* provided "as is" without express or implied warranty. *
**************************************************************************/
-////////////////////////////////////////////////////////////////////////////////
-// //
-// AliTPCCorrection class //
-// //
-// This class provides a general framework to deal with space point //
-// distortions. An correction class which inherits from here is for example //
-// AliTPCExBBShape or AliTPCExBTwist //
-// //
-// General functions are (for example): //
-// CorrectPoint(x,roc) where x is the vector of inital positions in //
-// cartesian coordinates and roc represents the Read Out chamber number //
-// according to the offline naming convention. The vector x is overwritten //
-// with the corrected coordinates. //
-// //
-// An alternative usage would be CorrectPoint(x,roc,dx), which leaves the //
-// vector x untouched, put returns the distortions via the vector dx //
-// //
-// The class allows "effective Omega Tau" corrections to be shifted to the //
-// single distortion classes. //
-// //
-// Note: This class is normally used via the class AliTPCComposedCorrection //
-// //
-// date: 27/04/2010 //
-// Authors: Magnus Mager, Stefan Rossegger, Jim Thomas //
-////////////////////////////////////////////////////////////////////////////////
+// _________________________________________________________________
+//
+// Begin_Html
+// <h2> AliTPCCorrection class </h2>
+//
+// The AliTPCCorrection class provides a general framework to deal with space point distortions.
+// An correction class which inherits from here is for example AliTPCExBBShape or AliTPCExBTwist. <br>
+// General virtual functions are (for example) CorrectPoint(x,roc) where x is the vector of initial
+// positions in cartesian coordinates and roc represents the read-out chamber number according to
+// the offline numbering convention. The vector x is overwritten with the corrected coordinates. <br>
+// An alternative usage would be CorrectPoint(x,roc,dx), which leaves the vector x untouched, but
+// returns the distortions via the vector dx. <br>
+// This class is normally used via the general class AliTPCComposedCorrection.
+// <p>
+// Furthermore, the class contains basic geometrical descriptions like field cage radii
+// (fgkIFCRadius, fgkOFCRadius) and length (fgkTPCZ0) plus the voltages. Also, the definitions
+// of size and widths of the fulcrums building the grid of the final look-up table, which is
+// then interpolated, is defined in kNX and fgkXList).
+// <p>
+// All physics-model classes below are derived from this class in order to not duplicate code
+// and to allow a uniform treatment of all physics models.
+// <p>
+// <h3> Poisson solver </h3>
+// A numerical solver of the Poisson equation (relaxation technique) is implemented for 2-dimensional
+// geometries (r,z) as well as for 3-dimensional problems (r,$\phi$,z). The corresponding function
+// names are PoissonRelaxation?D. The relevant function arguments are the arrays of the boundary and
+// initial conditions (ArrayofArrayV, ArrayofChargeDensities) as well as the grid granularity which
+// is used during the calculation. These inputs can be chosen according to the needs of the physical
+// effect which is supposed to be simulated. In the 3D version, different symmetry conditions can be set
+// in order to reduce the calculation time (used in AliTPCFCVoltError3D).
+// <p>
+// <h3> Unified plotting functionality </h3>
+// Generic plot functions were implemented. They return a histogram pointer in the chosen plane of
+// the TPC drift volume with a selectable grid granularity and the magnitude of the correction vector.
+// For example, the function CreateHistoDZinXY(z,nx,ny) returns a 2-dimensional histogram which contains
+// the longitudinal corrections $dz$ in the (x,y)-plane at the given z position with the granularity of
+// nx and ny. The magnitude of the corrections is defined by the class from which this function is called.
+// In the same manner, standard plots for the (r,$\phi$)-plane and for the other corrections like $dr$ and $rd\phi$ are available
+// <p>
+// Note: This class is normally used via the class AliTPCComposedCorrection
+// End_Html
+//
+// Begin_Macro(source)
+// {
+// gROOT->SetStyle("Plain"); gStyle->SetPalette(1);
+// TCanvas *c2 = new TCanvas("c2","c2",700,1050); c2->Divide(2,3);
+// AliTPCROCVoltError3D roc; // EXAMPLE PLOTS - SEE BELOW
+// roc.SetOmegaTauT1T2(0,1,1); // B=0
+// Float_t z0 = 1; // at +1 cm -> A side
+// c2->cd(1); roc.CreateHistoDRinXY(1.,300,300)->Draw("cont4z");
+// c2->cd(3);roc.CreateHistoDRPhiinXY(1.,300,300)->Draw("cont4z");
+// c2->cd(5);roc.CreateHistoDZinXY(1.,300,300)->Draw("cont4z");
+// Float_t phi0=0.5;
+// c2->cd(2);roc.CreateHistoDRinZR(phi0)->Draw("surf2");
+// c2->cd(4);roc.CreateHistoDRPhiinZR(phi0)->Draw("surf2");
+// c2->cd(6);roc.CreateHistoDZinZR(phi0)->Draw("surf2");
+// return c2;
+// }
+// End_Macro
+//
+// Begin_Html
+// <p>
+// Date: 27/04/2010 <br>
+// Authors: Magnus Mager, Stefan Rossegger, Jim Thomas
+// End_Html
+// _________________________________________________________________
+
+
#include "Riostream.h"
#include <TH2F.h>
#include <AliCDBStorage.h>
#include <AliCDBId.h>
#include <AliCDBMetaData.h>
-#include "TVectorD.h"
+#include "TVectorD.h"
+#include "AliTPCParamSR.h"
+#include "AliTPCCorrection.h"
+#include "AliLog.h"
-#include "TRandom.h"
#include "AliExternalTrackParam.h"
#include "AliTrackPointArray.h"
#include "TDatabasePDG.h"
#include "AliTPCROC.h"
#include "THnSparse.h"
+#include "AliTPCLaserTrack.h"
+#include "AliESDVertex.h"
+#include "AliVertexerTracks.h"
+#include "TDatabasePDG.h"
+#include "TF1.h"
#include "TRandom.h"
+
+#include "TDatabasePDG.h"
+
#include "AliTPCTransform.h"
#include "AliTPCcalibDB.h"
#include "AliTPCExB.h"
-#include "AliTPCCorrection.h"
+
#include "AliTPCRecoParam.h"
-#include "AliExternalTrackParam.h"
-#include "AliTrackPointArray.h"
-#include "TDatabasePDG.h"
-#include "AliTrackerBase.h"
-#include "AliTPCROC.h"
-#include "THnSparse.h"
-#include "AliTPCLaserTrack.h"
-#include "AliESDVertex.h"
-#include "AliVertexerTracks.h"
-#include "TDatabasePDG.h"
-#include "TF1.h"
