1 /**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
7 * Permission to use, copy, modify and distribute this software and its *
8 * documentation strictly for non-commercial purposes is hereby granted *
9 * without fee, provided that the above copyright notice appears in all *
10 * copies and that both the copyright notice and this permission notice *
11 * appear in the supporting documentation. The authors make no claims *
12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
14 **************************************************************************/
18 // Author: ruben.shahoyan@cern.ch 09/09/2006
20 ////////////////////////////////////////////////////////////////////////////////
22 // AliCheb3D produces the interpolation of the user 3D->NDimOut arbitrary //
23 // function supplied in "void (*fcn)(float* inp,float* out)" format //
24 // either in a separate macro file or as a function pointer. //
25 // Only coefficients needed to guarantee the requested precision are kept. //
27 // The user-callable methods are: //
28 // To create the interpolation use: //
29 // AliCheb3D(const char* funName, // name of the file with user function //
31 // AliCheb3D(void (*ptr)(float*,float*),// pointer on the user function //
32 // Int_t DimOut, // dimensionality of the function's output //
33 // Float_t *bmin, // lower 3D bounds of interpolation domain //
34 // Float_t *bmax, // upper 3D bounds of interpolation domain //
35 // Int_t *npoints, // number of points in each of 3 input //
36 // // dimension, defining the interpolation grid //
37 // Float_t prec=1E-6); // requested max.absolute difference between //
38 // // the interpolation and any point on grid //
40 // To test obtained parameterization use the method //
41 // TH1* TestRMS(int idim,int npoints = 1000,TH1* histo=0); //
42 // it will compare the user output of the user function and interpolation //
43 // for idim-th output dimension and fill the difference in the supplied //
44 // histogram. If no histogram is supplied, it will be created. //
46 // To save the interpolation data: //
47 // SaveData(const char* filename, Bool_t append ) //
48 // write text file with data. If append is kTRUE and the output file already //
49 // exists, data will be added in the end of the file. //
50 // Alternatively, SaveData(FILE* stream) will write the data to //
51 // already existing stream. //
53 // To read back already stored interpolation use either the constructor //
54 // AliCheb3D(const char* inpFile); //
55 // or the default constructor AliCheb3D() followed by //
56 // AliCheb3D::LoadData(const char* inpFile); //
58 // To compute the interpolation use Eval(float* par,float *res) method, with //
59 // par being 3D vector of arguments (inside the validity region) and res is //
60 // the array of DimOut elements for the output. //
62 // If only one component (say, idim-th) of the output is needed, use faster //
63 // Float_t Eval(Float_t *par,int idim) method. //
65 // void Print(option="") will print the name, the ranges of validity and //
66 // the absolute precision of the parameterization. Option "l" will also print //
67 // the information about the number of coefficients for each output //
70 // NOTE: during the evaluation no check is done for parameter vector being //
71 // outside the interpolation region. If there is such a risk, use //
72 // Bool_t IsInside(float *par) method. Chebyshev parameterization is not //
73 // good for extrapolation! //
75 // For the properties of Chebyshev parameterization see: //
76 // H.Wind, CERN EP Internal Report, 81-12/Rev. //
78 ////////////////////////////////////////////////////////////////////////////////
84 #include "AliCheb3D.h"
88 ClassImp(AliCheb3DCalc)
91 AliCheb3DCalc::AliCheb3DCalc():
105 // Default constructor
109 AliCheb3DCalc::AliCheb3DCalc(FILE* stream):
123 // Default constructor
128 //__________________________________________________________________________________________
129 void AliCheb3DCalc::Clear(Option_t*)
131 // delete all dynamycally allocated structures
132 if (fTmpCf1) { delete[] fTmpCf1; fTmpCf1 = 0;}
133 if (fTmpCf0) { delete[] fTmpCf0; fTmpCf0 = 0;}
134 if (fCoefs) { delete[] fCoefs; fCoefs = 0;}
135 if (fCoefBound2D0) { delete[] fCoefBound2D0; fCoefBound2D0 = 0; }
136 if (fCoefBound2D1) { delete[] fCoefBound2D1; fCoefBound2D1 = 0; }
137 if (fNColsAtRow) { delete[] fNColsAtRow; fNColsAtRow = 0; }
138 if (fColAtRowBg) { delete[] fColAtRowBg; fColAtRowBg = 0; }
142 //__________________________________________________________________________________________
143 void AliCheb3DCalc::Init0()
145 // reset everything to 0
146 fNCoefs = fNRows = fNCols = fNElemBound2D = 0;
148 fCoefBound2D0 = fCoefBound2D1 = 0;
149 fNColsAtRow = fColAtRowBg = 0;
150 fTmpCf0 = fTmpCf1 = 0;
153 //__________________________________________________________________________________________
154 void AliCheb3DCalc::Print(Option_t* ) const
156 printf("Chebyshev parameterization data %s for 3D->1 function.\n",GetName());
158 for (int i=fNElemBound2D;i--;) if (fCoefBound2D0[i]>nmax3d) nmax3d = fCoefBound2D0[i];
159 printf("%d coefficients in %dx%dx%d matrix\n",fNCoefs,fNRows,fNCols,nmax3d);
163 //__________________________________________________________________________________________
164 Float_t AliCheb3DCalc::Eval(Float_t *par) const
166 // evaluate Chebyshev parameterization for 3D function.
