Logo ROOT   master
Reference Guide
TF3.cxx
Go to the documentation of this file.
1 // @(#)root/hist:$Id$
2 // Author: Rene Brun 27/10/95
3 
4 /*************************************************************************
5  * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. *
6  * All rights reserved. *
7  * *
8  * For the licensing terms see $ROOTSYS/LICENSE. *
9  * For the list of contributors see $ROOTSYS/README/CREDITS. *
10  *************************************************************************/
11 
12 #include "TROOT.h"
13 #include "TF3.h"
14 #include "TBuffer.h"
15 #include "TMath.h"
16 #include "TH3.h"
17 #include "TVirtualPad.h"
18 #include "TRandom.h"
19 #include "TVectorD.h"
20 #include "Riostream.h"
21 #include "TColor.h"
22 #include "TVirtualFitter.h"
23 #include "TVirtualHistPainter.h"
24 #include <cassert>
25 
26 ClassImp(TF3);
27 
28 /** \class TF3
29  \ingroup Hist
30 A 3-Dim function with parameters
31 */
32 
33 ////////////////////////////////////////////////////////////////////////////////
34 /// F3 default constructor
35 
37 {
38  fNpz = 0;
39  fZmin = 0;
40  fZmax = 1;
41 }
42 
43 
44 ////////////////////////////////////////////////////////////////////////////////
45 /// F3 constructor using a formula definition
46 ///
47 /// See TFormula constructor for explanation of the formula syntax.
48 
49 TF3::TF3(const char *name,const char *formula, Double_t xmin, Double_t xmax, Double_t ymin, Double_t ymax, Double_t zmin, Double_t zmax, Option_t * opt)
50  :TF2(name,formula,xmin,xmax,ymax,ymin,opt)
51 {
52  fZmin = zmin;
53  fZmax = zmax;
54  fNpz = 30;
55  Int_t ndim = GetNdim();
56  // accept 1-d or 2-d formula
57  if (ndim < 3) fNdim = 3;
58  if (ndim > 3 && xmin < xmax && ymin < ymax && zmin < zmax) {
59  Error("TF3","function: %s/%s has dimension %d instead of 3",name,formula,ndim);
60  MakeZombie();
61  }
62 }
63 
64 ////////////////////////////////////////////////////////////////////////////////
65 /// F3 constructor using a pointer to real function
66 ///
67 /// \param[in] npar is the number of free parameters used by the function
68 ///
69 /// For example, for a 3-dim function with 3 parameters, the user function
70 /// looks like:
71 ///
72 /// Double_t fun1(Double_t *x, Double_t *par)
73 /// return par[0]*x[2] + par[1]*exp(par[2]*x[0]*x[1]);
74 ///
75 /// WARNING! A function created with this constructor cannot be Cloned.
76 
78  :TF2(name,fcn,xmin,xmax,ymin,ymax,npar,ndim)
79 {
80  fZmin = zmin;
81  fZmax = zmax;
82  fNpz = 30;
83 }
84 
85 ////////////////////////////////////////////////////////////////////////////////
86 /// F3 constructor using a pointer to real function---
87 ///
88 /// \param[in] npar is the number of free parameters used by the function
89 ///
90 /// For example, for a 3-dim function with 3 parameters, the user function
91 /// looks like:
92 ///
93 /// Double_t fun1(Double_t *x, Double_t *par)
94 /// return par[0]*x[2] + par[1]*exp(par[2]*x[0]*x[1]);
95 ///
96 /// WARNING! A function created with this constructor cannot be Cloned.
97 
98 TF3::TF3(const char *name,Double_t (*fcn)(const Double_t *, const Double_t *), Double_t xmin, Double_t xmax, Double_t ymin, Double_t ymax, Double_t zmin, Double_t zmax, Int_t npar, Int_t ndim)
99  : TF2(name,fcn,xmin,xmax,ymin,ymax,npar,ndim),
100  fZmin(zmin),
101  fZmax(zmax),
102  fNpz(30)
103 {
104 }
105 
106 ////////////////////////////////////////////////////////////////////////////////
107 /// F3 constructor using a ParamFunctor
108 ///
109 /// a functor class implementing operator() (double *, double *)
110 ///
111 /// \param[in] npar is the number of free parameters used by the function
112 ///
113 /// WARNING! A function created with this constructor cannot be Cloned.
114 
116  : TF2(name, f, xmin, xmax, ymin, ymax, npar, ndim),
117  fZmin(zmin),
118  fZmax(zmax),
119  fNpz(30)
120 {
121 }
122 
123 ////////////////////////////////////////////////////////////////////////////////
124 /// Operator =
125 
126 TF3& TF3::operator=(const TF3 &rhs)
127 {
128  if (this != &rhs) {
129  rhs.Copy(*this);
130  }
131  return *this;
132 }
133 
134 ////////////////////////////////////////////////////////////////////////////////
135 /// F3 default destructor
136 
138 {
139 }
140 
141 ////////////////////////////////////////////////////////////////////////////////
142 /// Copy constructor.
143 
144 TF3::TF3(const TF3 &f3) : TF2()
145 {
146  ((TF3&)f3).Copy(*this);
147 }
148 
149 ////////////////////////////////////////////////////////////////////////////////
150 /// Copy this F3 to a new F3
151 
152 void TF3::Copy(TObject &obj) const
153 {
154  TF2::Copy(obj);
155  ((TF3&)obj).fZmin = fZmin;
156  ((TF3&)obj).fZmax = fZmax;
157  ((TF3&)obj).fNpz = fNpz;
158 }
159 
160 ////////////////////////////////////////////////////////////////////////////////
161 /// Compute distance from point px,py to a function
162 ///
163 /// Compute the closest distance of approach from point px,py to this function.
