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0eea9d4d 1/**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
3 * *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
6 * *
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 **************************************************************************/
15
16/* $Id$ */
17
18// Author: ruben.shahoyan@cern.ch 09/09/2006
19//
20////////////////////////////////////////////////////////////////////////////////
21// //
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. //
26// //
27// The user-callable methods are: //
28// To create the interpolation use: //
29// AliCheb3D(const char* funName, // name of the file with user function //
30// or //
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 //
39// //
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. //
45// //
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. //
52// //
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); //
57// //
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. //
61// //
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. //
64// //
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 //
68// dimension. //
69// //
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! //
74// //
75// For the properties of Chebyshev parameterization see: //
76// H.Wind, CERN EP Internal Report, 81-12/Rev. //
77// //
78////////////////////////////////////////////////////////////////////////////////
79
80#include <TString.h>
81#include <TSystem.h>
82#include <TRandom.h>
83#include <TROOT.h>
84#include "AliCheb3D.h"
85
86
87
88ClassImp(AliCheb3DCalc)
89
90
91AliCheb3DCalc::AliCheb3DCalc():
92 TNamed("", ""),
93 fNCoefs(0),
94 fNRows(0),
95 fNCols(0),
96 fNElemBound2D(0),
97 fNColsAtRow(0),
98 fColAtRowBg(0),
99 fCoefBound2D0(0),
100 fCoefBound2D1(0),
101 fCoefs(0),
102 fTmpCf1(0),
103 fTmpCf0(0)
104{
105 // Default constructor
106 Init0();
107}
108
109AliCheb3DCalc::AliCheb3DCalc(FILE* stream):
110 TNamed("", ""),
111 fNCoefs(0),
112 fNRows(0),
113 fNCols(0),
114 fNElemBound2D(0),
115 fNColsAtRow(0),
116 fColAtRowBg(0),
117 fCoefBound2D0(0),
118 fCoefBound2D1(0),
119 fCoefs(0),
120 fTmpCf1(0),
121 fTmpCf0(0)
122{
123 // Default constructor
124 Init0();
125 LoadData(stream);
126}
127
128//__________________________________________________________________________________________
129void AliCheb3DCalc::Clear(Option_t*)
130{
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; }
139 //
140}
141
142//__________________________________________________________________________________________
143void AliCheb3DCalc::Init0()
144{
145 // reset everything to 0
146 fNCoefs = fNRows = fNCols = fNElemBound2D = 0;
147 fCoefs = 0;
148 fCoefBound2D0 = fCoefBound2D1 = 0;
149 fNColsAtRow = fColAtRowBg = 0;
150 fTmpCf0 = fTmpCf1 = 0;
151}
152
153//__________________________________________________________________________________________
154void AliCheb3DCalc::Print(Option_t* ) const
155{
156 printf("Chebyshev parameterization data %s for 3D->1 function.\n",GetName());
157 int nmax3d = 0;
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);
160 //
161}
162
163//__________________________________________________________________________________________
164Float_t AliCheb3DCalc::Eval(Float_t *par) const
165{
166 // evaluate Chebyshev parameterization for 3D function.