167 // VERY IMPORTANT: par must contain the function arguments ALREADY MAPPED to [-1:1] interval
173 for (int id0=fNRows;id0--;) {
174 int nCLoc = fNColsAtRow[id0]; // number of significant coefs on this row
175 int Col0 = fColAtRowBg[id0]; // beginning of local column in the 2D boundary matrix
176 for (int id1=nCLoc;id1--;) {
178 fTmpCf1[id1] = (ncfRC=fCoefBound2D0[id]) ? ChebEval1D(z,fCoefs + fCoefBound2D1[id], ncfRC) : 0.0;
180 fTmpCf0[id0] = nCLoc>0 ? ChebEval1D(y,fTmpCf1,nCLoc):0.0;
182 return ChebEval1D(x,fTmpCf0,fNRows);
186 //_______________________________________________
187 #ifdef _INC_CREATION_ALICHEB3D_
188 void AliCheb3DCalc::SaveData(const char* outfile,Bool_t append) const
190 // writes coefficients data to output text file, optionallt appending on the end of existing file
191 TString strf = outfile;
192 gSystem->ExpandPathName(strf);
193 FILE* stream = fopen(strf,append ? "a":"w");
200 //_______________________________________________
201 #ifdef _INC_CREATION_ALICHEB3D_
202 void AliCheb3DCalc::SaveData(FILE* stream) const
204 // writes coefficients data to existing output stream
205 // Note: fNCols, fNElemBound2D and fColAtRowBg is not stored, will be computed on fly during the loading of this file
206 fprintf(stream,"#\nSTART %s\n",GetName());
207 fprintf(stream,"# Number of rows\n%d\n",fNRows);
209 fprintf(stream,"# Number of columns per row\n");
210 for (int i=0;i<fNRows;i++) fprintf(stream,"%d\n",fNColsAtRow[i]);
212 fprintf(stream,"# Number of Coefs in each significant block of third dimension\n");
213 for (int i=0;i<fNElemBound2D;i++) fprintf(stream,"%d\n",fCoefBound2D0[i]);
215 fprintf(stream,"# Coefficients\n");
216 for (int i=0;i<fNCoefs;i++) fprintf(stream,"%+.8e\n",fCoefs[i]);
217 fprintf(stream,"END %s\n",GetName());
222 //_______________________________________________
223 void AliCheb3DCalc::LoadData(FILE* stream)
225 // Load coefs. from the stream
226 if (!stream) {Error("LoadData","No stream provided.\nStop"); exit(1);}
229 ReadLine(buffs,stream);
230 if (!buffs.BeginsWith("START")) {Error("LoadData","Expected: \"START <fit_name>\", found \"%s\"\nStop\n",buffs.Data());exit(1);}
231 if (buffs.First(' ')>0) SetName(buffs.Data()+buffs.First(' ')+1);
233 ReadLine(buffs,stream); // NRows
234 fNRows = buffs.Atoi();
235 if (fNRows<1) {Error("LoadData","Expected: '<number_of_rows>', found \"%s\"\nStop\n",buffs.Data());exit(1);}
241 for (int id0=0;id0<fNRows;id0++) {
242 ReadLine(buffs,stream); // n.cols at this row
243 fNColsAtRow[id0] = buffs.Atoi();
244 fColAtRowBg[id0] = fNElemBound2D; // begining of this row in 2D boundary surface
245 fNElemBound2D += fNColsAtRow[id0];
246 if (fNCols<fNColsAtRow[id0]) fNCols = fNColsAtRow[id0];
251 InitElemBound2D(fNElemBound2D);
253 for (int i=0;i<fNElemBound2D;i++) {
254 ReadLine(buffs,stream); // n.coeffs at 3-d dimension for the given column/row
255 fCoefBound2D0[i] = buffs.Atoi();
256 fCoefBound2D1[i] = fNCoefs;
257 fNCoefs += fCoefBound2D0[i];
260 if (fNCoefs<=0) {Error("LoadData","Negtive (%d) number of Chebychef coeffs. is obtained.\nStop\n",fNCoefs);exit(1);}
263 for (int i=0;i<fNCoefs;i++) {
264 ReadLine(buffs,stream);
265 fCoefs[i] = buffs.Atof();