164 /// The distance is computed in pixels units.
165 
166 
168 {
169  return TF1::DistancetoPrimitive(px, py);
170 
171 }
172 
173 ////////////////////////////////////////////////////////////////////////////////
174 /// Draw this function with its current attributes
175 
176 void TF3::Draw(Option_t *option)
177 {
178  TString opt = option;
179  opt.ToLower();
180  if (gPad && !opt.Contains("same")) gPad->Clear();
181 
182  AppendPad(option);
183 
184 }
185 
186 ////////////////////////////////////////////////////////////////////////////////
187 /// Execute action corresponding to one event
188 ///
189 /// This member function is called when a F3 is clicked with the locator
190 
191 void TF3::ExecuteEvent(Int_t event, Int_t px, Int_t py)
192 {
193  TF1::ExecuteEvent(event, px, py);
194 }
195 
196 ////////////////////////////////////////////////////////////////////////////////
197 /// Return minimum/maximum value of the function
198 ///
199 /// To find the minimum on a range, first set this range via the SetRange function
200 /// If a vector x of coordinate is passed it will be used as starting point for the minimum.
201 /// In addition on exit x will contain the coordinate values at the minimuma
202 /// If x is NULL or x is inifinity or NaN, first, a grid search is performed to find the initial estimate of the
203 /// minimum location. The range of the function is divided into fNpx and fNpy
204 /// sub-ranges. If the function is "good" (or "bad"), these values can be changed
205 /// by SetNpx and SetNpy functions
206 ///
207 /// Then, a minimization is used with starting values found by the grid search
208 /// The minimizer algorithm used (by default Minuit) can be changed by callinga
209 /// ROOT::Math::Minimizer::SetDefaultMinimizerType("..")
210 /// Other option for the minimizer can be set using the static method of the MinimizerOptions class
211 
213 {
214  //First do a grid search with step size fNpx and fNpy
215 
216  Double_t xx[3];
217  Double_t rsign = (findmax) ? -1. : 1.;
218  TF3 & function = const_cast<TF3&>(*this); // needed since EvalPar is not const
219  Double_t xxmin = 0, yymin = 0, zzmin = 0, ttmin = 0;
220  if (x == NULL || ( (x!= NULL) && ( !TMath::Finite(x[0]) || !TMath::Finite(x[1]) || !TMath::Finite(x[2]) ) ) ){
221  Double_t dx = (fXmax - fXmin)/fNpx;
222  Double_t dy = (fYmax - fYmin)/fNpy;
223  Double_t dz = (fZmax - fZmin)/fNpz;
224  xxmin = fXmin;
225  yymin = fYmin;
226  zzmin = fZmin;
227  ttmin = rsign * TMath::Infinity();
228  for (Int_t i=0; i<fNpx; i++){
229  xx[0]=fXmin + (i+0.5)*dx;
230  for (Int_t j=0; j<fNpy; j++){
231  xx[1]=fYmin+(j+0.5)*dy;
232  for (Int_t k=0; k<fNpz; k++){
233  xx[2] = fZmin+(k+0.5)*dz;
234  Double_t tt = function(xx);
235  if (rsign*tt < rsign*ttmin) {xxmin = xx[0], yymin = xx[1]; zzmin = xx[2]; ttmin=tt;}
236  }
237  }
238  }
239 
240  xxmin = TMath::Min(fXmax, xxmin);
241  yymin = TMath::Min(fYmax, yymin);
242  zzmin = TMath::Min(fZmax, zzmin);
243  }
244  else {
245  xxmin = x[0];
246  yymin = x[1];
247  zzmin = x[2];
248  zzmin = function(xx);
249  }
250  xx[0] = xxmin;
251  xx[1] = yymin;
252  xx[2] = zzmin;
253 
254  double fmin = GetMinMaxNDim(xx,findmax);
255  if (rsign*fmin < rsign*zzmin) {
256  if (x) {x[0] = xx[0]; x[1] = xx[1]; x[2] = xx[2];}
257  return fmin;
258  }
259  // here if minimization failed
260  if (x) { x[0] = xxmin; x[1] = yymin; x[2] = zzmin; }
261  return ttmin;
262 }
263 
264 ////////////////////////////////////////////////////////////////////////////////
265 /// Compute the X, Y and Z values corresponding to the minimum value of the function
266 /// on its range.
267 ///
268 /// Returns the function value at the minimum.
269 /// To find the minimum on a subrange, use the SetRange() function first.
270 ///
271 /// Method:
272 /// First, a grid search is performed to find the initial estimate of the
273 /// minimum location. The range of the function is divided
274 /// into fNpx,fNpy and fNpz sub-ranges. If the function is "good" (or "bad"),
275 /// these values can be changed by SetNpx(), SetNpy() and SetNpz() functions.
276 /// Then, Minuit minimization is used with starting values found by the grid search
277 ///
278 /// Note that this method will always do first a grid search in contrast to GetMinimum
279 
281 {
282  double xx[3] = { 0,0,0 };
283  xx[0] = TMath::QuietNaN(); // to force to do grid search in TF3::FindMinMax
284  double fmin = FindMinMax(xx, false);
285  x = xx[0]; y = xx[1]; z = xx[2];
286  return fmin;
287 
288 }
289 
290 ////////////////////////////////////////////////////////////////////////////////
291 /// Compute the X, Y and Z values corresponding to the maximum value of the function
292 /// on its range.
