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5406439e | 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 | **************************************************************************/ | |
0eea9d4d | 15 | |
16 | #include <TString.h> | |
17 | #include <TSystem.h> | |
0eea9d4d | 18 | #include <TROOT.h> |
40389866 | 19 | #include <TRandom.h> |
5406439e | 20 | #include <stdio.h> |
21 | #include <TMethodCall.h> | |
22 | #include <TMath.h> | |
23 | #include <TH1.h> | |
0eea9d4d | 24 | #include "AliCheb3D.h" |
5406439e | 25 | #include "AliCheb3DCalc.h" |
0eea9d4d | 26 | |
0eea9d4d | 27 | ClassImp(AliCheb3D) |
28 | ||
40389866 | 29 | //__________________________________________________________________________________________ |
30 | AliCheb3D::AliCheb3D() : | |
31 | fDimOut(0), | |
32 | fPrec(0), | |
33 | fChebCalc(1), | |
34 | fMaxCoefs(0), | |
35 | fResTmp(0), | |
36 | fGrid(0), | |
37 | fUsrFunName(""), | |
38 | fUsrMacro(0) | |
0eea9d4d | 39 | { |
40389866 | 40 | for (int i=3;i--;) fBMin[i] = fBMax[i] = fBScale[i] = fBOffset[i] = 0; |
0eea9d4d | 41 | } |
42 | ||
40389866 | 43 | //__________________________________________________________________________________________ |
44 | AliCheb3D::AliCheb3D(const AliCheb3D& src) : | |
45 | TNamed(src), | |
46 | fDimOut(src.fDimOut), | |
47 | fPrec(src.fPrec), | |
48 | fChebCalc(1), | |
49 | fMaxCoefs(src.fMaxCoefs), | |
50 | fResTmp(0), | |
51 | fGrid(0), | |
52 | fUsrFunName(src.fUsrFunName), | |
53 | fUsrMacro(0) | |
0eea9d4d | 54 | { |
40389866 | 55 | // read coefs from text file |
56 | for (int i=3;i--;) { | |
57 | fBMin[i] = src.fBMin[i]; | |
58 | fBMax[i] = src.fBMax[i]; | |
59 | fBScale[i] = src.fBScale[i]; | |
60 | fBOffset[i] = src.fBOffset[i]; | |
61 | fNPoints[i] = src.fNPoints[i]; | |
62 | } | |
63 | for (int i=0;i<fDimOut;i++) { | |
64 | AliCheb3DCalc* cbc = src.GetChebCalc(i); | |
65 | if (cbc) fChebCalc.AddAtAndExpand(new AliCheb3DCalc(*cbc),i); | |
66 | } | |
0eea9d4d | 67 | } |
68 | ||
40389866 | 69 | //__________________________________________________________________________________________ |
70 | AliCheb3D::AliCheb3D(const char* inpFile) : | |
71 | fDimOut(0), | |
72 | fPrec(0), | |
73 | fChebCalc(1), | |
74 | fMaxCoefs(0), | |
75 | fResTmp(0), | |
76 | fGrid(0), | |
77 | fUsrFunName(""), | |
78 | fUsrMacro(0) | |
0bc7b414 | 79 | { |
40389866 | 80 | // read coefs from text file |
81 | for (int i=3;i--;) fBMin[i] = fBMax[i] = fBScale[i] = fBOffset[i] = 0; | |
82 | LoadData(inpFile); | |
c437b1a5 | 83 | } |
84 | ||
40389866 | 85 | //__________________________________________________________________________________________ |
86 | AliCheb3D::AliCheb3D(FILE* stream) : | |
87 | fDimOut(0), | |
88 | fPrec(0), | |
89 | fChebCalc(1), | |
90 | fMaxCoefs(0), | |
91 | fResTmp(0), | |
92 | fGrid(0), | |
93 | fUsrFunName(""), | |
94 | fUsrMacro(0) | |
c437b1a5 | 95 | { |
40389866 | 96 | // read coefs from stream |
97 | for (int i=3;i--;) fBMin[i] = fBMax[i] = fBScale[i] = fBOffset[i] = 0; | |
98 | LoadData(stream); | |
0bc7b414 | 99 | } |
0eea9d4d | 100 | |
101 | //__________________________________________________________________________________________ | |
102 | #ifdef _INC_CREATION_ALICHEB3D_ | |
40389866 | 103 | AliCheb3D::AliCheb3D(const char* funName, int DimOut, Float_t *bmin,Float_t *bmax, Int_t *npoints, Float_t prec) : |
104 | TNamed(funName,funName), | |
105 | fDimOut(0), | |
106 | fPrec(TMath::Max(1.E-12f,prec)), | |
107 | fChebCalc(1), | |
108 | fMaxCoefs(0), | |
109 | fResTmp(0), | |
110 | fGrid(0), | |
111 | fUsrFunName("") , | |
112 | fUsrMacro(0) | |
0eea9d4d | 113 | { |
114 | // Construct the parameterization for the function | |
115 | // funName : name of the file containing the function: void funName(Float_t * inp,Float_t * out) | |
116 | // DimOut : dimension of the vector computed by the user function | |
117 | // bmin : array of 3 elements with the lower boundaries of the region where the function is defined | |
118 | // bmax : array of 3 elements with the upper boundaries of the region where the function is defined | |
119 | // npoints : array of 3 elements with the number of points to compute in each of 3 dimension | |
120 | // prec : max allowed absolute difference between the user function and computed parameterization on the requested grid | |
121 | // | |
0eea9d4d | 122 | if (DimOut<1) {Error("AliCheb3D","Requested output dimension is %d\nStop\n",fDimOut); exit(1);} |
