--- /dev/null
+/**************************************************************************
+ * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
+ * *
+ * Author: The ALICE Off-line Project. *
+ * Contributors are mentioned in the code where appropriate. *
+ * *
+ * Permission to use, copy, modify and distribute this software and its *
+ * documentation strictly for non-commercial purposes is hereby granted *
+ * without fee, provided that the above copyright notice appears in all *
+ * copies and that both the copyright notice and this permission notice *
+ * appear in the supporting documentation. The authors make no claims *
+ * about the suitability of this software for any purpose. It is *
+ * provided "as is" without express or implied warranty. *
+ **************************************************************************/
+
+/* $Id$ */
+
+// Author: ruben.shahoyan@cern.ch 09/09/2006
+//
+////////////////////////////////////////////////////////////////////////////////
+// //
+// AliCheb3D produces the interpolation of the user 3D->NDimOut arbitrary //
+// function supplied in "void (*fcn)(float* inp,float* out)" format //
+// either in a separate macro file or as a function pointer. //
+// Only coefficients needed to guarantee the requested precision are kept. //
+// //
+// The user-callable methods are: //
+// To create the interpolation use: //
+// AliCheb3D(const char* funName, // name of the file with user function //
+// or //
+// AliCheb3D(void (*ptr)(float*,float*),// pointer on the user function //
+// Int_t DimOut, // dimensionality of the function's output //
+// Float_t *bmin, // lower 3D bounds of interpolation domain //
+// Float_t *bmax, // upper 3D bounds of interpolation domain //
+// Int_t *npoints, // number of points in each of 3 input //
+// // dimension, defining the interpolation grid //
+// Float_t prec=1E-6); // requested max.absolute difference between //
+// // the interpolation and any point on grid //
+// //
+// To test obtained parameterization use the method //
+// TH1* TestRMS(int idim,int npoints = 1000,TH1* histo=0); //
+// it will compare the user output of the user function and interpolation //
+// for idim-th output dimension and fill the difference in the supplied //
+// histogram. If no histogram is supplied, it will be created. //
+// //
+// To save the interpolation data: //
+// SaveData(const char* filename, Bool_t append ) //
+// write text file with data. If append is kTRUE and the output file already //
+// exists, data will be added in the end of the file. //
+// Alternatively, SaveData(FILE* stream) will write the data to //
+// already existing stream. //
+// //
+// To read back already stored interpolation use either the constructor //
+// AliCheb3D(const char* inpFile); //
+// or the default constructor AliCheb3D() followed by //
+// AliCheb3D::LoadData(const char* inpFile); //
+// //
+// To compute the interpolation use Eval(float* par,float *res) method, with //
+// par being 3D vector of arguments (inside the validity region) and res is //
+// the array of DimOut elements for the output. //
+// //
+// If only one component (say, idim-th) of the output is needed, use faster //
+// Float_t Eval(Float_t *par,int idim) method. //
+// //
+// void Print(option="") will print the name, the ranges of validity and //
+// the absolute precision of the parameterization. Option "l" will also print //
+// the information about the number of coefficients for each output //
+// dimension. //
+// //
+// NOTE: during the evaluation no check is done for parameter vector being //
+// outside the interpolation region. If there is such a risk, use //
+// Bool_t IsInside(float *par) method. Chebyshev parameterization is not //
+// good for extrapolation! //
+// //
+// For the properties of Chebyshev parameterization see: //
+// H.Wind, CERN EP Internal Report, 81-12/Rev. //
+// //
+////////////////////////////////////////////////////////////////////////////////
+
+#include <TString.h>
+#include <TSystem.h>
+#include <TRandom.h>
+#include <TROOT.h>
+#include "AliCheb3D.h"
+
+
+
+ClassImp(AliCheb3DCalc)
+
+
+AliCheb3DCalc::AliCheb3DCalc():
+ TNamed("", ""),
+ fNCoefs(0),
+ fNRows(0),
+ fNCols(0),
+ fNElemBound2D(0),
+ fNColsAtRow(0),
+ fColAtRowBg(0),
+ fCoefBound2D0(0),
+ fCoefBound2D1(0),
+ fCoefs(0),
+ fTmpCf1(0),
+ fTmpCf0(0)
+{
+ // Default constructor
+ Init0();
+}
+
+AliCheb3DCalc::AliCheb3DCalc(FILE* stream):
+ TNamed("", ""),
+ fNCoefs(0),
+ fNRows(0),
+ fNCols(0),
+ fNElemBound2D(0),
+ fNColsAtRow(0),
+ fColAtRowBg(0),
+ fCoefBound2D0(0),
+ fCoefBound2D1(0),
+ fCoefs(0),
+ fTmpCf1(0),
+ fTmpCf0(0)
+{
+ // Default constructor
+ Init0();
+ LoadData(stream);
+}
+
+//__________________________________________________________________________________________
+void AliCheb3DCalc::Clear(Option_t*)
+{
+ // delete all dynamycally allocated structures
+ if (fTmpCf1) { delete[] fTmpCf1; fTmpCf1 = 0;}
+ if (fTmpCf0) { delete[] fTmpCf0; fTmpCf0 = 0;}
+ if (fCoefs) { delete[] fCoefs; fCoefs = 0;}
+ if (fCoefBound2D0) { delete[] fCoefBound2D0; fCoefBound2D0 = 0; }
+ if (fCoefBound2D1) { delete[] fCoefBound2D1; fCoefBound2D1 = 0; }
+ if (fNColsAtRow) { delete[] fNColsAtRow; fNColsAtRow = 0; }
+ if (fColAtRowBg) { delete[] fColAtRowBg; fColAtRowBg = 0; }
+ //
+}
+
+//__________________________________________________________________________________________
+void AliCheb3DCalc::Init0()
+{
+ // reset everything to 0
+ fNCoefs = fNRows = fNCols = fNElemBound2D = 0;
+ fCoefs = 0;
+ fCoefBound2D0 = fCoefBound2D1 = 0;
+ fNColsAtRow = fColAtRowBg = 0;
+ fTmpCf0 = fTmpCf1 = 0;
+}
+
+//__________________________________________________________________________________________
+void AliCheb3DCalc::Print(Option_t* ) const
+{
+ printf("Chebyshev parameterization data %s for 3D->1 function.\n",GetName());
+ int nmax3d = 0;
+ for (int i=fNElemBound2D;i--;) if (fCoefBound2D0[i]>nmax3d) nmax3d = fCoefBound2D0[i];
+ printf("%d coefficients in %dx%dx%d matrix\n",fNCoefs,fNRows,fNCols,nmax3d);
+ //
+}
+
+//__________________________________________________________________________________________
+Float_t AliCheb3DCalc::Eval(Float_t *par) const
+{
+ // evaluate Chebyshev parameterization for 3D function.