293 ///
294 /// Return the function value at the maximum. See TF3::GetMinimumXYZ
295 
297 {
298  double xx[3] = { 0,0,0 };
299  xx[0] = TMath::QuietNaN(); // to force to do grid search in TF3::FindMinMax
300  double fmax = FindMinMax(xx, true);
301  x = xx[0]; y = xx[1]; z = xx[2];
302  return fmax;
303 
304 }
305 
306 ////////////////////////////////////////////////////////////////////////////////
307 /// Return 3 random numbers following this function shape
308 ///
309 /// The distribution contained in this TF3 function is integrated
310 /// over the cell contents.
311 /// It is normalized to 1.
312 /// Getting the three random numbers implies:
313 /// - Generating a random number between 0 and 1 (say r1)
314 /// - Look in which cell in the normalized integral r1 corresponds to
315 /// - make a linear interpolation in the returned cell
316 ///
317 /// IMPORTANT NOTE
318 ///
319 /// The integral of the function is computed at fNpx * fNpy * fNpz points.
320 /// If the function has sharp peaks, you should increase the number of
321 /// points (SetNpx, SetNpy, SetNpz) such that the peak is correctly tabulated
322 /// at several points.
323 
324 void TF3::GetRandom3(Double_t &xrandom, Double_t &yrandom, Double_t &zrandom)
325 {
326  // Check if integral array must be build
327  Int_t i,j,k,cell;
328  Double_t dx = (fXmax-fXmin)/fNpx;
329  Double_t dy = (fYmax-fYmin)/fNpy;
330  Double_t dz = (fZmax-fZmin)/fNpz;
331  Int_t ncells = fNpx*fNpy*fNpz;
332  Double_t xx[3];
333  Double_t *parameters = GetParameters();
334  InitArgs(xx,parameters);
335  if (fIntegral.empty() ) {
336  fIntegral.resize(ncells+1);
337  //fIntegral = new Double_t[ncells+1];
338  fIntegral[0] = 0;
339  Double_t integ;
340  Int_t intNegative = 0;
341  cell = 0;
342  for (k=0;k<fNpz;k++) {
343  xx[2] = fZmin+(k+0.5)*dz;
344  for (j=0;j<fNpy;j++) {
345  xx[1] = fYmin+(j+0.5)*dy;
346  for (i=0;i<fNpx;i++) {
347  xx[0] = fXmin+(i+0.5)*dx;
348  integ = EvalPar(xx,parameters);
349  if (integ < 0) {intNegative++; integ = -integ;}
350  fIntegral[cell+1] = fIntegral[cell] + integ;
351  cell++;
352  }
353  }
354  }
355  if (intNegative > 0) {
356  Warning("GetRandom3","function:%s has %d negative values: abs assumed",GetName(),intNegative);
357  }
358  if (fIntegral[ncells] == 0) {
359  Error("GetRandom3","Integral of function is zero");
360  return;
361  }
362  for (i=1;i<=ncells;i++) { // normalize integral to 1
363  fIntegral[i] /= fIntegral[ncells];
364  }
365  }
366 
367 // return random numbers
368  Double_t r;
369  r = gRandom->Rndm();
370  cell = TMath::BinarySearch(ncells,fIntegral.data(),r);
371  k = cell/(fNpx*fNpy);
372  j = (cell -k*fNpx*fNpy)/fNpx;
373  i = cell -fNpx*(j +fNpy*k);
374  xrandom = fXmin +dx*i +dx*gRandom->Rndm();
375  yrandom = fYmin +dy*j +dy*gRandom->Rndm();
376  zrandom = fZmin +dz*k +dz*gRandom->Rndm();
377 }
378 
379 ////////////////////////////////////////////////////////////////////////////////
380 /// Return range of function
381 
383 {
384  xmin = fXmin;
385  xmax = fXmax;
386  ymin = fYmin;
387  ymax = fYmax;
388  zmin = fZmin;
389  zmax = fZmax;
390 }
391 
392 
393 ////////////////////////////////////////////////////////////////////////////////
394 /// Get value corresponding to X in array of fSave values
395 
397 {
398  //if (fNsave <= 0) return 0;
399  if (fSave.empty()) return 0;
400  Int_t np = fSave.size() - 9;
401  Double_t xmin = Double_t(fSave[np+0]);
402  Double_t xmax = Double_t(fSave[np+1]);
403  Double_t ymin = Double_t(fSave[np+2]);
404  Double_t ymax = Double_t(fSave[np+3]);
405  Double_t zmin = Double_t(fSave[np+4]);
406  Double_t zmax = Double_t(fSave[np+5]);
407  Int_t npx = Int_t(fSave[np+6]);
408  Int_t npy = Int_t(fSave[np+7]);
409  Int_t npz = Int_t(fSave[np+8]);
410  Double_t x = Double_t(xx[0]);