267 // check end_of_data record
268 ReadLine(buffs,stream);
269 if (!buffs.BeginsWith("END") || !buffs.Contains(GetName())) {
270 Error("LoadData","Expected \"END %s\", found \"%s\".\nStop\n",GetName(),buffs.Data());
276 //_______________________________________________
277 void AliCheb3DCalc::ReadLine(TString& str,FILE* stream)
279 // read single line from the stream, skipping empty and commented lines. EOF is not expected
280 while (str.Gets(stream)) {
281 str = str.Strip(TString::kBoth,' ');
282 if (str.IsNull()||str.BeginsWith("#")) continue;
285 fprintf(stderr,"AliCheb3D::ReadLine: Failed to read from stream.\nStop");exit(1); // normally, should not reach here
288 //_______________________________________________
289 void AliCheb3DCalc::InitCols(int nc)
291 // Set max.number of significant columns in the coefs matrix
293 if (fTmpCf1) delete[] fTmpCf1;
294 fTmpCf1 = new Float_t [fNCols];
297 //_______________________________________________
298 void AliCheb3DCalc::InitRows(int nr)
300 // Set max.number of significant rows in the coefs matrix
301 if (fNColsAtRow) delete[] fNColsAtRow;
302 if (fColAtRowBg) delete[] fColAtRowBg;
303 if (fTmpCf0) delete[] fTmpCf0;
305 fNColsAtRow = new Int_t[fNRows];
306 fTmpCf0 = new Float_t [fNRows];
307 fColAtRowBg = new Int_t[fNRows];
308 for (int i=fNRows;i--;) fNColsAtRow[i] = fColAtRowBg[i] = 0;
311 //_______________________________________________
312 void AliCheb3DCalc::InitElemBound2D(int ne)
314 // Set max number of significant coefs for given row/column of coefs 3D matrix
315 if (fCoefBound2D0) delete[] fCoefBound2D0;
316 if (fCoefBound2D1) delete[] fCoefBound2D1;
318 fCoefBound2D0 = new Int_t[fNElemBound2D];
319 fCoefBound2D1 = new Int_t[fNElemBound2D];
320 for (int i=fNElemBound2D;i--;) fCoefBound2D0[i] = fCoefBound2D1[i] = 0;
323 //_______________________________________________
324 void AliCheb3DCalc::InitCoefs(int nc)
326 // Set total number of significant coefs
327 if (fCoefs) delete[] fCoefs;
329 fCoefs = new Float_t [fNCoefs];
330 for (int i=fNCoefs;i--;) fCoefs[i] = 0.0;
338 AliCheb3D::AliCheb3D():
347 // Default constructor
351 AliCheb3D::AliCheb3D(const char* inputFile):
360 // Default constructor
367 AliCheb3D::AliCheb3D(FILE* stream):
376 // Default constructor
382 //__________________________________________________________________________________________
383 #ifdef _INC_CREATION_ALICHEB3D_
384 AliCheb3D::AliCheb3D(const char* funName, int DimOut, Float_t *bmin,Float_t *bmax, Int_t *npoints, Float_t prec) : TNamed(funName,funName)
386 // Construct the parameterization for the function
387 // funName : name of the file containing the function: void funName(Float_t * inp,Float_t * out)
388 // DimOut : dimension of the vector computed by the user function
389 // bmin : array of 3 elements with the lower boundaries of the region where the function is defined
390 // bmax : array of 3 elements with the upper boundaries of the region where the function is defined
391 // npoints : array of 3 elements with the number of points to compute in each of 3 dimension
392 // prec : max allowed absolute difference between the user function and computed parameterization on the requested grid
