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[u/mrichter/AliRoot.git] / STEER / AliExternalTrackParam.cxx
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51ad6848 1/**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
3 * *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
6 * *
7 * Permission to use, copy, modify and distribute this software and its *
8 * documentation strictly for non-commercial purposes is hereby granted *
9 * without fee, provided that the above copyright notice appears in all *
10 * copies and that both the copyright notice and this permission notice *
11 * appear in the supporting documentation. The authors make no claims *
12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
14 **************************************************************************/
15
16/* $Id$ */
17
18///////////////////////////////////////////////////////////////////////////////
19// //
49d13e89 20// Implementation of the external track parameterisation class. //
51ad6848 21// //
49d13e89 22// This parameterisation is used to exchange tracks between the detectors. //
23// A set of functions returning the position and the momentum of tracks //
24// in the global coordinate system as well as the track impact parameters //
25// are implemented.
26// Origin: I.Belikov, CERN, Jouri.Belikov@cern.ch //
51ad6848 27///////////////////////////////////////////////////////////////////////////////
51ad6848 28#include "AliExternalTrackParam.h"
29#include "AliKalmanTrack.h"
f76701bf 30#include "AliESDVertex.h"
5b77d93c 31
51ad6848 32
33ClassImp(AliExternalTrackParam)
34
51ad6848 35//_____________________________________________________________________________
90e48c0c 36AliExternalTrackParam::AliExternalTrackParam() :
90e48c0c 37 fX(0),
c9ec41e8 38 fAlpha(0)
51ad6848 39{
90e48c0c 40 //
41 // default constructor
42 //
c9ec41e8 43 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
44 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 45}
46
47//_____________________________________________________________________________
48AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha,
49 const Double_t param[5],
90e48c0c 50 const Double_t covar[15]) :
90e48c0c 51 fX(x),
c9ec41e8 52 fAlpha(alpha)
51ad6848 53{
90e48c0c 54 //
55 // create external track parameters from given arguments
56 //
c9ec41e8 57 for (Int_t i = 0; i < 5; i++) fP[i] = param[i];
58 for (Int_t i = 0; i < 15; i++) fC[i] = covar[i];
51ad6848 59}
60
90e48c0c 61//_____________________________________________________________________________
62AliExternalTrackParam::AliExternalTrackParam(const AliKalmanTrack& track) :
fe12e09c 63 fX(0),
c9ec41e8 64 fAlpha(track.GetAlpha())
51ad6848 65{
66 //
67 //
c9ec41e8 68 track.GetExternalParameters(fX,fP);
69 track.GetExternalCovariance(fC);
51ad6848 70}
71
51ad6848 72//_____________________________________________________________________________
c9ec41e8 73void AliExternalTrackParam::Set(const AliKalmanTrack& track) {
74 //
75 //
76 fAlpha=track.GetAlpha();
77 track.GetExternalParameters(fX,fP);
78 track.GetExternalCovariance(fC);
51ad6848 79}
80
81//_____________________________________________________________________________
c9ec41e8 82void AliExternalTrackParam::Reset() {
1530f89c 83 //
84 // Resets all the parameters to 0
85 //
c9ec41e8 86 fX=fAlpha=0.;
87 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
88 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 89}
90
c9ec41e8 91Double_t AliExternalTrackParam::GetP() const {
92 //---------------------------------------------------------------------
93 // This function returns the track momentum
94 // Results for (nearly) straight tracks are meaningless !
