--- /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. *
+ **************************************************************************/
+
+#include <TString.h>
+#include <TSystem.h>
+#include <TROOT.h>
+#include <TRandom.h>
+#include <stdio.h>
+#include <TMethodCall.h>
+#include <TMath.h>
+#include <TH1.h>
+#include "AliCheb3D.h"
+#include "AliCheb3DCalc.h"
+
+ClassImp(AliCheb3D)
+
+//__________________________________________________________________________________________
+AliCheb3D::AliCheb3D() :
+ fDimOut(0),
+ fPrec(0),
+ fChebCalc(1),
+ fMaxCoefs(0),
+ fResTmp(0),
+ fGrid(0),
+ fUsrFunName(""),
+ fUsrMacro(0)
+{
+// Default constructor
+ for (int i=3;i--;) {
+ fBMin[i] = fBMax[i] = fBScale[i] = fBOffset[i] = fArgsTmp[i] = 0;
+ fNPoints[i] = 0;
+ fGridOffs[i] = 0;
+ }
+}
+
+//__________________________________________________________________________________________
+AliCheb3D::AliCheb3D(const AliCheb3D& src) :
+ TNamed(src),
+ fDimOut(src.fDimOut),
+ fPrec(src.fPrec),
+ fChebCalc(1),
+ fMaxCoefs(src.fMaxCoefs),
+ fResTmp(0),
+ fGrid(0),
+ fUsrFunName(src.fUsrFunName),
+ fUsrMacro(0)
+{
+ // read coefs from text file
+ for (int i=3;i--;) {
+ fBMin[i] = src.fBMin[i];
+ fBMax[i] = src.fBMax[i];
+ fBScale[i] = src.fBScale[i];
+ fBOffset[i] = src.fBOffset[i];
+ fNPoints[i] = src.fNPoints[i];
+ fGridOffs[i] = src.fGridOffs[i];
+ fArgsTmp[i] = 0;
+ }
+ for (int i=0;i<fDimOut;i++) {
+ AliCheb3DCalc* cbc = src.GetChebCalc(i);
+ if (cbc) fChebCalc.AddAtAndExpand(new AliCheb3DCalc(*cbc),i);
+ }
+}
+
+//__________________________________________________________________________________________
+AliCheb3D::AliCheb3D(const char* inpFile) :
+ fDimOut(0),
+ fPrec(0),
+ fChebCalc(1),
+ fMaxCoefs(0),
+ fResTmp(0),
+ fGrid(0),
+ fUsrFunName(""),
+ fUsrMacro(0)
+{
+ // read coefs from text file
+ for (int i=3;i--;) {
+ fBMin[i] = fBMax[i] = fBScale[i] = fBOffset[i] = 0;
+ fNPoints[i] = 0;
+ fGridOffs[i] = 0;
+ fArgsTmp[i] = 0;
+ }
+ LoadData(inpFile);
+}
+
+//__________________________________________________________________________________________
+AliCheb3D::AliCheb3D(FILE* stream) :
+ fDimOut(0),
+ fPrec(0),
+ fChebCalc(1),
+ fMaxCoefs(0),
+ fResTmp(0),
+ fGrid(0),
+ fUsrFunName(""),
+ fUsrMacro(0)
+{
+ // read coefs from stream
+ for (int i=3;i--;) {
+ fBMin[i] = fBMax[i] = fBScale[i] = fBOffset[i] = 0;
+ fNPoints[i] = 0;
+ fGridOffs[i] = 0;
+ fArgsTmp[i] = 0;
+ }
+ LoadData(stream);
+}
+
+//__________________________________________________________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+AliCheb3D::AliCheb3D(const char* funName, int DimOut, const Float_t *bmin, const Float_t *bmax, Int_t *npoints, Float_t prec) :
+ TNamed(funName,funName),
+ fDimOut(0),
+ fPrec(TMath::Max(1.E-12f,prec)),
+ fChebCalc(1),
+ fMaxCoefs(0),
+ fResTmp(0),
+ fGrid(0),
+ fUsrFunName("") ,
+ fUsrMacro(0)
+{
+ // 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
+ //
+ if (DimOut<1) {Error("AliCheb3D","Requested output dimension is %d\nStop\n",fDimOut); exit(1);}
+ for (int i=3;i--;) {
+ fBMin[i] = fBMax[i] = fBScale[i] = fBOffset[i] = 0;
+ fNPoints[i] = 0;
+ fGridOffs[i] = 0.;
+ fArgsTmp[i] = 0;
+ }
+ 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) :
+ fDimOut(0),
+ fPrec(TMath::Max(1.E-12f,prec)),
+ fChebCalc(1),
+ fMaxCoefs(0),
+ fResTmp(0),
+ fGrid(0),
+ fUsrFunName(""),