123 | SetDimOut(DimOut); | |
124 | PrepareBoundaries(bmin,bmax); | |
125 | DefineGrid(npoints); | |
126 | SetUsrFunction(funName); | |
127 | ChebFit(); | |
128 | // | |
129 | } | |
130 | #endif | |
131 | ||
132 | //__________________________________________________________________________________________ | |
133 | #ifdef _INC_CREATION_ALICHEB3D_ | |
40389866 | 134 | AliCheb3D::AliCheb3D(void (*ptr)(float*,float*), int DimOut, Float_t *bmin,Float_t *bmax, Int_t *npoints, Float_t prec) : |
135 | fDimOut(0), | |
136 | fPrec(TMath::Max(1.E-12f,prec)), | |
137 | fChebCalc(1), | |
138 | fMaxCoefs(0), | |
139 | fResTmp(0), | |
140 | fGrid(0), | |
141 | fUsrFunName(""), | |
142 | fUsrMacro(0) | |
0eea9d4d | 143 | { |
144 | // Construct the parameterization for the function | |
145 | // ptr : pointer on the function: void fun(Float_t * inp,Float_t * out) | |
146 | // DimOut : dimension of the vector computed by the user function | |
147 | // bmin : array of 3 elements with the lower boundaries of the region where the function is defined | |
148 | // bmax : array of 3 elements with the upper boundaries of the region where the function is defined | |
149 | // npoints : array of 3 elements with the number of points to compute in each of 3 dimension | |
150 | // prec : max allowed absolute difference between the user function and computed parameterization on the requested grid | |
151 | // | |
0eea9d4d | 152 | if (DimOut<1) {Error("AliCheb3D","Requested output dimension is %d\nStop\n",fDimOut); exit(1);} |
153 | SetDimOut(DimOut); | |
154 | PrepareBoundaries(bmin,bmax); | |
155 | DefineGrid(npoints); | |
156 | SetUsrFunction(ptr); | |
157 | ChebFit(); | |
158 | // | |
159 | } | |
160 | #endif | |
161 | ||
40389866 | 162 | //__________________________________________________________________________________________ |
163 | #ifdef _INC_CREATION_ALICHEB3D_ | |
164 | 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) : | |
165 | fDimOut(0), | |
166 | fPrec(TMath::Max(1.E-12f,prec)), | |
167 | fChebCalc(1), | |
168 | fMaxCoefs(0), | |
169 | fResTmp(0), | |
170 | fGrid(0), | |
171 | fUsrFunName(""), | |
172 | fUsrMacro(0) | |
173 | { | |
174 | // Construct very economic parameterization for the function | |
175 | // ptr : pointer on the function: void fun(Float_t * inp,Float_t * out) | |
176 | // DimOut : dimension of the vector computed by the user function | |
177 | // bmin : array of 3 elements with the lower boundaries of the region where the function is defined | |
178 | // bmax : array of 3 elements with the upper boundaries of the region where the function is defined | |
179 | // npX : array of 3 elements with the number of points to compute in each dimension for 1st component | |
180 | // npY : array of 3 elements with the number of points to compute in each dimension for 2nd component | |
181 | // npZ : array of 3 elements with the number of points to compute in each dimension for 3d component | |
182 | // prec : max allowed absolute difference between the user function and computed parameterization on the requested grid | |
183 | // | |
184 | if (DimOut<1) {Error("AliCheb3D","Requested output dimension is %d\nStop\n",fDimOut); exit(1);} | |
185 | SetDimOut(DimOut); | |
186 | PrepareBoundaries(bmin,bmax); | |
187 | SetUsrFunction(ptr); | |
188 | // | |
189 | DefineGrid(npX); | |
190 | ChebFit(0); | |
191 | DefineGrid(npY); | |
192 | ChebFit(1); | |
193 | DefineGrid(npZ); | |
194 | ChebFit(2); | |
195 | // | |
196 | } | |
197 | #endif | |
198 | ||
199 | ||
200 | //__________________________________________________________________________________________ | |
201 | #ifdef _INC_CREATION_ALICHEB3D_ | |
202 | AliCheb3D::AliCheb3D(void (*ptr)(float*,float*), int DimOut, Float_t *bmin,Float_t *bmax, Float_t prec) : | |
203 | fDimOut(0), | |
204 | fPrec(TMath::Max(1.E-12f,prec)), | |
205 | fChebCalc(1), | |
206 | fMaxCoefs(0), | |
207 | fResTmp(0), | |
208 | fGrid(0), | |
209 | fUsrFunName(""), | |
210 | fUsrMacro(0) | |
211 | { | |
212 | // Construct very economic parameterization for the function with automatic calculation of the root's grid | |
213 | // ptr : pointer on the function: void fun(Float_t * inp,Float_t * out) | |
214 | // DimOut : dimension of the vector computed by the user function | |
215 | // bmin : array of 3 elements with the lower boundaries of the region where the function is defined | |