167 // VERY IMPORTANT: par must contain the function arguments ALREADY MAPPED to [-1:1] interval
168 Float_t &z = par[2];
169 Float_t &y = par[1];
170 Float_t &x = par[0];
171 //
172 int ncfRC;
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--;) {
177 int id = id1+Col0;
178 fTmpCf1[id1] = (ncfRC=fCoefBound2D0[id]) ? ChebEval1D(z,fCoefs + fCoefBound2D1[id], ncfRC) : 0.0;
179 }
180 fTmpCf0[id0] = nCLoc>0 ? ChebEval1D(y,fTmpCf1,nCLoc):0.0;
181 }
182 return ChebEval1D(x,fTmpCf0,fNRows);
183 //
184}
185
186//_______________________________________________
187#ifdef _INC_CREATION_ALICHEB3D_
188void AliCheb3DCalc::SaveData(const char* outfile,Bool_t append) const
189{
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");
194 SaveData(stream);
195 fclose(stream);
196 //
197}
198#endif
199
200//_______________________________________________
201#ifdef _INC_CREATION_ALICHEB3D_
202void AliCheb3DCalc::SaveData(FILE* stream) const
203{
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);
208 //
209 fprintf(stream,"# Number of columns per row\n");
210 for (int i=0;i<fNRows;i++) fprintf(stream,"%d\n",fNColsAtRow[i]);
211 //
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]);
214 //
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());
218 //
219}
220#endif
221
222//_______________________________________________
223void AliCheb3DCalc::LoadData(FILE* stream)
224{
225 // Load coefs. from the stream
226 if (!stream) {Error("LoadData","No stream provided.\nStop"); exit(1);}
227 TString buffs;
228 Clear();
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);
232 //
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);}
236 //
237 fNCols = 0;
238 fNElemBound2D = 0;
239 InitRows(fNRows);
240 //
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];
247 }
248 InitCols(fNCols);
249 //
250 fNCoefs = 0;
251 InitElemBound2D(fNElemBound2D);
252 //
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];
258 }
259 //
260 if (fNCoefs<=0) {Error("LoadData","Negtive (%d) number of Chebychef coeffs. is obtained.\nStop\n",fNCoefs);exit(1);}
261 //
262 InitCoefs(fNCoefs);
263 for (int i=0;i<fNCoefs;i++) {
264 ReadLine(buffs,stream);
265 fCoefs[i] = buffs.Atof();
266 }
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());
271 exit(1);
272 }
273 //
274}
275
276//_______________________________________________
277void AliCheb3DCalc::ReadLine(TString& str,FILE* stream)
278{
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;
283 return;
284 }
285 fprintf(stderr,"AliCheb3D::ReadLine: Failed to read from stream.\nStop");exit(1); // normally, should not reach here
286}
287
288//_______________________________________________
289void AliCheb3DCalc::InitCols(int nc)
290{
291 // Set max.number of significant columns in the coefs matrix
292 fNCols = nc;
293 if (fTmpCf1) delete[] fTmpCf1;
294 fTmpCf1 = new Float_t [fNCols];
295}
296
297//_______________________________________________
298void AliCheb3DCalc::InitRows(int nr)
299{
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;
304 fNRows = nr;
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;
309}
310
311//_______________________________________________
312void AliCheb3DCalc::InitElemBound2D(int ne)
313{
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;
317 fNElemBound2D = ne;
318 fCoefBound2D0 = new Int_t[fNElemBound2D];
319 fCoefBound2D1 = new Int_t[fNElemBound2D];
320 for (int i=fNElemBound2D;i--;) fCoefBound2D0[i] = fCoefBound2D1[i] = 0;
321}
322
323//_______________________________________________
324void AliCheb3DCalc::InitCoefs(int nc)
325{
326 // Set total number of significant coefs
327 if (fCoefs) delete[] fCoefs;
328 fNCoefs = nc;
329 fCoefs = new Float_t [fNCoefs];
330 for (int i=fNCoefs;i--;) fCoefs[i] = 0.0;
331}
332
333
334
335
336ClassImp(AliCheb3D)
337
338AliCheb3D::AliCheb3D():
339 TNamed("", ""),
340 fDimOut(0),
341 fPrec(0.),
342 fMaxCoefs(0),
343 fResTmp(0),
344 fGrid(0),
345 fUsrMacro(0)
346{
347 // Default constructor
348 Init0();
349}
350
351AliCheb3D::AliCheb3D(const char* inputFile):
352 TNamed("", ""),
353 fDimOut(0),
354 fPrec(0.),
355 fMaxCoefs(0),
356 fResTmp(0),
357 fGrid(0),
358 fUsrMacro(0)
359{
360 // Default constructor
361 Init0();
362 LoadData(inputFile);
363}
364
365
366
367AliCheb3D::AliCheb3D(FILE* stream):
368 TNamed("", ""),
369 fDimOut(0),
370 fPrec(0.),
371 fMaxCoefs(0),
