Logo ROOT  
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"
25#include <cassert>
26
28
29/** \class TF3
30 \ingroup Hist
31A 3-Dim function with parameters
32*/
33
34////////////////////////////////////////////////////////////////////////////////
35/// F3 default constructor
36
38{
39 fNpz = 0;
40 fZmin = 0;
41 fZmax = 1;
42}
43
44
45////////////////////////////////////////////////////////////////////////////////
46/// F3 constructor using a formula definition
47///
48/// See TFormula constructor for explanation of the formula syntax.
49
50TF3::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)
51 :TF2(name,formula,xmin,xmax,ymax,ymin,opt)
52{
53 fZmin = zmin;
54 fZmax = zmax;
55 fNpz = 30;
56 Int_t ndim = GetNdim();
57 // accept 1-d or 2-d formula
58 if (ndim < 3) fNdim = 3;
59 if (ndim > 3 && xmin < xmax && ymin < ymax && zmin < zmax) {
60 Error("TF3","function: %s/%s has dimension %d instead of 3",name,formula,ndim);
61 MakeZombie();
62 }
63}
64
65////////////////////////////////////////////////////////////////////////////////
66/// F3 constructor using a pointer to real function
67///
68/// \param[in] npar is the number of free parameters used by the function
69///
70/// For example, for a 3-dim function with 3 parameters, the user function
71/// looks like:
72///
73/// Double_t fun1(Double_t *x, Double_t *par)
74/// return par[0]*x[2] + par[1]*exp(par[2]*x[0]*x[1]);
75///
76/// WARNING! A function created with this constructor cannot be Cloned.
77
79 :TF2(name,fcn,xmin,xmax,ymin,ymax,npar,ndim)
80{
81 fZmin = zmin;
82 fZmax = zmax;
83 fNpz = 30;
84}
85
86////////////////////////////////////////////////////////////////////////////////
87/// F3 constructor using a pointer to real function---
88///
89/// \param[in] npar is the number of free parameters used by the function
90///
91/// For example, for a 3-dim function with 3 parameters, the user function
92/// looks like:
93///
94/// Double_t fun1(Double_t *x, Double_t *par)
95/// return par[0]*x[2] + par[1]*exp(par[2]*x[0]*x[1]);
96///
97/// WARNING! A function created with this constructor cannot be Cloned.
98
99TF3::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)
100 : TF2(name,fcn,xmin,xmax,ymin,ymax,npar,ndim),
101 fZmin(zmin),
102 fZmax(zmax),
103 fNpz(30)
104{
105}
106
107////////////////////////////////////////////////////////////////////////////////
108/// F3 constructor using a ParamFunctor
109///
110/// a functor class implementing operator() (double *, double *)
111///
112/// \param[in] npar is the number of free parameters used by the function
113///
114/// WARNING! A function created with this constructor cannot be Cloned.
115
117 : TF2(name, f, xmin, xmax, ymin, ymax, npar, ndim),
118 fZmin(zmin),
119 fZmax(zmax),
120 fNpz(30)
121{
122}
123
124////////////////////////////////////////////////////////////////////////////////
125/// Operator =
126
128{
129 if (this != &rhs) {
130 rhs.Copy(*this);
131 }
132 return *this;
133}
134
135////////////////////////////////////////////////////////////////////////////////
136/// F3 default destructor
137
139{
140}
141
142////////////////////////////////////////////////////////////////////////////////
143/// Copy constructor.
144
145TF3::TF3(const TF3 &f3) : TF2()
146{
147 ((TF3&)f3).Copy(*this);
148}
149
150////////////////////////////////////////////////////////////////////////////////
151/// Copy this F3 to a new F3
152
153void TF3::Copy(TObject &obj) const
154{
155 TF2::Copy(obj);
156 ((TF3&)obj).fZmin = fZmin;
157 ((TF3&)obj).fZmax = fZmax;
158 ((TF3&)obj).fNpz = fNpz;
159}
160
161////////////////////////////////////////////////////////////////////////////////
162/// Compute distance from point px,py to a function
163///
164/// Compute the closest distance of approach from point px,py to this function.
165/// The distance is computed in pixels units.
166
167
169{
170 return TF1::DistancetoPrimitive(px, py);
171
172}
173
174////////////////////////////////////////////////////////////////////////////////
175/// Draw this function with its current attributes
176
177void TF3::Draw(Option_t *option)
178{
179 TString opt = option;
180 opt.ToLower();
181 if (gPad && !opt.Contains("same")) gPad->Clear();
182
183 AppendPad(option);
184
185}
186
187////////////////////////////////////////////////////////////////////////////////
188/// Execute action corresponding to one event
189///
190/// This member function is called when a F3 is clicked with the locator
191
193{
194 TF1::ExecuteEvent(event, px, py);
195}
196
197////////////////////////////////////////////////////////////////////////////////
198/// Return minimum/maximum value of the function
199///
200/// To find the minimum on a range, first set this range via the SetRange function
201/// If a vector x of coordinate is passed it will be used as starting point for the minimum.