+ClassImp(AliTPCCorrection)
+
-#include "AliTPCCorrection.h"
-#include "AliLog.h"
+TObjArray *AliTPCCorrection::fgVisualCorrection=0;
+// instance of correction for visualization
-ClassImp(AliTPCCorrection)
// FIXME: the following values should come from the database
-const Double_t AliTPCCorrection::fgkTPCZ0 =249.7; // nominal gating grid position
-const Double_t AliTPCCorrection::fgkIFCRadius= 83.06; // Mean Radius of the Inner Field Cage ( 82.43 min, 83.70 max) (cm)
-const Double_t AliTPCCorrection::fgkOFCRadius=254.5; // Mean Radius of the Outer Field Cage (252.55 min, 256.45 max) (cm)
-const Double_t AliTPCCorrection::fgkZOffSet = 0.2; // Offset from CE: calculate all distortions closer to CE as if at this point
-const Double_t AliTPCCorrection::fgkCathodeV =-100000.0; // Cathode Voltage (volts)
-const Double_t AliTPCCorrection::fgkGG =-70.0; // Gating Grid voltage (volts)
-
-
-// FIXME: List of interpolation points (course grid in the middle, fine grid on the borders)
-const Double_t AliTPCCorrection::fgkRList[AliTPCCorrection::kNR] = {
-84.0, 84.5, 85.0, 85.5, 86.0, 87.0, 88.0,
-90.0, 92.0, 94.0, 96.0, 98.0, 100.0, 102.0, 104.0, 106.0, 108.0,
-110.0, 112.0, 114.0, 116.0, 118.0, 120.0, 122.0, 124.0, 126.0, 128.0,
-130.0, 132.0, 134.0, 136.0, 138.0, 140.0, 142.0, 144.0, 146.0, 148.0,
-150.0, 152.0, 154.0, 156.0, 158.0, 160.0, 162.0, 164.0, 166.0, 168.0,
-170.0, 172.0, 174.0, 176.0, 178.0, 180.0, 182.0, 184.0, 186.0, 188.0,
-190.0, 192.0, 194.0, 196.0, 198.0, 200.0, 202.0, 204.0, 206.0, 208.0,
-210.0, 212.0, 214.0, 216.0, 218.0, 220.0, 222.0, 224.0, 226.0, 228.0,
-230.0, 232.0, 234.0, 236.0, 238.0, 240.0, 242.0, 244.0, 246.0, 248.0,
-249.0, 249.5, 250.0, 251.5, 252.0 } ;
-
-const Double_t AliTPCCorrection::fgkZList[AliTPCCorrection::kNZ] = {
--249.5, -249.0, -248.5, -248.0, -247.0, -246.0, -245.0, -243.0, -242.0, -241.0,
--240.0, -238.0, -236.0, -234.0, -232.0, -230.0, -228.0, -226.0, -224.0, -222.0,
--220.0, -218.0, -216.0, -214.0, -212.0, -210.0, -208.0, -206.0, -204.0, -202.0,
--200.0, -198.0, -196.0, -194.0, -192.0, -190.0, -188.0, -186.0, -184.0, -182.0,
--180.0, -178.0, -176.0, -174.0, -172.0, -170.0, -168.0, -166.0, -164.0, -162.0,
--160.0, -158.0, -156.0, -154.0, -152.0, -150.0, -148.0, -146.0, -144.0, -142.0,
--140.0, -138.0, -136.0, -134.0, -132.0, -130.0, -128.0, -126.0, -124.0, -122.0,
--120.0, -118.0, -116.0, -114.0, -112.0, -110.0, -108.0, -106.0, -104.0, -102.0,
--100.0, -98.0, -96.0, -94.0, -92.0, -90.0, -88.0, -86.0, -84.0, -82.0,
--80.0, -78.0, -76.0, -74.0, -72.0, -70.0, -68.0, -66.0, -64.0, -62.0,
--60.0, -58.0, -56.0, -54.0, -52.0, -50.0, -48.0, -46.0, -44.0, -42.0,
--40.0, -38.0, -36.0, -34.0, -32.0, -30.0, -28.0, -26.0, -24.0, -22.0,
--20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0,
--1.0, -0.5, -0.2, -0.1, -0.05, 0.05, 0.1, 0.2, 0.5, 1.0,
- 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0,
- 22.0, 24.0, 26.0, 28.0, 30.0, 32.0, 34.0, 36.0, 38.0, 40.0,
- 42.0, 44.0, 46.0, 48.0, 50.0, 52.0, 54.0, 56.0, 58.0, 60.0,
- 62.0, 64.0, 66.0, 68.0, 70.0, 72.0, 74.0, 76.0, 78.0, 80.0,
- 82.0, 84.0, 86.0, 88.0, 90.0, 92.0, 94.0, 96.0, 98.0, 100.0,
-102.0, 104.0, 106.0, 108.0, 110.0, 112.0, 114.0, 116.0, 118.0, 120.0,
-122.0, 124.0, 126.0, 128.0, 130.0, 132.0, 134.0, 136.0, 138.0, 140.0,
-142.0, 144.0, 146.0, 148.0, 150.0, 152.0, 154.0, 156.0, 158.0, 160.0,
-162.0, 164.0, 166.0, 168.0, 170.0, 172.0, 174.0, 176.0, 178.0, 180.0,
-182.0, 184.0, 186.0, 188.0, 190.0, 192.0, 194.0, 196.0, 198.0, 200.0,
-202.0, 204.0, 206.0, 208.0, 210.0, 212.0, 214.0, 216.0, 218.0, 220.0,
-222.0, 224.0, 226.0, 228.0, 230.0, 232.0, 234.0, 236.0, 238.0, 240.0,
-242.0, 243.0, 244.0, 245.0, 246.0, 247.0, 248.0, 248.5, 249.0, 249.5 } ;
+const Double_t AliTPCCorrection::fgkTPCZ0 = 249.7; // nominal gating grid position
+const Double_t AliTPCCorrection::fgkIFCRadius= 83.5; // radius which renders the "18 rod manifold" best -> compare calc. of Jim Thomas
+// compare gkIFCRadius= 83.05: Mean Radius of the Inner Field Cage ( 82.43 min, 83.70 max) (cm)
+const Double_t AliTPCCorrection::fgkOFCRadius= 254.5; // Mean Radius of the Outer Field Cage (252.55 min, 256.45 max) (cm)
+const Double_t AliTPCCorrection::fgkZOffSet = 0.2; // Offset from CE: calculate all distortions closer to CE as if at this point
+const Double_t AliTPCCorrection::fgkCathodeV = -100000.0; // Cathode Voltage (volts)
+const Double_t AliTPCCorrection::fgkGG = -70.0; // Gating Grid voltage (volts)
+const Double_t AliTPCCorrection::fgkdvdE = 0.0024; // [cm/V] drift velocity dependency on the E field (from Magboltz for NeCO2N2 at standard environment)
+const Double_t AliTPCCorrection::fgkEM = -1.602176487e-19/9.10938215e-31; // charge/mass in [C/kg]
+const Double_t AliTPCCorrection::fgke0 = 8.854187817e-12; // vacuum permittivity [A·s/(V·m)]
+
AliTPCCorrection::AliTPCCorrection()
- : TNamed("correction_unity","unity"),fJLow(0),fKLow(0), fT1(1), fT2(1)
+ : TNamed("correction_unity","unity"),fILow(0),fJLow(0),fKLow(0), fT1(1), fT2(1)
{
//
// default constructor
//
+ if (!fgVisualCorrection) fgVisualCorrection= new TObjArray;
+
+ InitLookUpfulcrums();
+
}
AliTPCCorrection::AliTPCCorrection(const char *name,const char *title)
-: TNamed(name,title),fJLow(0),fKLow(0), fT1(1), fT2(1)
+: TNamed(name,title),fILow(0),fJLow(0),fKLow(0), fT1(1), fT2(1)
{
//
// default constructor, that set the name and title
//
+ if (!fgVisualCorrection) fgVisualCorrection= new TObjArray;
+
+ InitLookUpfulcrums();
+
}
AliTPCCorrection::~AliTPCCorrection() {
// in respect to position z within the XY plane.
// The histogramm has nx times ny entries.
//
-
+ AliTPCParam* tpcparam = new AliTPCParamSR;
+
TH2F *h=CreateTH2F("dr_xy",GetTitle(),"x [cm]","y [cm]","dr [cm]",
nx,-250.,250.,ny,-250.,250.);
Float_t x[3],dx[3];
x[0]=h->GetXaxis()->GetBinCenter(ix);
GetCorrection(x,roc,dx);
Float_t r0=TMath::Sqrt((x[0] )*(x[0] )+(x[1] )*(x[1] ));
- if (90.<=r0 && r0<=250.) {
+ if (tpcparam->GetPadRowRadii(0,0)<=r0 && r0<=tpcparam->GetPadRowRadii(36,95)) {
Float_t r1=TMath::Sqrt((x[0]+dx[0])*(x[0]+dx[0])+(x[1]+dx[1])*(x[1]+dx[1]));
h->SetBinContent(ix,iy,r1-r0);
}
h->SetBinContent(ix,iy,0.);
}
}
+ delete tpcparam;
return h;
}
// The histogramm has nx times ny entries.
