Bugfix
[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) :
c9ec41e8 63 fAlpha(track.GetAlpha())
51ad6848 64{
65 //
66 //
c9ec41e8 67 track.GetExternalParameters(fX,fP);
68 track.GetExternalCovariance(fC);
51ad6848 69}
70
51ad6848 71//_____________________________________________________________________________
c9ec41e8 72void AliExternalTrackParam::Set(const AliKalmanTrack& track) {
73 //
74 //
75 fAlpha=track.GetAlpha();
76 track.GetExternalParameters(fX,fP);
77 track.GetExternalCovariance(fC);
51ad6848 78}
79
80//_____________________________________________________________________________
c9ec41e8 81void AliExternalTrackParam::Reset() {
82 fX=fAlpha=0.;
83 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
84 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 85}
86
c9ec41e8 87Double_t AliExternalTrackParam::GetP() const {
88 //---------------------------------------------------------------------
89 // This function returns the track momentum
90 // Results for (nearly) straight tracks are meaningless !
91 //---------------------------------------------------------------------
06fb4a2f 92 if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig;
c9ec41e8 93 return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
51ad6848 94}
95
1d99986f 96Double_t AliExternalTrackParam::Get1P() const {
97 //---------------------------------------------------------------------
98 // This function returns the 1/(track momentum)
99 //---------------------------------------------------------------------
100 return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
101}
102
c9ec41e8 103//_______________________________________________________________________
c7bafca9 104Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
c9ec41e8 105 //------------------------------------------------------------------
106 // This function calculates the transverse impact parameter
107 // with respect to a point with global coordinates (x,y)
108 // in the magnetic field "b" (kG)
109 //------------------------------------------------------------------
5773defd 110 if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
49d13e89 111 Double_t rp4=kB2C*b*fP[4];
c9ec41e8 112
113 Double_t xt=fX, yt=fP[0];
114
115 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
116 Double_t a = x*cs + y*sn;
117 y = -x*sn + y*cs; x=a;
118 xt-=x; yt-=y;
119
120 sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]);
121 a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt);
122 if (rp4<0) a=-a;
123 return a/(1 + TMath::Sqrt(sn*sn + cs*cs));
51ad6848 124}
125
49d13e89 126//_______________________________________________________________________
127Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
128 //------------------------------------------------------------------
129 // This function calculates the transverse impact parameter
130 // with respect to a point with global coordinates (xv,yv)
131 // neglecting the track curvature.
132 //------------------------------------------------------------------
133 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
134 Double_t x= xv*cs + yv*sn;
135 Double_t y=-xv*sn + yv*cs;
136
137 Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]);
138
139 return d;
140}
141
c7bafca9 142Bool_t AliExternalTrackParam::
143CorrectForMaterial(Double_t d, Double_t x0, Double_t mass) {
144 //------------------------------------------------------------------
145 // This function corrects the track parameters for the crossed material
146 // "d" - the thickness (fraction of the radiation length)
147 // "x0" - the radiation length (g/cm^2)
148 // "mass" - the mass of this particle (GeV/c^2)
149 //------------------------------------------------------------------
150 Double_t &fP2=fP[2];
151 Double_t &fP3=fP[3];
152 Double_t &fP4=fP[4];
153
154 Double_t &fC22=fC[5];
155 Double_t &fC33=fC[9];
156 Double_t &fC43=fC[13];
157 Double_t &fC44=fC[14];
158
159 Double_t p2=(1.+ fP3*fP3)/(fP4*fP4);
160 Double_t beta2=p2/(p2 + mass*mass);
161 d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
162
163 //Multiple scattering******************
164 if (d!=0) {
165 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
166 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
167 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
168 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
169 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
170 fC44 += theta2*fP3*fP4*fP3*fP4;
171 }
172
173 //Energy losses************************
8fc1985d 174 if (x0!=0. && beta2<1) {
c7bafca9 175 d*=x0;
176 Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2)*d;
177 if (beta2/(1-beta2)>3.5*3.5)
178 dE=0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2)*d;
179
180 fP4*=(1.- TMath::Sqrt(p2 + mass*mass)/p2*dE);
181 }
182
183 return kTRUE;
184}
185
49d13e89 186Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
187 //------------------------------------------------------------------
188 // Transform this track to the local coord. system rotated
189 // by angle "alpha" (rad) with respect to the global coord. system.