216 | // bmax : array of 3 elements with the upper boundaries of the region where the function is defined | |
217 | // prec : max allowed absolute difference between the user function and computed parameterization on the requested grid | |
218 | // | |
219 | if (DimOut!=3) {Error("AliCheb3D","This constructor works only for 3D fits, %dD fit was requested\n",fDimOut); exit(1);} | |
220 | SetDimOut(DimOut); | |
221 | PrepareBoundaries(bmin,bmax); | |
222 | SetUsrFunction(ptr); | |
223 | // | |
224 | int gridNC[3][3]; | |
225 | EstimateNPoints(prec,gridNC); | |
226 | DefineGrid(gridNC[0]); | |
227 | ChebFit(0); | |
228 | DefineGrid(gridNC[1]); | |
229 | ChebFit(1); | |
230 | DefineGrid(gridNC[2]); | |
231 | ChebFit(2); | |
232 | // | |
233 | } | |
234 | #endif | |
235 | ||
236 | ||
237 | //__________________________________________________________________________________________ | |
238 | AliCheb3D& AliCheb3D::operator=(const AliCheb3D& rhs) | |
239 | { | |
5406439e | 240 | // assignment operator |
241 | // | |
40389866 | 242 | if (this != &rhs) { |
243 | Clear(); | |
244 | fDimOut = rhs.fDimOut; | |
245 | fPrec = rhs.fPrec; | |
246 | fMaxCoefs = rhs.fMaxCoefs; | |
247 | fUsrFunName = rhs.fUsrFunName; | |
248 | fUsrMacro = 0; | |
249 | for (int i=3;i--;) { | |
250 | fBMin[i] = rhs.fBMin[i]; | |
251 | fBMax[i] = rhs.fBMax[i]; | |
252 | fBScale[i] = rhs.fBScale[i]; | |
253 | fBOffset[i] = rhs.fBOffset[i]; | |
254 | fNPoints[i] = rhs.fNPoints[i]; | |
255 | } | |
256 | for (int i=0;i<fDimOut;i++) { | |
257 | AliCheb3DCalc* cbc = rhs.GetChebCalc(i); | |
258 | if (cbc) fChebCalc.AddAtAndExpand(new AliCheb3DCalc(*cbc),i); | |
259 | } | |
260 | } | |
261 | return *this; | |
262 | // | |
263 | } | |
0bc7b414 | 264 | |
0eea9d4d | 265 | //__________________________________________________________________________________________ |
5406439e | 266 | void AliCheb3D::Clear(const Option_t*) |
0eea9d4d | 267 | { |
5406439e | 268 | // clear all dynamic structures |
269 | // | |
0eea9d4d | 270 | if (fResTmp) { delete[] fResTmp; fResTmp = 0; } |
271 | if (fGrid) { delete[] fGrid; fGrid = 0; } | |
272 | if (fUsrMacro) { delete fUsrMacro; fUsrMacro = 0;} | |
273 | fChebCalc.Delete(); | |
274 | // | |
275 | } | |
276 | ||
277 | //__________________________________________________________________________________________ | |
5406439e | 278 | void AliCheb3D::Print(const Option_t* opt) const |
0eea9d4d | 279 | { |
5406439e | 280 | // print info |
281 | // | |
0eea9d4d | 282 | printf("%s: Chebyshev parameterization for 3D->%dD function. Precision: %e\n",GetName(),fDimOut,fPrec); |
283 | printf("Region of validity: [%+.5e:%+.5e] [%+.5e:%+.5e] [%+.5e:%+.5e]\n",fBMin[0],fBMax[0],fBMin[1],fBMax[1],fBMin[2],fBMax[2]); | |
284 | TString opts = opt; opts.ToLower(); | |
285 | if (opts.Contains("l")) for (int i=0;i<fDimOut;i++) {printf("Output dimension %d:\n",i+1); GetChebCalc(i)->Print();} | |
286 | // | |
287 | } | |
288 | ||
0eea9d4d | 289 | //__________________________________________________________________________________________ |
5406439e | 290 | void AliCheb3D::PrepareBoundaries(const Float_t *bmin, const Float_t *bmax) |
0eea9d4d | 291 | { |
292 | // Set and check boundaries defined by user, prepare coefficients for their conversion to [-1:1] interval | |
293 | // | |
294 | for (int i=3;i--;) { | |
295 | fBMin[i] = bmin[i]; | |
296 | fBMax[i] = bmax[i]; | |
297 | fBScale[i] = bmax[i]-bmin[i]; | |
298 | if (fBScale[i]<=0) { | |
299 | Error("PrepareBoundaries","Boundaries for %d-th dimension are not increasing: %+.4e %+.4e\nStop\n",i,fBMin[i],fBMax[i]); | |
300 | exit(1); | |
301 | } | |
302 | fBOffset[i] = bmin[i] + fBScale[i]/2.0; | |
303 | fBScale[i] = 2./fBScale[i]; | |
304 | } | |
305 | // | |
306 | } | |
307 | ||
40389866 | 308 | |
0eea9d4d | 309 | //__________________________________________________________________________________________ |
310 | #ifdef _INC_CREATION_ALICHEB3D_ | |
40389866 | 311 | |
312 | // Pointer on user function (faster altrnative to TMethodCall) | |
313 | void (*gUsrFunAliCheb3D) (float* ,float* ); | |
314 | ||
315 | void AliCheb3D::EvalUsrFunction() | |
316 | { | |
317 | // call user supplied function | |
318 | if (gUsrFunAliCheb3D) gUsrFunAliCheb3D(fArgsTmp,fResTmp); | |
319 | else fUsrMacro->Execute(); | |
320 | } | |
321 | ||
0eea9d4d | 322 | void AliCheb3D::SetUsrFunction(const char* name) |
