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3e87ef69 1// @(#) $Id$
9392f4fd 2
b661165c 3// Author: Anders Vestbo <mailto:vestbo@fi.uib.no>
3e87ef69 4//*-- Copyright &copy ALICE HLT Group
b661165c 5
118c26c3 6#include "AliL3StandardIncludes.h"
e9ecfae3 7#include "AliL3RootTypes.h"
108615fc 8#include "AliL3Logging.h"
108615fc 9#include "AliL3Vertex.h"
10#include "AliL3ConfMapTrack.h"
11#include "AliL3ConfMapPoint.h"
ef79795d 12#include "AliL3Transform.h"
e9ecfae3 13#include "AliL3ConfMapFit.h"
108615fc 14
3e87ef69 15/** \class AliL3ConfMapFit
16<pre>
b661165c 17//_____________________________________________________________
108615fc 18// AliL3ConfMapFit
19//
20// Fit class for conformal mapping tracking
3e87ef69 21</pre>
22*/
108615fc 23
5929c18d 24#if __GNUC__ >= 3
25using namespace std;
26#endif
27
108615fc 28ClassImp(AliL3ConfMapFit)
29
108615fc 30
31AliL3ConfMapFit::AliL3ConfMapFit(AliL3ConfMapTrack *track,AliL3Vertex *vertex)
32{
33 //constructor
34 fTrack = track;
35 fVertex = vertex;
108615fc 36}
37
38Int_t AliL3ConfMapFit::FitHelix()
39{
b1ed0288 40 //fit the helix
108615fc 41 if(FitCircle())
42 {
43 LOG(AliL3Log::kError,"AliL3ConfMapFit::FitHelix","TrackFit")<<AliL3Log::kDec<<
44 "Problems during circle fit"<<ENDLOG;
45 return 1;
46 }
47 if(FitLine())
48 {
49 LOG(AliL3Log::kError,"AliL3ConfMapFit::FitHelix","TrackFit")<<AliL3Log::kDec<<
50 "Problems during line fit"<<ENDLOG;
51 return 1;
52 }
53 return 0;
54}
55
56Int_t AliL3ConfMapFit::FitCircle()
57{
58 //-----------------------------------------------------------------
59 //Fits circle parameters using algorithm
60 //described by ChErnov and Oskov in Computer Physics
61 //Communications.
62 //
63 //Written in FORTRAN by Jawluen Tang, Physics department , UT-Austin
64 //Moved to C by Pablo Yepes
65 //Moved to AliROOT by ASV.
66 //------------------------------------------------------------------
67
68 Double_t wsum = 0.0 ;
69 Double_t xav = 0.0 ;
70 Double_t yav = 0.0 ;
71
72 Int_t num_of_hits = fTrack->GetNumberOfPoints();
73 //
74 // Loop over hits calculating average
75 Int_t co=0;
76
77 for(fTrack->StartLoop(); fTrack->LoopDone(); fTrack->GetNextHit())
78 {
79 co++;
b1ed0288 80 AliL3ConfMapPoint *cHit = (AliL3ConfMapPoint*)fTrack->GetCurrentHit();
108615fc 81 cHit->SetXYWeight( 1./ (Double_t)(cHit->GetXerr()*cHit->GetXerr() + cHit->GetYerr()*cHit->GetYerr()) );
82 wsum += cHit->GetXYWeight() ;
83 xav += cHit->GetXYWeight() * cHit->GetX() ;
84 yav += cHit->GetXYWeight() * cHit->GetY() ;
