1 /**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
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 **************************************************************************/
18 ///////////////////////////////////////////////////////////////////////////////
20 // Implementation of the external track parameterisation class. //
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 //
26 // Origin: I.Belikov, CERN, Jouri.Belikov@cern.ch //
27 ///////////////////////////////////////////////////////////////////////////////
28 #include "AliExternalTrackParam.h"
29 #include "AliKalmanTrack.h"
30 #include "AliESDVertex.h"
33 ClassImp(AliExternalTrackParam)
35 //_____________________________________________________________________________
36 AliExternalTrackParam::AliExternalTrackParam() :
41 // default constructor
43 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
44 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
47 //_____________________________________________________________________________
48 AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha,
49 const Double_t param[5],
50 const Double_t covar[15]) :
55 // create external track parameters from given arguments
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];
61 //_____________________________________________________________________________
62 AliExternalTrackParam::AliExternalTrackParam(const AliKalmanTrack& track) :
63 fAlpha(track.GetAlpha())
67 track.GetExternalParameters(fX,fP);
68 track.GetExternalCovariance(fC);
71 //_____________________________________________________________________________
72 void AliExternalTrackParam::Set(const AliKalmanTrack& track) {
75 fAlpha=track.GetAlpha();
76 track.GetExternalParameters(fX,fP);
77 track.GetExternalCovariance(fC);
80 //_____________________________________________________________________________
81 void AliExternalTrackParam::Reset() {
83 // Resets all the parameters to 0
86 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
87 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
90 Double_t AliExternalTrackParam::GetP() const {
91 //---------------------------------------------------------------------
92 // This function returns the track momentum
93 // Results for (nearly) straight tracks are meaningless !
94 //---------------------------------------------------------------------
95 if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig;
96 return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
99 Double_t AliExternalTrackParam::Get1P() const {
100 //---------------------------------------------------------------------
101 // This function returns the 1/(track momentum)
102 //---------------------------------------------------------------------
103 return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
106 //_______________________________________________________________________
107 Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
108 //------------------------------------------------------------------
109 // This function calculates the transverse impact parameter
110 // with respect to a point with global coordinates (x,y)
111 // in the magnetic field "b" (kG)
112 //------------------------------------------------------------------
113 if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
114 Double_t rp4=GetC(b);
116 Double_t xt=fX, yt=fP[0];
118 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
119 Double_t a = x*cs + y*sn;
120 y = -x*sn + y*cs; x=a;
123 sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]);
124 a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt);
125 return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
128 //_______________________________________________________________________
129 void AliExternalTrackParam::
130 GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const {
131 //------------------------------------------------------------------
132 // This function calculates the transverse and longitudinal impact parameters
133 // with respect to a point with global coordinates (x,y)
134 // in the magnetic field "b" (kG)
135 //------------------------------------------------------------------
136 Double_t f1 = fP[2], r1 = TMath::Sqrt(1. - f1*f1);
137 Double_t xt=fX, yt=fP[0];
138 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
139 Double_t a = x*cs + y*sn;
140 y = -x*sn + y*cs; x=a;
143 Double_t rp4=GetC(b);
144 if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) {
145 dz[0] = -(xt*f1 - yt*r1);
146 dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z;
150 sn=rp4*xt - f1; cs=rp4*yt + r1;
151 a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt);
152 Double_t rr=TMath::Sqrt(sn*sn + cs*cs);
154 Double_t f2 = -sn/rr, r2 = TMath::Sqrt(1. - f2*f2);
155 dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z;
158 //_______________________________________________________________________
159 Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
160 //------------------------------------------------------------------
161 // This function calculates the transverse impact parameter
162 // with respect to a point with global coordinates (xv,yv)
163 // neglecting the track curvature.