+ fUsrMacro(0)
+{
+ // 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
+ //
+ if (DimOut<1) {Error("AliCheb3D","Requested output dimension is %d\nStop\n",fDimOut); exit(1);}
+ if (DimOut<1) {Error("AliCheb3D","Requested output dimension is %d\nStop\n",fDimOut); exit(1);}
+ for (int i=3;i--;) {
+ fBMin[i] = fBMax[i] = fBScale[i] = fBOffset[i] = 0;
+ fNPoints[i] = 0;
+ fGridOffs[i] = 0.;
+ fArgsTmp[i] = 0;
+ }
+ SetDimOut(DimOut);
+ PrepareBoundaries(bmin,bmax);
+ DefineGrid(npoints);
+ SetUsrFunction(ptr);
+ ChebFit();
+ //
+}
+#endif
+
+//__________________________________________________________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+AliCheb3D::AliCheb3D(void (*ptr)(float*,float*), int DimOut, Float_t *bmin,Float_t *bmax, Int_t *npX,Int_t *npY,Int_t *npZ, Float_t prec) :
+ fDimOut(0),
+ fPrec(TMath::Max(1.E-12f,prec)),
+ fChebCalc(1),
+ fMaxCoefs(0),
+ fResTmp(0),
+ fGrid(0),
+ fUsrFunName(""),
+ fUsrMacro(0)
+{
+ // Construct very economic 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
+ // npX : array of 3 elements with the number of points to compute in each dimension for 1st component
+ // npY : array of 3 elements with the number of points to compute in each dimension for 2nd component
+ // npZ : array of 3 elements with the number of points to compute in each dimension for 3d component
+ // prec : max allowed absolute difference between the user function and computed parameterization on the requested grid
+ //
+ if (DimOut<1) {Error("AliCheb3D","Requested output dimension is %d\nStop\n",fDimOut); exit(1);}
+ if (DimOut<1) {Error("AliCheb3D","Requested output dimension is %d\nStop\n",fDimOut); exit(1);}
+ for (int i=3;i--;) {
+ fBMin[i] = fBMax[i] = fBScale[i] = fBOffset[i] = 0;
+ fNPoints[i] = 0;
+ fGridOffs[i] = 0.;
+ fArgsTmp[i] = 0;
+ }
+ SetDimOut(DimOut);
+ PrepareBoundaries(bmin,bmax);
+ SetUsrFunction(ptr);
+ //
+ DefineGrid(npX);
+ ChebFit(0);
+ DefineGrid(npY);
+ ChebFit(1);
+ DefineGrid(npZ);
+ ChebFit(2);
+ //
+}
+#endif
+
+
+//__________________________________________________________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+AliCheb3D::AliCheb3D(void (*ptr)(float*,float*), int DimOut, Float_t *bmin,Float_t *bmax, Float_t prec, Bool_t run) :
+ fDimOut(0),
+ fPrec(TMath::Max(1.E-12f,prec)),
+ fChebCalc(1),
+ fMaxCoefs(0),
+ fResTmp(0),
+ fGrid(0),
+ fUsrFunName(""),
+ fUsrMacro(0)
+{
+ // Construct very economic parameterization for the function with automatic calculation of the root's grid
+ // 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
+ // prec : max allowed absolute difference between the user function and computed parameterization on the requested grid
+ //
+ if (DimOut!=3) {Error("AliCheb3D","This constructor works only for 3D fits, %dD fit was requested\n",fDimOut); exit(1);}
+ if (DimOut<1) {Error("AliCheb3D","Requested output dimension is %d\nStop\n",fDimOut); exit(1);}
+ for (int i=3;i--;) {
+ fBMin[i] = fBMax[i] = fBScale[i] = fBOffset[i] = 0;
+ fNPoints[i] = 0;
+ fGridOffs[i] = 0.;
+ fArgsTmp[i] = 0;
+ }
+ SetDimOut(DimOut);
+ PrepareBoundaries(bmin,bmax);
+ SetUsrFunction(ptr);
+ //
+ if (run) {
+ int gridNC[3][3];
+ EstimateNPoints(prec,gridNC);
+ DefineGrid(gridNC[0]);
+ ChebFit(0);
+ DefineGrid(gridNC[1]);
+ ChebFit(1);
+ DefineGrid(gridNC[2]);
+ ChebFit(2);
+ }
+ //
+}
+#endif
+
+