//
+ AliTPCParam* tpcparam = new AliTPCParamSR;
+
TH2F *h=CreateTH2F("drphi_xy",GetTitle(),"x [cm]","y [cm]","drphi [cm]",
nx,-250.,250.,ny,-250.,250.);
Float_t x[3],dx[3];
x[0]=h->GetXaxis()->GetBinCenter(ix);
GetCorrection(x,roc,dx);
Float_t r0=TMath::Sqrt((x[0] )*(x[0] )+(x[1] )*(x[1] ));
- if (90.<=r0 && r0<=250.) {
+ if (tpcparam->GetPadRowRadii(0,0)<=r0 && r0<=tpcparam->GetPadRowRadii(36,95)) {
Float_t phi0=TMath::ATan2(x[1] ,x[0] );
Float_t phi1=TMath::ATan2(x[1]+dx[1],x[0]+dx[0]);
h->SetBinContent(ix,iy,0.);
}
}
+ delete tpcparam;
+ return h;
+}
+
+TH2F* AliTPCCorrection::CreateHistoDZinXY(Float_t z,Int_t nx,Int_t ny) {
+ //
+ // Simple plot functionality.
+ // Returns a 2d hisogram which represents the corrections in longitudinal direction (dz)
+ // in respect to position z within the XY plane.
+ // The histogramm has nx times ny entries.
+ //
+
+ AliTPCParam* tpcparam = new AliTPCParamSR;
+
+ TH2F *h=CreateTH2F("dz_xy",GetTitle(),"x [cm]","y [cm]","dz [cm]",
+ nx,-250.,250.,ny,-250.,250.);
+ Float_t x[3],dx[3];
+ x[2]=z;
+ Int_t roc=z>0.?0:18; // FIXME
+ for (Int_t iy=1;iy<=ny;++iy) {
+ x[1]=h->GetYaxis()->GetBinCenter(iy);
+ for (Int_t ix=1;ix<=nx;++ix) {
+ x[0]=h->GetXaxis()->GetBinCenter(ix);
+ GetCorrection(x,roc,dx);
+ Float_t r0=TMath::Sqrt((x[0] )*(x[0] )+(x[1] )*(x[1] ));
+ if (tpcparam->GetPadRowRadii(0,0)<=r0 && r0<=tpcparam->GetPadRowRadii(36,95)) {
+ h->SetBinContent(ix,iy,dx[2]);
+ }
+ else
+ h->SetBinContent(ix,iy,0.);
+ }
+ }
+ delete tpcparam;
return h;
}
return h;
}
+TH2F* AliTPCCorrection::CreateHistoDZinZR(Float_t phi,Int_t nz,Int_t nr) {
+ //
+ // Simple plot functionality.
+ // Returns a 2d hisogram which represents the corrections in longitudinal direction (dz)
+ // in respect to angle phi within the ZR plane.
+ // The histogramm has nx times ny entries.
+ //
+ TH2F *h=CreateTH2F("dz_zr",GetTitle(),"z [cm]","r [cm]","dz [cm]",
+ nz,-250.,250.,nr,85.,250.);
+ Float_t x[3],dx[3];
+ for (Int_t ir=1;ir<=nr;++ir) {
+ Float_t radius=h->GetYaxis()->GetBinCenter(ir);
+ x[0]=radius*TMath::Cos(phi);
+ x[1]=radius*TMath::Sin(phi);
+ for (Int_t iz=1;iz<=nz;++iz) {
+ x[2]=h->GetXaxis()->GetBinCenter(iz);
+ Int_t roc=x[2]>0.?0:18; // FIXME
+ GetCorrection(x,roc,dx);
+ h->SetBinContent(iz,ir,dx[2]);
+ }
+ }
+ return h;
+
+}
+
+
TH2F* AliTPCCorrection::CreateTH2F(const char *name,const char *title,
const char *xlabel,const char *ylabel,const char *zlabel,
Int_t nbinsx,Double_t xlow,Double_t xup,
return h;
}
-
// Simple Interpolation functions: e.g. with bi(tri)cubic interpolations (not yet in TH2 and TH3)
void AliTPCCorrection::Interpolate2DEdistortion( const Int_t order, const Double_t r, const Double_t z,
//
// Interpolate table - 2D interpolation
//
- Double_t saveEr[10] ;
+ Double_t saveEr[5] = {0,0,0,0,0};
Search( kNZ, fgkZList, z, fJLow ) ;
Search( kNR, fgkRList, r, fKLow ) ;
}
+void AliTPCCorrection::Interpolate3DEdistortion( const Int_t order, const Double_t r, const Float_t phi, const Double_t z,
+ const Double_t er[kNZ][kNPhi][kNR], const Double_t ephi[kNZ][kNPhi][kNR], const Double_t ez[kNZ][kNPhi][kNR],
+ Double_t &erValue, Double_t &ephiValue, Double_t &ezValue) {
+ //
+ // Interpolate table - 3D interpolation
+ //
+
+ Double_t saveEr[5]= {0,0,0,0,0};
+ Double_t savedEr[5]= {0,0,0,0,0} ;
+
+ Double_t saveEphi[5]= {0,0,0,0,0};
+ Double_t savedEphi[5]= {0,0,0,0,0} ;
+
+ Double_t saveEz[5]= {0,0,0,0,0};
+ Double_t savedEz[5]= {0,0,0,0,0} ;
+
+ Search( kNZ, fgkZList, z, fILow ) ;
+ Search( kNPhi, fgkPhiList, z, fJLow ) ;
+ Search( kNR, fgkRList, r, fKLow ) ;
+
+ if ( fILow < 0 ) fILow = 0 ; // check if out of range
+ if ( fJLow < 0 ) fJLow = 0 ;
+ if ( fKLow < 0 ) fKLow = 0 ;
+
+ if ( fILow + order >= kNZ - 1 ) fILow = kNZ - 1 - order ;
+ if ( fJLow + order >= kNPhi - 1 ) fJLow = kNPhi - 1 - order ;
+ if ( fKLow + order >= kNR - 1 ) fKLow = kNR - 1 - order ;
+
+ for ( Int_t i = fILow ; i < fILow + order + 1 ; i++ ) {
+ for ( Int_t j = fJLow ; j < fJLow + order + 1 ; j++ ) {
+ saveEr[j-fJLow] = Interpolate( &fgkRList[fKLow], &er[i][j][fKLow], order, r ) ;
+ saveEphi[j-fJLow] = Interpolate( &fgkRList[fKLow], &ephi[i][j][fKLow], order, r ) ;
+ saveEz[j-fJLow] = Interpolate( &fgkRList[fKLow], &ez[i][j][fKLow], order, r ) ;
+ }
+ savedEr[i-fILow] = Interpolate( &fgkPhiList[fJLow], saveEr, order, phi ) ;
+ savedEphi[i-fILow] = Interpolate( &fgkPhiList[fJLow], saveEphi, order, phi ) ;
+ savedEz[i-fILow] = Interpolate( &fgkPhiList[fJLow], saveEz, order, phi ) ;
+ }
+ erValue = Interpolate( &fgkZList[fILow], savedEr, order, z ) ;
+ ephiValue = Interpolate( &fgkZList[fILow], savedEphi, order, z ) ;
+ ezValue = Interpolate( &fgkZList[fILow], savedEz, order, z ) ;
+
+}
+
+Double_t AliTPCCorrection::Interpolate2DTable( const Int_t order, const Double_t x, const Double_t y,
+ const Int_t nx, const Int_t ny, const Double_t xv[], const Double_t yv[],
+ const TMatrixD &array ) {
+ //
+ // Interpolate table (TMatrix format) - 2D interpolation
