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TMinuit.cxx
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1// @(#)root/minuit:$Id$
2// Author: Rene Brun, Frederick James 12/08/95
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/**
13
14 \defgroup MinuitOld TMinuit
15 \ingroup Math
16
17 The Minuit Minimization package.
18 Direct C++ implementation of the Minuit minimization package.
19 This package was originally written in Fortran by Fred James
20 and part of PACKLIB (patch D506)
21 It has been converted to a C++ class, TMinuit, by R.Brun.
22*/
23
24/** \class TMinuit
25
26Implementation in C++ of the Minuit package written by Fred James.
27This is a straightforward conversion of the original Fortran version.
28
29The main changes are:
30
31 - The variables in the various Minuit labelled common blocks
32 have been changed to the TMinuit class data members.
33
34 - The internal arrays with a maximum dimension depending on the
35 maximum number of parameters are now data members arrays with
36 a dynamic dimension such that one can fit very large problems
37 by simply initialising the TMinuit constructor with the maximum
38 number of parameters.
39
40 - The include file Minuit.h has been commented as much as possible
41 using existing comments in the code or the printed documentation
42
43 - The original Minuit subroutines are now member functions.
44
45 - Constructors and destructor have been added.
46
47 - Instead of passing the FCN function in the argument
48 list, the addresses of this function is stored as pointer
49 in the data members of the class. This is by far more elegant
50 and flexible in an interactive environment.
51 The member function SetFCN can be used to define this pointer.
52
53 - The ROOT static function Printf is provided to replace all
54 format statements and to print on currently defined output file.
55 - The functions SetObjectFit(TObject * obj)/GetObjectFit() can be
56 used inside the FCN function to set/get a referenced object
57 instead of using global variables.
58
59
60## Basic concepts of MINUIT
61
62The [MINUIT](https://root.cern.ch/sites/d35c7d8c.web.cern.ch/files/minuit.pdf)
63package acts on a multiparameter Fortran function to which one
64must give the generic name <TT>FCN</TT>. In the ROOT implementation,
65the function <TT>FCN</TT> is defined via the MINUIT SetFCN member function
66when an Histogram.Fit command is invoked.
67The value of <TT>FCN</TT> will in general depend on one
68or more variable parameters.
69
70To take a simple example, in case of ROOT histograms (classes TH1C,TH1S,TH1F,TH1D)
71the Fit function defines the Minuit fitting function as being H1FitChisquare
72or H1FitLikelihood depending on the options selected.
73H1FitChisquare
74calculates the chisquare between the user fitting function (gaussian, polynomial,
75user defined,etc) and the data for given values of the parameters.
76It is the task of MINUIT to find those values of the parameters
77which give the lowest value of chisquare.
78
79### Basic concepts - The transformation for parameters with limits.
80
81For variable parameters with limits, MINUIT uses the following
82transformation:
83
84\f[
85P_{\mathrm{int}} = \arcsin
86 \left( 2\: \frac{P_{\mathrm{ext}}-a}{b-a} - 1 \right)
87P_{\mathrm{ext}} = a + \frac{b - a}{2} \left( \sin P_{\mathrm{int}} + 1 \right)
88\f]
89
90so that the internal value \f$P_{\mathrm{int}}\f$ can take on any value, while
91the external value \f$P_{\mathrm{ext}}\f$ can take on values only between the lower
92limit \f$a\f$ and the upper limit \f$b\f$.
93Since the transformation is necessarily non-linear, it would transform a
94nice linear problem into a nasty non-linear one, which is the reason why
95limits should be avoided if not necessary.
96In addition, the transformation
97does require some computer time, so it slows down the computation a little
98bit, and more importantly, it introduces additional numerical inaccuracy into
99the problem in addition to what is introduced in the numerical calculation
100of the FCN value.
101The effects of non-linearity and numerical roundoff both
102become more important as the external value gets closer to one of the limits
103(expressed as the distance to nearest limit divided by distance between limits).
104The user must therefore be aware of the fact that, for example,
105if he puts limits of \f$(0,10^{10})\f$ on a parameter, then the values \f$0.0\f$
106and \f$1.0\f$ will be indistinguishable to the accuracy of most machines.
107
108The transformation also affects the parameter error matrix, of course,
109so Minuit does a transformation of the error matrix (and the
110``parabolic'' parameter errors) when there are parameter limits.
111Users should however realize that the transformation is only a linear
112approximation, and that it cannot give a meaningful result if one or more
113parameters is very close to a limit, where
114\f$\partial P_{\mathrm{ext}} / \partial P_{\mathrm{int}} \approx 0\f$.
115Therefore, it is recommended that:
116
117 1. Limits on variable parameters should be used only when needed in order
118to prevent the parameter from taking on unphysical values.
119
120 2. When a satisfactory minimum has been found using limits, the limits
121should then be removed if possible, in order to perform or re-perform the
122error analysis without limits.
123
124
125### How to get the right answer from MINUIT.
126
127MINUIT offers the user a choice of several minimization algorithms. The
128MIGRAD algorithm is in general the best minimizer for
129nearly all functions. It is a variable-metric method with inexact line
130search, a stable metric updating scheme, and checks for
131positive-definiteness. Its main weakness is that it depends heavily on
132knowledge of the first derivatives, and fails miserably if they are very
133inaccurate.
134
135If parameter limits are needed, in spite of the side effects, then the
136user should be aware of the following techniques to alleviate problems
137caused by limits:
138
139#### Getting the right minimum with limits.
140
141If MIGRAD converges normally to a point where no parameter is near one of
142its limits, then the existence of limits has probably not prevented MINUIT
143from finding the right minimum. On the other hand, if one or more
144parameters is near its limit at the minimum, this may be because the true
145minimum is indeed at a limit, or it may be because the minimizer has
146become ``blocked'' at a limit. This may normally happen only if the
147parameter is so close to a limit (internal value at an odd multiple of
148\f$\pm \frac{\pi}{2}\f$
149that MINUIT prints a warning to this effect when it prints
150the parameter values.
151
152The minimizer can become blocked at a limit, because at a limit
153the derivative seen by the minimizer
154\f$\partial F / \partial P_{\mathrm{int}}\f$
155is zero no matter what the real derivative
156\f$\partial F / \partial P_{\mathrm{ext}}\f$ is.
157
158\f[
159\frac{\partial F}{\partial P_{\mathrm{int}}} =
160\frac{\partial F}{\partial P_{\mathrm{ext}}}
161\frac{\partial P_{\mathrm{ext}}}{\partial P_{\mathrm{int}}} =
162\frac{\partial F}{\partial P_{\mathrm{ext}}} = 0
163\f]
164
165#### Getting the right parameter errors with limits.
166
167In the best case, where the minimum is far from any limits, MINUIT will
168correctly transform the error matrix, and the parameter errors it reports
169should be accurate and very close to those you would have got without
170limits. In other cases (which should be more common, since otherwise you
171wouldn't need limits), the very meaning of parameter errors becomes
172problematic. Mathematically, since the limit is an absolute constraint on
173the parameter, a parameter at its limit has no error, at least in one
174direction. The error matrix, which can assign only symmetric errors, then
175becomes essentially meaningless.
176
177### Interpretation of Parameter Errors:
178
179There are two kinds of problems that can arise: the reliability of
180MINUIT's error estimates, and their statistical interpretation, assuming
181they are accurate.
182
183### Statistical interpretation:
184
185For discussion of basic concepts, such as the meaning of the elements of
186the error matrix, or setting of exact confidence levels see:
187
188 1. F.James.
189 Determining the statistical Significance of experimental Results.
190 Technical Report DD/81/02 and CERN Report 81-03, CERN, 1981.</li>
191
192 2. W.T.Eadie, D.Drijard, F.James, M.Roos, and B.Sadoulet.
193 Statistical Methods in Experimental Physics.
194 North-Holland, 1971.</li>
195
196### Reliability of MINUIT error estimates.
197
198MINUIT always carries around its own current estimates of the parameter
199errors, which it will print out on request, no matter how accurate they
200are at any given point in the execution. For example, at initialization,
201these estimates are just the starting step sizes as specified by the user.
202After a HESSE step, the errors are usually quite accurate,
203unless there has been a problem. MINUIT, when it prints out error values,
204also gives some indication of how reliable it thinks they are. For
205example, those marked <TT>CURRENT GUESS ERROR</TT> are only working values
206not to be believed, and <TT>APPROXIMATE ERROR</TT> means that they have
207been calculated but there is reason to believe that they may not be
208accurate.
209
210If no mitigating adjective is given, then at least MINUIT believes the
211errors are accurate, although there is always a small chance that MINUIT
212has been fooled. Some visible signs that MINUIT may have been fooled are:
213
214
215 1. Warning messages produced during the minimization or error analysis.
216
217 2. Failure to find new minimum.
218
219 3. Value of <TT>EDM</TT> too big (estimated Distance to Minimum).
220
221 4. Correlation coefficients exactly equal to zero, unless some parameters
222 are known to be uncorrelated with the others.
223
224 5. Correlation coefficients very close to one (greater than 0.99). This
225 indicates both an exceptionally difficult problem, and one which has been
226 badly parameterised so that individual errors are not very meaningful
227 because they are so highly correlated.
228
229 6. Parameter at limit. This condition, signalled by a MINUIT warning
230 message, may make both the function minimum and parameter errors
231 unreliable. See the discussion above ``Getting the right parameter errors
232 with limits''.
233
234
235The best way to be absolutely sure of the errors, is to use
236``independent'' calculations and compare them, or compare the calculated
237errors with a picture of the function. Theoretically, the covariance
238matrix for a ``physical'' function must be positive-definite at the
239minimum, although it may not be so for all points far away from the
240minimum, even for a well-determined physical problem. Therefore, if MIGRAD
241reports that it has found a non-positive-definite covariance matrix, this
242may be a sign of one or more of the following:
243
244##### A non-physical region:
245
246On its way to the minimum, MIGRAD may have traversed a region which has
247unphysical behaviour, which is of course not a serious problem as long as
248it recovers and leaves such a region.
249
250##### An underdetermined problem:
251
252If the matrix is not positive-definite even at the minimum, this may mean
253that the solution is not well-defined, for example that there are more
254unknowns than there are data points, or that the parameterisation of the
255fit contains a linear dependence. If this is the case, then MINUIT (or any
256other program) cannot solve your problem uniquely, and the error matrix
257will necessarily be largely meaningless, so the user must remove the
258under-determinedness by reformulating the parameterisation. MINUIT cannot
259do this itself.
260
261##### Numerical inaccuracies:
262
263It is possible that the apparent lack of positive-definiteness is in fact
264only due to excessive roundoff errors in numerical calculations in the
265user function or not enough precision. This is unlikely in general, but
266becomes more likely if the number of free parameters is very large, or if
267
268the parameters are badly scaled (not all of the same order of magnitude),
269and correlations are also large. In any case, whether the
270non-positive-definiteness is real or only numerical is largely irrelevant,
271since in both cases the error matrix will be unreliable and the minimum
272suspicious.
273
274##### An ill-posed problem:
275
276For questions of parameter dependence, see the discussion above on
277positive-definiteness.
278
279Possible other mathematical problems are the following:
280
281##### Excessive numerical roundoff:
282
283Be especially careful of exponential and factorial functions which get big
284very quickly and lose accuracy.
285
286##### Starting too far from the solution:
287
288The function may have unphysical local minima, especially at infinity in
289some variables.
290
291##### Minuit parameter errors in the presence of limits
292This concerns the way Minuit reports the symmetric (or parabolic) errors
293on parameters. It does not apply to the errors reported from Minos, which
294are in general asymmetric.
295
296The symmetric errors reported by Minuit are always calculated from
297the covariance matrix, assuming that this matrix has been calculated,
298usually as the result of a Migrad minimization or a direct
299calculation by Hesse which inverts the second derivative matrix.
300
301When there are no limits on the parameter in question, the error reported
302by Minuit should therefore be exactly equal to the square root of the
303corresponding diagonal element of the error matrix reported by Minuit.
304
305However, when there are limits on the parameter, there is a transformation
306between the internal parameter values seen by Minuit (which are unbounded)
307and the external parameter values seen by the user in FCN (which remain
308inside the desired limits). Therefore the internal error matrix kept by
309Minuit must be transformed to an external error matrix for the user.
310This is done by multiplying the (I,J)th element by DEXDIN(I)*DEXDIN(J),
311where DEXDIN is the derivative of the external value with respect to the
312internal value at the minimum. This is a linearisation of the
313transformation, and is the only way to produce an error matrix in external
314coordinates meaningful to the user. But when reporting the individual
315parabolic errors for limited parameters, Minuit can do a little better, so
316it does. In this case, Minuit actually transforms the ends of the
317internal "error bar" to external coordinates and reports the length of
318this transformed interval. Strictly speaking, it is now asymmetric, but
319since the origin of the asymmetry is only an artificial transformation it
320does not make much sense, so the transformed errors are symmetrized.
321
322The result of all the above is that for parameters with limits, the error
323reported by Minuit is not exactly equal to the square root of the diagonal
324element of the error matrix. The difference is a measure of how much the
325limits deform the problem. If possible, it is suggested not to use limits
326on parameters, and the problem goes away. If for some reason limits are
327necessary, and you are sensitive to the difference between the two ways of
328calculating the errors, it is suggested to use Minos errors which take
329into account the non-linearities much more precisely.
330
331@ingroup MinuitOld
332*/
333
334#include <stdlib.h>
335#include <stdio.h>
336
337#include "TROOT.h"
338#include "TMinuit.h"
339#include "TMath.h"
340#include "TError.h"
341#include "TPluginManager.h"
342#include "TClass.h"
343
344#include <atomic>
345
347
348static const char charal[29] = " .ABCDEFGHIJKLMNOPQRSTUVWXYZ";
349
351
352////////////////////////////////////////////////////////////////////////////////
353/// Minuit normal constructor
354///
355
356TMinuit::TMinuit(): TNamed("MINUIT","The Minimization package")
357{
358 if (TMinuit::Class()->IsCallingNew() != TClass::kRealNew) {
359 //preset all pointers to null
360 fCpnam = 0;
361 fU = 0;
362 fAlim = 0;
363 fBlim = 0;
364 fPstar = 0;
365 fGin = 0;
366 fNvarl = 0;
367 fNiofex = 0;
368
369 fNexofi = 0;
370 fIpfix = 0;
371 fErp = 0;
372 fErn = 0;
373 fWerr = 0;
374 fGlobcc = 0;
375 fX = 0;
376 fXt = 0;
377 fDirin = 0;
378 fXs = 0;
379 fXts = 0;
380 fDirins = 0;
381 fGrd = 0;
382 fG2 = 0;
383 fGstep = 0;
384 fDgrd = 0;
385 fGrds = 0;
386 fG2s = 0;
387 fGsteps = 0;
388 fPstst = 0;
389 fPbar = 0;
390 fPrho = 0;
391 fWord7 = 0;
392 fVhmat = 0;
393 fVthmat = 0;
394 fP = 0;
395 fXpt = 0;
396 fYpt = 0;
397 fChpt = 0;
398 fCONTgcc = 0;
399 fCONTw = 0;
400 fFIXPyy = 0;
401 fGRADgf = 0;
402 fHESSyy = 0;
403 fIMPRdsav = 0;
404 fIMPRy = 0;
405 fMATUvline = 0;
406 fMIGRflnu = 0;
407 fMIGRstep = 0;
408 fMIGRgs = 0;
409 fMIGRvg = 0;
410 fMIGRxxs = 0;
411 fMNOTxdev = 0;
412 fMNOTw = 0;
413 fMNOTgcc = 0;
414 fPSDFs = 0;
415 fSEEKxmid = 0;
416 fSEEKxbest = 0;
417 fSIMPy = 0;
418 fVERTq = 0;
419 fVERTs = 0;
420 fVERTpp = 0;
421 fCOMDplist = 0;
422 fPARSplist = 0;
423
424 fUp = 0;
425 fEpsi = 0;
426 fApsi = 0;
427 fXmidcr = 0;
428 fYmidcr = 0;
429 fXdircr = 0;
430 fYdircr = 0;
431
432 fStatus = 0;
433 fEmpty = 0;
434 fObjectFit = 0;
435 fMethodCall = 0;
436 fPlot = 0;
438
439 } else {
440 BuildArrays(25);
441
442 fUp = 0;
443 fEpsi = 0;
444 fApsi = 0;
445 fXmidcr = 0;
446 fYmidcr = 0;
447 fXdircr = 0;
448 fYdircr = 0;
449
450 fStatus = 0;
451 fEmpty = 0;
452 fObjectFit = 0;
453 fMethodCall = 0;
454 fPlot = 0;
457 mninit(5,6,7);
458 }
459
460 fFCN = 0;
461 {
463 gROOT->GetListOfSpecials()->Add(this);
464 }
465 gMinuit = this;
466}
467
468////////////////////////////////////////////////////////////////////////////////
469/// Minuit normal constructor
470///
471/// maxpar is the maximum number of parameters used with this TMinuit object.
472
473TMinuit::TMinuit(Int_t maxpar): TNamed("MINUIT","The Minimization package")
474{
475 fFCN = 0;
476
477 BuildArrays(maxpar);
478
479 fStatus = 0;
480 fEmpty = 0;
481 fObjectFit = 0;
482 fMethodCall = 0;
483 fPlot = 0;
486
487 mninit(5,6,7);
488 {
490 gROOT->GetListOfSpecials()->Add(this);
491 }
492 gMinuit = this;
493}
494
495////////////////////////////////////////////////////////////////////////////////
496/// Private TMinuit copy ctor. TMinuit can not be copied.
497
498TMinuit::TMinuit(const TMinuit &minuit) : TNamed(minuit)
499{
500 Error("TMinuit", "can not copy construct TMinuit");
501}
502
503////////////////////////////////////////////////////////////////////////////////
504/// Minuit default destructor
505
507{
508 DeleteArrays();
509 delete fPlot;
510 delete fMethodCall;
511 {
513 if (gROOT != 0 && gROOT->GetListOfSpecials() != 0) gROOT->GetListOfSpecials()->Remove(this);
514 }
515 if (gMinuit == this) gMinuit = nullptr;
516}
517
518////////////////////////////////////////////////////////////////////////////////
519/// Create internal Minuit arrays for the maxpar parameters
520
522{
523 fMaxpar = 25;
524 if (maxpar >= fMaxpar) fMaxpar = maxpar+1;
526 fMaxpar2= 2*fMaxpar;
528 fMaxcpt = 101;
529 fCpnam = new TString[fMaxpar2];
530 fU = new Double_t[fMaxpar2];
531 fAlim = new Double_t[fMaxpar2];
532 fBlim = new Double_t[fMaxpar2];
533 fPstar = new Double_t[fMaxpar2];
534 fGin = new Double_t[fMaxpar2];
535 fNvarl = new Int_t[fMaxpar2];
536 fNiofex = new Int_t[fMaxpar2];
537
538 fNexofi = new Int_t[fMaxpar];
539 fIpfix = new Int_t[fMaxpar];
540 fErp = new Double_t[fMaxpar];
541 fErn = new Double_t[fMaxpar];
542 fWerr = new Double_t[fMaxpar];
543 fGlobcc = new Double_t[fMaxpar];
544 fX = new Double_t[fMaxpar];
545 fXt = new Double_t[fMaxpar];
546 fDirin = new Double_t[fMaxpar];
547 fXs = new Double_t[fMaxpar];
548 fXts = new Double_t[fMaxpar];
549 fDirins = new Double_t[fMaxpar];
550 fGrd = new Double_t[fMaxpar];
551 fG2 = new Double_t[fMaxpar];
552 fGstep = new Double_t[fMaxpar];
553 fDgrd = new Double_t[fMaxpar];
554 fGrds = new Double_t[fMaxpar];
555 fG2s = new Double_t[fMaxpar];
556 fGsteps = new Double_t[fMaxpar];
557 fPstst = new Double_t[fMaxpar];
558 fPbar = new Double_t[fMaxpar];
559 fPrho = new Double_t[fMaxpar];
560 fWord7 = new Double_t[fMaxpar];
561 fVhmat = new Double_t[fMaxpar5];
563 fP = new Double_t[fMaxpar1];
564 fXpt = new Double_t[fMaxcpt];
565 fYpt = new Double_t[fMaxcpt];
566 fChpt = new char[fMaxcpt+1];
567 // initialisation of dynamic arrays used internally in some functions
568 // these arrays had a fix dimension in Minuit
570 fCONTw = new Double_t[fMaxpar];
571 fFIXPyy = new Double_t[fMaxpar];
572 fGRADgf = new Double_t[fMaxpar];
573 fHESSyy = new Double_t[fMaxpar];
575 fIMPRy = new Double_t[fMaxpar];
579 fMIGRgs = new Double_t[fMaxpar];
580 fMIGRvg = new Double_t[fMaxpar];
583 fMNOTw = new Double_t[fMaxpar];
585 fPSDFs = new Double_t[fMaxpar];
588 fSIMPy = new Double_t[fMaxpar];
589 fVERTq = new Double_t[fMaxpar];
590 fVERTs = new Double_t[fMaxpar];
591 fVERTpp = new Double_t[fMaxpar];
594
595 for (int i = 0; i < fMaxpar; i++) {
596 fErp[i] = 0;
597 fErn[i] = 0;
598 }
599}
600
601////////////////////////////////////////////////////////////////////////////////
602/// Make a clone of an object using the Streamer facility.
603/// Function pointer is copied to Clone
604
605TObject *TMinuit::Clone(const char *newname) const
606{
607 TMinuit *named = (TMinuit*)TNamed::Clone(newname);
608 named->fFCN=fFCN;
609 return named;
610}
611
612////////////////////////////////////////////////////////////////////////////////
613/// Execute a Minuit command
614///
615/// Equivalent to MNEXCM except that the command is given as a character string.
616/// See TMinuit::mnhelp for the full list of available commands
617/// See also the
618/// [complete documentation of all the available commands](https://root.cern.ch/sites/d35c7d8c.web.cern.ch/files/minuit.pdf)
619///
620/// Returns the status of the execution:
621/// - 0: command executed normally
622/// - 1: command is blank, ignored
623/// - 2: command line unreadable, ignored
624/// - 3: unknown command, ignored
625/// - 4: abnormal termination (e.g., MIGRAD not converged)
626/// - 5: command is a request to read PARAMETER definitions
627/// - 6: 'SET INPUT' command
628/// - 7: 'SET TITLE' command
629/// - 8: 'SET COVAR' command
630/// - 9: reserved
631/// - 10: END command
632/// - 11: EXIT or STOP command
633/// - 12: RETURN command
634
635Int_t TMinuit::Command(const char *command)
636{
637 Int_t status = 0;
638 mncomd(command,status);
639 return status;
640}
641
642////////////////////////////////////////////////////////////////////////////////
643/// Creates a TGraph object describing the n-sigma contour of a
644/// TMinuit fit. The contour of the parameters pa1 and pa2 is calculated
645/// using npoints (>=4) points. The TMinuit status will be
646/// - 0 on success and
647/// - -1 if errors in the calling sequence (pa1, pa2 not variable)
648/// - 1 if less than four points can be found
649/// - 2 if npoints<4
650/// - n>3 if only n points can be found (n < npoints)
651/// The status can be obtained via TMinuit::GetStatus().
652///
653/// To get the n-sigma contour the ERRDEF parameter in Minuit has to set
654/// to n^2. The fcn function has to be set before the routine is called.
655///
656/// The TGraph object is created via the interpreter. The user must cast it
657/// to a TGraph*. Note that the TGraph is created with npoints+1 in order to
658/// close the contour (setting last point equal to first point).
