--- /dev/null
+/**************************************************************************
+ * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
+ * *
+ * Author: The ALICE Off-line Project. *
+ * Contributors are mentioned in the code where appropriate. *
+ * *
+ * Permission to use, copy, modify and distribute this software and its *
+ * documentation strictly for non-commercial purposes is hereby granted *
+ * without fee, provided that the above copyright notice appears in all *
+ * copies and that both the copyright notice and this permission notice *
+ * appear in the supporting documentation. The authors make no claims *
+ * about the suitability of this software for any purpose. It is *
+ * provided "as is" without express or implied warranty. *
+ **************************************************************************/
+
+/* $Id$ */
+
+///////////////////////////////////////////////////
+//
+// Tools
+// for
+// track
+// extrapolation
+// in
+// ALICE
+// dimuon
+// spectrometer
+//
+///////////////////////////////////////////////////
+
+#include <Riostream.h>
+
+#include "AliMUONTrackExtrap.h"
+#include "AliMUONTrackParam.h"
+#include "AliMUONConstants.h"
+#include "AliMagF.h"
+#include "AliLog.h"
+#include "AliTracker.h"
+
+ClassImp(AliMUONTrackExtrap) // Class implementation in ROOT context
+
+const AliMagF* AliMUONTrackExtrap::fgkField = 0x0;
+
+ //__________________________________________________________________________
+void AliMUONTrackExtrap::ExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
+{
+ /// Track parameter extrapolation to the plane at "Z".
+ /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
+ if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z
+ Double_t forwardBackward; // +1 if forward, -1 if backward
+ if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
+ else forwardBackward = -1.0;
+ Double_t vGeant3[7], vGeant3New[7]; // 7 in parameter ????
+ Int_t iGeant3, stepNumber;
+ Int_t maxStepNumber = 5000; // in parameter ????
+ // For safety: return kTRUE or kFALSE ????
+ // Parameter vector for calling EXTRAP_ONESTEP
+ SetGeant3ParametersFromTrackParam(trackParam, vGeant3, forwardBackward);
+ // sign of charge (sign of fInverseBendingMomentum if forward motion)
+ // must be changed if backward extrapolation
+ Double_t chargeExtrap = forwardBackward *
+ TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
+ Double_t stepLength = 6.0; // in parameter ????
+ // Extrapolation loop
+ stepNumber = 0;
+ while (((-forwardBackward * (vGeant3[2] - zEnd)) <= 0.0) && // spectro. z<0
+ (stepNumber < maxStepNumber)) {
+ stepNumber++;
+ // Option for switching between helix and Runge-Kutta ????
+ //ExtrapOneStepRungekutta(chargeExtrap, stepLength, vGeant3, vGeant3New);
+ ExtrapOneStepHelix(chargeExtrap, stepLength, vGeant3, vGeant3New);
+ if ((-forwardBackward * (vGeant3New[2] - zEnd)) > 0.0) break; // one is beyond Z spectro. z<0
+ // better use TArray ????
+ for (iGeant3 = 0; iGeant3 < 7; iGeant3++)
+ {vGeant3[iGeant3] = vGeant3New[iGeant3];}
+ }
+ // check maxStepNumber ????
+ // Interpolation back to exact Z (2nd order)
+ // should be in function ???? using TArray ????
+ Double_t dZ12 = vGeant3New[2] - vGeant3[2]; // 1->2
+ if (TMath::Abs(dZ12) > 0) {
+ Double_t dZ1i = zEnd - vGeant3[2]; // 1-i
+ Double_t dZi2 = vGeant3New[2] - zEnd; // i->2
+ Double_t xPrime = (vGeant3New[0] - vGeant3[0]) / dZ12;
+ Double_t xSecond = ((vGeant3New[3] / vGeant3New[5]) - (vGeant3[3] / vGeant3[5])) / dZ12;
+ Double_t yPrime = (vGeant3New[1] - vGeant3[1]) / dZ12;
+ Double_t ySecond = ((vGeant3New[4] / vGeant3New[5]) - (vGeant3[4] / vGeant3[5])) / dZ12;
+ vGeant3[0] = vGeant3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X
+ vGeant3[1] = vGeant3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y
+ vGeant3[2] = zEnd; // Z
+ Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i);
+ Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i);
+ // (PX, PY, PZ)/PTOT assuming forward motion
+ vGeant3[5] =
+ 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT
+ vGeant3[3] = xPrimeI * vGeant3[5]; // PX/PTOT
+ vGeant3[4] = yPrimeI * vGeant3[5]; // PY/PTOT
+ } else {
+ cout<<"W-AliMUONTrackExtrap::ExtrapToZ: Extrap. to Z not reached, Z = "<<zEnd<<endl;
+ }
+ // Track parameters from Geant3 parameters,
+ // with charge back for forward motion
+ SetTrackParamFromGeant3Parameters(vGeant3, chargeExtrap * forwardBackward, trackParam);
+}
+
+ //__________________________________________________________________________
+void AliMUONTrackExtrap::SetGeant3ParametersFromTrackParam(AliMUONTrackParam* trackParam, Double_t *vGeant3, Double_t forwardBackward)
+{
+ /// Set vector of Geant3 parameters pointed to by "vGeant3" from track parameters in trackParam.