+//__________________________________________________________________________________________
+AliCheb3D& AliCheb3D::operator=(const AliCheb3D& rhs)
+{
+ // assignment operator
+ //
+ if (this != &rhs) {
+ Clear();
+ fDimOut = rhs.fDimOut;
+ fPrec = rhs.fPrec;
+ fMaxCoefs = rhs.fMaxCoefs;
+ fUsrFunName = rhs.fUsrFunName;
+ fUsrMacro = 0;
+ for (int i=3;i--;) {
+ fBMin[i] = rhs.fBMin[i];
+ fBMax[i] = rhs.fBMax[i];
+ fBScale[i] = rhs.fBScale[i];
+ fBOffset[i] = rhs.fBOffset[i];
+ fNPoints[i] = rhs.fNPoints[i];
+ }
+ for (int i=0;i<fDimOut;i++) {
+ AliCheb3DCalc* cbc = rhs.GetChebCalc(i);
+ if (cbc) fChebCalc.AddAtAndExpand(new AliCheb3DCalc(*cbc),i);
+ }
+ }
+ return *this;
+ //
+}
+
+//__________________________________________________________________________________________
+void AliCheb3D::Clear(const Option_t*)
+{
+ // clear all dynamic structures
+ //
+ if (fResTmp) { delete[] fResTmp; fResTmp = 0; }
+ if (fGrid) { delete[] fGrid; fGrid = 0; }
+ if (fUsrMacro) { delete fUsrMacro; fUsrMacro = 0;}
+ fChebCalc.SetOwner(kTRUE);
+ fChebCalc.Delete();
+ //
+}
+
+//__________________________________________________________________________________________
+void AliCheb3D::Print(const Option_t* opt) const
+{
+ // print info
+ //
+ 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::PrepareBoundaries(const Float_t *bmin, const 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_
+
+// Pointer on user function (faster altrnative to TMethodCall)
+void (*gUsrFunAliCheb3D) (float* ,float* );
+
+void AliCheb3D::EvalUsrFunction()
+{
+ // call user supplied function
+ if (gUsrFunAliCheb3D) gUsrFunAliCheb3D(fArgsTmp,fResTmp);
+ else fUsrMacro->Execute();
+}
+
+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*))
+{
+ // assign user training function
+ //
+ if (fUsrMacro) delete fUsrMacro;
+ fUsrMacro = 0;
+ fUsrFunName = "";
+ gUsrFunAliCheb3D = ptr;
+}
+#endif
+
+//__________________________________________________________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+void AliCheb3D::EvalUsrFunction(const Float_t *x, Float_t *res)
+{
+ // evaluate user function value
+ //
+ 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(const 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",id,fNPoints[id],kMinPoints);
+ exit(1);
+ }
+ ntot += fNPoints[id];
+ fMaxCoefs *= fNPoints[id];
+ }
+ printf("Computing Chebyshev nodes on [%2d/%2d/%2d] grid\n",npoints[0],npoints[1],npoints[2]);
+ if (fGrid) delete[] fGrid;
+ 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 = 0.1*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;
+ //
+ printf("Dim%d : 00.00%% Done",dmOut);fflush(stdout);
+ AliCheb3DCalc* cheb = GetChebCalc(dmOut);
+ //
+ float ncals2count = fNPoints[2]*fNPoints[1]*fNPoints[0];
+ float ncals = 0;
+ float frac = 0;
+ float fracStep = 0.001;
+ //
+ 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];
+ float fr = (++ncals)/ncals2count;
+ if (fr-frac>=fracStep) {
+ frac = fr;
+ printf("\b\b\b\b\b\b\b\b\b\b\b");
+ printf("%05.2f%% Done",fr*100);
+ fflush(stdout);
+ }
+ //
+ }
+ 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)
+ UShort_t *tmpCoefSurf = new UShort_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 coefs 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];
+ UShort_t *tmpCols = new UShort_t[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;