659///
660/// You can find an example in $ROOTSYS/tutorials/fit/fitcont.C
661
663{
664 if (npoints<4) {
665 // we need at least 4 points
666 fStatus= 2;
667 return (TObject *)0;
668 }
669 Int_t npfound;
670 Double_t *xcoor = new Double_t[npoints+1];
671 Double_t *ycoor = new Double_t[npoints+1];
672 mncont(pa1,pa2,npoints,xcoor,ycoor,npfound);
673 if (npfound<4) {
674 // mncont did go wrong
675 Warning("Contour","Cannot find more than 4 points, no TGraph returned");
676 fStatus= (npfound==0 ? 1 : npfound);
677 delete [] xcoor;
678 delete [] ycoor;
679 return (TObject *)0;
680 }
681 if (npfound!=npoints) {
682 // mncont did go wrong
683 Warning("Contour","Returning a TGraph with %d points only",npfound);
684 npoints = npfound;
685 }
686 fStatus=0;
687 // create graph via the PluginManager
688 xcoor[npoints] = xcoor[0]; // add first point at end to get closed polyline
689 ycoor[npoints] = ycoor[0];
690 TObject *gr = 0;
692 if ((h = gROOT->GetPluginManager()->FindHandler("TMinuitGraph"))) {
693 if (h->LoadPlugin() != -1)
694 gr = (TObject*)h->ExecPlugin(3,npoints+1,xcoor,ycoor);
695 }
696 delete [] xcoor;
697 delete [] ycoor;
698 return gr;
699}
700
701////////////////////////////////////////////////////////////////////////////////
702/// Define a parameter
703
704Int_t TMinuit::DefineParameter( Int_t parNo, const char *name, Double_t initVal, Double_t initErr, Double_t lowerLimit, Double_t upperLimit )
705{
706 Int_t err;
707
708 TString sname = name;
709 mnparm( parNo, sname, initVal, initErr, lowerLimit, upperLimit, err);
710
711 return err;
712}
713
714////////////////////////////////////////////////////////////////////////////////
715/// Delete internal Minuit arrays
716
718{
719 if (fEmpty) return;
720 delete [] fCpnam;
721 delete [] fU;
722 delete [] fAlim;
723 delete [] fBlim;
724 delete [] fErp;
725 delete [] fErn;
726 delete [] fWerr;
727 delete [] fGlobcc;
728 delete [] fNvarl;
729 delete [] fNiofex;
730 delete [] fNexofi;
731 delete [] fX;
732 delete [] fXt;
733 delete [] fDirin;
734 delete [] fXs;
735 delete [] fXts;
736 delete [] fDirins;
737 delete [] fGrd;
738 delete [] fG2;
739 delete [] fGstep;
740 delete [] fGin;
741 delete [] fDgrd;
742 delete [] fGrds;
743 delete [] fG2s;
744 delete [] fGsteps;
745 delete [] fIpfix;
746 delete [] fVhmat;
747 delete [] fVthmat;
748 delete [] fP;
749 delete [] fPstar;
750 delete [] fPstst;
751 delete [] fPbar;
752 delete [] fPrho;
753 delete [] fWord7;
754 delete [] fXpt;
755 delete [] fYpt;
756 delete [] fChpt;
757
758 delete [] fCONTgcc;
759 delete [] fCONTw;
760 delete [] fFIXPyy;
761 delete [] fGRADgf;
762 delete [] fHESSyy;
763 delete [] fIMPRdsav;
764 delete [] fIMPRy;
765 delete [] fMATUvline;
766 delete [] fMIGRflnu;
767 delete [] fMIGRstep;
768 delete [] fMIGRgs;
769 delete [] fMIGRvg;
770 delete [] fMIGRxxs;
771 delete [] fMNOTxdev;
772 delete [] fMNOTw;
773 delete [] fMNOTgcc;
774 delete [] fPSDFs;
775 delete [] fSEEKxmid;
776 delete [] fSEEKxbest;
777 delete [] fSIMPy;
778 delete [] fVERTq;
779 delete [] fVERTs;
780 delete [] fVERTpp;
781 delete [] fCOMDplist;
782 delete [] fPARSplist;
783
784 fEmpty = 1;
785}
786
787////////////////////////////////////////////////////////////////////////////////
788/// Evaluate the minimisation function
789/// Input parameters:
790/// - npar: number of currently variable parameters
791/// - par: array of (constant and variable) parameters
792/// - flag: Indicates what is to be calculated (see example below)
793/// - grad: array of gradients
794/// Output parameters:
795/// - fval: The calculated function value.
796/// - grad: The (optional) vector of first derivatives).
797///
798/// The meaning of the parameters par is of course defined by the user,
799/// who uses the values of those parameters to calculate their function value.
800/// The starting values must be specified by the user.
801/// Later values are determined by Minuit as it searches for the minimum
802/// or performs whatever analysis is requested by the user.
803///
804/// Note that this virtual function may be redefined in a class derived from TMinuit.
805/// The default function calls the function specified in SetFCN
806///
807/// Example of Minimisation function:
808
809Int_t TMinuit::Eval(Int_t npar, Double_t *grad, Double_t &fval, Double_t *par, Int_t flag)
810{
811/*
812 if (flag == 1) {
813 read input data,
814 calculate any necessary constants, etc.
815 }
816 if (flag == 2) {
817 calculate GRAD, the first derivatives of FVAL
818 (this is optional)
819 }
820 Always calculate the value of the function, FVAL,
821 which is usually a chisquare or log likelihood.
822 if (iflag == 3) {
823 will come here only after the fit is finished.
824 Perform any final calculations, output fitted data, etc.
825 }
826*/
827// See concrete examples in TH1::H1FitChisquare, H1FitLikelihood
828
829 if (fFCN) (*fFCN)(npar,grad,fval,par,flag);
830 return 0;
831}
832
833////////////////////////////////////////////////////////////////////////////////
834/// fix a parameter
835
837{
838 Int_t err;
839 Double_t tmp[1];
840 tmp[0] = parNo+1; //set internal Minuit numbering
841
842 mnexcm( "FIX", tmp, 1, err );
843
844 return err;
845}
846
847////////////////////////////////////////////////////////////////////////////////
848/// return parameter value and error
849
850Int_t TMinuit::GetParameter( Int_t parNo, Double_t &currentValue, Double_t &currentError ) const
851{
852 Int_t err;
853 TString name; // ignored
854 Double_t bnd1, bnd2; // ignored
855
856 mnpout( parNo, name, currentValue, currentError, bnd1, bnd2, err );
857
858 return err;
859}
860
861////////////////////////////////////////////////////////////////////////////////
862/// returns the number of currently fixed parameters
863
865{
866 return fNpfix;
867}
868
869////////////////////////////////////////////////////////////////////////////////
870/// returns the number of currently free parameters
871
873{
874 return fNpar;
875}
876
877////////////////////////////////////////////////////////////////////////////////
878/// returns the total number of parameters that have been defined
879/// as fixed or free. The constant parameters are not counted.
880
882{
883 return fNpar + fNpfix;
884}
885
886////////////////////////////////////////////////////////////////////////////////
887/// invokes the MIGRAD minimizer
888
890{
891 Int_t err;
892 Double_t tmp[1];
893 tmp[0] = 0;
894
895 mnexcm( "MIGRAD", tmp, 0, err );
896
897 return err;
898}
899
900////////////////////////////////////////////////////////////////////////////////
901/// release a parameter
902
904{
905 Int_t err;
906 Double_t tmp[1];
907 tmp[0] = parNo+1; //set internal Minuit numbering
908
909 mnexcm( "RELEASE", tmp, 1, err );
910
911 return err;
912}
913
914////////////////////////////////////////////////////////////////////////////////
915/// To get the n-sigma contour the error def parameter "up" has to set to n^2.
916
918{
919 Int_t err;
920
921 mnexcm( "SET ERRDEF", &up, 1, err );
922
923 return err;
924}
925
926////////////////////////////////////////////////////////////////////////////////
927/// To set the address of the minimization function
928
929void TMinuit::SetFCN(void (*fcn)(Int_t &, Double_t *, Double_t &f, Double_t *, Int_t))
930{
931 fFCN = fcn;
932}
933
934////////////////////////////////////////////////////////////////////////////////
935/// Static function called when SetFCN is called in interactive mode
936
937void InteractiveFCNm(Int_t &npar, Double_t *gin, Double_t &f, Double_t *u, Int_t flag)
938{
940 if (!m) return;
941
942 Long_t args[5];
943 args[0] = (Long_t)&npar;
944 args[1] = (Long_t)gin;
945 args[2] = (Long_t)&f;
946 args[3] = (Long_t)u;
947 args[4] = (Long_t)flag;
948 m->SetParamPtrs(args);
949 Double_t result;
950 m->Execute(result);
951}
952
953////////////////////////////////////////////////////////////////////////////////
954/// set Minuit print level.
955///
956/// printlevel:
957/// - = -1 quiet (also suppress all warnings)
958/// - = 0 normal
959/// - = 1 verbose
960
962{
963 Int_t err;
964 Double_t tmp[1];
965 tmp[0] = printLevel;
966
967 mnexcm( "SET PRINT", tmp, 1, err );
968
969 if (printLevel <=-1) mnexcm("SET NOWarnings",tmp,0,err);
970
971 return err;
972}
973
974////////////////////////////////////////////////////////////////////////////////
975/// Initialize AMIN
976///
977/// Called from many places. Initializes the value of AMIN by
978/// calling the user function. Prints out the function value and
979/// parameter values if Print Flag value is high enough.
980
982{
983 /* Local variables */
984 Double_t fnew;
985 Int_t nparx;
986
987 nparx = fNpar;
988 if (fISW[4] >= 1) {
989 Printf(" FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.");
990 }
991 mnexin(fX);
992 Eval(nparx, fGin, fnew, fU, 4); ++fNfcn;
993 fAmin = fnew;
994 fEDM = fBigedm;
995}
996
997////////////////////////////////////////////////////////////////////////////////
998/// Compute reasonable histogram intervals
999///
1000/// Function TO DETERMINE REASONABLE HISTOGRAM INTERVALS
1001/// GIVEN ABSOLUTE UPPER AND LOWER BOUNDS A1 AND A2
1002/// AND DESIRED MAXIMUM NUMBER OF BINS NAA
1003/// PROGRAM MAKES REASONABLE BINNING FROM BL TO BH OF WIDTH BWID
1004/// F. JAMES, AUGUST, 1974 , stolen for Minuit, 1988
1005
1006void TMinuit::mnbins(Double_t a1, Double_t a2, Int_t naa, Double_t &bl, Double_t &bh, Int_t &nb, Double_t &bwid)
1007{
1008 /* Local variables */
1009 Double_t awid,ah, al, sigfig, sigrnd, alb;
1010 Int_t kwid, lwid, na=0, log_;
1011
1012 al = TMath::Min(a1,a2);
1013 ah = TMath::Max(a1,a2);
1014 if (al == ah) ah = al + 1;
1015
1016// IF NAA .EQ. -1 , PROGRAM USES BWID INPUT FROM CALLING ROUTINE
1017 if (naa == -1) goto L150;
1018L10:
1019 na = naa - 1;
1020 if (na < 1) na = 1;
1021
1022// GET NOMINAL BIN WIDTH IN EXPON FORM
1023L20:
1024 awid = (ah-al) / Double_t(na);
1025 log_ = Int_t(TMath::Log10(awid));
1026 if (awid <= 1) --log_;
1027 sigfig = awid*TMath::Power(10, -log_);
1028// ROUND MANTISSA UP TO 2, 2.5, 5, OR 10
1029 if (sigfig > 2) goto L40;
1030 sigrnd = 2;
1031 goto L100;
1032L40:
1033 if (sigfig > 2.5) goto L50;
1034 sigrnd = 2.5;
1035 goto L100;
1036L50:
1037 if (sigfig > 5) goto L60;
1038 sigrnd = 5;
1039 goto L100;
1040L60:
1041 sigrnd = 1;
1042 ++log_;
1043L100:
1044 bwid = sigrnd*TMath::Power(10, log_);
1045 goto L200;
1046// GET NEW BOUNDS FROM NEW WIDTH BWID
1047L150:
1048 if (bwid <= 0) goto L10;
1049L200:
1050 alb = al / bwid;
1051 lwid = Int_t(alb);
1052 if (alb < 0) --lwid;
1053 bl = bwid*Double_t(lwid);
1054 alb = ah / bwid + 1;
1055 kwid = Int_t(alb);
1056 if (alb < 0) --kwid;
1057 bh = bwid*Double_t(kwid);
1058 nb = kwid - lwid;
1059 if (naa > 5) goto L240;
1060 if (naa == -1) return;
1061// REQUEST FOR ONE BIN IS DIFFICULT CASE
1062 if (naa > 1 || nb == 1) return;
1063 bwid *= 2;
1064 nb = 1;
1065 return;
1066L240:
1067 if (nb << 1 != naa) return;
1068 ++na;
1069 goto L20;
1070}
1071
1072////////////////////////////////////////////////////////////////////////////////
1073/// Transform FCN to find further minima
1074///
1075/// Called only from MNIMPR. Transforms the function FCN
1076/// by dividing out the quadratic part in order to find further
1077/// minima. Calculates `ycalf = (f-fmin)/(x-xmin)*v*(x-xmin)`
1078
1080{
1081 /* Local variables */
1082 Int_t ndex, i, j, m, n, nparx;
1083 Double_t denom, f;
1084
1085 nparx = fNpar;
1086 mninex(&pvec[0]);
1087 Eval(nparx, fGin, f, fU, 4); ++fNfcn;
1088 for (i = 1; i <= fNpar; ++i) {
1089 fGrd[i-1] = 0;
1090 for (j = 1; j <= fNpar; ++j) {
1091 m = TMath::Max(i,j);
1092 n = TMath::Min(i,j);
1093 ndex = m*(m-1) / 2 + n;
1094 fGrd[i-1] += fVthmat[ndex-1]*(fXt[j-1] - pvec[j-1]);
1095 }
1096 }
1097 denom = 0;
1098 for (i = 1; i <= fNpar; ++i) {denom += fGrd[i-1]*(fXt[i-1] - pvec[i-1]); }
1099 if (denom <= 0) {
1100 fDcovar = 1;
1101 fISW[1] = 0;
1102 denom = 1;
1103 }
1104 ycalf = (f - fApsi) / denom;
1105}
1106
1107////////////////////////////////////////////////////////////////////////////////
1108/// Resets the parameter list to UNDEFINED
1109///
1110/// Called from MINUIT and by option from MNEXCM
1111
1113{
1114 Int_t i;
1115
1116 fNpfix = 0;
1117 fNu = 0;
1118 fNpar = 0;
1119 fNfcn = 0;
1120 fNwrmes[0] = 0;
1121 fNwrmes[1] = 0;
1122 for (i = 1; i <= fMaxext; ++i) {
1123 fU[i-1] = 0;
1124 fCpnam[i-1] = fCundef;
1125 fNvarl[i-1] = -1;
1126 fNiofex[i-1] = 0;
1127 }
1128 mnrset(1);
1129 fCfrom = "CLEAR ";
1130 fNfcnfr = fNfcn;
1131 fCstatu = "UNDEFINED ";
1132 fLnolim = kTRUE;
1133 fLphead = kTRUE;
1134}
1135
1136////////////////////////////////////////////////////////////////////////////////
1137/// Print function contours in two variables, on line printer
1138///
1139/// input arguments: parx, pary, devs, ngrid
1140
1141void TMinuit::mncntr(Int_t ike1, Int_t ike2, Int_t &ierrf)
1142{
1143 static const char *const clabel = "0123456789ABCDEFGHIJ";
1144
1145 /* Local variables */
1146 Double_t d__1, d__2;
1147 Double_t fcna[115], fcnb[115], contur[20];
1148 Double_t ylabel, fmn, fmx, xlo, ylo, xup, yup;
1149 Double_t devs, xsav, ysav, bwidx, bwidy, unext, ff, xb4;
1150 Int_t i, ngrid, ixmid, nparx, ix, nx, ny, ki1, ki2, ixzero, iy, ics;
1151 TString chmid, chln, chzero;
1152
1153 Int_t ke1 = ike1+1;
1154 Int_t ke2 = ike2+1;
1155 if (ke1 <= 0 || ke2 <= 0) goto L1350;
1156 if (ke1 > fNu || ke2 > fNu) goto L1350;
1157 ki1 = fNiofex[ke1-1];
1158 ki2 = fNiofex[ke2-1];
1159 if (ki1 <= 0 || ki2 <= 0) goto L1350;
1160 if (ki1 == ki2) goto L1350;
1161
1162 if (fISW[1] < 1) {
1163 mnhess();
1164 mnwerr();
1165 }
1166 nparx = fNpar;
1167 xsav = fU[ke1-1];
1168 ysav = fU[ke2-1];
1169 devs = fWord7[2];
1170 if (devs <= 0) devs = 2;
1171 xlo = fU[ke1-1] - devs*fWerr[ki1-1];
1172 xup = fU[ke1-1] + devs*fWerr[ki1-1];
1173 ylo = fU[ke2-1] - devs*fWerr[ki2-1];
1174 yup = fU[ke2-1] + devs*fWerr[ki2-1];
1175 ngrid = Int_t(fWord7[3]);
1176 if (ngrid <= 0) {
1177 ngrid = 25;
1178// Computing MIN
1179 nx = TMath::Min(fNpagwd - 15,ngrid);
1180// Computing MIN
1181 ny = TMath::Min(fNpagln - 7,ngrid);
1182 } else {
1183 nx = ngrid;
1184 ny = ngrid;
1185 }
1186 if (nx < 11) nx = 11;
1187 if (ny < 11) ny = 11;
1188 if (nx >= 115) nx = 114;
1189
1190// ask if parameter outside limits
1191 if (fNvarl[ke1-1] > 1) {
1192 if (xlo < fAlim[ke1-1]) xlo = fAlim[ke1-1];
1193 if (xup > fBlim[ke1-1]) xup = fBlim[ke1-1];
1194 }
1195 if (fNvarl[ke2-1] > 1) {
1196 if (ylo < fAlim[ke2-1]) ylo = fAlim[ke2-1];
1197 if (yup > fBlim[ke2-1]) yup = fBlim[ke2-1];
1198 }
1199 bwidx = (xup - xlo) / Double_t(nx);
1200 bwidy = (yup - ylo) / Double_t(ny);
1201 ixmid = Int_t(((xsav - xlo)*Double_t(nx) / (xup - xlo)) + 1);
1202 if (ixmid < 1) ixmid = 1;
1203 if (fAmin == fUndefi) mnamin();
1204
1205 for (i = 1; i <= 20; ++i) { contur[i-1] = fAmin + fUp*(i-1)*(i-1); }
1206 contur[0] += fUp*.01;
1207// fill FCNB to prepare first row, and find column zero/
1208 fU[ke2-1] = yup;
1209 ixzero = 0;
1210 xb4 = 1;
1211//TH
1212 chmid.Resize(nx+1);
1213 chzero.Resize(nx+1);
1214 chln.Resize(nx+1);
1215 for (ix = 1; ix <= nx + 1; ++ix) {
1216 fU[ke1-1] = xlo + Double_t(ix-1)*bwidx;
1217 Eval(nparx, fGin, ff, fU, 4);
1218 fcnb[ix-1] = ff;
1219 if (xb4 < 0 && fU[ke1-1] > 0) ixzero = ix - 1;
1220 xb4 = fU[ke1-1];
1221 chmid[ix-1] = '*';
1222 chzero[ix-1] = '-';
1223 }
1224 Printf(" Y-AXIS: PARAMETER %3d: %s",ke2,(const char*)fCpnam[ke2-1]);
1225 if (ixzero > 0) {
1226 chzero[ixzero-1] = '+';
1227 chln = " ";
1228 Printf(" X=0");
1229 }
1230// loop over rows
1231 for (iy = 1; iy <= ny; ++iy) {
1232 unext = fU[ke2-1] - bwidy;
1233// prepare this line background pattern for contour
1234 chln = " ";
1235// TH
1236 chln.Resize(nx+1);
1237 chln[ixmid-1] = '*';
1238 if (ixzero != 0) chln[ixzero-1] = ':';
1239 if (fU[ke2-1] > ysav && unext < ysav) chln = chmid;
1240 if (fU[ke2-1] > 0 && unext < 0) chln = chzero;
1241 fU[ke2-1] = unext;
1242 ylabel = fU[ke2-1] + bwidy*.5;
1243// move FCNB to FCNA and fill FCNB with next row
1244 for (ix = 1; ix <= nx + 1; ++ix) {
1245 fcna[ix-1] = fcnb[ix-1];
1246 fU[ke1-1] = xlo + Double_t(ix-1)*bwidx;
1247 Eval(nparx, fGin, ff, fU, 4);
1248 fcnb[ix-1] = ff;
1249 }
1250// look for contours crossing the FCNxy squares
1251 for (ix = 1; ix <= nx; ++ix) {
1252 d__1 = TMath::Max(fcna[ix-1],fcnb[ix-1]),
1253 d__2 = TMath::Max(fcna[ix],fcnb[ix]);
1254 fmx = TMath::Max(d__1,d__2);
1255 d__1 = TMath::Min(fcna[ix-1],fcnb[ix-1]),
1256 d__2 = TMath::Min(fcna[ix],fcnb[ix]);
1257 fmn = TMath::Min(d__1,d__2);
1258 for (ics = 1; ics <= 20; ++ics) {
1259 if (contur[ics-1] > fmn) goto L240;
1260 }
1261 continue;
1262L240:
1263 if (contur[ics-1] < fmx) chln[ix-1] = clabel[ics-1];
1264 }
1265// print a row of the contour plot
1266 Printf(" %12.4g %s",ylabel,(const char*)chln);
1267 }
1268// contours printed, label x-axis
1269 chln = " ";
1270 chln(0,1) = 'I';
1271 chln(ixmid-1,1) = 'I';
1272 chln(nx-1,1) = 'I';
1273 Printf(" %s",(const char*)chln);
1274
1275// the hardest of all: print x-axis scale!
1276 chln = " ";
1277 if (nx <= 26) {
1278 Printf(" %12.4g%s%12.4g",xlo,(const char*)chln,xup);
1279 Printf(" %s%12.4g",(const char*)chln,xsav);
1280 } else {
1281 Printf(" %12.4g%s%12.4g%s%12.4g",xlo,(const char*)chln,xsav,(const char*)chln,xup);
1282 }
1283 Printf(" X-AXIS: PARAMETER %3d %s ONE COLUMN=%12.4g"
1284 ,ke1,(const char*)fCpnam[ke1-1],bwidx);
1285 Printf(" FUNCTION VALUES: F(I)=%12.4g +%12.4g *I**2",fAmin,fUp);
1286// finished. reset input values
1287 fU[ke1-1] = xsav;
1288 fU[ke2-1] = ysav;
1289 ierrf = 0;
1290 return;
1291L1350:
1292 Printf(" INVALID PARAMETER NUMBER(S) REQUESTED. IGNORED.");
1293 ierrf = 1;
1294}
1295
1296////////////////////////////////////////////////////////////////////////////////
1297/// Reads a command string and executes
1298///
1299/// Called by user. 'Reads' a command string and executes.
1300/// Equivalent to MNEXCM except that the command is given as a
1301/// character string.
1302///
1303/// ICONDN =
1304/// - 0: command executed normally
1305/// - 1: command is blank, ignored
1306/// - 2: command line unreadable, ignored
1307/// - 3: unknown command, ignored
1308/// - 4: abnormal termination (e.g., MIGRAD not converged)
1309/// - 5: command is a request to read PARAMETER definitions
1310/// - 6: 'SET INPUT' command
1311/// - 7: 'SET TITLE' command
1312/// - 8: 'SET COVAR' command
1313/// - 9: reserved
1314/// - 10: END command
1315/// - 11: EXIT or STOP command
1316/// - 12: RETURN command
1317///
1318
1319void TMinuit::mncomd(const char *crdbin, Int_t &icondn)
1320{
1321 /* Local variables */
1322 Int_t ierr, ipos, i, llist, lenbuf, lnc;
1323 Bool_t leader;
1324 TString comand, crdbuf, ctemp;
1325
1326 crdbuf = crdbin;
1327 crdbuf.ToUpper();
1328 lenbuf = crdbuf.Length();
1329 icondn = 0;
1330// record not case-sensitive, get upper case, strip leading blanks
1331 leader = kTRUE;
1332 ipos = 1;
1333 for (i = 1; i <= TMath::Min(20,lenbuf); ++i) {
1334 if (crdbuf[i-1] == '\'') break;
1335 if (crdbuf[i-1] == ' ') {
1336 if (leader) ++ipos;
1337 continue;
1338 }
1339 leader = kFALSE;
1340 }
1341
1342// blank or null command
1343 if (ipos > lenbuf) {
1344 Printf(" BLANK COMMAND IGNORED.");
1345 icondn = 1;
1346 return;
1347 }
1348// preemptive commands
1349// if command is 'PARAMETER'
1350 if (crdbuf(ipos-1,3) == "PAR") {
1351 icondn = 5;
1352 fLphead = kTRUE;
1353 return;
1354 }
1355// if command is 'SET INPUT'
1356 if (crdbuf(ipos-1,3) == "SET INP") {
1357 icondn = 6;
1358 fLphead = kTRUE;
1359 return;
1360 }
1361// if command is 'SET TITLE'
1362 if (crdbuf(ipos-1,7) == "SET TIT") {
1363 icondn = 7;
1364 fLphead = kTRUE;
1365 return;
1366 }
1367// if command is 'SET COVARIANCE'
1368 if (crdbuf(ipos-1,7) == "SET COV") {
1369 icondn = 8;
1370 fLphead = kTRUE;
1371 return;
1372 }
1373// crack the command
1374 ctemp = crdbuf(ipos-1,lenbuf-ipos+1);
1375 mncrck(ctemp, 20, comand, lnc, fMaxpar, fCOMDplist, llist, ierr, fIsyswr);
1376 if (ierr > 0) {
1377 Printf(" COMMAND CANNOT BE INTERPRETED");
1378 icondn = 2;
1379 return;
1380 }
1381
1382 mnexcm(comand.Data(), fCOMDplist, llist, ierr);
1383 icondn = ierr;
1384}
1385
1386////////////////////////////////////////////////////////////////////////////////
1387/// Find points along a contour where FCN is minimum
1388///
1389/// Find NPTU points along a contour where the function
1390///
1391/// FMIN (X(KE1),X(KE2)) = AMIN+UP
1392///
1393/// where FMIN is the minimum of FCN with respect to all
1394/// the other NPAR-2 variable parameters (if any).