202/// In addition on exit x will contain the coordinate values at the minimuma
203/// If x is NULL or x is inifinity or NaN, first, a grid search is performed to find the initial estimate of the
204/// minimum location. The range of the function is divided into fNpx and fNpy
205/// sub-ranges. If the function is "good" (or "bad"), these values can be changed
206/// by SetNpx and SetNpy functions
207///
208/// Then, a minimization is used with starting values found by the grid search
209/// The minimizer algorithm used (by default Minuit) can be changed by callinga
210/// ROOT::Math::Minimizer::SetDefaultMinimizerType("..")
211/// Other option for the minimizer can be set using the static method of the MinimizerOptions class
212
214{
215 //First do a grid search with step size fNpx and fNpy
216
217 Double_t xx[3];
218 Double_t rsign = (findmax) ? -1. : 1.;
219 TF3 & function = const_cast<TF3&>(*this); // needed since EvalPar is not const
220 Double_t xxmin = 0, yymin = 0, zzmin = 0, ttmin = 0;
221 if (x == NULL || ( (x!= NULL) && ( !TMath::Finite(x[0]) || !TMath::Finite(x[1]) || !TMath::Finite(x[2]) ) ) ){
222 Double_t dx = (fXmax - fXmin)/fNpx;
223 Double_t dy = (fYmax - fYmin)/fNpy;
224 Double_t dz = (fZmax - fZmin)/fNpz;
225 xxmin = fXmin;
226 yymin = fYmin;
227 zzmin = fZmin;
228 ttmin = rsign * TMath::Infinity();
229 for (Int_t i=0; i<fNpx; i++){
230 xx[0]=fXmin + (i+0.5)*dx;
231 for (Int_t j=0; j<fNpy; j++){
232 xx[1]=fYmin+(j+0.5)*dy;
233 for (Int_t k=0; k<fNpz; k++){
234 xx[2] = fZmin+(k+0.5)*dz;
235 Double_t tt = function(xx);
236 if (rsign*tt < rsign*ttmin) {xxmin = xx[0], yymin = xx[1]; zzmin = xx[2]; ttmin=tt;}
237 }
238 }
239 }
240
241 xxmin = TMath::Min(fXmax, xxmin);
242 yymin = TMath::Min(fYmax, yymin);
243 zzmin = TMath::Min(fZmax, zzmin);
244 }
245 else {
246 xxmin = x[0];
247 yymin = x[1];
248 zzmin = x[2];
249 zzmin = function(x);
250 }
251 xx[0] = xxmin;
252 xx[1] = yymin;
253 xx[2] = zzmin;
254
255 double fmin = GetMinMaxNDim(xx,findmax);
256 if (rsign*fmin < rsign*zzmin) {
257 if (x) {x[0] = xx[0]; x[1] = xx[1]; x[2] = xx[2];}
258 return fmin;
259 }
260 // here if minimization failed
261 if (x) { x[0] = xxmin; x[1] = yymin; x[2] = zzmin; }
262 return ttmin;
263}
264
265////////////////////////////////////////////////////////////////////////////////
266/// Compute the X, Y and Z values corresponding to the minimum value of the function
267/// on its range.
268///
269/// Returns the function value at the minimum.
270/// To find the minimum on a subrange, use the SetRange() function first.
271///
272/// Method:
273/// First, a grid search is performed to find the initial estimate of the
274/// minimum location. The range of the function is divided
275/// into fNpx,fNpy and fNpz sub-ranges. If the function is "good" (or "bad"),
276/// these values can be changed by SetNpx(), SetNpy() and SetNpz() functions.
277/// Then, Minuit minimization is used with starting values found by the grid search
278///
279/// Note that this method will always do first a grid search in contrast to GetMinimum
280
282{
283 double xx[3] = { 0,0,0 };
284 xx[0] = TMath::QuietNaN(); // to force to do grid search in TF3::FindMinMax
285 double fmin = FindMinMax(xx, false);
286 x = xx[0]; y = xx[1]; z = xx[2];
287 return fmin;
288
289}
290
291////////////////////////////////////////////////////////////////////////////////
292/// Compute the X, Y and Z values corresponding to the maximum value of the function
293/// on its range.
294///
295/// Return the function value at the maximum. See TF3::GetMinimumXYZ
296
298{
299 double xx[3] = { 0,0,0 };
300 xx[0] = TMath::QuietNaN(); // to force to do grid search in TF3::FindMinMax
301 double fmax = FindMinMax(xx, true);
302 x = xx[0]; y = xx[1]; z = xx[2];
303 return fmax;
304
305}
306
307////////////////////////////////////////////////////////////////////////////////
308/// Return 3 random numbers following this function shape
309///
310/// The distribution contained in this TF3 function is integrated
311/// over the cell contents.
312/// It is normalized to 1.
313/// Getting the three random numbers implies:
314/// - Generating a random number between 0 and 1 (say r1)
315/// - Look in which cell in the normalized integral r1 corresponds to
316/// - make a linear interpolation in the returned cell
317///
318/// IMPORTANT NOTE
319///
320/// The integral of the function is computed at fNpx * fNpy * fNpz points.
321/// If the function has sharp peaks, you should increase the number of
322/// points (SetNpx, SetNpy, SetNpz) such that the peak is correctly tabulated
323/// at several points.