395 fPrec = TMath::Max(1.E-12f,prec);
396 if (DimOut<1) {Error("AliCheb3D","Requested output dimension is %d\nStop\n",fDimOut); exit(1);}
398 PrepareBoundaries(bmin,bmax);
400 SetUsrFunction(funName);
406 //__________________________________________________________________________________________
407 #ifdef _INC_CREATION_ALICHEB3D_
408 AliCheb3D::AliCheb3D(void (*ptr)(float*,float*), int DimOut, Float_t *bmin,Float_t *bmax, Int_t *npoints, Float_t prec) : TNamed("AliCheb3D","AliCheb3D")
410 // Construct the parameterization for the function
411 // ptr : pointer on the function: void fun(Float_t * inp,Float_t * out)
412 // DimOut : dimension of the vector computed by the user function
413 // bmin : array of 3 elements with the lower boundaries of the region where the function is defined
414 // bmax : array of 3 elements with the upper boundaries of the region where the function is defined
415 // npoints : array of 3 elements with the number of points to compute in each of 3 dimension
416 // prec : max allowed absolute difference between the user function and computed parameterization on the requested grid
419 fPrec = TMath::Max(1.E-12f,prec);
420 if (DimOut<1) {Error("AliCheb3D","Requested output dimension is %d\nStop\n",fDimOut); exit(1);}
422 PrepareBoundaries(bmin,bmax);
430 //__________________________________________________________________________________________
431 void AliCheb3D::Clear(Option_t*)
433 if (fResTmp) { delete[] fResTmp; fResTmp = 0; }
434 if (fGrid) { delete[] fGrid; fGrid = 0; }
435 if (fUsrMacro) { delete fUsrMacro; fUsrMacro = 0;}
440 //__________________________________________________________________________________________
441 void AliCheb3D::Print(Option_t* opt) const
443 printf("%s: Chebyshev parameterization for 3D->%dD function. Precision: %e\n",GetName(),fDimOut,fPrec);
444 printf("Region of validity: [%+.5e:%+.5e] [%+.5e:%+.5e] [%+.5e:%+.5e]\n",fBMin[0],fBMax[0],fBMin[1],fBMax[1],fBMin[2],fBMax[2]);
445 TString opts = opt; opts.ToLower();
446 if (opts.Contains("l")) for (int i=0;i<fDimOut;i++) {printf("Output dimension %d:\n",i+1); GetChebCalc(i)->Print();}
450 //__________________________________________________________________________________________
451 void AliCheb3D::Init0()
453 for (int i=3;i--;) fBMin[i] = fBMax[i] = fBScale[i] = fBOffset[i] = 0;
459 #ifdef _INC_CREATION_ALICHEB3D_
460 gUsrFunAliCheb3D = 0;
464 //__________________________________________________________________________________________
465 void AliCheb3D::PrepareBoundaries(Float_t *bmin,Float_t *bmax)
467 // Set and check boundaries defined by user, prepare coefficients for their conversion to [-1:1] interval
472 fBScale[i] = bmax[i]-bmin[i];
474 Error("PrepareBoundaries","Boundaries for %d-th dimension are not increasing: %+.4e %+.4e\nStop\n",i,fBMin[i],fBMax[i]);
477 fBOffset[i] = bmin[i] + fBScale[i]/2.0;
478 fBScale[i] = 2./fBScale[i];
483 //__________________________________________________________________________________________
484 #ifdef _INC_CREATION_ALICHEB3D_
485 void AliCheb3D::SetUsrFunction(const char* name)
487 // load user macro with function definition and compile it
488 gUsrFunAliCheb3D = 0;
490 gSystem->ExpandPathName(fUsrFunName);