+ //
+
+ static Int_t jlow = 0, klow = 0 ;
+ Double_t saveArray[5] = {0,0,0,0,0} ;
+
+ Search( nx, xv, x, jlow ) ;
+ Search( ny, yv, y, klow ) ;
+ if ( jlow < 0 ) jlow = 0 ; // check if out of range
+ if ( klow < 0 ) klow = 0 ;
+ if ( jlow + order >= nx - 1 ) jlow = nx - 1 - order ;
+ if ( klow + order >= ny - 1 ) klow = ny - 1 - order ;
+
+ for ( Int_t j = jlow ; j < jlow + order + 1 ; j++ )
+ {
+ Double_t *ajkl = &((TMatrixD&)array)(j,klow);
+ saveArray[j-jlow] = Interpolate( &yv[klow], ajkl , order, y ) ;
+ }
+
+ return( Interpolate( &xv[jlow], saveArray, order, x ) ) ;
+
+}
+
+Double_t AliTPCCorrection::Interpolate3DTable( const Int_t order, const Double_t x, const Double_t y, const Double_t z,
+ const Int_t nx, const Int_t ny, const Int_t nz,
+ const Double_t xv[], const Double_t yv[], const Double_t zv[],
+ TMatrixD **arrayofArrays ) {
+ //
+ // Interpolate table (TMatrix format) - 3D interpolation
+ //
+
+ static Int_t ilow = 0, jlow = 0, klow = 0 ;
+ Double_t saveArray[5]= {0,0,0,0,0};
+ Double_t savedArray[5]= {0,0,0,0,0} ;
+
+ Search( nx, xv, x, ilow ) ;
+ Search( ny, yv, y, jlow ) ;
+ Search( nz, zv, z, klow ) ;
+
+ if ( ilow < 0 ) ilow = 0 ; // check if out of range
+ if ( jlow < 0 ) jlow = 0 ;
+ if ( klow < 0 ) klow = 0 ;
+
+ if ( ilow + order >= nx - 1 ) ilow = nx - 1 - order ;
+ if ( jlow + order >= ny - 1 ) jlow = ny - 1 - order ;
+ if ( klow + order >= nz - 1 ) klow = nz - 1 - order ;
+
+ for ( Int_t k = klow ; k < klow + order + 1 ; k++ )
+ {
+ TMatrixD &table = *arrayofArrays[k] ;
+ for ( Int_t i = ilow ; i < ilow + order + 1 ; i++ )
+ {
+ saveArray[i-ilow] = Interpolate( &yv[jlow], &table(i,jlow), order, y ) ;
+ }
+ savedArray[k-klow] = Interpolate( &xv[ilow], saveArray, order, x ) ;
+ }
+ return( Interpolate( &zv[klow], savedArray, order, z ) ) ;
+
+}
+
Double_t AliTPCCorrection::Interpolate( const Double_t xArray[], const Double_t yArray[],
const Int_t order, const Double_t x ) {
}
-void AliTPCCorrection::PoissonRelaxation2D(TMatrixD &arrayV, const TMatrixD &chargeDensity,
- TMatrixD &arrayErOverEz, const Int_t rows,
- const Int_t columns, const Int_t iterations ) {
+void AliTPCCorrection::InitLookUpfulcrums() {
+ //
+ // Initialization of interpolation points - for main look up table
+ // (course grid in the middle, fine grid on the borders)
+ //
+
+ AliTPCROC * roc = AliTPCROC::Instance();
+ const Double_t rLow = TMath::Floor(roc->GetPadRowRadii(0,0))-1; // first padRow plus some margin
+
+ // fulcrums in R
+ fgkRList[0] = rLow;
+ for (Int_t i = 1; i<kNR; i++) {
+ fgkRList[i] = fgkRList[i-1] + 3.5; // 3.5 cm spacing
+ if (fgkRList[i]<90 ||fgkRList[i]>245)
+ fgkRList[i] = fgkRList[i-1] + 0.5; // 0.5 cm spacing
+ else if (fgkRList[i]<100 || fgkRList[i]>235)
+ fgkRList[i] = fgkRList[i-1] + 1.5; // 1.5 cm spacing
+ else if (fgkRList[i]<120 || fgkRList[i]>225)
+ fgkRList[i] = fgkRList[i-1] + 2.5; // 2.5 cm spacing
+ }
+
+ // fulcrums in Z
+ fgkZList[0] = -249.5;
+ fgkZList[kNZ-1] = 249.5;
+ for (Int_t j = 1; j<kNZ/2; j++) {
+ fgkZList[j] = fgkZList[j-1];
+ if (TMath::Abs(fgkZList[j])< 0.15)
+ fgkZList[j] = fgkZList[j-1] + 0.09; // 0.09 cm spacing
+ else if(TMath::Abs(fgkZList[j])< 0.6)
+ fgkZList[j] = fgkZList[j-1] + 0.4; // 0.4 cm spacing
+ else if (TMath::Abs(fgkZList[j])< 2.5 || TMath::Abs(fgkZList[j])>248)
+ fgkZList[j] = fgkZList[j-1] + 0.5; // 0.5 cm spacing
+ else if (TMath::Abs(fgkZList[j])<10 || TMath::Abs(fgkZList[j])>235)
+ fgkZList[j] = fgkZList[j-1] + 1.5; // 1.5 cm spacing
+ else if (TMath::Abs(fgkZList[j])<25 || TMath::Abs(fgkZList[j])>225)
+ fgkZList[j] = fgkZList[j-1] + 2.5; // 2.5 cm spacing
+ else
+ fgkZList[j] = fgkZList[j-1] + 4; // 4 cm spacing
+
+ fgkZList[kNZ-j-1] = -fgkZList[j];
+ }
+
+ // fulcrums in phi
+ for (Int_t k = 0; k<kNPhi; k++)
+ fgkPhiList[k] = TMath::TwoPi()*k/(kNPhi-1);
+
+
+}
+
+
+void AliTPCCorrection::PoissonRelaxation2D(TMatrixD &arrayV, TMatrixD &chargeDensity,
+ TMatrixD &arrayErOverEz, TMatrixD &arrayDeltaEz,
+ const Int_t rows, const Int_t columns, const Int_t iterations,
+ const Bool_t rocDisplacement ) {
//
// Solve Poisson's Equation by Relaxation Technique in 2D (assuming cylindrical symmetry)
//
// NOTE: In order for this algorithmto work, the number of rows and columns must be a power of 2 plus one.
// So rows == 2**M + 1 and columns == 2**N + 1. The number of rows and columns can be different.
//
+ // NOTE: rocDisplacement is used to include (or ignore) the ROC misalignment in the dz calculation
+ //
// Original code by Jim Thomas (STAR TPC Collaboration)
//
iOne = iOne / 2 ; if ( iOne < 1 ) iOne = 1 ;
jOne = jOne / 2 ; if ( jOne < 1 ) jOne = 1 ;
+ sumChargeDensity.Clear();
}
// Differentiate V(r) and solve for E(r) using special equations for the first and last rows
// Integrate Er/Ez from Z to zero
for ( Int_t j = 0 ; j < columns ; j++ ) {
for ( Int_t i = 0 ; i < rows ; i++ ) {
+
Int_t index = 1 ; // Simpsons rule if N=odd. If N!=odd then add extra point by trapezoidal rule.