190 //------------------------------------------------------------------
dfcef74c 191 if (TMath::Abs(fP[2]) >= kAlmost1) {
192 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
193 return kFALSE;
194 }
195
49d13e89 196 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
197 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
198
199 Double_t &fP0=fP[0];
200 Double_t &fP2=fP[2];
201 Double_t &fC00=fC[0];
202 Double_t &fC10=fC[1];
203 Double_t &fC20=fC[3];
204 Double_t &fC21=fC[4];
205 Double_t &fC22=fC[5];
206 Double_t &fC30=fC[6];
207 Double_t &fC32=fC[8];
208 Double_t &fC40=fC[10];
209 Double_t &fC42=fC[12];
210
211 Double_t x=fX;
212 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
213 Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
214
dfcef74c 215 Double_t tmp=sf*ca - cf*sa;
216 if (TMath::Abs(tmp) >= kAlmost1) return kFALSE;
217
49d13e89 218 fAlpha = alpha;
219 fX = x*ca + fP0*sa;
220 fP0= -x*sa + fP0*ca;
dfcef74c 221 fP2= tmp;
49d13e89 222
06fb4a2f 223 if (TMath::Abs(cf)<kAlmost0) {
224 AliError(Form("Too small cosine value %f",cf));
225 cf = kAlmost0;
226 }
227
49d13e89 228 Double_t rr=(ca+sf/cf*sa);
229
230 fC00 *= (ca*ca);
231 fC10 *= ca;
232 fC20 *= ca*rr;
233 fC21 *= rr;
234 fC22 *= rr*rr;
235 fC30 *= ca;
236 fC32 *= rr;
237 fC40 *= ca;
238 fC42 *= rr;
239
240 return kTRUE;
241}
242
243Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
244 //----------------------------------------------------------------
245 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
246 //----------------------------------------------------------------
49d13e89 247 Double_t dx=xk-fX;
e421f556 248 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
18ebc5ef 249
250 Double_t crv=kB2C*b*fP[4];
5773defd 251 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
252
49d13e89 253 Double_t f1=fP[2], f2=f1 + crv*dx;
bbefa4c4 254 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 255 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
256
257 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
258 Double_t
259 &fC00=fC[0],
260 &fC10=fC[1], &fC11=fC[2],
261 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
262 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
263 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
264
265 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
266
267 fX=xk;
268 fP0 += dx*(f1+f2)/(r1+r2);
18ebc5ef 269 fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
49d13e89 270 fP2 += dx*crv;
271
272 //f = F - 1
273
274 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
275 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
276 Double_t f12= dx*fP3*f1/(r1*r1*r1);
277 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
278 Double_t f13= dx/r1;
279 Double_t f24= dx; f24*=cc;
280
281 //b = C*ft
282 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
283 Double_t b02=f24*fC40;
284 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
285 Double_t b12=f24*fC41;
286 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
287 Double_t b22=f24*fC42;
288 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
289 Double_t b42=f24*fC44;
290 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
291 Double_t b32=f24*fC43;
292
293 //a = f*b = f*C*ft
294 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
295 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
296 Double_t a22=f24*b42;
297
298 //F*C*Ft = C + (b + bt + a)
299 fC00 += b00 + b00 + a00;
300 fC10 += b10 + b01 + a01;
301 fC20 += b20 + b02 + a02;
302 fC30 += b30;
303 fC40 += b40;
304 fC11 += b11 + b11 + a11;
305 fC21 += b21 + b12 + a12;
306 fC31 += b31;
307 fC41 += b41;
308 fC22 += b22 + b22 + a22;
309 fC32 += b32;
310 fC42 += b42;
311
312 return kTRUE;
313}
314
315Double_t
316AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
317 //----------------------------------------------------------------
318 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
319 //----------------------------------------------------------------
320 Double_t sdd = fC[0] + cov[0];
321 Double_t sdz = fC[1] + cov[1];
322 Double_t szz = fC[2] + cov[2];
323 Double_t det = sdd*szz - sdz*sdz;
324
325 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
326
327 Double_t d = fP[0] - p[0];
328 Double_t z = fP[1] - p[1];
329
330 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
331}
332
333Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
334 //------------------------------------------------------------------
335 // Update the track parameters with the space point "p" having
336 // the covariance matrix "cov"
337 //------------------------------------------------------------------
338 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
339 Double_t
340 &fC00=fC[0],
341 &fC10=fC[1], &fC11=fC[2],
342 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
343 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
344 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
345
346 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
347 r00+=fC00; r01+=fC10; r11+=fC11;