+ // VERY IMPORTANT: par must contain the function arguments ALREADY MAPPED to [-1:1] interval
+ Float_t &z = par[2];
+ Float_t &y = par[1];
+ Float_t &x = par[0];
+ //
+ int ncfRC;
+ for (int id0=fNRows;id0--;) {
+ int nCLoc = fNColsAtRow[id0]; // number of significant coefs on this row
+ int Col0 = fColAtRowBg[id0]; // beginning of local column in the 2D boundary matrix
+ for (int id1=nCLoc;id1--;) {
+ int id = id1+Col0;
+ fTmpCf1[id1] = (ncfRC=fCoefBound2D0[id]) ? ChebEval1D(z,fCoefs + fCoefBound2D1[id], ncfRC) : 0.0;
+ }
+ fTmpCf0[id0] = nCLoc>0 ? ChebEval1D(y,fTmpCf1,nCLoc):0.0;
+ }
+ return ChebEval1D(x,fTmpCf0,fNRows);
+ //
+}
+
+//_______________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+void AliCheb3DCalc::SaveData(const char* outfile,Bool_t append) const
+{
+ // writes coefficients data to output text file, optionallt appending on the end of existing file
+ TString strf = outfile;
+ gSystem->ExpandPathName(strf);
+ FILE* stream = fopen(strf,append ? "a":"w");
+ SaveData(stream);
+ fclose(stream);
+ //
+}
+#endif
+
+//_______________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+void AliCheb3DCalc::SaveData(FILE* stream) const
+{
+ // writes coefficients data to existing output stream
+ // Note: fNCols, fNElemBound2D and fColAtRowBg is not stored, will be computed on fly during the loading of this file
+ fprintf(stream,"#\nSTART %s\n",GetName());
+ fprintf(stream,"# Number of rows\n%d\n",fNRows);
+ //
+ fprintf(stream,"# Number of columns per row\n");
+ for (int i=0;i<fNRows;i++) fprintf(stream,"%d\n",fNColsAtRow[i]);
+ //
+ fprintf(stream,"# Number of Coefs in each significant block of third dimension\n");
+ for (int i=0;i<fNElemBound2D;i++) fprintf(stream,"%d\n",fCoefBound2D0[i]);
+ //
+ fprintf(stream,"# Coefficients\n");
+ for (int i=0;i<fNCoefs;i++) fprintf(stream,"%+.8e\n",fCoefs[i]);
+ fprintf(stream,"END %s\n",GetName());
+ //
+}
+#endif
+
+//_______________________________________________
+void AliCheb3DCalc::LoadData(FILE* stream)
+{
+ // Load coefs. from the stream
+ if (!stream) {Error("LoadData","No stream provided.\nStop"); exit(1);}
+ TString buffs;
+ Clear();
+ ReadLine(buffs,stream);
+ if (!buffs.BeginsWith("START")) {Error("LoadData","Expected: \"START <fit_name>\", found \"%s\"\nStop\n",buffs.Data());exit(1);}
+ if (buffs.First(' ')>0) SetName(buffs.Data()+buffs.First(' ')+1);
+ //
+ ReadLine(buffs,stream); // NRows
+ fNRows = buffs.Atoi();
+ if (fNRows<1) {Error("LoadData","Expected: '<number_of_rows>', found \"%s\"\nStop\n",buffs.Data());exit(1);}
+ //
+ fNCols = 0;
+ fNElemBound2D = 0;
+ InitRows(fNRows);
+ //
+ for (int id0=0;id0<fNRows;id0++) {
+ ReadLine(buffs,stream); // n.cols at this row
+ fNColsAtRow[id0] = buffs.Atoi();
+ fColAtRowBg[id0] = fNElemBound2D; // begining of this row in 2D boundary surface
+ fNElemBound2D += fNColsAtRow[id0];
+ if (fNCols<fNColsAtRow[id0]) fNCols = fNColsAtRow[id0];
+ }
+ InitCols(fNCols);
+ //
+ fNCoefs = 0;
+ InitElemBound2D(fNElemBound2D);
+ //
+ for (int i=0;i<fNElemBound2D;i++) {
+ ReadLine(buffs,stream); // n.coeffs at 3-d dimension for the given column/row
+ fCoefBound2D0[i] = buffs.Atoi();
+ fCoefBound2D1[i] = fNCoefs;
+ fNCoefs += fCoefBound2D0[i];
+ }
+ //
+ if (fNCoefs<=0) {Error("LoadData","Negtive (%d) number of Chebychef coeffs. is obtained.\nStop\n",fNCoefs);exit(1);}
+ //
+ InitCoefs(fNCoefs);
+ for (int i=0;i<fNCoefs;i++) {
+ ReadLine(buffs,stream);
+ fCoefs[i] = buffs.Atof();
+ }
+ // check end_of_data record
+ ReadLine(buffs,stream);
+ if (!buffs.BeginsWith("END") || !buffs.Contains(GetName())) {
+ Error("LoadData","Expected \"END %s\", found \"%s\".\nStop\n",GetName(),buffs.Data());
+ exit(1);
+ }
+ //
+}
+
+//_______________________________________________
+void AliCheb3DCalc::ReadLine(TString& str,FILE* stream)
+{
+ // read single line from the stream, skipping empty and commented lines. EOF is not expected
+ while (str.Gets(stream)) {
+ str = str.Strip(TString::kBoth,' ');
+ if (str.IsNull()||str.BeginsWith("#")) continue;
+ return;
+ }
+ fprintf(stderr,"AliCheb3D::ReadLine: Failed to read from stream.\nStop");exit(1); // normally, should not reach here
+}
+
+//_______________________________________________
+void AliCheb3DCalc::InitCols(int nc)
+{
+ // Set max.number of significant columns in the coefs matrix
+ fNCols = nc;
+ if (fTmpCf1) delete[] fTmpCf1;
+ fTmpCf1 = new Float_t [fNCols];
+}
+
+//_______________________________________________
+void AliCheb3DCalc::InitRows(int nr)
+{
+ // Set max.number of significant rows in the coefs matrix
+ if (fNColsAtRow) delete[] fNColsAtRow;
+ if (fColAtRowBg) delete[] fColAtRowBg;
+ if (fTmpCf0) delete[] fTmpCf0;
+ fNRows = nr;
+ fNColsAtRow = new Int_t[fNRows];
+ fTmpCf0 = new Float_t [fNRows];
+ fColAtRowBg = new Int_t[fNRows];
+ for (int i=fNRows;i--;) fNColsAtRow[i] = fColAtRowBg[i] = 0;
+}
+
+//_______________________________________________
+void AliCheb3DCalc::InitElemBound2D(int ne)
+{
+ // Set max number of significant coefs for given row/column of coefs 3D matrix
+ if (fCoefBound2D0) delete[] fCoefBound2D0;
+ if (fCoefBound2D1) delete[] fCoefBound2D1;
+ fNElemBound2D = ne;
+ fCoefBound2D0 = new Int_t[fNElemBound2D];
+ fCoefBound2D1 = new Int_t[fNElemBound2D];
+ for (int i=fNElemBound2D;i--;) fCoefBound2D0[i] = fCoefBound2D1[i] = 0;
+}
+
+//_______________________________________________
+void AliCheb3DCalc::InitCoefs(int nc)
+{
+ // Set total number of significant coefs
+ if (fCoefs) delete[] fCoefs;
+ fNCoefs = nc;
+ fCoefs = new Float_t [fNCoefs];
+ for (int i=fNCoefs;i--;) fCoefs[i] = 0.0;
+}
+
+
+
+
+ClassImp(AliCheb3D)
+
+AliCheb3D::AliCheb3D():
+ TNamed("", ""),
+ fDimOut(0),
+ fPrec(0.),
+ fMaxCoefs(0),
+ fResTmp(0),
+ fGrid(0),
+ fUsrMacro(0)
+{
+ // Default constructor
+ Init0();
+}
+
+AliCheb3D::AliCheb3D(const char* inputFile):
+ TNamed("", ""),
+ fDimOut(0),
+ fPrec(0.),
+ fMaxCoefs(0),
+ fResTmp(0),
+ fGrid(0),
+ fUsrMacro(0)
+{
+ // Default constructor
+ Init0();
+ LoadData(inputFile);
+}
+
+
+
+AliCheb3D::AliCheb3D(FILE* stream):
+ TNamed("", ""),
+ fDimOut(0),
+ fPrec(0.),
+ fMaxCoefs(0),
+ fResTmp(0),
+ fGrid(0),
+ fUsrMacro(0)
