stivmc

STAR

StiVmc

V. PerevoztchikovBrookhaven National Laboratory,USA

STAR Victor Perevoztchikov, BNL StarSoft local

StiTGeo helper

StiVmc is based on TGeo representation of geometry. But there is no direct dependency between them. All the communication goes thru StiTGeo helper class. This class contains:

•Simple array of pointers to StVoluInfo objects. TGeoVolume::GetNumber() used as an index. These objects keep specific Sti information, related to each volume.

•Contains global StiHit container, only for hits used in SeedFinder.

•Map container of StHitPlane(s) with HardwarePosition of StHit as a key


For each TGeoVolume could be related one StVoluInfo object which contains:

• Some flags, like:• It is a module, like TPCE,SVTT;• It is a Module with Hits; • Active module;• It is a HitPlane

:

StVoluInfo class


StHitPlaneInfo inherited from StVoluInfo class and used instead of it for sensitive volumes :

• Center of Hit plane in mother system;

• Direction of Hit plane in mother system;

• Hit container, simultaneously sorted by two variables, like Phi/Z Phi/Rxy etc…;

• Pointer to functor, which provides activity of sensitive sub volume.

• Map container of StHitPlane objects. These ones related to each TGeoVolume instantiation. It is sorted by TGeo path of founded object.

:

StHitPlaneInfo class


This class represents concrete sensitive detector. It’s functionality close to StiDetector. Contains:

• Center of Hit plane in global system;

• Direction of Hit plane in global system;

• Hit container, simultaneously sorted by two variables, like Phi/Z Phi/Rxy etc…;

• Pointer to functor, which provides activity of sensitive sub volume.

• Container of StHitPlane and StHitTube classes. These classes

:

StiHitPlane class


Loading of hits is made maximally independent of hit nature and origin. To add into StiVmc new detector there is no need to modify even one line of code. No more StiSsd, StiSvt, StiTpc, StiRnD and StiXXX classes.

StiHitLoader does the following:

Iterate via StEventHitIter iterator; Adds it to StTGeoHelper object; StTGeoHelper tries to find according StHitPlane in StHitPlane map

container by StHit hardware position.If not found, search volume it in TGeoManager by x,y,z.

If not found, hit ignored;Get volume id and get according StHitPlaneInfo;Get StHitPlane by path and save it into StHitPlane map.

Save hit into StHitPlane object.

:

StiHitLoader


If geometry is not aligned, some hits could not find their volume. How many?

StiMaker:INFO - StTGeoHelper::AddHit : Hit in /HALL_1/CAVE_1/TPCE_1/TPGV_1/TPSS_3 Not Found






StiMaker:INFO - StiHitLoader::LoadHits : Loaded 14711 good and failed 25 Tpc hits

StiMaker:INFO - StiHitLoader::LoadHits : Loaded 14711 good and failed 25 of all hits

So in case of pp2009a 0.2% of hits lost. So not aligned TPC geometry does not affect reconstruction.

:

StiHitLoader(2)


StiSeedFinder in StiVmc used similar to Sti algorithm. The difference only different hit container. In StiVmc used 3 keys map container. In the following pictures:

Seeds + unused TPC outer hits;Only unused TPC outer hits;

You can see that new StiSeedFinder is rather good.

On the picture with only unused hits you can not notice the real tracks.

:

StiSeedFinder


:

Seeds + all hits


.

:

Unused hits

STAR

Victor Perevoztchikov, BNL StarSoft local

Hit Errors

D

w

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Track direction T.


Hit error parameterization

)12/()cos(/1)(tan)(tan

))(cos/1)(tan)((tan12/)(cos/)(tan

)(cos/1)(tan

:

)sin(

)sin()cos(

)cos()cos(

22

2222222

2222

WDdZdY

WDdZdZ

WDdYdY

xErrorMatri

T

T

T

z

y

x


Hit error + diffusion

Electron cloud around the track increased due to diffusion. Diffusion along Z and in X,Y directions is different and additional dispersion could be written as:

zF

zF

zz

xyxy

2

2

Resulting parameterization is:

))cos()(/(cos)12/()(sin)(sin

))(cos)(/(cos)))(cos)(sin)((sin12/)((sin

)(cos/)12/)((sin

222

22222222

2222

WDdZdY

zFWDdZdZ

zFWDdYdY

z

y

STAR

Comparing this with the previous it is unfortunately evident that old Sti error parameterization is completely wrong. All our production was made with wrong errors. Fortunately it does not mean that results are wrong, but accuracy is not such good as it could be. It could affect only such very precise physics as D0.


Old Sti Hit errors

0

)(tan)(cos/

)(tan)(cos/2

52

43

22

210

dZdY

CzCCdZdZ

CzCCdYdY

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It will be shown later that the best plane for a fit is DCA plane.