491 if (fUsrMacro) delete fUsrMacro;
492 TString tmpst = fUsrFunName;
493 tmpst += "+"; // prepare filename to compile
494 if (gROOT->LoadMacro(tmpst.Data())) {Error("SetUsrFunction","Failed to load user function from %s\nStop\n",name); exit(1);}
495 fUsrMacro = new TMethodCall();
496 tmpst = tmpst.Data() + tmpst.Last('/')+1; //Strip away any path preceding the macro file name
497 int dot = tmpst.Last('.');
498 if (dot>0) tmpst.Resize(dot);
499 fUsrMacro->InitWithPrototype(tmpst.Data(),"Float_t *,Float_t *");
501 args[0] = (long)fArgsTmp;
502 args[1] = (long)fResTmp;
503 fUsrMacro->SetParamPtrs(args);
508 //__________________________________________________________________________________________
509 #ifdef _INC_CREATION_ALICHEB3D_
510 void AliCheb3D::SetUsrFunction(void (*ptr)(float*,float*))
512 if (fUsrMacro) delete fUsrMacro;
515 gUsrFunAliCheb3D = ptr;
519 //__________________________________________________________________________________________
520 #ifdef _INC_CREATION_ALICHEB3D_
521 void AliCheb3D::EvalUsrFunction(Float_t *x, Float_t *res) {
522 for (int i=3;i--;) fArgsTmp[i] = x[i];
523 if (gUsrFunAliCheb3D) gUsrFunAliCheb3D(fArgsTmp,fResTmp);
524 else fUsrMacro->Execute();
525 for (int i=fDimOut;i--;) res[i] = fResTmp[i];
529 //__________________________________________________________________________________________
530 #ifdef _INC_CREATION_ALICHEB3D_
531 Int_t AliCheb3D::CalcChebCoefs(Float_t *funval,int np, Float_t *outCoefs, Float_t prec)
533 // Calculate Chebyshev coeffs using precomputed function values at np roots.
534 // If prec>0, estimate the highest coeff number providing the needed precision
536 double sm; // do summations in double to minimize the roundoff error
537 for (int ic=0;ic<np;ic++) { // compute coeffs
539 for (int ir=0;ir<np;ir++) {
540 float rt = TMath::Cos( ic*(ir+0.5)*TMath::Pi()/np);
543 outCoefs[ic] = Float_t( sm * ((ic==0) ? 1./np : 2./np) );
546 if (prec<=0) return np;
550 for (cfMax=np;cfMax--;) {
551 sm += TMath::Abs(outCoefs[cfMax]);
554 if (++cfMax==0) cfMax=1;
560 //__________________________________________________________________________________________
561 #ifdef _INC_CREATION_ALICHEB3D_
562 void AliCheb3D::DefineGrid(Int_t* npoints)
564 // prepare the grid of Chebyshev roots in each dimension
565 const int kMinPoints = 1;
568 for (int id=3;id--;) {
569 fNPoints[id] = npoints[id];
570 if (fNPoints[id]<kMinPoints) {
571 Error("DefineGrid","at %d-th dimension %d point is requested, at least %d is needed\nStop\n",fNPoints[id],kMinPoints);
574 ntot += fNPoints[id];
575 fMaxCoefs *= fNPoints[id];
577 fGrid = new Float_t [ntot];
580 for (int id=3;id--;) {
581 int np = fNPoints[id];
582 fGridOffs[id] = curp;
583 for (int ip=0;ip<np;ip++) {
584 Float_t x = TMath::Cos( TMath::Pi()*(ip+0.5)/np );
585 fGrid[curp++] = MapToExternal(x,id);
592 //__________________________________________________________________________________________
593 #ifdef _INC_CREATION_ALICHEB3D_
594 Int_t AliCheb3D::ChebFit()
596 // prepare parameterization for all output dimensions
598 for (int i=fDimOut;i--;) ir+=ChebFit(i);
603 //__________________________________________________________________________________________