+ /// Since AliMUONTrackParam is only geometry, one uses "forwardBackward"
+ /// to know whether the particle is going forward (+1) or backward (-1).
+ vGeant3[0] = trackParam->GetNonBendingCoor(); // X
+ vGeant3[1] = trackParam->GetBendingCoor(); // Y
+ vGeant3[2] = trackParam->GetZ(); // Z
+ Double_t pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum());
+ Double_t pZ = pYZ / TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope());
+ vGeant3[6] = TMath::Sqrt(pYZ * pYZ + pZ * pZ * trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()); // PTOT
+ vGeant3[5] = -forwardBackward * pZ / vGeant3[6]; // PZ/PTOT spectro. z<0
+ vGeant3[3] = trackParam->GetNonBendingSlope() * vGeant3[5]; // PX/PTOT
+ vGeant3[4] = trackParam->GetBendingSlope() * vGeant3[5]; // PY/PTOT
+}
+
+ //__________________________________________________________________________
+void AliMUONTrackExtrap::SetTrackParamFromGeant3Parameters(Double_t *vGeant3, Double_t charge, AliMUONTrackParam* trackParam)
+{
+ /// Set track parameters in trackParam from Geant3 parameters pointed to by "vGeant3",
+ /// assumed to be calculated for forward motion in Z.
+ /// "InverseBendingMomentum" is signed with "charge".
+ trackParam->SetNonBendingCoor(vGeant3[0]); // X
+ trackParam->SetBendingCoor(vGeant3[1]); // Y
+ trackParam->SetZ(vGeant3[2]); // Z
+ Double_t pYZ = vGeant3[6] * TMath::Sqrt(1.0 - vGeant3[3] * vGeant3[3]);
+ trackParam->SetInverseBendingMomentum(charge/pYZ);
+ trackParam->SetBendingSlope(vGeant3[4]/vGeant3[5]);
+ trackParam->SetNonBendingSlope(vGeant3[3]/vGeant3[5]);
+}
+
+ //__________________________________________________________________________
+void AliMUONTrackExtrap::ExtrapToStation(AliMUONTrackParam* trackParamIn, Int_t station, AliMUONTrackParam *trackParamOut)
+{
+ /// Track parameters extrapolated from "trackParamIn" to both chambers of the station(0..) "station"
+ /// are returned in the array (dimension 2) of track parameters pointed to by "TrackParamOut"
+ /// (index 0 and 1 for first and second chambers).
+ Double_t extZ[2], z1, z2;
+ Int_t i1 = -1, i2 = -1; // = -1 to avoid compilation warnings
+ // range of station to be checked ????
+ z1 = AliMUONConstants::DefaultChamberZ(2 * station);
+ z2 = AliMUONConstants::DefaultChamberZ(2 * station + 1);
+ // First and second Z to extrapolate at
+ if ((z1 > trackParamIn->GetZ()) && (z2 > trackParamIn->GetZ())) {i1 = 0; i2 = 1;}
+ else if ((z1 < trackParamIn->GetZ()) && (z2 < trackParamIn->GetZ())) {i1 = 1; i2 = 0;}
+ else {
+ cout<<"E-AliMUONTrackExtrap::ExtrapToStationAliError: Starting Z ("<<trackParamIn->GetZ()
+ <<") in between z1 ("<<z1<<") and z2 ("<<z2<<") of station(0..)"<<station<<endl;
+ exit(-1);
+ }
+ extZ[i1] = z1;
+ extZ[i2] = z2;
+ // copy of track parameters
+ trackParamOut[i1] = *trackParamIn;
+ // first extrapolation
+ ExtrapToZ(&(trackParamOut[i1]),extZ[0]);
+ trackParamOut[i2] = trackParamOut[i1];
+ // second extrapolation
+ ExtrapToZ(&(trackParamOut[i2]),extZ[1]);
+ return;
+}
+
+ //__________________________________________________________________________
+void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx)
+{
+ /// Extrapolation to the vertex.
+ /// Returns the track parameters resulting from the extrapolation in the current TrackParam.