164 //------------------------------------------------------------------
165 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
166 Double_t x= xv*cs + yv*sn;
167 Double_t y=-xv*sn + yv*cs;
169 Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]);
174 Bool_t AliExternalTrackParam::
175 CorrectForMaterial(Double_t d, Double_t x0, Double_t mass) {
176 //------------------------------------------------------------------
177 // This function corrects the track parameters for the crossed material
178 // "d" - the thickness (fraction of the radiation length)
179 // "x0" - the radiation length (g/cm^2)
180 // "mass" - the mass of this particle (GeV/c^2)
181 //------------------------------------------------------------------
186 Double_t &fC22=fC[5];
187 Double_t &fC33=fC[9];
188 Double_t &fC43=fC[13];
189 Double_t &fC44=fC[14];
191 Double_t p2=(1.+ fP3*fP3)/(fP4*fP4);
192 Double_t beta2=p2/(p2 + mass*mass);
193 d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
195 //Multiple scattering******************
197 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
198 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
199 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
200 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
201 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
202 fC44 += theta2*fP3*fP4*fP3*fP4;
205 //Energy losses************************
206 if (x0!=0. && beta2<1) {
208 Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2)*d;
209 if (beta2/(1-beta2)>3.5*3.5)
210 dE=0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2)*d;
212 fP4*=(1.- TMath::Sqrt(p2 + mass*mass)/p2*dE);
218 Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
219 //------------------------------------------------------------------
220 // Transform this track to the local coord. system rotated
221 // by angle "alpha" (rad) with respect to the global coord. system.
222 //------------------------------------------------------------------
223 if (TMath::Abs(fP[2]) >= kAlmost1) {
224 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
228 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
229 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
233 Double_t &fC00=fC[0];
234 Double_t &fC10=fC[1];
235 Double_t &fC20=fC[3];
236 Double_t &fC21=fC[4];
237 Double_t &fC22=fC[5];
238 Double_t &fC30=fC[6];
239 Double_t &fC32=fC[8];
240 Double_t &fC40=fC[10];
241 Double_t &fC42=fC[12];
244 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
245 Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
247 Double_t tmp=sf*ca - cf*sa;
248 if (TMath::Abs(tmp) >= kAlmost1) return kFALSE;
255 if (TMath::Abs(cf)<kAlmost0) {
256 AliError(Form("Too small cosine value %f",cf));
260 Double_t rr=(ca+sf/cf*sa);
275 Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
276 //----------------------------------------------------------------
277 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
278 //----------------------------------------------------------------
280 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
282 Double_t crv=GetC(b);
283 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
285 Double_t f1=fP[2], f2=f1 + crv*dx;
286 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
287 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
289 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
292 &fC10=fC[1], &fC11=fC[2],
293 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
294 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
295 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
297 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
300 fP0 += dx*(f1+f2)/(r1+r2);
301 fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
306 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
307 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
308 Double_t f12= dx*fP3*f1/(r1*r1*r1);
309 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
311 Double_t f24= dx; f24*=cc;
314 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
315 Double_t b02=f24*fC40;
316 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
317 Double_t b12=f24*fC41;
318 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
319 Double_t b22=f24*fC42;
320 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
321 Double_t b42=f24*fC44;
322 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
323 Double_t b32=f24*fC43;
326 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
327 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
328 Double_t a22=f24*b42;
330 //F*C*Ft = C + (b + bt + a)
331 fC00 += b00 + b00 + a00;
332 fC10 += b10 + b01 + a01;
333 fC20 += b20 + b02 + a02;
336 fC11 += b11 + b11 + a11;
337 fC21 += b21 + b12 + a12;
340 fC22 += b22 + b22 + a22;
348 AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
349 //----------------------------------------------------------------
350 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
351 //----------------------------------------------------------------
352 Double_t sdd = fC[0] + cov[0];
353 Double_t sdz = fC[1] + cov[1];
354 Double_t szz = fC[2] + cov[2];
355 Double_t det = sdd*szz - sdz*sdz;
357 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
359 Double_t d = fP[0] - p[0];
360 Double_t z = fP[1] - p[1];
362 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
365 Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
366 //------------------------------------------------------------------
367 // Update the track parameters with the space point "p" having
368 // the covariance matrix "cov"
369 //------------------------------------------------------------------
370 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
373 &fC10=fC[1], &fC11=fC[2],
374 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
375 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
376 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
378 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
379 r00+=fC00; r01+=fC10; r11+=fC11;
380 Double_t det=r00*r11 - r01*r01;