604 #ifdef _INC_CREATION_ALICHEB3D_
605 Int_t AliCheb3D::ChebFit(int dmOut)
607 // prepare paramaterization of 3D function for dmOut-th dimension
609 for (int i=0;i<3;i++) if (maxDim<fNPoints[i]) maxDim = fNPoints[i];
610 Float_t *fvals = new Float_t [ fNPoints[0] ];
611 Float_t *tmpCoef3D = new Float_t [ fNPoints[0]*fNPoints[1]*fNPoints[2] ];
612 Float_t *tmpCoef2D = new Float_t [ fNPoints[0]*fNPoints[1] ];
613 Float_t *tmpCoef1D = new Float_t [ maxDim ];
615 Float_t RTiny = fPrec/Float_t(maxDim); // neglect coefficient below this threshold
617 // 1D Cheb.fit for 0-th dimension at current steps of remaining dimensions
620 AliCheb3DCalc* cheb = GetChebCalc(dmOut);
622 for (int id2=fNPoints[2];id2--;) {
623 fArgsTmp[2] = fGrid[ fGridOffs[2]+id2 ];
625 for (int id1=fNPoints[1];id1--;) {
626 fArgsTmp[1] = fGrid[ fGridOffs[1]+id1 ];
628 for (int id0=fNPoints[0];id0--;) {
629 fArgsTmp[0] = fGrid[ fGridOffs[0]+id0 ];
630 EvalUsrFunction(); // compute function values at Chebyshev roots of 0-th dimension
631 fvals[id0] = fResTmp[dmOut];
633 int nc = CalcChebCoefs(fvals,fNPoints[0], tmpCoef1D, fPrec);
634 for (int id0=fNPoints[0];id0--;) tmpCoef2D[id1 + id0*fNPoints[1]] = tmpCoef1D[id0];
635 if (ncmax<nc) ncmax = nc; // max coefs to be kept in dim0 to guarantee needed precision
638 // once each 1d slice of given 2d slice is parametrized, parametrize the Cheb.coeffs
639 for (int id0=fNPoints[0];id0--;) {
640 CalcChebCoefs( tmpCoef2D+id0*fNPoints[1], fNPoints[1], tmpCoef1D, -1);
641 for (int id1=fNPoints[1];id1--;) tmpCoef3D[id2 + fNPoints[2]*(id1+id0*fNPoints[1])] = tmpCoef1D[id1];
645 // now fit the last dimensions Cheb.coefs
646 for (int id0=fNPoints[0];id0--;) {
647 for (int id1=fNPoints[1];id1--;) {
648 CalcChebCoefs( tmpCoef3D+ fNPoints[2]*(id1+id0*fNPoints[1]), fNPoints[2], tmpCoef1D, -1);
649 for (int id2=fNPoints[2];id2--;) tmpCoef3D[id2+ fNPoints[2]*(id1+id0*fNPoints[1])] = tmpCoef1D[id2]; // store on place
653 // now find 2D surface which separates significant coefficients of 3D matrix from nonsignificant ones (up to fPrec)
654 int *tmpCoefSurf = new Int_t[ fNPoints[0]*fNPoints[1] ];
655 for (int id0=fNPoints[0];id0--;) for (int id1=fNPoints[1];id1--;) tmpCoefSurf[id1+id0*fNPoints[1]]=0;
657 for (int id0=fNPoints[0];id0--;) {
658 for (int id1=fNPoints[1];id1--;) {
659 for (int id2=fNPoints[2];id2--;) {
660 int id = id2 + fNPoints[2]*(id1+id0*fNPoints[1]);
661 Float_t cfa = TMath::Abs(tmpCoef3D[id]);
662 if (cfa < RTiny) {tmpCoef3D[id] = 0; continue;} // neglect coeefs below the threshold
665 if (resid<fPrec) continue; // this coeff is negligible
666 // otherwise go back 1 step
668 tmpCoefSurf[id1+id0*fNPoints[1]] = id2+1; // how many coefs to keep
674 printf("\n\nCoeffs\n");
676 for (int id0=0;id0<fNPoints[0];id0++) {
677 for (int id1=0;id1<fNPoints[1];id1++) {
678 for (int id2=0;id2<fNPoints[2];id2++) {
679 printf("%2d%2d%2d %+.4e |",id0,id1,id2,tmpCoef3D[cnt++]);
686 // see if there are rows to reject, find max.significant column at each row
687 int NRows = fNPoints[0];
688 int *tmpCols = new int[NRows];
689 for (int id0=fNPoints[0];id0--;) {
690 int id1 = fNPoints[1];
691 while (id1>0 && tmpCoefSurf[(id1-1)+id0*fNPoints[1]]==0) id1--;
