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Reference Guide
MnFunctionCross.cxx
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1 // @(#)root/minuit2:$Id$
2 // Authors: M. Winkler, F. James, L. Moneta, A. Zsenei 2003-2005
3 
4 /**********************************************************************
5  * *
6  * Copyright (c) 2005 LCG ROOT Math team, CERN/PH-SFT *
7  * *
8  **********************************************************************/
9 
10 #include "Minuit2/MnFunctionCross.h"
11 #include "Minuit2/FunctionMinimum.h"
12 #include "Minuit2/MnMigrad.h"
13 #include "Minuit2/FCNBase.h"
14 #include "Minuit2/MnParabola.h"
15 #include "Minuit2/MnParabolaPoint.h"
16 #include "Minuit2/MnParabolaFactory.h"
17 #include "Minuit2/MnCross.h"
18 #include "Minuit2/MnMachinePrecision.h"
19 
20 //#define DEBUG
21 #include "Minuit2/MnPrint.h"
22 
23 
24 namespace ROOT {
25 
26  namespace Minuit2 {
27 
28 
29 
30 MnCross MnFunctionCross::operator()(const std::vector<unsigned int>& par, const std::vector<double>& pmid,
31  const std::vector<double>& pdir, double tlr, unsigned int maxcalls) const {
32  // evaluate crossing point where function is equal to MIN + UP,
33  // with direction pdir from values pmid
34  // tlr indicate tolerance and maxcalls maximum number of calls
35 
36 // double edmmax = 0.5*0.001*toler*fFCN.Up();
37 
38 
39  unsigned int npar = par.size();
40  unsigned int nfcn = 0;
41  const MnMachinePrecision& prec = fState.Precision();
42  // tolerance used when calling Migrad
43  double mgr_tlr = 0.5 * tlr; // to be consistent with F77 version (for default values of tlr which is 0.1)
44  // other olerance values are fixed at 0.01
45  tlr = 0.01;
46  // convergence when F is within tlf of aim and next prediction
47  // of aopt is within tla of previous value of aopt
48  double up = fFCN.Up();
49  // for finding the point :
50  double tlf = tlr*up;
51  double tla = tlr;
52  unsigned int maxitr = 15;
53  unsigned int ipt = 0;
54  double aminsv = fFval;
55  double aim = aminsv + up;
56  //std::cout<<"aim= "<<aim<<std::endl;
57  double aopt = 0.;
58  bool limset = false;
59  std::vector<double> alsb(3, 0.), flsb(3, 0.);
60 
61  int printLevel = MnPrint::Level();
62 #ifdef DEBUG
63  printLevel = 3;
64 #endif
65 
66 #ifdef DEBUG
67  for (unsigned int i = 0; i < par.size(); ++i)
68  std::cout << "MnFunctionCross for parameter " << par[i] << " value " << pmid[i] << " dir " << pdir[i]
69  << " function min = " << aminsv << " contur value aim = (fmin + up) = " << aim << std::endl;
70 #endif
71 
72 
73  // find the largest allowed aulim
74 
75  double aulim = 100.;
76  for(unsigned int i = 0; i < par.size(); i++) {
77  unsigned int kex = par[i];
78  if(fState.Parameter(kex).HasLimits()) {
79  double zmid = pmid[i];
80  double zdir = pdir[i];
81  // double zlim = 0.;
82  if(zdir > 0. && fState.Parameter(kex).HasUpperLimit()) {
83  double zlim = fState.Parameter(kex).UpperLimit();
84  if (fabs(zdir) < fState.Precision().Eps()) {
85  // we have a limit
86  if (fabs(zlim-zmid) < fState.Precision().Eps() ) limset = true;
87  continue;
88  }
89  aulim = std::min(aulim, (zlim-zmid)/zdir);
90  }