+ /// Changes parameters according to Branson correction through the absorber
+
+ Double_t zAbsorber = -503.0; // to be coherent with the Geant absorber geometry !!!!
+ // spectro. (z<0)
+ // Extrapolates track parameters upstream to the "Z" end of the front absorber
+ ExtrapToZ(trackParam,zAbsorber); // !!!
+ // Makes Branson correction (multiple scattering + energy loss)
+ BransonCorrection(trackParam,xVtx,yVtx,zVtx);
+ // Makes a simple magnetic field correction through the absorber
+ FieldCorrection(trackParam,zAbsorber);
+}
+
+
+// Keep this version for future developments
+ //__________________________________________________________________________
+// void AliMUONTrackExtrap::BransonCorrection(AliMUONTrackParam* trackParam)
+// {
+// /// Branson correction of track parameters
+// // the entry parameters have to be calculated at the end of the absorber
+// Double_t zEndAbsorber, zBP, xBP, yBP;
+// Double_t pYZ, pX, pY, pZ, pTotal, xEndAbsorber, yEndAbsorber, radiusEndAbsorber2, pT, theta;
+// Int_t sign;
+// // Would it be possible to calculate all that from Geant configuration ????
+// // and to get the Branson parameters from a function in ABSO module ????
+// // with an eventual contribution from other detectors like START ????
+// // Radiation lengths outer part theta > 3 degres
+// static Double_t x01[9] = { 18.8, // C (cm)
+// 10.397, // Concrete (cm)
+// 0.56, // Plomb (cm)
+// 47.26, // Polyethylene (cm)
+// 0.56, // Plomb (cm)
+// 47.26, // Polyethylene (cm)
+// 0.56, // Plomb (cm)
+// 47.26, // Polyethylene (cm)
+// 0.56 }; // Plomb (cm)
+// // inner part theta < 3 degres
+// static Double_t x02[3] = { 18.8, // C (cm)
+// 10.397, // Concrete (cm)
+// 0.35 }; // W (cm)
+// // z positions of the materials inside the absober outer part theta > 3 degres
+// static Double_t z1[10] = { 90, 315, 467, 472, 477, 482, 487, 492, 497, 502 };
+// // inner part theta < 3 degres
+// static Double_t z2[4] = { 90, 315, 467, 503 };
+// static Bool_t first = kTRUE;
+// static Double_t zBP1, zBP2, rLimit;
+// // Calculates z positions of the Branson's planes: zBP1 for outer part and zBP2 for inner part (only at the first call)
+// if (first) {
+// first = kFALSE;
+// Double_t aNBP = 0.0;
+// Double_t aDBP = 0.0;
+// Int_t iBound;
+//
+// for (iBound = 0; iBound < 9; iBound++) {
+// aNBP = aNBP +
+// (z1[iBound+1] * z1[iBound+1] * z1[iBound+1] -
+// z1[iBound] * z1[iBound] * z1[iBound] ) / x01[iBound];
+// aDBP = aDBP +
+// (z1[iBound+1] * z1[iBound+1] - z1[iBound] * z1[iBound] ) / x01[iBound];
+// }
+// zBP1 = (2.0 * aNBP) / (3.0 * aDBP);
+// aNBP = 0.0;
+// aDBP = 0.0;
+// for (iBound = 0; iBound < 3; iBound++) {
+// aNBP = aNBP +
+// (z2[iBound+1] * z2[iBound+1] * z2[iBound+1] -
+// z2[iBound] * z2[iBound ] * z2[iBound] ) / x02[iBound];
+// aDBP = aDBP +
+// (z2[iBound+1] * z2[iBound+1] - z2[iBound] * z2[iBound]) / x02[iBound];
+// }
+// zBP2 = (2.0 * aNBP) / (3.0 * aDBP);
+// rLimit = z2[3] * TMath::Tan(3.0 * (TMath::Pi()) / 180.);
+// }
+//
+// pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum());
+// sign = 1;
+// if (trackParam->GetInverseBendingMomentum() < 0) sign = -1;
+// pZ = pYZ / (TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope()));
+// pX = pZ * trackParam->GetNonBendingSlope();
+// pY = pZ * trackParam->GetBendingSlope();
+// pTotal = TMath::Sqrt(pYZ *pYZ + pX * pX);
+// xEndAbsorber = trackParam->GetNonBendingCoor();
+// yEndAbsorber = trackParam->GetBendingCoor();
+// radiusEndAbsorber2 = xEndAbsorber * xEndAbsorber + yEndAbsorber * yEndAbsorber;
+//
+// if (radiusEndAbsorber2 > rLimit*rLimit) {
+// zEndAbsorber = z1[9];
+// zBP = zBP1;
+// } else {
+// zEndAbsorber = z2[3];
+// zBP = zBP2;
+// }
+//
+// xBP = xEndAbsorber - (pX / pZ) * (zEndAbsorber - zBP);
+// yBP = yEndAbsorber - (pY / pZ) * (zEndAbsorber - zBP);
+//
+// // new parameters after Branson and energy loss corrections
+// pZ = pTotal * zBP / TMath::Sqrt(xBP * xBP + yBP * yBP + zBP * zBP);
+// pX = pZ * xBP / zBP;
+// pY = pZ * yBP / zBP;
+// trackParam->SetBendingSlope(pY/pZ);
+// trackParam->SetNonBendingSlope(pX/pZ);
+//
+// pT = TMath::Sqrt(pX * pX + pY * pY);
+// theta = TMath::ATan2(pT, pZ);
+// pTotal = TotalMomentumEnergyLoss(rLimit, pTotal, theta, xEndAbsorber, yEndAbsorber);
+//
+// trackParam->SetInverseBendingMomentum((sign / pTotal) *
+// TMath::Sqrt(1.0 +
+// trackParam->GetBendingSlope() * trackParam->GetBendingSlope() +
+// trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()) /
+// TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope()));
+//
+// // vertex position at (0,0,0)
+// // should be taken from vertex measurement ???