arrayErOverEz(i,j) = 0.0 ;
+ arrayDeltaEz(i,j) = 0.0 ;
+
for ( Int_t k = j ; k < columns ; k++ ) {
arrayErOverEz(i,j) += index*(gridSizeZ/3.0)*arrayEr(i,k)/arrayEz(i,k) ;
+ arrayDeltaEz(i,j) += index*(gridSizeZ/3.0)*(arrayEz(i,k)-ezField) ;
if ( index != 4 ) index = 4; else index = 2 ;
}
- if ( index == 4 ) arrayErOverEz(i,j) -= (gridSizeZ/3.0)*arrayEr(i,columns-1)/arrayEz(i,columns-1) ;
- if ( index == 2 ) arrayErOverEz(i,j) +=
- (gridSizeZ/3.0) * ( 0.5*arrayEr(i,columns-2)/arrayEz(i,columns-2)
- -2.5*arrayEr(i,columns-1)/arrayEz(i,columns-1) ) ;
- if ( j == columns-2 ) arrayErOverEz(i,j) =
- (gridSizeZ/3.0) * ( 1.5*arrayEr(i,columns-2)/arrayEz(i,columns-2)
- +1.5*arrayEr(i,columns-1)/arrayEz(i,columns-1) ) ;
- if ( j == columns-1 ) arrayErOverEz(i,j) = 0.0 ;
+ if ( index == 4 ) {
+ arrayErOverEz(i,j) -= (gridSizeZ/3.0)*arrayEr(i,columns-1)/arrayEz(i,columns-1) ;
+ arrayDeltaEz(i,j) -= (gridSizeZ/3.0)*(arrayEz(i,columns-1)-ezField) ;
+ }
+ if ( index == 2 ) {
+ arrayErOverEz(i,j) += (gridSizeZ/3.0) * ( 0.5*arrayEr(i,columns-2)/arrayEz(i,columns-2)
+ -2.5*arrayEr(i,columns-1)/arrayEz(i,columns-1));
+ arrayDeltaEz(i,j) += (gridSizeZ/3.0) * ( 0.5*(arrayEz(i,columns-2)-ezField)
+ -2.5*(arrayEz(i,columns-1)-ezField));
+ }
+ if ( j == columns-2 ) {
+ arrayErOverEz(i,j) = (gridSizeZ/3.0) * ( 1.5*arrayEr(i,columns-2)/arrayEz(i,columns-2)
+ +1.5*arrayEr(i,columns-1)/arrayEz(i,columns-1) ) ;
+ arrayDeltaEz(i,j) = (gridSizeZ/3.0) * ( 1.5*(arrayEz(i,columns-2)-ezField)
+ +1.5*(arrayEz(i,columns-1)-ezField) ) ;
+ }
+ if ( j == columns-1 ) {
+ arrayErOverEz(i,j) = 0.0 ;
+ arrayDeltaEz(i,j) = 0.0 ;
+ }
}
}
+ // calculate z distortion from the integrated Delta Ez residuals
+ // and include the aquivalence (Volt to cm) of the ROC shift !!
+
+ for ( Int_t j = 0 ; j < columns ; j++ ) {
+ for ( Int_t i = 0 ; i < rows ; i++ ) {
+
+ // Scale the Ez distortions with the drift velocity pertubation -> delivers cm
+ arrayDeltaEz(i,j) = arrayDeltaEz(i,j)*fgkdvdE;
+
+ // ROC Potential in cm aquivalent
+ Double_t dzROCShift = arrayV(i, columns -1)/ezField;
+ if ( rocDisplacement ) arrayDeltaEz(i,j) = arrayDeltaEz(i,j) + dzROCShift; // add the ROC misaligment
+
+ }
+ }
+
+ arrayEr.Clear();
+ arrayEz.Clear();
+
}
+void AliTPCCorrection::PoissonRelaxation3D( TMatrixD**arrayofArrayV, TMatrixD**arrayofChargeDensities,
+ TMatrixD**arrayofEroverEz, TMatrixD**arrayofEPhioverEz, TMatrixD**arrayofDeltaEz,
+ const Int_t rows, const Int_t columns, const Int_t phislices,
+ const Float_t deltaphi, const Int_t iterations, const Int_t symmetry,
+ Bool_t rocDisplacement ) {
+ //
+ // 3D - Solve Poisson's Equation in 3D by Relaxation Technique
+ //
+ // NOTE: In order for this algorith to work, the number of rows and columns must be a power of 2 plus one.
+ // The number of rows and COLUMNS can be different.
+ //
+ // ROWS == 2**M + 1
+ // COLUMNS == 2**N + 1
+ // PHISLICES == Arbitrary but greater than 3
+ //
+ // DeltaPhi in Radians
+ //
+ // SYMMETRY = 0 if no phi symmetries, and no phi boundary conditions
+ // = 1 if we have reflection symmetry at the boundaries (eg. sector symmetry or half sector symmetries).
+ //
+ // NOTE: rocDisplacement is used to include (or ignore) the ROC misalignment in the dz calculation
+
+ const Double_t ezField = (fgkCathodeV-fgkGG)/fgkTPCZ0; // = ALICE Electric Field (V/cm) Magnitude ~ -400 V/cm;
+
+ const Float_t gridSizeR = (fgkOFCRadius-fgkIFCRadius) / (rows-1) ;
+ const Float_t gridSizePhi = deltaphi ;
+ const Float_t gridSizeZ = fgkTPCZ0 / (columns-1) ;
+ const Float_t ratioPhi = gridSizeR*gridSizeR / (gridSizePhi*gridSizePhi) ;
+ const Float_t ratioZ = gridSizeR*gridSizeR / (gridSizeZ*gridSizeZ) ;
+
+ TMatrixD arrayE(rows,columns) ;
+
+ // Check that the number of rows and columns is suitable for a binary expansion
+ if ( !IsPowerOfTwo((rows-1)) ) {
+ AliError("Poisson3DRelaxation - Error in the number of rows. Must be 2**M - 1");
+ return; }
+ if ( !IsPowerOfTwo((columns-1)) ) {
+ AliError("Poisson3DRelaxation - Error in the number of columns. Must be 2**N - 1");
+ return; }
+ if ( phislices <= 3 ) {
+ AliError("Poisson3DRelaxation - Error in the number of phislices. Must be larger than 3");
+ return; }
+ if ( phislices > 1000 ) {
+ AliError("Poisson3D phislices > 1000 is not allowed (nor wise) ");
+ return; }
+
+ // Solve Poisson's equation in cylindrical coordinates by relaxation technique
+ // Allow for different size grid spacing in R and Z directions
+ // Use a binary expansion of the matrix to speed up the solution of the problem
+
+ Int_t loops, mplus, mminus, signplus, signminus ;
+ Int_t ione = (rows-1)/4 ;
+ Int_t jone = (columns-1)/4 ;
+ loops = TMath::Max(ione, jone) ; // Calculate the number of loops for the binary expansion
+ loops = 1 + (int) ( 0.5 + TMath::Log2((double)loops) ) ; // Solve for N in 2**N
+
+ TMatrixD* arrayofSumChargeDensities[1000] ; // Create temporary arrays to store low resolution charge arrays
+
+ for ( Int_t i = 0 ; i < phislices ; i++ ) { arrayofSumChargeDensities[i] = new TMatrixD(rows,columns) ; }
+
+ for ( Int_t count = 0 ; count < loops ; count++ ) { // START the master loop and do the binary expansion
+
+ Float_t tempgridSizeR = gridSizeR * ione ;
+ Float_t tempratioPhi = ratioPhi * ione * ione ; // Used tobe divided by ( m_one * m_one ) when m_one was != 1
+ Float_t tempratioZ = ratioZ * ione * ione / ( jone * jone ) ;
+
+ std::vector<float> coef1(rows) ; // Do this the standard C++ way to avoid gcc extensions for Float_t coef1[rows]
+ std::vector<float> coef2(rows) ; // Do this the standard C++ way to avoid gcc extensions for Float_t coef1[rows]
+ std::vector<float> coef3(rows) ; // Do this the standard C++ way to avoid gcc extensions for Float_t coef1[rows]
+ std::vector<float> coef4(rows) ; // Do this the standard C++ way to avoid gcc extensions for Float_t coef1[rows]
+
+ for ( Int_t i = ione ; i < rows-1 ; i+=ione ) {
+ Float_t radius = fgkIFCRadius + i*gridSizeR ;
+ coef1[i] = 1.0 + tempgridSizeR/(2*radius);
+ coef2[i] = 1.0 - tempgridSizeR/(2*radius);
+ coef3[i] = tempratioPhi/(radius*radius);
+ coef4[i] = 0.5 / (1.0 + tempratioZ + coef3[i]);
+ }
+
+ for ( Int_t m = 0 ; m < phislices ; m++ ) {
+ TMatrixD &chargeDensity = *arrayofChargeDensities[m] ;
+ TMatrixD &sumChargeDensity = *arrayofSumChargeDensities[m] ;
+ for ( Int_t i = ione ; i < rows-1 ; i += ione ) {
+ Float_t radius = fgkIFCRadius + i*gridSizeR ;
+ for ( Int_t j = jone ; j < columns-1 ; j += jone ) {
+ if ( ione == 1 && jone == 1 ) sumChargeDensity(i,j) = chargeDensity(i,j) ;
+ else { // Add up all enclosed charge density contributions within 1/2 unit in all directions
+ Float_t weight = 0.0 ;
+ Float_t sum = 0.0 ;
+ sumChargeDensity(i,j) = 0.0 ;
+ for ( Int_t ii = i-ione/2 ; ii <= i+ione/2 ; ii++ ) {
+ for ( Int_t jj = j-jone/2 ; jj <= j+jone/2 ; jj++ ) {
+ if ( ii == i-ione/2 || ii == i+ione/2 || jj == j-jone/2 || jj == j+jone/2 ) weight = 0.5 ;
+ else
+ weight = 1.0 ;
+ sumChargeDensity(i,j) += chargeDensity(ii,jj)*weight*radius ;
+ sum += weight*radius ;
+ }
+ }
+ sumChargeDensity(i,j) /= sum ;
+ }
+ sumChargeDensity(i,j) *= tempgridSizeR*tempgridSizeR; // just saving a step later on
+ }
+ }
+ }
+
+ for ( Int_t k = 1 ; k <= iterations; k++ ) {
+
+ // over-relaxation index, >= 1 but < 2
+ Float_t overRelax = 1.0 + TMath::Sqrt( TMath::Cos( (k*TMath::PiOver2())/iterations ) ) ;
+ Float_t overRelaxM1 = overRelax - 1.0 ;
+
+ std::vector<float> overRelaxcoef4(rows) ; // Do this the standard C++ way to avoid gcc extensions
+ std::vector<float> overRelaxcoef5(rows) ; // Do this the standard C++ way to avoid gcc extensions
+
+ for ( Int_t i = ione ; i < rows-1 ; i+=ione ) {
+ overRelaxcoef4[i] = overRelax * coef4[i] ;
+ overRelaxcoef5[i] = overRelaxM1 / overRelaxcoef4[i] ;
+ }
+
+ for ( Int_t m = 0 ; m < phislices ; m++ ) {
+
+ mplus = m + 1; signplus = 1 ;
+ mminus = m - 1 ; signminus = 1 ;
+ if (symmetry==1) { // Reflection symmetry in phi (e.g. symmetry at sector boundaries, or half sectors, etc.)