85 }
86 if(co!=num_of_hits)
87 LOG(AliL3Log::kError,"AliL3ConfMapFit::FitCircle","TrackFit")<<AliL3Log::kDec<<
88 "Mismatch of hits. Counter: "<<co<<" nHits: "<<num_of_hits<<ENDLOG;
89 if (fTrack->ComesFromMainVertex() == true)
90 {
91 wsum += fVertex->GetXYWeight() ;
92 xav += fVertex->GetX() ;
93 yav += fVertex->GetY() ;
94 }
95
96 xav = xav / wsum ;
97 yav = yav / wsum ;
98//
99// CALCULATE <X**2>, <XY>, AND <Y**2> WITH <X> = 0, & <Y> = 0
100//
101 Double_t xxav = 0.0 ;
102 Double_t xyav = 0.0 ;
103 Double_t yyav = 0.0 ;
104 Double_t xi, yi ;
105
106 for(fTrack->StartLoop(); fTrack->LoopDone(); fTrack->GetNextHit())
107 {
108 //AliL3ConfMapPoint *cHit = (AliL3ConfMapPoint *)hits->At(hit_counter);
b1ed0288 109 AliL3ConfMapPoint *cHit = (AliL3ConfMapPoint*)fTrack->GetCurrentHit();
108615fc 110 xi = cHit->GetX() - xav ;
111 yi = cHit->GetY() - yav ;
112 xxav += xi * xi * cHit->GetXYWeight() ;
113 xyav += xi * yi * cHit->GetXYWeight() ;
114 yyav += yi * yi * cHit->GetXYWeight() ;
115 }
116
117 if (fTrack->ComesFromMainVertex() == true)
118 {
119 xi = fVertex->GetX() - xav ;
120 yi = fVertex->GetY() - yav ;
121 xxav += xi * xi * fVertex->GetXYWeight() ;
122 xyav += xi * yi * fVertex->GetXYWeight() ;
123 yyav += yi * yi * fVertex->GetXYWeight() ;
124 }
125 xxav = xxav / wsum ;
126 xyav = xyav / wsum ;
127 yyav = yyav / wsum ;
128//
129//--> ROTATE COORDINATES SO THAT <XY> = 0
130//
131//--> SIGN(C**2 - S**2) = SIGN(XXAV - YYAV) >
132//--> & > ==> NEW : (XXAV-YYAV) > 0
133//--> SIGN(S) = SIGN(XYAV) >
134
135 Double_t a = fabs( xxav - yyav ) ;
136 Double_t b = 4.0 * xyav * xyav ;
137
138 Double_t asqpb = a * a + b ;
139 Double_t rasqpb = sqrt ( asqpb) ;
140
141 Double_t splus = 1.0 + a / rasqpb ;
142 Double_t sminus = b / (asqpb * splus) ;
143
144 splus = sqrt (0.5 * splus ) ;
145 sminus = sqrt (0.5 * sminus) ;
146//
147//-> FIRST REQUIRE : SIGN(C**2 - S**2) = SIGN(XXAV - YYAV)
148//
149 Double_t sinrot, cosrot ;
150 if ( xxav <= yyav ) {
151 cosrot = sminus ;
152 sinrot = splus ;
153 }
154 else {
155 cosrot = splus ;
156 sinrot = sminus ;
157 }
158//
159//-> REQUIRE : SIGN(S) = SIGN(XYAV) * SIGN(C) (ASSUMING SIGN(C) > 0)
160//
161 if ( xyav < 0.0 ) sinrot = - sinrot ;
162//
163//--> WE NOW HAVE THE SMALLEST ANGLE THAT GUARANTEES <X**2> > <Y**2>
164//--> TO GET THE SIGN OF THE CHARGE RIGHT, THE NEW X-AXIS MUST POINT
165//--> OUTWARD FROM THE ORGIN. WE ARE FREE TO CHANGE SIGNS OF BOTH
166//--> COSROT AND SINROT SIMULTANEOUSLY TO ACCOMPLISH THIS.
