X-Git-Url: http://git.uio.no/git/?p=u%2Fmrichter%2FAliRoot.git;a=blobdiff_plain;f=TPC%2FAliTPCCorrection.cxx;h=547d24f80e337bfb14aedf76e98f961bf4259fcc;hp=3fcc1b5d7c267627034d47b18447729e475d8b4d;hb=d0c1b3419f7d2eeb3063d5d3ffc65146a564b877;hpb=b5c28b5efe8ecad86bf8ab911ad2c4941499f99a diff --git a/TPC/AliTPCCorrection.cxx b/TPC/AliTPCCorrection.cxx index 3fcc1b5d7c2..547d24f80e3 100644 --- a/TPC/AliTPCCorrection.cxx +++ b/TPC/AliTPCCorrection.cxx @@ -50,42 +50,72 @@ #include #include #include +#include "TVectorD.h" +#include "AliTPCParamSR.h" -#include "TRandom.h" -#include "AliExternalTrackParam.h" -#include "AliTrackPointArray.h" -#include "TDatabasePDG.h" -#include "AliTrackerBase.h" -#include "AliTPCROC.h" -#include "THnSparse.h" +#include "AliTPCCorrection.h" +#include "AliLog.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" +#include "TRandom.h" + +#include "TDatabasePDG.h" + +#include "AliTPCTransform.h" +#include "AliTPCcalibDB.h" +#include "AliTPCExB.h" + +#include "AliTPCRecoParam.h" -#include "AliTPCCorrection.h" ClassImp(AliTPCCorrection) + +TObjArray *AliTPCCorrection::fgVisualCorrection=0; +// instance of correction for visualization + + // FIXME: the following values should come from the database -const Double_t AliTPCCorrection::fgkTPC_Z0 =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) +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)] // 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 } ; - + 83.06, 83.5, 84.0, 84.5, 85.0, 85.5, 86.0, 86.5, + 87.0, 87.5, 88.0, 88.5, 89.0, 89.5, 90.0, 90.5, 91.0, 92.0, + 93.0, 94.0, 95.0, 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, 241.0, 242.0, 243.0, 244.0, + 245.0, 245.5, 246.0, 246.5, 247.0, 247.5, 248.0, 248.5, 249.0, 249.5, + 250.0, 250.5, 251.0, 251.5, 252.0, 252.5, 253.0, 253.5, 254.0, 254.5 +} ; + 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, @@ -118,19 +148,33 @@ const Double_t AliTPCCorrection::fgkZList[AliTPCCorrection::kNZ] = { 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; + + // Initialization of interpolation points + for (Int_t i = 0; iGetXaxis()->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); } @@ -260,6 +305,7 @@ TH2F* AliTPCCorrection::CreateHistoDRinXY(Float_t z,Int_t nx,Int_t ny) { h->SetBinContent(ix,iy,0.); } } + delete tpcparam; return h; } @@ -271,6 +317,8 @@ TH2F* AliTPCCorrection::CreateHistoDRPhiinXY(Float_t z,Int_t nx,Int_t ny) { // 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]; @@ -282,7 +330,7 @@ TH2F* AliTPCCorrection::CreateHistoDRPhiinXY(Float_t z,Int_t nx,Int_t ny) { 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]); @@ -296,6 +344,39 @@ TH2F* AliTPCCorrection::CreateHistoDRPhiinXY(Float_t z,Int_t nx,Int_t ny) { 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; } @@ -322,7 +403,6 @@ TH2F* AliTPCCorrection::CreateHistoDRinZR(Float_t phi,Int_t nz,Int_t nr) { h->SetBinContent(iz,ir,r1-r0); } } - printf("SDF\n"); return h; } @@ -359,6 +439,32 @@ TH2F* AliTPCCorrection::CreateHistoDRPhiinZR(Float_t phi,Int_t nz,Int_t nr) { 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, @@ -387,16 +493,14 @@ TH2F* AliTPCCorrection::CreateTH2F(const char *name,const char *title, 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, - const Double_t