+{
+ // Default constructor
+ Init0();
+ LoadData(stream);
+}
+
+
+//__________________________________________________________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+AliCheb3D::AliCheb3D(const char* funName, int DimOut, Float_t *bmin,Float_t *bmax, Int_t *npoints, Float_t prec) : TNamed(funName,funName)
+{
+ // Construct the parameterization for the function
+ // funName : name of the file containing the function: void funName(Float_t * inp,Float_t * out)
+ // DimOut : dimension of the vector computed by the user function
+ // bmin : array of 3 elements with the lower boundaries of the region where the function is defined
+ // bmax : array of 3 elements with the upper boundaries of the region where the function is defined
+ // npoints : array of 3 elements with the number of points to compute in each of 3 dimension
+ // prec : max allowed absolute difference between the user function and computed parameterization on the requested grid
+ //
+ Init0();
+ fPrec = TMath::Max(1.E-12f,prec);
+ if (DimOut<1) {Error("AliCheb3D","Requested output dimension is %d\nStop\n",fDimOut); exit(1);}
+ SetDimOut(DimOut);
+ PrepareBoundaries(bmin,bmax);
+ DefineGrid(npoints);
+ SetUsrFunction(funName);
+ ChebFit();
+ //
+}
+#endif
+
+//__________________________________________________________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+AliCheb3D::AliCheb3D(void (*ptr)(float*,float*), int DimOut, Float_t *bmin,Float_t *bmax, Int_t *npoints, Float_t prec) : TNamed("AliCheb3D","AliCheb3D")
+{
+ // Construct the parameterization for the function
+ // ptr : pointer on the function: void fun(Float_t * inp,Float_t * out)
+ // DimOut : dimension of the vector computed by the user function
+ // bmin : array of 3 elements with the lower boundaries of the region where the function is defined
+ // bmax : array of 3 elements with the upper boundaries of the region where the function is defined
+ // npoints : array of 3 elements with the number of points to compute in each of 3 dimension
+ // prec : max allowed absolute difference between the user function and computed parameterization on the requested grid
+ //
+ Init0();
+ fPrec = TMath::Max(1.E-12f,prec);
+ if (DimOut<1) {Error("AliCheb3D","Requested output dimension is %d\nStop\n",fDimOut); exit(1);}
+ SetDimOut(DimOut);
+ PrepareBoundaries(bmin,bmax);
+ DefineGrid(npoints);
+ SetUsrFunction(ptr);
+ ChebFit();
+ //
+}
+#endif
+
+//__________________________________________________________________________________________
+void AliCheb3D::Clear(Option_t*)
+{
+ if (fResTmp) { delete[] fResTmp; fResTmp = 0; }
+ if (fGrid) { delete[] fGrid; fGrid = 0; }
+ if (fUsrMacro) { delete fUsrMacro; fUsrMacro = 0;}
+ fChebCalc.Delete();
+ //
+}
+
+//__________________________________________________________________________________________
+void AliCheb3D::Print(Option_t* opt) const
+{
+ printf("%s: Chebyshev parameterization for 3D->%dD function. Precision: %e\n",GetName(),fDimOut,fPrec);
+ printf("Region of validity: [%+.5e:%+.5e] [%+.5e:%+.5e] [%+.5e:%+.5e]\n",fBMin[0],fBMax[0],fBMin[1],fBMax[1],fBMin[2],fBMax[2]);
+ TString opts = opt; opts.ToLower();
+ if (opts.Contains("l")) for (int i=0;i<fDimOut;i++) {printf("Output dimension %d:\n",i+1); GetChebCalc(i)->Print();}
+ //
+}
+
+//__________________________________________________________________________________________
+void AliCheb3D::Init0()
+{
+ for (int i=3;i--;) fBMin[i] = fBMax[i] = fBScale[i] = fBOffset[i] = 0;
+ fMaxCoefs = 0;
+ fGrid = 0;
+ fResTmp = 0;
+ fUsrFunName = "";
+ fUsrMacro = 0;
+#ifdef _INC_CREATION_ALICHEB3D_
+ gUsrFunAliCheb3D = 0;
+#endif
+}
+
+//__________________________________________________________________________________________
+void AliCheb3D::PrepareBoundaries(Float_t *bmin,Float_t *bmax)
+{
+ // Set and check boundaries defined by user, prepare coefficients for their conversion to [-1:1] interval
+ //
+ for (int i=3;i--;) {
+ fBMin[i] = bmin[i];
+ fBMax[i] = bmax[i];
+ fBScale[i] = bmax[i]-bmin[i];
+ if (fBScale[i]<=0) {
+ Error("PrepareBoundaries","Boundaries for %d-th dimension are not increasing: %+.4e %+.4e\nStop\n",i,fBMin[i],fBMax[i]);
+ exit(1);
+ }
+ fBOffset[i] = bmin[i] + fBScale[i]/2.0;
+ fBScale[i] = 2./fBScale[i];
+ }
+ //
+}
+
+//__________________________________________________________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+void AliCheb3D::SetUsrFunction(const char* name)
+{
+ // load user macro with function definition and compile it
+ gUsrFunAliCheb3D = 0;
+ fUsrFunName = name;
+ gSystem->ExpandPathName(fUsrFunName);
+ if (fUsrMacro) delete fUsrMacro;
+ TString tmpst = fUsrFunName;
+ tmpst += "+"; // prepare filename to compile
+ if (gROOT->LoadMacro(tmpst.Data())) {Error("SetUsrFunction","Failed to load user function from %s\nStop\n",name); exit(1);}
+ fUsrMacro = new TMethodCall();
+ tmpst = tmpst.Data() + tmpst.Last('/')+1; //Strip away any path preceding the macro file name
+ int dot = tmpst.Last('.');
+ if (dot>0) tmpst.Resize(dot);
+ fUsrMacro->InitWithPrototype(tmpst.Data(),"Float_t *,Float_t *");
+ long args[2];
+ args[0] = (long)fArgsTmp;
+ args[1] = (long)fResTmp;
+ fUsrMacro->SetParamPtrs(args);
+ //
+}
+#endif
+
+//__________________________________________________________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+void AliCheb3D::SetUsrFunction(void (*ptr)(float*,float*))
+{
+ if (fUsrMacro) delete fUsrMacro;
+ fUsrMacro = 0;
+ fUsrFunName = "";
+ gUsrFunAliCheb3D = ptr;
+}
+#endif
+
+//__________________________________________________________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+void AliCheb3D::EvalUsrFunction(Float_t *x, Float_t *res) {
+ for (int i=3;i--;) fArgsTmp[i] = x[i];
+ if (gUsrFunAliCheb3D) gUsrFunAliCheb3D(fArgsTmp,fResTmp);
+ else fUsrMacro->Execute();
+ for (int i=fDimOut;i--;) res[i] = fResTmp[i];
+}
+#endif
+
+//__________________________________________________________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+Int_t AliCheb3D::CalcChebCoefs(Float_t *funval,int np, Float_t *outCoefs, Float_t prec)
+{
+ // Calculate Chebyshev coeffs using precomputed function values at np roots.