382 if (TMath::Abs(det) < kAlmost0) return kFALSE;
385 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
387 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
388 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
389 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
390 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
391 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
393 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
394 Double_t sf=fP2 + k20*dy + k21*dz;
395 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
397 fP0 += k00*dy + k01*dz;
398 fP1 += k10*dy + k11*dz;
400 fP3 += k30*dy + k31*dz;
401 fP4 += k40*dy + k41*dz;
403 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
404 Double_t c12=fC21, c13=fC31, c14=fC41;
406 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
407 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
408 fC40-=k00*c04+k01*c14;
410 fC11-=k10*c01+k11*fC11;
411 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
412 fC41-=k10*c04+k11*c14;
414 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
415 fC42-=k20*c04+k21*c14;
417 fC33-=k30*c03+k31*c13;
418 fC43-=k30*c04+k31*c14;
420 fC44-=k40*c04+k41*c14;
426 AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
427 //--------------------------------------------------------------------
428 // External track parameters -> helix parameters
429 // "b" - magnetic field (kG)
430 //--------------------------------------------------------------------
431 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
433 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
435 hlx[5]=fX*cs - hlx[0]*sn; // x0
436 hlx[0]=fX*sn + hlx[0]*cs; // y0
438 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
444 static void Evaluate(const Double_t *h, Double_t t,
445 Double_t r[3], //radius vector
446 Double_t g[3], //first defivatives
447 Double_t gg[3]) //second derivatives
449 //--------------------------------------------------------------------
450 // Calculate position of a point on a track and some derivatives
451 //--------------------------------------------------------------------
452 Double_t phase=h[4]*t+h[2];
453 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
455 r[0] = h[5] + (sn - h[6])/h[4];
456 r[1] = h[0] - (cs - h[7])/h[4];
457 r[2] = h[1] + h[3]*t;
459 g[0] = cs; g[1]=sn; g[2]=h[3];
461 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
464 Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
465 Double_t b, Double_t &xthis, Double_t &xp) const {
466 //------------------------------------------------------------
467 // Returns the (weighed !) distance of closest approach between
468 // this track and the track "p".
469 // Other returned values:
470 // xthis, xt - coordinates of tracks' reference planes at the DCA
471 //-----------------------------------------------------------
472 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
473 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
478 Double_t p1[8]; GetHelixParameters(p1,b);
479 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
480 Double_t p2[8]; p->GetHelixParameters(p2,b);
481 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
484 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
485 Evaluate(p1,t1,r1,g1,gg1);
486 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
487 Evaluate(p2,t2,r2,g2,gg2);
489 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
490 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
494 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
495 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
496 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
497 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
498 (g1[2]*g1[2] - dz*gg1[2])/dz2;
499 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
500 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
501 (g2[2]*g2[2] + dz*gg2[2])/dz2;
502 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
504 Double_t det=h11*h22-h12*h12;
507 if (TMath::Abs(det)<1.e-33) {
508 //(quasi)singular Hessian
511 dt1=-(gt1*h22 - gt2*h12)/det;
512 dt2=-(h11*gt2 - h12*gt1)/det;
515 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
517 //check delta(phase1) ?
518 //check delta(phase2) ?
520 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
521 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
522 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
523 AliWarning(" stopped at not a stationary point !");
524 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
526 AliWarning(" stopped at not a minimum !");
531 for (Int_t div=1 ; ; div*=2) {
532 Evaluate(p1,t1+dt1,r1,g1,gg1);
533 Evaluate(p2,t2+dt2,r2,g2,gg2);
534 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
535 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
539 AliWarning(" overshoot !"); break;
549 if (max<=0) AliWarning(" too many iterations !");
551 Double_t cs=TMath::Cos(GetAlpha());
552 Double_t sn=TMath::Sin(GetAlpha());
553 xthis=r1[0]*cs + r1[1]*sn;
555 cs=TMath::Cos(p->GetAlpha());
556 sn=TMath::Sin(p->GetAlpha());
557 xp=r2[0]*cs + r2[1]*sn;
559 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
562 Double_t AliExternalTrackParam::
563 PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
564 //--------------------------------------------------------------
565 // Propagates this track and the argument track to the position of the
566 // distance of closest approach.
567 // Returns the (weighed !) distance of closest approach.
568 //--------------------------------------------------------------
570 Double_t dca=GetDCA(p,b,xthis,xp);
572 if (!PropagateTo(xthis,b)) {
573 //AliWarning(" propagation failed !");
577 if (!p->PropagateTo(xp,b)) {
578 //AliWarning(" propagation failed !";
588 Bool_t AliExternalTrackParam::PropagateToDCA(const AliESDVertex *vtx, Double_t b, Double_t maxd){
590 // Try to relate this track to the vertex "vtx",
591 // if the (rough) transverse impact parameter is not bigger then "maxd".