1395///
1396/// IERRF on return will be equal to the number of points found:
1397/// - NPTU if normal termination with NPTU points found
1398/// - -1 if errors in the calling sequence (KE1, KE2 not variable)
1399/// - 0 if less than four points can be found (using MNMNOT)
1400/// - n>3 if only n points can be found (n < NPTU)
1401///
1402/// input arguments: parx, pary, devs, ngrid
1403
1404void TMinuit::mncont(Int_t ike1, Int_t ike2, Int_t nptu, Double_t *xptu, Double_t *yptu, Int_t &ierrf)
1405{
1406 /* System generated locals */
1407 Int_t i__1;
1408
1409 /* Local variables */
1410 Double_t d__1, d__2;
1411 Double_t dist, xdir, ydir, aopt, u1min, u2min;
1412 Double_t abest, scalx, scaly;
1413 Double_t a1, a2, val2mi, val2pl, dc, sclfac, bigdis, sigsav;
1414 Int_t nall, iold, line, mpar, ierr, inew, move, next, i, j, nfcol, iercr;
1415 Int_t idist=0, npcol, kints, i2, i1, lr, nfcnco=0, ki1, ki2, ki3, ke3;
1416 Int_t nowpts, istrav, nfmxin, isw2, isw4;
1417 Bool_t ldebug;
1418
1419 /* Function Body */
1420 Int_t ke1 = ike1+1;
1421 Int_t ke2 = ike2+1;
1422 ldebug = fIdbg[6] >= 1;
1423 if (ke1 <= 0 || ke2 <= 0) goto L1350;
1424 if (ke1 > fNu || ke2 > fNu) goto L1350;
1425 ki1 = fNiofex[ke1-1];
1426 ki2 = fNiofex[ke2-1];
1427 if (ki1 <= 0 || ki2 <= 0) goto L1350;
1428 if (ki1 == ki2) goto L1350;
1429 if (nptu < 4) goto L1400;
1430
1431 nfcnco = fNfcn;
1432 fNfcnmx = (nptu + 5)*100*(fNpar + 1);
1433// The minimum
1434 mncuve();
1435 u1min = fU[ke1-1];
1436 u2min = fU[ke2-1];
1437 ierrf = 0;
1438 fCfrom = "MNContour ";
1439 fNfcnfr = nfcnco;
1440 if (fISW[4] >= 0) {
1441 Printf(" START MNCONTOUR CALCULATION OF %4d POINTS ON CONTOUR.",nptu);
1442 if (fNpar > 2) {
1443 if (fNpar == 3) {
1444 ki3 = 6 - ki1 - ki2;
1445 ke3 = fNexofi[ki3-1];
1446 Printf(" EACH POINT IS A MINIMUM WITH RESPECT TO PARAMETER %3d %s",ke3,(const char*)fCpnam[ke3-1]);
1447 } else {
1448 Printf(" EACH POINT IS A MINIMUM WITH RESPECT TO THE OTHER %3d VARIABLE PARAMETERS.",fNpar - 2);
1449 }
1450 }
1451 }
1452
1453// Find the first four points using MNMNOT
1454// first two points
1455 mnmnot(ke1, ke2, val2pl, val2mi);
1456 if (fErn[ki1-1] == fUndefi) {
1457 xptu[0] = fAlim[ke1-1];
1458 mnwarn("W", "MNContour ", "Contour squeezed by parameter limits.");
1459 } else {
1460 if (fErn[ki1-1] >= 0) goto L1500;
1461 xptu[0] = u1min + fErn[ki1-1];
1462 }
1463 yptu[0] = val2mi;
1464
1465 if (fErp[ki1-1] == fUndefi) {
1466 xptu[2] = fBlim[ke1-1];
1467 mnwarn("W", "MNContour ", "Contour squeezed by parameter limits.");
1468 } else {
1469 if (fErp[ki1-1] <= 0) goto L1500;
1470 xptu[2] = u1min + fErp[ki1-1];
1471 }
1472 yptu[2] = val2pl;
1473 scalx = 1 / (xptu[2] - xptu[0]);
1474// next two points
1475 mnmnot(ke2, ke1, val2pl, val2mi);
1476 if (fErn[ki2-1] == fUndefi) {
1477 yptu[1] = fAlim[ke2-1];
1478 mnwarn("W", "MNContour ", "Contour squeezed by parameter limits.");
1479 } else {
1480 if (fErn[ki2-1] >= 0) goto L1500;
1481 yptu[1] = u2min + fErn[ki2-1];
1482 }
1483 xptu[1] = val2mi;
1484 if (fErp[ki2-1] == fUndefi) {
1485 yptu[3] = fBlim[ke2-1];
1486 mnwarn("W", "MNContour ", "Contour squeezed by parameter limits.");
1487 } else {
1488 if (fErp[ki2-1] <= 0) goto L1500;
1489 yptu[3] = u2min + fErp[ki2-1];
1490 }
1491 xptu[3] = val2pl;
1492 scaly = 1 / (yptu[3] - yptu[1]);
1493 nowpts = 4;
1494 next = 5;
1495 if (ldebug) {
1496 Printf(" Plot of four points found by MINOS");
1497 fXpt[0] = u1min;
1498 fYpt[0] = u2min;
1499 fChpt[0] = ' ';
1500// Computing MIN
1501 nall = TMath::Min(nowpts + 1,101);
1502 for (i = 2; i <= nall; ++i) {
1503 fXpt[i-1] = xptu[i-2];
1504 fYpt[i-1] = yptu[i-2];
1505 }
1506 sprintf(fChpt,"%s"," ABCD");
1507 mnplot(fXpt, fYpt, fChpt, nall, fNpagwd, fNpagln);
1508 }
1509
1510// save some values before fixing
1511 isw2 = fISW[1];
1512 isw4 = fISW[3];
1513 sigsav = fEDM;
1514 istrav = fIstrat;
1515 dc = fDcovar;
1516 fApsi = fEpsi*.5;
1517 abest = fAmin;
1518 mpar = fNpar;
1519 nfmxin = fNfcnmx;
1520 for (i = 1; i <= mpar; ++i) { fXt[i-1] = fX[i-1]; }
1521 i__1 = mpar*(mpar + 1) / 2;
1522 for (j = 1; j <= i__1; ++j) { fVthmat[j-1] = fVhmat[j-1]; }
1523 for (i = 1; i <= mpar; ++i) {
1524 fCONTgcc[i-1] = fGlobcc[i-1];
1525 fCONTw[i-1] = fWerr[i-1];
1526 }
1527// fix the two parameters in question
1528 kints = fNiofex[ke1-1];
1529 mnfixp(kints-1, ierr);
1530 kints = fNiofex[ke2-1];
1531 mnfixp(kints-1, ierr);
1532// Fill in the rest of the points
1533 for (inew = next; inew <= nptu; ++inew) {
1534// find the two neighbouring points with largest separation
1535 bigdis = 0;
1536 for (iold = 1; iold <= inew - 1; ++iold) {
1537 i2 = iold + 1;
1538 if (i2 == inew) i2 = 1;
1539 d__1 = scalx*(xptu[iold-1] - xptu[i2-1]);
1540 d__2 = scaly*(yptu[iold-1] - yptu[i2-1]);
1541 dist = d__1*d__1 + d__2*d__2;
1542 if (dist > bigdis) {
1543 bigdis = dist;
1544 idist = iold;
1545 }
1546 }
1547 i1 = idist;
1548 i2 = i1 + 1;
1549 if (i2 == inew) i2 = 1;
1550// next point goes between I1 and I2
1551 a1 = .5;
1552 a2 = .5;
1553L300:
1554 fXmidcr = a1*xptu[i1-1] + a2*xptu[i2-1];
1555 fYmidcr = a1*yptu[i1-1] + a2*yptu[i2-1];
1556 xdir = yptu[i2-1] - yptu[i1-1];
1557 ydir = xptu[i1-1] - xptu[i2-1];
1558 sclfac = TMath::Max(TMath::Abs(xdir*scalx),TMath::Abs(ydir*scaly));
1559 fXdircr = xdir / sclfac;
1560 fYdircr = ydir / sclfac;
1561 fKe1cr = ke1;
1562 fKe2cr = ke2;
1563// Find the contour crossing point along DIR
1564 fAmin = abest;
1565 mncros(aopt, iercr);
1566 if (iercr > 1) {
1567// If cannot find mid-point, try closer to point 1
1568 if (a1 > .5) {
1569 if (fISW[4] >= 0) {
1570 Printf(" MNCONT CANNOT FIND NEXT POINT ON CONTOUR. ONLY %3d POINTS FOUND.",nowpts);
1571 }
1572 goto L950;
1573 }
1574 mnwarn("W", "MNContour ", "Cannot find midpoint, try closer.");
1575 a1 = .75;
1576 a2 = .25;
1577 goto L300;
1578 }
1579// Contour has been located, insert new point in list
1580 for (move = nowpts; move >= i1 + 1; --move) {
1581 xptu[move] = xptu[move-1];
1582 yptu[move] = yptu[move-1];
1583 }
1584 ++nowpts;
1585 xptu[i1] = fXmidcr + fXdircr*aopt;
1586 yptu[i1] = fYmidcr + fYdircr*aopt;
1587 }
1588L950:
1589
1590 ierrf = nowpts;
1591 fCstatu = "SUCCESSFUL";
1592 if (nowpts < nptu) fCstatu = "INCOMPLETE";
1593
1594// make a lineprinter plot of the contour
1595 if (fISW[4] >= 0) {
1596 fXpt[0] = u1min;
1597 fYpt[0] = u2min;
1598 fChpt[0] = ' ';
1599 nall = TMath::Min(nowpts + 1,101);
1600 for (i = 2; i <= nall; ++i) {
1601 fXpt[i-1] = xptu[i-2];
1602 fYpt[i-1] = yptu[i-2];
1603 fChpt[i-1] = 'X';
1604 }
1605 fChpt[nall] = 0;
1606 Printf(" Y-AXIS: PARAMETER %3d %s",ke2,(const char*)fCpnam[ke2-1]);
1607
1608 mnplot(fXpt, fYpt, fChpt, nall, fNpagwd, fNpagln);
1609
1610 Printf(" X-AXIS: PARAMETER %3d %s",ke1,(const char*)fCpnam[ke1-1]);
1611 }
1612// print out the coordinates around the contour
1613 if (fISW[4] >= 1) {
1614 npcol = (nowpts + 1) / 2;
1615 nfcol = nowpts / 2;
1616 Printf("%5d POINTS ON CONTOUR. FMIN=%13.5e ERRDEF=%11.3g",nowpts,abest,fUp);
1617 Printf(" %s%s%s%s",(const char*)fCpnam[ke1-1],
1618 (const char*)fCpnam[ke2-1],
1619 (const char*)fCpnam[ke1-1],
1620 (const char*)fCpnam[ke2-1]);
1621 for (line = 1; line <= nfcol; ++line) {
1622 lr = line + npcol;
1623 Printf(" %5d%13.5e%13.5e %5d%13.5e%13.5e",line,xptu[line-1],yptu[line-1],lr,xptu[lr-1],yptu[lr-1]);
1624 }
1625 if (nfcol < npcol) {
1626 Printf(" %5d%13.5e%13.5e",npcol,xptu[npcol-1],yptu[npcol-1]);
1627 }
1628 }
1629// contour finished. reset v
1630 fItaur = 1;
1631 mnfree(1);
1632 mnfree(1);
1633 i__1 = mpar*(mpar + 1) / 2;
1634 for (j = 1; j <= i__1; ++j) { fVhmat[j-1] = fVthmat[j-1]; }
1635 for (i = 1; i <= mpar; ++i) {
1636 fGlobcc[i-1] = fCONTgcc[i-1];
1637 fWerr[i-1] = fCONTw[i-1];
1638 fX[i-1] = fXt[i-1];
1639 }
1640 mninex(fX);
1641 fEDM = sigsav;
1642 fAmin = abest;
1643 fISW[1] = isw2;
1644 fISW[3] = isw4;
1645 fDcovar = dc;
1646 fItaur = 0;
1647 fNfcnmx = nfmxin;
1648 fIstrat = istrav;
1649 fU[ke1-1] = u1min;
1650 fU[ke2-1] = u2min;
1651 goto L2000;
1652// Error returns
1653L1350:
1654 Printf(" INVALID PARAMETER NUMBERS.");
1655 goto L1450;
1656L1400:
1657 Printf(" LESS THAN FOUR POINTS REQUESTED.");
1658L1450:
1659 ierrf = -1;
1660 fCstatu = "USER ERROR";
1661 goto L2000;
1662L1500:
1663 Printf(" MNCONT UNABLE TO FIND FOUR POINTS.");
1664 fU[ke1-1] = u1min;
1665 fU[ke2-1] = u2min;
1666 ierrf = 0;
1667 fCstatu = "FAILED";
1668L2000:
1669 fCfrom = "MNContour ";
1670 fNfcnfr = nfcnco;
1671}
1672
1673////////////////////////////////////////////////////////////////////////////////
1674/// Cracks the free-format input
1675///
1676/// Cracks the free-format input, expecting zero or more
1677/// alphanumeric fields (which it joins into COMAND(1:LNC))
1678/// followed by one or more numeric fields separated by
1679/// blanks and/or one comma. The numeric fields are put into
1680/// the LLIST (but at most MXP) elements of PLIST.
1681///
1682/// IERR :
1683/// - = 0 if no errors,
1684/// - = 1 if error(s).
1685
1686void TMinuit::mncrck(TString cardbuf, Int_t maxcwd, TString &comand, Int_t &lnc,
1687 Int_t mxp, Double_t *plist, Int_t &llist, Int_t &ierr, Int_t)
1688{
1689 /* Initialized data */
1690
1691 char *cnull = 0;
1692 const char *cnumer = "123456789-.0+";
1693
1694 /* Local variables */
1695 Int_t ifld, iend, lend, left, nreq, ipos, kcmnd, nextb, ic, ibegin, ltoadd;
1696 Int_t ielmnt, lelmnt[25], nelmnt;
1697 TString ctemp;
1698 char *celmnt[25];
1699 char command[25];
1700
1701 /* Function Body */
1702 char *crdbuf = (char*)cardbuf.Data();
1703 lend = cardbuf.Length();
1704 ielmnt = 0;
1705 nextb = 1;
1706 ierr = 0;
1707// loop over words CELMNT
1708L10:
1709 for (ipos = nextb; ipos <= lend; ++ipos) {
1710 ibegin = ipos;
1711 if (crdbuf[ipos-1] == ' ') continue;
1712 if (crdbuf[ipos-1] == ',') goto L250;
1713 goto L150;
1714 }
1715 goto L300;
1716L150:
1717// found beginning of word, look for end
1718 for (ipos = ibegin + 1; ipos <= lend; ++ipos) {
1719 if (crdbuf[ipos-1] == ' ') goto L250;
1720 if (crdbuf[ipos-1] == ',') goto L250;
1721 }
1722 ipos = lend + 1;
1723L250:
1724 iend = ipos - 1;
1725 ++ielmnt;
1726 if (iend >= ibegin) celmnt[ielmnt-1] = &crdbuf[ibegin-1];
1727 else celmnt[ielmnt-1] = cnull;
1728 lelmnt[ielmnt-1] = iend - ibegin + 1;
1729 if (lelmnt[ielmnt-1] > 19) {
1730 Printf(" MINUIT WARNING: INPUT DATA WORD TOO LONG.");
1731 ctemp = cardbuf(ibegin-1,iend-ibegin+1);
1732 Printf(" ORIGINAL:%s",ctemp.Data());
1733 Printf(" TRUNCATED TO:%s",celmnt[ielmnt-1]);
1734 lelmnt[ielmnt-1] = 19;
1735 }
1736 if (ipos >= lend) goto L300;
1737 if (ielmnt >= 25) goto L300;
1738// look for comma or beginning of next word
1739 for (ipos = iend + 1; ipos <= lend; ++ipos) {
1740 if (crdbuf[ipos-1] == ' ') continue;
1741 nextb = ipos;
1742 if (crdbuf[ipos-1] == ',') nextb = ipos + 1;
1743 goto L10;
1744 }
1745// All elements found, join the alphabetic ones to
1746// form a command
1747L300:
1748 nelmnt = ielmnt;
1749 command[0] = ' '; command[1] = 0;
1750 lnc = 1;
1751 plist[0] = 0;
1752 llist = 0;
1753 if (ielmnt == 0) goto L900;
1754 kcmnd = 0;
1755 for (ielmnt = 1; ielmnt <= nelmnt; ++ielmnt) {
1756 if ( celmnt[ielmnt-1] == cnull) goto L450;
1757 for (ic = 1; ic <= 13; ++ic) {
1758 if (*celmnt[ielmnt-1] == cnumer[ic-1]) goto L450;
1759 }
1760 if (kcmnd >= maxcwd) continue;
1761 left = maxcwd - kcmnd;
1762 ltoadd = lelmnt[ielmnt-1];
1763 if (ltoadd > left) ltoadd = left;
1764 strncpy(&command[kcmnd],celmnt[ielmnt-1],ltoadd);
1765 kcmnd += ltoadd;
1766 if (kcmnd == maxcwd) continue;
1767 command[kcmnd] = ' ';
1768 ++kcmnd;
1769 command[kcmnd] = 0;
1770 }
1771 lnc = kcmnd;
1772 goto L900;
1773L450:
1774 lnc = kcmnd;
1775// we have come to a numeric field
1776 llist = 0;
1777 for (ifld = ielmnt; ifld <= nelmnt; ++ifld) {
1778 ++llist;
1779 if (llist > mxp) {
1780 nreq = nelmnt - ielmnt + 1;
1781 Printf(" MINUIT WARNING IN MNCRCK: ");
1782 Printf(" COMMAND HAS INPUT %5d NUMERIC FIELDS, BUT MINUIT CAN ACCEPT ONLY%3d",nreq,mxp);
1783 goto L900;
1784 }
1785 if (celmnt[ifld-1] == cnull) plist[llist-1] = 0;
1786 else {
1787 sscanf(celmnt[ifld-1],"%lf",&plist[llist-1]);
1788 }
1789 }
1790// end loop over numeric fields
1791L900:
1792 if (lnc <= 0) lnc = 1;
1793 comand = command;
1794}
1795
1796////////////////////////////////////////////////////////////////////////////////
1797/// Find point where MNEVAL=AMIN+UP
1798///
1799/// Find point where MNEVAL=AMIN+UP, along the line through
1800/// XMIDCR,YMIDCR with direction XDIRCR,YDIRCR, where X and Y
1801/// are parameters KE1CR and KE2CR. If KE2CR=0 (from MINOS),
1802/// only KE1CR is varied. From MNCONT, both are varied.
1803/// Crossing point is at
1804///
1805/// (U(KE1),U(KE2)) = (XMID,YMID) + AOPT*(XDIR,YDIR)
1806
1807void TMinuit::mncros(Double_t &aopt, Int_t &iercr)
1808{
1809 /* Local variables */
1810 Double_t alsb[3], flsb[3], bmin, bmax, zmid, sdev, zdir, zlim;
1811 Double_t coeff[3], aleft, aulim, fdist, adist, aminsv;
1812 Double_t anext, fnext, slope, s1, s2, x1, x2, ecarmn, ecarmx;
1813 Double_t determ, rt, smalla, aright, aim, tla, tlf, dfda,ecart;
1814 Int_t iout=0, i, ileft, ierev, maxlk, ibest, ik, it;
1815 Int_t noless, iworst=0, iright, itoohi, kex, ipt;
1816 Bool_t ldebug;
1817 const char *chsign;
1818 x2 = 0;
1819
1820 ldebug = fIdbg[6] >= 1;
1821 aminsv = fAmin;
1822// convergence when F is within TLF of AIM and next prediction
1823// of AOPT is within TLA of previous value of AOPT
1824 aim = fAmin + fUp;
1825 tlf = fUp*.01;
1826 tla = .01;
1827 fXpt[0] = 0;
1828 fYpt[0] = aim;
1829 fChpt[0] = ' ';
1830 ipt = 1;
1831 if (fKe2cr == 0) {
1832 fXpt[1] = -1;
1833 fYpt[1] = fAmin;
1834 fChpt[1] = '.';
1835 ipt = 2;
1836 }
1837// find the largest allowed A
1838 aulim = 100;
1839 for (ik = 1; ik <= 2; ++ik) {
1840 if (ik == 1) {
1841 kex = fKe1cr;
1842 zmid = fXmidcr;
1843 zdir = fXdircr;
1844 } else {
1845 if (fKe2cr == 0) continue;
1846 kex = fKe2cr;
1847 zmid = fYmidcr;
1848 zdir = fYdircr;
1849 }
1850 if (fNvarl[kex-1] <= 1) continue;
1851 if (zdir == 0) continue;
1852 zlim = fAlim[kex-1];
1853 if (zdir > 0) zlim = fBlim[kex-1];
1854 aulim = TMath::Min(aulim,(zlim - zmid) / zdir);
1855 }
1856// LSB = Line Search Buffer
1857// first point
1858 anext = 0;
1859 aopt = anext;
1860 fLimset = kFALSE;
1861 if (aulim < aopt + tla) fLimset = kTRUE;
1862 mneval(anext, fnext, ierev);
1863// debug printout:
1864 if (ldebug) {
1865 Printf(" MNCROS: calls=%8d AIM=%10.5f F,A=%10.5f%10.5f",fNfcn,aim,fnext,aopt);
1866 }
1867 if (ierev > 0) goto L900;
1868 if (fLimset && fnext <= aim) goto L930;
1869 ++ipt;
1870 fXpt[ipt-1] = anext;
1871 fYpt[ipt-1] = fnext;
1872 fChpt[ipt-1] = charal[ipt-1];
1873 alsb[0] = anext;
1874 flsb[0] = fnext;
1875 fnext = TMath::Max(fnext,aminsv + fUp*.1);
1876 aopt = TMath::Sqrt(fUp / (fnext - aminsv)) - 1;
1877 if (TMath::Abs(fnext - aim) < tlf) goto L800;
1878
1879 if (aopt < -.5)aopt = -.5;
1880 if (aopt > 1) aopt = 1;
1881 fLimset = kFALSE;
1882 if (aopt > aulim) {
1883 aopt = aulim;
1884 fLimset = kTRUE;
1885 }
1886 mneval(aopt, fnext, ierev);
1887// debug printout:
1888 if (ldebug) {
1889 Printf(" MNCROS: calls=%8d AIM=%10.5f F,A=%10.5f%10.5f",fNfcn,aim,fnext,aopt);
1890 }
1891 if (ierev > 0) goto L900;
1892 if (fLimset && fnext <= aim) goto L930;
1893 alsb[1] = aopt;
1894 ++ipt;
1895 fXpt[ipt-1] = alsb[1];
1896 fYpt[ipt-1] = fnext;
1897 fChpt[ipt-1] = charal[ipt-1];
1898 flsb[1] = fnext;
1899 dfda = (flsb[1] - flsb[0]) / (alsb[1] - alsb[0]);
1900// DFDA must be positive on the contour
1901 if (dfda > 0) goto L460;
1902L300:
1903 mnwarn("D", "MNCROS ", "Looking for slope of the right sign");
1904 maxlk = 15 - ipt;
1905 for (it = 1; it <= maxlk; ++it) {
1906 alsb[0] = alsb[1];
1907 flsb[0] = flsb[1];
1908 aopt = alsb[0] + Double_t(it)*.2;
1909 fLimset = kFALSE;
1910 if (aopt > aulim) {
1911 aopt = aulim;
1912 fLimset = kTRUE;
1913 }
1914 mneval(aopt, fnext, ierev);
1915// debug printout:
1916 if (ldebug) {
1917 Printf(" MNCROS: calls=%8d AIM=%10.5f F,A=%10.5f%10.5f",fNfcn,aim,fnext,aopt);
1918 }
1919 if (ierev > 0) goto L900;
1920 if (fLimset && fnext <= aim) goto L930;
1921 alsb[1] = aopt;
1922 ++ipt;
1923 fXpt[ipt-1] = alsb[1];
1924 fYpt[ipt-1] = fnext;
1925 fChpt[ipt-1] = charal[ipt-1];
1926 flsb[1] = fnext;
1927 dfda = (flsb[1] - flsb[0]) / (alsb[1] - alsb[0]);
1928 if (dfda > 0) goto L450;
1929 }
1930 mnwarn("W", "MNCROS ", "Cannot find slope of the right sign");
1931 goto L950;
1932L450:
1933// we have two points with the right slope
1934L460:
1935 aopt = alsb[1] + (aim - flsb[1]) / dfda;
1936 fdist = TMath::Min(TMath::Abs(aim - flsb[0]),TMath::Abs(aim - flsb[1]));
1937 adist = TMath::Min(TMath::Abs(aopt - alsb[0]),TMath::Abs(aopt - alsb[1]));
1938 tla = .01;
1939 if (TMath::Abs(aopt) > 1) tla = TMath::Abs(aopt)*.01;
1940 if (adist < tla && fdist < tlf) goto L800;
1941 if (ipt >= 15) goto L950;
1942 bmin = TMath::Min(alsb[0],alsb[1]) - 1;
1943 if (aopt < bmin) aopt = bmin;
1944 bmax = TMath::Max(alsb[0],alsb[1]) + 1;
1945 if (aopt > bmax) aopt = bmax;
1946// Try a third point
1947 fLimset = kFALSE;
1948 if (aopt > aulim) {
1949 aopt = aulim;
1950 fLimset = kTRUE;
1951 }
1952 mneval(aopt, fnext, ierev);
1953// debug printout:
1954 if (ldebug) {
1955 Printf(" MNCROS: calls=%8d AIM=%10.5f F,A=%10.5f%10.5f",fNfcn,aim,fnext,aopt);
1956 }
1957 if (ierev > 0) goto L900;
1958 if (fLimset && fnext <= aim) goto L930;
1959 alsb[2] = aopt;
1960 ++ipt;
1961 fXpt[ipt-1] = alsb[2];
1962 fYpt[ipt-1] = fnext;
1963 fChpt[ipt-1] = charal[ipt-1];
1964 flsb[2] = fnext;
1965// now we have three points, ask how many <AIM
1966 ecarmn = TMath::Abs(fnext-aim);
1967 ibest = 3;
1968 ecarmx = 0;
1969 noless = 0;
1970 for (i = 1; i <= 3; ++i) {
1971 ecart = TMath::Abs(flsb[i-1] - aim);
1972 if (ecart > ecarmx) { ecarmx = ecart; iworst = i; }
1973 if (ecart < ecarmn) { ecarmn = ecart; ibest = i; }
1974 if (flsb[i-1] < aim) ++noless;
1975 }
1976// if at least one on each side of AIM, fit a parabola
1977 if (noless == 1 || noless == 2) goto L500;
1978// if all three are above AIM, third must be closest to AIM
1979 if (noless == 0 && ibest != 3) goto L950;
1980// if all three below, and third is not best, then slope
1981// has again gone negative, look for positive slope.