91  else if(zdir < 0. && fState.Parameter(kex).HasLowerLimit()) {
92  double zlim = fState.Parameter(kex).LowerLimit();
93  if (fabs(zdir) < fState.Precision().Eps()) {
94  // we have a limit
95  if (fabs(zlim-zmid) < fState.Precision().Eps() ) limset = true;
96  continue;
97  }
98  aulim = std::min(aulim, (zlim-zmid)/zdir);
99  }
100  }
101  }
102 
103 #ifdef DEBUG
104  std::cout<<"Largest allowed aulim "<< aulim << std::endl;
105 #endif
106 
107 
108  // case of a single parameter and we are at limit
109  if (limset && npar == 1) {
110  if (printLevel > 1)
111  std::cout << "MnFunctionCross: parameter is at limit " << pmid[0] << " delta "
112  << pdir[0] << std::endl;
113  return MnCross(fState, nfcn, MnCross::CrossParLimit());
114  }
115 
116  if (aulim < aopt + tla)
117  limset = true;
118 
119  MnMigrad migrad(fFCN, fState, MnStrategy(std::max(0, int(fStrategy.Strategy()-1))));
120 
121  if (printLevel > 2) {
122  std::cout << "MnFunctionCross: Run Migrad fixing parameters :";
123  if (npar > 1) std::cout << std::endl;
124  }
125  for (unsigned int i = 0; i < npar; i++) {
126 
127  migrad.SetValue(par[i], pmid[i]);
128 
129  if (printLevel > 2) {
130  std::cout << "\t" << fState.Name(par[i]) << " #" << par[i] << " to " << pmid[i] << std::endl;
131  }
132  }
133  // find minimum with respect all the other parameters (n- npar) (npar are the fixed ones)
134 
135  FunctionMinimum min0 = migrad(maxcalls, mgr_tlr);
136  nfcn += min0.NFcn();
137 
138  if (printLevel > 2) {
139  MnPrint::PrintState(std::cout, min0.State(), "MnFunctionCross: Result after Migrad");
140  std::cout << min0.UserState().Parameters() << std::endl;
141  }
142 
143  // case a new minimum is found
144  if (min0.Fval() < fFval - tlf) {
145  // case of new minimum is found
146  if (printLevel > 1) {
147  std::cout << "MnFunctionCross: A new minimum is found when scanning parameter " << par.front() << " new value = "
148  << min0.Fval() << " old value : " << fFval << std::endl;
149  }
150  return MnCross(min0.UserState(), nfcn, MnCross::CrossNewMin());
151  }
152  if(min0.HasReachedCallLimit())
153  return MnCross(min0.UserState(), nfcn, MnCross::CrossFcnLimit());
154  if(!min0.IsValid()) return MnCross(fState, nfcn);
155  if(limset == true && min0.Fval() < aim)
156  return MnCross(min0.UserState(), nfcn, MnCross::CrossParLimit());
157 
158  ipt++;
159  alsb[0] = 0.;
160  flsb[0] = min0.Fval();
161  flsb[0] = std::max(flsb[0], aminsv + 0.1*up);
162  aopt = sqrt(up/(flsb[0]-aminsv)) - 1.;
163  if(fabs(flsb[0] - aim) < tlf) return MnCross(aopt, min0.UserState(), nfcn);
164 
165  if(aopt > 1.) aopt = 1.;
166  if(aopt < -0.5) aopt = -0.5;
167  limset = false;
168  if(aopt > aulim) {
169  aopt = aulim;
170  limset = true;
171  }
172 #ifdef DEBUG
173  std::cout << "MnFunctionCross: flsb[0] = " << flsb[0] << " aopt = " << aopt << std::endl;
174 #endif
175 
176  if (printLevel > 2) {
177  std::cout << "MnFunctionCross: Run Migrad again (#2) : ";
178  if (npar > 1) std::cout << std::endl;
179  }
180  for (unsigned int i = 0; i < npar; i++) {
181  migrad.SetValue(par[i], pmid[i] + (aopt)*pdir[i]);
182  if (printLevel > 2) {