592 // Magnetic field is "b" (kG).
594 // a) The track gets extapolated to the DCA to the vertex.
595 // b) The impact parameters and their covariance matrix are calculated.
597 // In the case of success, the returned value is kTRUE
598 // (otherwise, it's kFALSE)
600 Double_t alpha=GetAlpha();
601 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
602 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
603 Double_t xv= vtx->GetXv()*cs + vtx->GetYv()*sn;
604 Double_t yv=-vtx->GetXv()*sn + vtx->GetYv()*cs;
607 //Estimate the impact parameter neglecting the track curvature
608 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp));
609 if (d > maxd) return kFALSE;
611 //Propagate to the DCA
612 Double_t crv=0.299792458e-3*b*GetParameter()[4];
613 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
614 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
617 yv=-xv*sn + yv*cs; xv=x;
619 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
626 Bool_t Local2GlobalMomentum(Double_t p[3],Double_t alpha) {
627 //----------------------------------------------------------------
628 // This function performs local->global transformation of the
630 // When called, the arguments are:
631 // p[0] = 1/pt of the track;
632 // p[1] = sine of local azim. angle of the track momentum;
633 // p[2] = tangent of the track momentum dip angle;
634 // alpha - rotation angle.
635 // The result is returned as:
639 // Results for (nearly) straight tracks are meaningless !
640 //----------------------------------------------------------------
641 if (TMath::Abs(p[0])<=kAlmost0) return kFALSE;
642 if (TMath::Abs(p[1])> kAlmost1) return kFALSE;
644 Double_t pt=1./TMath::Abs(p[0]);
645 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha);
646 Double_t r=TMath::Sqrt(1 - p[1]*p[1]);
647 p[0]=pt*(r*cs - p[1]*sn); p[1]=pt*(p[1]*cs + r*sn); p[2]=pt*p[2];
652 Bool_t Local2GlobalPosition(Double_t r[3],Double_t alpha) {
653 //----------------------------------------------------------------
654 // This function performs local->global transformation of the
656 // When called, the arguments are:
660 // alpha - rotation angle.
661 // The result is returned as:
665 //----------------------------------------------------------------
666 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha), x=r[0];
667 r[0]=x*cs - r[1]*sn; r[1]=x*sn + r[1]*cs;
672 Bool_t AliExternalTrackParam::GetPxPyPz(Double_t *p) const {
673 //---------------------------------------------------------------------
674 // This function returns the global track momentum components
675 // Results for (nearly) straight tracks are meaningless !
676 //---------------------------------------------------------------------
677 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
678 return Local2GlobalMomentum(p,fAlpha);
681 Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
682 //---------------------------------------------------------------------
683 // This function returns the global track position
684 //---------------------------------------------------------------------
685 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
686 return Local2GlobalPosition(r,fAlpha);
689 Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
690 //---------------------------------------------------------------------
691 // This function returns the global covariance matrix of the track params
693 // Cov(x,x) ... : cv[0]
694 // Cov(y,x) ... : cv[1] cv[2]
695 // Cov(z,x) ... : cv[3] cv[4] cv[5]
696 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
697 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
698 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
700 // Results for (nearly) straight tracks are meaningless !
701 //---------------------------------------------------------------------
702 if (TMath::Abs(fP[4])<=kAlmost0) {
703 for (Int_t i=0; i<21; i++) cv[i]=0.;
706 if (TMath::Abs(fP[2]) > kAlmost1) {
707 for (Int_t i=0; i<21; i++) cv[i]=0.;
710 Double_t pt=1./TMath::Abs(fP[4]);
711 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
712 Double_t r=TMath::Sqrt(1-fP[2]*fP[2]);
714 Double_t m00=-sn, m10=cs;
715 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
716 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
717 Double_t m35=pt, m45=-pt*pt*fP[3];
719 cv[0 ] = fC[0]*m00*m00;
720 cv[1 ] = fC[0]*m00*m10;
721 cv[2 ] = fC[0]*m10*m10;
725 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
726 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
727 cv[8 ] = fC[4]*m23 + fC[11]*m43;
728 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
729 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
730 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
731 cv[12] = fC[4]*m24 + fC[11]*m44;
732 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
733 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
734 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
735 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
736 cv[17] = fC[7]*m35 + fC[11]*m45;
737 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
738 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
739 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
746 AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
747 //---------------------------------------------------------------------
748 // This function returns the global track momentum extrapolated to
749 // the radial position "x" (cm) in the magnetic field "b" (kG)
750 //---------------------------------------------------------------------
752 p[1]=fP[2]+(x-fX)*GetC(b);
754 return Local2GlobalMomentum(p,fAlpha);
758 AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
759 //---------------------------------------------------------------------
760 // This function returns the local Y-coordinate of the intersection
761 // point between this track and the reference plane "x" (cm).