+// trackParam->SetBendingCoor(0.);
+// trackParam->SetNonBendingCoor(0.);
+// trackParam->SetZ(0.);
+// }
+
+void AliMUONTrackExtrap::BransonCorrection(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx)
+{
+ /// Branson correction of track parameters
+ // the entry parameters have to be calculated at the end of the absorber
+ // simplified version: the z positions of Branson's planes are no longer calculated
+ // but are given as inputs. One can use the macros MUONTestAbso.C and DrawTestAbso.C
+ // to test this correction.
+ // Would it be possible to calculate all that from Geant configuration ????
+ // and to get the Branson parameters from a function in ABSO module ????
+ // with an eventual contribution from other detectors like START ????
+ // change to take into account the vertex postition (real, reconstruct,....)
+
+ Double_t zBP, xBP, yBP;
+ Double_t pYZ, pX, pY, pZ, pTotal, xEndAbsorber, yEndAbsorber, radiusEndAbsorber2, pT, theta;
+ Int_t sign;
+ static Bool_t first = kTRUE;
+ static Double_t zBP1, zBP2, rLimit, thetaLimit, zEndAbsorber;
+ // zBP1 for outer part and zBP2 for inner part (only at the first call)
+ if (first) {
+ first = kFALSE;
+
+ zEndAbsorber = -503; // spectro (z<0)
+ thetaLimit = 3.0 * (TMath::Pi()) / 180.;
+ rLimit = TMath::Abs(zEndAbsorber) * TMath::Tan(thetaLimit);
+ zBP1 = -450; // values close to those calculated with EvalAbso.C
+ zBP2 = -480;
+ }
+
+ pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum());
+ sign = 1;
+ if (trackParam->GetInverseBendingMomentum() < 0) sign = -1;
+ pZ = trackParam->Pz();
+ pX = trackParam->Px();
+ pY = trackParam->Py();
+ pTotal = TMath::Sqrt(pYZ *pYZ + pX * pX);
+ xEndAbsorber = trackParam->GetNonBendingCoor();
+ yEndAbsorber = trackParam->GetBendingCoor();
+ radiusEndAbsorber2 = xEndAbsorber * xEndAbsorber + yEndAbsorber * yEndAbsorber;
+
+ if (radiusEndAbsorber2 > rLimit*rLimit) {
+ zBP = zBP1;
+ } else {
+ zBP = zBP2;
+ }
+
+ xBP = xEndAbsorber - (pX / pZ) * (zEndAbsorber - zBP);
+ yBP = yEndAbsorber - (pY / pZ) * (zEndAbsorber - zBP);
+
+ // new parameters after Branson and energy loss corrections
+// Float_t zSmear = zBP - gRandom->Gaus(0.,2.); // !!! possible smearing of Z vertex position
+
+ Float_t zSmear = zBP ;
+
+ pZ = pTotal * (zSmear-zVtx) / TMath::Sqrt((xBP-xVtx) * (xBP-xVtx) + (yBP-yVtx) * (yBP-yVtx) +( zSmear-zVtx) * (zSmear-zVtx) );
+ pX = pZ * (xBP - xVtx)/ (zSmear-zVtx);
+ pY = pZ * (yBP - yVtx) / (zSmear-zVtx);
+ trackParam->SetBendingSlope(pY/pZ);
+ trackParam->SetNonBendingSlope(pX/pZ);
+
+
+ pT = TMath::Sqrt(pX * pX + pY * pY);
+ theta = TMath::ATan2(pT, TMath::Abs(pZ));
+ pTotal = TotalMomentumEnergyLoss(thetaLimit, pTotal, theta);
+
+ trackParam->SetInverseBendingMomentum((sign / pTotal) *
+ TMath::Sqrt(1.0 +
+ trackParam->GetBendingSlope() * trackParam->GetBendingSlope() +
+ trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()) /
+ TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope()));
+
+ // vertex position at (0,0,0)
+ // should be taken from vertex measurement ???