95 //---------------------------------------------------------------------
06fb4a2f 96 if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig;
c9ec41e8 97 return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
51ad6848 98}
99
1d99986f 100Double_t AliExternalTrackParam::Get1P() const {
101 //---------------------------------------------------------------------
102 // This function returns the 1/(track momentum)
103 //---------------------------------------------------------------------
104 return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
105}
106
c9ec41e8 107//_______________________________________________________________________
c7bafca9 108Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
c9ec41e8 109 //------------------------------------------------------------------
110 // This function calculates the transverse impact parameter
111 // with respect to a point with global coordinates (x,y)
112 // in the magnetic field "b" (kG)
113 //------------------------------------------------------------------
5773defd 114 if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
1530f89c 115 Double_t rp4=GetC(b);
c9ec41e8 116
117 Double_t xt=fX, yt=fP[0];
118
119 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
120 Double_t a = x*cs + y*sn;
121 y = -x*sn + y*cs; x=a;
122 xt-=x; yt-=y;
123
124 sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]);
125 a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt);
1530f89c 126 return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
127}
128
129//_______________________________________________________________________
130void AliExternalTrackParam::
131GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const {
132 //------------------------------------------------------------------
133 // This function calculates the transverse and longitudinal impact parameters
134 // with respect to a point with global coordinates (x,y)
135 // in the magnetic field "b" (kG)
136 //------------------------------------------------------------------
137 Double_t f1 = fP[2], r1 = TMath::Sqrt(1. - f1*f1);
138 Double_t xt=fX, yt=fP[0];
139 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
140 Double_t a = x*cs + y*sn;
141 y = -x*sn + y*cs; x=a;
142 xt-=x; yt-=y;
143
144 Double_t rp4=GetC(b);
145 if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) {
146 dz[0] = -(xt*f1 - yt*r1);
147 dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z;
148 return;
149 }
150
151 sn=rp4*xt - f1; cs=rp4*yt + r1;
152 a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt);
153 Double_t rr=TMath::Sqrt(sn*sn + cs*cs);
154 dz[0] = -a/(1 + rr);
155 Double_t f2 = -sn/rr, r2 = TMath::Sqrt(1. - f2*f2);
156 dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z;
51ad6848 157}
158
49d13e89 159//_______________________________________________________________________
160Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
161 //------------------------------------------------------------------
162 // This function calculates the transverse impact parameter
163 // with respect to a point with global coordinates (xv,yv)
164 // neglecting the track curvature.
165 //------------------------------------------------------------------
166 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
167 Double_t x= xv*cs + yv*sn;
168 Double_t y=-xv*sn + yv*cs;
169
170 Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]);
171
1530f89c 172 return -d;
49d13e89 173}
174
c7bafca9 175Bool_t AliExternalTrackParam::
176CorrectForMaterial(Double_t d, Double_t x0, Double_t mass) {
177 //------------------------------------------------------------------
178 // This function corrects the track parameters for the crossed material
179 // "d" - the thickness (fraction of the radiation length)
180 // "x0" - the radiation length (g/cm^2)
181 // "mass" - the mass of this particle (GeV/c^2)
182 //------------------------------------------------------------------
183 Double_t &fP2=fP[2];
184 Double_t &fP3=fP[3];
185 Double_t &fP4=fP[4];
186
187 Double_t &fC22=fC[5];
188 Double_t &fC33=fC[9];
189 Double_t &fC43=fC[13];
190 Double_t &fC44=fC[14];
191
192 Double_t p2=(1.+ fP3*fP3)/(fP4*fP4);
193 Double_t beta2=p2/(p2 + mass*mass);
194 d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
195
196 //Multiple scattering******************
197 if (d!=0) {
198 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
199 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
200 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
201 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
202 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
203 fC44 += theta2*fP3*fP4*fP3*fP4;
204 }
205
206 //Energy losses************************
8fc1985d 207 if (x0!=0. && beta2<1) {
c7bafca9 208 d*=x0;
209 Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2)*d;
210 if (beta2/(1-beta2)>3.5*3.5)
211 dE=0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2)*d;
212
213 fP4*=(1.- TMath::Sqrt(p2 + mass*mass)/p2*dE);
214 }
215
216 return kTRUE;
217}
218
49d13e89 219Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
220 //------------------------------------------------------------------
221 // Transform this track to the local coord. system rotated
222 // by angle "alpha" (rad) with respect to the global coord. system.