167//
168//--> CHOOSE SIGN OF C WISELY TO BE ABLE TO GET THE SIGN OF THE CHARGE
169//
170 if ( cosrot*xav+sinrot*yav < 0.0 ) {
171 cosrot = -cosrot ;
172 sinrot = -sinrot ;
173 }
174//
175//-> NOW GET <R**2> AND RSCALE= SQRT(<R**2>)
176//
177 Double_t rrav = xxav + yyav ;
178 Double_t rscale = sqrt(rrav) ;
179
180 xxav = 0.0 ;
181 yyav = 0.0 ;
182 xyav = 0.0 ;
183 Double_t xrrav = 0.0 ;
184 Double_t yrrav = 0.0 ;
185 Double_t rrrrav = 0.0 ;
186
187 Double_t xixi, yiyi, riri, wiriri, xold, yold ;
188
189 //for (hit_counter=0; hit_counter<num_of_hits; hit_counter++)
190 for(fTrack->StartLoop(); fTrack->LoopDone(); fTrack->GetNextHit())
191 {
192 //AliL3ConfMapPoint *cHit = (AliL3ConfMapPoint*)hits->At(hit_counter);
b1ed0288 193 AliL3ConfMapPoint* cHit = (AliL3ConfMapPoint*)fTrack->GetCurrentHit();
108615fc 194
195 xold = cHit->GetX() - xav ;
196 yold = cHit->GetY() - yav ;
197 //
198 //--> ROTATE SO THAT <XY> = 0 & DIVIDE BY RSCALE SO THAT <R**2> = 1
199 //
200 xi = ( cosrot * xold + sinrot * yold ) / rscale ;
201 yi = ( -sinrot * xold + cosrot * yold ) / rscale ;
202
203 xixi = xi * xi ;
204 yiyi = yi * yi ;
205 riri = xixi + yiyi ;
206 wiriri = cHit->GetXYWeight() * riri ;
207
208 xyav += cHit->GetXYWeight() * xi * yi ;
209 xxav += cHit->GetXYWeight() * xixi ;
210 yyav += cHit->GetXYWeight() * yiyi ;
211
212 xrrav += wiriri * xi ;
213 yrrav += wiriri * yi ;
214 rrrrav += wiriri * riri ;
215 }
216 //
217// Include vertex if required
218//
219 if (fTrack->ComesFromMainVertex() == true)
220 {
221 xold = fVertex->GetX() - xav ;
222 yold = fVertex->GetY() - yav ;
223 //
224 //--> ROTATE SO THAT <XY> = 0 & DIVIDE BY RSCALE SO THAT <R**2> = 1
225 //
226 xi = ( cosrot * xold + sinrot * yold ) / rscale ;
227 yi = ( -sinrot * xold + cosrot * yold ) / rscale ;
228
229 xixi = xi * xi ;
230 yiyi = yi * yi ;
231 riri = xixi + yiyi ;
232 wiriri = fVertex->GetXYWeight() * riri ;
233
234 xyav += fVertex->GetXYWeight() * xi * yi ;
235 xxav += fVertex->GetXYWeight() * xixi ;
236 yyav += fVertex->GetXYWeight() * yiyi ;
237
238 xrrav += wiriri * xi ;
239 yrrav += wiriri * yi ;
240 rrrrav += wiriri * riri ;
241 }
242 //
243 //
244 //
245 //--> DIVIDE BY WSUM TO MAKE AVERAGES
246 //
247 xxav = xxav / wsum ;
248 yyav = yyav / wsum ;
249 xrrav = xrrav / wsum ;
250 yrrav = yrrav / wsum ;
251 rrrrav = rrrrav / wsum ;
252 xyav = xyav / wsum ;
253
254 Int_t const ntry = 5 ;
255//
256//--> USE THESE TO GET THE COEFFICIENTS OF THE 4-TH ORDER POLYNIMIAL
257//--> DON'T PANIC - THE THIRD ORDER TERM IS ZERO !