+
+ trackParam->SetBendingCoor(xVtx);
+ trackParam->SetNonBendingCoor(yVtx);
+ trackParam->SetZ(zVtx);
+
+}
+
+ //__________________________________________________________________________
+Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(Double_t thetaLimit, Double_t pTotal, Double_t theta)
+{
+ /// Returns the total momentum corrected from energy loss in the front absorber
+ // One can use the macros MUONTestAbso.C and DrawTestAbso.C
+ // to test this correction.
+ // Momentum energy loss behaviour evaluated with the simulation of single muons (april 2002)
+ Double_t deltaP, pTotalCorrected;
+
+ // Parametrization to be redone according to change of absorber material ????
+ // See remark in function BransonCorrection !!!!
+ // The name is not so good, and there are many arguments !!!!
+ if (theta < thetaLimit ) {
+ if (pTotal < 20) {
+ deltaP = 2.5938 + 0.0570 * pTotal - 0.001151 * pTotal * pTotal;
+ } else {
+ deltaP = 3.0714 + 0.011767 *pTotal;
+ }
+ deltaP *= 0.75; // AZ
+ } else {
+ if (pTotal < 20) {
+ deltaP = 2.1207 + 0.05478 * pTotal - 0.00145079 * pTotal * pTotal;
+ } else {
+ deltaP = 2.6069 + 0.0051705 * pTotal;
+ }
+ deltaP *= 0.9; // AZ
+ }
+ pTotalCorrected = pTotal + deltaP / TMath::Cos(theta);
+ return pTotalCorrected;
+}
+
+ //__________________________________________________________________________
+void AliMUONTrackExtrap::FieldCorrection(AliMUONTrackParam *trackParam, Double_t zEnd)
+{
+ /// Correction of the effect of the magnetic field in the absorber
+ // Assume a constant field along Z axis.
+ Float_t b[3],x[3];
+ Double_t bZ;
+ Double_t pYZ,pX,pY,pZ,pT;
+ Double_t pXNew,pYNew;
+ Double_t c;
+
+ pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum());
+ c = TMath::Sign(1.0,trackParam->GetInverseBendingMomentum()); // particle charge
+
+ pZ = trackParam->Pz();
+ pX = trackParam->Px();
+ pY = trackParam->Py();
+ pT = TMath::Sqrt(pX*pX+pY*pY);
+
+ if (TMath::Abs(pZ) <= 0) return;
+ x[2] = zEnd/2;
+ x[0] = x[2]*trackParam->GetNonBendingSlope();
+ x[1] = x[2]*trackParam->GetBendingSlope();
+
+ // Take magn. field value at position x.
+ if (fgkField) fgkField->Field(x,b);
+ else {
+ cout<<"F-AliMUONTrackExtrap::FieldCorrection: fgkField = 0x0"<<endl;
+ exit(-1);
+ }
+ bZ = b[2];
+
+ // Transverse momentum rotation
+ // Parameterized with the study of DeltaPhi = phiReco - phiGen as a function of pZ.
+ Double_t phiShift = c*0.436*0.0003*bZ*zEnd/pZ;
+ // Rotate momentum around Z axis.