+ if ( mplus > phislices-1 ) mplus = phislices - 2 ;
+ if ( mminus < 0 ) mminus = 1 ;
+ }
+ else if (symmetry==-1) { // Anti-symmetry in phi
+ if ( mplus > phislices-1 ) { mplus = phislices - 2 ; signplus = -1 ; }
+ if ( mminus < 0 ) { mminus = 1 ; signminus = -1 ; }
+ }
+ else { // No Symmetries in phi, no boundaries, the calculation is continuous across all phi
+ if ( mplus > phislices-1 ) mplus = m + 1 - phislices ;
+ if ( mminus < 0 ) mminus = m - 1 + phislices ;
+ }
+ TMatrixD& arrayV = *arrayofArrayV[m] ;
+ TMatrixD& arrayVP = *arrayofArrayV[mplus] ;
+ TMatrixD& arrayVM = *arrayofArrayV[mminus] ;
+ TMatrixD& sumChargeDensity = *arrayofSumChargeDensities[m] ;
+
+ for ( Int_t i = ione ; i < rows-1 ; i+=ione ) {
+ for ( Int_t j = jone ; j < columns-1 ; j+=jone ) {
+
+ arrayV(i,j) = ( coef2[i] * arrayV(i-ione,j)
+ + tempratioZ * ( arrayV(i,j-jone) + arrayV(i,j+jone) )
+ - overRelaxcoef5[i] * arrayV(i,j)
+ + coef1[i] * arrayV(i+ione,j)
+ + coef3[i] * ( signplus*arrayVP(i,j) + signminus*arrayVM(i,j) )
+ + sumChargeDensity(i,j)
+ ) * overRelaxcoef4[i] ;
+ // Note: over-relax the solution at each step. This speeds up the convergance.
+
+ }
+ }
+
+ if ( k == iterations ) { // After full solution is achieved, copy low resolution solution into higher res array
+ for ( Int_t i = ione ; i < rows-1 ; i+=ione ) {
+ for ( Int_t j = jone ; j < columns-1 ; j+=jone ) {
+
+ if ( ione > 1 ) {
+ arrayV(i+ione/2,j) = ( arrayV(i+ione,j) + arrayV(i,j) ) / 2 ;
+ if ( i == ione ) arrayV(i-ione/2,j) = ( arrayV(0,j) + arrayV(ione,j) ) / 2 ;
+ }
+ if ( jone > 1 ) {
+ arrayV(i,j+jone/2) = ( arrayV(i,j+jone) + arrayV(i,j) ) / 2 ;
+ if ( j == jone ) arrayV(i,j-jone/2) = ( arrayV(i,0) + arrayV(i,jone) ) / 2 ;
+ }
+ if ( ione > 1 && jone > 1 ) {
+ arrayV(i+ione/2,j+jone/2) = ( arrayV(i+ione,j+jone) + arrayV(i,j) ) / 2 ;
+ if ( i == ione ) arrayV(i-ione/2,j-jone/2) = ( arrayV(0,j-jone) + arrayV(ione,j) ) / 2 ;
+ if ( j == jone ) arrayV(i-ione/2,j-jone/2) = ( arrayV(i-ione,0) + arrayV(i,jone) ) / 2 ;
+ // Note that this leaves a point at the upper left and lower right corners uninitialized. Not a big deal.
+ }
+ }
+ }
+ }
+
+ }
+ }
+
+ ione = ione / 2 ; if ( ione < 1 ) ione = 1 ;
+ jone = jone / 2 ; if ( jone < 1 ) jone = 1 ;
+
+ }
+
+ //Differentiate V(r) and solve for E(r) using special equations for the first and last row
+ //Integrate E(r)/E(z) from point of origin to pad plane
+
+ for ( Int_t m = 0 ; m < phislices ; m++ ) {
+ TMatrixD& arrayV = *arrayofArrayV[m] ;
+ TMatrixD& eroverEz = *arrayofEroverEz[m] ;
+
+ for ( Int_t j = columns-1 ; j >= 0 ; j-- ) { // Count backwards to facilitate integration over Z
+
+ // Differentiate in R
+ for ( Int_t i = 1 ; i < rows-1 ; i++ ) arrayE(i,j) = -1 * ( arrayV(i+1,j) - arrayV(i-1,j) ) / (2*gridSizeR) ;
+ arrayE(0,j) = -1 * ( -0.5*arrayV(2,j) + 2.0*arrayV(1,j) - 1.5*arrayV(0,j) ) / gridSizeR ;
+ arrayE(rows-1,j) = -1 * ( 1.5*arrayV(rows-1,j) - 2.0*arrayV(rows-2,j) + 0.5*arrayV(rows-3,j) ) / gridSizeR ;
+ // Integrate over Z
+ for ( Int_t i = 0 ; i < rows ; i++ ) {
+ Int_t index = 1 ; // Simpsons rule if N=odd. If N!=odd then add extra point by trapezoidal rule.
+ eroverEz(i,j) = 0.0 ;
+ for ( Int_t k = j ; k < columns ; k++ ) {
+
+ eroverEz(i,j) += index*(gridSizeZ/3.0)*arrayE(i,k)/(-1*ezField) ;
+ if ( index != 4 ) index = 4; else index = 2 ;
+ }
+ if ( index == 4 ) eroverEz(i,j) -= (gridSizeZ/3.0)*arrayE(i,columns-1)/ (-1*ezField) ;
+ if ( index == 2 ) eroverEz(i,j) +=
+ (gridSizeZ/3.0)*(0.5*arrayE(i,columns-2)-2.5*arrayE(i,columns-1))/(-1*ezField) ;
+ if ( j == columns-2 ) eroverEz(i,j) =
+ (gridSizeZ/3.0)*(1.5*arrayE(i,columns-2)+1.5*arrayE(i,columns-1))/(-1*ezField) ;
+ if ( j == columns-1 ) eroverEz(i,j) = 0.0 ;
+ }
+ }
+ // if ( m == 0 ) { TCanvas* c1 = new TCanvas("erOverEz","erOverEz",50,50,840,600) ; c1 -> cd() ;
+ // eroverEz.Draw("surf") ; } // JT test
+ }
+
+ //Differentiate V(r) and solve for E(phi)
+ //Integrate E(phi)/E(z) from point of origin to pad plane
+
+ for ( Int_t m = 0 ; m < phislices ; m++ ) {
+
+ mplus = m + 1; signplus = 1 ;
+ mminus = m - 1 ; signminus = 1 ;
+ if (symmetry==1) { // Reflection symmetry in phi (e.g. symmetry at sector boundaries, or half sectors, etc.)