323 | { | |
324 | // load user macro with function definition and compile it | |
325 | gUsrFunAliCheb3D = 0; | |
326 | fUsrFunName = name; | |
327 | gSystem->ExpandPathName(fUsrFunName); | |
328 | if (fUsrMacro) delete fUsrMacro; | |
329 | TString tmpst = fUsrFunName; | |
330 | tmpst += "+"; // prepare filename to compile | |
331 | if (gROOT->LoadMacro(tmpst.Data())) {Error("SetUsrFunction","Failed to load user function from %s\nStop\n",name); exit(1);} | |
332 | fUsrMacro = new TMethodCall(); | |
333 | tmpst = tmpst.Data() + tmpst.Last('/')+1; //Strip away any path preceding the macro file name | |
334 | int dot = tmpst.Last('.'); | |
335 | if (dot>0) tmpst.Resize(dot); | |
336 | fUsrMacro->InitWithPrototype(tmpst.Data(),"Float_t *,Float_t *"); | |
337 | long args[2]; | |
338 | args[0] = (long)fArgsTmp; | |
339 | args[1] = (long)fResTmp; | |
340 | fUsrMacro->SetParamPtrs(args); | |
341 | // | |
342 | } | |
343 | #endif | |
344 | ||
345 | //__________________________________________________________________________________________ | |
346 | #ifdef _INC_CREATION_ALICHEB3D_ | |
347 | void AliCheb3D::SetUsrFunction(void (*ptr)(float*,float*)) | |
348 | { | |
5406439e | 349 | // assign user training function |
350 | // | |
0eea9d4d | 351 | if (fUsrMacro) delete fUsrMacro; |
352 | fUsrMacro = 0; | |
353 | fUsrFunName = ""; | |
354 | gUsrFunAliCheb3D = ptr; | |
355 | } | |
356 | #endif | |
357 | ||
358 | //__________________________________________________________________________________________ | |
359 | #ifdef _INC_CREATION_ALICHEB3D_ | |
5406439e | 360 | void AliCheb3D::EvalUsrFunction(const Float_t *x, const Float_t *res) |
361 | { | |
362 | // evaluate user function value | |
363 | // | |
0eea9d4d | 364 | for (int i=3;i--;) fArgsTmp[i] = x[i]; |
365 | if (gUsrFunAliCheb3D) gUsrFunAliCheb3D(fArgsTmp,fResTmp); | |
366 | else fUsrMacro->Execute(); | |
367 | for (int i=fDimOut;i--;) res[i] = fResTmp[i]; | |
368 | } | |
369 | #endif | |
370 | ||
371 | //__________________________________________________________________________________________ | |
372 | #ifdef _INC_CREATION_ALICHEB3D_ | |
5406439e | 373 | Int_t AliCheb3D::CalcChebCoefs(const Float_t *funval,int np, Float_t *outCoefs, Float_t prec) |
0eea9d4d | 374 | { |
375 | // Calculate Chebyshev coeffs using precomputed function values at np roots. | |
376 | // If prec>0, estimate the highest coeff number providing the needed precision | |
377 | // | |
378 | double sm; // do summations in double to minimize the roundoff error | |
379 | for (int ic=0;ic<np;ic++) { // compute coeffs | |
380 | sm = 0; | |
381 | for (int ir=0;ir<np;ir++) { | |
382 | float rt = TMath::Cos( ic*(ir+0.5)*TMath::Pi()/np); | |
383 | sm += funval[ir]*rt; | |
384 | } | |
385 | outCoefs[ic] = Float_t( sm * ((ic==0) ? 1./np : 2./np) ); | |
386 | } | |
387 | // | |
388 | if (prec<=0) return np; | |
389 | // | |
390 | sm = 0; | |
391 | int cfMax = 0; | |
392 | for (cfMax=np;cfMax--;) { | |
393 | sm += TMath::Abs(outCoefs[cfMax]); | |
394 | if (sm>=prec) break; | |
395 | } | |
396 | if (++cfMax==0) cfMax=1; | |
397 | return cfMax; | |
398 | // | |
399 | } | |
400 | #endif | |
401 | ||
402 | //__________________________________________________________________________________________ | |
403 | #ifdef _INC_CREATION_ALICHEB3D_ | |
404 | void AliCheb3D::DefineGrid(Int_t* npoints) | |
405 | { | |
406 | // prepare the grid of Chebyshev roots in each dimension | |
407 | const int kMinPoints = 1; | |
408 | int ntot = 0; | |
409 | fMaxCoefs = 1; | |
410 | for (int id=3;id--;) { | |
411 | fNPoints[id] = npoints[id]; | |
412 | if (fNPoints[id]<kMinPoints) { | |
40389866 | 413 | Error("DefineGrid","at %d-th dimension %d point is requested, at least %d is needed\nStop\n",id,fNPoints[id],kMinPoints); |
0eea9d4d | 414 | exit(1); |
415 | } | |
416 | ntot += fNPoints[id]; | |
417 | fMaxCoefs *= fNPoints[id]; | |
418 | } | |
40389866 | 419 | printf("Computing Chebyshev nodes on [%2d/%2d/%2d] grid\n",npoints[0],npoints[1],npoints[2]); |
420 | if (fGrid) delete[] fGrid; | |
0eea9d4d | 421 | fGrid = new Float_t [ntot]; |
422 | // | |
423 | int curp = 0; | |
424 | for (int id=3;id--;) { | |
425 | int np = fNPoints[id]; | |
426 | fGridOffs[id] = curp; | |
427 | for (int ip=0;ip<np;ip++) { | |
428 | Float_t x = TMath::Cos( TMath::Pi()*(ip+0.5)/np ); | |
429 | fGrid[curp++] = MapToExternal(x,id); | |