+ pXNew = pX*TMath::Cos(phiShift) - pY*TMath::Sin(phiShift);
+ pYNew = pX*TMath::Sin(phiShift) + pY*TMath::Cos(phiShift);
+
+ trackParam->SetBendingSlope(pYNew/pZ);
+ trackParam->SetNonBendingSlope(pXNew/pZ);
+
+ trackParam->SetInverseBendingMomentum(c/TMath::Sqrt(pYNew*pYNew+pZ*pZ));
+
+}
+
+ //__________________________________________________________________________
+void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, Double_t *vect, Double_t *vout)
+{
+/// ******************************************************************
+/// * *
+/// * Performs the tracking of one step in a magnetic field *
+/// * The trajectory is assumed to be a helix in a constant field *
+/// * taken at the mid point of the step. *
+/// * Parameters: *
+/// * input *
+/// * STEP =arc length of the step asked *
+/// * VECT =input vector (position,direction cos and momentum) *
+/// * CHARGE= electric charge of the particle *
+/// * output *
+/// * VOUT = same as VECT after completion of the step *
+/// * *
+/// * ==>Called by : <USER>, GUSWIM *
+/// * Author m.hansroul ********* *
+/// * modified s.egli, s.v.levonian *
+/// * modified v.perevoztchikov
+/// * *
+/// ******************************************************************
+
+// modif: everything in double precision
+
+ Double_t xyz[3], h[4], hxp[3];
+ Double_t h2xy, hp, rho, tet;
+ Double_t sint, sintt, tsint, cos1t;
+ Double_t f1, f2, f3, f4, f5, f6;
+
+ const Int_t kix = 0;
+ const Int_t kiy = 1;
+ const Int_t kiz = 2;
+ const Int_t kipx = 3;
+ const Int_t kipy = 4;
+ const Int_t kipz = 5;
+ const Int_t kipp = 6;
+
+ const Double_t kec = 2.9979251e-4;
+ //
+ // ------------------------------------------------------------------
+ //
+ // units are kgauss,centimeters,gev/c
+ //
+ vout[kipp] = vect[kipp];
+ if (TMath::Abs(charge) < 0.00001) {
+ for (Int_t i = 0; i < 3; i++) {
+ vout[i] = vect[i] + step * vect[i+3];
+ vout[i+3] = vect[i+3];
+ }
+ return;
+ }
+ xyz[0] = vect[kix] + 0.5 * step * vect[kipx];
+ xyz[1] = vect[kiy] + 0.5 * step * vect[kipy];
+ xyz[2] = vect[kiz] + 0.5 * step * vect[kipz];
+
+ //cmodif: call gufld (xyz, h) changed into:
+ GetField (xyz, h);
+
+ h2xy = h[0]*h[0] + h[1]*h[1];
+ h[3] = h[2]*h[2]+ h2xy;
+ if (h[3] < 1.e-12) {
+ for (Int_t i = 0; i < 3; i++) {
+ vout[i] = vect[i] + step * vect[i+3];
+ vout[i+3] = vect[i+3];
+ }
+ return;
+ }
+ if (h2xy < 1.e-12*h[3]) {
+ ExtrapOneStepHelix3(charge*h[2], step, vect, vout);
+ return;
+ }
+ h[3] = TMath::Sqrt(h[3]);
+ h[0] /= h[3];
+ h[1] /= h[3];
+ h[2] /= h[3];
+ h[3] *= kec;
+
+ hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy];
+ hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz];
+ hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx];
+
+ hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz];
+
+ rho = -charge*h[3]/vect[kipp];
+ tet = rho * step;
+
+ if (TMath::Abs(tet) > 0.15) {
+ sint = TMath::Sin(tet);
+ sintt = (sint/tet);
+ tsint = (tet-sint)/tet;
+ cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet;
+ } else {
+ tsint = tet*tet/36.;
+ sintt = (1. - tsint);
+ sint = tet*sintt;
+ cos1t = 0.5*tet;
+ }
+
+ f1 = step * sintt;
+ f2 = step * cos1t;
+ f3 = step * tsint * hp;
+ f4 = -tet*cos1t;
+ f5 = sint;
+ f6 = tet * cos1t * hp;
+
+ vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0];
+ vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1];
+ vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2];
+
+ vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0];
+ vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1];
+ vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2];
+
+ return;
+}
+
+ //__________________________________________________________________________
+void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, Double_t *vect, Double_t *vout)
+{
+/// ******************************************************************
+/// * *
+/// * Tracking routine in a constant field oriented *
+/// * along axis 3 *
+/// * Tracking is performed with a conventional *
+/// * helix step method *
+/// * *
+/// * ==>Called by : <USER>, GUSWIM *
+/// * Authors R.Brun, M.Hansroul ********* *