+ if ( mplus > phislices-1 ) mplus = phislices - 2 ;
+ if ( mminus < 0 ) mminus = 1 ;
+ }
+ else if (symmetry==-1) { // Anti-symmetry in phi
+ if ( mplus > phislices-1 ) { mplus = phislices - 2 ; signplus = -1 ; }
+ if ( mminus < 0 ) { mminus = 1 ; signminus = -1 ; }
+ }
+ else { // No Symmetries in phi, no boundaries, the calculations is continuous across all phi
+ if ( mplus > phislices-1 ) mplus = m + 1 - phislices ;
+ if ( mminus < 0 ) mminus = m - 1 + phislices ;
+ }
+ TMatrixD &arrayVP = *arrayofArrayV[mplus] ;
+ TMatrixD &arrayVM = *arrayofArrayV[mminus] ;
+ TMatrixD &ePhioverEz = *arrayofEPhioverEz[m] ;
+ for ( Int_t j = columns-1 ; j >= 0 ; j-- ) { // Count backwards to facilitate integration over Z
+ // Differentiate in Phi
+ for ( Int_t i = 0 ; i < rows ; i++ ) {
+ Float_t radius = fgkIFCRadius + i*gridSizeR ;
+ arrayE(i,j) = -1 * (signplus * arrayVP(i,j) - signminus * arrayVM(i,j) ) / (2*radius*gridSizePhi) ;
+ }
+ // Integrate over Z
+ for ( Int_t i = 0 ; i < rows ; i++ ) {
+ Int_t index = 1 ; // Simpsons rule if N=odd. If N!=odd then add extra point by trapezoidal rule.
+ ePhioverEz(i,j) = 0.0 ;
+ for ( Int_t k = j ; k < columns ; k++ ) {
+
+ ePhioverEz(i,j) += index*(gridSizeZ/3.0)*arrayE(i,k)/(-1*ezField) ;
+ if ( index != 4 ) index = 4; else index = 2 ;
+ }
+ if ( index == 4 ) ePhioverEz(i,j) -= (gridSizeZ/3.0)*arrayE(i,columns-1)/ (-1*ezField) ;
+ if ( index == 2 ) ePhioverEz(i,j) +=
+ (gridSizeZ/3.0)*(0.5*arrayE(i,columns-2)-2.5*arrayE(i,columns-1))/(-1*ezField) ;
+ if ( j == columns-2 ) ePhioverEz(i,j) =
+ (gridSizeZ/3.0)*(1.5*arrayE(i,columns-2)+1.5*arrayE(i,columns-1))/(-1*ezField) ;
+ if ( j == columns-1 ) ePhioverEz(i,j) = 0.0 ;
+ }
+ }
+ // if ( m == 5 ) { TCanvas* c2 = new TCanvas("arrayE","arrayE",50,50,840,600) ; c2 -> cd() ;
+ // arrayE.Draw("surf") ; } // JT test
+ }
+
+
+ // Differentiate V(r) and solve for E(z) using special equations for the first and last row
+ // Integrate (E(z)-Ezstd) from point of origin to pad plane
+
+ for ( Int_t m = 0 ; m < phislices ; m++ ) {
+ TMatrixD& arrayV = *arrayofArrayV[m] ;
+ TMatrixD& deltaEz = *arrayofDeltaEz[m] ;
+
+ // Differentiate V(z) and solve for E(z) using special equations for the first and last columns
+ for ( Int_t i = 0 ; i < rows ; i++) {
+ for ( Int_t j = 1 ; j < columns-1 ; j++ ) arrayE(i,j) = -1 * ( arrayV(i,j+1) - arrayV(i,j-1) ) / (2*gridSizeZ) ;
+ arrayE(i,0) = -1 * ( -0.5*arrayV(i,2) + 2.0*arrayV(i,1) - 1.5*arrayV(i,0) ) / gridSizeZ ;
+ arrayE(i,columns-1) = -1 * ( 1.5*arrayV(i,columns-1) - 2.0*arrayV(i,columns-2) + 0.5*arrayV(i,columns-3) ) / gridSizeZ ;
+ }
+
+ for ( Int_t j = columns-1 ; j >= 0 ; j-- ) { // Count backwards to facilitate integration over Z
+ // Integrate over Z
+ for ( Int_t i = 0 ; i < rows ; i++ ) {
+ Int_t index = 1 ; // Simpsons rule if N=odd. If N!=odd then add extra point by trapezoidal rule.
+ deltaEz(i,j) = 0.0 ;
+ for ( Int_t k = j ; k < columns ; k++ ) {
+ deltaEz(i,j) += index*(gridSizeZ/3.0)*arrayE(i,k) ;
+ if ( index != 4 ) index = 4; else index = 2 ;
+ }
+ if ( index == 4 ) deltaEz(i,j) -= (gridSizeZ/3.0)*arrayE(i,columns-1) ;
+ if ( index == 2 ) deltaEz(i,j) +=
+ (gridSizeZ/3.0)*(0.5*arrayE(i,columns-2)-2.5*arrayE(i,columns-1)) ;
+ if ( j == columns-2 ) deltaEz(i,j) =
+ (gridSizeZ/3.0)*(1.5*arrayE(i,columns-2)+1.5*arrayE(i,columns-1)) ;
+ if ( j == columns-1 ) deltaEz(i,j) = 0.0 ;
+ }
+ }
+ // if ( m == 0 ) { TCanvas* c1 = new TCanvas("erOverEz","erOverEz",50,50,840,600) ; c1 -> cd() ;
+ // eroverEz.Draw("surf") ; } // JT test
+
+ // calculate z distortion from the integrated Delta Ez residuals
+ // and include the aquivalence (Volt to cm) of the ROC shift !!