694 // find max significant row
695 for (int id0=NRows;id0--;) {if (tmpCols[id0]>0) break; NRows--;}
696 // find max significant column and fill the permanent storage for the max sigificant column of each row
697 cheb->InitRows(NRows); // create needed arrays;
698 int *NColsAtRow = cheb->GetNColsAtRow();
699 int *ColAtRowBg = cheb->GetColAtRowBg();
701 int NElemBound2D = 0;
702 for (int id0=0;id0<NRows;id0++) {
703 NColsAtRow[id0] = tmpCols[id0]; // number of columns to store for this row
704 ColAtRowBg[id0] = NElemBound2D; // begining of this row in 2D boundary surface
705 NElemBound2D += tmpCols[id0];
706 if (NCols<NColsAtRow[id0]) NCols = NColsAtRow[id0];
708 cheb->InitCols(NCols);
711 // create the 2D matrix defining the boundary of significance for 3D coeffs.matrix
712 // and count the number of siginifacnt coefficients
714 cheb->InitElemBound2D(NElemBound2D);
715 int *CoefBound2D0 = cheb->GetCoefBound2D0();
716 int *CoefBound2D1 = cheb->GetCoefBound2D1();
717 fMaxCoefs = 0; // redefine number of coeffs
718 for (int id0=0;id0<NRows;id0++) {
719 int nCLoc = NColsAtRow[id0];
720 int Col0 = ColAtRowBg[id0];
721 for (int id1=0;id1<nCLoc;id1++) {
722 CoefBound2D0[Col0 + id1] = tmpCoefSurf[id1+id0*fNPoints[1]]; // number of coefs to store for 3-d dimension
723 CoefBound2D1[Col0 + id1] = fMaxCoefs;
724 fMaxCoefs += CoefBound2D0[Col0 + id1];
728 // create final compressed 3D matrix for significant coeffs
729 cheb->InitCoefs(fMaxCoefs);
730 Float_t *Coefs = cheb->GetCoefs();
732 for (int id0=0;id0<NRows;id0++) {
733 int ncLoc = NColsAtRow[id0];
734 int Col0 = ColAtRowBg[id0];
735 for (int id1=0;id1<ncLoc;id1++) {
736 int ncf2 = CoefBound2D0[Col0 + id1];
737 for (int id2=0;id2<ncf2;id2++) {
738 Coefs[count++] = tmpCoef3D[id2 + fNPoints[2]*(id1+id0*fNPoints[1])];
743 printf("\n\nNewSurf\n");
744 for (int id0=0;id0<fNPoints[0];id0++) {
745 for (int id1=0;id1<fNPoints[1];id1++) {
746 printf("(%2d %2d) %2d |",id0,id1,tmpCoefSurf[id1+id0*fNPoints[1]]);
752 delete[] tmpCoefSurf;
762 //_______________________________________________
763 #ifdef _INC_CREATION_ALICHEB3D_
764 void AliCheb3D::SaveData(const char* outfile,Bool_t append) const
766 // writes coefficients data to output text file, optionallt appending on the end of existing file
767 TString strf = outfile;
768 gSystem->ExpandPathName(strf);
769 FILE* stream = fopen(strf,append ? "a":"w");
776 //_______________________________________________
777 #ifdef _INC_CREATION_ALICHEB3D_
778 void AliCheb3D::SaveData(FILE* stream) const
780 // writes coefficients data to existing output stream
782 fprintf(stream,"\n# These are automatically generated data for the Chebyshev interpolation of 3D->%dD function\n",fDimOut);
783 fprintf(stream,"#\nSTART %s\n",GetName());
784 fprintf(stream,"# Dimensionality of the output\n%d\n",fDimOut);
785 fprintf(stream,"# Interpolation abs. precision\n%+.8e\n",fPrec);
787 fprintf(stream,"# Lower boundaries of interpolation region\n");
788 for (int i=0;i<3;i++) fprintf(stream,"%+.8e\n",fBMin[i]);
789 fprintf(stream,"# Upper boundaries of interpolation region\n");
790 for (int i=0;i<3;i++) fprintf(stream,"%+.8e\n",fBMax[i]);