1982 if (noless == 3 && ibest != 3) {
1983 alsb[1] = alsb[2];
1984 flsb[1] = flsb[2];
1985 goto L300;
1986 }
1987// in other cases, new straight line thru last two points
1988 alsb[iworst-1] = alsb[2];
1989 flsb[iworst-1] = flsb[2];
1990 dfda = (flsb[1] - flsb[0]) / (alsb[1] - alsb[0]);
1991 goto L460;
1992// parabola fit
1993L500:
1994 mnpfit(alsb, flsb, 3, coeff, sdev);
1995 if (coeff[2] <= 0) {
1996 mnwarn("D", "MNCROS ", "Curvature is negative near contour line.");
1997 }
1998 determ = coeff[1]*coeff[1] - coeff[2]*4*(coeff[0] - aim);
1999 if (determ <= 0) {
2000 mnwarn("D", "MNCROS ", "Problem 2, impossible determinant");
2001 goto L950;
2002 }
2003// Find which root is the right one
2004 rt = TMath::Sqrt(determ);
2005 x1 = (-coeff[1] + rt) / (coeff[2]*2);
2006 x2 = (-coeff[1] - rt) / (coeff[2]*2);
2007 s1 = coeff[1] + x1*2*coeff[2];
2008 s2 = coeff[1] + x2*2*coeff[2];
2009 if (s1*s2 > 0) {
2010 Printf(" MNCONTour problem 1");
2011 }
2012 aopt = x1;
2013 slope = s1;
2014 if (s2 > 0) {
2015 aopt = x2;
2016 slope = s2;
2017 }
2018// ask if converged
2019 tla = .01;
2020 if (TMath::Abs(aopt) > 1) tla = TMath::Abs(aopt)*.01;
2021 if (TMath::Abs(aopt - alsb[ibest-1]) < tla && TMath::Abs(flsb[ibest-1] - aim) < tlf) {
2022 goto L800;
2023 }
2024 if (ipt >= 15) goto L950;
2025
2026// see if proposed point is in acceptable zone between L and R
2027// first find ILEFT, IRIGHT, IOUT and IBEST
2028 ileft = 0;
2029 iright = 0;
2030 ibest = 1;
2031 ecarmx = 0;
2032 ecarmn = TMath::Abs(aim - flsb[0]);
2033 for (i = 1; i <= 3; ++i) {
2034 ecart = TMath::Abs(flsb[i-1] - aim);
2035 if (ecart < ecarmn) { ecarmn = ecart; ibest = i; }
2036 if (ecart > ecarmx) { ecarmx = ecart; }
2037 if (flsb[i-1] > aim) {
2038 if (iright == 0) iright = i;
2039 else if (flsb[i-1] > flsb[iright-1]) iout = i;
2040 else { iout = iright; iright = i; }
2041 }
2042 else if (ileft == 0) ileft = i;
2043 else if (flsb[i-1] < flsb[ileft-1]) iout = i;
2044 else { iout = ileft; ileft = i; }
2045 }
2046// avoid keeping a very bad point next time around
2047 if (ecarmx > TMath::Abs(flsb[iout-1] - aim)*10) {
2048 aopt = aopt*.5 + (alsb[iright-1] + alsb[ileft-1])*.25;
2049 }
2050// knowing ILEFT and IRIGHT, get acceptable window
2051 smalla = tla*.1;
2052 if (slope*smalla > tlf) smalla = tlf / slope;
2053 aleft = alsb[ileft-1] + smalla;
2054 aright = alsb[iright-1] - smalla;
2055// move proposed point AOPT into window if necessary
2056 if (aopt < aleft) aopt = aleft;
2057 if (aopt > aright) aopt = aright;
2058 if (aleft > aright) aopt = (aleft + aright)*.5;
2059
2060// see if proposed point outside limits (should be impossible!)
2061 fLimset = kFALSE;
2062 if (aopt > aulim) {
2063 aopt = aulim;
2064 fLimset = kTRUE;
2065 }
2066// Evaluate function at new point AOPT
2067 mneval(aopt, fnext, ierev);
2068// debug printout:
2069 if (ldebug) {
2070 Printf(" MNCROS: calls=%8d AIM=%10.5f F,A=%10.5f%10.5f",fNfcn,aim,fnext,aopt);
2071 }
2072 if (ierev > 0) goto L900;
2073 if (fLimset && fnext <= aim) goto L930;
2074 ++ipt;
2075 fXpt[ipt-1] = aopt;
2076 fYpt[ipt-1] = fnext;
2077 fChpt[ipt-1] = charal[ipt-1];
2078// Replace odd point by new one
2079 alsb[iout-1] = aopt;
2080 flsb[iout-1] = fnext;
2081// the new point may not be the best, but it is the only one
2082// which could be good enough to pass convergence criteria
2083 ibest = iout;
2084 goto L500;
2085
2086// Contour has been located, return point to MNCONT OR MINOS
2087L800:
2088 iercr = 0;
2089 goto L1000;
2090// error in the minimization
2091L900:
2092 if (ierev == 1) goto L940;
2093 goto L950;
2094// parameter up against limit
2095L930:
2096 iercr = 1;
2097 goto L1000;
2098// too many calls to FCN
2099L940:
2100 iercr = 2;
2101 goto L1000;
2102// cannot find next point
2103L950:
2104 iercr = 3;
2105// in any case
2106L1000:
2107 if (ldebug) {
2108 itoohi = 0;
2109 for (i = 1; i <= ipt; ++i) {
2110 if (fYpt[i-1] > aim + fUp) {
2111 fYpt[i-1] = aim + fUp;
2112 fChpt[i-1] = '+';
2113 itoohi = 1;
2114 }
2115 }
2116 fChpt[ipt] = 0;
2117 chsign = "POSI";
2118 if (fXdircr < 0) chsign = "NEGA";
2119 if (fKe2cr == 0) {
2120 Printf(" %sTIVE MINOS ERROR, PARAMETER %3d",chsign,fKe1cr);
2121 }
2122 if (itoohi == 1) {
2123 Printf("POINTS LABELLED '+' WERE TOO HIGH TO PLOT.");
2124 }
2125 if (iercr == 1) {
2126 Printf("RIGHTMOST POINT IS UP AGAINST LIMIT.");
2127 }
2128 mnplot(fXpt, fYpt, fChpt, ipt, fNpagwd, fNpagln);
2129 }
2130}
2131
2132////////////////////////////////////////////////////////////////////////////////
2133/// Makes sure that the current point is a local minimum
2134///
2135/// Makes sure that the current point is a local
2136/// minimum and that the error matrix exists,
2137/// or at least something good enough for MINOS and MNCONT
2138
2140{
2141 /* Local variables */
2142 Double_t dxdi, wint;
2143 Int_t ndex, iext, i, j;
2144
2145 if (fISW[3] < 1) {
2146 Printf(" FUNCTION MUST BE MINIMIZED BEFORE CALLING %s",(const char*)fCfrom);
2147 fApsi = fEpsi;
2148 mnmigr();
2149 }
2150 if (fISW[1] < 3) {
2151 mnhess();
2152 if (fISW[1] < 1) {
2153 mnwarn("W", fCfrom, "NO ERROR MATRIX. WILL IMPROVISE.");
2154 for (i = 1; i <= fNpar; ++i) {
2155 ndex = i*(i-1) / 2;
2156 for (j = 1; j <= i-1; ++j) {
2157 ++ndex;
2158 fVhmat[ndex-1] = 0;
2159 }
2160 ++ndex;
2161 if (fG2[i-1] <= 0) {
2162 wint = fWerr[i-1];
2163 iext = fNexofi[i-1];
2164 if (fNvarl[iext-1] > 1) {
2165 mndxdi(fX[i-1], i-1, dxdi);
2166 if (TMath::Abs(dxdi) < .001) wint = .01;
2167 else wint /= TMath::Abs(dxdi);
2168 }
2169 fG2[i-1] = fUp / (wint*wint);
2170 }
2171 fVhmat[ndex-1] = 2 / fG2[i-1];
2172 }
2173 fISW[1] = 1;
2174 fDcovar = 1;
2175 } else mnwerr();
2176 }
2177}
2178
2179////////////////////////////////////////////////////////////////////////////////
2180/// Calculates the first derivatives of FCN (GRD)
2181///
2182/// Calculates the first derivatives of FCN (GRD),
2183/// either by finite differences or by transforming the user-
2184/// supplied derivatives to internal coordinates,
2185/// according to whether fISW[2] is zero or one.
2186
2188{
2189 /* Local variables */
2190 Double_t step, dfmin, stepb4, dd, df, fs1;
2191 Double_t tlrstp, tlrgrd, epspri, optstp, stpmax, stpmin, fs2, grbfor=0, d1d2, xtf;
2192 Int_t icyc, ncyc, iint, iext, i, nparx;
2193 Bool_t ldebug;
2194
2195 nparx = fNpar;
2196 ldebug = fIdbg[2] >= 1;
2197 if (fAmin == fUndefi) mnamin();
2198 if (fISW[2] == 1) goto L100;
2199
2200 if (ldebug) {
2201// make sure starting at the right place
2202 mninex(fX);
2203 nparx = fNpar;
2204 Eval(nparx, fGin, fs1, fU, 4); ++fNfcn;
2205 if (fs1 != fAmin) {
2206 df = fAmin - fs1;
2207 mnwarn("D", "MNDERI", TString::Format("function value differs from AMIN by %12.3g",df));
2208 fAmin = fs1;
2209 }
2210 Printf(" FIRST DERIVATIVE DEBUG PRINTOUT. MNDERI");
2211 Printf(" PAR DERIV STEP MINSTEP OPTSTEP D1-D2 2ND DRV");
2212 }
2213 dfmin = fEpsma2*8*(TMath::Abs(fAmin) + fUp);
2214 if (fIstrat <= 0) {
2215 ncyc = 2;
2216 tlrstp = .5;
2217 tlrgrd = .1;
2218 } else if (fIstrat == 1) {
2219 ncyc = 3;
2220 tlrstp = .3;
2221 tlrgrd = .05;
2222 } else {
2223 ncyc = 5;
2224 tlrstp = .1;
2225 tlrgrd = .02;
2226 }
2227// loop over variable parameters
2228 for (i = 1; i <= fNpar; ++i) {
2229 epspri = fEpsma2 + TMath::Abs(fGrd[i-1]*fEpsma2);
2230// two-point derivatives always assumed necessary
2231// maximum number of cycles over step size depends on strategy
2232 xtf = fX[i-1];
2233 stepb4 = 0;
2234// loop as little as possible here!/
2235 for (icyc = 1; icyc <= ncyc; ++icyc) {
2236// theoretically best step
2237 optstp = TMath::Sqrt(dfmin / (TMath::Abs(fG2[i-1]) + epspri));
2238// step cannot decrease by more than a factor of ten
2239 step = TMath::Max(optstp,TMath::Abs(fGstep[i-1]*.1));
2240// but if parameter has limits, max step size = 0.5
2241 if (fGstep[i-1] < 0 && step > .5) step = .5;
2242// and not more than ten times the previous step
2243 stpmax = TMath::Abs(fGstep[i-1])*10;
2244 if (step > stpmax) step = stpmax;
2245// minimum step size allowed by machine precision
2246 stpmin = TMath::Abs(fEpsma2*fX[i-1])*8;
2247 if (step < stpmin) step = stpmin;
2248// end of iterations if step change less than factor 2
2249 if (TMath::Abs((step - stepb4) / step) < tlrstp) goto L50;
2250// take step positive
2251 stepb4 = step;
2252 if (fGstep[i-1] > 0) fGstep[i-1] = TMath::Abs(step);
2253 else fGstep[i-1] = -TMath::Abs(step);
2254 stepb4 = step;
2255 fX[i-1] = xtf + step;
2256 mninex(fX);
2257 Eval(nparx, fGin, fs1, fU, 4); ++fNfcn;
2258// take step negative
2259 fX[i-1] = xtf - step;
2260 mninex(fX);
2261 Eval(nparx, fGin, fs2, fU, 4); ++fNfcn;
2262 grbfor = fGrd[i-1];
2263 fGrd[i-1] = (fs1 - fs2) / (step*2);
2264 fG2[i-1] = (fs1 + fs2 - fAmin*2) / (step*step);
2265 fX[i-1] = xtf;
2266 if (ldebug) {
2267 d1d2 = (fs1 + fs2 - fAmin*2) / step;
2268 Printf("%4d%11.3g%11.3g%10.2g%10.2g%10.2g%10.2g",i,fGrd[i-1],step,stpmin,optstp,d1d2,fG2[i-1]);
2269 }
2270// see if another iteration is necessary
2271 if (TMath::Abs(grbfor - fGrd[i-1]) / (TMath::Abs(fGrd[i-1]) + dfmin/step) < tlrgrd)
2272 goto L50;
2273 }
2274// end of ICYC loop. too many iterations
2275 if (ncyc == 1) goto L50;
2276 mnwarn("D", "MNDERI", TString::Format("First derivative not converged. %g%g",fGrd[i-1],grbfor));
2277L50:
2278 ;
2279 }
2280 mninex(fX);
2281 return;
2282// derivatives calc by fcn
2283L100:
2284 for (iint = 1; iint <= fNpar; ++iint) {
2285 iext = fNexofi[iint-1];
2286 if (fNvarl[iext-1] <= 1) {
2287 fGrd[iint-1] = fGin[iext-1];
2288 } else {
2289 dd = (fBlim[iext-1] - fAlim[iext-1])*.5*TMath::Cos(fX[iint-1]);
2290 fGrd[iint-1] = fGin[iext-1]*dd;
2291 }
2292 }
2293}
2294
2295////////////////////////////////////////////////////////////////////////////////
2296/// Calculates the transformation factor between ext/internal values
2297///
2298/// calculates the transformation factor between external and
2299/// internal parameter values. this factor is one for
2300/// parameters which are not limited. called from MNEMAT.
2301
2303{
2304 Int_t i = fNexofi[ipar];
2305 dxdi = 1;
2306 if (fNvarl[i-1] > 1) {
2307 dxdi = TMath::Abs((fBlim[i-1] - fAlim[i-1])*TMath::Cos(pint))*.5;
2308 }
2309}
2310
2311////////////////////////////////////////////////////////////////////////////////
2312/// Compute matrix eigen values
2313
2314void TMinuit::mneig(Double_t *a, Int_t ndima, Int_t n, Int_t mits, Double_t *work, Double_t precis, Int_t &ifault)
2315{
2316 /* System generated locals */
2317 Int_t a_offset;
2318 Double_t d__1;
2319
2320 /* Local variables */
2321 Double_t b, c, f, h, r, s, hh, gl, pr, pt;
2322 Int_t i, j, k, l, m=0, i0, i1, j1, m1, n1;
2323
2324// PRECIS is the machine precision EPSMAC
2325 /* Parameter adjustments */
2326 a_offset = ndima + 1;
2327 a -= a_offset;
2328 --work;
2329
2330 /* Function Body */
2331 ifault = 1;
2332
2333 i = n;
2334 for (i1 = 2; i1 <= n; ++i1) {
2335 l = i-2;
2336 f = a[i + (i-1)*ndima];
2337 gl = 0;
2338
2339 if (l < 1) goto L25;
2340
2341 for (k = 1; k <= l; ++k) {
2342 d__1 = a[i + k*ndima];
2343 gl += d__1*d__1;
2344 }
2345L25:
2346 h = gl + f*f;
2347
2348 if (gl > 1e-35) goto L30;
2349
2350 work[i] = 0;
2351 work[n + i] = f;
2352 goto L65;
2353L30:
2354 ++l;
2355 gl = TMath::Sqrt(h);
2356 if (f >= 0) gl = -gl;
2357 work[n + i] = gl;
2358 h -= f*gl;
2359 a[i + (i-1)*ndima] = f - gl;
2360 f = 0;
2361 for (j = 1; j <= l; ++j) {
2362 a[j + i*ndima] = a[i + j*ndima] / h;
2363 gl = 0;
2364 for (k = 1; k <= j; ++k) { gl += a[j + k*ndima]*a[i + k*ndima]; }
2365 if (j >= l) goto L47;
2366 j1 = j + 1;
2367 for (k = j1; k <= l; ++k) { gl += a[k + j*ndima]*a[i + k*ndima]; }
2368L47:
2369 work[n + j] = gl / h;
2370 f += gl*a[j + i*ndima];
2371 }
2372 hh = f / (h + h);
2373 for (j = 1; j <= l; ++j) {
2374 f = a[i + j*ndima];
2375 gl = work[n + j] - hh*f;
2376 work[n + j] = gl;
2377 for (k = 1; k <= j; ++k) {
2378 a[j + k*ndima] = a[j + k*ndima] - f*work[n + k] - gl*a[i + k*ndima];
2379 }
2380 }
2381 work[i] = h;
2382L65:
2383 --i;
2384 }
2385 work[1] = 0;
2386 work[n + 1] = 0;
2387 for (i = 1; i <= n; ++i) {
2388 l = i-1;
2389 if (work[i] == 0 || l == 0) goto L100;
2390
2391 for (j = 1; j <= l; ++j) {
2392 gl = 0;
2393 for (k = 1; k <= l; ++k) { gl += a[i + k*ndima]*a[k + j*ndima]; }
2394 for (k = 1; k <= l; ++k) { a[k + j*ndima] -= gl*a[k + i*ndima]; }
2395 }
2396L100:
2397 work[i] = a[i + i*ndima];
2398 a[i + i*ndima] = 1;
2399 if (l == 0) continue;
2400
2401 for (j = 1; j <= l; ++j) {
2402 a[i + j*ndima] = 0;
2403 a[j + i*ndima] = 0;
2404 }
2405 }
2406
2407 n1 = n - 1;
2408 for (i = 2; i <= n; ++i) {
2409 i0 = n + i-1;
2410 work[i0] = work[i0 + 1];
2411 }
2412 work[n + n] = 0;
2413 b = 0;
2414 f = 0;
2415 for (l = 1; l <= n; ++l) {
2416 j = 0;
2417 h = precis*(TMath::Abs(work[l]) + TMath::Abs(work[n + l]));
2418 if (b < h) b = h;
2419 for (m1 = l; m1 <= n; ++m1) {
2420 m = m1;
2421 if (TMath::Abs(work[n + m]) <= b) goto L150;
2422 }
2423
2424L150:
2425 if (m == l) goto L205;
2426
2427L160:
2428 if (j == mits) return;
2429 ++j;
2430 pt = (work[l + 1] - work[l]) / (work[n + l]*2);
2431 r = TMath::Sqrt(pt*pt + 1);
2432 pr = pt + r;
2433 if (pt < 0) pr = pt - r;
2434
2435 h = work[l] - work[n + l] / pr;
2436 for (i = l; i <= n; ++i) { work[i] -= h; }
2437 f += h;
2438 pt = work[m];
2439 c = 1;
2440 s = 0;
2441 m1 = m - 1;
2442 i = m;
2443 for (i1 = l; i1 <= m1; ++i1) {
2444 j = i;
2445 --i;
2446 gl = c*work[n + i];
2447 h = c*pt;
2448 if (TMath::Abs(pt) >= TMath::Abs(work[n + i])) goto L180;
2449
2450 c = pt / work[n + i];
2451 r = TMath::Sqrt(c*c + 1);
2452 work[n + j] = s*work[n + i]*r;
2453 s = 1 / r;
2454 c /= r;
2455 goto L190;
2456L180:
2457 c = work[n + i] / pt;
2458 r = TMath::Sqrt(c*c + 1);
2459 work[n + j] = s*pt*r;
2460 s = c / r;
2461 c = 1 / r;
2462L190:
2463 pt = c*work[i] - s*gl;
2464 work[j] = h + s*(c*gl + s*work[i]);
2465 for (k = 1; k <= n; ++k) {
2466 h = a[k + j*ndima];
2467 a[k + j*ndima] = s*a[k + i*ndima] + c*h;
2468 a[k + i*ndima] = c*a[k + i*ndima] - s*h;
2469 }
2470 }
2471 work[n + l] = s*pt;
2472 work[l] = c*pt;
2473
2474 if (TMath::Abs(work[n + l]) > b) goto L160;
2475
2476L205:
2477 work[l] += f;
2478 }
2479 for (i = 1; i <= n1; ++i) {
2480 k = i;
2481 pt = work[i];
2482 i1 = i + 1;
2483 for (j = i1; j <= n; ++j) {
2484 if (work[j] >= pt) continue;
2485 k = j;
2486 pt = work[j];
2487 }
2488
2489 if (k == i) continue;
2490
2491 work[k] = work[i];
2492 work[i] = pt;
2493 for (j = 1; j <= n; ++j) {
2494 pt = a[j + i*ndima];
2495 a[j + i*ndima] = a[j + k*ndima];
2496 a[j + k*ndima] = pt;
2497 }
2498 }
2499 ifault = 0;
2500}
2501
2502////////////////////////////////////////////////////////////////////////////////
2503/// Calculates the external error matrix from the internal matrix
2504///
2505/// Note that if the matrix is declared like Double_t matrix[5][5]
2506/// in the calling program, one has to call mnemat with, eg
2507///
2508/// gMinuit->mnemat(&matrix[0][0],5);
2509
2511{
2512 /* System generated locals */
2513 Int_t emat_dim1, emat_offset;
2514
2515 /* Local variables */
2516 Double_t dxdi, dxdj;
2517 Int_t i, j, k, npard, k2, kk, iz, nperln, kga, kgb;
2518 TString ctemp;
2519
2520 /* Parameter adjustments */
2521 emat_dim1 = ndim;
2522 emat_offset = emat_dim1 + 1;
2523 emat -= emat_offset;
2524
2525 /* Function Body */
2526 if (fISW[1] < 1) return;
2527 if (fISW[4] >= 2) {
2528 Printf(" EXTERNAL ERROR MATRIX. NDIM=%4d NPAR=%3d ERR DEF=%g",ndim,fNpar,fUp);
2529 }
2530// size of matrix to be printed
2531 npard = fNpar;
2532 if (ndim < fNpar) {
2533 npard = ndim;
2534 if (fISW[4] >= 0) {
2535 Printf(" USER-DIMENSIONED ARRAY EMAT NOT BIG ENOUGH. REDUCED MATRIX CALCULATED.");
2536 }
2537 }
2538// NPERLN is the number of elements that fit on one line
2539
2540 nperln = (fNpagwd - 5) / 10;
2541 nperln = TMath::Min(nperln,13);
2542 if (fISW[4] >= 1 && npard > nperln) {
2543 Printf(" ELEMENTS ABOVE DIAGONAL ARE NOT PRINTED.");
2544 }
2545// I counts the rows of the matrix
2546 for (i = 1; i <= npard; ++i) {
2547 mndxdi(fX[i-1], i-1, dxdi);
2548 kga = i*(i-1) / 2;
2549 for (j = 1; j <= i; ++j) {
2550 mndxdi(fX[j-1], j-1, dxdj);
2551 kgb = kga + j;
2552 emat[i + j*emat_dim1] = dxdi*fVhmat[kgb-1]*dxdj*fUp;
2553 emat[j + i*emat_dim1] = emat[i + j*emat_dim1];
2554 }
2555 }
2556// IZ is number of columns to be printed in row I
2557 if (fISW[4] >= 2) {
2558 for (i = 1; i <= npard; ++i) {
2559 iz = npard;
2560 if (npard >= nperln) iz = i;
2561 ctemp = " ";
2562 for (k = 1; nperln < 0 ? k >= iz : k <= iz; k += nperln) {
2563 k2 = k + nperln - 1;
2564 if (k2 > iz) k2 = iz;
2565 for (kk = k; kk <= k2; ++kk) {
2566 ctemp += TString::Format("%10.3e ",emat[i + kk*emat_dim1]);
2567 }
2568 Printf("%s",(const char*)ctemp);
2569 }
2570 }
2571 }
2572}
2573
2574////////////////////////////////////////////////////////////////////////////////
2575/// Utility routine to get MINOS errors
2576///
2577/// Called by user.
2578///
2579/// NUMBER is the parameter number
2580///
2581/// values returned by MNERRS:
2582/// - EPLUS, EMINUS are MINOS errors of parameter NUMBER,
2583/// - EPARAB is 'parabolic' error (from error matrix).