DCA plane is a plane orthogonal track direction and includes hit point and DCA point to this hit. Projecting hit errors on detector plane into DCA plane along the track direction gives errors:

You see, these formulas are much simpler than in detector plane and there is no any bad divisions by zero, like in previous case. So DCA plane is much better for fit. All these formulas were tested by Monte-Carlo, which gave exactly same result.


DCA plane hit errors

)sin()sin()cos()12/(

))(cos)(sin)(sin()(sin)(cos)12/(

)(cos)(sin)12/(

2

2222222

2222

DdZdY

zFFWDdZdZ

zFWDdYdY

zy

y

STAR

StiNavigate class provides navigation thru geometry volumes. In current version it is based on VMC navigation but in future probably directly on Tgeo. StiNavigate:

• Initialized by current space point, direction and momentum;

• Navigates thru volumes. On each volume:•Updates matrix of derivatives, using helix approximation;•Calculates energy loss and multiple scattering;

• If volume is sensitive and active, navigation is stopped;

• Then get from StiHitPlane double sorted StiHit container, StiHitPlane direction, passed length, accumulated material info, position, track parameters and errors, volume path, derivative matrix.

• Fitting started.


Navigation


Fitting

Let consider simplified, 2d case. Hitting plane along Y axis, track crossed Y axis with angle α wrt X axis. So : global track parameter α projected into local Y and proportional to sin(α). when α << 1, then sin(α ) = α – α**3/6, second term is very small and projection from global to local system is linear. Projections of error matrix is also linear.

In local frame fit is linear. Back transformation of fitted parameters and errors is linear too. When α is small then curvature ρ is also projected into local Y linearly.

So life is good.

But when α >1 , life is bad. Linearization is wrong, linear fit is wrong,Backward transformation into global is also wrong. All the times, when I saw unstable fit in Sti, it was α >1


Fit continueCould we do something with bad fit with α > 1?

Yes, we can! Why we fit in local frame? There are only two reasons: We know that track is crossing our hit plane; We know hit errors on this plane;

Let invent another local frame, where linearization is working always.

The evident candidate is DCA frame. This frame is:

Plane perpendicular to the track and crossing the hit point. Look the following picture.


DCA Frame

α

α δd

D

δD

d

β


Picture caption

Vertical bold line: Hit Plane; Green star: Hit on hit plane; Red star: DCA point of track wrt hit (green star). Arrow is a predicted track with the parameters in DCA point.Blue star is a new position of track with the modified parameters in this point;

α is a crossing angle of the predicted track; β is an angle between predicted track and fitted o α ne; α+β is a crossing angle of the fitted track;D is the distance between hit and crossing point of the predicted track;D+δD is the distance between hit and crossing point of the fitted track;


Picture caption continue d is the distance between hit and DCA point of the predicted track; d+δd is the distance between hit and fitted track point in DCA plane;


Fitting in DCA frame

In DCA frame, linearization with β and d is correct, track is perpendicular to DCA plane. In hit plane we minimizing the:

((D+δD) / σ)**2 where σ is a hit error.

Let express it in DCA parameters. Looking on the previous picture and using sine rule:

(D+δD) / cos(β) = (d+δd) / cos(α+β)

In linearization β is small and cos(β) = 1

Then:

((D+δD) / σ)**2 == ((d+δd) / (σ * cos(α+β) )**2


Fitting in DCA frame(2)

((D+δD) / σ)**2 == ((d+δd) / (σ * cos(α+β) ))**2

So now we can minimize: ((d+δd) / (σ * cos(α+β) ))**2

It still does not look like much better. Still cos(α+β) when α is not small could not be linearized.

But now is a time to remember that for TPC and for all other detectors:

σ = σ0 / cos(α+β)

So cos(α+β) is canceled out. We minimize:

((d+δd) / σ0)**2 without any loss of accuracy.


Local or DCA frame?

From the discussion above it is clear that fit in DCA frame always is better than in local one. In addition , fit in DCA frame is irrelevant to hit plane orientation. It is proper for TPC, FTPC and all other detectors.

But amount of computation in DCA is slightly bigger. I propose to use strategy:TPC like detector: |α| < 0.5 use local frame fit. It is about 90% of all tracks;TPC like detector: |α| > 0.5 use DCA frame fit. Not a TPC like detector: use DCA frame fit.


The role of alignment

We see, that for fit, we need only: To know the space position of the hits; Hit errors. These errors are calculated from hit plane orientation and predicted track parameters; Hit plane position is not used at all.