258//
259 Double_t xrrxrr = xrrav * xrrav ;
260 Double_t yrryrr = yrrav * yrrav ;
261 Double_t rrrrm1 = rrrrav - 1.0 ;
262 Double_t xxyy = xxav * yyav ;
263
264 Double_t c0 = rrrrm1*xxyy - xrrxrr*yyav - yrryrr*xxav ;
265 Double_t c1 = - rrrrm1 + xrrxrr + yrryrr - 4.0*xxyy ;
266 Double_t c2 = 4.0 + rrrrm1 - 4.0*xxyy ;
267 Double_t c4 = - 4.0 ;
268//
269//--> COEFFICIENTS OF THE DERIVATIVE - USED IN NEWTON-RAPHSON ITERATIONS
270//
271 Double_t c2d = 2.0 * c2 ;
272 Double_t c4d = 4.0 * c4 ;
273//
274//--> 0'TH VALUE OF LAMDA - LINEAR INTERPOLATION BETWEEN P(0) & P(YYAV)
275//
276// LAMDA = YYAV * C0 / (C0 + YRRSQ * (XXAV-YYAV))
277 Double_t lamda = 0.0 ;
278 Double_t dlamda = 0.0 ;
279//
280 Double_t chiscl = wsum * rscale * rscale ;
281 Double_t dlamax = 0.001 / chiscl ;
282
283 Double_t p, pd ;
284 for ( int itry = 1 ; itry <= ntry ; itry++ ) {
285 p = c0 + lamda * (c1 + lamda * (c2 + lamda * lamda * c4 )) ;
286 pd = (c1 + lamda * (c2d + lamda * lamda * c4d)) ;
287 dlamda = -p / pd ;
288 lamda = lamda + dlamda ;
289 if (fabs(dlamda)< dlamax) break ;
290 }
291
292 Double_t chi2 = (Double_t)(chiscl * lamda) ;
293
294 fTrack->SetChiSq1(chi2);
295 // Double_t dchisq = chiscl * dlamda ;
296//
297//--> NOW CALCULATE THE MATRIX ELEMENTS FOR ALPHA, BETA & KAPPA
298//
299 Double_t h11 = xxav - lamda ;
300 Double_t h14 = xrrav ;
301 Double_t h22 = yyav - lamda ;
302 Double_t h24 = yrrav ;
303 Double_t h34 = 1.0 + 2.0*lamda ;
304 if ( h11 == 0.0 || h22 == 0.0 ){
305 LOG(AliL3Log::kError,"AliL3ConfMapFit::FitCircle","TrackFit")<<AliL3Log::kDec<<
306 "Problems fitting circle"<<ENDLOG;
307 return 1 ;
308 }
309 Double_t rootsq = (h14*h14)/(h11*h11) + 4.0*h34 ;
310
311 Double_t ratio, kappa, beta ;
312 if ( fabs(h22) > fabs(h24) ) {
313 ratio = h24 / h22 ;
314 rootsq = ratio * ratio + rootsq ;
315 kappa = 1.0 / sqrt(rootsq) ;
316 beta = - ratio * kappa ;
317 }
318 else {
319 ratio = h22 / h24 ;
320 rootsq = 1.0 + ratio * ratio * rootsq ;
321 beta = 1.0 / sqrt(rootsq) ;
322 if ( h24 > 0 ) beta = - beta ;
323 kappa = -ratio * beta ;
324 }
325 Double_t alpha = - (h14/h11) * kappa ;
326//
327//--> transform these into the lab coordinate system
328//--> first get kappa and back to real dimensions
329//
330 Double_t kappa1 = kappa / rscale ;
331 Double_t dbro = 0.5 / kappa1 ;
332//
333//--> next rotate alpha and beta and scale
334//
335 Double_t alphar = (cosrot * alpha - sinrot * beta)* dbro ;
336 Double_t betar = (sinrot * alpha + cosrot * beta)* dbro ;
337//
338//--> then translate by (xav,yav)
339//
340 Double_t acent = (double)(xav - alphar) ;
341 Double_t bcent = (double)(yav - betar ) ;
342 Double_t radius = (double)dbro ;
343//
344// Get charge
345//
5dd30052 346 Int_t q = ( ( yrrav < 0 ) ? 1 : -1 ) ;
108615fc 347
348 fTrack->SetCharge(q);
349
1f1942b8 350
351 //Set the first point on the track to the space point coordinates of the innermost track
352 //This will be updated to lie on the fit later on (AliL3Track::UpdateToFirstPoint).