2584/// (Errors not calculated are set = 0)
2585/// - GCC is global correlation coefficient from error matrix
2586
2587void TMinuit::mnerrs(Int_t number, Double_t &eplus, Double_t &eminus, Double_t &eparab, Double_t &gcc)
2588{
2589 Double_t dxdi;
2590 Int_t ndiag, iin, iex;
2591
2592 iex = number+1;
2593
2594 if (iex > fNu || iex <= 0) goto L900;
2595 iin = fNiofex[iex-1];
2596 if (iin <= 0) goto L900;
2597
2598// IEX is external number, IIN is internal number
2599 eplus = fErp[iin-1];
2600 if (eplus == fUndefi) eplus = 0;
2601 eminus = fErn[iin-1];
2602 if (eminus == fUndefi) eminus = 0;
2603 mndxdi(fX[iin-1], iin-1, dxdi);
2604 ndiag = iin*(iin + 1) / 2;
2605 eparab = TMath::Abs(dxdi*TMath::Sqrt(TMath::Abs(fUp*fVhmat[ndiag- 1])));
2606// global correlation coefficient
2607 gcc = 0;
2608 if (fISW[1] < 2) return;
2609 gcc = fGlobcc[iin-1];
2610 return;
2611// ERROR. parameter number not valid
2612L900:
2613 eplus = 0;
2614 eminus = 0;
2615 eparab = 0;
2616 gcc = 0;
2617}
2618
2619////////////////////////////////////////////////////////////////////////////////
2620/// Evaluates the function being analysed by MNCROS
2621///
2622/// Evaluates the function being analysed by MNCROS, which is
2623/// generally the minimum of FCN with respect to all remaining
2624/// variable parameters. The class data members contains the
2625/// data necessary to know the values of U(KE1CR) and U(KE2CR)
2626/// to be used, namely U(KE1CR) = XMIDCR + ANEXT*XDIRCR
2627/// and (if KE2CR .NE. 0) U(KE2CR) = YMIDCR + ANEXT*YDIRCR
2628
2629void TMinuit::mneval(Double_t anext, Double_t &fnext, Int_t &ierev)
2630{
2631 Int_t nparx;
2632
2633 fU[fKe1cr-1] = fXmidcr + anext*fXdircr;
2634 if (fKe2cr != 0) fU[fKe2cr-1] = fYmidcr + anext*fYdircr;
2635 mninex(fX);
2636 nparx = fNpar;
2637 Eval(nparx, fGin, fnext, fU, 4); ++fNfcn;
2638 ierev = 0;
2639 if (fNpar > 0) {
2640 fItaur = 1;
2641 fAmin = fnext;
2642 fISW[0] = 0;
2643 mnmigr();
2644 fItaur = 0;
2645 fnext = fAmin;
2646 if (fISW[0] >= 1) ierev = 1;
2647 if (fISW[3] < 1) ierev = 2;
2648 }
2649}
2650
2651////////////////////////////////////////////////////////////////////////////////
2652/// Interprets a command and takes appropriate action
2653///
2654/// either directly by skipping to the corresponding code in
2655/// MNEXCM, or by setting up a call to a function
2656///
2657/// recognized MINUIT commands:
2658/// obsolete commands:
2659/// IERFLG is now (94.5) defined the same as ICONDN in MNCOMD =
2660/// - 0: command executed normally
2661/// - 1: command is blank, ignored
2662/// - 2: command line unreadable, ignored
2663/// - 3: unknown command, ignored
2664/// - 4: abnormal termination (e.g., MIGRAD not converged)
2665/// - 9: reserved
2666/// - 10: END command
2667/// - 11: EXIT or STOP command
2668/// - 12: RETURN command
2669///
2670/// see also
2671/// [the possible list of all Minuit commands](https://root.cern.ch/sites/d35c7d8c.web.cern.ch/files/minuit.pdf).
2672
2673void TMinuit::mnexcm(const char *command, Double_t *plist, Int_t llist, Int_t &ierflg)
2674{
2675 /* Initialized data */
2676
2677 TString comand = command;
2678 static const char *const cname[40] = {
2679 "MINImize ",
2680 "SEEk ",
2681 "SIMplex ",
2682 "MIGrad ",
2683 "MINOs ",
2684 "SET xxx ",
2685 "SHOw xxx ",
2686 "TOP of pag",
2687 "FIX ",
2688 "REStore ",
2689 "RELease ",
2690 "SCAn ",
2691 "CONtour ",
2692 "HESse ",
2693 "SAVe ",
2694 "IMProve ",
2695 "CALl fcn ",
2696 "STAndard ",
2697 "END ",
2698 "EXIt ",
2699 "RETurn ",
2700 "CLEar ",
2701 "HELP ",
2702 "MNContour ",
2703 "STOp ",
2704 "JUMp ",
2705 " ",
2706 " ",
2707 " ",
2708 " ",
2709 " ",
2710 " ",
2711 " ",
2712 "COVARIANCE",
2713 "PRINTOUT ",
2714 "GRADIENT ",
2715 "MATOUT ",
2716 "ERROR DEF ",
2717 "LIMITS ",
2718 "PUNCH "};
2719
2720 Int_t nntot = 40;
2721
2722 /* Local variables */
2723 Double_t step, xptu[101], yptu[101], f, rno;
2724 Int_t icol, kcol, ierr, iint, iext, lnow, nptu, i, iflag, ierrf;
2725 Int_t ilist, nparx, izero, nf, lk, it, iw, inonde, nsuper;
2726 Int_t it2, ke1, ke2, nowprt, kll, krl;
2727 TString chwhy, c26, cvblnk, cneway, comd;
2728 TString ctemp;
2729 Bool_t lfreed, ltofix, lfixed;
2730
2731// alphabetical order of command names!
2732
2733 /* Function Body */
2734
2735 lk = comand.Length();
2736 if (lk > 20) lk = 20;
2737 fCword = comand;
2738 fCword.ToUpper();
2739// Copy the first MAXP arguments into WORD7, making
2740// sure that WORD7(1)=0 if LLIST=0
2741 for (iw = 1; iw <= fMaxpar; ++iw) {
2742 fWord7[iw-1] = 0;
2743 if (iw <= llist) fWord7[iw-1] = plist[iw-1];
2744 }
2745 ++fIcomnd;
2746 fNfcnlc = fNfcn;
2747 if (fCword(0,7) != "SET PRI" || fWord7[0] >= 0) {
2748 if (fISW[4] >= 0) {
2749 lnow = llist;
2750 if (lnow > 4) lnow = 4;
2751 Printf(" **********");
2752 ctemp.Form(" **%5d **%s",fIcomnd,(const char*)fCword);
2753 for (i = 1; i <= lnow; ++i) {
2754 ctemp += TString::Format("%12.4g",plist[i-1]);
2755 }
2756 Printf("%s",(const char*)ctemp);
2757 inonde = 0;
2758 if (llist > lnow) {
2759 kll = llist;
2760 if (llist > fMaxpar) {
2761 inonde = 1;
2762 kll = fMaxpar;
2763 }
2764 Printf(" ***********");
2765 for (i = lnow + 1; i <= kll; ++i) {
2766 Printf("%12.4g",plist[i-1]);
2767 }
2768 }
2769 Printf(" **********");
2770 if (inonde > 0) {
2771 Printf(" ERROR: ABOVE CALL TO MNEXCM TRIED TO PASS MORE THAN %d PARAMETERS.", fMaxpar);
2772 }
2773 }
2774 }
2775 fNfcnmx = Int_t(fWord7[0]);
2776 if (fNfcnmx <= 0) {
2777 fNfcnmx = fNpar*100 + 200 + fNpar*fNpar*5;
2778 }
2779 fEpsi = fWord7[1];
2780 if (fEpsi <= 0) {
2781 fEpsi = fUp*.1;
2782 }
2783 fLnewmn = kFALSE;
2784 fLphead = kTRUE;
2785 fISW[0] = 0;
2786 ierflg = 0;
2787// look for command in list CNAME
2788 ctemp = fCword(0,3);
2789 for (i = 1; i <= nntot; ++i) {
2790 if (strncmp(ctemp.Data(),cname[i-1],3) == 0) goto L90;
2791 }
2792 Printf("UNKNOWN COMMAND IGNORED:%s", comand.Data());
2793 ierflg = 3;
2794 return;
2795// normal case: recognized MINUIT command
2796L90:
2797 if (fCword(0,4) == "MINO") i = 5;
2798 if (i != 6 && i != 7 && i != 8 && i != 23) {
2799 fCfrom = cname[i-1];
2800 fNfcnfr = fNfcn;
2801 }
2802// 1 2 3 4 5 6 7 8 9 10
2803 switch (i) {
2804 case 1: goto L400;
2805 case 2: goto L200;
2806 case 3: goto L300;
2807 case 4: goto L400;
2808 case 5: goto L500;
2809 case 6: goto L700;
2810 case 7: goto L700;
2811 case 8: goto L800;
2812 case 9: goto L900;
2813 case 10: goto L1000;
2814 case 11: goto L1100;
2815 case 12: goto L1200;
2816 case 13: goto L1300;
2817 case 14: goto L1400;
2818 case 15: goto L1500;
2819 case 16: goto L1600;
2820 case 17: goto L1700;
2821 case 18: goto L1800;
2822 case 19: goto L1900;
2823 case 20: goto L1900;
2824 case 21: goto L1900;
2825 case 22: goto L2200;
2826 case 23: goto L2300;
2827 case 24: goto L2400;
2828 case 25: goto L1900;
2829 case 26: goto L2600;
2830 case 27: goto L3300;
2831 case 28: goto L3300;
2832 case 29: goto L3300;
2833 case 30: goto L3300;
2834 case 31: goto L3300;
2835 case 32: goto L3300;
2836 case 33: goto L3300;
2837 case 34: goto L3400;
2838 case 35: goto L3500;
2839 case 36: goto L3600;
2840 case 37: goto L3700;
2841 case 38: goto L3800;
2842 case 39: goto L3900;
2843 case 40: goto L4000;
2844 }
2845// seek
2846L200:
2847 mnseek();
2848 return;
2849// simplex
2850L300:
2851 mnsimp();
2852 if (fISW[3] < 1) ierflg = 4;
2853 return;
2854// migrad, minimize
2855L400:
2856 nf = fNfcn;
2857 fApsi = fEpsi;
2858 mnmigr();
2859 mnwerr();
2860 if (fISW[3] >= 1) return;
2861 ierflg = 4;
2862 if (fISW[0] == 1) return;
2863 if (fCword(0,3) == "MIG") return;
2864
2865 fNfcnmx = fNfcnmx + nf - fNfcn;
2866 nf = fNfcn;
2867 mnsimp();
2868 if (fISW[0] == 1) return;
2869 fNfcnmx = fNfcnmx + nf - fNfcn;
2870 mnmigr();
2871 if (fISW[3] >= 1) ierflg = 0;
2872 mnwerr();
2873 return;
2874// minos
2875L500:
2876 nsuper = fNfcn + ((fNpar + 1) << 1)*fNfcnmx;
2877// possible loop over new minima
2878 fEpsi = fUp*.1;
2879L510:
2880 fCfrom = cname[i-1]; // ensure that mncuve complains about MINOS not MIGRAD
2881 mncuve();
2882 mnmnos();
2883 if (! fLnewmn) return;
2884 mnrset(0);
2885 mnmigr();
2886 mnwerr();
2887 if (fNfcn < nsuper) goto L510;
2888 Printf(" TOO MANY FUNCTION CALLS. MINOS GIVES UP");
2889 ierflg = 4;
2890 return;
2891// set, show
2892L700:
2893 mnset();
2894 return;
2895// top of page
2896
2897L800:
2898 Printf("1");
2899 return;
2900// fix
2901L900:
2902 ltofix = kTRUE;
2903// (also release)
2904L901:
2905 lfreed = kFALSE;
2906 lfixed = kFALSE;
2907 if (llist == 0) {
2908 Printf("%s: NO PARAMETERS REQUESTED ",(const char*)fCword);
2909 return;
2910 }
2911 for (ilist = 1; ilist <= llist; ++ilist) {
2912 iext = Int_t(plist[ilist-1]);
2913 chwhy = " IS UNDEFINED.";
2914 if (iext <= 0) goto L930;
2915 if (iext > fNu) goto L930;
2916 if (fNvarl[iext-1] < 0) goto L930;
2917 chwhy = " IS CONSTANT. ";
2918 if (fNvarl[iext-1] == 0) goto L930;
2919 iint = fNiofex[iext-1];
2920 if (ltofix) {
2921 chwhy = " ALREADY FIXED.";
2922 if (iint == 0) goto L930;
2923 mnfixp(iint-1, ierr);
2924 if (ierr == 0) lfixed = kTRUE;
2925 else ierflg = 4;
2926 } else {
2927 chwhy = " ALREADY VARIABLE.";
2928 if (iint > 0) goto L930;
2929 krl = -abs(iext);
2930 mnfree(krl);
2931 lfreed = kTRUE;
2932 }
2933 continue;
2934L930:
2935 if (fISW[4] >= 0) Printf(" PARAMETER %4d %s IGNORED.",iext,(const char*)chwhy);
2936 }
2937 if (lfreed || lfixed) mnrset(0);
2938 if (lfreed) {
2939 fISW[1] = 0;
2940 fDcovar = 1;
2941 fEDM = fBigedm;
2942 fISW[3] = 0;
2943 }
2944 mnwerr();
2945 if (fISW[4] > 1) mnprin(5, fAmin);
2946 return;
2947// restore
2948L1000:
2949 it = Int_t(fWord7[0]);
2950 if (it > 1 || it < 0) goto L1005;
2951 lfreed = fNpfix > 0;
2952 mnfree(it);
2953 if (lfreed) {
2954 mnrset(0);
2955 fISW[1] = 0;
2956 fDcovar = 1;
2957 fEDM = fBigedm;
2958 }
2959 return;
2960L1005:
2961 Printf(" IGNORED. UNKNOWN ARGUMENT:%4d",it);
2962 ierflg = 3;
2963 return;
2964// release
2965L1100:
2966 ltofix = kFALSE;
2967 goto L901;
2968// scan
2969L1200:
2970 iext = Int_t(fWord7[0]);
2971 if (iext <= 0) goto L1210;
2972 it2 = 0;
2973 if (iext <= fNu) it2 = fNiofex[iext-1];
2974 if (it2 <= 0) goto L1250;
2975
2976L1210:
2977 mnscan();
2978 return;
2979L1250:
2980 Printf(" PARAMETER %4d NOT VARIABLE.",iext);
2981 ierflg = 3;
2982 return;
2983// contour
2984L1300:
2985 ke1 = Int_t(fWord7[0]);
2986 ke2 = Int_t(fWord7[1]);
2987 if (ke1 == 0) {
2988 if (fNpar == 2) {
2989 ke1 = fNexofi[0];
2990 ke2 = fNexofi[1];
2991 } else {
2992 Printf("%s: NO PARAMETERS REQUESTED ",(const char*)fCword);
2993 ierflg = 3;
2994 return;
2995 }
2996 }
2997 fNfcnmx = 1000;
2998 mncntr(ke1-1, ke2-1, ierrf);
2999 if (ierrf > 0) ierflg = 3;
3000 return;
3001// hesse
3002L1400:
3003 mnhess();
3004 mnwerr();
3005 if (fISW[4] >= 0) mnprin(2, fAmin);
3006 if (fISW[4] >= 1) mnmatu(1);
3007 return;
3008// save
3009L1500:
3010 mnsave();
3011 return;
3012// improve
3013L1600:
3014 mncuve();
3015 mnimpr();
3016 if (fLnewmn) goto L400;
3017 ierflg = 4;
3018 return;
3019// call fcn
3020L1700:
3021 iflag = Int_t(fWord7[0]);
3022 nparx = fNpar;
3023 f = fUndefi;
3024 Eval(nparx, fGin, f, fU, iflag); ++fNfcn;
3025 nowprt = 0;
3026 if (f != fUndefi) {
3027 if (fAmin == fUndefi) {
3028 fAmin = f;
3029 nowprt = 1;
3030 } else if (f < fAmin) {
3031 fAmin = f;
3032 nowprt = 1;
3033 }
3034 if (fISW[4] >= 0 && iflag <= 5 && nowprt == 1) {
3035 mnprin(5, fAmin);
3036 }
3037 if (iflag == 3) fFval3 = f;
3038 }
3039 if (iflag > 5) mnrset(1);
3040 return;
3041// standard
3042L1800:
3043// stand();
3044 return;
3045// return, stop, end, exit
3046L1900:
3047 it = Int_t(fWord7[0]);
3048 if (fFval3 != fAmin && it == 0) {
3049 iflag = 3;
3050 if (fISW[4] >= 0) Printf(" CALL TO USER FUNCTION WITH IFLAG = 3");
3051 nparx = fNpar;
3052 Eval(nparx, fGin, f, fU, iflag); ++fNfcn;
3053 }
3054 ierflg = 11;
3055 if (fCword(0,3) == "END") ierflg = 10;
3056 if (fCword(0,3) == "RET") ierflg = 12;
3057 return;
3058// clear
3059L2200:
3060 mncler();
3061 if (fISW[4] >= 1) {
3062 Printf(" MINUIT MEMORY CLEARED. NO PARAMETERS NOW DEFINED.");
3063 }
3064 return;
3065// help
3066L2300:
3067 kcol = 0;
3068 for (icol = 5; icol <= lk; ++icol) {
3069 if (fCword[icol-1] == ' ') continue;
3070 kcol = icol;
3071 goto L2320;
3072 }
3073L2320:
3074 if (kcol == 0) comd = "* ";
3075 else comd = fCword(kcol-1,lk-kcol+1);
3076 mnhelp(comd);
3077 return;
3078// MNContour
3079L2400:
3080 fEpsi = fUp*.05;
3081 ke1 = Int_t(fWord7[0]);
3082 ke2 = Int_t(fWord7[1]);
3083 if (ke1 == 0 && fNpar == 2) {
3084 ke1 = fNexofi[0];
3085 ke2 = fNexofi[1];
3086 }
3087 nptu = Int_t(fWord7[2]);
3088 if (nptu <= 0) nptu = 20;
3089 if (nptu > 101) nptu = 101;
3090 fNfcnmx = (nptu + 5)*100*(fNpar + 1);
3091 mncont(ke1-1, ke2-1, nptu, xptu, yptu, ierrf);
3092 if (ierrf < nptu) ierflg = 4;
3093 if (ierrf == -1) ierflg = 3;
3094 return;
3095// jump
3096L2600:
3097 step = fWord7[0];
3098 if (step <= 0) step = 2;
3099 rno = 0;
3100 izero = 0;
3101 for (i = 1; i <= fNpar; ++i) {
3102 mnrn15(rno, izero);
3103 rno = rno*2 - 1;
3104 fX[i-1] += rno*step*fWerr[i-1];
3105 }
3106 mninex(fX);
3107 mnamin();
3108 mnrset(0);
3109 return;
3110// blank line
3111L3300:
3112 Printf(" BLANK COMMAND IGNORED.");
3113 ierflg = 1;
3114 return;
3115// obsolete commands
3116// covariance
3117L3400:
3118 Printf(" THE *COVARIANCE* COMMAND IS OSBSOLETE. THE COVARIANCE MATRIX IS NOW SAVED IN A DIFFERENT FORMAT WITH THE *SAVE* COMMAND AND READ IN WITH:*SET COVARIANCE*");
3119 ierflg = 3;
3120 return;
3121// printout
3122L3500:
3123 cneway = "SET PRInt ";
3124 goto L3100;
3125// gradient
3126L3600:
3127 cneway = "SET GRAd ";
3128 goto L3100;
3129// matout
3130L3700:
3131 cneway = "SHOW COVar";
3132 goto L3100;
3133// error def
3134L3800:
3135 cneway = "SET ERRdef";
3136 goto L3100;
3137// limits
3138L3900:
3139 cneway = "SET LIMits";
3140 goto L3100;
3141// punch
3142L4000:
3143 cneway = "SAVE ";
3144// come from obsolete commands
3145L3100:
3146 Printf(" OBSOLETE COMMAND:%s PLEASE USE:%s",(const char*)fCword
3147 ,(const char*)cneway);
3148 fCword = cneway;
3149 if (fCword == "SAVE ") goto L1500;
3150 goto L700;
3151//
3152}
3153
3154////////////////////////////////////////////////////////////////////////////////
3155/// Transforms the external parameter values U to internal values
3156///
3157/// Transforms the external parameter values U to internal
3158/// values in the dense array PINT.
3159
3161{
3162 Double_t pinti;
3163 Int_t iint, iext;
3164
3165 fLimset = kFALSE;
3166 for (iint = 1; iint <= fNpar; ++iint) {
3167 iext = fNexofi[iint-1];
3168 mnpint(fU[iext-1], iext-1, pinti);
3169 pint[iint-1] = pinti;
3170 }
3171}
3172
3173////////////////////////////////////////////////////////////////////////////////
3174/// Removes parameter IINT from the internal parameter list
3175///
3176/// and arranges the rest of the list to fill the hole.
3177
3178void TMinuit::mnfixp(Int_t iint1, Int_t &ierr)
3179{
3180 /* Local variables */
3181 Double_t yyover;
3182 Int_t kold, nold, ndex, knew, iext, i, j, m, n, lc, ik;
3183
3184// first see if it can be done
3185 ierr = 0;
3186 Int_t iint = iint1+1;
3187 if (iint > fNpar || iint <= 0) {
3188 ierr = 1;
3189 Printf(" MINUIT ERROR. ARGUMENT TO MNFIXP=%4d",iint);
3190 return;
3191 }
3192 iext = fNexofi[iint-1];
3193 if (fNpfix >= fMaxpar) {
3194 ierr = 1;
3195 Printf(" MINUIT CANNOT FIX PARAMETER %4d MAXIMUM NUMBER THAT CAN BE FIXED IS %d",iext,fMaxpar);
3196 return;
3197 }
3198// reduce number of variable parameters by one
3199
3200 fNiofex[iext-1] = 0;
3201 nold = fNpar;
3202 --fNpar;
3203// save values in case parameter is later restored
3204
3205 ++fNpfix;
3206 fIpfix[fNpfix-1] = iext;
3207 lc = iint;
3208 fXs[fNpfix-1] = fX[lc-1];
3209 fXts[fNpfix-1] = fXt[lc-1];
3210 fDirins[fNpfix-1] = fWerr[lc-1];
3211 fGrds[fNpfix-1] = fGrd[lc-1];
3212 fG2s[fNpfix-1] = fG2[lc-1];
3213 fGsteps[fNpfix-1] = fGstep[lc-1];
3214// shift values for other parameters to fill hole
3215 for (ik = iext + 1; ik <= fNu; ++ik) {
3216 if (fNiofex[ik-1] > 0) {
3217 lc = fNiofex[ik-1] - 1;
3218 fNiofex[ik-1] = lc;
3219 fNexofi[lc-1] = ik;
3220 fX[lc-1] = fX[lc];
3221 fXt[lc-1] = fXt[lc];
3222 fDirin[lc-1] = fDirin[lc];
3223 fWerr[lc-1] = fWerr[lc];
3224 fGrd[lc-1] = fGrd[lc];
3225 fG2[lc-1] = fG2[lc];
3226 fGstep[lc-1] = fGstep[lc];
3227 }
3228 }
3229 if (fISW[1] <= 0) return;
3230// remove one row and one column from variance matrix
3231 if (fNpar <= 0) return;
3232 for (i = 1; i <= nold; ++i) {
3233 m = TMath::Max(i,iint);
3234 n = TMath::Min(i,iint);
3235 ndex = m*(m-1) / 2 + n;
3236 fFIXPyy[i-1] = fVhmat[ndex-1];
3237 }
3238 yyover = 1 / fFIXPyy[iint-1];
3239 knew = 0;
3240 kold = 0;
3241 for (i = 1; i <= nold; ++i) {
3242 for (j = 1; j <= i; ++j) {
3243 ++kold;
3244 if (j == iint || i == iint) continue;
3245 ++knew;
3246 fVhmat[knew-1] = fVhmat[kold-1] - fFIXPyy[j-1]*fFIXPyy[i-1]*yyover;
3247 }
3248 }
3249}
3250
3251////////////////////////////////////////////////////////////////////////////////
3252/// Restores one or more fixed parameter(s) to variable status
3253///
3254/// Restores one or more fixed parameter(s) to variable status
3255/// by inserting it into the internal parameter list at the
3256/// appropriate place.
3257///
3258/// - K = 0 means restore all parameters
3259/// - K = 1 means restore the last parameter fixed
3260/// - K = -I means restore external parameter I (if possible)
3261/// - IQ = fix-location where internal parameters were stored
3262/// - IR = external number of parameter being restored
3263/// - IS = internal number of parameter being restored
3264
3266{
3267 /* Local variables */
3268 Double_t grdv, xv, dirinv, g2v, gstepv, xtv;
3269 Int_t i, ipsav, ka, lc, ik, iq, ir, is;
3270
3271 if (k > 1) {
3272 Printf(" CALL TO MNFREE IGNORED. ARGUMENT GREATER THAN ONE");
3273 }
3274 if (fNpfix < 1) {
3275 Printf(" CALL TO MNFREE IGNORED. THERE ARE NO FIXED PARAMETERS");
3276 }
3277 if (k == 1 || k == 0) goto L40;
3278
3279// release parameter with specified external number
3280 ka = abs(k);
3281 if (fNiofex[ka-1] == 0) goto L15;
3282 Printf(" IGNORED. PARAMETER SPECIFIED IS ALREADY VARIABLE.");
3283 return;
3284L15:
3285 if (fNpfix < 1) goto L21;
3286 for (ik = 1; ik <= fNpfix; ++ik) { if (fIpfix[ik-1] == ka) goto L24; }
3287L21:
3288 Printf(" PARAMETER %4d NOT FIXED. CANNOT BE RELEASED.",ka);
3289 return;
3290L24:
3291 if (ik == fNpfix) goto L40;
3292
3293// move specified parameter to end of list
3294 ipsav = ka;
3295 xv = fXs[ik-1];
3296 xtv = fXts[ik-1];
3297 dirinv = fDirins[ik-1];
3298 grdv = fGrds[ik-1];
3299 g2v = fG2s[ik-1];
3300 gstepv = fGsteps[ik-1];
3301 for (i = ik + 1; i <= fNpfix; ++i) {
3302 fIpfix[i-2] = fIpfix[i-1];
3303 fXs[i-2] = fXs[i-1];
3304 fXts[i-2] = fXts[i-1];
3305 fDirins[i-2] = fDirins[i-1];
3306 fGrds[i-2] = fGrds[i-1];
3307 fG2s[i-2] = fG2s[i-1];
3308 fGsteps[i-2] = fGsteps[i-1];
3309 }
3310 fIpfix[fNpfix-1] = ipsav;
3311 fXs[fNpfix-1] = xv;
3312 fXts[fNpfix-1] = xtv;
3313 fDirins[fNpfix-1] = dirinv;
3314 fGrds[fNpfix-1] = grdv;
3315 fG2s[fNpfix-1] = g2v;
3316 fGsteps[fNpfix-1] = gstepv;
3317// restore last parameter in fixed list -- IPFIX(NPFIX)
3318L40:
3319 if (fNpfix < 1) goto L300;
3320 ir = fIpfix[fNpfix-1];
3321 is = 0;
3322 for (ik = fNu; ik >= ir; --ik) {
3323 if (fNiofex[ik-1] > 0) {
3324 lc = fNiofex[ik-1] + 1;
3325 is = lc - 1;
3326 fNiofex[ik-1] = lc;
3327 fNexofi[lc-1] = ik;
3328 fX[lc-1] = fX[lc-2];
3329 fXt[lc-1] = fXt[lc-2];
3330 fDirin[lc-1] = fDirin[lc-2];
3331 fWerr[lc-1] = fWerr[lc-2];
3332 fGrd[lc-1] = fGrd[lc-2];
3333 fG2[lc-1] = fG2[lc-2];
3334 fGstep[lc-1] = fGstep[lc-2];
3335 }
3336 }
3337 ++fNpar;
3338 if (is == 0) is = fNpar;
3339 fNiofex[ir-1] = is;
3340 fNexofi[is-1] = ir;
3341 iq = fNpfix;
3342 fX[is-1] = fXs[iq-1];
3343 fXt[is-1] = fXts[iq-1];
3344 fDirin[is-1] = fDirins[iq-1];
3345 fWerr[is-1] = fDirins[iq-1];
3346 fGrd[is-1] = fGrds[iq-1];
3347 fG2[is-1] = fG2s[iq-1];
3348 fGstep[is-1] = fGsteps[iq-1];
3349 --fNpfix;
3350 fISW[1] = 0;
3351 fDcovar = 1;
3352 if (fISW[4] - fItaur >= 1) {
3353 Printf(" PARAMETER %4d %s RESTORED TO VARIABLE.",ir,
3354 (const char*)fCpnam[ir-1]);
3355 }
3356 if (k == 0) goto L40;
3357L300:
3358// if different from internal, external values are taken
3359 mnexin(fX);
3360}
3361
3362////////////////////////////////////////////////////////////////////////////////
3363/// Interprets the SET GRAD command
3364///
3365/// - Called from MNSET
3366/// - Interprets the SET GRAD command, which informs MINUIT whether
3367/// - the first derivatives of FCN will be calculated by the user
3368/// - inside FCN. It can check the user derivative calculation
3369/// - by comparing it with a finite difference approximation.