324
325void TF3::GetRandom3(Double_t &xrandom, Double_t &yrandom, Double_t &zrandom, TRandom * rng)
326{
327 // Check if integral array must be built
328 Int_t i,j,k,cell;
329 Double_t dx = (fXmax-fXmin)/fNpx;
330 Double_t dy = (fYmax-fYmin)/fNpy;
331 Double_t dz = (fZmax-fZmin)/fNpz;
332 Int_t ncells = fNpx*fNpy*fNpz;
333 Double_t xx[3];
334 Double_t *parameters = GetParameters();
335 InitArgs(xx,parameters);
336 if (fIntegral.empty() ) {
337 fIntegral.resize(ncells+1);
338 //fIntegral = new Double_t[ncells+1];
339 fIntegral[0] = 0;
340 Double_t integ;
341 Int_t intNegative = 0;
342 cell = 0;
343 for (k=0;k<fNpz;k++) {
344 xx[2] = fZmin+(k+0.5)*dz;
345 for (j=0;j<fNpy;j++) {
346 xx[1] = fYmin+(j+0.5)*dy;
347 for (i=0;i<fNpx;i++) {
348 xx[0] = fXmin+(i+0.5)*dx;
349 integ = EvalPar(xx,parameters);
350 if (integ < 0) {intNegative++; integ = -integ;}
351 fIntegral[cell+1] = fIntegral[cell] + integ;
352 cell++;
353 }
354 }
355 }
356 if (intNegative > 0) {
357 Warning("GetRandom3","function:%s has %d negative values: abs assumed",GetName(),intNegative);
358 }
359 if (fIntegral[ncells] == 0) {
360 Error("GetRandom3","Integral of function is zero");
361 return;
362 }
363 for (i=1;i<=ncells;i++) { // normalize integral to 1
364 fIntegral[i] /= fIntegral[ncells];
365 }
366 }
367
368// return random numbers
369 Double_t r;
370 if (!rng) rng = gRandom;
371 r = rng->Rndm();
372 cell = TMath::BinarySearch(ncells,fIntegral.data(),r);
373 k = cell/(fNpx*fNpy);
374 j = (cell -k*fNpx*fNpy)/fNpx;
375 i = cell -fNpx*(j +fNpy*k);
376 xrandom = fXmin +dx*i +dx*rng->Rndm();
377 yrandom = fYmin +dy*j +dy*rng->Rndm();
378 zrandom = fZmin +dz*k +dz*rng->Rndm();
379}
380
381////////////////////////////////////////////////////////////////////////////////
382/// Return range of function
383
385{
386 xmin = fXmin;
387 xmax = fXmax;
388 ymin = fYmin;
389 ymax = fYmax;
390 zmin = fZmin;
391 zmax = fZmax;
392}
393
394
395////////////////////////////////////////////////////////////////////////////////
396/// Get value corresponding to X in array of fSave values
397
399{
400 //if (fNsave <= 0) return 0;
401 if (fSave.empty()) return 0;
402 Int_t np = fSave.size() - 9;
403 Double_t xmin = Double_t(fSave[np+0]);
404 Double_t xmax = Double_t(fSave[np+1]);
405 Double_t ymin = Double_t(fSave[np+2]);
406 Double_t ymax = Double_t(fSave[np+3]);
407 Double_t zmin = Double_t(fSave[np+4]);
408 Double_t zmax = Double_t(fSave[np+5]);
409 Int_t npx = Int_t(fSave[np+6]);
410 Int_t npy = Int_t(fSave[np+7]);
411 Int_t npz = Int_t(fSave[np+8]);
412 Double_t x = Double_t(xx[0]);
413 Double_t dx = (xmax-xmin)/npx;
414 if (x < xmin || x > xmax) return 0;
415 if (dx <= 0) return 0;
416 Double_t y = Double_t(xx[1]);
417 Double_t dy = (ymax-ymin)/npy;
418 if (y < ymin || y > ymax) return 0;
419 if (dy <= 0) return 0;
420 Double_t z = Double_t(xx[2]);
421 Double_t dz = (zmax-zmin)/npz;
422 if (z < zmin || z > zmax) return 0;
423 if (dz <= 0) return 0;
424
425 //we make a trilinear interpolation using the 8 points surrounding x,y,z
426 Int_t ibin = Int_t((x-xmin)/dx);
427 Int_t jbin = Int_t((y-ymin)/dy);
428 Int_t kbin = Int_t((z-zmin)/dz);
429 Double_t xlow = xmin + ibin*dx;
430 Double_t ylow = ymin + jbin*dy;
431 Double_t zlow = zmin + kbin*dz;
432 Double_t t = (x-xlow)/dx;
433 Double_t u = (y-ylow)/dy;
434 Double_t v = (z-zlow)/dz;
435 Int_t k1 = (ibin ) + (npx+1)*((jbin ) + (npy+1)*(kbin ));
436 Int_t k2 = (ibin+1) + (npx+1)*((jbin ) + (npy+1)*(kbin ));
437 Int_t k3 = (ibin+1) + (npx+1)*((jbin+1) + (npy+1)*(kbin ));
438 Int_t k4 = (ibin ) + (npx+1)*((jbin+1) + (npy+1)*(kbin ));
439 Int_t k5 = (ibin ) + (npx+1)*((jbin ) + (npy+1)*(kbin+1));
440 Int_t k6 = (ibin+1) + (npx+1)*((jbin ) + (npy+1)*(kbin+1));
441 Int_t k7 = (ibin+1) + (npx+1)*((jbin+1) + (npy+1)*(kbin+1));
442 Int_t k8 = (ibin ) + (npx+1)*((jbin+1) + (npy+1)*(kbin+1));
443 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] +
444 (1-t)*(1-u)*v*fSave[k5] + t*(1-u)*v*fSave[k6] + t*u*v*fSave[k7] + (1-t)*u*v*fSave[k8];
445 return r;
446}
447
448////////////////////////////////////////////////////////////////////////////////
449/// Return Integral of a 3d function in range [ax,bx],[ay,by],[az,bz]
450/// with a desired relative accuracy.