791 fprintf(stream,"# Parameterization for each output dimension follows:\n",GetName());
793 for (int i=0;i<fDimOut;i++) GetChebCalc(i)->SaveData(stream);
794 fprintf(stream,"#\nEND %s\n#\n",GetName());
799 //_______________________________________________
800 void AliCheb3D::LoadData(const char* inpFile)
802 TString strf = inpFile;
803 gSystem->ExpandPathName(strf);
804 FILE* stream = fopen(strf.Data(),"r");
810 //_______________________________________________
811 void AliCheb3D::LoadData(FILE* stream)
813 if (!stream) {Error("LoadData","No stream provided.\nStop"); exit(1);}
816 AliCheb3DCalc::ReadLine(buffs,stream);
817 if (!buffs.BeginsWith("START")) {Error("LoadData","Expected: \"START <fit_name>\", found \"%s\"\nStop\n",buffs.Data());exit(1);}
818 SetName(buffs.Data()+buffs.First(' ')+1);
820 AliCheb3DCalc::ReadLine(buffs,stream); // N output dimensions
821 fDimOut = buffs.Atoi();
822 if (fDimOut<1) {Error("LoadData","Expected: '<number_of_output_dimensions>', found \"%s\"\nStop\n",buffs.Data());exit(1);}
826 AliCheb3DCalc::ReadLine(buffs,stream); // Interpolation abs. precision
827 fPrec = buffs.Atof();
828 if (fPrec<=0) {Error("LoadData","Expected: '<abs.precision>', found \"%s\"\nStop\n",buffs.Data());exit(1);}
830 for (int i=0;i<3;i++) { // Lower boundaries of interpolation region
831 AliCheb3DCalc::ReadLine(buffs,stream);
832 fBMin[i] = buffs.Atof();
834 for (int i=0;i<3;i++) { // Upper boundaries of interpolation region
835 AliCheb3DCalc::ReadLine(buffs,stream);
836 fBMax[i] = buffs.Atof();
838 PrepareBoundaries(fBMin,fBMax);
840 // data for each output dimension
841 for (int i=0;i<fDimOut;i++) GetChebCalc(i)->LoadData(stream);
843 // check end_of_data record
844 AliCheb3DCalc::ReadLine(buffs,stream);
845 if (!buffs.BeginsWith("END") || !buffs.Contains(GetName())) {
846 Error("LoadData","Expected \"END %s\", found \"%s\".\nStop\n",GetName(),buffs.Data());
852 //_______________________________________________
853 void AliCheb3D::SetDimOut(int d)
856 if (fResTmp) delete fResTmp;
857 fResTmp = new Float_t[fDimOut]; // RRR
859 for (int i=0;i<d;i++) fChebCalc.AddAtAndExpand(new AliCheb3DCalc(),i);
862 //_______________________________________________
863 void AliCheb3D::ShiftBound(int id,float dif)
865 if (id<0||id>2) {printf("Maximum 3 dimensions are supported\n"); return;}
871 //_______________________________________________
872 #ifdef _INC_CREATION_ALICHEB3D_
873 TH1* AliCheb3D::TestRMS(int idim,int npoints,TH1* histo)
875 // fills the difference between the original function and parameterization (for idim-th component of the output)
876 // to supplied histogram. Calculations are done in npoints random points.
877 // If the hostgram was not supplied, it will be created. It is up to the user to delete it!
879 printf("No user function is set\n");
882 if (!histo) histo = new TH1D(GetName(),"Control: Function - Parametrization",100,-2*fPrec,2*fPrec);
883 for (int ip=npoints;ip--;) {
884 gRandom->RndmArray(3,(Float_t *)fArgsTmp);
885 for (int i=3;i--;) fArgsTmp[i] = fBMin[i] + fArgsTmp[i]*(fBMax[i]-fBMin[i]);
887 Float_t valFun = fResTmp[idim];
888 Eval(fArgsTmp,fResTmp);
889 Float_t valPar = fResTmp[idim];
890 histo->Fill(valFun - valPar);