3370
3372{
3373 /* Local variables */
3374 Double_t fzero, err;
3375 Int_t i, nparx, lc, istsav;
3376 Bool_t lnone;
3377
3378 fISW[2] = 1;
3379 nparx = fNpar;
3380 if (fWord7[0] > 0) goto L2000;
3381
3382// get user-calculated first derivatives from FCN
3383 for (i = 1; i <= fNu; ++i) { fGin[i-1] = fUndefi; }
3384 mninex(fX);
3385 Eval(nparx, fGin, fzero, fU, 2); ++fNfcn;
3386 mnderi();
3387 for (i = 1; i <= fNpar; ++i) { fGRADgf[i-1] = fGrd[i-1]; }
3388// get MINUIT-calculated first derivatives
3389 fISW[2] = 0;
3390 istsav = fIstrat;
3391 fIstrat = 2;
3392 mnhes1();
3393 fIstrat = istsav;
3394 Printf(" CHECK OF GRADIENT CALCULATION IN FCN");
3395 Printf(" PARAMETER G(IN FCN) G(MINUIT) DG(MINUIT) AGREEMENT");
3396 fISW[2] = 1;
3397 lnone = kFALSE;
3398 for (lc = 1; lc <= fNpar; ++lc) {
3399 i = fNexofi[lc-1];
3400 const char *cwd = "GOOD";
3401 err = fDgrd[lc-1];
3402 if (TMath::Abs(fGRADgf[lc-1] - fGrd[lc-1]) > err) {
3403 cwd = " BAD";
3404 fISW[2] = 0;
3405 }
3406 if (fGin[i-1] == fUndefi) {
3407 cwd = "NONE";
3408 lnone = kTRUE;
3409 fGRADgf[lc-1] = 0;
3410 fISW[2] = 0;
3411 }
3412 Printf(" %5d %10s%12.4e%12.4e%12.4e %s",i
3413 ,(const char*)fCpnam[i-1]
3414 ,fGRADgf[lc-1],fGrd[lc-1],err,cwd);
3415 }
3416 if (lnone) {
3417 Printf(" AGREEMENT=NONE MEANS FCN DID NOT CALCULATE THE DERIVATIVE");
3418 }
3419 if (fISW[2] == 0) {
3420 Printf(" MINUIT DOES NOT ACCEPT DERIVATIVE CALCULATIONS BY FCN");
3421 Printf(" TO FORCE ACCEPTANCE, ENTER *SET GRAD 1*");
3422 }
3423
3424L2000:
3425 return;
3426}
3427
3428////////////////////////////////////////////////////////////////////////////////
3429/// interface to Minuit help
3430
3431void TMinuit::mnhelp(const char *command)
3432{
3433 TString comd = command;
3434 mnhelp(comd);
3435}
3436
3437////////////////////////////////////////////////////////////////////////////////
3438/// HELP routine for MINUIT interactive commands
3439///
3440/// - COMD ='*' or "" prints a global help for all commands
3441/// - COMD =Command_name: print detailed help for one command.
3442/// Note that at least 3 characters must be given for the command
3443/// name.
3444///
3445/// Author: Rene Brun
3446/// comments extracted from the MINUIT documentation file.
3447
3449{
3450//______________________________________________________________________________
3451//
3452// Global HELP: Summary of all commands
3453//
3454 comd.ToUpper();
3455 if( comd.Length() == 0 || comd[0] == '*' || comd[0] == '?' || comd[0] == 0 || comd=="HELP" ) {
3456 Printf(" ==>List of MINUIT Interactive commands:");
3457 Printf(" CLEar Reset all parameter names and values undefined");
3458 Printf(" CONtour Make contour map of the user function");
3459 Printf(" EXIT Exit from Interactive Minuit");
3460 Printf(" FIX Cause parameter(s) to remain constant");
3461 Printf(" HESse Calculate the Hessian or error matrix.");
3462 Printf(" IMPROVE Search for a new minimum around current minimum");
3463 Printf(" MIGrad Minimize by the method of Migrad");
3464 Printf(" MINImize MIGRAD + SIMPLEX method if Migrad fails");
3465 Printf(" MINOs Exact (non-linear) parameter error analysis");
3466 Printf(" MNContour Calculate one MINOS function contour");
3467 Printf(" PARameter Define or redefine new parameters and values");
3468 Printf(" RELease Make previously FIXed parameters variable again");
3469 Printf(" REStore Release last parameter fixed");
3470 Printf(" SAVe Save current parameter values on a file");
3471 Printf(" SCAn Scan the user function by varying parameters");
3472 Printf(" SEEk Minimize by the method of Monte Carlo");
3473 Printf(" SET Set various MINUIT constants or conditions");
3474 Printf(" SHOw Show values of current constants or conditions");
3475 Printf(" SIMplex Minimize by the method of Simplex");
3476 goto L99;
3477 }
3478
3479//______________________________________________________________________________
3480//
3481// Command CLEAR
3482//
3483 if( !strncmp(comd.Data(),"CLE",3) ) {
3484 Printf(" ***>CLEAR");
3485 Printf(" Resets all parameter names and values to undefined.");
3486 Printf(" Must normally be followed by a PARameters command or ");
3487 Printf(" equivalent, in order to define parameter values.");
3488 goto L99;
3489 }
3490//______________________________________________________________________________
3491//
3492// Command CONTOUR
3493//
3494 if( !strncmp(comd.Data(),"CON",3) ) {
3495 Printf(" ***>CONTOUR <par1> <par2> [devs] [ngrid]");
3496 Printf(" Instructs Minuit to trace contour lines of the user function");
3497 Printf(" with respect to the two parameters whose external numbers");
3498 Printf(" are <par1> and <par2>.");
3499 Printf(" Other variable parameters of the function, if any, will have");
3500 Printf(" their values fixed at the current values during the contour");
3501 Printf(" tracing. The optional parameter [devs] (default value 2.)");
3502 Printf(" gives the number of standard deviations in each parameter");
3503 Printf(" which should lie entirely within the plotting area.");
3504 Printf(" Optional parameter [ngrid] (default value 25 unless page");
3505 Printf(" size is too small) determines the resolution of the plot,");
3506 Printf(" i.e. the number of rows and columns of the grid at which the");
3507 Printf(" function will be evaluated. [See also MNContour.]");
3508 goto L99;
3509 }
3510//______________________________________________________________________________
3511//
3512// Command END
3513//
3514 if( !strncmp(comd.Data(),"END",3) ) {
3515 Printf(" ***>END");
3516 Printf(" Signals the end of a data block (i.e., the end of a fit),");
3517 Printf(" and implies that execution should continue, because another");
3518 Printf(" Data Block follows. A Data Block is a set of Minuit data");
3519 Printf(" consisting of");
3520 Printf(" (1) A Title,");
3521 Printf(" (2) One or more Parameter Definitions,");
3522 Printf(" (3) A blank line, and");
3523 Printf(" (4) A set of Minuit Commands.");
3524 Printf(" The END command is used when more than one Data Block is to");
3525 Printf(" be used with the same FCN function. It first causes Minuit");
3526 Printf(" to issue a CALL FCN with IFLAG=3, in order to allow FCN to");
3527 Printf(" perform any calculations associated with the final fitted");
3528 Printf(" parameter values, unless a CALL FCN 3 command has already");
3529 Printf(" been executed at the current FCN value.");
3530 goto L99;
3531 }
3532//______________________________________________________________________________
3533//
3534// Command EXIT
3535//
3536 if( !strncmp(comd.Data(),"EXI",3) ) {
3537 Printf(" ***>EXIT");
3538 Printf(" Signals the end of execution.");
3539 Printf(" The EXIT command first causes Minuit to issue a CALL FCN");
3540 Printf(" with IFLAG=3, to allow FCN to perform any calculations");
3541 Printf(" associated with the final fitted parameter values, unless a");
3542 Printf(" CALL FCN 3 command has already been executed.");
3543 goto L99;
3544 }
3545//______________________________________________________________________________
3546//
3547// Command FIX
3548//
3549 if( !strncmp(comd.Data(),"FIX",3) ) {
3550 Printf(" ***>FIX} <parno> [parno] ... [parno]");
3551 Printf(" Causes parameter(s) <parno> to be removed from the list of");
3552 Printf(" variable parameters, and their value(s) will remain constant");
3553 Printf(" during subsequent minimizations, etc., until another command");
3554 Printf(" changes their value(s) or status.");
3555 goto L99;
3556 }
3557//______________________________________________________________________________
3558//
3559// Command HESSE
3560//
3561 if( !strncmp(comd.Data(),"HES",3) ) {
3562 Printf(" ***>HESse [maxcalls]");
3563 Printf(" Calculate, by finite differences, the Hessian or error matrix.");
3564 Printf(" That is, it calculates the full matrix of second derivatives");
3565 Printf(" of the function with respect to the currently variable");
3566 Printf(" parameters, and inverts it, printing out the resulting error");
3567 Printf(" matrix. The optional argument [maxcalls] specifies the");
3568 Printf(" (approximate) maximum number of function calls after which");
3569 Printf(" the calculation will be stopped.");
3570 goto L99;
3571 }
3572//______________________________________________________________________________
3573//
3574// Command IMPROVE
3575//
3576 if( !strncmp(comd.Data(),"IMP",3) ) {
3577 Printf(" ***>IMPROVE [maxcalls]");
3578 Printf(" If a previous minimization has converged, and the current");
3579 Printf(" values of the parameters therefore correspond to a local");
3580 Printf(" minimum of the function, this command requests a search for");
3581 Printf(" additional distinct local minima.");
3582 Printf(" The optional argument [maxcalls] specifies the (approximate");
3583 Printf(" maximum number of function calls after which the calculation");
3584 Printf(" will be stopped.");
3585 goto L99;
3586 }
3587//______________________________________________________________________________
3588//
3589// Command MIGRAD
3590//
3591 if( !strncmp(comd.Data(),"MIG",3) ) {
3592 Printf(" ***>MIGrad [maxcalls] [tolerance]");
3593 Printf(" Causes minimization of the function by the method of Migrad,");
3594 Printf(" the most efficient and complete single method, recommended");
3595 Printf(" for general functions (see also MINImize).");
3596 Printf(" The minimization produces as a by-product the error matrix");
3597 Printf(" of the parameters, which is usually reliable unless warning");
3598 Printf(" messages are produced.");
3599 Printf(" The optional argument [maxcalls] specifies the (approximate)");
3600 Printf(" maximum number of function calls after which the calculation");
3601 Printf(" will be stopped even if it has not yet converged.");
3602 Printf(" The optional argument [tolerance] specifies required tolerance");
3603 Printf(" on the function value at the minimum.");
3604 Printf(" The default tolerance is 0.1, and the minimization will stop");
3605 Printf(" when the estimated vertical distance to the minimum (EDM) is");
3606 Printf(" less than 0.001*[tolerance]*UP (see [SET ERRordef]).");
3607 goto L99;
3608 }
3609//______________________________________________________________________________
3610//
3611// Command MINIMIZE
3612//
3613 if( !strncmp(comd.Data(),"MINI",4) ) {
3614 Printf(" ***>MINImize [maxcalls] [tolerance]");
3615 Printf(" Causes minimization of the function by the method of Migrad,");
3616 Printf(" as does the MIGrad command, but switches to the SIMplex method");
3617 Printf(" if Migrad fails to converge. Arguments are as for MIGrad.");
3618 Printf(" Note that command requires four characters to be unambiguous.");
3619 goto L99;
3620 }
3621//______________________________________________________________________________
3622//
3623// Command MINOS
3624//
3625 if( !strncmp(comd.Data(),"MIN0",4) ) {
3626 Printf(" ***>MINOs [maxcalls] [parno] [parno] ...");
3627 Printf(" Causes a Minos error analysis to be performed on the parameters");
3628 Printf(" whose numbers [parno] are specified. If none are specified,");
3629 Printf(" Minos errors are calculated for all variable parameters.");
3630 Printf(" Minos errors may be expensive to calculate, but are very");
3631 Printf(" reliable since they take account of non-linearities in the");
3632 Printf(" problem as well as parameter correlations, and are in general");
3633 Printf(" asymmetric.");
3634 Printf(" The optional argument [maxcalls] specifies the (approximate)");
3635 Printf(" maximum number of function calls per parameter requested,");
3636 Printf(" after which the calculation will stop for that parameter.");
3637 goto L99;
3638 }
3639//______________________________________________________________________________
3640//
3641// Command MNCONTOUR
3642//
3643 if( !strncmp(comd.Data(),"MNC",3) ) {
3644 Printf(" ***>MNContour <par1> <par2> [npts]");
3645 Printf(" Calculates one function contour of FCN with respect to");
3646 Printf(" parameters par1 and par2, with FCN minimized always with");
3647 Printf(" respect to all other NPAR-2 variable parameters (if any).");
3648 Printf(" Minuit will try to find npts points on the contour (default 20)");
3649 Printf(" If only two parameters are variable at the time, it is not");
3650 Printf(" necessary to specify their numbers. To calculate more than");
3651 Printf(" one contour, it is necessary to SET ERRordef to the appropriate");
3652 Printf(" value and issue the MNContour command for each contour.");
3653 goto L99;
3654 }
3655//______________________________________________________________________________
3656//
3657// Command PARAMETER
3658//
3659 if( !strncmp(comd.Data(),"PAR",3) ) {
3660 Printf(" ***>PARameters");
3661 Printf(" followed by one or more parameter definitions.");
3662 Printf(" Parameter definitions are of the form:");
3663 Printf(" <number> ''name'' <value> <step> [lolim] [uplim] ");
3664 Printf(" for example:");
3665 Printf(" 3 ''K width'' 1.2 0.1");
3666 Printf(" the last definition is followed by a blank line or a zero.");
3667 goto L99;
3668 }
3669//______________________________________________________________________________
3670//
3671// Command RELEASE
3672//
3673 if( !strncmp(comd.Data(),"REL",3) ) {
3674 Printf(" ***>RELease <parno> [parno] ... [parno]");
3675 Printf(" If <parno> is the number of a previously variable parameter");
3676 Printf(" which has been fixed by a command: FIX <parno>, then that");
3677 Printf(" parameter will return to variable status. Otherwise a warning");
3678 Printf(" message is printed and the command is ignored.");
3679 Printf(" Note that this command operates only on parameters which were");
3680 Printf(" at one time variable and have been FIXed. It cannot make");
3681 Printf(" constant parameters variable; that must be done by redefining");
3682 Printf(" the parameter with a PARameters command.");
3683 goto L99;
3684 }
3685//______________________________________________________________________________
3686//
3687// Command RESTORE
3688//
3689 if( !strncmp(comd.Data(),"RES",3) ) {
3690 Printf(" ***>REStore [code]");
3691 Printf(" If no [code] is specified, this command restores all previously");
3692 Printf(" FIXed parameters to variable status. If [code]=1, then only");
3693 Printf(" the last parameter FIXed is restored to variable status.");
3694 Printf(" If code is neither zero nor one, the command is ignored.");
3695 goto L99;
3696 }
3697//______________________________________________________________________________
3698//
3699// Command RETURN
3700//
3701 if( !strncmp(comd.Data(),"RET",3) ) {
3702 Printf(" ***>RETURN");
3703 Printf(" Signals the end of a data block, and instructs Minuit to return");
3704 Printf(" to the program which called it. The RETurn command first");
3705 Printf(" causes Minuit to CALL FCN with IFLAG=3, in order to allow FCN");
3706 Printf(" to perform any calculations associated with the final fitted");
3707 Printf(" parameter values, unless a CALL FCN 3 command has already been");
3708 Printf(" executed at the current FCN value.");
3709 goto L99;
3710 }
3711//______________________________________________________________________________
3712//
3713// Command SAVE
3714//
3715 if( !strncmp(comd.Data(),"SAV",3) ) {
3716 Printf(" ***>SAVe");
3717 Printf(" Causes the current parameter values to be saved on a file in");
3718 Printf(" such a format that they can be read in again as Minuit");
3719 Printf(" parameter definitions. If the covariance matrix exists, it is");
3720 Printf(" also output in such a format. The unit number is by default 7,");
3721 Printf(" or that specified by the user in their call to MINTIO or");
3722 Printf(" MNINIT. The user is responsible for opening the file previous");
3723 Printf(" to issuing the [SAVe] command (except where this can be done");
3724 Printf(" interactively).");
3725 goto L99;
3726 }
3727//______________________________________________________________________________
3728//
3729// Command SCAN
3730//
3731 if( !strncmp(comd.Data(),"SCA",3) ) {
3732 Printf(" ***>SCAn [parno] [numpts] [from] [to]");
3733 Printf(" Scans the value of the user function by varying parameter");
3734 Printf(" number [parno], leaving all other parameters fixed at the");
3735 Printf(" current value. If [parno] is not specified, all variable");
3736 Printf(" parameters are scanned in sequence.");
3737 Printf(" The number of points [numpts] in the scan is 40 by default,");
3738 Printf(" and cannot exceed 100. The range of the scan is by default");
3739 Printf(" 2 standard deviations on each side of the current best value,");
3740 Printf(" but can be specified as from [from] to [to].");
3741 Printf(" After each scan, if a new minimum is found, the best parameter");
3742 Printf(" values are retained as start values for future scans or");
3743 Printf(" minimizations. The curve resulting from each scan is plotted");
3744 Printf(" on the output unit in order to show the approximate behaviour");
3745 Printf(" of the function.");
3746 Printf(" This command is not intended for minimization, but is sometimes");
3747 Printf(" useful for debugging the user function or finding a");
3748 Printf(" reasonable starting point.");
3749 goto L99;
3750 }
3751//______________________________________________________________________________
3752//
3753// Command SEEK
3754//
3755 if( !strncmp(comd.Data(),"SEE",3) ) {
3756 Printf(" ***>SEEk [maxcalls] [devs]");
3757 Printf(" Causes a Monte Carlo minimization of the function, by choosing");
3758 Printf(" random values of the variable parameters, chosen uniformly");
3759 Printf(" over a hypercube centered at the current best value.");
3760 Printf(" The region size is by default 3 standard deviations on each");
3761 Printf(" side, but can be changed by specifying the value of [devs].");
3762 goto L99;
3763 }
3764//______________________________________________________________________________
3765//
3766// Command SET
3767//
3768 if( !strncmp(comd.Data(),"SET",3) ) {
3769 Printf(" ***>SET <option_name>");
3770 Printf(" SET BATch");
3771 Printf(" Informs Minuit that it is running in batch mode.");
3772
3773 Printf(" ");
3774 Printf(" SET EPSmachine <accuracy>");
3775 Printf(" Informs Minuit that the relative floating point arithmetic");
3776 Printf(" precision is <accuracy>. Minuit determines the nominal");
3777 Printf(" precision itself, but the SET EPSmachine command can be");
3778 Printf(" used to override Minuit own determination, when the user");
3779 Printf(" knows that the FCN function value is not calculated to");
3780 Printf(" the nominal machine accuracy. Typical values of <accuracy>");
3781 Printf(" are between 10**-5 and 10**-14.");
3782
3783 Printf(" ");
3784 Printf(" SET ERRordef <up>");
3785 Printf(" Sets the value of UP (default value= 1.), defining parameter");
3786 Printf(" errors. Minuit defines parameter errors as the change");
3787 Printf(" in parameter value required to change the function value");
3788 Printf(" by UP. Normally, for chisquared fits UP=1, and for negative");
3789 Printf(" log likelihood, UP=0.5.");
3790
3791 Printf(" ");
3792 Printf(" SET GRAdient [force]");
3793 Printf(" Informs Minuit that the user function is prepared to");
3794 Printf(" calculate its own first derivatives and return their values");
3795 Printf(" in the array GRAD when IFLAG=2 (see specs of FCN).");
3796 Printf(" If [force] is not specified, Minuit will calculate");
3797 Printf(" the FCN derivatives by finite differences at the current");
3798 Printf(" point and compare with the user calculation at that point,");
3799 Printf(" accepting the user values only if they agree.");
3800 Printf(" If [force]=1, Minuit does not do its own derivative");
3801 Printf(" calculation, and uses the derivatives calculated in FCN.");
3802
3803 Printf(" ");
3804 Printf(" SET INPut [unitno] [filename]");
3805 Printf(" Causes Minuit, in data-driven mode only, to read subsequent");
3806 Printf(" commands (or parameter definitions) from a different input");
3807 Printf(" file. If no [unitno] is specified, reading reverts to the");
3808 Printf(" previous input file, assuming that there was one.");
3809 Printf(" If [unitno] is specified, and that unit has not been opened,");
3810 Printf(" then Minuit attempts to open the file [filename]} if a");
3811 Printf(" name is specified. If running in interactive mode and");
3812 Printf(" [filename] is not specified and [unitno] is not opened,");
3813 Printf(" Minuit prompts the user to enter a file name.");
3814 Printf(" If the word REWIND is added to the command (note:no blanks");
3815 Printf(" between INPUT and REWIND), the file is rewound before");
3816 Printf(" reading. Note that this command is implemented in standard");
3817 Printf(" Fortran 77 and the results may depend on the system;");
3818 Printf(" for example, if a filename is given under VM/CMS, it must");
3819 Printf(" be preceded by a slash.");
3820
3821 Printf(" ");
3822 Printf(" SET INTeractive");
3823 Printf(" Informs Minuit that it is running interactively.");
3824
3825 Printf(" ");
3826 Printf(" SET LIMits [parno] [lolim] [uplim]");
3827 Printf(" Allows the user to change the limits on one or all");
3828 Printf(" parameters. If no arguments are specified, all limits are");
3829 Printf(" removed from all parameters. If [parno] alone is specified,");
3830 Printf(" limits are removed from parameter [parno].");
3831 Printf(" If all arguments are specified, then parameter [parno] will");
3832 Printf(" be bounded between [lolim] and [uplim].");
3833 Printf(" Limits can be specified in either order, Minuit will take");
3834 Printf(" the smaller as [lolim] and the larger as [uplim].");
3835 Printf(" However, if [lolim] is equal to [uplim], an error condition");
3836 Printf(" results.");
3837
3838 Printf(" ");
3839 Printf(" SET LINesperpage");
3840 Printf(" Sets the number of lines for one page of output.");
3841 Printf(" Default value is 24 for interactive mode");
3842
3843 Printf(" ");
3844 Printf(" SET NOGradient");
3845 Printf(" The inverse of SET GRAdient, instructs Minuit not to");
3846 Printf(" use the first derivatives calculated by the user in FCN.");
3847
3848 Printf(" ");
3849 Printf(" SET NOWarnings");
3850 Printf(" Supresses Minuit warning messages.");
3851
3852 Printf(" ");
3853 Printf(" SET OUTputfile <unitno>");
3854 Printf(" Instructs Minuit to write further output to unit <unitno>.");
3855
3856 Printf(" ");
3857 Printf(" SET PAGethrow <integer>");
3858 Printf(" Sets the carriage control character for ``new page'' to");
3859 Printf(" <integer>. Thus the value 1 produces a new page, and 0");
3860 Printf(" produces a blank line, on some devices (see TOPofpage)");
3861
3862
3863 Printf(" ");
3864 Printf(" SET PARameter <parno> <value>");
3865 Printf(" Sets the value of parameter <parno> to <value>.");
3866 Printf(" The parameter in question may be variable, fixed, or");
3867 Printf(" constant, but must be defined.");
3868
3869 Printf(" ");
3870 Printf(" SET PRIntout <level>");
3871 Printf(" Sets the print level, determining how much output will be");
3872 Printf(" produced. Allowed values and their meanings are displayed");
3873 Printf(" after a SHOw PRInt command, and are currently <level>=:");
3874 Printf(" [-1] no output except from SHOW commands");
3875 Printf(" [0] minimum output");
3876 Printf(" [1] default value, normal output");
3877 Printf(" [2] additional output giving intermediate results.");
3878 Printf(" [3] maximum output, showing progress of minimizations.");
3879 Printf(" Note: See also the SET WARnings command.");
3880
3881 Printf(" ");
3882 Printf(" SET RANdomgenerator <seed>");
3883 Printf(" Sets the seed of the random number generator used in SEEk.");
3884 Printf(" This can be any integer between 10000 and 900000000, for");
3885 Printf(" example one which was output from a SHOw RANdom command of");
3886 Printf(" a previous run.");
3887
3888 Printf(" ");
3889 Printf(" SET STRategy <level>");
3890 Printf(" Sets the strategy to be used in calculating first and second");
3891 Printf(" derivatives and in certain minimization methods.");
3892 Printf(" In general, low values of <level> mean fewer function calls");
3893 Printf(" and high values mean more reliable minimization.");
3894 Printf(" Currently allowed values are 0, 1 (default), and 2.");
3895
3896 Printf(" ");
3897 Printf(" SET TITle");
3898 Printf(" Informs Minuit that the next input line is to be considered");
3899 Printf(" the (new) title for this task or sub-task. This is for");
3900 Printf(" the convenience of the user in reading their output.");
3901
3902 Printf(" ");
3903 Printf(" SET WARnings");
3904 Printf(" Instructs Minuit to output warning messages when suspicious");
3905 Printf(" conditions arise which may indicate unreliable results.");
3906 Printf(" This is the default.");
3907
3908 Printf(" ");
3909 Printf(" SET WIDthpage");
3910 Printf(" Informs Minuit of the output page width.");
3911 Printf(" Default values are 80 for interactive jobs");
3912 goto L99;
3913 }
3914//______________________________________________________________________________
3915//
3916// Command SHOW
3917//
3918 if( !strncmp(comd.Data(),"SHO",3) ) {
3919 Printf(" ***>SHOw <option_name>");
3920 Printf(" All SET XXXX commands have a corresponding SHOw XXXX command.");
3921 Printf(" In addition, the SHOw commands listed starting here have no");
3922 Printf(" corresponding SET command for obvious reasons.");
3923
3924 Printf(" ");
3925 Printf(" SHOw CORrelations");
3926 Printf(" Calculates and prints the parameter correlations from the");
3927 Printf(" error matrix.");
3928
3929 Printf(" ");
3930 Printf(" SHOw COVariance");
3931 Printf(" Prints the (external) covariance (error) matrix.");
3932
3933 Printf(" ");
3934 Printf(" SHOw EIGenvalues");
3935 Printf(" Calculates and prints the eigenvalues of the covariance");
3936 Printf(" matrix.");
3937
3938 Printf(" ");
3939 Printf(" SHOw FCNvalue");
3940 Printf(" Prints the current value of FCN.");
3941 goto L99;
3942 }
3943//______________________________________________________________________________
3944//
3945// Command SIMPLEX
3946//
3947 if( !strncmp(comd.Data(),"SIM",3) ) {
3948 Printf(" ***>SIMplex [maxcalls] [tolerance]");
3949 Printf(" Performs a function minimization using the simplex method of");
3950 Printf(" Nelder and Mead. Minimization terminates either when the");
3951 Printf(" function has been called (approximately) [maxcalls] times,");
3952 Printf(" or when the estimated vertical distance to minimum (EDM) is");
3953 Printf(" less than [tolerance].");
3954 Printf(" The default value of [tolerance] is 0.1*UP(see SET ERRordef).");
3955 goto L99;
3956 }
3957//______________________________________________________________________________
3958//
3959// Command STANDARD
3960//
3961 if( !strncmp(comd.Data(),"STA",3) ) {
3962 Printf(" ***>STAndard");
3963 goto L99;
3964 }
3965//______________________________________________________________________________
3966//
3967// Command STOP
3968//
3969 if( !strncmp(comd.Data(),"STO",3) ) {
3970 Printf(" ***>STOP");
3971 Printf(" Same as EXIT.");
3972 goto L99;
3973 }
3974//______________________________________________________________________________
3975//
3976// Command TOPOFPAGE
3977//
3978 if( !strncmp(comd.Data(),"TOP",3) ) {
3979 Printf(" ***>TOPofpage");
3980 Printf(" Causes Minuit to write the character specified in a");
3981 Printf(" SET PAGethrow command (default = 1) to column 1 of the output");
3982 Printf(" file, which may or may not position your output medium to");
3983 Printf(" the top of a page depending on the device and system.");
3984 goto L99;
3985 }
3986//______________________________________________________________________________
3987 Printf(" Unknown MINUIT command. Type HELP for list of commands.");
3988
3989L99:
3990 return;
3991}
3992
3993////////////////////////////////////////////////////////////////////////////////
3994/// Calculates the full second-derivative matrix of FCN
3995///
3996/// by taking finite differences. When calculating diagonal
3997/// elements, it may iterate so that step size is nearly that
3998/// which gives function change= UP/10. The first derivatives
3999/// of course come as a free side effect, but with a smaller
4000/// step size in order to obtain a known accuracy.