223 //------------------------------------------------------------------
dfcef74c 224 if (TMath::Abs(fP[2]) >= kAlmost1) {
225 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
226 return kFALSE;
227 }
228
49d13e89 229 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
230 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
231
232 Double_t &fP0=fP[0];
233 Double_t &fP2=fP[2];
234 Double_t &fC00=fC[0];
235 Double_t &fC10=fC[1];
236 Double_t &fC20=fC[3];
237 Double_t &fC21=fC[4];
238 Double_t &fC22=fC[5];
239 Double_t &fC30=fC[6];
240 Double_t &fC32=fC[8];
241 Double_t &fC40=fC[10];
242 Double_t &fC42=fC[12];
243
244 Double_t x=fX;
245 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
246 Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
247
dfcef74c 248 Double_t tmp=sf*ca - cf*sa;
249 if (TMath::Abs(tmp) >= kAlmost1) return kFALSE;
250
49d13e89 251 fAlpha = alpha;
252 fX = x*ca + fP0*sa;
253 fP0= -x*sa + fP0*ca;
dfcef74c 254 fP2= tmp;
49d13e89 255
06fb4a2f 256 if (TMath::Abs(cf)<kAlmost0) {
257 AliError(Form("Too small cosine value %f",cf));
258 cf = kAlmost0;
259 }
260
49d13e89 261 Double_t rr=(ca+sf/cf*sa);
262
263 fC00 *= (ca*ca);
264 fC10 *= ca;
265 fC20 *= ca*rr;
266 fC21 *= rr;
267 fC22 *= rr*rr;
268 fC30 *= ca;
269 fC32 *= rr;
270 fC40 *= ca;
271 fC42 *= rr;
272
273 return kTRUE;
274}
275
276Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
277 //----------------------------------------------------------------
278 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
279 //----------------------------------------------------------------
49d13e89 280 Double_t dx=xk-fX;
e421f556 281 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
18ebc5ef 282
1530f89c 283 Double_t crv=GetC(b);
5773defd 284 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
285
49d13e89 286 Double_t f1=fP[2], f2=f1 + crv*dx;
bbefa4c4 287 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 288 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
289
290 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
291 Double_t
292 &fC00=fC[0],
293 &fC10=fC[1], &fC11=fC[2],
294 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
295 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
296 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
297
298 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
299
300 fX=xk;
301 fP0 += dx*(f1+f2)/(r1+r2);
18ebc5ef 302 fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
49d13e89 303 fP2 += dx*crv;
304
305 //f = F - 1
306
307 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
308 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
309 Double_t f12= dx*fP3*f1/(r1*r1*r1);
310 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
311 Double_t f13= dx/r1;
312 Double_t f24= dx; f24*=cc;
313
314 //b = C*ft
315 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
316 Double_t b02=f24*fC40;
317 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
318 Double_t b12=f24*fC41;
319 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
320 Double_t b22=f24*fC42;
321 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
322 Double_t b42=f24*fC44;
323 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
324 Double_t b32=f24*fC43;
325
326 //a = f*b = f*C*ft
327 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
328 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
329 Double_t a22=f24*b42;
330
331 //F*C*Ft = C + (b + bt + a)
332 fC00 += b00 + b00 + a00;
333 fC10 += b10 + b01 + a01;
334 fC20 += b20 + b02 + a02;
335 fC30 += b30;
336 fC40 += b40;
337 fC11 += b11 + b11 + a11;
338 fC21 += b21 + b12 + a12;
339 fC31 += b31;
340 fC41 += b41;
341 fC22 += b22 + b22 + a22;
342 fC32 += b32;
343 fC42 += b42;
344
345 return kTRUE;
346}
347
348Double_t
349AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
350 //----------------------------------------------------------------
351 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
352 //----------------------------------------------------------------
353 Double_t sdd = fC[0] + cov[0];
354 Double_t sdz = fC[1] + cov[1];
355 Double_t szz = fC[2] + cov[2];
356 Double_t det = sdd*szz - sdz*sdz;
357
358 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
359
360 Double_t d = fP[0] - p[0];
361 Double_t z = fP[1] - p[1];
362
363 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
364}
365
366Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
367 //------------------------------------------------------------------
368 // Update the track parameters with the space point "p" having
369 // the covariance matrix "cov"
370 //------------------------------------------------------------------
371 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
372 Double_t
373 &fC00=fC[0],
374 &fC10=fC[1], &fC11=fC[2],
375 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
376 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
377 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
378
379 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
380 r00+=fC00; r01+=fC10; r11+=fC11;
381 Double_t det=r00*r11 - r01*r01;
382
383 if (TMath::Abs(det) < kAlmost0) return kFALSE;
384
385
386 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
387
388 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
389 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
390 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
391 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
392 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
393
394 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
395 Double_t sf=fP2 + k20*dy + k21*dz;
