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