+/// * Rewritten V.Perevoztchikov
+/// * *
+/// ******************************************************************
+
+ Double_t hxp[3];
+ Double_t h4, hp, rho, tet;
+ Double_t sint, sintt, tsint, cos1t;
+ Double_t f1, f2, f3, f4, f5, f6;
+
+ const Int_t kix = 0;
+ const Int_t kiy = 1;
+ const Int_t kiz = 2;
+ const Int_t kipx = 3;
+ const Int_t kipy = 4;
+ const Int_t kipz = 5;
+ const Int_t kipp = 6;
+
+ const Double_t kec = 2.9979251e-4;
+
+//
+// ------------------------------------------------------------------
+//
+// units are kgauss,centimeters,gev/c
+//
+ vout[kipp] = vect[kipp];
+ h4 = field * kec;
+
+ hxp[0] = - vect[kipy];
+ hxp[1] = + vect[kipx];
+
+ hp = vect[kipz];
+
+ rho = -h4/vect[kipp];
+ tet = rho * step;
+ if (TMath::Abs(tet) > 0.15) {
+ sint = TMath::Sin(tet);
+ sintt = (sint/tet);
+ tsint = (tet-sint)/tet;
+ cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet;
+ } else {
+ tsint = tet*tet/36.;
+ sintt = (1. - tsint);
+ sint = tet*sintt;
+ cos1t = 0.5*tet;
+ }
+
+ f1 = step * sintt;
+ f2 = step * cos1t;
+ f3 = step * tsint * hp;
+ f4 = -tet*cos1t;
+ f5 = sint;
+ f6 = tet * cos1t * hp;
+
+ vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0];
+ vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1];
+ vout[kiz] = vect[kiz] + f1*vect[kipz] + f3;
+
+ vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0];
+ vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1];
+ vout[kipz] = vect[kipz] + f4*vect[kipz] + f6;
+
+ return;
+}
+ //__________________________________________________________________________
+void AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, Double_t* vect, Double_t* vout)
+{
+/// ******************************************************************
+/// * *
+/// * Runge-Kutta method for tracking a particle through a magnetic *
+/// * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of *
+/// * Standards, procedure 25.5.20) *
+/// * *
+/// * Input parameters *
+/// * CHARGE Particle charge *
+/// * STEP Step size *
+/// * VECT Initial co-ords,direction cosines,momentum *
+/// * Output parameters *
+/// * VOUT Output co-ords,direction cosines,momentum *
+/// * User routine called *
+/// * CALL GUFLD(X,F) *
+/// * *
+/// * ==>Called by : <USER>, GUSWIM *
+/// * Authors R.Brun, M.Hansroul ********* *
+/// * V.Perevoztchikov (CUT STEP implementation) *
+/// * *
+/// * *
+/// ******************************************************************
+
+ Double_t h2, h4, f[4];
+ Double_t xyzt[3], a, b, c, ph,ph2;
+ Double_t secxs[4],secys[4],seczs[4],hxp[3];
+ Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt;
+ Double_t est, at, bt, ct, cba;
+ Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost;
+
+ Double_t x;
+ Double_t y;
+ Double_t z;
+
+ Double_t xt;
+ Double_t yt;
+ Double_t zt;
+
+ Double_t maxit = 1992;
+ Double_t maxcut = 11;
+
+ const Double_t kdlt = 1e-4;
+ const Double_t kdlt32 = kdlt/32.;
+ const Double_t kthird = 1./3.;
+ const Double_t khalf = 0.5;
+ const Double_t kec = 2.9979251e-4;
+
+ const Double_t kpisqua = 9.86960440109;
+ const Int_t kix = 0;
+ const Int_t kiy = 1;
+ const Int_t kiz = 2;
+ const Int_t kipx = 3;
+ const Int_t kipy = 4;
+ const Int_t kipz = 5;
+
+ // *.
+ // *. ------------------------------------------------------------------
+ // *.
+ // * this constant is for units cm,gev/c and kgauss
+ // *
+ Int_t iter = 0;
+ Int_t ncut = 0;
+ for(Int_t j = 0; j < 7; j++)
+ vout[j] = vect[j];
+
+ Double_t pinv = kec * charge / vect[6];
+ Double_t tl = 0.;
+ Double_t h = step;
+ Double_t rest;
+
+
+ do {
+ rest = step - tl;
+ if (TMath::Abs(h) > TMath::Abs(rest)) h = rest;
+ //cmodif: call gufld(vout,f) changed into:
+
+ GetField(vout,f);
+
+ // *
+ // * start of integration
+ // *
+ x = vout[0];
+ y = vout[1];
+ z = vout[2];
+ a = vout[3];
+ b = vout[4];
+ c = vout[5];
+
+ h2 = khalf * h;
+ h4 = khalf * h2;
+ ph = pinv * h;
+ ph2 = khalf * ph;
+ secxs[0] = (b * f[2] - c * f[1]) * ph2;
+ secys[0] = (c * f[0] - a * f[2]) * ph2;
+ seczs[0] = (a * f[1] - b * f[0]) * ph2;
+ ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]);