Hit errors are proportional to 1/cos(α). So for small α to know precise orientation of hit plane is not too important. Some inaccuracy arise only for |α| > 1. But even here it is not dangerous. Even completely wrong errors do not lead to the shifted estimate. Only estimation error are increased in this case. So some inaccuracy in the hit errors is not too critical.

Precise alignment of hit planes is not important for fit.


The role of alignment(2)

The correct geometry description is important for accounting energy loss and multiple scattering. We see it Sti, which does not work properly for UPC, due to wrong Sti geometry. In the same time alignment of dead material volumes also not important. The correct, “ideal” geometry is absolutely enough for the material accounting.

Precise Geometry alignment is not important for reconstruction.


What is already done(Old) StEvent StHit iterator;TGeoVolume iterator;StiTGeo helper class;Multi key (2 & 3) sorted container. 3 key global hit container used in seed finder. 2 key hit container in each hit plane. SeedFinder based on 3 key sorted container. Helix derivatives matrixStiNavigate is ready. Multiple scattering and energy loss accounting implemented and working also for geometry comparison.


What is already done(Now)

StiHitLoader, no dependency of detectors ;StiDefault Seed Finder. Now tuned for TPC but only tuned;StiGeometryLoader, with no detector dependency;Propagation thru TGeo using TGeant3 + derivatives and errorsHitErrorCalculator with two modes:

Standard detector plane errorsDCA plane errors


Loading of hits is made maximally independent of hit nature and origin. To add into StiVmc new detector there is no need to modify even one line of code. No more StiSsd, StiSvt, StiTpc, StiRnD and StiXXX classes.

StiHitLoader does the following: Iterate via StEventHitIter iterator; Adds it to StTGeoHelper object; StTGeoHelper searches according StHitPlane in

StHitPlane map container by StHit hardware position.If not found, search volume it in TGeoManager by x,y,z. If not found, hit ignored;Get volume id and get according StHitPlaneInfo;Get StHitPlane by path and save it into StHitPlane map.

:

StiHitLoader


:

Seeds + all hits


.

:

Unused hits


:

Geant track propagation


What is needed to be done

StiTrackFinder (copy & paste from old Sti);StiTrackFitter (copy & paste from old Sti);StiRefit (copy & paste from old Sti);Total reshape.

When: with free hands, beginning of June.

But free hands is impossible, so +1 month.

:


:

Fitted tracks propagation


Status Jul 2010

To avoid clashes with Sti new Sti is renamed to Stv. Now alpha version of Stv is ready. What is included? Hit loader;Seed Finder;Track finder , based on Kalman fitter/filter;Vertex finder (not PPV);StEvent filler;Pull filler

What is not: No backward track finder; No smoother or refit;No primary track fitter;


Comparison and testing

Right now real comparison is not possible yet. It is related to new hit error model. Before testing, we must obtain hit error parameters.

For Sti StiFiterr application is used. There is no such application for Stv yet.

During this week I hope the new StvFitErr will be ready.

Then the end of Jul and Aug I will perform the testing and comparison.

In parallel all the “NO” points above will be implemented.

If above will be successful, in September, the massive testing will be

performed


Local Y pull distribution


lZPull


lYHit


lZHit


Status Nov 2010

Geometry loader:Loads TGeo geometry. Automatically recognize sensitive volumes, their orientations, positions. Creates structures to support hits

Hit Loader:Loads hits. Automatically recognition to which volume each hit belongs. No need for RND developer to create specific software for each version of detector. Geant geometry is enough.

Seed finder & Track reconstruction is ready.

Track smoother or refit is ready;

Primary track assignment and fitting in process.

Right now is mainly tuning and testing


:

Fitted tracks propagation


.

:

Unused hits


Status Feb 2011

Alpha version is finished. Now testing.

For test was selected file st_physics_10169042_raw_4030001.daq

First 10000 events was used.

Sti has 260 good globals per event. Stv 349. 34% more

Sti has 10 good primary per event. Stv 17. 70% more

Sti has 4% primaries per global. Stv 5%

Sti 28 hits per global. Stv 21. Stv 25% less

Sti 32 hits per Primary. Stv 22. Stv 32% less (???)

Sti Dca00, DcaXY & DcaZ are much worse then Stv ones(???)


Sti/Stv: good globals & primaries


Sti/Stv: Hits globals & primaries

.


Sti/Stv: Dca globals of primaries

.


Status Feb 2011. Discussion

Sti has more globals but less hits per global. Why?

Let us count total amount of global hits.

Sti = 260*28 = 7280

Stv= 349*22 = 7678. It looks like Sti steals hits from other tracks.

Then these robbed tracks became bad (<15 hits)

Now the same for primaries:

Sti=10*32 = 320

Stv=17*22 = 374. The previous guess works here as well

Now why Dca’s for Sti are such bad? The same explanation fits.