+ // If prec>0, estimate the highest coeff number providing the needed precision
+ //
+ double sm; // do summations in double to minimize the roundoff error
+ for (int ic=0;ic<np;ic++) { // compute coeffs
+ sm = 0;
+ for (int ir=0;ir<np;ir++) {
+ float rt = TMath::Cos( ic*(ir+0.5)*TMath::Pi()/np);
+ sm += funval[ir]*rt;
+ }
+ outCoefs[ic] = Float_t( sm * ((ic==0) ? 1./np : 2./np) );
+ }
+ //
+ if (prec<=0) return np;
+ //
+ sm = 0;
+ int cfMax = 0;
+ for (cfMax=np;cfMax--;) {
+ sm += TMath::Abs(outCoefs[cfMax]);
+ if (sm>=prec) break;
+ }
+ if (++cfMax==0) cfMax=1;
+ return cfMax;
+ //
+}
+#endif
+
+//__________________________________________________________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+void AliCheb3D::DefineGrid(Int_t* npoints)
+{
+ // prepare the grid of Chebyshev roots in each dimension
+ const int kMinPoints = 1;
+ int ntot = 0;
+ fMaxCoefs = 1;
+ for (int id=3;id--;) {
+ fNPoints[id] = npoints[id];
+ if (fNPoints[id]<kMinPoints) {
+ Error("DefineGrid","at %d-th dimension %d point is requested, at least %d is needed\nStop\n",fNPoints[id],kMinPoints);
+ exit(1);
+ }
+ ntot += fNPoints[id];
+ fMaxCoefs *= fNPoints[id];
+ }
+ fGrid = new Float_t [ntot];
+ //
+ int curp = 0;
+ for (int id=3;id--;) {
+ int np = fNPoints[id];
+ fGridOffs[id] = curp;
+ for (int ip=0;ip<np;ip++) {
+ Float_t x = TMath::Cos( TMath::Pi()*(ip+0.5)/np );
+ fGrid[curp++] = MapToExternal(x,id);
+ }
+ }
+ //
+}
+#endif
+
+//__________________________________________________________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+Int_t AliCheb3D::ChebFit()
+{
+ // prepare parameterization for all output dimensions
+ int ir=0;
+ for (int i=fDimOut;i--;) ir+=ChebFit(i);
+ return ir;
+}
+#endif
+
+//__________________________________________________________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+Int_t AliCheb3D::ChebFit(int dmOut)
+{
+ // prepare paramaterization of 3D function for dmOut-th dimension
+ int maxDim = 0;
+ for (int i=0;i<3;i++) if (maxDim<fNPoints[i]) maxDim = fNPoints[i];
+ Float_t *fvals = new Float_t [ fNPoints[0] ];
+ Float_t *tmpCoef3D = new Float_t [ fNPoints[0]*fNPoints[1]*fNPoints[2] ];
+ Float_t *tmpCoef2D = new Float_t [ fNPoints[0]*fNPoints[1] ];
+ Float_t *tmpCoef1D = new Float_t [ maxDim ];
+ //
+ Float_t RTiny = fPrec/Float_t(maxDim); // neglect coefficient below this threshold
+ //
+ // 1D Cheb.fit for 0-th dimension at current steps of remaining dimensions
+ int ncmax = 0;
+ //
+ AliCheb3DCalc* cheb = GetChebCalc(dmOut);
+ //
+ for (int id2=fNPoints[2];id2--;) {
+ fArgsTmp[2] = fGrid[ fGridOffs[2]+id2 ];
+ //
+ for (int id1=fNPoints[1];id1--;) {
+ fArgsTmp[1] = fGrid[ fGridOffs[1]+id1 ];
+ //
+ for (int id0=fNPoints[0];id0--;) {
+ fArgsTmp[0] = fGrid[ fGridOffs[0]+id0 ];
+ EvalUsrFunction(); // compute function values at Chebyshev roots of 0-th dimension
+ fvals[id0] = fResTmp[dmOut];
+ }
+ int nc = CalcChebCoefs(fvals,fNPoints[0], tmpCoef1D, fPrec);
+ for (int id0=fNPoints[0];id0--;) tmpCoef2D[id1 + id0*fNPoints[1]] = tmpCoef1D[id0];
+ if (ncmax<nc) ncmax = nc; // max coefs to be kept in dim0 to guarantee needed precision
+ }
+ //
+ // once each 1d slice of given 2d slice is parametrized, parametrize the Cheb.coeffs
+ for (int id0=fNPoints[0];id0--;) {
+ CalcChebCoefs( tmpCoef2D+id0*fNPoints[1], fNPoints[1], tmpCoef1D, -1);
+ for (int id1=fNPoints[1];id1--;) tmpCoef3D[id2 + fNPoints[2]*(id1+id0*fNPoints[1])] = tmpCoef1D[id1];
+ }
+ }
+ //
+ // now fit the last dimensions Cheb.coefs
+ for (int id0=fNPoints[0];id0--;) {
+ for (int id1=fNPoints[1];id1--;) {
+ CalcChebCoefs( tmpCoef3D+ fNPoints[2]*(id1+id0*fNPoints[1]), fNPoints[2], tmpCoef1D, -1);
+ for (int id2=fNPoints[2];id2--;) tmpCoef3D[id2+ fNPoints[2]*(id1+id0*fNPoints[1])] = tmpCoef1D[id2]; // store on place
+ }
+ }
+ //
+ // now find 2D surface which separates significant coefficients of 3D matrix from nonsignificant ones (up to fPrec)
+ int *tmpCoefSurf = new Int_t[ fNPoints[0]*fNPoints[1] ];
+ for (int id0=fNPoints[0];id0--;) for (int id1=fNPoints[1];id1--;) tmpCoefSurf[id1+id0*fNPoints[1]]=0;
+ Double_t resid = 0;
+ for (int id0=fNPoints[0];id0--;) {
+ for (int id1=fNPoints[1];id1--;) {
+ for (int id2=fNPoints[2];id2--;) {
+ int id = id2 + fNPoints[2]*(id1+id0*fNPoints[1]);
+ Float_t cfa = TMath::Abs(tmpCoef3D[id]);
+ if (cfa < RTiny) {tmpCoef3D[id] = 0; continue;} // neglect coeefs below the threshold
+
+ resid += cfa;
+ if (resid<fPrec) continue; // this coeff is negligible
+ // otherwise go back 1 step
+ resid -= cfa;
+ tmpCoefSurf[id1+id0*fNPoints[1]] = id2+1; // how many coefs to keep
+ break;
+ }
+ }
+ }
+ /*
+ printf("\n\nCoeffs\n");
+ int cnt = 0;
+ for (int id0=0;id0<fNPoints[0];id0++) {
+ for (int id1=0;id1<fNPoints[1];id1++) {
+ for (int id2=0;id2<fNPoints[2];id2++) {
+ printf("%2d%2d%2d %+.4e |",id0,id1,id2,tmpCoef3D[cnt++]);
+ }
+ printf("\n");
+ }
+ printf("\n");
+ }
+ */
+ // see if there are rows to reject, find max.significant column at each row
+ int NRows = fNPoints[0];
+ int *tmpCols = new int[NRows];
+ for (int id0=fNPoints[0];id0--;) {
+ int id1 = fNPoints[1];
+ while (id1>0 && tmpCoefSurf[(id1-1)+id0*fNPoints[1]]==0) id1--;
+ tmpCols[id0] = id1;
+ }
+ // find max significant row
+ for (int id0=NRows;id0--;) {if (tmpCols[id0]>0) break; NRows--;}
+ // find max significant column and fill the permanent storage for the max sigificant column of each row
+ cheb->InitRows(NRows); // create needed arrays;
+ int *NColsAtRow = cheb->GetNColsAtRow();
+ int *ColAtRowBg = cheb->GetColAtRowBg();
+ int NCols = 0;
+ int NElemBound2D = 0;
+ for (int id0=0;id0<NRows;id0++) {
+ NColsAtRow[id0] = tmpCols[id0]; // number of columns to store for this row
+ ColAtRowBg[id0] = NElemBound2D; // begining of this row in 2D boundary surface
+ NElemBound2D += tmpCols[id0];
+ if (NCols<NColsAtRow[id0]) NCols = NColsAtRow[id0];
+ }
+ cheb->InitCols(NCols);
+ delete[] tmpCols;
+ //
+ // create the 2D matrix defining the boundary of significance for 3D coeffs.matrix
+ // and count the number of siginifacnt coefficients
+ //
+ cheb->InitElemBound2D(NElemBound2D);
+ int *CoefBound2D0 = cheb->GetCoefBound2D0();
+ int *CoefBound2D1 = cheb->GetCoefBound2D1();
+ fMaxCoefs = 0; // redefine number of coeffs
+ for (int id0=0;id0<NRows;id0++) {
+ int nCLoc = NColsAtRow[id0];
+ int Col0 = ColAtRowBg[id0];
+ for (int id1=0;id1<nCLoc;id1++) {
+ CoefBound2D0[Col0 + id1] = tmpCoefSurf[id1+id0*fNPoints[1]]; // number of coefs to store for 3-d dimension
+ CoefBound2D1[Col0 + id1] = fMaxCoefs;
+ fMaxCoefs += CoefBound2D0[Col0 + id1];
+ }
+ }
+ //
+ // create final compressed 3D matrix for significant coeffs
+ cheb->InitCoefs(fMaxCoefs);
+ Float_t *Coefs = cheb->GetCoefs();
+ int count = 0;
+ for (int id0=0;id0<NRows;id0++) {
+ int ncLoc = NColsAtRow[id0];
+ int Col0 = ColAtRowBg[id0];
+ for (int id1=0;id1<ncLoc;id1++) {
+ int ncf2 = CoefBound2D0[Col0 + id1];
+ for (int id2=0;id2<ncf2;id2++) {
+ Coefs[count++] = tmpCoef3D[id2 + fNPoints[2]*(id1+id0*fNPoints[1])];
+ }
+ }
+ }
+ /*
+ printf("\n\nNewSurf\n");
+ for (int id0=0;id0<fNPoints[0];id0++) {
+ for (int id1=0;id1<fNPoints[1];id1++) {
+ printf("(%2d %2d) %2d |",id0,id1,tmpCoefSurf[id1+id0*fNPoints[1]]);
+ }
+ printf("\n");
+ }
+ */
+ //
+ delete[] tmpCoefSurf;
+ delete[] tmpCoef1D;
+ delete[] tmpCoef2D;
+ delete[] tmpCoef3D;
+ delete[] fvals;
+ //
+ return 1;
+}
+#endif
+
+//_______________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+void AliCheb3D::SaveData(const char* outfile,Bool_t append) const
+{
+ // writes coefficients data to output text file, optionallt appending on the end of existing file
+ TString strf = outfile;
+ gSystem->ExpandPathName(strf);
+ FILE* stream = fopen(strf,append ? "a":"w");
+ SaveData(stream);
+ fclose(stream);
+ //
+}
+#endif
+