348 Double_t det=r00*r11 - r01*r01;
349
350 if (TMath::Abs(det) < kAlmost0) return kFALSE;
351
352
353 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
354
355 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
356 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
357 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
358 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
359 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
360
361 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
362 Double_t sf=fP2 + k20*dy + k21*dz;
363 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
364
365 fP0 += k00*dy + k01*dz;
366 fP1 += k10*dy + k11*dz;
367 fP2 = sf;
368 fP3 += k30*dy + k31*dz;
369 fP4 += k40*dy + k41*dz;
370
371 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
372 Double_t c12=fC21, c13=fC31, c14=fC41;
373
374 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
375 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
376 fC40-=k00*c04+k01*c14;
377
378 fC11-=k10*c01+k11*fC11;
379 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
380 fC41-=k10*c04+k11*c14;
381
382 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
383 fC42-=k20*c04+k21*c14;
384
385 fC33-=k30*c03+k31*c13;
386 fC43-=k30*c04+k31*c14;
387
388 fC44-=k40*c04+k41*c14;
389
390 return kTRUE;
391}
392
c7bafca9 393void
394AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
395 //--------------------------------------------------------------------
396 // External track parameters -> helix parameters
397 // "b" - magnetic field (kG)
398 //--------------------------------------------------------------------
399 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
400
401 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3]; hlx[4]=fP[4];
402
403 hlx[5]=fX*cs - hlx[0]*sn; // x0
404 hlx[0]=fX*sn + hlx[0]*cs; // y0
405//hlx[1]= // z0
406 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
407//hlx[3]= // tgl
408 hlx[4]=hlx[4]*kB2C*b; // C
409}
410
411
412static void Evaluate(const Double_t *h, Double_t t,
413 Double_t r[3], //radius vector
414 Double_t g[3], //first defivatives
415 Double_t gg[3]) //second derivatives
416{
417 //--------------------------------------------------------------------
418 // Calculate position of a point on a track and some derivatives
419 //--------------------------------------------------------------------
420 Double_t phase=h[4]*t+h[2];
421 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
422
423 r[0] = h[5] + (sn - h[6])/h[4];
424 r[1] = h[0] - (cs - h[7])/h[4];
425 r[2] = h[1] + h[3]*t;
426
427 g[0] = cs; g[1]=sn; g[2]=h[3];
428
429 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
430}
431
432Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
433Double_t b, Double_t &xthis, Double_t &xp) const {
434 //------------------------------------------------------------
435 // Returns the (weighed !) distance of closest approach between
436 // this track and the track "p".
437 // Other returned values:
438 // xthis, xt - coordinates of tracks' reference planes at the DCA
439 //-----------------------------------------------------------
440 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
441 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
442 Double_t dx2=dy2;
443
444 //dx2=dy2=dz2=1.;
445
446 Double_t p1[8]; GetHelixParameters(p1,b);
447 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
448 Double_t p2[8]; p->GetHelixParameters(p2,b);
449 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
450
451
452 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
453 Evaluate(p1,t1,r1,g1,gg1);
454 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
455 Evaluate(p2,t2,r2,g2,gg2);
456
457 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
458 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
459
460 Int_t max=27;
461 while (max--) {
462 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
463 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
464 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
465 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
466 (g1[2]*g1[2] - dz*gg1[2])/dz2;
467 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
468 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
469 (g2[2]*g2[2] + dz*gg2[2])/dz2;
470 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
471
472 Double_t det=h11*h22-h12*h12;
473
474 Double_t dt1,dt2;
475 if (TMath::Abs(det)<1.e-33) {
476 //(quasi)singular Hessian
477 dt1=-gt1; dt2=-gt2;
478 } else {
479 dt1=-(gt1*h22 - gt2*h12)/det;
480 dt2=-(h11*gt2 - h12*gt1)/det;
481 }
482
483 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
484
485 //check delta(phase1) ?
486 //check delta(phase2) ?
487
488 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
489 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
490 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
491 AliWarning(" stopped at not a stationary point !");
492 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
493 if (lmb < 0.)