+ if (ang2 > kpisqua) break;
+
+ dxt = h2 * a + h4 * secxs[0];
+ dyt = h2 * b + h4 * secys[0];
+ dzt = h2 * c + h4 * seczs[0];
+ xt = x + dxt;
+ yt = y + dyt;
+ zt = z + dzt;
+ // *
+ // * second intermediate point
+ // *
+
+ est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt);
+ if (est > h) {
+ if (ncut++ > maxcut) break;
+ h *= khalf;
+ continue;
+ }
+
+ xyzt[0] = xt;
+ xyzt[1] = yt;
+ xyzt[2] = zt;
+
+ //cmodif: call gufld(xyzt,f) changed into:
+ GetField(xyzt,f);
+
+ at = a + secxs[0];
+ bt = b + secys[0];
+ ct = c + seczs[0];
+
+ secxs[1] = (bt * f[2] - ct * f[1]) * ph2;
+ secys[1] = (ct * f[0] - at * f[2]) * ph2;
+ seczs[1] = (at * f[1] - bt * f[0]) * ph2;
+ at = a + secxs[1];
+ bt = b + secys[1];
+ ct = c + seczs[1];
+ secxs[2] = (bt * f[2] - ct * f[1]) * ph2;
+ secys[2] = (ct * f[0] - at * f[2]) * ph2;
+ seczs[2] = (at * f[1] - bt * f[0]) * ph2;
+ dxt = h * (a + secxs[2]);
+ dyt = h * (b + secys[2]);
+ dzt = h * (c + seczs[2]);
+ xt = x + dxt;
+ yt = y + dyt;
+ zt = z + dzt;
+ at = a + 2.*secxs[2];
+ bt = b + 2.*secys[2];
+ ct = c + 2.*seczs[2];
+
+ est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt);
+ if (est > 2.*TMath::Abs(h)) {
+ if (ncut++ > maxcut) break;
+ h *= khalf;
+ continue;
+ }
+
+ xyzt[0] = xt;
+ xyzt[1] = yt;
+ xyzt[2] = zt;
+
+ //cmodif: call gufld(xyzt,f) changed into:
+ GetField(xyzt,f);
+
+ z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h;
+ y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h;
+ x = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h;
+
+ secxs[3] = (bt*f[2] - ct*f[1])* ph2;
+ secys[3] = (ct*f[0] - at*f[2])* ph2;
+ seczs[3] = (at*f[1] - bt*f[0])* ph2;
+ a = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird;
+ b = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird;
+ c = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird;
+
+ est = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2]))
+ + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2]))
+ + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2]));
+
+ if (est > kdlt && TMath::Abs(h) > 1.e-4) {
+ if (ncut++ > maxcut) break;
+ h *= khalf;
+ continue;
+ }
+
+ ncut = 0;
+ // * if too many iterations, go to helix
+ if (iter++ > maxit) break;
+
+ tl += h;
+ if (est < kdlt32)
+ h *= 2.;
+ cba = 1./ TMath::Sqrt(a*a + b*b + c*c);
+ vout[0] = x;
+ vout[1] = y;
+ vout[2] = z;
+ vout[3] = cba*a;
+ vout[4] = cba*b;
+ vout[5] = cba*c;
+ rest = step - tl;
+ if (step < 0.) rest = -rest;
+ if (rest < 1.e-5*TMath::Abs(step)) return;
+
+ } while(1);
+
+ // angle too big, use helix
+
+ f1 = f[0];
+ f2 = f[1];
+ f3 = f[2];
+ f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3);
+ rho = -f4*pinv;
+ tet = rho * step;
+
+ hnorm = 1./f4;
+ f1 = f1*hnorm;
+ f2 = f2*hnorm;
+ f3 = f3*hnorm;
+
+ hxp[0] = f2*vect[kipz] - f3*vect[kipy];
+ hxp[1] = f3*vect[kipx] - f1*vect[kipz];
+ hxp[2] = f1*vect[kipy] - f2*vect[kipx];
+
+ hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz];
+
+ rho1 = 1./rho;
+ sint = TMath::Sin(tet);
+ cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet);
+
+ g1 = sint*rho1;
+ g2 = cost*rho1;
+ g3 = (tet-sint) * hp*rho1;
+ g4 = -cost;
+ g5 = sint;
+ g6 = cost * hp;
+
+ vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1;
+ vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2;
+ vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3;
+
+ vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1;
+ vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2;
+ vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3;
+
+ return;
+}
+//___________________________________________________________
+ void AliMUONTrackExtrap::GetField(Double_t *Position, Double_t *Field)
+{
+ /// interface for arguments in double precision (Why ? ChF)
+ Float_t x[3], b[3];
+
+ x[0] = Position[0]; x[1] = Position[1]; x[2] = Position[2];
+
+ if (fgkField) fgkField->Field(x,b);
+ else {
+ cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl;
+ exit(-1);
+ }
+
+ Field[0] = b[0]; Field[1] = b[1]; Field[2] = b[2];
+
+ return;
+}
+
git://git.uio.no / u/mrichter/AliRoot.git / commitdiff