183  std::cout << "\t - parameter " << i << " fixed to " << pmid[i] + (aopt)*pdir[i] << std::endl;
184  }
185  }
186 
187  FunctionMinimum min1 = migrad(maxcalls, mgr_tlr);
188  nfcn += min1.NFcn();
189 
190  if (printLevel > 2) {
191  MnPrint::PrintState(std::cout, min1.State(), "MnFunctionCross: Result after 2nd Migrad");
192  std::cout << min1.UserState().Parameters() << std::endl;
193  }
194 
195  if (min1.Fval() < fFval - tlf) // case of new minimum found
196  return MnCross(min1.UserState(), nfcn, MnCross::CrossNewMin());
197  if(min1.HasReachedCallLimit())
198  return MnCross(min1.UserState(), nfcn, MnCross::CrossFcnLimit());
199  if(!min1.IsValid()) return MnCross(fState, nfcn);
200  if(limset == true && min1.Fval() < aim)
201  return MnCross(min1.UserState(), nfcn, MnCross::CrossParLimit());
202 
203  ipt++;
204  alsb[1] = aopt;
205  flsb[1] = min1.Fval();
206  double dfda = (flsb[1] - flsb[0])/(alsb[1] - alsb[0]);
207 
208 #ifdef DEBUG
209  std::cout << "aopt = " << aopt << " min1Val = " << flsb[1] << " dfda = " << dfda << std::endl;
210 #endif
211 
212 
213 L300:
214  if(dfda < 0.) {
215  // looking for slope of the right sign
216 #ifdef DEBUG
217  std::cout << "MnFunctionCross: dfda < 0 - iterate from " << ipt << " to max of " << maxitr << std::endl;
218 #endif
219  // iterate (max times is maxitr) incrementing aopt
220 
221  unsigned int maxlk = maxitr - ipt;
222  for(unsigned int it = 0; it < maxlk; it++) {
223  alsb[0] = alsb[1];
224  flsb[0] = flsb[1];
225  // LM: Add + 1, looking at Fortran code it starts from 1 ( see bug #8396)
226  aopt = alsb[0] + 0.2*(it+1);
227  limset = false;
228  if(aopt > aulim) {
229  aopt = aulim;
230  limset = true;
231  }
232  if (printLevel > 2) {
233  std::cout << "MnFunctionCross: Run Migrad again (iteration " << it << " ) : ";
234  if (npar > 1) std::cout << std::endl;
235  }
236  for(unsigned int i = 0; i < npar; i++) {
237  migrad.SetValue(par[i], pmid[i] + (aopt)*pdir[i]);
238  if (printLevel > 2) {
239  std::cout << "\t - parameter " << i << " fixed to " << pmid[i] + (aopt)*pdir[i] << std::endl;
240  }
241  }
242  min1 = migrad(maxcalls, mgr_tlr);
243  nfcn += min1.NFcn();
244 
245  if (printLevel > 2) {
246  MnPrint::PrintState(std::cout, min1.State(), "MnFunctionCross: Result after Migrad");
247  std::cout << min1.UserState().Parameters() << std::endl;
248  }
249 
250  if (min1.Fval() < fFval - tlf) // case of new minimum found
251  return MnCross(min1.UserState(), nfcn, MnCross::CrossNewMin());
252  if(min1.HasReachedCallLimit())
253  return MnCross(min1.UserState(), nfcn, MnCross::CrossFcnLimit());
254  if(!min1.IsValid()) return MnCross(fState, nfcn);
255  if(limset == true && min1.Fval() < aim)
256  return MnCross(min1.UserState(), nfcn, MnCross::CrossParLimit());
257  ipt++;
258  alsb[1] = aopt;
259  flsb[1] = min1.Fval();
260  dfda = (flsb[1] - flsb[0])/(alsb[1] - alsb[0]);
261  // if(dfda > 0.) goto L460;
262 
263 #ifdef DEBUG
264  std::cout << "aopt = " << aopt << " min1Val = " << flsb[1] << " dfda = " << dfda << std::endl;
265 #endif
266 
267  if(dfda > 0.) break;
268  }
269  if(ipt > maxitr) return MnCross(fState, nfcn);
270  } //if(dfda < 0.)