+
+ for ( Int_t j = 0 ; j < columns ; j++ ) {
+ for ( Int_t i = 0 ; i < rows ; i++ ) {
+
+ // Scale the Ez distortions with the drift velocity pertubation -> delivers cm
+ deltaEz(i,j) = deltaEz(i,j)*fgkdvdE;
+
+ // ROC Potential in cm aquivalent
+ Double_t dzROCShift = arrayV(i, columns -1)/ezField;
+ if ( rocDisplacement ) deltaEz(i,j) = deltaEz(i,j) + dzROCShift; // add the ROC misaligment
+
+ }
+ }
+
+ } // end loop over phi
+
+
+
+ for ( Int_t k = 0 ; k < phislices ; k++ )
+ {
+ arrayofSumChargeDensities[k]->Delete() ;
+ }
+
+
+
+ arrayE.Clear();
+}
Int_t AliTPCCorrection::IsPowerOfTwo(Int_t i) const {
if (npoints2<npoints) return 0;
AliTrackerBase::PropagateTrackToBxByBz(track0,refX,kMass,2.,kTRUE,kMaxSnp);
track1->Rotate(track0->GetAlpha());
- AliTrackerBase::PropagateTrackToBxByBz(track1,refX,kMass,2.,kTRUE,kMaxSnp);
+ AliTrackerBase::PropagateTrackToBxByBz(track1,refX,kMass,2.,kFALSE,kMaxSnp);
if (pcstream) (*pcstream)<<Form("fitDistort%s",GetName())<<
"point0.="<<&pointArray0<< // points
// corrArray - array with partial corrections
// step - skipe entries - if 1 all entries processed - it is slow
// debug 0 if debug on also space points dumped - it is slow
+
const Double_t kMaxSnp = 0.85;
const Double_t kMass = TDatabasePDG::Instance()->GetParticle("pi+")->Mass();
// const Double_t kB2C=-0.299792458e-3;
void AliTPCCorrection::FastSimDistortedVertex(Double_t orgVertex[3], Int_t nTracks, AliESDVertex &aV, AliESDVertex &avOrg, AliESDVertex &cV, AliESDVertex &cvOrg, TTreeSRedirector * const pcstream, Double_t etaCuts){
+ //
+ // Fast method to simulate the influence of the given distortion on the vertex reconstruction
+ //
- AliVertexerTracks *vertexer = new AliVertexerTracks(5);// 5kGaus
+ AliMagF* magF= (AliMagF*)TGeoGlobalMagField::Instance()->GetField();
+ if (!magF) AliError("Magneticd field - not initialized");
+ Double_t bz = magF->SolenoidField(); //field in kGauss
+ printf("bz: %lf\n",bz);
+ AliVertexerTracks *vertexer = new AliVertexerTracks(bz); // bz in kGauss
- TObjArray ATrk; // Original Track array of Aside
- TObjArray dATrk; // Distorted Track array of A side
- UShort_t *AId = new UShort_t[nTracks]; // A side Track ID
- TObjArray CTrk;
- TObjArray dCTrk;
- UShort_t *CId = new UShort_t [nTracks];
- Int_t ID=0;
+ TObjArray aTrk; // Original Track array of Aside
+ TObjArray daTrk; // Distorted Track array of A side
+ UShort_t *aId = new UShort_t[nTracks]; // A side Track ID
+ TObjArray cTrk;
+ TObjArray dcTrk;
+ UShort_t *cId = new UShort_t [nTracks];
+ Int_t id=0;
Double_t mass = TDatabasePDG::Instance()->GetParticle("pi+")->Mass();
TF1 fpt("fpt",Form("x*(1+(sqrt(x*x+%f^2)-%f)/([0]*[1]))^(-[0])",mass,mass),0.4,10);
fpt.SetParameters(7.24,0.120);
for(Int_t nt=0; nt<nTracks; nt++){
Double_t phi = gRandom->Uniform(0.0, 2*TMath::Pi());
Double_t eta = gRandom->Uniform(-etaCuts, etaCuts);
- Double_t pt = fpt.GetRandom();// momentum for f1
+ Double_t pt = fpt.GetRandom(); // momentum for f1
+ // printf("phi %lf eta %lf pt %lf\n",phi,eta,pt);
Short_t sign=1;
if(gRandom->Rndm() < 0.5){
sign =1;
"\n";
if(( eta>0.07 )&&( eta<etaCuts )) { // - log(tan(0.5*theta)), theta = 0.5*pi - ATan(5.0/80.0)
if (td){
- dATrk.AddLast(td);
- ATrk.AddLast(t);
- Int_t nn=ATrk.GetEntriesFast();
- AId[nn]=ID;
+ daTrk.AddLast(td);
+ aTrk.AddLast(t);
+ Int_t nn=aTrk.GetEntriesFast();
+ aId[nn]=id;
}
}else if(( eta<-0.07 )&&( eta>-etaCuts )){
if (td){
- dCTrk.AddLast(td);
- CTrk.AddLast(t);
- Int_t nn=CTrk.GetEntriesFast();
- CId[nn]=ID;
+ dcTrk.AddLast(td);
+ cTrk.AddLast(t);
+ Int_t nn=cTrk.GetEntriesFast();
+ cId[nn]=id;
}
}
- ID++;
+ id++;
}// end of track loop
vertexer->SetTPCMode();
vertexer->SetConstraintOff();
- aV = *((AliESDVertex*)vertexer->FindPrimaryVertex(&dATrk,AId));
- avOrg = *((AliESDVertex*)vertexer->FindPrimaryVertex(&ATrk,AId));
- cV = *((AliESDVertex*)vertexer->FindPrimaryVertex(&dCTrk,CId));
- cvOrg = *((AliESDVertex*)vertexer->FindPrimaryVertex(&CTrk,CId));
+ aV = *((AliESDVertex*)vertexer->FindPrimaryVertex(&daTrk,aId));
+ avOrg = *((AliESDVertex*)vertexer->FindPrimaryVertex(&aTrk,aId));
+ cV = *((AliESDVertex*)vertexer->FindPrimaryVertex(&dcTrk,cId));
+ cvOrg = *((AliESDVertex*)vertexer->FindPrimaryVertex(&cTrk,cId));
if (pcstream) (*pcstream)<<"vertex"<<
"x="<<orgVertex[0]<<
"y="<<orgVertex[1]<<
"avO.="<<&avOrg<< // original vertex A side
"cvO.="<<&cvOrg<<
"\n";
- delete []AId;
- delete []CId;
+ delete []aId;
+ delete []cId;
+}
+
+void AliTPCCorrection::AddVisualCorrection(AliTPCCorrection* corr, Int_t position){
+ //
+ // make correction available for visualization using
+ // TFormula, TFX and TTree::Draw
+ // important in order to check corrections and also compute dervied variables
+ // e.g correction partial derivatives
+ //
+ // NOTE - class is not owner of correction
+ //
+ if (!fgVisualCorrection) fgVisualCorrection=new TObjArray;
+ if (position!=0&&position>=fgVisualCorrection->GetEntriesFast())
+ fgVisualCorrection->Expand(position*2);
+ fgVisualCorrection->AddAt(corr, position);
+}
+
+
+
+Double_t AliTPCCorrection::GetCorrSector(Double_t sector, Double_t r, Double_t kZ, Int_t axisType, Int_t corrType){
+ //
+ // calculate the correction at given position - check the geffCorr
+ //
+ if (!fgVisualCorrection) return 0;
+ AliTPCCorrection *corr = (AliTPCCorrection*)fgVisualCorrection->At(corrType);
+ if (!corr) return 0;
+
+ Double_t phi=sector*TMath::Pi()/9.;
+ Double_t gx = r*TMath::Cos(phi);
+ Double_t gy = r*TMath::Sin(phi);
+ Double_t gz = r*kZ;
+ Int_t nsector=(gz>0) ? 0:18;
+ //
+ //
+ //
+ Float_t distPoint[3]={gx,gy,gz};
+ corr->DistortPoint(distPoint, nsector);
+ Double_t r0=TMath::Sqrt(gx*gx+gy*gy);
+ Double_t r1=TMath::Sqrt(distPoint[0]*distPoint[0]+distPoint[1]*distPoint[1]);
+ Double_t phi0=TMath::ATan2(gy,gx);
+ Double_t phi1=TMath::ATan2(distPoint[1],distPoint[0]);
+ if (axisType==0) return r1-r0;
+ if (axisType==1) return (phi1-phi0)*r0;
+ if (axisType==2) return distPoint[2]-gz;
+ return phi1-phi0;
+}
+
+Double_t AliTPCCorrection::GetCorrXYZ(Double_t gx, Double_t gy, Double_t gz, Int_t axisType, Int_t corrType){
+ //
+ // return correction at given x,y,z
+ //
+ if (!fgVisualCorrection) return 0;
+ AliTPCCorrection *corr = (AliTPCCorrection*)fgVisualCorrection->At(corrType);
+ if (!corr) return 0;
+ Double_t phi0= TMath::ATan2(gy,gx);
+ Int_t nsector=(gz>0) ? 0:18;
+ Float_t distPoint[3]={gx,gy,gz};
+ corr->DistortPoint(distPoint, nsector);
+ Double_t r0=TMath::Sqrt(gx*gx+gy*gy);
+ Double_t r1=TMath::Sqrt(distPoint[0]*distPoint[0]+distPoint[1]*distPoint[1]);
+ Double_t phi1=TMath::ATan2(distPoint[1],distPoint[0]);
+ if (axisType==0) return r1-r0;
+ if (axisType==1) return (phi1-phi0)*r0;
+ if (axisType==2) return distPoint[2]-gz;
+ return phi1-phi0;
}
git://git.uio.no / u / mrichter / AliRoot.git / blobdiff