0bd0c1ef 353 Double_t x0,y0,psi,pt ;
b1ed0288 354 AliL3ConfMapPoint *lHit = (AliL3ConfMapPoint*)fTrack->GetLastHit();
0bd0c1ef 355 x0 = lHit->GetX();
356 y0 = lHit->GetY();
1f1942b8 357 fTrack->SetFirstPoint(x0,y0,0); //Z-value is set in FitLine
358
108615fc 359 psi = (Double_t)atan2(bcent-y0,acent-x0) ;
5a31e9df 360 psi = psi + q * AliL3Transform::PiHalf();
361 if ( psi < 0 ) psi = psi + AliL3Transform::TwoPi();
362 pt = (Double_t)(AliL3Transform::GetBFieldValue() * radius ) ;
1f1942b8 363
364 //Update the track parameters with the parameters from this fit:
108615fc 365 fTrack->SetPsi(psi);
366 fTrack->SetPt(pt);
1f1942b8 367 fTrack->SetRadius(radius);
368 fTrack->SetCenterX(acent);
369 fTrack->SetCenterY(bcent);
108615fc 370
371 //
372// Get errors from fast fit
373//
374 //if ( getPara()->getErrors ) getErrorsCircleFit ( acent, bcent, radius ) ;
375//
376 return 0 ;
377
378}
379
380//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
381// Fit Line in s-z plane
382//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
383Int_t AliL3ConfMapFit::FitLine ( )
384{
385 //
386 //Initialization
387 //
388 Double_t sum = 0.F ;
389 Double_t ss = 0.F ;
390 Double_t sz = 0.F ;
391 Double_t sss = 0.F ;
392 Double_t ssz = 0.F ;
393 //
394 //find sum , sums ,sumz, sumss
395 //
396 Double_t dx, dy ;
5a31e9df 397 Double_t radius = (Double_t)(fTrack->GetPt() / AliL3Transform::GetBFieldValue() ) ;
108615fc 398
399 //TObjArray *hits = fTrack->GetHits();
400 //Int_t num_of_hits = fTrack->GetNumberOfPoints();
401
0bd0c1ef 402 if (0)// fTrack->ComesFromMainVertex() == true )
108615fc 403 {
b1ed0288 404 dx = ((AliL3ConfMapPoint*)fTrack->GetFirstHit())->GetX() - fVertex->GetX();
405 dy = ((AliL3ConfMapPoint*)fTrack->GetFirstHit())->GetY() - fVertex->GetY() ;
108615fc 406 }
407 else
408 {
b1ed0288 409 dx = ((AliL3ConfMapPoint *)fTrack->GetFirstHit())->GetX() - ((AliL3ConfMapPoint *)fTrack->GetLastHit())->GetX() ;
410 dy = ((AliL3ConfMapPoint *)fTrack->GetFirstHit())->GetY() - ((AliL3ConfMapPoint *)fTrack->GetLastHit())->GetY() ;
108615fc 411 //dx = ((AliL3ConfMapPoint *)hits->First())->GetX() - ((AliL3ConfMapPoint *)hits->Last())->GetX() ;
412 //dy = ((AliL3ConfMapPoint *)hits->First())->GetY() - ((AliL3ConfMapPoint *)hits->Last())->GetY() ;
413 }
414
415 Double_t localPsi = 0.5F * sqrt ( dx*dx + dy*dy ) / radius ;
416 Double_t total_s ;
417
418 if ( fabs(localPsi) < 1. )
419 {
420 total_s = 2.0 * radius * asin ( localPsi ) ;
421 }
422 else
423 {
5a31e9df 424 total_s = 2.0 * radius * AliL3Transform::Pi() ;