451
453{
454 Double_t a[3], b[3];
455 a[0] = ax;
456 b[0] = bx;
457 a[1] = ay;
458 b[1] = by;
459 a[2] = az;
460 b[2] = bz;
461 Double_t relerr = 0;
462 Int_t n = 3;
464 Int_t nfnevl, ifail;
465 Double_t result = IntegralMultiple(n,a,b,maxpts,epsrel,epsrel, relerr,nfnevl,ifail);
466 if (ifail > 0) {
467 Warning("Integral","failed for %s code=%d, maxpts=%d, epsrel=%g, nfnevl=%d, relerr=%g ",GetName(),ifail,maxpts,epsrel,nfnevl,relerr);
468 }
469 if (gDebug) {
470 Info("Integral","Integral of %s using %d and tol=%f is %f , relerr=%f nfcn=%d",GetName(),maxpts,epsrel,result,relerr,nfnevl);
471 }
472 return result;
473}
474
475////////////////////////////////////////////////////////////////////////////////
476/// Return kTRUE is the point is inside the function range
477
479{
480 if (x[0] < fXmin || x[0] > fXmax) return kFALSE;
481 if (x[1] < fYmin || x[1] > fYmax) return kFALSE;
482 if (x[2] < fZmin || x[2] > fZmax) return kFALSE;
483 return kTRUE;
484}
485
486////////////////////////////////////////////////////////////////////////////////
487/// Create a histogram for axis range.
488
490{
491 TH1* h = new TH3F("R__TF3",(char*)GetTitle(),fNpx,fXmin,fXmax
493 ,fNpz,fZmin,fZmax);
494 h->SetDirectory(0);
495 return h;
496}
497
498////////////////////////////////////////////////////////////////////////////////
499/// Paint this 3-D function with its current attributes
500
501void TF3::Paint(Option_t *option)
502{
503
504 TString opt = option;
505 opt.ToLower();
506
507//- Create a temporary histogram and fill each channel with the function value
508 if (!fHistogram) {
509 fHistogram = new TH3F("R__TF3",(char*)GetTitle(),fNpx,fXmin,fXmax
511 ,fNpz,fZmin,fZmax);
513 }
514
515 fHistogram->GetPainter(option)->ProcessMessage("SetF3",this);
516
517 if (opt.Index("tf3") == kNPOS)
518 opt.Append("tf3");
519
520 fHistogram->Paint(opt.Data());
521}
522
523////////////////////////////////////////////////////////////////////////////////
524/// Set the function clipping box (for drawing) "off".
525
527{
529 fClipBox[0] = fClipBox[1] = fClipBox[2] = 0;
530}
531
532////////////////////////////////////////////////////////////////////////////////
533/// Save values of function in array fSave
534
536{
537 if (!fSave.empty()) fSave.clear();
538 Int_t nsave = (fNpx+1)*(fNpy+1)*(fNpz+1);
539 Int_t fNsave = nsave+9;
540 assert(fNsave > 9);
541 //fSave = new Double_t[fNsave];
542 fSave.resize(fNsave);
543 Int_t i,j,k,l=0;
544 Double_t dx = (xmax-xmin)/fNpx;
545 Double_t dy = (ymax-ymin)/fNpy;
546 Double_t dz = (zmax-zmin)/fNpz;
547 if (dx <= 0) {
548 dx = (fXmax-fXmin)/fNpx;
549 xmin = fXmin +0.5*dx;
550 xmax = fXmax -0.5*dx;
551 }
552 if (dy <= 0) {
553 dy = (fYmax-fYmin)/fNpy;
554 ymin = fYmin +0.5*dy;
555 ymax = fYmax -0.5*dy;
556 }
557 if (dz <= 0) {
558 dz = (fZmax-fZmin)/fNpz;
559 zmin = fZmin +0.5*dz;
560 zmax = fZmax -0.5*dz;
561 }
562 Double_t xv[3];
563 Double_t *pp = GetParameters();
564 InitArgs(xv,pp);
565 for (k=0;k<=fNpz;k++) {
566 xv[2] = zmin + dz*k;
567 for (j=0;j<=fNpy;j++) {
568 xv[1] = ymin + dy*j;
569 for (i=0;i<=fNpx;i++) {
570 xv[0] = xmin + dx*i;
571 fSave[l] = EvalPar(xv,pp);
572 l++;
573 }
574 }
575 }
576 fSave[nsave+0] = xmin;
577 fSave[nsave+1] = xmax;
578 fSave[nsave+2] = ymin;
579 fSave[nsave+3] = ymax;
580 fSave[nsave+4] = zmin;
581 fSave[nsave+5] = zmax;
582 fSave[nsave+6] = fNpx;
583 fSave[nsave+7] = fNpy;
584 fSave[nsave+8] = fNpz;
585}
586
587////////////////////////////////////////////////////////////////////////////////