430 | } | |
431 | } | |
432 | // | |
433 | } | |
434 | #endif | |
435 | ||
436 | //__________________________________________________________________________________________ | |
437 | #ifdef _INC_CREATION_ALICHEB3D_ | |
438 | Int_t AliCheb3D::ChebFit() | |
439 | { | |
440 | // prepare parameterization for all output dimensions | |
441 | int ir=0; | |
442 | for (int i=fDimOut;i--;) ir+=ChebFit(i); | |
443 | return ir; | |
444 | } | |
445 | #endif | |
446 | ||
447 | //__________________________________________________________________________________________ | |
448 | #ifdef _INC_CREATION_ALICHEB3D_ | |
449 | Int_t AliCheb3D::ChebFit(int dmOut) | |
450 | { | |
451 | // prepare paramaterization of 3D function for dmOut-th dimension | |
452 | int maxDim = 0; | |
453 | for (int i=0;i<3;i++) if (maxDim<fNPoints[i]) maxDim = fNPoints[i]; | |
454 | Float_t *fvals = new Float_t [ fNPoints[0] ]; | |
455 | Float_t *tmpCoef3D = new Float_t [ fNPoints[0]*fNPoints[1]*fNPoints[2] ]; | |
456 | Float_t *tmpCoef2D = new Float_t [ fNPoints[0]*fNPoints[1] ]; | |
457 | Float_t *tmpCoef1D = new Float_t [ maxDim ]; | |
458 | // | |
5406439e | 459 | Float_t rTiny = fPrec/Float_t(maxDim); // neglect coefficient below this threshold |
0eea9d4d | 460 | // |
461 | // 1D Cheb.fit for 0-th dimension at current steps of remaining dimensions | |
462 | int ncmax = 0; | |
463 | // | |
40389866 | 464 | printf("Dim%d : 00.00%% Done",dmOut);fflush(stdout); |
0eea9d4d | 465 | AliCheb3DCalc* cheb = GetChebCalc(dmOut); |
466 | // | |
40389866 | 467 | float ncals2count = fNPoints[2]*fNPoints[1]*fNPoints[0]; |
468 | float ncals = 0; | |
469 | float frac = 0; | |
470 | float fracStep = 0.001; | |
471 | // | |
0eea9d4d | 472 | for (int id2=fNPoints[2];id2--;) { |
473 | fArgsTmp[2] = fGrid[ fGridOffs[2]+id2 ]; | |
474 | // | |
475 | for (int id1=fNPoints[1];id1--;) { | |
476 | fArgsTmp[1] = fGrid[ fGridOffs[1]+id1 ]; | |
477 | // | |
478 | for (int id0=fNPoints[0];id0--;) { | |
479 | fArgsTmp[0] = fGrid[ fGridOffs[0]+id0 ]; | |
480 | EvalUsrFunction(); // compute function values at Chebyshev roots of 0-th dimension | |
481 | fvals[id0] = fResTmp[dmOut]; | |
40389866 | 482 | float fr = (++ncals)/ncals2count; |
483 | if (fr-frac>=fracStep) { | |
484 | frac = fr; | |
485 | printf("\b\b\b\b\b\b\b\b\b\b\b"); | |
486 | printf("%05.2f%% Done",fr*100); | |
487 | fflush(stdout); | |
488 | } | |
489 | // | |
0eea9d4d | 490 | } |
491 | int nc = CalcChebCoefs(fvals,fNPoints[0], tmpCoef1D, fPrec); | |
492 | for (int id0=fNPoints[0];id0--;) tmpCoef2D[id1 + id0*fNPoints[1]] = tmpCoef1D[id0]; | |
493 | if (ncmax<nc) ncmax = nc; // max coefs to be kept in dim0 to guarantee needed precision | |
494 | } | |
495 | // | |
496 | // once each 1d slice of given 2d slice is parametrized, parametrize the Cheb.coeffs | |
497 | for (int id0=fNPoints[0];id0--;) { | |
498 | CalcChebCoefs( tmpCoef2D+id0*fNPoints[1], fNPoints[1], tmpCoef1D, -1); | |
499 | for (int id1=fNPoints[1];id1--;) tmpCoef3D[id2 + fNPoints[2]*(id1+id0*fNPoints[1])] = tmpCoef1D[id1]; | |
500 | } | |
501 | } | |
502 | // | |
503 | // now fit the last dimensions Cheb.coefs | |
504 | for (int id0=fNPoints[0];id0--;) { | |
505 | for (int id1=fNPoints[1];id1--;) { | |
506 | CalcChebCoefs( tmpCoef3D+ fNPoints[2]*(id1+id0*fNPoints[1]), fNPoints[2], tmpCoef1D, -1); | |
507 | for (int id2=fNPoints[2];id2--;) tmpCoef3D[id2+ fNPoints[2]*(id1+id0*fNPoints[1])] = tmpCoef1D[id2]; // store on place | |
508 | } | |
509 | } | |
510 | // | |
511 | // now find 2D surface which separates significant coefficients of 3D matrix from nonsignificant ones (up to fPrec) | |
512 | int *tmpCoefSurf = new Int_t[ fNPoints[0]*fNPoints[1] ]; | |
513 | for (int id0=fNPoints[0];id0--;) for (int id1=fNPoints[1];id1--;) tmpCoefSurf[id1+id0*fNPoints[1]]=0; | |
514 | Double_t resid = 0; | |
515 | for (int id0=fNPoints[0];id0--;) { | |
516 | for (int id1=fNPoints[1];id1--;) { | |
517 | for (int id2=fNPoints[2];id2--;) { | |
518 | int id = id2 + fNPoints[2]*(id1+id0*fNPoints[1]); | |
519 | Float_t cfa = TMath::Abs(tmpCoef3D[id]); | |
5406439e | 520 | if (cfa < rTiny) {tmpCoef3D[id] = 0; continue;} // neglect coefs below the threshold |
0eea9d4d | 521 | resid += cfa; |
522 | if (resid<fPrec) continue; // this coeff is negligible | |
523 | // otherwise go back 1 step | |
524 | resid -= cfa; | |
525 | tmpCoefSurf[id1+id0*fNPoints[1]] = id2+1; // how many coefs to keep | |