396 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
397
398 fP0 += k00*dy + k01*dz;
399 fP1 += k10*dy + k11*dz;
400 fP2 = sf;
401 fP3 += k30*dy + k31*dz;
402 fP4 += k40*dy + k41*dz;
403
404 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
405 Double_t c12=fC21, c13=fC31, c14=fC41;
406
407 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
408 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
409 fC40-=k00*c04+k01*c14;
410
411 fC11-=k10*c01+k11*fC11;
412 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
413 fC41-=k10*c04+k11*c14;
414
415 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
416 fC42-=k20*c04+k21*c14;
417
418 fC33-=k30*c03+k31*c13;
419 fC43-=k30*c04+k31*c14;
420
421 fC44-=k40*c04+k41*c14;
422
423 return kTRUE;
424}
425
c7bafca9 426void
427AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
428 //--------------------------------------------------------------------
429 // External track parameters -> helix parameters
430 // "b" - magnetic field (kG)
431 //--------------------------------------------------------------------
432 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
433
1530f89c 434 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
c7bafca9 435
436 hlx[5]=fX*cs - hlx[0]*sn; // x0
437 hlx[0]=fX*sn + hlx[0]*cs; // y0
438//hlx[1]= // z0
439 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
440//hlx[3]= // tgl
1530f89c 441 hlx[4]=GetC(b); // C
c7bafca9 442}
443
444
445static void Evaluate(const Double_t *h, Double_t t,
446 Double_t r[3], //radius vector
447 Double_t g[3], //first defivatives
448 Double_t gg[3]) //second derivatives
449{
450 //--------------------------------------------------------------------
451 // Calculate position of a point on a track and some derivatives
452 //--------------------------------------------------------------------
453 Double_t phase=h[4]*t+h[2];
454 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
455
456 r[0] = h[5] + (sn - h[6])/h[4];
457 r[1] = h[0] - (cs - h[7])/h[4];
458 r[2] = h[1] + h[3]*t;
459
460 g[0] = cs; g[1]=sn; g[2]=h[3];
461
462 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
463}
464
465Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
466Double_t b, Double_t &xthis, Double_t &xp) const {
467 //------------------------------------------------------------
468 // Returns the (weighed !) distance of closest approach between
469 // this track and the track "p".
470 // Other returned values:
471 // xthis, xt - coordinates of tracks' reference planes at the DCA
472 //-----------------------------------------------------------
473 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
474 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
475 Double_t dx2=dy2;
476
477 //dx2=dy2=dz2=1.;
478
479 Double_t p1[8]; GetHelixParameters(p1,b);
480 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
481 Double_t p2[8]; p->GetHelixParameters(p2,b);
482 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
483
484
485 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
486 Evaluate(p1,t1,r1,g1,gg1);
487 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
488 Evaluate(p2,t2,r2,g2,gg2);
489
490 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
491 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
492
493 Int_t max=27;
494 while (max--) {
495 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
496 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
497 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
498 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
499 (g1[2]*g1[2] - dz*gg1[2])/dz2;
500 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
501 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
502 (g2[2]*g2[2] + dz*gg2[2])/dz2;
503 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
504
505 Double_t det=h11*h22-h12*h12;
506
507 Double_t dt1,dt2;
508 if (TMath::Abs(det)<1.e-33) {
509 //(quasi)singular Hessian
510 dt1=-gt1; dt2=-gt2;
511 } else {
512 dt1=-(gt1*h22 - gt2*h12)/det;
513 dt2=-(h11*gt2 - h12*gt1)/det;
514 }
515
516 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
517
518 //check delta(phase1) ?
519 //check delta(phase2) ?
520
521 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
522 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
523 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
524 AliWarning(" stopped at not a stationary point !");
525 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
526 if (lmb < 0.)
527 AliWarning(" stopped at not a minimum !");
528 break;
529 }
530
531 Double_t dd=dm;
532 for (Int_t div=1 ; ; div*=2) {
533 Evaluate(p1,t1+dt1,r1,g1,gg1);
534 Evaluate(p2,t2+dt2,r2,g2,gg2);
535 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
536 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
537 if (dd<dm) break;
538 dt1*=0.5; dt2*=0.5;
539 if (div>512) {
540 AliWarning(" overshoot !"); break;
541 }
542 }
543 dm=dd;
544
545 t1+=dt1;
546 t2+=dt2;
547
548 }
549
550 if (max<=0) AliWarning(" too many iterations !");
551
552 Double_t cs=TMath::Cos(GetAlpha());
553 Double_t sn=TMath::Sin(GetAlpha());
554 xthis=r1[0]*cs + r1[1]*sn;
555
556 cs=TMath::Cos(p->GetAlpha());
557 sn=TMath::Sin(p->GetAlpha());
558 xp=r2[0]*cs + r2[1]*sn;
559
560 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
561}
562
563Double_t AliExternalTrackParam::
564PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
565 //--------------------------------------------------------------
566 // Propagates this track and the argument track to the position of the
567 // distance of closest approach.