411  Double_t dx = (xmax-xmin)/npx;
412  if (x < xmin || x > xmax) return 0;
413  if (dx <= 0) return 0;
414  Double_t y = Double_t(xx[1]);
415  Double_t dy = (ymax-ymin)/npy;
416  if (y < ymin || y > ymax) return 0;
417  if (dy <= 0) return 0;
418  Double_t z = Double_t(xx[2]);
419  Double_t dz = (zmax-zmin)/npz;
420  if (z < zmin || z > zmax) return 0;
421  if (dz <= 0) return 0;
422 
423  //we make a trilinear interpolation using the 8 points surrounding x,y,z
424  Int_t ibin = Int_t((x-xmin)/dx);
425  Int_t jbin = Int_t((y-ymin)/dy);
426  Int_t kbin = Int_t((z-zmin)/dz);
427  Double_t xlow = xmin + ibin*dx;
428  Double_t ylow = ymin + jbin*dy;
429  Double_t zlow = zmin + kbin*dz;
430  Double_t t = (x-xlow)/dx;
431  Double_t u = (y-ylow)/dy;
432  Double_t v = (z-zlow)/dz;
433  Int_t k1 = (ibin ) + (npx+1)*((jbin ) + (npy+1)*(kbin ));
434  Int_t k2 = (ibin+1) + (npx+1)*((jbin ) + (npy+1)*(kbin ));
435  Int_t k3 = (ibin+1) + (npx+1)*((jbin+1) + (npy+1)*(kbin ));
436  Int_t k4 = (ibin ) + (npx+1)*((jbin+1) + (npy+1)*(kbin ));
437  Int_t k5 = (ibin ) + (npx+1)*((jbin ) + (npy+1)*(kbin+1));
438  Int_t k6 = (ibin+1) + (npx+1)*((jbin ) + (npy+1)*(kbin+1));
439  Int_t k7 = (ibin+1) + (npx+1)*((jbin+1) + (npy+1)*(kbin+1));
440  Int_t k8 = (ibin ) + (npx+1)*((jbin+1) + (npy+1)*(kbin+1));
441  Double_t r = (1-t)*(1-u)*(1-v)*fSave[k1] + t*(1-u)*(1-v)*fSave[k2] + t*u*(1-v)*fSave[k3] + (1-t)*u*(1-v)*fSave[k4] +
442  (1-t)*(1-u)*v*fSave[k5] + t*(1-u)*v*fSave[k6] + t*u*v*fSave[k7] + (1-t)*u*v*fSave[k8];
443  return r;
444 }
445 
446 ////////////////////////////////////////////////////////////////////////////////
447 /// Return Integral of a 3d function in range [ax,bx],[ay,by],[az,bz]
448 /// with a desired relative accuracy.
449 
451 {
452  Double_t a[3], b[3];
453  a[0] = ax;
454  b[0] = bx;
455  a[1] = ay;
456  b[1] = by;
457  a[2] = az;
458  b[2] = bz;
459  Double_t relerr = 0;
460  Int_t n = 3;
461  Int_t maxpts = TMath::Min(100000, 20*fNpx*fNpy*fNpz);
462  Int_t nfnevl,ifail;
463  Double_t result = IntegralMultiple(n,a,b,maxpts,epsrel,epsrel, relerr,nfnevl,ifail);
464  if (ifail > 0) {
465  Warning("Integral","failed code=%d, maxpts=%d, epsrel=%g, nfnevl=%d, relerr=%g ",ifail,maxpts,epsrel,nfnevl,relerr);
466  }
467  return result;
468 }
469 
470 ////////////////////////////////////////////////////////////////////////////////
471 /// Return kTRUE is the point is inside the function range
472 
474 {
475  if (x[0] < fXmin || x[0] > fXmax) return kFALSE;
476  if (x[1] < fYmin || x[1] > fYmax) return kFALSE;
477  if (x[2] < fZmin || x[2] > fZmax) return kFALSE;
478  return kTRUE;
479 }
480 
481 ////////////////////////////////////////////////////////////////////////////////
482 /// Create a histogram for axis range.
483 
485 {
486  TH1* h = new TH3F("R__TF3",(char*)GetTitle(),fNpx,fXmin,fXmax
487  ,fNpy,fYmin,fYmax
488  ,fNpz,fZmin,fZmax);
489  h->SetDirectory(0);
490  return h;
491 }
492 
493 ////////////////////////////////////////////////////////////////////////////////
494 /// Paint this 3-D function with its current attributes
495 
496 void TF3::Paint(Option_t *option)
497 {
498 
499  TString opt = option;
500  opt.ToLower();
501 
502 //- Create a temporary histogram and fill each channel with the function value
503  if (!fHistogram) {
504  fHistogram = new TH3F("R__TF3",(char*)GetTitle(),fNpx,fXmin,fXmax
505  ,fNpy,fYmin,fYmax
506  ,fNpz,fZmin,fZmax);
508  }
509 
510  fHistogram->GetPainter(option)->ProcessMessage("SetF3",this);
511 
512  if (opt.Index("tf3") == kNPOS)
513  opt.Append("tf3");
514 
515  fHistogram->Paint(opt.Data());
516 }
517 
518 ////////////////////////////////////////////////////////////////////////////////
519 /// Set the function clipping box (for drawing) "off".