+//_______________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+void AliCheb3D::SaveData(FILE* stream) const
+{
+ // writes coefficients data to existing output stream
+ //
+ fprintf(stream,"\n# These are automatically generated data for the Chebyshev interpolation of 3D->%dD function\n",fDimOut);
+ fprintf(stream,"#\nSTART %s\n",GetName());
+ fprintf(stream,"# Dimensionality of the output\n%d\n",fDimOut);
+ fprintf(stream,"# Interpolation abs. precision\n%+.8e\n",fPrec);
+ //
+ fprintf(stream,"# Lower boundaries of interpolation region\n");
+ for (int i=0;i<3;i++) fprintf(stream,"%+.8e\n",fBMin[i]);
+ fprintf(stream,"# Upper boundaries of interpolation region\n");
+ for (int i=0;i<3;i++) fprintf(stream,"%+.8e\n",fBMax[i]);
+ fprintf(stream,"# Parameterization for each output dimension follows:\n",GetName());
+ //
+ for (int i=0;i<fDimOut;i++) GetChebCalc(i)->SaveData(stream);
+ fprintf(stream,"#\nEND %s\n#\n",GetName());
+ //
+}
+#endif
+
+//_______________________________________________
+void AliCheb3D::LoadData(const char* inpFile)
+{
+ TString strf = inpFile;
+ gSystem->ExpandPathName(strf);
+ FILE* stream = fopen(strf.Data(),"r");
+ LoadData(stream);
+ fclose(stream);
+ //
+}
+
+//_______________________________________________
+void AliCheb3D::LoadData(FILE* stream)
+{
+ if (!stream) {Error("LoadData","No stream provided.\nStop"); exit(1);}
+ TString buffs;
+ Clear();
+ AliCheb3DCalc::ReadLine(buffs,stream);
+ if (!buffs.BeginsWith("START")) {Error("LoadData","Expected: \"START <fit_name>\", found \"%s\"\nStop\n",buffs.Data());exit(1);}
+ SetName(buffs.Data()+buffs.First(' ')+1);
+ //
+ AliCheb3DCalc::ReadLine(buffs,stream); // N output dimensions
+ fDimOut = buffs.Atoi();
+ if (fDimOut<1) {Error("LoadData","Expected: '<number_of_output_dimensions>', found \"%s\"\nStop\n",buffs.Data());exit(1);}
+ //
+ SetDimOut(fDimOut);
+ //
+ AliCheb3DCalc::ReadLine(buffs,stream); // Interpolation abs. precision
+ fPrec = buffs.Atof();
+ if (fPrec<=0) {Error("LoadData","Expected: '<abs.precision>', found \"%s\"\nStop\n",buffs.Data());exit(1);}
+ //
+ for (int i=0;i<3;i++) { // Lower boundaries of interpolation region
+ AliCheb3DCalc::ReadLine(buffs,stream);
+ fBMin[i] = buffs.Atof();
+ }
+ for (int i=0;i<3;i++) { // Upper boundaries of interpolation region
+ AliCheb3DCalc::ReadLine(buffs,stream);
+ fBMax[i] = buffs.Atof();
+ }
+ PrepareBoundaries(fBMin,fBMax);
+ //
+ // data for each output dimension
+ for (int i=0;i<fDimOut;i++) GetChebCalc(i)->LoadData(stream);
+ //
+ // check end_of_data record
+ AliCheb3DCalc::ReadLine(buffs,stream);
+ if (!buffs.BeginsWith("END") || !buffs.Contains(GetName())) {
+ Error("LoadData","Expected \"END %s\", found \"%s\".\nStop\n",GetName(),buffs.Data());
+ exit(1);
+ }
+ //
+}
+
+//_______________________________________________
+void AliCheb3D::SetDimOut(int d)
+{
+ fDimOut = d;
+ if (fResTmp) delete fResTmp;
+ fResTmp = new Float_t[fDimOut]; // RRR
+ fChebCalc.Delete();
+ for (int i=0;i<d;i++) fChebCalc.AddAtAndExpand(new AliCheb3DCalc(),i);
+}
+
+//_______________________________________________
+void AliCheb3D::ShiftBound(int id,float dif)
+{
+ if (id<0||id>2) {printf("Maximum 3 dimensions are supported\n"); return;}
+ fBMin[id] += dif;
+ fBMax[id] += dif;
+ fBOffset[id] += dif;
+}
+
+//_______________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+TH1* AliCheb3D::TestRMS(int idim,int npoints,TH1* histo)
+{
+ // fills the difference between the original function and parameterization (for idim-th component of the output)
+ // to supplied histogram. Calculations are done in npoints random points.
+ // If the hostgram was not supplied, it will be created. It is up to the user to delete it!
+ if (!fUsrMacro) {
+ printf("No user function is set\n");
+ return 0;
+ }
+ if (!histo) histo = new TH1D(GetName(),"Control: Function - Parametrization",100,-2*fPrec,2*fPrec);
+ for (int ip=npoints;ip--;) {
+ gRandom->RndmArray(3,(Float_t *)fArgsTmp);
+ for (int i=3;i--;) fArgsTmp[i] = fBMin[i] + fArgsTmp[i]*(fBMax[i]-fBMin[i]);
+ EvalUsrFunction();
+ Float_t valFun = fResTmp[idim];
+ Eval(fArgsTmp,fResTmp);
+ Float_t valPar = fResTmp[idim];
+ histo->Fill(valFun - valPar);
+ }
+ return histo;
+ //
+}
+#endif
--- /dev/null
+#ifndef ALICHEB3D_H
+#define ALICHEB3D_H
+/* Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
+ * See cxx source for full Copyright notice */
+
+/* $Id$ */
+
+// Author: ruben.shahoyan@cern.ch 09/09/2006
+//
+////////////////////////////////////////////////////////////////////////////////
+// //
+// AliCheb3D produces the interpolation of the user 3D->NDimOut arbitrary //
+// function supplied in "void (*fcn)(float* inp,float* out)" format //
+// either in a separate macro file or as a function pointer. //
+// Only coefficients needed to guarantee the requested precision are kept. //
+// //
+// The user-callable methods are: //
+// To create the interpolation use: //
+// AliCheb3D(const char* funName, // name of the file with user function //
+// or //
+// AliCheb3D(void (*ptr)(float*,float*),// pointer on the user function //
+// Int_t DimOut, // dimensionality of the function's output //
+// Float_t *bmin, // lower 3D bounds of interpolation domain //
+// Float_t *bmax, // upper 3D bounds of interpolation domain //
+// Int_t *npoints, // number of points in each of 3 input //
+// // dimension, defining the interpolation grid //
+// Float_t prec=1E-6); // requested max.absolute difference between //
+// // the interpolation and any point on grid //
+// //
+// To test obtained parameterization use the method //
+// TH1* TestRMS(int idim,int npoints = 1000,TH1* histo=0); //
+// it will compare the user output of the user function and interpolation //
+// for idim-th output dimension and fill the difference in the supplied //
+// histogram. If no histogram is supplied, it will be created. //
+// //
+// To save the interpolation data: //
+// SaveData(const char* filename, Bool_t append ) //
+// write text file with data. If append is kTRUE and the output file already //
+// exists, data will be added in the end of the file. //
+// Alternatively, SaveData(FILE* stream) will write the data to //
+// already existing stream. //
+// //
+// To read back already stored interpolation use either the constructor //
+// AliCheb3D(const char* inpFile); //
+// or the default constructor AliCheb3D() followed by //
+// AliCheb3D::LoadData(const char* inpFile); //
+// //
+// To compute the interpolation use Eval(float* par,float *res) method, with //
+// par being 3D vector of arguments (inside the validity region) and res is //
+// the array of DimOut elements for the output. //
+// //
+// If only one component (say, idim-th) of the output is needed, use faster //
+// Float_t Eval(Float_t *par,int idim) method. //
+// //
+// void Print(option="") will print the name, the ranges of validity and //
+// the absolute precision of the parameterization. Option "l" will also print //
+// the information about the number of coefficients for each output //
+// dimension. //
+// //
+// NOTE: during the evaluation no check is done for parameter vector being //
+// outside the interpolation region. If there is such a risk, use //
+// Bool_t IsInside(float *par) method. Chebyshev parameterization is not //
+// good for extrapolation! //
+// //
+// For the properties of Chebyshev parameterization see: //
+// H.Wind, CERN EP Internal Report, 81-12/Rev. //
+// //
+////////////////////////////////////////////////////////////////////////////////
+
+
+#include <stdio.h>
+#include <TNamed.h>
+#include <TMethodCall.h>
+#include <TMath.h>
+#include <TH1.h>
+#include <TObjArray.h>
+
+class TString;
+class TSystem;
+class TRandom;
+
+
+// to decrease the compilable code size comment this define. This will exclude the routines
+// used for the calculation and saving of the coefficients.