494 AliWarning(" stopped at not a minimum !");
495 break;
496 }
497
498 Double_t dd=dm;
499 for (Int_t div=1 ; ; div*=2) {
500 Evaluate(p1,t1+dt1,r1,g1,gg1);
501 Evaluate(p2,t2+dt2,r2,g2,gg2);
502 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
503 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
504 if (dd<dm) break;
505 dt1*=0.5; dt2*=0.5;
506 if (div>512) {
507 AliWarning(" overshoot !"); break;
508 }
509 }
510 dm=dd;
511
512 t1+=dt1;
513 t2+=dt2;
514
515 }
516
517 if (max<=0) AliWarning(" too many iterations !");
518
519 Double_t cs=TMath::Cos(GetAlpha());
520 Double_t sn=TMath::Sin(GetAlpha());
521 xthis=r1[0]*cs + r1[1]*sn;
522
523 cs=TMath::Cos(p->GetAlpha());
524 sn=TMath::Sin(p->GetAlpha());
525 xp=r2[0]*cs + r2[1]*sn;
526
527 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
528}
529
530Double_t AliExternalTrackParam::
531PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
532 //--------------------------------------------------------------
533 // Propagates this track and the argument track to the position of the
534 // distance of closest approach.
535 // Returns the (weighed !) distance of closest approach.
536 //--------------------------------------------------------------
537 Double_t xthis,xp;
538 Double_t dca=GetDCA(p,b,xthis,xp);
539
540 if (!PropagateTo(xthis,b)) {
541 //AliWarning(" propagation failed !");
542 return 1e+33;
543 }
544
545 if (!p->PropagateTo(xp,b)) {
546 //AliWarning(" propagation failed !";
547 return 1e+33;
548 }
549
550 return dca;
551}
552
553
554
f76701bf 555
556Bool_t AliExternalTrackParam::PropagateToDCA(const AliESDVertex *vtx, Double_t b, Double_t maxd){
557 //
558 // Try to relate this track to the vertex "vtx",
559 // if the (rough) transverse impact parameter is not bigger then "maxd".
560 // Magnetic field is "b" (kG).
561 //
562 // a) The track gets extapolated to the DCA to the vertex.
563 // b) The impact parameters and their covariance matrix are calculated.
564 //
565 // In the case of success, the returned value is kTRUE
566 // (otherwise, it's kFALSE)
567 //
568 Double_t alpha=GetAlpha();
569 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
570 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
571 Double_t xv= vtx->GetXv()*cs + vtx->GetYv()*sn;
29fbcc93 572 Double_t yv=-vtx->GetXv()*sn + vtx->GetYv()*cs;
f76701bf 573 x-=xv; y-=yv;
574
575 //Estimate the impact parameter neglecting the track curvature
576 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp));
577 if (d > maxd) return kFALSE;
578
579 //Propagate to the DCA
580 Double_t crv=0.299792458e-3*b*GetParameter()[4];
581 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
582 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
583
584 x = xv*cs + yv*sn;
585 yv=-xv*sn + yv*cs; xv=x;
586
587 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
29fbcc93 588 return kTRUE;
f76701bf 589}
590
591
592
593
c9ec41e8 594Bool_t Local2GlobalMomentum(Double_t p[3],Double_t alpha) {
595 //----------------------------------------------------------------
596 // This function performs local->global transformation of the
597 // track momentum.
598 // When called, the arguments are:
599 // p[0] = 1/pt of the track;
600 // p[1] = sine of local azim. angle of the track momentum;
601 // p[2] = tangent of the track momentum dip angle;
602 // alpha - rotation angle.
603 // The result is returned as:
604 // p[0] = px
605 // p[1] = py
606 // p[2] = pz
607 // Results for (nearly) straight tracks are meaningless !
608 //----------------------------------------------------------------
e421f556 609 if (TMath::Abs(p[0])<=kAlmost0) return kFALSE;
49d13e89 610 if (TMath::Abs(p[1])> kAlmost1) return kFALSE;
c9ec41e8 611
612 Double_t pt=1./TMath::Abs(p[0]);
613 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha);
614 Double_t r=TMath::Sqrt(1 - p[1]*p[1]);
615 p[0]=pt*(r*cs - p[1]*sn); p[1]=pt*(p[1]*cs + r*sn); p[2]=pt*p[2];
a5e407e9 616
617 return kTRUE;
618}
619
c9ec41e8 620Bool_t Local2GlobalPosition(Double_t r[3],Double_t alpha) {
621 //----------------------------------------------------------------
622 // This function performs local->global transformation of the
623 // track position.