er[kNZ][kNR], Double_t &er_value ) -{ + const Double_t er[kNZ][kNR], Double_t &erValue ) { // // Interpolate table - 2D interpolation // - Double_t save_er[10] ; + Double_t saveEr[5] = {0,0,0,0,0}; Search( kNZ, fgkZList, z, fJLow ) ; Search( kNR, fgkRList, r, fKLow ) ; @@ -406,16 +510,124 @@ void AliTPCCorrection::Interpolate2DEdistortion( const Int_t order, const Double if ( fKLow + order >= kNR - 1 ) fKLow = kNR - 1 - order ; for ( Int_t j = fJLow ; j < fJLow + order + 1 ; j++ ) { - save_er[j-fJLow] = Interpolate( &fgkRList[fKLow], &er[j][fKLow], order, r ) ; + saveEr[j-fJLow] = Interpolate( &fgkRList[fKLow], &er[j][fKLow], order, r ) ; } - er_value = Interpolate( &fgkZList[fJLow], save_er, order, z ) ; + erValue = Interpolate( &fgkZList[fJLow], saveEr, order, z ) ; } +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 ) -{ + const Int_t order, const Double_t x ) { // // Interpolate function Y(x) using linear (order=1) or quadratic (order=2) interpolation. // @@ -434,8 +646,7 @@ Double_t AliTPCCorrection::Interpolate( const Double_t xArray[], const Double_t } -void AliTPCCorrection::Search( const Int_t n, const Double_t xArray[], const Double_t x, Int_t &low ) -{ +void AliTPCCorrection::Search( const Int_t n, const Double_t xArray[], const Double_t x, Int_t &low ) { // // Search an ordered table by starting at the most recently used point // @@ -482,8 +693,590 @@ void AliTPCCorrection::Search( const Int_t n, const Double_t xArray[], const Dou } +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) + // + // Solve Poissons equation in a cylindrical coordinate system. The arrayV matrix must be filled with the + // boundary conditions on the first and last rows, and the first and last columns. The remainder of the + // array can be blank or contain a preliminary guess at the solution. The Charge density matrix contains + // the enclosed spacecharge density at each point. The charge density matrix can be full of zero's if + // you wish to solve Laplaces equation however it should not contain random numbers or you will get + // random numbers back as a solution. + // Poisson's equation is solved by iteratively relaxing the matrix to the final solution. In order to + // speed up the convergence to the best solution, this algorithm does a binary expansion of the solution + // space. First it solves the problem on a very sparse grid by skipping rows and columns in the original + // matrix. Then it doubles the number of points and solves the problem again. Then it doubles the + // number of points and solves the problem again. This happens several times until the maximum number + // of points has been included in the array. + // + // 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) + // + + 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 gridSizeZ = fgkTPCZ0 / (columns-1) ; + const Float_t ratio = gridSizeR*gridSizeR / (gridSizeZ*gridSizeZ) ; + + TMatrixD arrayEr(rows,columns) ; + TMatrixD arrayEz(rows,columns) ; + + //Check that number of rows and columns is suitable for a binary expansion + + if ( !IsPowerOfTwo(rows-1) ) { + AliError("PoissonRelaxation - Error in the number of rows. Must be 2**M - 1"); + return; + } + if ( !IsPowerOfTwo(columns-1) ) { + AliError("PoissonRelaxation - Error in the number of