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 2 Track Alignment

 2 Track Alignment. Oxford Alignment Group Meeting Oxford 18/05/05. Pawel Br ü ckman de Renstrom M ü ge Karag ö z- Ü nel. The plan. ATLAS CHALLENGE: Set the scene. THE  2 FORMALISM : The goal Elementary formalism The Full Solution A bit of History and Outlook.

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 2 Track Alignment

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  1. 2Track Alignment Oxford Alignment Group Meeting Oxford 18/05/05 Pawel Brückman de RenstromMüge Karagöz-Ünel The plan ATLAS CHALLENGE: Set the scene THE 2 FORMALISM: The goal Elementary formalism The Full Solution A bit of History and Outlook CONSTRAINTS: FSI induced constraints -discussion

  2. Offline Track Alignment of PIX+SCT 3 translations & 3 rotations of each module In total we have to deal with 34,992 DoF’s!

  3. B3: 54 modules mounted The hardware is really under construction now WE NEED TO GET READY BEFORE TURNING ON! Disk 8C at Liverpool

  4. Track Alignment – the idea The task is to determine actual positions (and orientations) of all detector elements exploring hit information from real tracks. In the known magnetic field tracks follow well defined trajectories (locally a helix). Asking for the best fit to the observed hits in the detector elements one can optimize geometry of the latter.

  5. track Intrinsic measurement error + MCS hit residual Key relation! The formalism written up in:ATL-COM-INDET-2005-004 The “brute force” approach consists of minimizing the giant 2resulting from a simultaneous fit of all particle trajectories and alignment parameters: Let us consequently use the linear expansion (we assume all second order derivatives are negligible). The track fit is solved by: while the alignment parameters are given by:

  6. Example “lowest modes” in PIX+SCT as reconstructed by the 2algorithm Global Freedom has been removed (only one Z slice shown) • + generic, powerful, optimal to address all DoF’s, • + fully explores the available information, • + Any arbitrary constraint can be easily implemented (see later), • - inherent numerical difficulties: exec. time & precision, • requires large computing resources: • Execution time grows asN3 !

  7. Common vertex and External Constraints • The solution is generally ill-defined due to multiple weak modes (eigenvalues span over ~eight orders of magnitude) • Some of them can be controlled by imposing a common vertex (origin) of tracks from the same event. • Others remain weak. One could either explicitly drop them in the solution – very risky! • Alternatively, we may use external constraints and incorporate them into the general solution. • FSI is a perfect candidate! • There are others: • Beam spot constraint on the vertex position, • Constraints on track parameters from other tracking detectors, • Mass constraints of known resonances, • E/p constraint from calorimeters, • Constraints on the geometry deformations coming from known mechanical properties, • etc.

  8. V.Blobel’s Millepede Aposteriori we realised that our baseline formalism is equivalent to the one of Blobel. He arrives at the same final formula using purely algebraic means:  VERY reassuring! Still, I don’t know how to extend Blobel’s formalism to VTX, constraints, etc. V.Blobel, C.Kleinwort, “A new method for the high-precision alignment of track detectors” Proceedings of the Conference on: Advanced Statistical Techniques in Particle Physics University of Durham, UK March 18th-22nd, 2002 http://www.ippp.dur.ac.uk/Workshops/02/statistics/proceedings.shtml

  9. FSI constraint FSI constraint The Complete 2Formalism Coded in the prototype

  10. A bit of history • The activity started in 2000. • Assumptions and prejudices: • Use simplest linear expansion, • Relay as much as possible on information from the reconstruction, • Second order derivatives MUST be neglected. • First demonstration of the method was done using a self-contained program generating detector geometry and simulating tracks. MCS was properly implemented. B-field was set to zero. • Next stage: the fully functional (still stand-alone) program to process tracks simulated by GEANT and reconstructed by the official ATLAS software (initially iPatRec now ATHENA). This program is referred to as “the prototype” and is still in use. • Early this year the code migration into ATHENA was started. By now the basic functionalities have been implemented but yet not tested. • Study of the numerical issues associated with solving the system pioneered by the Marseille group (2002). Recently we have started exploration of the 64-bit PC cluster at RAL as recommended by the Marseille people.

  11. Marseille Team Parallelizing the prototype and precision issues • Earlier, Marseille team showed that current computing power will be a limiting factor in the storage of the alignment matrix and the precision of the alignment corrections. • Suggested resort was to use 64-bit architectures (double=128b) and parallel architecture. • 35k DoF (full PIX+SCT has a size of 9GB) and precision is washed out around 16k on with 64b floating point) • Currently, we have been testing matrix manipulations on a 64-bit Beowulf cluster@RAL. • Lessons we have learned so far: • we can improve marginally over earlier tests (cputime and accuracy), w/o making use of 128b prec (e.g. log(WALL time)=2.3log(N)+C) • PGI does not, but GNU supports 128-bit. • However, ScaLapack (parallel-proc. Lapack, matrix/algebra library) has not been tried earlier for 128b and will require some further work to fully confirm the predicted accuracy by Marseille team. More info: http://www-pnp.physics.ox.ac.uk/~karagozm/Oxford/scarf/

  12. Outlook • Full verification of the implementation still needs to be done. • ATHENA based package needs a lot of coding and debugging. • The performance of the Beowulf cluster has to be further investigated – work in progress. • Various strategies of alignment must be studied and assessed. • Short term: • We need to be able to apply our code to the ID cosmic run next winter, • DC3 will involve the full re-alignment exercise. • FSI constraints (and possibly some other – purely mechanical?) need to be understood and put in place. In particular we need to know how to use the “initial geometry”. • Reminder: The free-flying detector is nearly impossible to constrain! • There is more and more people getting interested in the alignment. We should not be short of manpower. • Close coordination with the development on the FSI end seems to be vital.

  13. Frequency Scanning Interferometry 842 simultaneous length measurements in SCT! • Single FSI Grid Line Interferometer has a precision below 1m! • Entire Grid shape can be determined to better than 10m in 3D. • FSI is beautifully complementing the offline track alignment wherever the latter is not sufficiently sensitive – lowest modes of global distortions! • It also provides quasi real-time response to time dependent deformations.

  14. FSI-like constraints ‘s need to be orthonormal but can act on any subspace of N

  15. FSI-like constraints (naïve example) • Let us simplify the implementation. • Consider constraints on distances between chosen modules. XY projection of the Barrel FSI grid lines

  16. FSI-like constraints general comments • Despite the level of complexity we may or may not use FSI to do the quasi real time corrections. • If we do, the track alignment should set the amplitudes Akto zero in order to extract consecutive sets of alignment corrections. • Choice of the Fkfunctions is arbitrary as long as they are orthogonal and normalised. (In the most general case think of double-Fourier series on the surface of a cylinder.)

  17. Summary • We have developed a direct Least-Squares approach to solve the alignment problem of big systems. • It is generic and powerful allowing for variety of extensions and constraints. • Still, numerical challenge is of an issue. • The software is evolving but still needs a lot of debugging. • The formalism to incorporate FSI constraints has been established. • Yet the exact implementation and interfaces have to be defined.

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