568 // Returns the (weighed !) distance of closest approach.
569 //--------------------------------------------------------------
570 Double_t xthis,xp;
571 Double_t dca=GetDCA(p,b,xthis,xp);
572
573 if (!PropagateTo(xthis,b)) {
574 //AliWarning(" propagation failed !");
575 return 1e+33;
576 }
577
578 if (!p->PropagateTo(xp,b)) {
579 //AliWarning(" propagation failed !";
580 return 1e+33;
581 }
582
583 return dca;
584}
585
586
587
f76701bf 588
589Bool_t AliExternalTrackParam::PropagateToDCA(const AliESDVertex *vtx, Double_t b, Double_t maxd){
590 //
591 // Try to relate this track to the vertex "vtx",
592 // if the (rough) transverse impact parameter is not bigger then "maxd".
593 // Magnetic field is "b" (kG).
594 //
595 // a) The track gets extapolated to the DCA to the vertex.
596 // b) The impact parameters and their covariance matrix are calculated.
597 //
598 // In the case of success, the returned value is kTRUE
599 // (otherwise, it's kFALSE)
600 //
601 Double_t alpha=GetAlpha();
602 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
603 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
604 Double_t xv= vtx->GetXv()*cs + vtx->GetYv()*sn;
29fbcc93 605 Double_t yv=-vtx->GetXv()*sn + vtx->GetYv()*cs;
f76701bf 606 x-=xv; y-=yv;
607
608 //Estimate the impact parameter neglecting the track curvature
609 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp));
610 if (d > maxd) return kFALSE;
611
612 //Propagate to the DCA
613 Double_t crv=0.299792458e-3*b*GetParameter()[4];
614 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
615 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
616
617 x = xv*cs + yv*sn;
618 yv=-xv*sn + yv*cs; xv=x;
619
620 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
29fbcc93 621 return kTRUE;
f76701bf 622}
623
624
625
626
c9ec41e8 627Bool_t Local2GlobalMomentum(Double_t p[3],Double_t alpha) {
628 //----------------------------------------------------------------
629 // This function performs local->global transformation of the
630 // track momentum.
631 // When called, the arguments are:
632 // p[0] = 1/pt of the track;
633 // p[1] = sine of local azim. angle of the track momentum;
634 // p[2] = tangent of the track momentum dip angle;
635 // alpha - rotation angle.
636 // The result is returned as:
637 // p[0] = px
638 // p[1] = py
639 // p[2] = pz
640 // Results for (nearly) straight tracks are meaningless !
641 //----------------------------------------------------------------
e421f556 642 if (TMath::Abs(p[0])<=kAlmost0) return kFALSE;
49d13e89 643 if (TMath::Abs(p[1])> kAlmost1) return kFALSE;
c9ec41e8 644
645 Double_t pt=1./TMath::Abs(p[0]);
646 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha);
647 Double_t r=TMath::Sqrt(1 - p[1]*p[1]);
648 p[0]=pt*(r*cs - p[1]*sn); p[1]=pt*(p[1]*cs + r*sn); p[2]=pt*p[2];
a5e407e9 649
650 return kTRUE;
651}
652
c9ec41e8 653Bool_t Local2GlobalPosition(Double_t r[3],Double_t alpha) {
654 //----------------------------------------------------------------
655 // This function performs local->global transformation of the
656 // track position.
657 // When called, the arguments are:
658 // r[0] = local x
659 // r[1] = local y
660 // r[2] = local z
661 // alpha - rotation angle.