520 
522 {
523  fClipBoxOn = kFALSE;
524  fClipBox[0] = fClipBox[1] = fClipBox[2] = 0;
525 }
526 
527 ////////////////////////////////////////////////////////////////////////////////
528 /// Save values of function in array fSave
529 
531 {
532  if (!fSave.empty()) fSave.clear();
533  Int_t nsave = (fNpx+1)*(fNpy+1)*(fNpz+1);
534  Int_t fNsave = nsave+9;
535  assert(fNsave > 9);
536  //fSave = new Double_t[fNsave];
537  fSave.resize(fNsave);
538  Int_t i,j,k,l=0;
539  Double_t dx = (xmax-xmin)/fNpx;
540  Double_t dy = (ymax-ymin)/fNpy;
541  Double_t dz = (zmax-zmin)/fNpz;
542  if (dx <= 0) {
543  dx = (fXmax-fXmin)/fNpx;
544  xmin = fXmin +0.5*dx;
545  xmax = fXmax -0.5*dx;
546  }
547  if (dy <= 0) {
548  dy = (fYmax-fYmin)/fNpy;
549  ymin = fYmin +0.5*dy;
550  ymax = fYmax -0.5*dy;
551  }
552  if (dz <= 0) {
553  dz = (fZmax-fZmin)/fNpz;
554  zmin = fZmin +0.5*dz;
555  zmax = fZmax -0.5*dz;
556  }
557  Double_t xv[3];
558  Double_t *pp = GetParameters();
559  InitArgs(xv,pp);
560  for (k=0;k<=fNpz;k++) {
561  xv[2] = zmin + dz*k;
562  for (j=0;j<=fNpy;j++) {
563  xv[1] = ymin + dy*j;
564  for (i=0;i<=fNpx;i++) {
565  xv[0] = xmin + dx*i;
566  fSave[l] = EvalPar(xv,pp);
567  l++;
568  }
569  }
570  }
571  fSave[nsave+0] = xmin;
572  fSave[nsave+1] = xmax;
573  fSave[nsave+2] = ymin;
574  fSave[nsave+3] = ymax;
575  fSave[nsave+4] = zmin;
576  fSave[nsave+5] = zmax;
577  fSave[nsave+6] = fNpx;
578  fSave[nsave+7] = fNpy;
579  fSave[nsave+8] = fNpz;
580 }
581 
582 ////////////////////////////////////////////////////////////////////////////////
583 /// Save primitive as a C++ statement(s) on output stream out
584 
585 void TF3::SavePrimitive(std::ostream &out, Option_t *option /*= ""*/)
586 {
587  char quote = '"';
588  out<<" "<<std::endl;
589  if (gROOT->ClassSaved(TF3::Class())) {
590  out<<" ";
591  } else {
592  out<<" TF3 *";
593  }
594  if (!fMethodCall) {
595  out<<GetName()<<" = new TF3("<<quote<<GetName()<<quote<<","<<quote<<GetTitle()<<quote<<","<<fXmin<<","<<fXmax<<","<<fYmin<<","<<fYmax<<","<<fZmin<<","<<fZmax<<");"<<std::endl;
596  } else {
597  out<<GetName()<<" = new TF3("<<quote<<GetName()<<quote<<","<<GetTitle()<<","<<fXmin<<","<<fXmax<<","<<fYmin<<","<<fYmax<<","<<fZmin<<","<<fZmax<<","<<GetNpar()<<");"<<std::endl;
598  }
599 
600  if (GetFillColor() != 0) {
601  if (GetFillColor() > 228) {
603  out<<" "<<GetName()<<"->SetFillColor(ci);" << std::endl;
604  } else
605  out<<" "<<GetName()<<"->SetFillColor("<<GetFillColor()<<");"<<std::endl;
606  }
607  if (GetLineColor() != 1) {
608  if (GetLineColor() > 228) {
610  out<<" "<<GetName()<<"->SetLineColor(ci);" << std::endl;
611  } else
612  out<<" "<<GetName()<<"->SetLineColor("<<GetLineColor()<<");"<<std::endl;
613  }
614  if (GetNpz() != 100) {
615  out<<" "<<GetName()<<"->SetNpz("<<GetNpz()<<");"<<std::endl;
616  }
617  if (GetChisquare() != 0) {
618  out<<" "<<GetName()<<"->SetChisquare("<<GetChisquare()<<");"<<std::endl;
619  }
620  Double_t parmin, parmax;
621  for (Int_t i=0;i<GetNpar();i++) {
622  out<<" "<<GetName()<<"->SetParameter("<<i<<","<<GetParameter(i)<<");"<<std::endl;
623  out<<" "<<GetName()<<"->SetParError("<<i<<","<<GetParError(i)<<");"<<std::endl;
624  GetParLimits(i,parmin,parmax);
625  out<<" "<<GetName()<<"->SetParLimits("<<i<<","<<parmin<<","<<parmax<<");"<<std::endl;
626  }
627  out<<" "<<GetName()<<"->Draw("
628  <<quote<<option<<quote<<");"<<std::endl;
629 }
630 
631 ////////////////////////////////////////////////////////////////////////////////
632 /// Set the function clipping box (for drawing) "on" and define the clipping box.
633 /// xclip, yclip and zclip is a point within the function range. All the
634 /// function values having x<=xclip and y<=yclip and z>=zclip are clipped.
635 
637 {
638  fClipBoxOn = kTRUE;
639  fClipBox[0] = xclip;
640  fClipBox[1] = yclip;
641  fClipBox[2] = zclip;
642 }
643 
644 ////////////////////////////////////////////////////////////////////////////////
645 /// Set the number of points used to draw the function
646 ///
647 /// The default number of points along x is 30 for 2-d/3-d functions.