+// #define _INC_CREATION_ALICHEB3D_
+
+class AliCheb3DCalc: public TNamed
+{
+ public:
+ AliCheb3DCalc();
+ AliCheb3DCalc(FILE* stream); // read coefs from text file
+ ~AliCheb3DCalc() {Clear();}
+ //
+ void Print(Option_t* opt="") const;
+ void LoadData(FILE* stream);
+ Float_t Eval(Float_t *par) const;
+ //
+#ifdef _INC_CREATION_ALICHEB3D_
+ void SaveData(const char* outfile,Bool_t append=kFALSE) const;
+ void SaveData(FILE* stream=stdout) const;
+#endif
+ //
+ static void ReadLine(TString& str,FILE* stream);
+ //
+ protected:
+ //
+ void Clear(Option_t* option = "");
+ void Init0();
+ Float_t ChebEval1D(Float_t x, const Float_t * array, int ncf) const;
+ void InitRows(int nr);
+ void InitCols(int nc);
+ void InitElemBound2D(int ne);
+ void InitCoefs(int nc);
+ Int_t* GetNColsAtRow() const {return fNColsAtRow;}
+ Int_t* GetColAtRowBg() const {return fColAtRowBg;}
+ Int_t* GetCoefBound2D0() const {return fCoefBound2D0;}
+ Int_t* GetCoefBound2D1() const {return fCoefBound2D1;}
+ Float_t * GetCoefs() const {return fCoefs;}
+ //
+ protected:
+ Int_t fNCoefs; // total number of coeeficients
+ Int_t fNRows; // number of significant rows in the 3D coeffs matrix
+ Int_t fNCols; // max number of significant cols in the 3D coeffs matrix
+ Int_t fNElemBound2D; // number of elements (fNRows*fNCols) to store for the 2D boundary of significant coeffs
+ Int_t* fNColsAtRow; //[fNRows] number of sighificant columns (2nd dim) at each row of 3D coefs matrix
+ Int_t* fColAtRowBg; //[fNRows] beginnig of significant columns (2nd dim) for row in the 2D boundary matrix
+ Int_t* fCoefBound2D0; //[fNElemBound2D] 2D matrix defining the boundary of significance for 3D coeffs.matrix (Ncoefs for col/row)
+ Int_t* fCoefBound2D1; //[fNElemBound2D] 2D matrix defining the start beginnig of significant coeffs for col/row
+ Float_t * fCoefs; //[fNCoefs] array of Chebyshev coefficients
+ //
+ Float_t * fTmpCf1; //[fNCols] temp. coeffs for 2d summation
+ Float_t * fTmpCf0; //[fNRows] temp. coeffs for 1d summation
+ //
+ ClassDef(AliCheb3DCalc,1) // Class for interpolation of 3D->1 function by Chebyshev parametrization
+};
+
+
+class AliCheb3D: public TNamed
+{
+ public:
+ AliCheb3D();
+ AliCheb3D(const char* inpFile); // read coefs from text file
+ AliCheb3D(FILE*); // read coefs from stream
+ //
+#ifdef _INC_CREATION_ALICHEB3D_
+ AliCheb3D(const char* funName, Int_t DimOut, Float_t *bmin,Float_t *bmax, Int_t *npoints, Float_t prec=1E-6);
+ AliCheb3D(void (*ptr)(float*,float*), Int_t DimOut, Float_t *bmin,Float_t *bmax, Int_t *npoints, Float_t prec=1E-6);
+#endif
+ //
+ ~AliCheb3D() {Clear();}
+ //
+ void Eval(Float_t *par,Float_t *res);
+ Float_t Eval(Float_t *par,int idim);
+ void Print(Option_t* opt="") const;
+ Bool_t IsInside(Float_t *par) const;
+ AliCheb3DCalc* GetChebCalc(int i) const {return (AliCheb3DCalc*)fChebCalc.UncheckedAt(i);}
+ Float_t GetBoundMin(int i) const {return fBMin[i];}
+ Float_t GetBoundMax(int i) const {return fBMax[i];}
+ Float_t GetPrecision() const {return fPrec;}
+ void ShiftBound(int id,float dif);
+ //
+ void LoadData(const char* inpFile);
+ void LoadData(FILE* stream);
+ //
+#ifdef _INC_CREATION_ALICHEB3D_
+ void SaveData(const char* outfile,Bool_t append=kFALSE) const;
+ void SaveData(FILE* stream=stdout) const;
+ //
+ void SetUsrFunction(const char* name);
+ void SetUsrFunction(void (*ptr)(float*,float*));
+ void EvalUsrFunction(Float_t *x, Float_t *res);
+ TH1* TestRMS(int idim,int npoints = 1000,TH1* histo=0);
+#endif
+ //
+ protected:
+ void Init0();
+ void Clear(Option_t* option = "");
+ void SetDimOut(int d);
+ void PrepareBoundaries(Float_t *bmin,Float_t *bmax);
+ //
+#ifdef _INC_CREATION_ALICHEB3D_
+ void EvalUsrFunction();
+ void DefineGrid(Int_t* npoints);
+ Int_t ChebFit(); // fit all output dimensions
+ Int_t ChebFit(int dmOut);
+ Int_t CalcChebCoefs(Float_t *funval,int np, Float_t *outCoefs, Float_t prec=-1);
+#endif
+ //
+ void Cyl2CartCyl(float *rphiz, float *b) const;
+ void Cart2Cyl(float *xyz,float *rphiz) const;
+ //
+ Float_t MapToInternal(Float_t x,Int_t d) const {return (x-fBOffset[d])*fBScale[d];} // map x to [-1:1]
+ Float_t MapToExternal(Float_t x,Int_t d) const {return x/fBScale[d]+fBOffset[d];} // map from [-1:1] to x
+ //
+ protected:
+ Int_t fDimOut; // dimension of the ouput array
+ Float_t fPrec; // requested precision
+ Float_t fBMin[3]; // min boundaries in each dimension
+ Float_t fBMax[3]; // max boundaries in each dimension
+ Float_t fBScale[3]; // scale for boundary mapping to [-1:1] interval
+ Float_t fBOffset[3]; // offset for boundary mapping to [-1:1] interval
+ TObjArray fChebCalc; // Chebyshev parameterization for each output dimension
+ //
+ Int_t fMaxCoefs; //! max possible number of coefs per parameterization
+ Int_t fNPoints[3]; //! number of used points in each dimension
+ Float_t fArgsTmp[3]; //! temporary vector for coefs caluclation
+ Float_t fBuff[6]; //! buffer for coordinate transformations
+ Float_t * fResTmp; //! temporary vector for results of user function caluclation
+ Float_t * fGrid; //! temporary buffer for Chebyshef roots grid
+ Int_t fGridOffs[3]; //! start of grid for each dimension
+ TString fUsrFunName; //! name of user macro containing the function of "void (*fcn)(float*,float*)" format
+ TMethodCall* fUsrMacro; //! Pointer to MethodCall for function from user macro
+ //
+ ClassDef(AliCheb3D,1) // Chebyshev parametrization for 3D->N function
+};
+
+// Pointer on user function (faster altrnative to TMethodCall)
+#ifdef _INC_CREATION_ALICHEB3D_
+void (*gUsrFunAliCheb3D) (float* ,float* );