4001
4003{
4004 /* Local variables */
4005 Double_t dmin_, dxdi, elem, wint, tlrg2, d, dlast, ztemp, g2bfor;
4006 Double_t df, aimsag, fs1, tlrstp, fs2, stpinm, g2i, sag=0, xtf, xti, xtj;
4007 Int_t icyc, ncyc, ndex, idrv, iext, npar2, i, j, ifail, npard, nparx, id, multpy;
4008 Bool_t ldebug;
4009
4010 ldebug = fIdbg[3] >= 1;
4011 if (fAmin == fUndefi) {
4012 mnamin();
4013 }
4014 if (fIstrat <= 0) {
4015 ncyc = 3;
4016 tlrstp = .5;
4017 tlrg2 = .1;
4018 } else if (fIstrat == 1) {
4019 ncyc = 5;
4020 tlrstp = .3;
4021 tlrg2 = .05;
4022 } else {
4023 ncyc = 7;
4024 tlrstp = .1;
4025 tlrg2 = .02;
4026 }
4027 if (fISW[4] >= 2 || ldebug) {
4028 Printf(" START COVARIANCE MATRIX CALCULATION.");
4029 }
4030 fCfrom = "HESSE ";
4031 fNfcnfr = fNfcn;
4032 fCstatu = "OK ";
4033 npard = fNpar;
4034// make sure starting at the right place
4035 mninex(fX);
4036 nparx = fNpar;
4037 Eval(nparx, fGin, fs1, fU, 4); ++fNfcn;
4038 if (fs1 != fAmin) {
4039 df = fAmin - fs1;
4040 mnwarn("D", "MNHESS", TString::Format("function value differs from AMIN by %g",df));
4041 }
4042 fAmin = fs1;
4043 if (ldebug) {
4044 Printf(" PAR D GSTEP D G2 GRD SAG ");
4045 }
4046// diagonal elements .
4047
4048// fISW[1] = 1 if approx, 2 if not posdef, 3 if ok
4049// AIMSAG is the sagitta we are aiming for in second deriv calc.
4050
4051 aimsag = TMath::Sqrt(fEpsma2)*(TMath::Abs(fAmin) + fUp);
4052// Zero the second derivative matrix
4053 npar2 = fNpar*(fNpar + 1) / 2;
4054 for (i = 1; i <= npar2; ++i) { fVhmat[i-1] = 0; }
4055
4056// Loop over variable parameters for second derivatives
4057 idrv = 2;
4058 for (id = 1; id <= npard; ++id) {
4059 i = id + fNpar - npard;
4060 iext = fNexofi[i-1];
4061 if (fG2[i-1] == 0) {
4062 mnwarn("W", "HESSE", Form("Second derivative enters zero, param %d",iext));
4063 wint = fWerr[i-1];
4064 if (fNvarl[iext-1] > 1) {
4065 mndxdi(fX[i-1], i-1, dxdi);
4066 if (TMath::Abs(dxdi) < .001) wint = .01;
4067 else wint /= TMath::Abs(dxdi);
4068 }
4069 fG2[i-1] = fUp / (wint*wint);
4070 }
4071 xtf = fX[i-1];
4072 dmin_ = fEpsma2*8*TMath::Abs(xtf);
4073
4074// find step which gives sagitta = AIMSAG
4075 d = TMath::Abs(fGstep[i-1]);
4076 int skip50 = 0;
4077 for (icyc = 1; icyc <= ncyc; ++icyc) {
4078// loop here only if SAG=0
4079 for (multpy = 1; multpy <= 5; ++multpy) {
4080// take two steps
4081 fX[i-1] = xtf + d;
4082 mninex(fX);
4083 nparx = fNpar;
4084 Eval(nparx, fGin, fs1, fU, 4); ++fNfcn;
4085 fX[i-1] = xtf - d;
4086 mninex(fX);
4087 Eval(nparx, fGin, fs2, fU, 4); ++fNfcn;
4088 fX[i-1] = xtf;
4089 sag = (fs1 + fs2 - fAmin*2)*.5;
4090 if (sag != 0) goto L30;
4091 if (fGstep[i-1] < 0) {
4092 if (d >= .5) goto L26;
4093 d *= 10;
4094 if (d > .5) d = .51;
4095 continue;
4096 }
4097 d *= 10;
4098 }
4099L26:
4100 mnwarn("W", "HESSE", TString::Format("Second derivative zero for parameter%d",iext));
4101 goto L390;
4102// SAG is not zero
4103L30:
4104 g2bfor = fG2[i-1];
4105 fG2[i-1] = sag*2 / (d*d);
4106 fGrd[i-1] = (fs1 - fs2) / (d*2);
4107 if (ldebug) {
4108 Printf("%4d%2d%12.5g%12.5g%12.5g%12.5g%12.5g",i,idrv,fGstep[i-1],d,fG2[i-1],fGrd[i-1],sag);
4109 }
4110 if (fGstep[i-1] > 0) fGstep[i-1] = TMath::Abs(d);
4111 else fGstep[i-1] = -TMath::Abs(d);
4112 fDirin[i-1] = d;
4113 fHESSyy[i-1]= fs1;
4114 dlast = d;
4115 d = TMath::Sqrt(aimsag*2 / TMath::Abs(fG2[i-1]));
4116// if parameter has limits, max int step size = 0.5
4117 stpinm = .5;
4118 if (fGstep[i-1] < 0) d = TMath::Min(d,stpinm);
4119 if (d < dmin_) d = dmin_;
4120// see if converged
4121 if (TMath::Abs((d - dlast) / d) < tlrstp ||
4122 TMath::Abs((fG2[i-1] - g2bfor) / fG2[i-1]) < tlrg2) {
4123 skip50 = 1;
4124 break;
4125 }
4126 d = TMath::Min(d,dlast*102);
4127 d = TMath::Max(d,dlast*.1);
4128 }
4129// end of step size loop
4130 if (!skip50)
4131 mnwarn("D", "MNHESS", TString::Format("Second Deriv. SAG,AIM= %d%g%g",iext,sag,aimsag));
4132
4133 ndex = i*(i + 1) / 2;
4134 fVhmat[ndex-1] = fG2[i-1];
4135 }
4136// end of diagonal second derivative loop
4137 mninex(fX);
4138// refine the first derivatives
4139 if (fIstrat > 0) mnhes1();
4140 fISW[1] = 3;
4141 fDcovar = 0;
4142// off-diagonal elements
4143
4144 if (fNpar == 1) goto L214;
4145 for (i = 1; i <= fNpar; ++i) {
4146 for (j = 1; j <= i-1; ++j) {
4147 xti = fX[i-1];
4148 xtj = fX[j-1];
4149 fX[i-1] = xti + fDirin[i-1];
4150 fX[j-1] = xtj + fDirin[j-1];
4151 mninex(fX);
4152 Eval(nparx, fGin, fs1, fU, 4); ++fNfcn;
4153 fX[i-1] = xti;
4154 fX[j-1] = xtj;
4155 elem = (fs1 + fAmin - fHESSyy[i-1] - fHESSyy[j-1]) / (
4156 fDirin[i-1]*fDirin[j-1]);
4157 ndex = i*(i-1) / 2 + j;
4158 fVhmat[ndex-1] = elem;
4159 }
4160 }
4161L214:
4162 mninex(fX);
4163// verify matrix positive-definite
4164 mnpsdf();
4165 for (i = 1; i <= fNpar; ++i) {
4166 for (j = 1; j <= i; ++j) {
4167 ndex = i*(i-1) / 2 + j;
4168 fP[i + j*fMaxpar - fMaxpar-1] = fVhmat[ndex-1];
4169 fP[j + i*fMaxpar - fMaxpar-1] = fP[i + j*fMaxpar - fMaxpar-1];
4170 }
4171 }
4172 mnvert(fP, fMaxint, fMaxint, fNpar, ifail);
4173 if (ifail > 0) {
4174 mnwarn("W", "HESSE", "Matrix inversion fails.");
4175 goto L390;
4176 }
4177// calculate e d m
4178 fEDM = 0;
4179
4180 for (i = 1; i <= fNpar; ++i) {
4181// off-diagonal elements
4182 ndex = i*(i-1) / 2;
4183 for (j = 1; j <= i-1; ++j) {
4184 ++ndex;
4185 ztemp = fP[i + j*fMaxpar - fMaxpar-1]*2;
4186 fEDM += fGrd[i-1]*ztemp*fGrd[j-1];
4187 fVhmat[ndex-1] = ztemp;
4188 }
4189// diagonal elements
4190 ++ndex;
4191 fVhmat[ndex-1] = fP[i + i*fMaxpar - fMaxpar-1]*2;
4192 fEDM += fP[i + i*fMaxpar - fMaxpar-1]*(fGrd[i-1]*fGrd[i-1]);
4193 }
4194 if (fISW[4] >= 1 && fISW[1] == 3 && fItaur == 0) {
4195 Printf(" COVARIANCE MATRIX CALCULATED SUCCESSFULLY");
4196 }
4197 goto L900;
4198// failure to invert 2nd deriv matrix
4199L390:
4200 fISW[1] = 1;
4201 fDcovar = 1;
4202 fCstatu = "FAILED ";
4203 if (fISW[4] >= 0) {
4204 Printf(" MNHESS FAILS AND WILL RETURN DIAGONAL MATRIX. ");
4205 }
4206 for (i = 1; i <= fNpar; ++i) {
4207 ndex = i*(i-1) / 2;
4208 for (j = 1; j <= i-1; ++j) {
4209 ++ndex;
4210 fVhmat[ndex-1] = 0;
4211 }
4212 ++ndex;
4213 g2i = fG2[i-1];
4214 if (g2i <= 0) g2i = 1;
4215 fVhmat[ndex-1] = 2 / g2i;
4216 }
4217L900:
4218 return;
4219}
4220
4221////////////////////////////////////////////////////////////////////////////////
4222/// Calculate first derivatives (GRD) and uncertainties (DGRD)
4223///
4224/// and appropriate step sizes GSTEP
4225/// Called from MNHESS and MNGRAD
4226
4228{
4229 /* Local variables */
4230 Double_t dmin_, d, dfmin, dgmin=0, change, chgold, grdold=0, epspri;
4231 Double_t fs1, optstp, fs2, grdnew=0, sag, xtf;
4232 Int_t icyc, ncyc=0, idrv, i, nparx;
4233 Bool_t ldebug;
4234
4235 ldebug = fIdbg[5] >= 1;
4236 if (fIstrat <= 0) ncyc = 1;
4237 if (fIstrat == 1) ncyc = 2;
4238 if (fIstrat > 1) ncyc = 6;
4239 idrv = 1;
4240 nparx = fNpar;
4241 dfmin = fEpsma2*4*(TMath::Abs(fAmin) + fUp);
4242// main loop over parameters
4243 for (i = 1; i <= fNpar; ++i) {
4244 xtf = fX[i-1];
4245 dmin_ = fEpsma2*4*TMath::Abs(xtf);
4246 epspri = fEpsma2 + TMath::Abs(fGrd[i-1]*fEpsma2);
4247 optstp = TMath::Sqrt(dfmin / (TMath::Abs(fG2[i-1]) + epspri));
4248 d = TMath::Abs(fGstep[i-1])*.2;
4249 if (d > optstp) d = optstp;
4250 if (d < dmin_) d = dmin_;
4251 chgold = 1e4;
4252// iterate reducing step size
4253 for (icyc = 1; icyc <= ncyc; ++icyc) {
4254 fX[i-1] = xtf + d;
4255 mninex(fX);
4256 Eval(nparx, fGin, fs1, fU, 4); ++fNfcn;
4257 fX[i-1] = xtf - d;
4258 mninex(fX);
4259 Eval(nparx, fGin, fs2, fU, 4); ++fNfcn;
4260 fX[i-1] = xtf;
4261// check if step sizes appropriate
4262 sag = (fs1 + fs2 - fAmin*2)*.5;
4263 grdold = fGrd[i-1];
4264 grdnew = (fs1 - fs2) / (d*2);
4265 dgmin = fEpsmac*(TMath::Abs(fs1) + TMath::Abs(fs2)) / d;
4266 if (ldebug) {
4267 Printf("%4d%2d%12.5g%12.5g%12.5g%12.5g%12.5g",i,idrv,fGstep[i-1],d,fG2[i-1],grdnew,sag);
4268 }
4269 if (grdnew == 0) goto L60;
4270 change = TMath::Abs((grdold - grdnew) / grdnew);
4271 if (change > chgold && icyc > 1) goto L60;
4272 chgold = change;
4273 fGrd[i-1] = grdnew;
4274 if (fGstep[i-1] > 0) fGstep[i-1] = TMath::Abs(d);
4275 else fGstep[i-1] = -TMath::Abs(d);
4276// decrease step until first derivative changes by <5%
4277 if (change < .05) goto L60;
4278 if (TMath::Abs(grdold - grdnew) < dgmin) goto L60;
4279 if (d < dmin_) {
4280 mnwarn("D", "MNHES1", "Step size too small for 1st drv.");
4281 goto L60;
4282 }
4283 d *= .2;
4284 }
4285// loop satisfied = too many iter
4286 mnwarn("D", "MNHES1", TString::Format("Too many iterations on D1.%g%g",grdold,grdnew));
4287L60:
4288 fDgrd[i-1] = TMath::Max(dgmin,TMath::Abs(grdold - grdnew));
4289 }
4290// end of first deriv. loop
4291 mninex(fX);
4292}
4293
4294////////////////////////////////////////////////////////////////////////////////
4295/// Attempts to improve on a good local minimum
4296///
4297/// Attempts to improve on a good local minimum by finding a
4298/// better one. The quadratic part of FCN is removed by MNCALF
4299/// and this transformed function is minimised using the simplex
4300/// method from several random starting points.
4301///
4302/// ref. -- Goldstein and Price, Math.Comp. 25, 569 (1971)
4303
4305{
4306 /* Initialized data */
4307
4308 Double_t rnum = 0;
4309
4310 /* Local variables */
4311 Double_t amax, ycalf, ystar, ystst;
4312 Double_t pb, ep, wg, xi, sigsav, reg, sig2;
4313 Int_t npfn, ndex, loop=0, i, j, ifail, iseed=0;
4314 Int_t jhold, nloop, nparx, nparp1, jh, jl, iswtr;
4315
4316 if (fNpar <= 0) return;
4317 if (fAmin == fUndefi) mnamin();
4318 fCstatu = "UNCHANGED ";
4319 fItaur = 1;
4320 fEpsi = fUp*.1;
4321 npfn = fNfcn;
4322 nloop = Int_t(fWord7[1]);
4323 if (nloop <= 0) nloop = fNpar + 4;
4324 nparx = fNpar;
4325 nparp1 = fNpar + 1;
4326 wg = 1 / Double_t(fNpar);
4327 sigsav = fEDM;
4328 fApsi = fAmin;
4329 iswtr = fISW[4] - 2*fItaur;
4330 for (i = 1; i <= fNpar; ++i) {
4331 fXt[i-1] = fX[i-1];
4332 fIMPRdsav[i-1] = fWerr[i-1];
4333 for (j = 1; j <= i; ++j) {
4334 ndex = i*(i-1) / 2 + j;
4335 fP[i + j*fMaxpar - fMaxpar-1] = fVhmat[ndex-1];
4336 fP[j + i*fMaxpar - fMaxpar-1] = fP[i + j*fMaxpar - fMaxpar-1];
4337 }
4338 }
4339 mnvert(fP, fMaxint, fMaxint, fNpar, ifail);
4340 if (ifail >= 1) goto L280;
4341// Save inverted matrix in VT
4342 for (i = 1; i <= fNpar; ++i) {
4343 ndex = i*(i-1) / 2;
4344 for (j = 1; j <= i; ++j) {
4345 ++ndex;
4346 fVthmat[ndex-1] = fP[i + j*fMaxpar - fMaxpar-1];
4347 }
4348 }
4349 loop = 0;
4350
4351L20:
4352 for (i = 1; i <= fNpar; ++i) {
4353 fDirin[i-1] = fIMPRdsav[i-1]*2;
4354 mnrn15(rnum, iseed);
4355 fX[i-1] = fXt[i-1] + fDirin[i-1]*2*(rnum - .5);
4356 }
4357 ++loop;
4358 reg = 2;
4359 if (fISW[4] >= 0) {
4360 Printf("START ATTEMPT NO.%2d TO FIND NEW MINIMUM",loop);
4361 }
4362L30:
4363 mncalf(fX, ycalf);
4364 fAmin = ycalf;
4365// set up random simplex
4366 jl = nparp1;
4367 jh = nparp1;
4368 fIMPRy[nparp1-1] = fAmin;
4369 amax = fAmin;
4370 for (i = 1; i <= fNpar; ++i) {
4371 xi = fX[i-1];
4372 mnrn15(rnum, iseed);
4373 fX[i-1] = xi - fDirin[i-1]*(rnum - .5);
4374 mncalf(fX, ycalf);
4375 fIMPRy[i-1] = ycalf;
4376 if (fIMPRy[i-1] < fAmin) {
4377 fAmin = fIMPRy[i-1];
4378 jl = i;
4379 } else if (fIMPRy[i-1] > amax) {
4380 amax = fIMPRy[i-1];
4381 jh = i;
4382 }
4383 for (j = 1; j <= fNpar; ++j) { fP[j + i*fMaxpar - fMaxpar-1] = fX[j-1]; }
4384 fP[i + nparp1*fMaxpar - fMaxpar-1] = xi;
4385 fX[i-1] = xi;
4386 }
4387
4388 fEDM = fAmin;
4389 sig2 = fEDM;
4390// start main loop
4391L50:
4392 if (fAmin < 0) goto L95;
4393 if (fISW[1] <= 2) goto L280;
4394 ep = fAmin*.1;
4395 if (sig2 < ep && fEDM < ep) goto L100;
4396 sig2 = fEDM;
4397 if (fNfcn - npfn > fNfcnmx) goto L300;
4398// calculate new point * by reflection
4399 for (i = 1; i <= fNpar; ++i) {
4400 pb = 0;
4401 for (j = 1; j <= nparp1; ++j) { pb += wg*fP[i + j*fMaxpar - fMaxpar-1]; }
4402 fPbar[i-1] = pb - wg*fP[i + jh*fMaxpar - fMaxpar-1];
4403 fPstar[i-1] = fPbar[i-1]*2 - fP[i + jh*fMaxpar - fMaxpar-1]*1;
4404 }
4405 mncalf(fPstar, ycalf);
4406 ystar = ycalf;
4407 if (ystar >= fAmin) goto L70;
4408// point * better than jl, calculate new point **
4409 for (i = 1; i <= fNpar; ++i) {
4410 fPstst[i-1] = fPstar[i-1]*2 + fPbar[i- 1]*-1;
4411 }
4412 mncalf(fPstst, ycalf);
4413 ystst = ycalf;
4414 if (ystst < fIMPRy[jl-1]) goto L67;
4415 mnrazz(ystar, fPstar, fIMPRy, jh, jl);
4416 goto L50;
4417L67:
4418 mnrazz(ystst, fPstst, fIMPRy, jh, jl);
4419 goto L50;
4420// point * is not as good as jl
4421L70:
4422 if (ystar >= fIMPRy[jh-1]) goto L73;
4423 jhold = jh;
4424 mnrazz(ystar, fPstar, fIMPRy, jh, jl);
4425 if (jhold != jh) goto L50;
4426// calculate new point **
4427L73:
4428 for (i = 1; i <= fNpar; ++i) {
4429 fPstst[i-1] = fP[i + jh*fMaxpar - fMaxpar-1]*.5 + fPbar[i-1]*.5;
4430 }
4431 mncalf(fPstst, ycalf);
4432 ystst = ycalf;
4433 if (ystst > fIMPRy[jh-1]) goto L30;
4434// point ** is better than jh
4435 if (ystst < fAmin) goto L67;
4436 mnrazz(ystst, fPstst, fIMPRy, jh, jl);
4437 goto L50;
4438// end main loop
4439L95:
4440 if (fISW[4] >= 0) {
4441 Printf(" AN IMPROVEMENT ON THE PREVIOUS MINIMUM HAS BEEN FOUND");
4442 }
4443 reg = .1;
4444// ask if point is new
4445L100:
4446 mninex(fX);
4447 Eval(nparx, fGin, fAmin, fU, 4); ++fNfcn;
4448 for (i = 1; i <= fNpar; ++i) {
4449 fDirin[i-1] = reg*fIMPRdsav[i-1];
4450 if (TMath::Abs(fX[i-1] - fXt[i-1]) > fDirin[i-1]) goto L150;
4451 }
4452 goto L230;
4453L150:
4454 fNfcnmx = fNfcnmx + npfn - fNfcn;
4455 npfn = fNfcn;
4456 mnsimp();
4457 if (fAmin >= fApsi) goto L325;
4458 for (i = 1; i <= fNpar; ++i) {
4459 fDirin[i-1] = fIMPRdsav[i-1]*.1;
4460 if (TMath::Abs(fX[i-1] - fXt[i-1]) > fDirin[i-1]) goto L250;
4461 }
4462L230:
4463 if (fAmin < fApsi) goto L350;
4464 goto L325;
4465/* truly new minimum */
4466L250:
4467 fLnewmn = kTRUE;
4468 if (fISW[1] >= 1) {
4469 fISW[1] = 1;
4471 } else fDcovar = 1;
4472 fItaur = 0;
4473 fNfcnmx = fNfcnmx + npfn - fNfcn;
4474 fCstatu = "NEW MINIMU";
4475 if (fISW[4] >= 0) {
4476 Printf(" IMPROVE HAS FOUND A TRULY NEW MINIMUM");
4477 Printf(" *************************************");
4478 }
4479 return;
4480// return to previous region
4481L280:
4482 if (fISW[4] > 0) {
4483 Printf(" COVARIANCE MATRIX WAS NOT POSITIVE-DEFINITE");
4484 }
4485 goto L325;
4486L300:
4487 fISW[0] = 1;
4488L325:
4489 for (i = 1; i <= fNpar; ++i) {
4490 fDirin[i-1] = fIMPRdsav[i-1]*.01;
4491 fX[i-1] = fXt[i-1];
4492 }
4493 fAmin = fApsi;
4494 fEDM = sigsav;
4495L350:
4496 mninex(fX);
4497 if (fISW[4] > 0) {
4498 Printf(" IMPROVE HAS RETURNED TO REGION OF ORIGINAL MINIMUM");
4499 }
4500 fCstatu = "UNCHANGED ";
4501 mnrset(0);
4502 if (fISW[1] < 2) goto L380;
4503 if (loop < nloop && fISW[0] < 1) goto L20;
4504L380:
4505 if (iswtr >= 0) mnprin(5, fAmin);
4506 fItaur = 0;
4507}
4508
4509////////////////////////////////////////////////////////////////////////////////
4510/// Transforms from internal coordinates (PINT) to external (U)
4511///
4512/// The minimising routines which work in
4513/// internal coordinates call this routine before calling FCN.