108615fc 425 }
426
427 AliL3ConfMapPoint *previousHit = NULL;
428
429 // FtfBaseHit *previousHit = 0 ;
430
431 //for ( startLoop() ; done() ; nextHit() ) {
432 Double_t dpsi,s;
433
434 // for(hit_counter=0; hit_counter<num_of_hits; hit_counter++)
435 for(fTrack->StartLoop(); fTrack->LoopDone(); fTrack->GetNextHit())
436 {
437 // AliL3ConfMapPoint *cHit = (AliL3ConfMapPoint*)hits->At(hit_counter);
b1ed0288 438 AliL3ConfMapPoint *cHit = (AliL3ConfMapPoint*)fTrack->GetCurrentHit();
439 // if ( GetCurrentHit() != GetFirstHit() )
440 if(cHit != fTrack->GetFirstHit())// hits->First())
108615fc 441 {
442 dx = cHit->GetX() - previousHit->GetX() ;
443 dy = cHit->GetY() - previousHit->GetY() ;
444 dpsi = 0.5 * (Double_t)sqrt ( dx*dx + dy*dy ) / radius ;
445 fTrack->SetPsierr(dpsi);
446 s = previousHit->GetS() - 2.0 * radius * (Double_t)asin ( dpsi ) ;
447 cHit->SetS(s);
448 }
449 else
450 cHit->SetS(total_s);
451 // cHit->s = total_s ;
452
453 sum += cHit->GetZWeight() ;
454 ss += cHit->GetZWeight() * cHit->GetS() ;
455 sz += cHit->GetZWeight() * cHit->GetZ() ;
456 sss += cHit->GetZWeight() * cHit->GetS() * cHit->GetS() ;
457 ssz += cHit->GetZWeight() * cHit->GetS() * cHit->GetZ() ;
458 previousHit = cHit ;
459 }
460
461 Double_t chi2,det = sum * sss - ss * ss;
462 if ( fabs(det) < 1e-20)
463 {
464 chi2 = 99999.F ;
465 fTrack->SetChiSq2(chi2);
466 return 0 ;
467 }
468
469 //Compute the best fitted parameters A,B
470 Double_t tanl,z0,dtanl,dz0;
471
472 tanl = (Double_t)((sum * ssz - ss * sz ) / det );
473 z0 = (Double_t)((sz * sss - ssz * ss ) / det );
474
475 fTrack->SetTgl(tanl);
476 fTrack->SetZ0(z0);
477
478 // calculate chi-square
479
480 chi2 = 0.;
481 Double_t r1 ;
482
483 //for(hit_counter=0; hit_counter<num_of_hits; hit_counter++)
484 for(fTrack->StartLoop(); fTrack->LoopDone(); fTrack->GetNextHit())
485 {
486 //AliL3ConfMapPoint *cHit = (AliL3ConfMapPoint*)hits->At(hit_counter);
b1ed0288 487 AliL3ConfMapPoint *cHit = (AliL3ConfMapPoint*)fTrack->GetCurrentHit();
108615fc 488 r1 = cHit->GetZ() - tanl * cHit->GetS() - z0 ;
489 chi2 += (Double_t) ( (Double_t)cHit->GetZWeight() * (r1 * r1) );
490 }
491 fTrack->SetChiSq2(chi2);
492 //
493 // calculate estimated variance
494 // varsq=chi/(double(n)-2.)
495 // calculate covariance matrix
496 // siga=sqrt(varsq*sxx/det)
497 // sigb=sqrt(varsq*sum/det)
498 //
499 dtanl = (Double_t) ( sum / det );
500 dz0 = (Double_t) ( sss / det );
501
502 fTrack->SetTglerr(dtanl);
503 fTrack->SetZ0err(dz0);
504
505 return 0 ;
506}