+#endif
+
+//__________________________________________________________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+inline void AliCheb3D::EvalUsrFunction()
+{
+ // call user supplied function
+ if (gUsrFunAliCheb3D) gUsrFunAliCheb3D(fArgsTmp,fResTmp);
+ else fUsrMacro->Execute();
+}
+#endif
+
+//__________________________________________________________________________________________
+inline Bool_t AliCheb3D::IsInside(Float_t *par) const
+{
+ // check if the point is inside of the fitted box
+ for (int i=3;i--;) if(par[i]<fBMin[i]||par[i]>fBMax[i]) return kFALSE;
+ return kTRUE;
+}
+
+//__________________________________________________________________________________________
+inline Float_t AliCheb3DCalc::ChebEval1D(Float_t x, const Float_t * array, int ncf ) const
+{
+ // evaluate 1D Chebyshev parameterization. x is the argument mapped to [-1:1] interval
+ Float_t b0, b1, b2;
+ Float_t x2 = x+x;
+ b0 = array[--ncf];
+ b1 = b2 = 0;
+ for (int i=ncf;i--;) {
+ b2 = b1;
+ b1 = b0;
+ b0 = array[i] + x2*b1 -b2;
+ }
+ return b0 - x*b1;
+}
+
+//__________________________________________________________________________________________
+inline void AliCheb3D::Eval(Float_t *par, Float_t *res)
+{
+ // evaluate Chebyshev parameterization for 3d->DimOut function
+ for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i);
+ for (int i=fDimOut;i--;) res[i] = GetChebCalc(i)->Eval(fArgsTmp);
+ //
+}
+
+//__________________________________________________________________________________________
+inline Float_t AliCheb3D::Eval(Float_t *par, int idim)
+{
+ // evaluate Chebyshev parameterization for idim-th output dimension of 3d->DimOut function
+ for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i);
+ return GetChebCalc(idim)->Eval(fArgsTmp);
+ //
+}
+
+//__________________________________________________________________________________________________
+inline void AliCheb3D::Cyl2CartCyl(float *rphiz, float *b) const
+{
+ // convert field in cylindrical coordinates to cartesian system, point is in cyl.system
+ float btr = TMath::Sqrt(b[0]*b[0]+b[1]*b[1]);
+ float ang = TMath::ATan2(b[1],b[0]) + rphiz[1];
+ b[0] = btr*TMath::Cos(ang);
+ b[1] = btr*TMath::Sin(ang);
+ //
+}
+
+//__________________________________________________________________________________________________
+inline void AliCheb3D::Cart2Cyl(float *xyz,float *rphiz) const
+{
+ // convert cartesian coordinate to cylindrical one
+ rphiz[0] = TMath::Sqrt(xyz[0]*xyz[0]+xyz[1]*xyz[1]);
+ rphiz[1] = TMath::ATan2(xyz[1],xyz[0]);
+ rphiz[2] = xyz[2];
+}
+
+#endif
--- /dev/null
+/**************************************************************************
+ * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
+ * *
+ * Author: The ALICE Off-line Project. *
+ * Contributors are mentioned in the code where appropriate. *
+ * *
+ * Permission to use, copy, modify and distribute this software and its *
+ * documentation strictly for non-commercial purposes is hereby granted *
+ * without fee, provided that the above copyright notice appears in all *
+ * copies and that both the copyright notice and this permission notice *
+ * appear in the supporting documentation. The authors make no claims *
+ * about the suitability of this software for any purpose. It is *
+ * provided "as is" without express or implied warranty. *
+ **************************************************************************/
+
+/* $Id$ */
+
+///////////////////////////////////////////////////////////////////////////////////
+// //
+// Wrapper for the set of mag.field parameterizations by Chebyshev polinomials //
+// To obtain the field in cartesian coordinates/components use //
+// Field(float* xyz, float* bxyz); //
+// For cylindrical coordinates/components: //
+// FieldCyl(float* rphiz, float* brphiz) //
+// //
+// For the moment only the solenoid part is parameterized in the volume defined //
+// by R<500, -550<Z<550 cm //
+// //
+// The region R<423 cm, -343.3<Z<481.3 for 30kA and -343.3<Z<481.3 for 12kA //
+// is parameterized using measured data while outside the Tosca calculation //
+// is used (matched to data on the boundary of the measurements) //
+// //
+// If the querried point is outside the validity region no the return values //
+// for the field components are set to 0. //
+// //
+///////////////////////////////////////////////////////////////////////////////////
+
+#include "AliMagFCheb.h"
+
+ClassImp(AliMagFCheb)
+
+
+
+//__________________________________________________________________________________________
+AliMagFCheb::AliMagFCheb(const char* inputFile) :
+ TNamed("Field Map", inputFile),
+ fNParamsSol(0),
+ fNSegZSol(0),
+ fNParamsDip(0),
+ fSegZSol(0),
+ fSegRSol(0),
+ fNSegRSol(0),
+ fSegZIdSol(0),
+ fMinZSol(0.),
+ fMaxZSol(0.),
+ fMaxRSol(0.)
+{
+ Init0();
+ LoadData(inputFile);
+}
+
+//__________________________________________________________________________________________
+AliMagFCheb::~AliMagFCheb()
+{
+ if (fNParamsSol) {
+ delete fParamsSol;
+ delete[] fSegZSol;
+ delete[] fSegRSol;
+ delete[] fNSegRSol;
+ delete[] fSegZIdSol;
+ }
+ //
+ // Dipole part ...
+ if (fNParamsDip) {
+ delete fParamsDip;
+ }
+}
+
+//__________________________________________________________________________________________
+void AliMagFCheb::Init0()
+{
+ // Solenoid part
+ fNParamsSol = 0;
+ fNSegZSol = 0;
+ //
+ fSegZSol = 0;
+ fSegRSol = 0;
+ //
+ fNSegRSol = 0;
+ fSegZIdSol = 0;
+ //
+ fMinZSol = fMaxZSol = fMaxRSol = fMaxRSol = 0;
+ fParamsSol = 0;
+ //
+ // Dipole part ...