648 /// You can increase this value to get a better resolution when drawing
649 /// pictures with sharp peaks or to get a better result when using TF3::GetRandom2
650 /// the minimum number of points is 4, the maximum is 10000 for 2-d/3-d functions
651 
653 {
654  if (npz < 4) {
655  Warning("SetNpz","Number of points must be >=4 && <= 10000, fNpz set to 4");
656  fNpz = 4;
657  } else if(npz > 10000) {
658  Warning("SetNpz","Number of points must be >=4 && <= 10000, fNpz set to 10000");
659  fNpz = 10000;
660  } else {
661  fNpz = npz;
662  }
663  Update();
664 }
665 
666 ////////////////////////////////////////////////////////////////////////////////
667 /// Initialize the upper and lower bounds to draw the function
668 
670 {
671  fXmin = xmin;
672  fXmax = xmax;
673  fYmin = ymin;
674  fYmax = ymax;
675  fZmin = zmin;
676  fZmax = zmax;
677  Update();
678 }
679 
680 ////////////////////////////////////////////////////////////////////////////////
681 /// Stream an object of class TF3.
682 
683 void TF3::Streamer(TBuffer &R__b)
684 {
685  if (R__b.IsReading()) {
686  UInt_t R__s, R__c;
687  Version_t R__v = R__b.ReadVersion(&R__s, &R__c);
688  if (R__v > 0) {
689  R__b.ReadClassBuffer(TF3::Class(), this, R__v, R__s, R__c);
690  return;
691  }
692 
693  } else {
694  Int_t saved = 0;
695  if (fType != EFType::kFormula && fSave.empty() ) { saved = 1; Save(fXmin,fXmax,fYmin,fYmax,fZmin,fZmax);}
696 
697  R__b.WriteClassBuffer(TF3::Class(),this);
698 
699  if (saved) { fSave.clear(); }
700  }
701 }
702 
703 ////////////////////////////////////////////////////////////////////////////////
704 /// Return x^nx * y^ny * z^nz moment of a 3d function in range [ax,bx],[ay,by],[az,bz]
705 /// \author Gene Van Buren <gene@bnl.gov>
706 
708 {
709  Double_t norm = Integral(ax,bx,ay,by,az,bz,epsilon);
710  if (norm == 0) {
711  Error("Moment3", "Integral zero over range");
712  return 0;
713  }
714 
715  TF3 fnc("TF3_ExpValHelper",Form("%s*pow(x,%f)*pow(y,%f)*pow(z,%f)",GetName(),nx,ny,nz));
716  return fnc.Integral(ax,bx,ay,by,az,bz,epsilon)/norm;
717 }
718 
719 ////////////////////////////////////////////////////////////////////////////////
720 /// Return x^nx * y^ny * z^nz central moment of a 3d function in range [ax,bx],[ay,by],[az,bz]
721 /// \author Gene Van Buren <gene@bnl.gov>
722 
724 {
725  Double_t norm = Integral(ax,bx,ay,by,az,bz,epsilon);
726  if (norm == 0) {
727  Error("CentralMoment3", "Integral zero over range");
728  return 0;
729  }
730 
731  Double_t xbar = 0;
732  Double_t ybar = 0;
733  Double_t zbar = 0;
734  if (nx!=0) {
735  TF3 fncx("TF3_ExpValHelperx",Form("%s*x",GetName()));
736  xbar = fncx.Integral(ax,bx,ay,by,az,bz,epsilon)/norm;
737  }
738  if (ny!=0) {
739  TF3 fncy("TF3_ExpValHelpery",Form("%s*y",GetName()));
740  ybar = fncy.Integral(ax,bx,ay,by,az,bz,epsilon)/norm;
741  }
742  if (nz!=0) {
743  TF3 fncz("TF3_ExpValHelperz",Form("%s*z",GetName()));
744  zbar = fncz.Integral(ax,bx,ay,by,az,bz,epsilon)/norm;
745  }
746  TF3 fnc("TF3_ExpValHelper",Form("%s*pow(x-%f,%f)*pow(y-%f,%f)*pow(z-%f,%f)",GetName(),xbar,nx,ybar,ny,zbar,nz));
747  return fnc.Integral(ax,bx,ay,by,az,bz,epsilon)/norm;
748 }
749 
virtual const char * GetName() const
Returns name of object.
Definition: TNamed.h:47
virtual void Copy(TObject &f3) const
Copy this F3 to a new F3.
Definition: TF3.cxx:152
Bool_t IsReading() const
Definition: TBuffer.h:85
virtual void Paint(Option_t *option="")
Control routine to paint any kind of histograms.
Definition: TH1.cxx:5837
Int_t fNpx
Definition: TF1.h:244
float xmin
Definition: THbookFile.cxx:93
virtual Int_t WriteClassBuffer(const TClass *cl, void *pointer)=0
virtual Double_t Moment3(Double_t nx, Double_t ax, Double_t bx, Double_t ny, Double_t ay, Double_t by, Double_t nz, Double_t az, Double_t bz, Double_t epsilon=0.000001)
Return x^nx * y^ny * z^nz moment of a 3d function in range [ax,bx],[ay,by],[az,bz].
Definition: TF3.cxx:707
auto * tt
Definition: textangle.C:16
Param Functor class for Multidimensional functions.
Definition: ParamFunctor.h:274
virtual void Draw(Option_t *option="")
Draw this function with its current attributes.
Definition: TF3.cxx:176
Double_t fZmax
Definition: TF3.h:32
short Version_t
Definition: RtypesCore.h:63
TVirtualHistPainter * GetPainter(Option_t *option="")
Return pointer to painter.
Definition: TH1.cxx:4368
virtual void SetDirectory(TDirectory *dir)
By default when an histogram is created, it is added to the list of histogram objects in the current ...