271 
272 L460:
273 
274  // dfda > 0: we have two points with the right slope
275 
276  aopt = alsb[1] + (aim-flsb[1])/dfda;
277 
278 #ifdef DEBUG
279  std::cout << "MnFunctionCross: dfda > 0 : aopt = " << aopt << std::endl;
280 #endif
281 
282  double fdist = std::min(fabs(aim - flsb[0]), fabs(aim - flsb[1]));
283  double adist = std::min(fabs(aopt - alsb[0]), fabs(aopt - alsb[1]));
284  tla = tlr;
285  if(fabs(aopt) > 1.) tla = tlr*fabs(aopt);
286  if(adist < tla && fdist < tlf) return MnCross(aopt, min1.UserState(), nfcn);
287  if(ipt > maxitr) return MnCross(fState, nfcn);
288  double bmin = std::min(alsb[0], alsb[1]) - 1.;
289  if(aopt < bmin) aopt = bmin;
290  double bmax = std::max(alsb[0], alsb[1]) + 1.;
291  if(aopt > bmax) aopt = bmax;
292 
293  limset = false;
294  if(aopt > aulim) {
295  aopt = aulim;
296  limset = true;
297  }
298 
299  if (printLevel > 2) {
300  std::cout << "MnFunctionCross: Run Migrad again (#3) : ";
301  if (npar > 1) std::cout << std::endl;
302  }
303  for(unsigned int i = 0; i < npar; i++) {
304  migrad.SetValue(par[i], pmid[i] + (aopt)*pdir[i]);
305  if (printLevel > 2) {
306  std::cout << "\t : parameter " << i << " fixed to " << pmid[i] + (aopt)*pdir[i] << std::endl;
307  }
308  }
309  FunctionMinimum min2 = migrad(maxcalls, mgr_tlr);
310  nfcn += min2.NFcn();
311 
312  if (printLevel > 2) {
313  MnPrint::PrintState(std::cout, min2.State(), "MnFunctionCross: Result after Migrad (#3): ");
314  std::cout << min2.UserState().Parameters() << std::endl;
315  }
316 
317  if (min2.Fval() < fFval - tlf) // case of new minimum found
318  return MnCross(min2.UserState(), nfcn, MnCross::CrossNewMin());
319  if(min2.HasReachedCallLimit())
320  return MnCross(min2.UserState(), nfcn, MnCross::CrossFcnLimit());
321  if(!min2.IsValid()) return MnCross(fState, nfcn);
322  if(limset == true && min2.Fval() < aim)
323  return MnCross(min2.UserState(), nfcn, MnCross::CrossParLimit());
324 
325  ipt++;
326  alsb[2] = aopt;
327  flsb[2] = min2.Fval();
328 
329  // now we have three points, ask how many < AIM
330 
331  double ecarmn = fabs(flsb[2] - aim);
332  double ecarmx = 0.;
333  unsigned int ibest = 2;
334  unsigned int iworst = 0;
335  unsigned int noless = 0;
336 
337  for(unsigned int i = 0; i < 3; i++) {
338  double ecart = fabs(flsb[i] - aim);
339  if(ecart > ecarmx) {
340  ecarmx = ecart;
341  iworst = i;
342  }
343  if(ecart < ecarmn) {
344  ecarmn = ecart;
345  ibest = i;
346  }
347  if(flsb[i] < aim) noless++;
348  }
349 
350 #ifdef DEBUG
351  std::cout << "MnFunctionCross: have three points : nless < aim = " << noless << " ibest = " << ibest << " iworst = " << iworst << std::endl;
352 #endif
353 
354  //std::cout<<"480"<<std::endl;
355 
356  // at least one on each side of AIM (contour), fit a parabola
357  if(noless == 1 || noless == 2) goto L500;
358  // if all three are above AIM, third point must be the closest to AIM, return it
359  if(noless == 0 && ibest != 2) return MnCross(fState, nfcn);