+ fNParamsDip = 0;
+ fParamsDip = 0;
+ //
+}
+
+//__________________________________________________________________________________________
+void AliMagFCheb::AddParamSol(AliCheb3D* param)
+{
+ // adds new parameterization piece for Sol
+ // NOTE: pieces must be added strictly in increasing R then increasing Z order
+ //
+ if (!fParamsSol) fParamsSol = new TObjArray();
+ fParamsSol->Add(param);
+ fNParamsSol++;
+ //
+}
+
+//__________________________________________________________________________________________
+void AliMagFCheb::AddParamDip(AliCheb3D* param)
+{
+ // adds new parameterization piece for Dipole
+ //
+ if (!fParamsDip) fParamsDip = new TObjArray();
+ fParamsDip->Add(param);
+ fNParamsDip++;
+ //
+}
+
+//__________________________________________________________________________________________
+void AliMagFCheb::BuildTableSol()
+{
+ // build the indexes for each parameterization of Solenoid
+ //
+ const float kSafety=0.001;
+ //
+ fSegRSol = new Float_t[fNParamsSol];
+ float *tmpbufF = new float[fNParamsSol+1];
+ int *tmpbufI = new int[fNParamsSol+1];
+ int *tmpbufI1 = new int[fNParamsSol+1];
+ //
+ // count number of Z slices and number of R slices in each Z slice
+ for (int ip=0;ip<fNParamsSol;ip++) {
+ if (ip==0 || (GetParamSol(ip)->GetBoundMax(2)-GetParamSol(ip-1)->GetBoundMax(2))>kSafety) { // new Z slice
+ tmpbufF[fNSegZSol] = GetParamSol(ip)->GetBoundMax(2); //
+ tmpbufI[fNSegZSol] = 0;
+ tmpbufI1[fNSegZSol++] = ip;
+ }
+ fSegRSol[ip] = GetParamSol(ip)->GetBoundMax(0); // upper R
+ tmpbufI[fNSegZSol-1]++;
+ }
+ //
+ fSegZSol = new Float_t[fNSegZSol];
+ fSegZIdSol = new Int_t[fNSegZSol];
+ fNSegRSol = new Int_t[fNSegZSol];
+ for (int iz=0;iz<fNSegZSol;iz++) {
+ fSegZSol[iz] = tmpbufF[iz];
+ fNSegRSol[iz] = tmpbufI[iz];
+ fSegZIdSol[iz] = tmpbufI1[iz];
+ }
+ //
+ fMinZSol = GetParamSol(0)->GetBoundMin(2);
+ fMaxZSol = GetParamSol(fNParamsSol-1)->GetBoundMax(2);
+ fMaxRSol = GetParamSol(fNParamsSol-1)->GetBoundMax(0);
+ //
+ delete[] tmpbufF;
+ delete[] tmpbufI;
+ delete[] tmpbufI1;
+ //
+ //
+}
+
+//__________________________________________________________________________________________
+void AliMagFCheb::Field(Float_t *xyz, Float_t *b) const
+{
+ // compute field in cartesian coordinates
+ float rphiz[3];
+ if (xyz[2]>GetMaxZSol() || xyz[2]<GetMinZSol()) {for (int i=3;i--;) b[i]=0; return;}
+ //
+ // Sol region
+ // convert coordinates to cyl system
+ rphiz[0] = TMath::Sqrt(xyz[0]*xyz[0]+xyz[1]*xyz[1]);
+ rphiz[1] = TMath::ATan2(xyz[1],xyz[0]);
+ rphiz[2] = xyz[2];
+ if (rphiz[0]>GetMaxRSol()) {for (int i=3;i--;) b[i]=0; return;}
+ //
+ FieldCylSol(rphiz,b);
+ //
+ // convert field to cartesian system
+ float btr = TMath::Sqrt(b[0]*b[0]+b[1]*b[1]);
+ float psiPLUSphi = rphiz[1] + TMath::ATan2(b[1],b[0]);
+ b[0] = btr*TMath::Cos(psiPLUSphi);
+ b[1] = btr*TMath::Sin(psiPLUSphi);
+ //
+}
+
+//__________________________________________________________________________________________
+void AliMagFCheb::FieldCylSol(Float_t *rphiz, Float_t *b) const
+{
+ // compute Solenoid field in Cylindircal coordinates
+ // note: the check for the point being inside the parameterized region is done outside
+ float &r = rphiz[0];
+ float &z = rphiz[2];
+ int SolZId = 0;
+ while (z>fSegZSol[SolZId]) ++SolZId; // find Z segment
+ int SolRId = fSegZIdSol[SolZId]; // first R segment for this Z
+ while (r>fSegRSol[SolRId]) ++SolRId; // find R segment
+ GetParamSol( SolRId )->Eval(rphiz,b);
+ //
+}
+
+//__________________________________________________________________________________________
+void AliMagFCheb::Print(Option_t *) const
+{
+ printf("Alice magnetic field parameterized by Chebyshev polynomials\n");
+ printf("Segmentation for Solenoid (%+.2f<Z<%+.2f cm | R<%.2f cm)\n",fMinZSol,fMaxZSol,fMaxRSol);
+ //
+ for (int iz=0;iz<fNSegZSol;iz++) {
+ AliCheb3D* param = GetParamSol( fSegZIdSol[iz] );
+ printf("*** Z Segment %2d (%+7.2f<Z<%+7.2f)\t***\n",iz,param->GetBoundMin(2),param->GetBoundMax(2));
+ for (int ir=0;ir<fNSegRSol[iz];ir++) {
+ param = GetParamSol( fSegZIdSol[iz]+ir );
+ printf(" R Segment %2d (%+7.2f<R<%+7.2f, Precision: %.1e) (ID=%2d)\n",ir, param->GetBoundMin(0),param->GetBoundMax(0),
+ param->GetPrecision(),fSegZIdSol[iz]+ir);
+ }
+ }
+}
+
+//_______________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+void AliMagFCheb::SaveData(const char* outfile) const
+{
+ // writes coefficients data to output text file
+ TString strf = outfile;
+ gSystem->ExpandPathName(strf);
+ FILE* stream = fopen(strf,"w+");
+ //
+ // Sol part
+ fprintf(stream,"# Set of Chebyshev parameterizations for ALICE magnetic field\nSTART %s\n",GetName());
+ fprintf(stream,"START SOLENOID\n#Number of pieces\n%d\n",fNParamsSol);
+ for (int ip=0;ip<fNParamsSol;ip++) GetParamSol(ip)->SaveData(stream);
+ fprintf(stream,"#\nEND SOLENOID\n");
+ //
+ // Dip part
+ fprintf(stream,"START DIPOLE\n#Number of pieces\n%d\n",fNParamsDip);
+ for (int ip=0;ip<fNParamsDip;ip++) GetParamDip(ip)->SaveData(stream);
+ fprintf(stream,"#\nEND DIPOLE\n");
+ //
+ fprintf(stream,"#\nEND %s\n",GetName());
+ //
+ fclose(stream);
+ //
+}
+#endif
+
+//_______________________________________________
+void AliMagFCheb::LoadData(const char* inpfile)
+{
+ // read coefficients data from the text file
+ //
+ TString strf = inpfile;
+ gSystem->ExpandPathName(strf);
+ FILE* stream = fopen(strf,"r");
+ if (!stream) {
+ printf("Did not find input file %s\n",strf.Data());
+ return;
+ }
+ //
+ TString buffs;
+ AliCheb3DCalc::ReadLine(buffs,stream);
+ if (!buffs.BeginsWith("START")) {Error("LoadData","Expected: \"START <name>\", found \"%s\"\nStop\n",buffs.Data());exit(1);}
+ if (buffs.First(' ')>0) SetName(buffs.Data()+buffs.First(' ')+1);
+ //
+ // Solenoid part
+ AliCheb3DCalc::ReadLine(buffs,stream);
+ if (!buffs.BeginsWith("START SOLENOID")) {Error("LoadData","Expected: \"START SOLENOID\", found \"%s\"\nStop\n",buffs.Data());exit(1);}
+ AliCheb3DCalc::ReadLine(buffs,stream); // nparam
+ int nparSol = buffs.Atoi();
+ //
+ for (int ip=0;ip<nparSol;ip++) {
+ AliCheb3D* cheb = new AliCheb3D();
+ cheb->LoadData(stream);
+ AddParamSol(cheb);
+ }
+ //
+ AliCheb3DCalc::ReadLine(buffs,stream);
+ if (!buffs.BeginsWith("END SOLENOID")) {Error("LoadData","Expected \"END SOLENOID\", found \"%s\"\nStop\n",buffs.Data());exit(1);}
+ //
+ // Dipole part
+ AliCheb3DCalc::ReadLine(buffs,stream);
+ if (!buffs.BeginsWith("START DIPOLE")) {Error("LoadData","Expected: \"START DIPOLE\", found \"%s\"\nStop\n",buffs.Data());exit(1);}
+ AliCheb3DCalc::ReadLine(buffs,stream); // nparam
+ int nparDip = buffs.Atoi();
+ //
+ for (int ip=0;ip<nparDip;ip++) {
+ AliCheb3D* cheb = new AliCheb3D();
+ cheb->LoadData(stream);
+ AddParamDip(cheb);
+ }
+ //
+ AliCheb3DCalc::ReadLine(buffs,stream);
+ if (!buffs.BeginsWith("END DIPOLE")) {Error("LoadData","Expected \"END DIPOLE\", found \"%s\"\nStop\n",GetName(),buffs.Data());exit(1);}
+ //
+ AliCheb3DCalc::ReadLine(buffs,stream);
+ if (!buffs.BeginsWith("END") || !buffs.Contains(GetName())) {Error("LoadData","Expected: \"END %s\", found \"%s\"\nStop\n",GetName(),buffs.Data());exit(1);}
+ //
+ fclose(stream);
+ BuildTableSol();
+ // BuildDipTable();
+ printf("Loaded magnetic field \"%s\" from %s\n",GetName(),strf.Data());
+ //
+}
git://git.uio.no / u / mrichter / AliRoot.git / commitdiff