762 // Magnetic field "b" (kG)
763 //---------------------------------------------------------------------
765 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
767 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
769 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
770 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
772 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
773 y = fP[0] + dx*(f1+f2)/(r1+r2);
778 AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
779 //---------------------------------------------------------------------
780 // This function returns the global track position extrapolated to
781 // the radial position "x" (cm) in the magnetic field "b" (kG)
782 //---------------------------------------------------------------------
784 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
786 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
788 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
789 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
791 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
793 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
794 r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3];
795 return Local2GlobalPosition(r,fAlpha);
798 //_____________________________________________________________________________
799 void AliExternalTrackParam::Print(Option_t* /*option*/) const
801 // print the parameters and the covariance matrix
803 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
804 printf(" parameters: %12g %12g %12g %12g %12g\n",
805 fP[0], fP[1], fP[2], fP[3], fP[4]);
806 printf(" covariance: %12g\n", fC[0]);
807 printf(" %12g %12g\n", fC[1], fC[2]);
808 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
809 printf(" %12g %12g %12g %12g\n",
810 fC[6], fC[7], fC[8], fC[9]);
811 printf(" %12g %12g %12g %12g %12g\n",
812 fC[10], fC[11], fC[12], fC[13], fC[14]);
815 Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
817 // Get sinus at given x
819 Double_t crv=GetC(b);
820 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
822 Double_t res = fP[2]+dx*crv;
826 Bool_t AliExternalTrackParam::PropagateTo(Double_t xToGo, Double_t b, Double_t mass, Double_t maxStep, Bool_t rotateTo, Double_t maxSnp){
827 //----------------------------------------------------------------
829 // Very expensive function ! Don't abuse it !
831 // Propagates this track to the plane X=xk (cm)
832 // in the magnetic field "b" (kG),
833 // the correction for the material is included
835 // Requires acces to geomanager
837 // mass - mass used in propagation - used for energy loss correction
838 // maxStep - maximal step for propagation
839 //----------------------------------------------------------------
840 const Double_t kEpsilon = 0.00001;
841 Double_t xpos = GetX();
842 Double_t dir = (xpos<xToGo) ? 1.:-1.;
844 while ( (xToGo-xpos)*dir > kEpsilon){
845 Double_t step = dir*TMath::Min(TMath::Abs(xToGo-xpos), maxStep);
846 Double_t x = xpos+step;
847 Double_t xyz0[3],xyz1[3],param[7];
848 GetXYZ(xyz0); //starting global position
849 if (!GetXYZAt(x,b,xyz1)) return kFALSE; // no prolongation
850 xyz1[2]+=kEpsilon; // waiting for bug correction in geo
851 AliKalmanTrack::MeanMaterialBudget(xyz0,xyz1,param);
852 if (TMath::Abs(GetSnpAt(x,b)) >= maxSnp) return kFALSE;
853 if (!PropagateTo(x,b)) return kFALSE;
855 Double_t rho=param[0],x0=param[1],distance=param[4];
856 Double_t d=distance*rho/x0;
858 if (!CorrectForMaterial(d,x0,mass)) return kFALSE;
860 if (TMath::Abs(fP[2]) >= maxSnp) return kFALSE;
861 GetXYZ(xyz0); // global position
862 Double_t alphan = TMath::ATan2(xyz0[1], xyz0[0]);
864 Double_t ca=TMath::Cos(alphan-fAlpha), sa=TMath::Sin(alphan-fAlpha);
865 Double_t sf=fP[2], cf=TMath::Sqrt(1.- fP[2]*fP[2]);
866 Double_t sinNew = sf*ca - cf*sa;
867 if (TMath::Abs(sinNew) >= maxSnp) return kFALSE;
868 if (!Rotate(alphan)) return kFALSE;