662 // The result is returned as:
663 // r[0] = global x
664 // r[1] = global y
665 // r[2] = global z
666 //----------------------------------------------------------------
667 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha), x=r[0];
668 r[0]=x*cs - r[1]*sn; r[1]=x*sn + r[1]*cs;
a5e407e9 669
a5e407e9 670 return kTRUE;
51ad6848 671}
672
c9ec41e8 673Bool_t AliExternalTrackParam::GetPxPyPz(Double_t *p) const {
674 //---------------------------------------------------------------------
675 // This function returns the global track momentum components
676 // Results for (nearly) straight tracks are meaningless !
677 //---------------------------------------------------------------------
678 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
679 return Local2GlobalMomentum(p,fAlpha);
680}
a5e407e9 681
c9ec41e8 682Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
683 //---------------------------------------------------------------------
684 // This function returns the global track position
685 //---------------------------------------------------------------------
686 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
687 return Local2GlobalPosition(r,fAlpha);
51ad6848 688}
689
c9ec41e8 690Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
691 //---------------------------------------------------------------------
692 // This function returns the global covariance matrix of the track params
693 //
694 // Cov(x,x) ... : cv[0]
695 // Cov(y,x) ... : cv[1] cv[2]
696 // Cov(z,x) ... : cv[3] cv[4] cv[5]
697 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
698 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
699 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
a5e407e9 700 //
c9ec41e8 701 // Results for (nearly) straight tracks are meaningless !
702 //---------------------------------------------------------------------
e421f556 703 if (TMath::Abs(fP[4])<=kAlmost0) {
c9ec41e8 704 for (Int_t i=0; i<21; i++) cv[i]=0.;
705 return kFALSE;
a5e407e9 706 }
49d13e89 707 if (TMath::Abs(fP[2]) > kAlmost1) {
c9ec41e8 708 for (Int_t i=0; i<21; i++) cv[i]=0.;
709 return kFALSE;
710 }
711 Double_t pt=1./TMath::Abs(fP[4]);
712 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
713 Double_t r=TMath::Sqrt(1-fP[2]*fP[2]);
714
715 Double_t m00=-sn, m10=cs;
716 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
717 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
718 Double_t m35=pt, m45=-pt*pt*fP[3];
719
720 cv[0 ] = fC[0]*m00*m00;
721 cv[1 ] = fC[0]*m00*m10;
722 cv[2 ] = fC[0]*m10*m10;
723 cv[3 ] = fC[1]*m00;
724 cv[4 ] = fC[1]*m10;
725 cv[5 ] = fC[2];
726 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
727 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
728 cv[8 ] = fC[4]*m23 + fC[11]*m43;
729 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
730 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
731 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
732 cv[12] = fC[4]*m24 + fC[11]*m44;
733 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
734 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
735 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
736 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
737 cv[17] = fC[7]*m35 + fC[11]*m45;
738 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
739 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
740 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
51ad6848 741
c9ec41e8 742 return kTRUE;
51ad6848 743}
744
51ad6848 745
c9ec41e8 746Bool_t
747AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
748 //---------------------------------------------------------------------
749 // This function returns the global track momentum extrapolated to
750 // the radial position "x" (cm) in the magnetic field "b" (kG)
751 //---------------------------------------------------------------------
c9ec41e8 752 p[0]=fP[4];
1530f89c 753 p[1]=fP[2]+(x-fX)*GetC(b);
c9ec41e8 754 p[2]=fP[3];
755 return Local2GlobalMomentum(p,fAlpha);
51ad6848 756}
757
c9ec41e8 758Bool_t
7cf7bb6c 759AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
760 //---------------------------------------------------------------------
761 // This function returns the local Y-coordinate of the intersection
762 // point between this track and the reference plane "x" (cm).
763 // Magnetic field "b" (kG)
764 //---------------------------------------------------------------------
765 Double_t dx=x-fX;
766 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
767
1530f89c 768 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
7cf7bb6c 769
770 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
771 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
772
773 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
774 y = fP[0] + dx*(f1+f2)/(r1+r2);
775 return kTRUE;
776}
777
778Bool_t
c9ec41e8 779AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
780 //---------------------------------------------------------------------
781 // This function returns the global track position extrapolated to
782 // the radial position "x" (cm) in the magnetic field "b" (kG)
783 //---------------------------------------------------------------------
c9ec41e8 784 Double_t dx=x-fX;
e421f556 785 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
786
1530f89c 787 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
c9ec41e8 788
e421f556 789 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 790 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
c9ec41e8 791
792 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
793 r[0] = x;
794 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
1ce63cae 795 r[2] = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3];//Many thanks to P.Hristov !