624 // When called, the arguments are:
625 // r[0] = local x
626 // r[1] = local y
627 // r[2] = local z
628 // alpha - rotation angle.
629 // The result is returned as:
630 // r[0] = global x
631 // r[1] = global y
632 // r[2] = global z
633 //----------------------------------------------------------------
634 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha), x=r[0];
635 r[0]=x*cs - r[1]*sn; r[1]=x*sn + r[1]*cs;
a5e407e9 636
a5e407e9 637 return kTRUE;
51ad6848 638}
639
c9ec41e8 640Bool_t AliExternalTrackParam::GetPxPyPz(Double_t *p) const {
641 //---------------------------------------------------------------------
642 // This function returns the global track momentum components
643 // Results for (nearly) straight tracks are meaningless !
644 //---------------------------------------------------------------------
645 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
646 return Local2GlobalMomentum(p,fAlpha);
647}
a5e407e9 648
c9ec41e8 649Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
650 //---------------------------------------------------------------------
651 // This function returns the global track position
652 //---------------------------------------------------------------------
653 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
654 return Local2GlobalPosition(r,fAlpha);
51ad6848 655}
656
c9ec41e8 657Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
658 //---------------------------------------------------------------------
659 // This function returns the global covariance matrix of the track params
660 //
661 // Cov(x,x) ... : cv[0]
662 // Cov(y,x) ... : cv[1] cv[2]
663 // Cov(z,x) ... : cv[3] cv[4] cv[5]
664 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
665 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
666 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
a5e407e9 667 //
c9ec41e8 668 // Results for (nearly) straight tracks are meaningless !
669 //---------------------------------------------------------------------
e421f556 670 if (TMath::Abs(fP[4])<=kAlmost0) {
c9ec41e8 671 for (Int_t i=0; i<21; i++) cv[i]=0.;
672 return kFALSE;
a5e407e9 673 }
49d13e89 674 if (TMath::Abs(fP[2]) > kAlmost1) {
c9ec41e8 675 for (Int_t i=0; i<21; i++) cv[i]=0.;
676 return kFALSE;
677 }
678 Double_t pt=1./TMath::Abs(fP[4]);
679 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
680 Double_t r=TMath::Sqrt(1-fP[2]*fP[2]);
681
682 Double_t m00=-sn, m10=cs;
683 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
684 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
685 Double_t m35=pt, m45=-pt*pt*fP[3];
686
687 cv[0 ] = fC[0]*m00*m00;
688 cv[1 ] = fC[0]*m00*m10;
689 cv[2 ] = fC[0]*m10*m10;
690 cv[3 ] = fC[1]*m00;
691 cv[4 ] = fC[1]*m10;
692 cv[5 ] = fC[2];
693 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
694 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
695 cv[8 ] = fC[4]*m23 + fC[11]*m43;
696 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
697 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
698 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
699 cv[12] = fC[4]*m24 + fC[11]*m44;
700 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
701 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
702 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
703 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
704 cv[17] = fC[7]*m35 + fC[11]*m45;
705 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
706 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
707 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
51ad6848 708
c9ec41e8 709 return kTRUE;
51ad6848 710}
711
51ad6848 712
c9ec41e8 713Bool_t
714AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
715 //---------------------------------------------------------------------
716 // This function returns the global track momentum extrapolated to
717 // the radial position "x" (cm) in the magnetic field "b" (kG)
718 //---------------------------------------------------------------------
c9ec41e8 719 p[0]=fP[4];
49d13e89 720 p[1]=fP[2]+(x-fX)*fP[4]*b*kB2C;
c9ec41e8 721 p[2]=fP[3];
722 return Local2GlobalMomentum(p,fAlpha);
51ad6848 723}
724
c9ec41e8 725Bool_t
7cf7bb6c 726AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
727 //---------------------------------------------------------------------
728 // This function returns the local Y-coordinate of the intersection
729 // point between this track and the reference plane "x" (cm).