526 | break; | |
527 | } | |
528 | } | |
529 | } | |
530 | /* | |
531 | printf("\n\nCoeffs\n"); | |
532 | int cnt = 0; | |
533 | for (int id0=0;id0<fNPoints[0];id0++) { | |
534 | for (int id1=0;id1<fNPoints[1];id1++) { | |
535 | for (int id2=0;id2<fNPoints[2];id2++) { | |
536 | printf("%2d%2d%2d %+.4e |",id0,id1,id2,tmpCoef3D[cnt++]); | |
537 | } | |
538 | printf("\n"); | |
539 | } | |
540 | printf("\n"); | |
541 | } | |
542 | */ | |
543 | // see if there are rows to reject, find max.significant column at each row | |
5406439e | 544 | int nRows = fNPoints[0]; |
545 | int *tmpCols = new int[nRows]; | |
0eea9d4d | 546 | for (int id0=fNPoints[0];id0--;) { |
547 | int id1 = fNPoints[1]; | |
548 | while (id1>0 && tmpCoefSurf[(id1-1)+id0*fNPoints[1]]==0) id1--; | |
549 | tmpCols[id0] = id1; | |
550 | } | |
551 | // find max significant row | |
5406439e | 552 | for (int id0=nRows;id0--;) {if (tmpCols[id0]>0) break; nRows--;} |
0eea9d4d | 553 | // find max significant column and fill the permanent storage for the max sigificant column of each row |
5406439e | 554 | cheb->InitRows(nRows); // create needed arrays; |
555 | int *nColsAtRow = cheb->GetNColsAtRow(); | |
556 | int *colAtRowBg = cheb->GetColAtRowBg(); | |
557 | int nCols = 0; | |
0eea9d4d | 558 | int NElemBound2D = 0; |
5406439e | 559 | for (int id0=0;id0<nRows;id0++) { |
560 | nColsAtRow[id0] = tmpCols[id0]; // number of columns to store for this row | |
561 | colAtRowBg[id0] = NElemBound2D; // begining of this row in 2D boundary surface | |
0eea9d4d | 562 | NElemBound2D += tmpCols[id0]; |
5406439e | 563 | if (nCols<nColsAtRow[id0]) nCols = nColsAtRow[id0]; |
0eea9d4d | 564 | } |
5406439e | 565 | cheb->InitCols(nCols); |
0eea9d4d | 566 | delete[] tmpCols; |
567 | // | |
568 | // create the 2D matrix defining the boundary of significance for 3D coeffs.matrix | |
569 | // and count the number of siginifacnt coefficients | |
570 | // | |
571 | cheb->InitElemBound2D(NElemBound2D); | |
5406439e | 572 | int *coefBound2D0 = cheb->GetCoefBound2D0(); |
573 | int *coefBound2D1 = cheb->GetCoefBound2D1(); | |
0eea9d4d | 574 | fMaxCoefs = 0; // redefine number of coeffs |
5406439e | 575 | for (int id0=0;id0<nRows;id0++) { |
576 | int nCLoc = nColsAtRow[id0]; | |
577 | int col0 = colAtRowBg[id0]; | |
0eea9d4d | 578 | for (int id1=0;id1<nCLoc;id1++) { |
5406439e | 579 | coefBound2D0[col0 + id1] = tmpCoefSurf[id1+id0*fNPoints[1]]; // number of coefs to store for 3-d dimension |
580 | coefBound2D1[col0 + id1] = fMaxCoefs; | |
581 | fMaxCoefs += coefBound2D0[col0 + id1]; | |
0eea9d4d | 582 | } |
583 | } | |
584 | // | |
585 | // create final compressed 3D matrix for significant coeffs | |
586 | cheb->InitCoefs(fMaxCoefs); | |
5406439e | 587 | Float_t *coefs = cheb->GetCoefs(); |
0eea9d4d | 588 | int count = 0; |
5406439e | 589 | for (int id0=0;id0<nRows;id0++) { |
590 | int ncLoc = nColsAtRow[id0]; | |
591 | int col0 = colAtRowBg[id0]; | |
0eea9d4d | 592 | for (int id1=0;id1<ncLoc;id1++) { |
5406439e | 593 | int ncf2 = coefBound2D0[col0 + id1]; |
0eea9d4d | 594 | for (int id2=0;id2<ncf2;id2++) { |
5406439e | 595 | coefs[count++] = tmpCoef3D[id2 + fNPoints[2]*(id1+id0*fNPoints[1])]; |
0eea9d4d | 596 | } |
597 | } | |
598 | } | |
599 | /* | |
600 | printf("\n\nNewSurf\n"); | |
601 | for (int id0=0;id0<fNPoints[0];id0++) { | |
602 | for (int id1=0;id1<fNPoints[1];id1++) { | |
603 | printf("(%2d %2d) %2d |",id0,id1,tmpCoefSurf[id1+id0*fNPoints[1]]); | |
604 | } | |
605 | printf("\n"); | |
606 | } | |
607 | */ | |
608 | // | |
609 | delete[] tmpCoefSurf; | |
610 | delete[] tmpCoef1D; | |
611 | delete[] tmpCoef2D; | |
612 | delete[] tmpCoef3D; | |
613 | delete[] fvals; | |
614 | // | |
40389866 | 615 | printf("\b\b\b\b\b\b\b\b\b\b\b\b"); |
616 | printf("100.00%% Done\n"); | |
0eea9d4d | 617 | return 1; |
618 | } | |
619 | #endif | |
620 | ||
621 | //_______________________________________________ | |
622 | #ifdef _INC_CREATION_ALICHEB3D_ | |
623 | void AliCheb3D::SaveData(const char* outfile,Bool_t append) const | |
624 | { | |
625 | // writes coefficients data to output text file, optionallt appending on the end of existing file | |
626 | TString strf = outfile; | |
627 | gSystem->ExpandPathName(strf); | |
628 | FILE* stream = fopen(strf,append ? "a":"w"); | |
629 | SaveData(stream); | |
630 | fclose(stream); | |
631 | // | |
632 | } | |
633 | #endif | |