588/// Save primitive as a C++ statement(s) on output stream out
589
590void TF3::SavePrimitive(std::ostream &out, Option_t *option /*= ""*/)
591{
592 char quote = '"';
593 out<<" "<<std::endl;
594 if (gROOT->ClassSaved(TF3::Class())) {
595 out<<" ";
596 } else {
597 out<<" TF3 *";
598 }
599 if (!fMethodCall) {
600 out<<GetName()<<" = new TF3("<<quote<<GetName()<<quote<<","<<quote<<GetTitle()<<quote<<","<<fXmin<<","<<fXmax<<","<<fYmin<<","<<fYmax<<","<<fZmin<<","<<fZmax<<");"<<std::endl;
601 } else {
602 out<<GetName()<<" = new TF3("<<quote<<GetName()<<quote<<","<<GetTitle()<<","<<fXmin<<","<<fXmax<<","<<fYmin<<","<<fYmax<<","<<fZmin<<","<<fZmax<<","<<GetNpar()<<");"<<std::endl;
603 }
604
605 if (GetFillColor() != 0) {
606 if (GetFillColor() > 228) {
608 out<<" "<<GetName()<<"->SetFillColor(ci);" << std::endl;
609 } else
610 out<<" "<<GetName()<<"->SetFillColor("<<GetFillColor()<<");"<<std::endl;
611 }
612 if (GetLineColor() != 1) {
613 if (GetLineColor() > 228) {
615 out<<" "<<GetName()<<"->SetLineColor(ci);" << std::endl;
616 } else
617 out<<" "<<GetName()<<"->SetLineColor("<<GetLineColor()<<");"<<std::endl;
618 }
619 if (GetNpz() != 100) {
620 out<<" "<<GetName()<<"->SetNpz("<<GetNpz()<<");"<<std::endl;
621 }
622 if (GetChisquare() != 0) {
623 out<<" "<<GetName()<<"->SetChisquare("<<GetChisquare()<<");"<<std::endl;
624 }
625 Double_t parmin, parmax;
626 for (Int_t i=0;i<GetNpar();i++) {
627 out<<" "<<GetName()<<"->SetParameter("<<i<<","<<GetParameter(i)<<");"<<std::endl;
628 out<<" "<<GetName()<<"->SetParError("<<i<<","<<GetParError(i)<<");"<<std::endl;
629 GetParLimits(i,parmin,parmax);
630 out<<" "<<GetName()<<"->SetParLimits("<<i<<","<<parmin<<","<<parmax<<");"<<std::endl;
631 }
632 out<<" "<<GetName()<<"->Draw("
633 <<quote<<option<<quote<<");"<<std::endl;
634}
635
636////////////////////////////////////////////////////////////////////////////////
637/// Set the function clipping box (for drawing) "on" and define the clipping box.
638/// xclip, yclip and zclip is a point within the function range. All the
639/// function values having x<=xclip and y<=yclip and z>=zclip are clipped.
640
642{
644 fClipBox[0] = xclip;
645 fClipBox[1] = yclip;
646 fClipBox[2] = zclip;
647}
648
649////////////////////////////////////////////////////////////////////////////////
650/// Set the number of points used to draw the function
651///
652/// The default number of points along x is 30 for 2-d/3-d functions.
653/// You can increase this value to get a better resolution when drawing
654/// pictures with sharp peaks or to get a better result when using TF3::GetRandom2
655/// the minimum number of points is 4, the maximum is 10000 for 2-d/3-d functions
656
658{
659 if (npz < 4) {
660 Warning("SetNpz","Number of points must be >=4 && <= 10000, fNpz set to 4");
661 fNpz = 4;
662 } else if(npz > 10000) {
663 Warning("SetNpz","Number of points must be >=4 && <= 10000, fNpz set to 10000");
664 fNpz = 10000;
665 } else {
666 fNpz = npz;
667 }
668 Update();
669}
670
671////////////////////////////////////////////////////////////////////////////////
672/// Initialize the upper and lower bounds to draw the function
673
675{
676 fXmin = xmin;
677 fXmax = xmax;
678 fYmin = ymin;
679 fYmax = ymax;
680 fZmin = zmin;
681 fZmax = zmax;
682 Update();
683}
684
685////////////////////////////////////////////////////////////////////////////////
686/// Stream an object of class TF3.