Wrong hits stolen by Sti deteriorate Dca’s

Of course, it is only guess.


Status Nov 2012.

Problems: Fixing wrong pulls; Shortage of short tracks (nHits<15); K-Nearest Neighbor seed finder


Fixing wrong pulls

In current case pulls are the difference between fitted parameter and simulated one, divided by fitted error. If everything is correct, this value should be distributed around zero with width =1. We had something different. See pulls for Sti and Stv on the next page


Wrong pulls show for globals


Wrong pulls show for primaries


Fixing wrong pulls continue

You can see that Stv pulls much worse than Sti ones, which are not ideal as well.

Especially bad result for primaries. Even average is far from zero.

Big work was done to find a reason: StvFitErrors application was revised and rewritten; Many testing routines was written and according algorithms were tested. Some bugs were found and fixed. Fitting and refitting algorithms were cleaned up and partially rewritten. Some bugs were found.

No one of this point was golden key, but in total it gave the following results, see the next page:


Fixed pulls


Pulls improvement

Now pulls of Stv and Sti became comparable:

Stv results are not ideal but better than for Sti ones

Pt TanL Psi

Ave Sigma Ave Sigma Ave Sigma

Stv -.13 1.5 0 0.9 0 0.8

Sti -.45 1.9 0 1.4 0 1.5


Shortage of tracks in Stv

This shortage is seen especially for short tracks with nHits<15,

But also seen for others.

:

Thi

nGlob nPrim nGlob15 nPrim15

Stv 551 230 288 193

Sti 1133 275 356 198


Tracks with KNN seed finder

I suppose that guilty party in track shortage is seed finder. To check it I tried to use CA seed finder. Unfortunately I failed to reanimate it.

Then KNN seed finder was developed and implemented.

KNN seed finder, give better result. But in this case only small statistics (two events) is used. KNN seed finder gives better result without tuning.

There is a hope, that with tuning it will be even better.

:

nGlob nPrim nGlob15 nPrim15

Stv 1312 395 568 318

StvKNN 1470 375 673 356

Sti 1842 421 613 298


K-Nearest Neighbor(KNN) seed finderK Nearest Neighbor is one of those algorithms that are very simple to understand but works incredibly well in practice (Saravan Thirumuruganathan ))http://saravananthirumuruganathan.wordpress.com/2010/05/17/a-detailed-introduction-to-k-nearest-neighbor-knn-algorithm

The site above gives rather good description of KNN method.

Short description of KNN seed finder. The main idea, if you look along the track, you see the dot.

1. Select first hit;

2.Direction from hit to point (0,0,0) is X axis in spherical coordinate system;

3.Arbitrary define orthogonal axis’s Y and Z

4. Select not too big volume near first hit;

5.Loop over hits in volume , calculate Phi and Theta;

6.Calculate distance in (Phi,Theta) space to previous hits;

7.Save K smallest distances for each hit;

8.Select hit with the smallest K distance;

9.This hit and the nearest ones forms the seed.


KNN seed finder(2)

If founded KNN distance is too big, there is no seed.

If track is not strait, then in (Phi,Theta) space it will be not a dot but short line.

Calculate the width of this line. If width is too big, it is not a seed.

On the next page two figures of good seed.

Afterwards there is an example of bad seed.


Good KNN seed


KNN bad seed


KNN statistics wide cuts

n

No tracks Found tracks


KNN statistics narrow cuts

No tracks Found tracks


Summary

Wrong pulls problem solved (~) Tracks shortage probably related to bad default seed finder; KNN seed finder implemented,is promising and needs tuning; CA TPC seed finder is not working anymore. Something was changed, needed attention.


Status Dec 2012.

Comparison StiKNN & StvKNN: Sti was modified to accept list of seed finders. Code is not committed. StiKNNSeedFinder was implemented. Code of StvKNN was directly used, via #include. So all the parameters of StvKNN & StiKNN seed finders exactly the same. Results of comparison are very controversial.


Comparison Sti, StiKNN & StvKNN

nGlob nPrim nGlob15 nPrim15 gDom pDom

Sti 1133 275 356 198 88.13 92.18

StiKNN 683 220 376 204 87.9 92.13

StvKNN 1206 231 415 221 85.57 91.72


Globals & Primaries

Sti StiKnn StvKnn


Good Globals & Primaries

Sti15 StiKnn15 StvKnn15


Championship Sti, StiKNN & StvKNN

nGlob nPrim nGlob15 nPrim15 Split

Sti 2nd 1st 3rd 3rd 2nd

StiKNN 3rd 3rd 2nd 2nd 1st

StvKNN 1st 2nd 1st 1st 3rd

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Dominant contributors


Sti StiKnn StvKnn

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