372 fResTmp(0),
373 fGrid(0),
374 fUsrMacro(0)
375{
376 // Default constructor
377 Init0();
378 LoadData(stream);
379}
380
381
382//__________________________________________________________________________________________
383#ifdef _INC_CREATION_ALICHEB3D_
384AliCheb3D::AliCheb3D(const char* funName, int DimOut, Float_t *bmin,Float_t *bmax, Int_t *npoints, Float_t prec) : TNamed(funName,funName)
385{
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
393 //
394 Init0();
395 fPrec = TMath::Max(1.E-12f,prec);
396 if (DimOut<1) {Error("AliCheb3D","Requested output dimension is %d\nStop\n",fDimOut); exit(1);}
397 SetDimOut(DimOut);
398 PrepareBoundaries(bmin,bmax);
399 DefineGrid(npoints);
400 SetUsrFunction(funName);
401 ChebFit();
402 //
403}
404#endif
405
406//__________________________________________________________________________________________
407#ifdef _INC_CREATION_ALICHEB3D_
408AliCheb3D::AliCheb3D(void (*ptr)(float*,float*), int DimOut, Float_t *bmin,Float_t *bmax, Int_t *npoints, Float_t prec) : TNamed("AliCheb3D","AliCheb3D")
409{
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
417 //
418 Init0();
419 fPrec = TMath::Max(1.E-12f,prec);
420 if (DimOut<1) {Error("AliCheb3D","Requested output dimension is %d\nStop\n",fDimOut); exit(1);}
421 SetDimOut(DimOut);
422 PrepareBoundaries(bmin,bmax);
423 DefineGrid(npoints);
424 SetUsrFunction(ptr);
425 ChebFit();
426 //
427}
428#endif
429
430//__________________________________________________________________________________________
431void AliCheb3D::Clear(Option_t*)
432{
433 if (fResTmp) { delete[] fResTmp; fResTmp = 0; }
434 if (fGrid) { delete[] fGrid; fGrid = 0; }
435 if (fUsrMacro) { delete fUsrMacro; fUsrMacro = 0;}
436 fChebCalc.Delete();
437 //
438}
439
440//__________________________________________________________________________________________
441void AliCheb3D::Print(Option_t* opt) const
442{
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();}
447 //
448}
449
450//__________________________________________________________________________________________
451void AliCheb3D::Init0()
452{
453 for (int i=3;i--;) fBMin[i] = fBMax[i] = fBScale[i] = fBOffset[i] = 0;
454 fMaxCoefs = 0;
455 fGrid = 0;
456 fResTmp = 0;
457 fUsrFunName = "";
458 fUsrMacro = 0;
459#ifdef _INC_CREATION_ALICHEB3D_
460 gUsrFunAliCheb3D = 0;
461#endif
462}
463
464//__________________________________________________________________________________________
465void AliCheb3D::PrepareBoundaries(Float_t *bmin,Float_t *bmax)
466{
467 // Set and check boundaries defined by user, prepare coefficients for their conversion to [-1:1] interval
468 //
469 for (int i=3;i--;) {
470 fBMin[i] = bmin[i];
471 fBMax[i] = bmax[i];
472 fBScale[i] = bmax[i]-bmin[i];
473 if (fBScale[i]<=0) {
474 Error("PrepareBoundaries","Boundaries for %d-th dimension are not increasing: %+.4e %+.4e\nStop\n",i,fBMin[i],fBMax[i]);
475 exit(1);
476 }
477 fBOffset[i] = bmin[i] + fBScale[i]/2.0;
478 fBScale[i] = 2./fBScale[i];
479 }
480 //
481}
482
483//__________________________________________________________________________________________
484#ifdef _INC_CREATION_ALICHEB3D_
485void AliCheb3D::SetUsrFunction(const char* name)
486{
487 // load user macro with function definition and compile it
488 gUsrFunAliCheb3D = 0;
489 fUsrFunName = name;
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 *");
500 long args[2];
501 args[0] = (long)fArgsTmp;
502 args[1] = (long)fResTmp;
503 fUsrMacro->SetParamPtrs(args);
504 //
505}
506#endif
507
508//__________________________________________________________________________________________
509#ifdef _INC_CREATION_ALICHEB3D_
510void AliCheb3D::SetUsrFunction(void (*ptr)(float*,float*))
511{
512 if (fUsrMacro) delete fUsrMacro;
513 fUsrMacro = 0;
514 fUsrFunName = "";
515 gUsrFunAliCheb3D = ptr;
516}
517#endif
518
519//__________________________________________________________________________________________
520#ifdef _INC_CREATION_ALICHEB3D_
521void 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];
526}
527#endif
528
529//__________________________________________________________________________________________
530#ifdef _INC_CREATION_ALICHEB3D_
531Int_t AliCheb3D::CalcChebCoefs(Float_t *funval,int np, Float_t *outCoefs, Float_t prec)
532{
533 // Calculate Chebyshev coeffs using precomputed function values at np roots.