687
688void TF3::Streamer(TBuffer &R__b)
689{
690 if (R__b.IsReading()) {
691 UInt_t R__s, R__c;
692 Version_t R__v = R__b.ReadVersion(&R__s, &R__c);
693 if (R__v > 0) {
694 R__b.ReadClassBuffer(TF3::Class(), this, R__v, R__s, R__c);
695 return;
696 }
697
698 } else {
699 Int_t saved = 0;
700 if (fType != EFType::kFormula && fSave.empty() ) { saved = 1; Save(fXmin,fXmax,fYmin,fYmax,fZmin,fZmax);}
701
702 R__b.WriteClassBuffer(TF3::Class(),this);
703
704 if (saved) { fSave.clear(); }
705 }
706}
707
708////////////////////////////////////////////////////////////////////////////////
709/// Return x^nx * y^ny * z^nz moment of a 3d function in range [ax,bx],[ay,by],[az,bz]
710/// \author Gene Van Buren <gene@bnl.gov>
711
713{
714 Double_t norm = Integral(ax,bx,ay,by,az,bz,epsilon);
715 if (norm == 0) {
716 Error("Moment3", "Integral zero over range");
717 return 0;
718 }
719
720 // define integrand function as a lambda : g(x,y,z)= x^(nx) * y^(ny) * z^(nz) * f(x,y,z)
721 auto integrand = [&](double *x, double *) {
722 return std::pow(x[0], nx) * std::pow(x[1], ny) * std::pow(x[2], nz) * this->EvalPar(x, nullptr);
723 };
724 // compute integral of g(x,y,z)
725 TF3 fnc("TF3_ExpValHelper", integrand, ax, bx, ay, by, az, bz, 0);
726 // set same points as current function to get correct max points when computing the integral
727 fnc.fNpx = fNpx;
728 fnc.fNpy = fNpy;
729 fnc.fNpz = fNpz;
730 return fnc.Integral(ax, bx, ay, by, az, bz, epsilon) / norm;
731}
732
733////////////////////////////////////////////////////////////////////////////////
734/// Return x^nx * y^ny * z^nz central moment of a 3d function in range [ax,bx],[ay,by],[az,bz]
735/// \author Gene Van Buren <gene@bnl.gov>
736
738{
739 Double_t norm = Integral(ax,bx,ay,by,az,bz,epsilon);
740 if (norm == 0) {
741 Error("CentralMoment3", "Integral zero over range");
742 return 0;
743 }
744
745 Double_t xbar = 0;
746 Double_t ybar = 0;
747 Double_t zbar = 0;
748 if (nx!=0) {
749 // compute first momentum in x
750 auto integrandX = [&](double *x, double *) { return x[0] * this->EvalPar(x, nullptr); };
751 TF3 fncx("TF3_ExpValHelperx", integrandX, ax, bx, ay, by, az, bz, 0);
752 fncx.fNpx = fNpx;
753 fncx.fNpy = fNpy;
754 fncx.fNpz = fNpz;
755 xbar = fncx.Integral(ax, bx, ay, by, az, bz, epsilon) / norm;
756 }
757 if (ny!=0) {
758 auto integrandY = [&](double *x, double *) { return x[1] * this->EvalPar(x, nullptr); };
759 TF3 fncy("TF3_ExpValHelpery", integrandY, ax, bx, ay, by, az, bz, 0);
760 fncy.fNpx = fNpx;
761 fncy.fNpy = fNpy;
762 fncy.fNpz = fNpz;
763 ybar = fncy.Integral(ax,bx,ay,by,az,bz,epsilon)/norm;
764 }
765 if (nz!=0) {
766 auto integrandZ = [&](double *x, double *) { return x[2] * this->EvalPar(x, nullptr); };
767 TF3 fncz("TF3_ExpValHelperz", integrandZ, ax, bx, ay, by, az, bz, 0);
768 fncz.fNpx = fNpx;
769 fncz.fNpy = fNpy;
770 fncz.fNpz = fNpz;
771 zbar = fncz.Integral(ax,bx,ay,by,az,bz,epsilon)/norm;
772 }
773 // define integrand function as a lambda : g(x,y)= (x-xbar)^(nx) * (y-ybar)^(ny) * f(x,y)
774 auto integrand = [&](double *x, double *) {
775 double xxx = (nx != 0) ? std::pow(x[0] - xbar, nx) : 1.;
776 double yyy = (ny != 0) ? std::pow(x[1] - ybar, ny) : 1.;
777 double zzz = (nz != 0) ? std::pow(x[2] - zbar, nz) : 1.;
778 return xxx * yyy * zzz * this->EvalPar(x, nullptr);
779 };
780 // compute integral of g(x,y, z)
781 TF3 fnc("TF3_ExpValHelper",integrand,ax,bx,ay,by,az,bz,0) ;
782 fnc.fNpx = fNpx;
783 fnc.fNpy = fNpy;
784 fnc.fNpz = fNpz;
785 return fnc.Integral(ax,bx,ay,by,az,bz,epsilon)/norm;
786}
int Int_t
Definition: CPyCppyy.h:43
unsigned int UInt_t
Definition: CPyCppyy.h:44
void Class()
Definition: Class.C:29
ROOT::R::TRInterface & r
Definition: Object.C:4
#define b(i)
Definition: RSha256.hxx:100
#define f(i)
Definition: RSha256.hxx:104
#define h(i)
Definition: RSha256.hxx:106
const Ssiz_t kNPOS
Definition: RtypesCore.h:124
short Version_t
Definition: RtypesCore.h:65
const Bool_t kFALSE
Definition: RtypesCore.h:101
bool Bool_t
Definition: RtypesCore.h:63
double Double_t
Definition: RtypesCore.h:59
const Bool_t kTRUE
Definition: RtypesCore.h:100
const char Option_t
Definition: RtypesCore.h:66
#define ClassImp(name)
Definition: Rtypes.h:364
float xmin
Definition: THbookFile.cxx:95
float ymin
Definition: THbookFile.cxx:95
float xmax
Definition: THbookFile.cxx:95
float ymax
Definition: THbookFile.cxx:95
double pow(double, double)
Int_t gDebug
Definition: TROOT.cxx:589
#define gROOT
Definition: TROOT.h:404
R__EXTERN TRandom * gRandom
Definition: TRandom.h:62
#define gPad
Definition: TVirtualPad.h:287
Param Functor class for Multidimensional functions.