columns. Must be 2**N - 1"); + 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 size of the matrix to speed up the solution of the problem + + Int_t iOne = (rows-1)/4 ; + Int_t jOne = (columns-1)/4 ; + // Solve for N in 2**N, add one. + Int_t loops = 1 + (int) ( 0.5 + TMath::Log2( (double) TMath::Max(iOne,jOne) ) ) ; + + for ( Int_t count = 0 ; count < loops ; count++ ) { + // Loop while the matrix expands & the resolution increases. + + Float_t tempGridSizeR = gridSizeR * iOne ; + Float_t tempRatio = ratio * iOne * iOne / ( jOne * jOne ) ; + Float_t tempFourth = 1.0 / (2.0 + 2.0*tempRatio) ; + + // Do this the standard C++ way to avoid gcc extensions for Float_t coef1[rows] + std::vector coef1(rows) ; + std::vector coef2(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); + } + + TMatrixD sumChargeDensity(rows,columns) ; + + for ( Int_t i = iOne ; i < rows-1 ; i += iOne ) { + Float_t radius = fgkIFCRadius + iOne*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 ; + // Note that this is cylindrical geometry + 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++ ) { + // Solve Poisson's Equation + // Over-relaxation index, must be >= 1 but < 2. Arrange for it to evolve from 2 => 1 + // as interations increase. + Float_t overRelax = 1.0 + TMath::Sqrt( TMath::Cos( (k*TMath::PiOver2())/iterations ) ) ; + Float_t overRelaxM1 = overRelax - 1.0 ; + Float_t overRelaxtempFourth, overRelaxcoef5 ; + overRelaxtempFourth = overRelax * tempFourth ; + overRelaxcoef5 = overRelaxM1 / overRelaxtempFourth ; + + 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) + + tempRatio * ( arrayV(i,j-jOne) + arrayV(i,j+jOne) ) + - overRelaxcoef5 * arrayV(i,j) + + coef1[i] * arrayV(i+iOne,j) + + sumChargeDensity(i,j) + ) * overRelaxtempFourth; + } + } + + 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 ; + + sumChargeDensity.Clear(); + } + + // Differentiate V(r) and solve for E(r) using special equations for the first and last rows + for ( Int_t j = 0 ; j < columns ; j++ ) { + for ( Int_t i = 1 ; i < rows-1 ; i++ ) arrayEr(i,j) = -1 * ( arrayV(i+1,j) - arrayV(i-1,j) ) / (2*gridSizeR) ; + arrayEr(0,j) = -1 * ( -0.5*arrayV(2,j) + 2.0*arrayV(1,j) - 1.5*arrayV(0,j) ) / gridSizeR ; + arrayEr(rows-1,j) = -1 * ( 1.5*arrayV(rows-1,j) - 2.0*arrayV(rows-2,j) + 0.5*arrayV(rows-3,j) ) / gridSizeR ; + } + + // 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++ ) arrayEz(i,j) = -1 * ( arrayV(i,j+1) - arrayV(i,j-1) ) / (2*gridSizeZ) ; + arrayEz(i,0) = -1 * ( -0.5*arrayV(i,2) + 2.0*arrayV(i,1) - 1.5*arrayV(i,0) ) / gridSizeZ ; + arrayEz(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 i = 0 ; i < rows ; i++) { + // Note: go back and compare to old version of this code. See notes below. + // JT Test ... attempt to divide by real Ez not Ez to first order + for ( Int_t j = 0 ; j < columns ; j++ ) { + arrayEz(i,j) += ezField; + // This adds back the overall Z gradient of the field (main E field component) + } + // Warning: (-=) assumes you are using an error potetial without the overall Field included + } + + // 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) ; + 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 coef1(rows) ; // Do this the standard C++ way to avoid gcc extensions for Float_t coef1[rows] + std::vector