360  // if all three below and third is not best then the slope has again gone negative,
361  // re-iterate and look for positive slope
362  if(noless == 3 && ibest != 2) {
363  alsb[1] = alsb[2];
364  flsb[1] = flsb[2];
365 #ifdef DEBUG
366  std::cout << "MnFunctionCross: all three points below - look again fir positive slope " << std::endl;
367 #endif
368  goto L300;
369  }
370 
371  // in other case new straight line thru first two points
372 
373  flsb[iworst] = flsb[2];
374  alsb[iworst] = alsb[2];
375  dfda = (flsb[1] - flsb[0])/(alsb[1] - alsb[0]);
376 #ifdef DEBUG
377  std::cout << "MnFunctionCross: new straight line using point 1-2 - dfda = " << dfda << std::endl;
378 #endif
379  goto L460;
380 
381 L500:
382 
383  do {
384  // do parabola fit
385  MnParabola parbol = MnParabolaFactory()(MnParabolaPoint(alsb[0], flsb[0]), MnParabolaPoint(alsb[1], flsb[1]), MnParabolaPoint(alsb[2], flsb[2]));
386  // aopt = parbol.X_pos(aim);
387  //std::cout<<"alsb1,2,3= "<<alsb[0]<<", "<<alsb[1]<<", "<<alsb[2]<<std::endl;
388  //std::cout<<"flsb1,2,3= "<<flsb[0]<<", "<<flsb[1]<<", "<<flsb[2]<<std::endl;
389 
390 #ifdef DEBUG
391  std::cout << "MnFunctionCross: parabola fit: iteration " << ipt << std::endl;
392 #endif
393 
394  double coeff1 = parbol.C();
395  double coeff2 = parbol.B();
396  double coeff3 = parbol.A();
397  double determ = coeff2*coeff2 - 4.*coeff3*(coeff1 - aim);
398 
399 #ifdef DEBUG
400  std::cout << "MnFunctionCross: parabola fit: a = " << coeff3 << " b = "
401  << coeff2 << " c = " << coeff1 << " determ = " << determ << std::endl;
402 #endif
403  // curvature is negative
404  if(determ < prec.Eps()) return MnCross(fState, nfcn);
405  double rt = sqrt(determ);
406  double x1 = (-coeff2 + rt)/(2.*coeff3);
407  double x2 = (-coeff2 - rt)/(2.*coeff3);
408  double s1 = coeff2 + 2.*x1*coeff3;
409  double s2 = coeff2 + 2.*x2*coeff3;
410 
411 #ifdef DEBUG
412  std::cout << "MnFunctionCross: parabola fit: x1 = " << x1 << " x2 = "
413  << x2 << " s1 = " << s1 << " s2 = " << s2 << std::endl;
414 #endif
415 
416 #ifdef WARNINGMSG
417  if(s1*s2 > 0.) MN_INFO_MSG("MnFunctionCross problem 1");
418 #endif
419  // find with root is the right one
420  aopt = x1;
421  double slope = s1;
422  if(s2 > 0.) {
423  aopt = x2;
424  slope = s2;
425  }
426 #ifdef DEBUG
427  std::cout << "MnFunctionCross: parabola fit: aopt = " << aopt << " slope = "
428  << slope << std::endl;
429 #endif
430 
431  // ask if converged
432  tla = tlr;
433  if(fabs(aopt) > 1.) tla = tlr*fabs(aopt);
434 
435 #ifdef DEBUG
436  std::cout << "MnFunctionCross: Delta(aopt) = " << fabs(aopt - alsb[ibest]) << " tla = "
437  << tla << "Delta(F) = " << fabs(flsb[ibest] - aim) << " tlf = " << tlf << std::endl;
438 #endif
439 
440 
441  if(fabs(aopt - alsb[ibest]) < tla && fabs(flsb[ibest] - aim) < tlf)
442  return MnCross(aopt, min2.UserState(), nfcn);
443 
444  // if(ipt > maxitr) return MnCross();
445 
446  // see if proposed point is in acceptable zone between L and R