Definition: TH1.cxx:8393
3-D histogram with a float per channel (see TH1 documentation)}
Definition: TH3.h:267
virtual void Save(Double_t xmin, Double_t xmax, Double_t ymin, Double_t ymax, Double_t zmin, Double_t zmax)
Save values of function in array fSave.
Definition: TF3.cxx:530
const char Option_t
Definition: RtypesCore.h:64
float ymin
Definition: THbookFile.cxx:93
virtual TH1 * CreateHistogram()
Create a histogram for axis range.
Definition: TF3.cxx:484
Double_t QuietNaN()
Returns a quiet NaN as defined by IEEE 754
Definition: TMath.h:891
const Ssiz_t kNPOS
Definition: RtypesCore.h:113
static void SaveColor(std::ostream &out, Int_t ci)
Save a color with index > 228 as a C++ statement(s) on output stream out.
Definition: TColor.cxx:2118
virtual ~TF3()
F3 default destructor.
Definition: TF3.cxx:137
virtual void ExecuteEvent(Int_t event, Int_t px, Int_t py)
Execute action corresponding to one event.
Definition: TF1.cxx:1545
Buffer base class used for serializing objects.
Definition: TBuffer.h:42
Double_t fZmin
Definition: TF3.h:31
Int_t GetNpz() const
Definition: TF3.h:94
virtual Double_t IntegralMultiple(Int_t n, const Double_t *a, const Double_t *b, Int_t maxpts, Double_t epsrel, Double_t epsabs, Double_t &relerr, Int_t &nfnevl, Int_t &ifail)
This function computes, to an attempted specified accuracy, the value of the integral.
Definition: TF1.cxx:2840
#define gROOT
Definition: TROOT.h:404
Ssiz_t Index(const char *pat, Ssiz_t i=0, ECaseCompare cmp=kExact) const
Definition: TString.h:634
Basic string class.
Definition: TString.h:131
#define f(i)
Definition: RSha256.hxx:104
Short_t Min(Short_t a, Short_t b)
Definition: TMathBase.h:180
void ToLower()
Change string to lower-case.
Definition: TString.cxx:1125
int Int_t
Definition: RtypesCore.h:43
virtual Double_t GetParError(Int_t ipar) const
Return value of parameter number ipar.
Definition: TF1.cxx:1929
virtual void SavePrimitive(std::ostream &out, Option_t *option="")
Save primitive as a C++ statement(s) on output stream out.
Definition: TF3.cxx:585
Double_t fYmin
Definition: TF2.h:32
virtual Double_t GetMinimumXYZ(Double_t &x, Double_t &y, Double_t &z)
Compute the X, Y and Z values corresponding to the minimum value of the function on its range...
Definition: TF3.cxx:280
virtual void AppendPad(Option_t *option="")
Append graphics object to current pad.
Definition: TObject.cxx:105
virtual void SetClippingBoxOn(Double_t xclip=0, Double_t yclip=0, Double_t zclip=0)
Set the function clipping box (for drawing) "on" and define the clipping box.
Definition: TF3.cxx:636
virtual Int_t DistancetoPrimitive(Int_t px, Int_t py)
Compute distance from point px,py to a function.
Definition: TF1.cxx:1296
EFType fType
Definition: TF1.h:245
virtual void ExecuteEvent(Int_t event, Int_t px, Int_t py)
Execute action corresponding to one event.
Definition: TF3.cxx:191
Double_t x[n]
Definition: legend1.C:17
void Class()
Definition: Class.C:29
virtual void Copy(TObject &f2) const
Copy this F2 to a new F2.
Definition: TF2.cxx:192
Int_t fNdim
Definition: TF1.h:243
virtual Double_t GetMaximumXYZ(Double_t &x, Double_t &y, Double_t &z)
Compute the X, Y and Z values corresponding to the maximum value of the function on its range...
Definition: TF3.cxx:296
TF3()
coordinates of clipbox
Definition: TF3.cxx:36
Double_t fYmax
Definition: TF2.h:33
virtual void Paint(Option_t *option="")
Paint this 3-D function with its current attributes.
Definition: TF3.cxx:496
TString & Append(const char *cs)
Definition: TString.h:559
Bool_t fClipBoxOn
Definition: TF3.h:34
Int_t Finite(Double_t x)
Check if it is finite with a mask in order to be consistent in presence of fast math.
Definition: TMath.h:761
virtual Int_t GetNdim() const
Definition: TF1.h:479
virtual void ProcessMessage(const char *mess, const TObject *obj)=0
Double_t Infinity()
Returns an infinity as defined by the IEEE standard.
Definition: TMath.h:904
Double_t fClipBox[3]
is clip box on
Definition: TF3.h:35
std::vector< Double_t > fIntegral
Definition: TF1.h:255
virtual Double_t Rndm()
Machine independent random number generator.
Definition: TRandom.cxx:541
float ymax
Definition: THbookFile.cxx:93
TH1 * fHistogram
Parent object hooking this function (if one)
Definition: TF1.h:260
virtual Double_t Integral(Double_t ax, Double_t bx, Double_t ay, Double_t by, Double_t az, Double_t bz, Double_t epsrel=1.e-6)
Return Integral of a 3d function in range [ax,bx],[ay,by],[az,bz] with a desired relative accuracy...
Definition: TF3.cxx:450
ROOT::R::TRInterface & r
Definition: Object.C:4
virtual Double_t CentralMoment3(Double_t nx, Double_t ax, Double_t bx, Double_t ny, Double_t ay, Double_t by, Double_t nz, Double_t az, Double_t bz, Double_t epsilon=0.000001)
Return x^nx * y^ny * z^nz central moment of a 3d function in range [ax,bx],[ay,by],[az,bz].