Definition: ParamFunctor.h:273
virtual Color_t GetFillColor() const
Return the fill area color.
Definition: TAttFill.h:30
virtual Color_t GetLineColor() const
Return the line color.
Definition: TAttLine.h:33
Buffer base class used for serializing objects.
Definition: TBuffer.h:43
virtual Int_t ReadClassBuffer(const TClass *cl, void *pointer, const TClass *onfile_class=0)=0
virtual Version_t ReadVersion(UInt_t *start=0, UInt_t *bcnt=0, const TClass *cl=0)=0
Bool_t IsReading() const
Definition: TBuffer.h:86
virtual Int_t WriteClassBuffer(const TClass *cl, void *pointer)=0
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:2127
Int_t fNdim
Function dimension.
Definition: TF1.h:246
virtual void GetParLimits(Int_t ipar, Double_t &parmin, Double_t &parmax) const
Return limits for parameter ipar.
Definition: TF1.cxx:1936
virtual Double_t GetParError(Int_t ipar) const
Return value of parameter number ipar.
Definition: TF1.cxx:1926
Double_t GetChisquare() const
Definition: TF1.h:444
Double_t fXmin
Lower bounds for the range.
Definition: TF1.h:243
std::unique_ptr< TMethodCall > fMethodCall
! Pointer to MethodCall in case of interpreted function
Definition: TF1.h:264
virtual void Update()
Called by functions such as SetRange, SetNpx, SetParameters to force the deletion of the associated h...
Definition: TF1.cxx:3630
virtual Int_t GetNpar() const
Definition: TF1.h:481
TH1 * fHistogram
! Pointer to histogram used for visualisation
Definition: TF1.h:263
virtual Int_t DistancetoPrimitive(Int_t px, Int_t py)
Compute distance from point px,py to a function.
Definition: TF1.cxx:1288
virtual Double_t EvalPar(const Double_t *x, const Double_t *params=0)
Evaluate function with given coordinates and parameters.
Definition: TF1.cxx:1469
virtual void InitArgs(const Double_t *x, const Double_t *params)
Initialize parameters addresses.
Definition: TF1.cxx:2473
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:2841
EFType fType
Definition: TF1.h:248
Int_t fNpx
Number of points used for the graphical representation.
Definition: TF1.h:247
std::vector< Double_t > fSave
Array of fNsave function values.
Definition: TF1.h:257
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:1719
virtual Double_t * GetParameters() const
Definition: TF1.h:520
std::vector< Double_t > fIntegral
! Integral of function binned on fNpx bins
Definition: TF1.h:258
Double_t fXmax
Upper bounds for the range.
Definition: TF1.h:244
virtual Int_t GetNdim() const
Definition: TF1.h:485
virtual Double_t GetParameter(Int_t ipar) const
Definition: TF1.h:512
virtual void ExecuteEvent(Int_t event, Int_t px, Int_t py)
Execute action corresponding to one event.
Definition: TF1.cxx:1537
A 2-Dim function with parameters.
Definition: TF2.h:29
Int_t fNpy
Number of points along y used for the graphical representation.
Definition: TF2.h:34
Double_t fYmax
Upper bound for the range in y.
Definition: TF2.h:33
Double_t fYmin
Lower bound for the range in y.
Definition: TF2.h:32
virtual void Copy(TObject &f2) const
Copy this F2 to a new F2.
Definition: TF2.cxx:192
A 3-Dim function with parameters.
Definition: TF3.h:28
TF3()
F3 default constructor.
Definition: TF3.cxx:37
Int_t GetNpz() const
Definition: TF3.h:93
virtual void GetRandom3(Double_t &xrandom, Double_t &yrandom, Double_t &zrandom, TRandom *rng=nullptr)
Return 3 random numbers following this function shape.
Definition: TF3.cxx:325
virtual void SavePrimitive(std::ostream &out, Option_t *option="")
Save primitive as a C++ statement(s) on output stream out.
Definition: TF3.cxx:590
Double_t fZmin
Lower bound for the range in z.