534 // If prec>0, estimate the highest coeff number providing the needed precision
535 //
536 double sm; // do summations in double to minimize the roundoff error
537 for (int ic=0;ic<np;ic++) { // compute coeffs
538 sm = 0;
539 for (int ir=0;ir<np;ir++) {
540 float rt = TMath::Cos( ic*(ir+0.5)*TMath::Pi()/np);
541 sm += funval[ir]*rt;
542 }
543 outCoefs[ic] = Float_t( sm * ((ic==0) ? 1./np : 2./np) );
544 }
545 //
546 if (prec<=0) return np;
547 //
548 sm = 0;
549 int cfMax = 0;
550 for (cfMax=np;cfMax--;) {
551 sm += TMath::Abs(outCoefs[cfMax]);
552 if (sm>=prec) break;
553 }
554 if (++cfMax==0) cfMax=1;
555 return cfMax;
556 //
557}
558#endif
559
560//__________________________________________________________________________________________
561#ifdef _INC_CREATION_ALICHEB3D_
562void AliCheb3D::DefineGrid(Int_t* npoints)
563{
564 // prepare the grid of Chebyshev roots in each dimension
565 const int kMinPoints = 1;
566 int ntot = 0;
567 fMaxCoefs = 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);
572 exit(1);
573 }
574 ntot += fNPoints[id];
575 fMaxCoefs *= fNPoints[id];
576 }
577 fGrid = new Float_t [ntot];
578 //
579 int curp = 0;
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);
586 }
587 }
588 //
589}
590#endif
591
592//__________________________________________________________________________________________
593#ifdef _INC_CREATION_ALICHEB3D_
594Int_t AliCheb3D::ChebFit()
595{
596 // prepare parameterization for all output dimensions
597 int ir=0;
598 for (int i=fDimOut;i--;) ir+=ChebFit(i);
599 return ir;
600}
601#endif
602
603//__________________________________________________________________________________________
604#ifdef _INC_CREATION_ALICHEB3D_
605Int_t AliCheb3D::ChebFit(int dmOut)
606{
607 // prepare paramaterization of 3D function for dmOut-th dimension
608 int maxDim = 0;
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 ];
614 //
615 Float_t RTiny = fPrec/Float_t(maxDim); // neglect coefficient below this threshold
616 //
617 // 1D Cheb.fit for 0-th dimension at current steps of remaining dimensions
618 int ncmax = 0;
619 //
620 AliCheb3DCalc* cheb = GetChebCalc(dmOut);
621 //
622 for (int id2=fNPoints[2];id2--;) {
623 fArgsTmp[2] = fGrid[ fGridOffs[2]+id2 ];
624 //
625 for (int id1=fNPoints[1];id1--;) {
626 fArgsTmp[1] = fGrid[ fGridOffs[1]+id1 ];
627 //
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];
632 }
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
636 }
637 //
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];
642 }
643 }
644 //
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
650 }
651 }
652 //
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;
656 Double_t resid = 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
663
664 resid += cfa;
665 if (resid<fPrec) continue; // this coeff is negligible
666 // otherwise go back 1 step
667 resid -= cfa;
668 tmpCoefSurf[id1+id0*fNPoints[1]] = id2+1; // how many coefs to keep
669 break;
670 }
671 }
672 }
673 /*
674 printf("\n\nCoeffs\n");
675 int cnt = 0;
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++]);
680 }
681 printf("\n");
682 }
683 printf("\n");
684 }
685 */
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--;
692 tmpCols[id0] = id1;
693 }
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();
700 int NCols = 0;
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];
707 }
708 cheb->InitCols(NCols);
709 delete[] tmpCols;
710 //
711 // create the 2D matrix defining the boundary of significance for 3D coeffs.matrix
712 // and count the number of siginifacnt coefficients
713 //
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];