634 | ||
635 | //_______________________________________________ | |
636 | #ifdef _INC_CREATION_ALICHEB3D_ | |
637 | void AliCheb3D::SaveData(FILE* stream) const | |
638 | { | |
639 | // writes coefficients data to existing output stream | |
640 | // | |
641 | fprintf(stream,"\n# These are automatically generated data for the Chebyshev interpolation of 3D->%dD function\n",fDimOut); | |
642 | fprintf(stream,"#\nSTART %s\n",GetName()); | |
643 | fprintf(stream,"# Dimensionality of the output\n%d\n",fDimOut); | |
644 | fprintf(stream,"# Interpolation abs. precision\n%+.8e\n",fPrec); | |
645 | // | |
646 | fprintf(stream,"# Lower boundaries of interpolation region\n"); | |
647 | for (int i=0;i<3;i++) fprintf(stream,"%+.8e\n",fBMin[i]); | |
648 | fprintf(stream,"# Upper boundaries of interpolation region\n"); | |
649 | for (int i=0;i<3;i++) fprintf(stream,"%+.8e\n",fBMax[i]); | |
40389866 | 650 | fprintf(stream,"# Parameterization for each output dimension follows:\n"); |
0eea9d4d | 651 | // |
652 | for (int i=0;i<fDimOut;i++) GetChebCalc(i)->SaveData(stream); | |
653 | fprintf(stream,"#\nEND %s\n#\n",GetName()); | |
654 | // | |
655 | } | |
656 | #endif | |
657 | ||
658 | //_______________________________________________ | |
659 | void AliCheb3D::LoadData(const char* inpFile) | |
660 | { | |
5406439e | 661 | // load coefficients data from txt file |
662 | // | |
0eea9d4d | 663 | TString strf = inpFile; |
664 | gSystem->ExpandPathName(strf); | |
665 | FILE* stream = fopen(strf.Data(),"r"); | |
666 | LoadData(stream); | |
667 | fclose(stream); | |
668 | // | |
669 | } | |
670 | ||
671 | //_______________________________________________ | |
672 | void AliCheb3D::LoadData(FILE* stream) | |
673 | { | |
5406439e | 674 | // load coefficients data from stream |
675 | // | |
0eea9d4d | 676 | if (!stream) {Error("LoadData","No stream provided.\nStop"); exit(1);} |
677 | TString buffs; | |
678 | Clear(); | |
679 | AliCheb3DCalc::ReadLine(buffs,stream); | |
680 | if (!buffs.BeginsWith("START")) {Error("LoadData","Expected: \"START <fit_name>\", found \"%s\"\nStop\n",buffs.Data());exit(1);} | |
681 | SetName(buffs.Data()+buffs.First(' ')+1); | |
682 | // | |
683 | AliCheb3DCalc::ReadLine(buffs,stream); // N output dimensions | |
684 | fDimOut = buffs.Atoi(); | |
685 | if (fDimOut<1) {Error("LoadData","Expected: '<number_of_output_dimensions>', found \"%s\"\nStop\n",buffs.Data());exit(1);} | |
686 | // | |
687 | SetDimOut(fDimOut); | |
688 | // | |
689 | AliCheb3DCalc::ReadLine(buffs,stream); // Interpolation abs. precision | |
690 | fPrec = buffs.Atof(); | |
691 | if (fPrec<=0) {Error("LoadData","Expected: '<abs.precision>', found \"%s\"\nStop\n",buffs.Data());exit(1);} | |
692 | // | |
693 | for (int i=0;i<3;i++) { // Lower boundaries of interpolation region | |
694 | AliCheb3DCalc::ReadLine(buffs,stream); | |
695 | fBMin[i] = buffs.Atof(); | |
696 | } | |
697 | for (int i=0;i<3;i++) { // Upper boundaries of interpolation region | |
698 | AliCheb3DCalc::ReadLine(buffs,stream); | |
699 | fBMax[i] = buffs.Atof(); | |
700 | } | |
701 | PrepareBoundaries(fBMin,fBMax); | |
702 | // | |
703 | // data for each output dimension | |
704 | for (int i=0;i<fDimOut;i++) GetChebCalc(i)->LoadData(stream); | |
705 | // | |
706 | // check end_of_data record | |
707 | AliCheb3DCalc::ReadLine(buffs,stream); | |
708 | if (!buffs.BeginsWith("END") || !buffs.Contains(GetName())) { | |
709 | Error("LoadData","Expected \"END %s\", found \"%s\".\nStop\n",GetName(),buffs.Data()); | |
710 | exit(1); | |
711 | } | |
712 | // | |
713 | } | |
714 | ||
715 | //_______________________________________________ | |
5406439e | 716 | void AliCheb3D::SetDimOut(const int d) |
0eea9d4d | 717 | { |
5406439e | 718 | // init output dimensions |
0eea9d4d | 719 | fDimOut = d; |
720 | if (fResTmp) delete fResTmp; | |
40389866 | 721 | fResTmp = new Float_t[fDimOut]; |
0eea9d4d | 722 | fChebCalc.Delete(); |
723 | for (int i=0;i<d;i++) fChebCalc.AddAtAndExpand(new AliCheb3DCalc(),i); | |
724 | } | |
725 | ||
726 | //_______________________________________________ | |
727 | void AliCheb3D::ShiftBound(int id,float dif) | |
728 | { | |
5406439e | 729 | // modify the bounds of the grid |
730 | // | |
0eea9d4d | 731 | if (id<0||id>2) {printf("Maximum 3 dimensions are supported\n"); return;} |
732 | fBMin[id] += dif; | |
733 | fBMax[id] += dif; | |
734 | fBOffset[id] += dif; | |