Definition: TF3.cxx:723
auto * a
Definition: textangle.C:12
A 3-Dim function with parameters.
Definition: TF3.h:28
unsigned int UInt_t
Definition: RtypesCore.h:44
virtual void GetRange(Double_t &xmin, Double_t &xmax) const
Return range of a 1-D function.
Definition: TF3.h:142
virtual void Error(const char *method, const char *msgfmt,...) const
Issue error message.
Definition: TObject.cxx:888
char * Form(const char *fmt,...)
virtual void GetRandom3(Double_t &xrandom, Double_t &yrandom, Double_t &zrandom)
Return 3 random numbers following this function shape.
Definition: TF3.cxx:324
float xmax
Definition: THbookFile.cxx:93
virtual void Update()
Called by functions such as SetRange, SetNpx, SetParameters to force the deletion of the associated h...
Definition: TF1.cxx:3634
A 2-Dim function with parameters.
Definition: TF2.h:29
R__EXTERN TRandom * gRandom
Definition: TRandom.h:62
Int_t fNpz
Definition: TF3.h:33
REAL epsilon
Definition: triangle.c:617
#define h(i)
Definition: RSha256.hxx:106
const Bool_t kFALSE
Definition: RtypesCore.h:90
virtual Color_t GetLineColor() const
Return the line color.
Definition: TAttLine.h:33
TF3 & operator=(const TF3 &rhs)
Operator =.
Definition: TF3.cxx:126
virtual Int_t ReadClassBuffer(const TClass *cl, void *pointer, const TClass *onfile_class=0)=0
Double_t GetChisquare() const
Definition: TF1.h:438
#define ClassImp(name)
Definition: Rtypes.h:361
double Double_t
Definition: RtypesCore.h:57
std::vector< Double_t > fSave
Definition: TF1.h:254
Double_t fXmin
Definition: TF1.h:240
Double_t y[n]
Definition: legend1.C:17
virtual Color_t GetFillColor() const
Return the fill area color.
Definition: TAttFill.h:30
Bool_t Contains(const char *pat, ECaseCompare cmp=kExact) const
Definition: TString.h:619
The TH1 histogram class.
Definition: TH1.h:56
virtual void SetClippingBoxOff()
Set the function clipping box (for drawing) "off".
Definition: TF3.cxx:521
virtual void InitArgs(const Double_t *x, const Double_t *params)
Initialize parameters addresses.
Definition: TF1.cxx:2473
Mother of all ROOT objects.
Definition: TObject.h:37
you should not use this method at all Int_t Int_t z
Definition: TRolke.cxx:630
TMethodCall * fMethodCall
Pointer to histogram used for visualisation.
Definition: TF1.h:261
virtual Int_t GetNpar() const
Definition: TF1.h:475
virtual void GetParLimits(Int_t ipar, Double_t &parmin, Double_t &parmax) const
Return limits for parameter ipar.
Definition: TF1.cxx:1939
virtual void SetRange(Double_t xmin, Double_t xmax)
Initialize the upper and lower bounds to draw the function.
Definition: TF3.h:146
auto * l
Definition: textangle.C:4
virtual Double_t GetMinMaxNDim(Double_t *x, Bool_t findmax, Double_t epsilon=0, Int_t maxiter=0) const
Find the minimum of a function of whatever dimension.
Definition: TF1.cxx:1722
virtual Double_t GetParameter(Int_t ipar) const
Definition: TF1.h:506
virtual Bool_t IsInside(const Double_t *x) const
Return kTRUE is the point is inside the function range.
Definition: TF3.cxx:473
void MakeZombie()
Definition: TObject.h:49
virtual Double_t FindMinMax(Double_t *x, bool findmax) const
Return minimum/maximum value of the function.
Definition: TF3.cxx:212
you should not use this method at all Int_t Int_t Double_t Double_t Double_t Int_t Double_t Double_t Double_t Double_t b
Definition: TRolke.cxx:630
#define gPad
Definition: TVirtualPad.h:287
virtual Double_t * GetParameters() const
Definition: TF1.h:514
virtual Double_t EvalPar(const Double_t *x, const Double_t *params=0)
Evaluate function with given coordinates and parameters.
Definition: TF1.cxx:1477
const Bool_t kTRUE
Definition: RtypesCore.h:89
const Int_t n
Definition: legend1.C:16
Double_t fXmax
Definition: TF1.h:241
Long64_t BinarySearch(Long64_t n, const T *array, T value)
Definition: TMathBase.h:278
virtual Int_t DistancetoPrimitive(Int_t px, Int_t py)
Compute distance from point px,py to a function.
Definition: TF3.cxx:167
char name[80]
Definition: TGX11.cxx:109
virtual Double_t GetSave(const Double_t *x)
Get value corresponding to X in array of fSave values.
Definition: TF3.cxx:396
virtual void Warning(const char *method, const char *msgfmt,...) const
Issue warning message.
Definition: TObject.cxx:874
virtual Version_t ReadVersion(UInt_t *start=0, UInt_t *bcnt=0, const TClass *cl=0)=0
virtual const char * GetTitle() const
Returns title of object.
Definition: TNamed.h:48
Int_t fNpy
Definition: TF2.h:34
const char * Data() const
Definition: TString.h:364
virtual void SetNpz(Int_t npz=30)
Set the number of points used to draw the function.
Definition: TF3.cxx:652