+ UShort_t *nColsAtRow = cheb->GetNColsAtRow();
+ UShort_t *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);
+ UShort_t *coefBound2D0 = cheb->GetCoefBound2D0();
+ UShort_t *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;
+ //
+ printf("\b\b\b\b\b\b\b\b\b\b\b\b");
+ printf("100.00%% Done\n");
+ 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");
+ //
+ for (int i=0;i<fDimOut;i++) GetChebCalc(i)->SaveData(stream);
+ fprintf(stream,"#\nEND %s\n#\n",GetName());
+ //
+}
+#endif
+
+//__________________________________________________________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+void AliCheb3D::InvertSign()
+{
+ // invert the sign of all parameterizations
+ for (int i=fDimOut;i--;) {
+ AliCheb3DCalc* par = GetChebCalc(i);
+ int ncf = par->GetNCoefs();
+ float *coefs = par->GetCoefs();
+ for (int j=ncf;j--;) coefs[j] = -coefs[j];
+ }
+}
+#endif
+
+
+//_______________________________________________
+void AliCheb3D::LoadData(const char* inpFile)
+{
+ // load coefficients data from txt file
+ //
+ TString strf = inpFile;
+ gSystem->ExpandPathName(strf);
+ FILE* stream = fopen(strf.Data(),"r");
+ LoadData(stream);
+ fclose(stream);
+ //
+}
+
+//_______________________________________________
+void AliCheb3D::LoadData(FILE* stream)
+{
+ // load coefficients data from 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(const int d)
+{
+ // init output dimensions
+ fDimOut = d;
+ if (fResTmp) delete fResTmp;
+ fResTmp = new Float_t[fDimOut];
+ fChebCalc.Delete();
+ for (int i=0;i<d;i++) fChebCalc.AddAtAndExpand(new AliCheb3DCalc(),i);
+}
+
+//_______________________________________________
+void AliCheb3D::ShiftBound(int id,float dif)
+{
+ // modify the bounds of the grid
+ //
+ 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
+
+//_______________________________________________
+#ifdef _INC_CREATION_ALICHEB3D_
+
+void AliCheb3D::EstimateNPoints(float Prec, int gridBC[3][3],Int_t npd1,Int_t npd2,Int_t npd3)
+{
+ // Estimate number of points to generate a training data
+ //
+ const int kScp = 9;
+ const float kScl[9] = {0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9};
+ //
+ const float sclDim[2] = {0.001,0.999};
+ const int compDim[3][2] = { {1,2}, {2,0}, {0,1} };
+ static float xyz[3];
+ Int_t npdTst[3] = {npd1,npd2,npd3};
+ //
+
+ for (int i=3;i--;)for (int j=3;j--;) gridBC[i][j] = -1;
+ //
+ for (int idim=0;idim<3;idim++) {
+ float dimMN = fBMin[idim] + sclDim[0]*(fBMax[idim]-fBMin[idim]);
+ float dimMX = fBMin[idim] + sclDim[1]*(fBMax[idim]-fBMin[idim]);
+ //
+ int id1 = compDim[idim][0]; // 1st fixed dim
+ int id2 = compDim[idim][1]; // 2nd fixed dim
+ for (int i1=0;i1<kScp;i1++) {
+ xyz[ id1 ] = fBMin[id1] + kScl[i1]*( fBMax[id1]-fBMin[id1] );
+ for (int i2=0;i2<kScp;i2++) {
+ xyz[ id2 ] = fBMin[id2] + kScl[i2]*( fBMax[id2]-fBMin[id2] );
+ int* npt = GetNCNeeded(xyz,idim, dimMN,dimMX, Prec, npdTst[idim]); // npoints for Bx,By,Bz
+ for (int ib=0;ib<3;ib++) if (npt[ib]>gridBC[ib][idim]) gridBC[ib][idim] = npt[ib];
+ }
+ }
+ }
+}
+
+/*
+void AliCheb3D::EstimateNPoints(float Prec, int gridBC[3][3])
+{
+ // Estimate number of points to generate a training data
+ //
+ const float sclA[9] = {0.1, 0.5, 0.9, 0.1, 0.5, 0.9, 0.1, 0.5, 0.9} ;
+ const float sclB[9] = {0.1, 0.1, 0.1, 0.5, 0.5, 0.5, 0.9, 0.9, 0.9} ;