447  // first find ileft, iright, iout and ibest
448 
449  unsigned int ileft = 3;
450  unsigned int iright = 3;
451  unsigned int iout = 3;
452  ibest = 0;
453  ecarmx = 0.;
454  ecarmn = fabs(aim-flsb[0]);
455  for(unsigned int i = 0; i < 3; i++) {
456  double ecart = fabs(flsb[i] - aim);
457  if(ecart < ecarmn) {
458  ecarmn = ecart;
459  ibest = i;
460  }
461  if(ecart > ecarmx) ecarmx = ecart;
462  if(flsb[i] > aim) {
463  if(iright == 3) iright = i;
464  else if(flsb[i] > flsb[iright]) iout = i;
465  else {
466  iout = iright;
467  iright = i;
468  }
469  } else if(ileft == 3) ileft = i;
470  else if(flsb[i] < flsb[ileft]) iout = i;
471  else {
472  iout = ileft;
473  ileft = i;
474  }
475  }
476 
477 #ifdef DEBUG
478  std::cout << "MnFunctionCross: ileft = " << ileft << " iright = "
479  << iright << " iout = " << iout << " ibest = " << ibest << std::endl;
480 #endif
481 
482  // avoid keeping a bad point nest time around
483 
484  if(ecarmx > 10.*fabs(flsb[iout] - aim))
485  aopt = 0.5*(aopt + 0.5*(alsb[iright] + alsb[ileft]));
486 
487  // knowing ileft and iright, get acceptable window
488  double smalla = 0.1*tla;
489  if(slope*smalla > tlf) smalla = tlf/slope;
490  double aleft = alsb[ileft] + smalla;
491  double aright = alsb[iright] - smalla;
492 
493  // move proposed point AOPT into window if necessary
494  if(aopt < aleft) aopt = aleft;
495  if(aopt > aright) aopt = aright;
496  if(aleft > aright) aopt = 0.5*(aleft + aright);
497 
498  // see if proposed point outside limits (should be impossible)
499  limset = false;
500  if(aopt > aulim) {
501  aopt = aulim;
502  limset = true;
503  }
504 
505  // evaluate at new point aopt
506  if (printLevel > 2) {
507  std::cout << "MnFunctionCross: Run Migrad again at new point (#iter = " << ipt << " ): ";
508  if (npar > 1) std::cout << std::endl;
509  }
510  for(unsigned int i = 0; i < npar; i++) {
511  migrad.SetValue(par[i], pmid[i] + (aopt)*pdir[i]);
512  if (printLevel > 2) {
513  std::cout << "\t : parameter " << i << " fixed to " << pmid[i] + (aopt)*pdir[i] << std::endl;
514  }
515  }
516  min2 = migrad(maxcalls, mgr_tlr);
517  nfcn += min2.NFcn();
518 
519  if (printLevel > 2) {
520  MnPrint::PrintState(std::cout, min2.State(), "MnFunctionCross: Result after new Migrad : ");
521  std::cout << min2.UserState().Parameters() << std::endl;
522  }
523 
524  if (min2.Fval() < fFval - tlf) // case of new minimum found
525  return MnCross(min2.UserState(), nfcn, MnCross::CrossNewMin());
526  if(min2.HasReachedCallLimit())
527  return MnCross(min2.UserState(), nfcn, MnCross::CrossFcnLimit());
528  if(!min2.IsValid()) return MnCross(fState, nfcn);
529  if(limset == true && min2.Fval() < aim)
530  return MnCross(min2.UserState(), nfcn, MnCross::CrossParLimit());
531 
532  ipt++;
533  // replace odd point with new one (which is the best of three)
534  alsb[iout] = aopt;
535  flsb[iout] = min2.Fval();
536  ibest = iout;
537  } while(ipt < maxitr);
538 
539  // goto L500;