4514
4516{
4517 Int_t i, j;
4518
4519 for (j = 0; j < fNpar; ++j) {
4520 i = fNexofi[j]-1;
4521 if (fNvarl[i] == 1) {
4522 fU[i] = pint[j];
4523 } else {
4524 fU[i] = fAlim[i] + (TMath::Sin(pint[j]) + 1)*.5*(fBlim[i] - fAlim[i]);
4525 }
4526 }
4527}
4528
4529////////////////////////////////////////////////////////////////////////////////
4530/// Main initialization member function for MINUIT
4531///
4532/// It initializes some constants
4533/// (including the logical I/O unit nos.),
4534
4536{
4537 /* Local variables */
4538 volatile Double_t epsp1;
4539 Double_t piby2, epstry, epsbak, distnn;
4540 Int_t i, idb;
4541
4542// I/O unit numbers
4543 fIsysrd = i1;
4544 fIsyswr = i2;
4545 fIstkwr[0] = fIsyswr;
4546 fNstkwr = 1;
4547 fIsyssa = i3;
4548 fNstkrd = 0;
4549// version identifier
4550 fCvrsn = "95.03++ ";
4551// some CONSTANT
4552 fMaxint = fMaxpar;
4553 fMaxext = 2*fMaxpar;
4554 fUndefi = -54321;
4555 fBigedm = 123456;
4556 fCundef = ")UNDEFINED";
4557 fCovmes[0] = "NO ERROR MATRIX ";
4558 fCovmes[1] = "ERR MATRIX APPROXIMATE";
4559 fCovmes[2] = "ERR MATRIX NOT POS-DEF";
4560 fCovmes[3] = "ERROR MATRIX ACCURATE ";
4561// some starting values
4562 fNblock = 0;
4563 fIcomnd = 0;
4564 fCtitl = fCundef;
4565 fCfrom = "INPUT ";
4566 fNfcn = 0;
4567 fNfcnfr = fNfcn;
4568 fCstatu = "INITIALIZE";
4569 fISW[2] = 0;
4570 fISW[3] = 0;
4571 fISW[4] = 1;
4572// fISW[5]=0 for batch jobs, =1 for interactive jobs
4573// =-1 for originally interactive temporarily batch
4574
4575 fISW[5] = 0;
4576// if (intrac(&dummy)) fISW[5] = 1;
4577// DEBUG options set to default values
4578 for (idb = 0; idb <= 10; ++idb) { fIdbg[idb] = 0; }
4579 fLrepor = kFALSE;
4580 fLwarn = kTRUE;
4581 fLimset = kFALSE;
4582 fLnewmn = kFALSE;
4583 fIstrat = 1;
4584 fItaur = 0;
4585// default page dimensions and 'new page' carriage control integer
4586 fNpagwd = 120;
4587 fNpagln = 56;
4588 fNewpag = 1;
4589 if (fISW[5] > 0) {
4590 fNpagwd = 80;
4591 fNpagln = 30;
4592 fNewpag = 0;
4593 }
4594 fUp = 1;
4595 fUpdflt = fUp;
4596// determine machine accuracy epsmac
4597 epstry = .5;
4598 for (i = 1; i <= 100; ++i) {
4599 epstry *= .5;
4600 epsp1 = epstry + 1;
4601 mntiny(epsp1, epsbak);
4602 if (epsbak < epstry) goto L35;
4603 }
4604 epstry = 1e-7;
4605 fEpsmac = epstry*4;
4606 Printf(" MNINIT UNABLE TO DETERMINE ARITHMETIC PRECISION. WILL ASSUME:%g",fEpsmac);
4607L35:
4608 fEpsmac = epstry*8;
4610// the vlims are a non-negligible distance from pi/2
4611// used by MNPINT to set variables "near" the physical limits
4612 piby2 = TMath::ATan(1)*2;
4613 distnn = TMath::Sqrt(fEpsma2)*8;
4614 fVlimhi = piby2 - distnn;
4615 fVlimlo = -piby2 + distnn;
4616 mncler();
4617// Printf(" MINUIT RELEASE %s INITIALIZED. DIMENSIONS 100/50 EPSMAC=%g",(const char*)fCvrsn,fEpsmac);
4618}
4619
4620////////////////////////////////////////////////////////////////////////////////
4621/// Interprets the SET LIM command, to reset the parameter limits
4622///
4623/// Called from MNSET
4624
4626{
4627 /* Local variables */
4628 Double_t dxdi, snew;
4629 Int_t kint, i2, newcod, ifx=0, inu;
4630
4631 fCfrom = "SET LIM ";
4632 fNfcnfr = fNfcn;
4633 fCstatu = "NO CHANGE ";
4634 i2 = Int_t(fWord7[0]);
4635 if (i2 > fMaxext || i2 < 0) goto L900;
4636 if (i2 > 0) goto L30;
4637// set limits on all parameters
4638 newcod = 4;
4639 if (fWord7[1] == fWord7[2]) newcod = 1;
4640 for (inu = 1; inu <= fNu; ++inu) {
4641 if (fNvarl[inu-1] <= 0) continue;
4642 if (fNvarl[inu-1] == 1 && newcod == 1) continue;
4643 kint = fNiofex[inu-1];
4644// see if parameter has been fixed
4645 if (kint <= 0) {
4646 if (fISW[4] >= 0) {
4647 Printf(" LIMITS NOT CHANGED FOR FIXED PARAMETER:%4d",inu);
4648 }
4649 continue;
4650 }
4651 if (newcod == 1) {
4652// remove limits from parameter
4653 if (fISW[4] > 0) {
4654 Printf(" LIMITS REMOVED FROM PARAMETER :%3d",inu);
4655 }
4656 fCstatu = "NEW LIMITS";
4657 mndxdi(fX[kint-1], kint-1, dxdi);
4658 snew = fGstep[kint-1]*dxdi;
4659 fGstep[kint-1] = TMath::Abs(snew);
4660 fNvarl[inu-1] = 1;
4661 } else {
4662// put limits on parameter
4663 fAlim[inu-1] = TMath::Min(fWord7[1],fWord7[2]);
4664 fBlim[inu-1] = TMath::Max(fWord7[1],fWord7[2]);
4665 if (fISW[4] > 0) {
4666 Printf(" PARAMETER %3d LIMITS SET TO %15.5g%15.5g",inu,fAlim[inu-1],fBlim[inu-1]);
4667 }
4668 fNvarl[inu-1] = 4;
4669 fCstatu = "NEW LIMITS";
4670 fGstep[kint-1] = -.1;
4671 }
4672 }
4673 goto L900;
4674// set limits on one parameter
4675L30:
4676 if (fNvarl[i2-1] <= 0) {
4677 Printf(" PARAMETER %3d IS NOT VARIABLE.", i2);
4678 goto L900;
4679 }
4680 kint = fNiofex[i2-1];
4681// see if parameter was fixed
4682 if (kint == 0) {
4683 Printf(" REQUEST TO CHANGE LIMITS ON FIXED PARAMETER:%3d",i2);
4684 for (ifx = 1; ifx <= fNpfix; ++ifx) {
4685 if (i2 == fIpfix[ifx-1]) goto L92;
4686 }
4687 Printf(" MINUIT BUG IN MNLIMS. SEE F. JAMES");
4688L92:
4689 ;
4690 }
4691 if (fWord7[1] != fWord7[2]) goto L235;
4692// remove limits
4693 if (fNvarl[i2-1] != 1) {
4694 if (fISW[4] > 0) {
4695 Printf(" LIMITS REMOVED FROM PARAMETER %2d",i2);
4696 }
4697 fCstatu = "NEW LIMITS";
4698 if (kint <= 0) {
4699 fGsteps[ifx-1] = TMath::Abs(fGsteps[ifx-1]);
4700 } else {
4701 mndxdi(fX[kint-1], kint-1, dxdi);
4702 if (TMath::Abs(dxdi) < .01) dxdi = .01;
4703 fGstep[kint-1] = TMath::Abs(fGstep[kint-1]*dxdi);
4704 fGrd[kint-1] *= dxdi;
4705 }
4706 fNvarl[i2-1] = 1;
4707 } else {
4708 Printf(" NO LIMITS SPECIFIED. PARAMETER %3d IS ALREADY UNLIMITED. NO CHANGE.",i2);
4709 }
4710 goto L900;
4711// put on limits
4712L235:
4713 fAlim[i2-1] = TMath::Min(fWord7[1],fWord7[2]);
4714 fBlim[i2-1] = TMath::Max(fWord7[1],fWord7[2]);
4715 fNvarl[i2-1] = 4;
4716 if (fISW[4] > 0) {
4717 Printf(" PARAMETER %3d LIMITS SET TO %15.5g%15.5g",i2,fAlim[i2-1],fBlim[i2-1]);
4718 }
4719 fCstatu = "NEW LIMITS";
4720 if (kint <= 0) fGsteps[ifx-1] = -.1;
4721 else fGstep[kint-1] = -.1;
4722
4723L900:
4724 if (fCstatu != "NO CHANGE ") {
4725 mnexin(fX);
4726 mnrset(1);
4727 }
4728}
4729
4730////////////////////////////////////////////////////////////////////////////////
4731/// Perform a line search from position START
4732///
4733/// along direction STEP, where the length of vector STEP
4734/// gives the expected position of minimum.
4735/// - FSTART is value of function at START
4736/// - SLOPE (if non-zero) is df/dx along STEP at START
4737/// - TOLER is initial tolerance of minimum in direction STEP
4738///
4739/// SLAMBG and ALPHA control the maximum individual steps allowed.
4740/// The first step is always =1. The max length of second step is SLAMBG.
4741/// The max size of subsequent steps is the maximum previous successful
4742/// step multiplied by ALPHA + the size of most recent successful step,
4743/// but cannot be smaller than SLAMBG.
4744
4745void TMinuit::mnline(Double_t *start, Double_t fstart, Double_t *step, Double_t slope, Double_t toler)
4746{
4747 /* Local variables */
4748 Double_t xpq[12], ypq[12], slam, sdev, coeff[3], denom, flast;
4749 Double_t fvals[3], xvals[3], f1, fvmin, xvmin, ratio, f2, f3 = 0., fvmax;
4750 Double_t toler8, toler9, overal, undral, slamin, slamax, slopem;
4751 Int_t i, nparx=0, nvmax=0, nxypt, kk, ipt;
4752 Bool_t ldebug;
4753 TString cmess;
4754 char chpq[13];
4755 int l65, l70, l80;
4756
4757 /* Function Body */
4758 l65 = 0; l70 = 0; l80 = 0;
4759 ldebug = fIdbg[1] >= 1;
4760// starting values for overall limits on total step SLAM
4761 overal = 1e3;
4762 undral = -100;
4763// debug check if start is ok
4764 if (ldebug) {
4765 mninex(&start[0]);
4766 Eval(nparx, fGin, f1, fU, 4); ++fNfcn;
4767 if (f1 != fstart) {
4768 Printf(" MNLINE start point not consistent, F values, parameters=");
4769 for (kk = 1; kk <= fNpar; ++kk) {
4770 Printf(" %14.5e",fX[kk-1]);
4771 }
4772 }
4773 }
4774// set up linear search along STEP
4775 fvmin = fstart;
4776 xvmin = 0;
4777 nxypt = 1;
4778 chpq[0] = charal[0];
4779 xpq[0] = 0;
4780 ypq[0] = fstart;
4781// SLAMIN = smallest possible value of ABS(SLAM)
4782 slamin = 0;
4783 for (i = 1; i <= fNpar; ++i) {
4784 if (step[i-1] != 0) {
4785 ratio = TMath::Abs(start[i-1] / step[i-1]);
4786 if (slamin == 0) slamin = ratio;
4787 if (ratio < slamin) slamin = ratio;
4788 }
4789 fX[i-1] = start[i-1] + step[i-1];
4790 }
4791 if (slamin == 0) slamin = fEpsmac;
4792 slamin *= fEpsma2;
4793 nparx = fNpar;
4794
4795 mninex(fX);
4796 Eval(nparx, fGin, f1, fU, 4); ++fNfcn;
4797 ++nxypt;
4798 chpq[nxypt-1] = charal[nxypt-1];
4799 xpq[nxypt-1] = 1;
4800 ypq[nxypt-1] = f1;
4801 if (f1 < fstart) {
4802 fvmin = f1;
4803 xvmin = 1;
4804 }
4805// quadr interp using slope GDEL and two points
4806 slam = 1;
4807 toler8 = toler;
4808 slamax = 5;
4809 flast = f1;
4810// can iterate on two-points (cut) if no imprvmnt
4811
4812 do {
4813 denom = (flast - fstart - slope*slam)*2 / (slam*slam);
4814 slam = 1;
4815 if (denom != 0) slam = -slope / denom;
4816 if (slam < 0) slam = slamax;
4817 if (slam > slamax) slam = slamax;
4818 if (slam < toler8) slam = toler8;
4819 if (slam < slamin) {
4820 l80 = 1;
4821 break;
4822 }
4823 if (TMath::Abs(slam - 1) < toler8 && f1 < fstart) {
4824 l70 = 1;
4825 break;
4826 }
4827 if (TMath::Abs(slam - 1) < toler8) slam = toler8 + 1;
4828 if (nxypt >= 12) {
4829 l65 = 1;
4830 break;
4831 }
4832 for (i = 1; i <= fNpar; ++i) { fX[i-1] = start[i-1] + slam*step[i-1]; }
4833 mninex(fX);
4834 nparx = fNpar;
4835 Eval(nparx, fGin, f2, fU, 4); ++fNfcn;
4836 ++nxypt;
4837 chpq[nxypt-1] = charal[nxypt-1];
4838 xpq[nxypt-1] = slam;
4839 ypq[nxypt-1] = f2;
4840 if (f2 < fvmin) {
4841 fvmin = f2;
4842 xvmin = slam;
4843 }
4844 if (fstart == fvmin) {
4845 flast = f2;
4846 toler8 = toler*slam;
4847 overal = slam - toler8;
4848 slamax = overal;
4849 }
4850 } while (fstart == fvmin);
4851
4852 if (!l65 && !l70 && !l80) {
4853// quadr interp using 3 points
4854 xvals[0] = xpq[0];
4855 fvals[0] = ypq[0];
4856 xvals[1] = xpq[nxypt-2];
4857 fvals[1] = ypq[nxypt-2];
4858 xvals[2] = xpq[nxypt-1];
4859 fvals[2] = ypq[nxypt-1];
4860// begin iteration, calculate desired step
4861 do {
4862 slamax = TMath::Max(slamax,TMath::Abs(xvmin)*2);
4863 mnpfit(xvals, fvals, 3, coeff, sdev);
4864 if (coeff[2] <= 0) {
4865 slopem = coeff[2]*2*xvmin + coeff[1];
4866 if (slopem <= 0) slam = xvmin + slamax;
4867 else slam = xvmin - slamax;
4868 } else {
4869 slam = -coeff[1] / (coeff[2]*2);
4870 if (slam > xvmin + slamax) slam = xvmin + slamax;
4871 if (slam < xvmin - slamax) slam = xvmin - slamax;
4872 }
4873 if (slam > 0) {
4874 if (slam > overal)
4875 slam = overal;
4876 else if (slam < undral)
4877 slam = undral;
4878 }
4879
4880// come here if step was cut below
4881 do {
4882 toler9 = TMath::Max(toler8,TMath::Abs(toler8*slam));
4883 for (ipt = 1; ipt <= 3; ++ipt) {
4884 if (TMath::Abs(slam - xvals[ipt-1]) < toler9) {
4885 l70 = 1;
4886 break;
4887 }
4888 }
4889 if (l70) break;
4890// take the step
4891 if (nxypt >= 12) {
4892 l65 = 1;
4893 break;
4894 }
4895 for (i = 1; i <= fNpar; ++i) { fX[i-1] = start[i-1] + slam*step[i-1]; }
4896 mninex(fX);
4897 Eval(nparx, fGin, f3, fU, 4); ++fNfcn;
4898 ++nxypt;
4899 chpq[nxypt-1] = charal[nxypt-1];
4900 xpq[nxypt-1] = slam;
4901 ypq[nxypt-1] = f3;
4902// find worst previous point out of three
4903 fvmax = fvals[0];
4904 nvmax = 1;
4905 if (fvals[1] > fvmax) {
4906 fvmax = fvals[1];
4907 nvmax = 2;
4908 }
4909 if (fvals[2] > fvmax) {
4910 fvmax = fvals[2];
4911 nvmax = 3;
4912 }
4913// if latest point worse than all three previous, cut step
4914 if (f3 >= fvmax) {
4915 if (nxypt >= 12) {
4916 l65 = 1;
4917 break;
4918 }
4919 if (slam > xvmin) overal = TMath::Min(overal,slam - toler8);
4920 if (slam < xvmin) undral = TMath::Max(undral,slam + toler8);
4921 slam = (slam + xvmin)*.5;
4922 }
4923 } while (f3 >= fvmax);
4924
4925// prepare another iteration, replace worst previous point
4926 if (l65 || l70) break;
4927
4928 xvals[nvmax-1] = slam;
4929 fvals[nvmax-1] = f3;
4930 if (f3 < fvmin) {
4931 fvmin = f3;
4932 xvmin = slam;
4933 } else {
4934 if (slam > xvmin) overal = TMath::Min(overal,slam - toler8);
4935 if (slam < xvmin) undral = TMath::Max(undral,slam + toler8);
4936 }
4937 } while (nxypt < 12);
4938 }
4939
4940// end of iteration
4941// stop because too many iterations
4942 if (!l70 && !l80) {
4943 cmess = " LINE SEARCH HAS EXHAUSTED THE LIMIT OF FUNCTION CALLS ";
4944 if (ldebug) {
4945 Printf(" MNLINE DEBUG: steps=");
4946 for (kk = 1; kk <= fNpar; ++kk) {
4947 Printf(" %12.4g",step[kk-1]);
4948 }
4949 }
4950 }
4951// stop because within tolerance
4952 if (l70) cmess = " LINE SEARCH HAS ATTAINED TOLERANCE ";
4953 if (l80) cmess = " STEP SIZE AT ARITHMETICALLY ALLOWED MINIMUM";
4954
4955 fAmin = fvmin;
4956 for (i = 1; i <= fNpar; ++i) {
4957 fDirin[i-1] = step[i-1]*xvmin;
4958 fX[i-1] = start[i-1] + fDirin[i-1];
4959 }
4960 mninex(fX);
4961 if (xvmin < 0) {
4962 mnwarn("D", "MNLINE", " LINE MINIMUM IN BACKWARDS DIRECTION");
4963 }
4964 if (fvmin == fstart) {
4965 mnwarn("D", "MNLINE", " LINE SEARCH FINDS NO IMPROVEMENT ");
4966 }
4967 if (ldebug) {
4968 Printf(" AFTER %3d POINTS,%s",nxypt,(const char*)cmess);
4969 mnplot(xpq, ypq, chpq, nxypt, fNpagwd, fNpagln);
4970 }
4971}
4972
4973////////////////////////////////////////////////////////////////////////////////
4974/// Prints the covariance matrix v when KODE=1
4975///
4976/// always prints the global correlations, and
4977/// calculates and prints the individual correlation coefficients
4978
4980{
4981 /* Local variables */
4982 Int_t ndex, i, j, m, n, ncoef, nparm, id, it, ix;
4983 Int_t nsofar, ndi, ndj, iso, isw2, isw5;
4984 TString ctemp;
4985
4986 isw2 = fISW[1];
4987 if (isw2 < 1) {
4988 Printf("%s",(const char*)fCovmes[isw2]);
4989 return;
4990 }
4991 if (fNpar == 0) {
4992 Printf(" MNMATU: NPAR=0");
4993 return;
4994 }
4995// external error matrix
4996 if (kode == 1) {
4997 isw5 = fISW[4];
4998 fISW[4] = 2;
4999 mnemat(fP, fMaxint);
5000 if (isw2 < 3) {
5001 Printf("%s",(const char*)fCovmes[isw2]);
5002 }
5003 fISW[4] = isw5;
5004 }
5005// correlation coeffs
5006 if (fNpar <= 1) return;
5007 mnwerr();
5008// NCOEF is number of coeff. that fit on one line, not to exceed 20
5009 ncoef = (fNpagwd - 19) / 6;
5010 ncoef = TMath::Min(ncoef,20);
5011 nparm = TMath::Min(fNpar,ncoef);
5012 Printf(" PARAMETER CORRELATION COEFFICIENTS ");
5013 ctemp = " NO. GLOBAL";
5014 for (id = 1; id <= nparm; ++id) {
5015 ctemp += TString::Format(" %6d",fNexofi[id-1]);
5016 }
5017 Printf("%s",(const char*)ctemp);
5018 for (i = 1; i <= fNpar; ++i) {
5019 ix = fNexofi[i-1];
5020 ndi = i*(i + 1) / 2;
5021 for (j = 1; j <= fNpar; ++j) {
5022 m = TMath::Max(i,j);
5023 n = TMath::Min(i,j);
5024 ndex = m*(m-1) / 2 + n;
5025 ndj = j*(j + 1) / 2;
5026 fMATUvline[j-1] = fVhmat[ndex-1] / TMath::Sqrt(TMath::Abs(fVhmat[ndi-1]*fVhmat[ndj-1]));
5027 }
5028 nparm = TMath::Min(fNpar,ncoef);
5029 ctemp.Form(" %3d %7.5f ",ix,fGlobcc[i-1]);
5030 for (it = 1; it <= nparm; ++it) {
5031 ctemp += TString::Format(" %6.3f",fMATUvline[it-1]);
5032 }
5033 Printf("%s",(const char*)ctemp);
5034 if (i <= nparm) continue;
5035 ctemp = " ";
5036 for (iso = 1; iso <= 10; ++iso) {
5037 nsofar = nparm;
5038 nparm = TMath::Min(fNpar,nsofar + ncoef);
5039 for (it = nsofar + 1; it <= nparm; ++it) {
5040 ctemp = ctemp + TString::Format(" %6.3f",fMATUvline[it-1]);
5041 }
5042 Printf("%s",(const char*)ctemp);
5043 if (i <= nparm) break;
5044 }
5045 }
5046 if (isw2 < 3) {
5047 Printf(" %s",(const char*)fCovmes[isw2]);
5048 }
5049}
5050
5051////////////////////////////////////////////////////////////////////////////////
5052/// Performs a local function minimization
5053///
5054/// Performs a local function minimization using basically the
5055/// method of Davidon-Fletcher-Powell as modified by Fletcher
5056///
5057/// ref. -- Fletcher, Comp.J. 13,317 (1970) "switching method"
5058
5060{
5061 /* Local variables */
5062 Double_t gdel, gami, vlen, dsum, gssq, vsum, d;
5063 Double_t fzero, fs, ri, delgam, rhotol;
5064 Double_t gdgssq, gvg, vgi;
5065 Int_t npfn, ndex, iext, i, j, m, n, npsdf, nparx;
5066 Int_t iswtr, lined2, kk, nfcnmg, nrstrt,iter;
5067 Bool_t ldebug;
5068 Double_t toler = 0.05;
5069
5070 if (fNpar <= 0) return;
5071 if (fAmin == fUndefi) mnamin();
5072 ldebug = kFALSE; if ( fIdbg[4] >= 1) ldebug = kTRUE;
5073 fCfrom = "MIGRAD ";
5074 fNfcnfr = fNfcn;
5075 nfcnmg = fNfcn;
5076 fCstatu = "INITIATE ";
5077 iswtr = fISW[4] - 2*fItaur;
5078 npfn = fNfcn;