+ const float sclDim[2] = {0.01,0.99};
+ const int compDim[3][2] = { {1,2}, {2,0}, {0,1} };
+ static float xyz[3];
+ //
+ for (int i=3;i--;)for (int j=3;j--;) gridBC[i][j] = -1;
+ //
+ for (int idim=0;idim<3;idim++) {
+ float dimMN = fBMin[idim] + sclDim[0]*(fBMax[idim]-fBMin[idim]);
+ float dimMX = fBMin[idim] + sclDim[1]*(fBMax[idim]-fBMin[idim]);
+ //
+ for (int it=0;it<9;it++) { // test in 9 points
+ int id1 = compDim[idim][0]; // 1st fixed dim
+ int id2 = compDim[idim][1]; // 2nd fixed dim
+ xyz[ id1 ] = fBMin[id1] + sclA[it]*( fBMax[id1]-fBMin[id1] );
+ xyz[ id2 ] = fBMin[id2] + sclB[it]*( fBMax[id2]-fBMin[id2] );
+ //
+ int* npt = GetNCNeeded(xyz,idim, dimMN,dimMX, Prec); // npoints for Bx,By,Bz
+ for (int ib=0;ib<3;ib++) if (npt[ib]>gridBC[ib][idim]) gridBC[ib][idim] = npt[ib];//+2;
+ //
+ }
+ }
+}
+
+
+int* AliCheb3D::GetNCNeeded(float xyz[3],int DimVar, float mn,float mx, float prec)
+{
+ // estimate needed number of chebyshev coefs for given function description in DimVar dimension
+ // The values for two other dimensions must be set beforehand
+ //
+ static int curNC[3];
+ static int retNC[3];
+ const int kMaxPoint = 400;
+ float* gridVal = new float[3*kMaxPoint];
+ float* coefs = new float[3*kMaxPoint];
+ //
+ float scale = mx-mn;
+ float offs = mn + scale/2.0;
+ scale = 2./scale;
+ //
+ int curNP;
+ int maxNC=-1;
+ int maxNCPrev=-1;
+ for (int i=0;i<3;i++) retNC[i] = -1;
+ for (int i=0;i<3;i++) fArgsTmp[i] = xyz[i];
+ //
+ for (curNP=3; curNP<kMaxPoint; curNP+=3) {
+ maxNCPrev = maxNC;
+ //
+ for (int i=0;i<curNP;i++) { // get function values on Cheb. nodes
+ float x = TMath::Cos( TMath::Pi()*(i+0.5)/curNP );
+ fArgsTmp[DimVar] = x/scale+offs; // map to requested interval
+ EvalUsrFunction();
+ for (int ib=3;ib--;) gridVal[ib*kMaxPoint + i] = fResTmp[ib];
+ }
+ //
+ for (int ib=0;ib<3;ib++) {
+ curNC[ib] = AliCheb3D::CalcChebCoefs(&gridVal[ib*kMaxPoint], curNP, &coefs[ib*kMaxPoint],prec);
+ if (maxNC < curNC[ib]) maxNC = curNC[ib];
+ if (retNC[ib] < curNC[ib]) retNC[ib] = curNC[ib];
+ }
+ if ( (curNP-maxNC)>3 && (maxNC-maxNCPrev)<1 ) break;
+ maxNCPrev = maxNC;
+ //
+ }
+ delete[] gridVal;
+ delete[] coefs;
+ return retNC;
+ //
+}
+*/
+
+
+int* AliCheb3D::GetNCNeeded(float xyz[3],int DimVar, float mn,float mx, float prec, Int_t npCheck)
+{
+ // estimate needed number of chebyshev coefs for given function description in DimVar dimension
+ // The values for two other dimensions must be set beforehand
+ //
+ static int retNC[3];
+ static int npChLast = 0;
+ static float *gridVal=0,*coefs=0;
+ if (npCheck<3) npCheck = 3;
+ if (npChLast<npCheck) {
+ if (gridVal) delete[] gridVal;
+ if (coefs) delete[] coefs;
+ gridVal = new float[3*npCheck];
+ coefs = new float[3*npCheck];
+ npChLast = npCheck;
+ }
+ //
+ float scale = mx-mn;
+ float offs = mn + scale/2.0;
+ scale = 2./scale;
+ //
+ for (int i=0;i<3;i++) fArgsTmp[i] = xyz[i];
+ for (int i=0;i<npCheck;i++) {
+ fArgsTmp[DimVar] = TMath::Cos( TMath::Pi()*(i+0.5)/npCheck)/scale+offs; // map to requested interval
+ EvalUsrFunction();
+ for (int ib=3;ib--;) gridVal[ib*npCheck + i] = fResTmp[ib];
+ }
+ //
+ for (int ib=0;ib<3;ib++) retNC[ib] = AliCheb3D::CalcChebCoefs(&gridVal[ib*npCheck], npCheck, &coefs[ib*npCheck],prec);
+ return retNC;
+ //
+}
+
+
+#endif
git://git.uio.no / u / mrichter / AliRoot.git / blobdiff