 1 Ge. V looks reasonable The ghosts in principle do not hurt too much because they are close to the good tracks ALICE offline week 23

Future plans n n n Next week everything to CVS Work on Peak Finder

Future plans n n n Next week everything to CVS Work on Peak Finder and investigation of inefficiencies and ghosts Preparation of physics trigger algorithms and their evaluation As soon as Computing DC is restarted try the whole machinery in online mode Closer integration with Ali. Root 11/03/2004 ALICE offline week 24