#include <AliCDBMetaData.h>
#include "TVectorD.h"
+
+#include "TRandom.h"
+#include "AliExternalTrackParam.h"
+#include "AliTrackPointArray.h"
+#include "TDatabasePDG.h"
+#include "AliTrackerBase.h"
+#include "AliTPCROC.h"
+#include "THnSparse.h"
+
#include "TRandom.h"
#include "AliTPCTransform.h"
#include "AliTPCcalibDB.h"
#include "AliTrackerBase.h"
#include "AliTPCROC.h"
#include "THnSparse.h"
+
#include "AliTPCLaserTrack.h"
#include "AliTPCCorrection.h"
+#include "AliLog.h"
ClassImp(AliTPCCorrection)
h->SetBinContent(iz,ir,r1-r0);
}
}
- printf("SDF\n");
return h;
}
}
+void AliTPCCorrection::PoissonRelaxation2D(TMatrixD &arrayV, const TMatrixD &chargeDensity,
+ TMatrixD &arrayErOverEz, const Int_t rows,
+ const Int_t columns, const Int_t iterations ) {
+ //
+ // 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.
+ //
+ // 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<float> coef1(rows) ;
+ std::vector<float> 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 ;
+
+ }
+
+ // 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 ;
+ for ( Int_t k = j ; k < columns ; k++ ) {
+ arrayErOverEz(i,j) += index*(gridSizeZ/3.0)*arrayEr(i,k)/arrayEz(i,k) ;
+ 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 ;
+ }
+ }
+
+}
+
+
+
+const Int_t AliTPCCorrection::IsPowerOfTwo(Int_t i) {
+ //
+ // 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){
//
// 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);
if (r0>80){
corr->DistortPoint(distPoint, sector);
}
- Double_t value=distPoint[2]-gz;
+ // Double_t value=distPoint[2]-gz;
if (itype==0){
Double_t r1 = TMath::Sqrt(distPoint[0]*distPoint[0]+distPoint[1]*distPoint[1]);
Double_t phi1 = TMath::ATan2(distPoint[1],distPoint[0]);
git://git.uio.no / u / mrichter / AliRoot.git / blobdiff