735 | } | |
736 | ||
737 | //_______________________________________________ | |
738 | #ifdef _INC_CREATION_ALICHEB3D_ | |
739 | TH1* AliCheb3D::TestRMS(int idim,int npoints,TH1* histo) | |
740 | { | |
741 | // fills the difference between the original function and parameterization (for idim-th component of the output) | |
742 | // to supplied histogram. Calculations are done in npoints random points. | |
743 | // If the hostgram was not supplied, it will be created. It is up to the user to delete it! | |
744 | if (!fUsrMacro) { | |
745 | printf("No user function is set\n"); | |
746 | return 0; | |
747 | } | |
748 | if (!histo) histo = new TH1D(GetName(),"Control: Function - Parametrization",100,-2*fPrec,2*fPrec); | |
749 | for (int ip=npoints;ip--;) { | |
750 | gRandom->RndmArray(3,(Float_t *)fArgsTmp); | |
751 | for (int i=3;i--;) fArgsTmp[i] = fBMin[i] + fArgsTmp[i]*(fBMax[i]-fBMin[i]); | |
752 | EvalUsrFunction(); | |
753 | Float_t valFun = fResTmp[idim]; | |
754 | Eval(fArgsTmp,fResTmp); | |
755 | Float_t valPar = fResTmp[idim]; | |
756 | histo->Fill(valFun - valPar); | |
757 | } | |
758 | return histo; | |
759 | // | |
760 | } | |
761 | #endif | |
40389866 | 762 | |
763 | //_______________________________________________ | |
764 | #ifdef _INC_CREATION_ALICHEB3D_ | |
765 | void AliCheb3D::EstimateNPoints(float Prec, int gridBC[3][3]) | |
766 | { | |
5406439e | 767 | // Estimate number of points to generate a training data |
768 | // | |
40389866 | 769 | const float sclA[9] = {0.1, 0.5, 0.9, 0.1, 0.5, 0.9, 0.1, 0.5, 0.9} ; |
770 | const float sclB[9] = {0.1, 0.1, 0.1, 0.5, 0.5, 0.5, 0.9, 0.9, 0.9} ; | |
771 | const float sclDim[2] = {0.01,0.99}; | |
772 | const int compDim[3][2] = { {1,2}, {2,0}, {0,1} }; | |
773 | static float xyz[3]; | |
774 | // | |
775 | for (int i=3;i--;)for (int j=3;j--;) gridBC[i][j] = -1; | |
776 | // | |
777 | for (int idim=0;idim<3;idim++) { | |
778 | float dimMN = fBMin[idim] + sclDim[0]*(fBMax[idim]-fBMin[idim]); | |
779 | float dimMX = fBMin[idim] + sclDim[1]*(fBMax[idim]-fBMin[idim]); | |
780 | // | |
781 | for (int it=0;it<9;it++) { // test in 9 points | |
782 | int id1 = compDim[idim][0]; // 1st fixed dim | |
783 | int id2 = compDim[idim][1]; // 2nd fixed dim | |
784 | xyz[ id1 ] = fBMin[id1] + sclA[it]*( fBMax[id1]-fBMin[id1] ); | |
785 | xyz[ id2 ] = fBMin[id2] + sclB[it]*( fBMax[id2]-fBMin[id2] ); | |
786 | // | |
787 | int* npt = GetNCNeeded(xyz,idim, dimMN,dimMX, Prec); // npoints for Bx,By,Bz | |
788 | for (int ib=0;ib<3;ib++) if (npt[ib]>gridBC[ib][idim]) gridBC[ib][idim] = npt[ib]+2; | |
789 | // | |
790 | } | |
791 | } | |
792 | } | |
793 | ||
794 | ||
795 | int* AliCheb3D::GetNCNeeded(float xyz[3],int DimVar, float mn,float mx, float prec) | |
796 | { | |
797 | // estimate needed number of chebyshev coefs for given function desctiption in DimVar dimension | |
798 | // The values for two other dimensions must be set beforehand | |
799 | // | |
800 | static int curNC[3]; | |
801 | static int retNC[3]; | |
802 | const int kMaxPoint = 400; | |
803 | float* gridVal = new float[3*kMaxPoint]; | |
804 | float* coefs = new float[3*kMaxPoint]; | |
805 | // | |
806 | float scale = mx-mn; | |
807 | float offs = mn + scale/2.0; | |
808 | scale = 2./scale; | |
809 | // | |
810 | int curNP; | |
811 | int maxNC=-1; | |
812 | int maxNCPrev=-1; | |
813 | for (int i=0;i<3;i++) retNC[i] = -1; | |
814 | for (int i=0;i<3;i++) fArgsTmp[i] = xyz[i]; | |
815 | // | |
816 | for (curNP=5; curNP<kMaxPoint; curNP+=5) { | |
817 | maxNCPrev = maxNC; | |
818 | // | |
819 | for (int i=0;i<curNP;i++) { // get function values on Cheb. nodes | |
820 | float x = TMath::Cos( TMath::Pi()*(i+0.5)/curNP ); | |
821 | fArgsTmp[DimVar] = x/scale+offs; // map to requested interval | |
822 | EvalUsrFunction(); | |
823 | for (int ib=3;ib--;) gridVal[ib*kMaxPoint + i] = fResTmp[ib]; | |
824 | } | |
825 | // | |
826 | for (int ib=0;ib<3;ib++) { | |
827 | curNC[ib] = AliCheb3D::CalcChebCoefs(&gridVal[ib*kMaxPoint], curNP, &coefs[ib*kMaxPoint],prec); | |
828 | if (maxNC < curNC[ib]) maxNC = curNC[ib]; | |
829 | if (retNC[ib] < curNC[ib]) retNC[ib] = curNC[ib]; | |
830 | } | |
831 | if ( (curNP-maxNC)>3 && (maxNC-maxNCPrev)<1 ) break; | |
832 | maxNCPrev = maxNC; | |
833 | // | |
834 | } | |
835 | delete[] gridVal; | |
836 | delete[] coefs; | |
837 | return retNC; | |
838 | // | |
839 | } | |
840 | #endif |