coef2(rows) ; // Do this the standard C++ way to avoid gcc extensions for Float_t coef1[rows] + std::vector coef3(rows) ; // Do this the standard C++ way to avoid gcc extensions for Float_t coef1[rows] + std::vector 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 overRelaxcoef4(rows) ; // Do this the standard C++ way to avoid gcc extensions + std::vector 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 + + -AliExternalTrackParam * AliTPCCorrection::FitDistortedTrack(AliExternalTrackParam & trackIn, Double_t refX, Int_t dir,TTreeSRedirector *pcstream){ + for ( Int_t k = 0 ; k < phislices ; k++ ) + { + arrayofSumChargeDensities[k]->Delete() ; + } + + + + arrayE.Clear(); +} + + +Int_t AliTPCCorrection::IsPowerOfTwo(Int_t i) const { + // + // Helperfunction: Check if integer is a power of 2 + // + Int_t j = 0; + while( i > 0 ) { j += (i&1) ; i = (i>>1) ; } + if ( j == 1 ) return(1) ; // True + return(0) ; // False +} + + +AliExternalTrackParam * AliTPCCorrection::FitDistortedTrack(AliExternalTrackParam & trackIn, Double_t refX, Int_t dir, TTreeSRedirector * const pcstream){ // // Fit the track parameters - without and with distortion // 1. Space points in the TPC are simulated along the trajectory @@ -502,31 +1295,38 @@ AliExternalTrackParam * AliTPCCorrection::FitDistortedTrack(AliExternalTrackPara // track1.fP[2] - sinus of local inclination angle // track1.fP[3] - tangent of deep angle // track1.fP[4] - 1/pt + AliTPCROC * roc = AliTPCROC::Instance(); const Int_t npoints0=roc->GetNRows(0)+roc->GetNRows(36); const Double_t kRTPC0 =roc->GetPadRowRadii(0,0); const Double_t kRTPC1 =roc->GetPadRowRadii(36,roc->GetNRows(36)-1); - const Double_t kMaxSnp = 0.85; const Double_t kSigmaY=0.1; const Double_t kSigmaZ=0.1; + const Double_t kMaxR=500; + const Double_t kMaxZ=500; const Double_t kMass = TDatabasePDG::Instance()->GetParticle("pi+")->Mass(); + Int_t npoints1=0; + Int_t npoints2=0; AliExternalTrackParam track(trackIn); // // generate points AliTrackPointArray pointArray0(npoints0); AliTrackPointArray pointArray1(npoints0); Double_t xyz[3]; - AliTrackerBase::PropagateTrackToBxByBz(&track,kRTPC0,kMass,3,kTRUE,kMaxSnp); + if (!AliTrackerBase::PropagateTrackToBxByBz(&track,kRTPC0,kMass,3,kTRUE,kMaxSnp)) return 0; // // simulate the track Int_t npoints=0; Float_t covPoint[6]={0,0,0, kSigmaY*kSigmaY,0,kSigmaZ*kSigmaZ}; //covariance at the local frame for (Double_t radius=kRTPC0; radiusGaus(0,0.001); - xyz[1]+=gRandom->Gaus(0,0.001); + xyz[0]+=gRandom->Gaus(0,0.00005); + xyz[1]+=gRandom->Gaus(0,0.00005); + xyz[2]+=gRandom->Gaus(0,0.00005); + if (TMath::Abs(track.GetZ())>kMaxZ) break; + if (TMath::Abs(track.GetX())>kMaxR) break; AliTrackPoint pIn0; // space point AliTrackPoint pIn1; Int_t sector= (xyz[2]>0)? 0:18; @@ -550,6 +1350,7 @@ AliExternalTrackParam * AliTPCCorrection::FitDistortedTrack(AliExternalTrackPara npoints++; if (npoints>=npoints0) break; } + if (npoints0) ? jpoint: npoints-1-jpoint; // @@ -580,8 +1380,13 @@ AliExternalTrackParam * AliTPCCorrection::FitDistortedTrack(AliExternalTrackPara AliTrackPoint prot0 = pIn0.Rotate(track0->GetAlpha()); // rotate to the local frame - non distoted point AliTrackPoint prot1 = pIn1.Rotate(track1->GetAlpha()); // rotate to the local frame - distorted point // - AliTrackerBase::PropagateTrackToBxByBz(track0,prot0.GetX(),kMass,3,kFALSE,kMaxSnp); - AliTrackerBase::PropagateTrackToBxByBz(track1,prot0.GetX(),kMass,3,kFALSE,kMaxSnp); + if (!AliTrackerBase::PropagateTrackToBxByBz(track0,prot0.GetX(),kMass,3,kFALSE,kMaxSnp)) break; + if (!AliTrackerBase::PropagateTrackToBxByBz(track1,prot0.GetX(),kMass,3,kFALSE,kMaxSnp)) break; + if (TMath::Abs(track0->GetZ())>kMaxZ) break; + if (TMath::Abs(track0->GetX())>kMaxR) break; + if (TMath::Abs(track1->GetZ())>kMaxZ) break; + if (TMath::Abs(track1->GetX())>kMaxR) break; + track.GetXYZ(xyz); // distorted track also propagated to the same reference radius // Double_t pointPos[2]={0,0}; @@ -591,23 +1396,25 @@ AliExternalTrackParam * AliTPCCorrection::FitDistortedTrack(AliExternalTrackPara pointCov[0]=prot0.GetCov()[3];//simay^2 pointCov[1]=prot0.GetCov()[4];//sigmayz pointCov[2]=prot0.GetCov()[5];//sigmaz^2 - track0->Update(pointPos,pointCov); + if (!track0->Update(pointPos,pointCov)) break; // Double_t deltaX=prot1.GetX()-prot0.GetX(); // delta X Double_t deltaYX=deltaX*TMath::Tan(TMath::ASin(track1->GetSnp())); // deltaY due delta X Double_t deltaZX=deltaX*track1->GetTgl(); // deltaZ due delta X - pointPos[0]=prot1.GetY()-deltaYX;//local y - pointPos[1]=prot1.GetZ()-deltaZX;//local z + pointPos[0]=prot1.GetY()-deltaYX;//local y is sign correct? should be minus + pointPos[1]=prot1.GetZ()-deltaZX;//local z is sign correct? should be minus pointCov[0]=prot1.GetCov()[3];//simay^2 pointCov[1]=prot1.GetCov()[4];//sigmayz pointCov[2]=prot1.GetCov()[5];//sigmaz^2 - track1->Update(pointPos,pointCov); + if (!track1->Update(pointPos,pointCov)) break; + npoints1++; + npoints2++; } - + if (npoints2Rotate(track0->GetAlpha()); - track1->PropagateTo(track0->GetX(),AliTrackerBase::GetBz()); + AliTrackerBase::PropagateTrackToBxByBz(track1,refX,kMass,2.,kTRUE,kMaxSnp); if (pcstream) (*pcstream)<Mass(); // const Double_t kB2C=-0.299792458e-3; - const Int_t kMinEntries=50; + const Int_t kMinEntries=50; Double_t phi,theta, snp, mean,rms, entries; tinput->SetBranchAddress("theta",&theta); tinput->SetBranchAddress("phi", &phi); @@ -720,17 +1528,19 @@ void AliTPCCorrection::MakeTrackDistortionTree(TTree *tinput, Int_t dtype, Int_t // Int_t nentries=tinput->GetEntries(); Int_t ncorr=corrArray->GetEntries(); - Double_t corrections[100]; // + Double_t corrections[100]={0}; // Double_t tPar[5]; Double_t cov[15]={0,0,0,0,0,0,0,0,0,0,0,0,0,0}; Double_t refX=0; Int_t dir=0; - if (dtype==0) {refX=85; dir=-1;} - if (dtype==1) {refX=275; dir=1;} - if (dtype==2) {refX=85; dir=-1;} + if (dtype==0) {refX=85.; dir=-1;} + if (dtype==1) {refX=275.; dir=1;} + if (dtype==2) {refX=85.; dir=-1;} + if (dtype==3) {refX=360.; dir=-1;} // for (Int_t ientry=0; ientryGetEntry(ientry); + if (TMath::Abs(snp)>kMaxSnp) continue; tPar[0]=0; tPar[1]=theta*refX; tPar[2]=snp; @@ -739,7 +1549,12 @@ void AliTPCCorrection::MakeTrackDistortionTree(TTree *tinput, Int_t dtype, Int_t Double_t bz=AliTrackerBase::GetBz(); if (refX>10. && TMath::Abs(bz)>0.1 ) tPar[4]=snp/(refX*bz*kB2C*2); tPar[4]+=(gRandom->Rndm()-0.5)*0.02; - if (TMath::Abs(snp)>0.251) continue; + AliExternalTrackParam track(refX,phi,tPar,cov); + Double_t xyz[3]; + track.GetXYZ(xyz); + Int_t id=0; + Double_t dRrec=0; // dummy