Definition: TF3.h:31
TF3 & operator=(const TF3 &rhs)
Operator =.
Definition: TF3.cxx:127
virtual void SetNpz(Int_t npz=30)
Set the number of points used to draw the function.
Definition: TF3.cxx:657
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:297
virtual void SetRange(Double_t xmin, Double_t xmax)
Initialize the upper and lower bounds to draw the function.
Definition: TF3.h:145
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],...
Definition: TF3.cxx:737
virtual Double_t FindMinMax(Double_t *x, bool findmax) const
Return minimum/maximum value of the function.
Definition: TF3.cxx:213
virtual void ExecuteEvent(Int_t event, Int_t px, Int_t py)
Execute action corresponding to one event.
Definition: TF3.cxx:192
Bool_t fClipBoxOn
! Is clip box on
Definition: TF3.h:34
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:281
virtual void Paint(Option_t *option="")
Paint this 3-D function with its current attributes.
Definition: TF3.cxx:501
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:535
virtual Double_t GetSave(const Double_t *x)
Get value corresponding to X in array of fSave values.
Definition: TF3.cxx:398
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:712
Int_t fNpz
Number of points along z used for the graphical representation.
Definition: TF3.h:33
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:641
virtual void Copy(TObject &f3) const
Copy this F3 to a new F3.
Definition: TF3.cxx:153
virtual void SetClippingBoxOff()
Set the function clipping box (for drawing) "off".
Definition: TF3.cxx:526
virtual Bool_t IsInside(const Double_t *x) const
Return kTRUE is the point is inside the function range.
Definition: TF3.cxx:478
Double_t fZmax
Upper bound for the range in z.
Definition: TF3.h:32
virtual ~TF3()
F3 default destructor.
Definition: TF3.cxx:138
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:452
virtual void Draw(Option_t *option="")
Draw this function with its current attributes.
Definition: TF3.cxx:177
virtual void GetRange(Double_t &xmin, Double_t &xmax) const
Return range of a 1-D function.
Definition: TF3.h:141
virtual Int_t DistancetoPrimitive(Int_t px, Int_t py)
Compute distance from point px,py to a function.
Definition: TF3.cxx:168
virtual TH1 * CreateHistogram()
Create a histogram for axis range.
Definition: TF3.cxx:489
Double_t fClipBox[3]
! Coordinates of clipbox
Definition: TF3.h:35
TH1 is the base class of all histogram classes in ROOT.
Definition: TH1.h:58
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:8779
TVirtualHistPainter * GetPainter(Option_t *option="")
Return pointer to painter.
Definition: TH1.cxx:4452
virtual void Paint(Option_t *option="")
Control routine to paint any kind of histograms.
Definition: TH1.cxx:6156
3-D histogram with a float per channel (see TH1 documentation)}
Definition: TH3.h:268
virtual const char * GetName() const
Returns name of object.
Definition: TNamed.h:47
virtual const char * GetTitle() const
Returns title of object.
Definition: TNamed.h:48
Mother of all ROOT objects.
Definition: TObject.h:37
virtual void Warning(const char *method, const char *msgfmt,...) const
Issue warning message.
Definition: TObject.cxx:879
virtual void AppendPad(Option_t *option="")
Append graphics object to current pad.
Definition: TObject.cxx:107
virtual void Error(const char *method, const char *msgfmt,...) const
Issue error message.
Definition: TObject.cxx:893
void MakeZombie()
Definition: TObject.h:49
virtual void Info(const char *method, const char *msgfmt,...) const
Issue info message.
Definition: TObject.cxx:867
This is the base class for the ROOT Random number generators.
Definition: TRandom.h:27
virtual Double_t Rndm()
Machine independent random number generator.
Definition: TRandom.cxx:552
Basic string class.
Definition: TString.h:136
void ToLower()
Change string to lower-case.
Definition: TString.cxx:1150
const char * Data() const
Definition: TString.h:369
TString & Append(const char *cs)
Definition: TString.h:564
Bool_t Contains(const char *pat, ECaseCompare cmp=kExact) const
Definition: TString.h:624
Ssiz_t Index(const char *pat, Ssiz_t i=0, ECaseCompare cmp=kExact) const
Definition: TString.h:639
virtual void ProcessMessage(const char *mess, const TObject *obj)=0
Double_t y[n]
Definition: legend1.C:17
Double_t x[n]
Definition: legend1.C:17
const Int_t n
Definition: legend1.C:16
static const std::string name("name")
Short_t Max(Short_t a, Short_t b)
Definition: TMathBase.h:212
Double_t QuietNaN()
Returns a quiet NaN as defined by IEEE 754
Definition: TMath.h:901
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:771
Short_t Min(Short_t a, Short_t b)
Definition: TMathBase.h:180
Long64_t BinarySearch(Long64_t n, const T *array, T value)
Definition: TMathBase.h:278
Double_t Infinity()
Returns an infinity as defined by the IEEE standard.
Definition: TMath.h:914
auto * tt
Definition: textangle.C:16
auto * l
Definition: textangle.C:4
auto * a
Definition: textangle.C:12
REAL epsilon
Definition: triangle.c:618