c9ec41e8 796 return Local2GlobalPosition(r,fAlpha);
51ad6848 797}
798
edc97986 799//_____________________________________________________________________________
51ad6848 800void AliExternalTrackParam::Print(Option_t* /*option*/) const
801{
802// print the parameters and the covariance matrix
803
804 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
805 printf(" parameters: %12g %12g %12g %12g %12g\n",
c9ec41e8 806 fP[0], fP[1], fP[2], fP[3], fP[4]);
807 printf(" covariance: %12g\n", fC[0]);
808 printf(" %12g %12g\n", fC[1], fC[2]);
809 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
51ad6848 810 printf(" %12g %12g %12g %12g\n",
c9ec41e8 811 fC[6], fC[7], fC[8], fC[9]);
51ad6848 812 printf(" %12g %12g %12g %12g %12g\n",
c9ec41e8 813 fC[10], fC[11], fC[12], fC[13], fC[14]);
51ad6848 814}
5b77d93c 815
c194ba83 816Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
817 //
818 // Get sinus at given x
819 //
1530f89c 820 Double_t crv=GetC(b);
c194ba83 821 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
822 Double_t dx = x-fX;
823 Double_t res = fP[2]+dx*crv;
824 return res;
825}
5b77d93c 826
c194ba83 827Bool_t AliExternalTrackParam::PropagateTo(Double_t xToGo, Double_t b, Double_t mass, Double_t maxStep, Bool_t rotateTo, Double_t maxSnp){
5b77d93c 828 //----------------------------------------------------------------
08df6187 829 //
830 // Very expensive function ! Don't abuse it !
831 //
832 // Propagates this track to the plane X=xk (cm)
833 // in the magnetic field "b" (kG),
5b77d93c 834 // the correction for the material is included
835 //
08df6187 836 // Requires acces to geomanager
5b77d93c 837 //
838 // mass - mass used in propagation - used for energy loss correction
839 // maxStep - maximal step for propagation
840 //----------------------------------------------------------------
841 const Double_t kEpsilon = 0.00001;
842 Double_t xpos = GetX();
843 Double_t dir = (xpos<xToGo) ? 1.:-1.;
844 //
845 while ( (xToGo-xpos)*dir > kEpsilon){
846 Double_t step = dir*TMath::Min(TMath::Abs(xToGo-xpos), maxStep);
847 Double_t x = xpos+step;
848 Double_t xyz0[3],xyz1[3],param[7];
849 GetXYZ(xyz0); //starting global position
08df6187 850 if (!GetXYZAt(x,b,xyz1)) return kFALSE; // no prolongation
20e5d17c 851 xyz1[2]+=kEpsilon; // waiting for bug correction in geo
5b77d93c 852 AliKalmanTrack::MeanMaterialBudget(xyz0,xyz1,param);
c194ba83 853 if (TMath::Abs(GetSnpAt(x,b)) >= maxSnp) return kFALSE;
08df6187 854 if (!PropagateTo(x,b)) return kFALSE;
855
856 Double_t rho=param[0],x0=param[1],distance=param[4];
857 Double_t d=distance*rho/x0;
858
859 if (!CorrectForMaterial(d,x0,mass)) return kFALSE;
5b77d93c 860 if (rotateTo){
c194ba83 861 if (TMath::Abs(fP[2]) >= maxSnp) return kFALSE;
5b77d93c 862 GetXYZ(xyz0); // global position
c194ba83 863 Double_t alphan = TMath::ATan2(xyz0[1], xyz0[0]);
864 //
865 Double_t ca=TMath::Cos(alphan-fAlpha), sa=TMath::Sin(alphan-fAlpha);
866 Double_t sf=fP[2], cf=TMath::Sqrt(1.- fP[2]*fP[2]);
867 Double_t sinNew = sf*ca - cf*sa;
868 if (TMath::Abs(sinNew) >= maxSnp) return kFALSE;
5b77d93c 869 if (!Rotate(alphan)) return kFALSE;
870 }
871 xpos = GetX();
872 }
873 return kTRUE;
874}
875
5b77d93c 876
5b77d93c 877
878