value - needed for points - e.g for laser + if (ptype==4 &&bz<0) mean*=-1; // interpret as curvature (*pcstream)<<"fit"<< "bz="<SetBranchAddress("dY.",&vecdY); + tree->SetBranchAddress("dZ.",&vecdZ); + tree->SetBranchAddress("eY.",&veceY); + tree->SetBranchAddress("eZ.",&veceZ); + tree->SetBranchAddress("LTr.",<r); + Int_t entries= tree->GetEntries(); + TTreeSRedirector *pcstream= new TTreeSRedirector("distortion4_0.root"); + Double_t bz=AliTrackerBase::GetBz(); + // + + for (Int_t ientry=0; ientryGetEntry(ientry); + if (!ltr->GetVecGX()){ + ltr->UpdatePoints(); + } + TVectorD * delta= (itype==0)? vecdY:vecdZ; + TVectorD * err= (itype==0)? veceY:veceZ; + + for (Int_t irow=0; irow<159; irow++){ + Int_t nentries = 1000; + if (veceY->GetMatrixArray()[irow]>cutErrY||veceZ->GetMatrixArray()[irow]>cutErrZ) nentries=0; + if (veceY->GetMatrixArray()[irow]GetMatrixArray()[irow]GetVecPhi())[irow]; + Double_t theta =ltr->GetTgl(); + Double_t mean=delta->GetMatrixArray()[irow]; + Double_t gx=0,gy=0,gz=0; + Double_t snp = (*ltr->GetVecP2())[irow]; + Double_t rms = 0.1+err->GetMatrixArray()[irow]; + gx = (*ltr->GetVecGX())[irow]; + gy = (*ltr->GetVecGY())[irow]; + gz = (*ltr->GetVecGZ())[irow]; + Int_t bundle= ltr->GetBundle(); + Double_t dRrec=0; + // + // get delta R used in reconstruction + AliTPCcalibDB* calib=AliTPCcalibDB::Instance(); + AliTPCCorrection * correction = calib->GetTPCComposedCorrection(); + const AliTPCRecoParam * recoParam = calib->GetTransform()->GetCurrentRecoParam(); + Double_t xyz0[3]={gx,gy,gz}; + Double_t oldR=TMath::Sqrt(gx*gx+gy*gy); + // + // old ExB correction + // + if(recoParam&&recoParam->GetUseExBCorrection()) { + Double_t xyz1[3]={gx,gy,gz}; + calib->GetExB()->Correct(xyz0,xyz1); + Double_t newR=TMath::Sqrt(xyz1[0]*xyz1[0]+xyz1[1]*xyz1[1]); + dRrec=oldR-newR; + } + if(recoParam&&recoParam->GetUseComposedCorrection()&&correction) { + Float_t xyz1[3]={gx,gy,gz}; + Int_t sector=(gz>0)?0:18; + correction->CorrectPoint(xyz1, sector); + Double_t newR=TMath::Sqrt(xyz1[0]*xyz1[0]+xyz1[1]*xyz1[1]); + dRrec=oldR-newR; + } + + + (*pcstream)<<"fit"<< + "bz="<Put(this, (*id1), metaData); } + +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 + // + + 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; + 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); + fpt.SetNpx(10000); + for(Int_t nt=0; ntUniform(0.0, 2*TMath::Pi()); + Double_t eta = gRandom->Uniform(-etaCuts, etaCuts); + 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; + }else{ + sign=-1; + } + + Double_t theta = 2*TMath::ATan(TMath::Exp(-eta))-TMath::Pi()/2.; + Double_t pxyz[3]; + pxyz[0]=pt*TMath::Cos(phi); + pxyz[1]=pt*TMath::Sin(phi); + pxyz[2]=pt*TMath::Tan(theta); + Double_t cv[21]={0}; + AliExternalTrackParam *t= new AliExternalTrackParam(orgVertex, pxyz, cv, sign); + + Double_t refX=1.; + Int_t dir=-1; + AliExternalTrackParam *td = FitDistortedTrack(*t, refX, dir, NULL); + if (!td) continue; + if (pcstream) (*pcstream)<<"track"<< + "eta="<0.07 )&&( eta-etaCuts )){ + if (td){ + dcTrk.AddLast(td); + cTrk.AddLast(t); + Int_t nn=cTrk.GetEntriesFast(); + cId[nn]=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)); + if (pcstream) (*pcstream)<<"vertex"<< + "x="<=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; +}