725 }
726 }
727 //
728 // create final compressed 3D matrix for significant coeffs
729 cheb->InitCoefs(fMaxCoefs);
730 Float_t *Coefs = cheb->GetCoefs();
731 int count = 0;
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])];
739 }
740 }
741 }
742 /*
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]]);
747 }
748 printf("\n");
749 }
750 */
751 //
752 delete[] tmpCoefSurf;
753 delete[] tmpCoef1D;
754 delete[] tmpCoef2D;
755 delete[] tmpCoef3D;
756 delete[] fvals;
757 //
758 return 1;
759}
760#endif
761
762//_______________________________________________
763#ifdef _INC_CREATION_ALICHEB3D_
764void AliCheb3D::SaveData(const char* outfile,Bool_t append) const
765{
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");
770 SaveData(stream);
771 fclose(stream);
772 //
773}
774#endif
775
776//_______________________________________________
777#ifdef _INC_CREATION_ALICHEB3D_
778void AliCheb3D::SaveData(FILE* stream) const
779{
780 // writes coefficients data to existing output stream
781 //
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);
786 //
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());
792 //
793 for (int i=0;i<fDimOut;i++) GetChebCalc(i)->SaveData(stream);
794 fprintf(stream,"#\nEND %s\n#\n",GetName());
795 //
796}
797#endif
798
799//_______________________________________________
800void AliCheb3D::LoadData(const char* inpFile)
801{
802 TString strf = inpFile;
803 gSystem->ExpandPathName(strf);
804 FILE* stream = fopen(strf.Data(),"r");
805 LoadData(stream);
806 fclose(stream);
807 //
808}
809
810//_______________________________________________
811void AliCheb3D::LoadData(FILE* stream)
812{
813 if (!stream) {Error("LoadData","No stream provided.\nStop"); exit(1);}
814 TString buffs;
815 Clear();
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);
819 //
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);}
823 //
824 SetDimOut(fDimOut);
825 //
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);}
829 //
830 for (int i=0;i<3;i++) { // Lower boundaries of interpolation region
831 AliCheb3DCalc::ReadLine(buffs,stream);
832 fBMin[i] = buffs.Atof();
833 }
834 for (int i=0;i<3;i++) { // Upper boundaries of interpolation region
835 AliCheb3DCalc::ReadLine(buffs,stream);
836 fBMax[i] = buffs.Atof();
837 }
838 PrepareBoundaries(fBMin,fBMax);
839 //
840 // data for each output dimension
841 for (int i=0;i<fDimOut;i++) GetChebCalc(i)->LoadData(stream);
842 //
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());
847 exit(1);
848 }
849 //
850}
851
852//_______________________________________________
853void AliCheb3D::SetDimOut(int d)
854{
855 fDimOut = d;
856 if (fResTmp) delete fResTmp;
857 fResTmp = new Float_t[fDimOut]; // RRR
858 fChebCalc.Delete();
859 for (int i=0;i<d;i++) fChebCalc.AddAtAndExpand(new AliCheb3DCalc(),i);
860}
861
862//_______________________________________________
863void AliCheb3D::ShiftBound(int id,float dif)
864{
865 if (id<0||id>2) {printf("Maximum 3 dimensions are supported\n"); return;}
866 fBMin[id] += dif;
867 fBMax[id] += dif;
868 fBOffset[id] += dif;
869}
870
871//_______________________________________________
872#ifdef _INC_CREATION_ALICHEB3D_
873TH1* AliCheb3D::TestRMS(int idim,int npoints,TH1* histo)
874{
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!
878 if (!fUsrMacro) {
879 printf("No user function is set\n");
880 return 0;
881 }
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]);
886 EvalUsrFunction();
887 Float_t valFun = fResTmp[idim];
888 Eval(fArgsTmp,fResTmp);
889 Float_t valPar = fResTmp[idim];
890 histo->Fill(valFun - valPar);
891 }
892 return histo;
893 //
894}
895#endif