730 // Magnetic field "b" (kG)
731 //---------------------------------------------------------------------
732 Double_t dx=x-fX;
733 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
734
735 Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C;
736
737 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
738 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
739
740 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
741 y = fP[0] + dx*(f1+f2)/(r1+r2);
742 return kTRUE;
743}
744
745Bool_t
c9ec41e8 746AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
747 //---------------------------------------------------------------------
748 // This function returns the global track position extrapolated to
749 // the radial position "x" (cm) in the magnetic field "b" (kG)
750 //---------------------------------------------------------------------
c9ec41e8 751 Double_t dx=x-fX;
e421f556 752 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
753
49d13e89 754 Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C;
c9ec41e8 755
e421f556 756 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 757 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
c9ec41e8 758
759 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
760 r[0] = x;
761 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
762 r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3];
763 return Local2GlobalPosition(r,fAlpha);
51ad6848 764}
765
edc97986 766//_____________________________________________________________________________
51ad6848 767void AliExternalTrackParam::Print(Option_t* /*option*/) const
768{
769// print the parameters and the covariance matrix
770
771 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
772 printf(" parameters: %12g %12g %12g %12g %12g\n",
c9ec41e8 773 fP[0], fP[1], fP[2], fP[3], fP[4]);
774 printf(" covariance: %12g\n", fC[0]);
775 printf(" %12g %12g\n", fC[1], fC[2]);
776 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
51ad6848 777 printf(" %12g %12g %12g %12g\n",
c9ec41e8 778 fC[6], fC[7], fC[8], fC[9]);
51ad6848 779 printf(" %12g %12g %12g %12g %12g\n",
c9ec41e8 780 fC[10], fC[11], fC[12], fC[13], fC[14]);
51ad6848 781}
5b77d93c 782
c194ba83 783Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
784 //
785 // Get sinus at given x
786 //
787 Double_t crv=kB2C*b*fP[4];
788 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
789 Double_t dx = x-fX;
790 Double_t res = fP[2]+dx*crv;
791 return res;
792}
5b77d93c 793
c194ba83 794Bool_t AliExternalTrackParam::PropagateTo(Double_t xToGo, Double_t b, Double_t mass, Double_t maxStep, Bool_t rotateTo, Double_t maxSnp){
5b77d93c 795 //----------------------------------------------------------------
08df6187 796 //
797 // Very expensive function ! Don't abuse it !
798 //
799 // Propagates this track to the plane X=xk (cm)
800 // in the magnetic field "b" (kG),
5b77d93c 801 // the correction for the material is included
802 //
08df6187 803 // Requires acces to geomanager
5b77d93c 804 //
805 // mass - mass used in propagation - used for energy loss correction
806 // maxStep - maximal step for propagation
807 //----------------------------------------------------------------
808 const Double_t kEpsilon = 0.00001;
809 Double_t xpos = GetX();
810 Double_t dir = (xpos<xToGo) ? 1.:-1.;
811 //
812 while ( (xToGo-xpos)*dir > kEpsilon){
813 Double_t step = dir*TMath::Min(TMath::Abs(xToGo-xpos), maxStep);
814 Double_t x = xpos+step;
815 Double_t xyz0[3],xyz1[3],param[7];
816 GetXYZ(xyz0); //starting global position
08df6187 817 if (!GetXYZAt(x,b,xyz1)) return kFALSE; // no prolongation
20e5d17c 818 xyz1[2]+=kEpsilon; // waiting for bug correction in geo
5b77d93c 819 AliKalmanTrack::MeanMaterialBudget(xyz0,xyz1,param);
c194ba83 820 if (TMath::Abs(GetSnpAt(x,b)) >= maxSnp) return kFALSE;
08df6187 821 if (!PropagateTo(x,b)) return kFALSE;
822
823 Double_t rho=param[0],x0=param[1],distance=param[4];
824 Double_t d=distance*rho/x0;
825
826 if (!CorrectForMaterial(d,x0,mass)) return kFALSE;
5b77d93c 827 if (rotateTo){
c194ba83 828 if (TMath::Abs(fP[2]) >= maxSnp) return kFALSE;
5b77d93c 829 GetXYZ(xyz0); // global position
c194ba83 830 Double_t alphan = TMath::ATan2(xyz0[1], xyz0[0]);
831 //
832 Double_t ca=TMath::Cos(alphan-fAlpha), sa=TMath::Sin(alphan-fAlpha);
833 Double_t sf=fP[2], cf=TMath::Sqrt(1.- fP[2]*fP[2]);
834 Double_t sinNew = sf*ca - cf*sa;
835 if (TMath::Abs(sinNew) >= maxSnp) return kFALSE;
5b77d93c 836 if (!Rotate(alphan)) return kFALSE;
837 }
838 xpos = GetX();
839 }
840 return kTRUE;
841}
842
5b77d93c 843
5b77d93c 844
845