540 
541  return MnCross(fState, nfcn);
542 }
543 
544  } // namespace Minuit2
545 
546 } // namespace ROOT
ROOT::Minuit2::MnStrategy::Strategy
unsigned int Strategy() const
Definition: MnStrategy.h:51
ROOT::Minuit2::MnFunctionCross::operator()
MnCross operator()(const std::vector< unsigned int > &, const std::vector< double > &, const std::vector< double > &, double, unsigned int) const
Definition: MnFunctionCross.cxx:38
MnMachinePrecision.h
ROOT::Minuit2::MinuitParameter::UpperLimit
double UpperLimit() const
Definition: MinuitParameter.h:169
FunctionMinimum.h
MnFunctionCross.h
MnMigrad.h
ROOT::Minuit2::MnPrint::Level
static int Level()
Definition: MnPrint.cxx:47
ROOT::Minuit2::MinuitParameter::HasUpperLimit
bool HasUpperLimit() const
Definition: MinuitParameter.h:167
MnCross.h
x1
static const double x1[5]
Definition: RooGaussKronrodIntegrator1D.cxx:346
ROOT::Minuit2::MnMachinePrecision::Eps
double Eps() const
eps returns the smallest possible number so that 1.+eps > 1.
Definition: MnMachinePrecision.h:53
MnParabolaPoint.h
ROOT::Math::fabs
VecExpr< UnaryOp< Fabs< T >, VecExpr< A, T, D >, T >, T, D > fabs(const VecExpr< A, T, D > &rhs)
Definition: UnaryOperators.h:131
ROOT::Minuit2::MnFunctionCross::fState
const MnUserParameterState & fState
Definition: MnFunctionCross.h:52
ROOT::Minuit2::MnUserParameterState::Name
const char * Name(unsigned int) const
Definition: MnUserParameterState.cxx:406
ROOT::Minuit2::MnFunctionCross::fFval
double fFval
Definition: MnFunctionCross.h:53
ROOT::Minuit2::MnUserParameterState::Precision
const MnMachinePrecision & Precision() const
Definition: MnUserParameterState.cxx:437
s1
#define s1(x)
Definition: RSha256.hxx:109
ROOT::Minuit2::FCNBase::Up
virtual double Up() const =0
Error definition of the function.
ROOT::Minuit2::MnMachinePrecision
Sets the relative floating point (double) arithmetic precision.
Definition: MnMachinePrecision.h:41
sqrt
double sqrt(double)
MnParabolaFactory.h
ROOT::Minuit2::MnPrint::PrintState
static void PrintState(std::ostream &os, const MinimumState &state, const char *msg, int iter=-1)
Definition: MnPrint.cxx:58
MN_INFO_MSG
#define MN_INFO_MSG(str)
Definition: MnPrint.h:111
ROOT::Minuit2::MinuitParameter::HasLimits
bool HasLimits() const
Definition: MinuitParameter.h:165
ROOT::Minuit2::MnFunctionCross::fFCN
const FCNBase & fFCN
Definition: MnFunctionCross.h:51
ROOT::Minuit2::MnUserParameterState::Parameter
const MinuitParameter & Parameter(unsigned int i) const
Definition: MnUserParameterState.cxx:207
MnParabola.h
x2
static const double x2[5]
Definition: RooGaussKronrodIntegrator1D.cxx:364
FCNBase.h
ROOT::Minuit2::MinuitParameter::LowerLimit
double LowerLimit() const
Definition: MinuitParameter.h:168
MnPrint.h
ROOT
VSD Structures.
Definition: StringConv.hxx:21
ROOT::Minuit2::MinuitParameter::HasLowerLimit
bool HasLowerLimit() const
Definition: MinuitParameter.h:166
ROOT::Minuit2::MnFunctionCross::fStrategy
const MnStrategy & fStrategy
Definition: MnFunctionCross.h:54