// @(#)root/minuit:$Name: $:$Id: TMinuit.cxx,v 1.28 2003/05/14 20:58:22 brun Exp $ // Author: Rene Brun, Frederick James 12/08/95 /************************************************************************* * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. * * All rights reserved. * * * * For the licensing terms see $ROOTSYS/LICENSE. * * For the list of contributors see $ROOTSYS/README/CREDITS. * *************************************************************************/ //______________________________________________________________________________ //*-*-*-*-*-*-*-*-*-*-*-*The Minimization package*-*--*-*-*-*-*-*-*-*-*-*-* //*-* ======================== * //*-* * //*-* This package was originally written in Fortran by Fred James * //*-* and part of PACKLIB (patch D506) * //*-* * //*-* It has been converted to a C++ class by R.Brun * //*-* The current implementation in C++ is a straightforward conversion * //*-* of the original Fortran version: The main changes are: * //*-* * //*-* - The variables in the various Minuit labelled common blocks * //*-* have been changed to the TMinuit class data members. * //*-* - The internal arrays with a maximum dimension depending on the * //*-* maximum number of parameters are now data members arrays with * //*-* a dynamic dimension such that one can fit very large problems * //*-* by simply initialising the TMinuit constructor with the maximum * //*-* number of parameters. * //*-* - The include file Minuit.h has been commented as much as possible* //*-* using existing comments in the code or the printed documentation* //*-* - The original Minuit subroutines are now member functions. * //*-* - Constructors and destructor have been added. * //*-* - Instead of passing the FCN function in the argument * //*-* list, the addresses of this function is stored as pointer * //*-* in the data members of the class. This is by far more elegant * //*-* and flexible in an interactive environment. * //*-* The member function SetFCN can be used to define this pointer. * //*-* - The ROOT static function Printf is provided to replace all * //*-* format statements and to print on currently defined output file.* //*-* - The derived class TMinuitOld contains obsolete routines from * //*-* the Fortran based version. * //*-* - The functions SetObjectFit(TObject *obj)/GetObjectFit() can be * //*-* used inside the FCN function to set/get a referenced object * //*-* instead of using global variables. * //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* // /*
Basic concepts of MINUIT
The MINUIT package acts on a multiparameter Fortran function to which one must give the generic name FCN. In the ROOT implementation, the function FCN is defined via the MINUIT SetFCN member function when an Histogram.Fit command is invoked. The value of FCN will in general depend on one or more variable parameters.
To take a simple example, in case of ROOT histograms (classes TH1C,TH1S,TH1F,TH1D) the Fit function defines the Minuit fitting function as being H1FitChisquare or H1FitLikelihood depending on the options selected. H1FitChisquare calculates the chisquare between the user fitting function (gaussian, polynomial, user defined,etc) and the data for given values of the parameters. It is the task of MINUIT to find those values of the parameters which give the lowest value of chisquare.
Basic concepts - The transformation for parameters with limits.
For variable parameters with limits, MINUIT uses the following transformation:
P = arcsin(2((P -a)/(b- a))-1) P = a+((b- a)/(2))(sinP +1) int ext ext int
so that the internal value P can take on any value, while the external int value P can take on values only between the lower limit a and the ext upper limit b. Since the transformation is necessarily non-linear, it would transform a nice linear problem into a nasty non-linear one, which is the reason why limits should be avoided if not necessary. In addition, the transformation does require some computer time, so it slows down the computation a little bit, and more importantly, it introduces additional numerical inaccuracy into the problem in addition to what is introduced in the numerical calculation of the FCN value. The effects of non-linearity and numerical roundoff both become more important as the external value gets closer to one of the limits (expressed as the distance to nearest limit divided by distance between limits). The user must therefore be aware of the fact that, for example, if he puts limits of 10 (0,10 ) on a parameter, then the values 0.0 and 1. 0 will be indistinguishable to the accuracy of most machines.
The transformation also affects the parameter error matrix, of course, so MINUIT does a transformation of the error matrix (and the ``parabolic'' parameter errors) when there are parameter limits. Users should however realize that the transformation is only a linear approximation, and that it cannot give a meaningful result if one or more parameters is very close to a limit, where partial P /partial P #0. Therefore, it is ext int recommended that:
- Limits on variable parameters should be used only when needed in order to prevent the parameter from taking on unphysical values.
- When a satisfactory minimum has been found using limits, the limits should then be removed if possible, in order to perform or re-perform the error analysis without limits.
How to get the right answer from MINUIT.
MINUIT offers the user a choice of several minimization algorithms. The MIGRAD algorithm is in general the best minimizer for nearly all functions. It is a variable-metric method with inexact line search, a stable metric updating scheme, and checks for positive-definiteness. Its main weakness is that it depends heavily on knowledge of the first derivatives, and fails miserably if they are very inaccurate.
If parameter limits are needed, in spite of the side effects, then the user should be aware of the following techniques to alleviate problems caused by limits:
Getting the right minimum with limits.
If MIGRAD converges normally to a point where no parameter is near one of its limits, then the existence of limits has probably not prevented MINUIT from finding the right minimum. On the other hand, if one or more parameters is near its limit at the minimum, this may be because the true minimum is indeed at a limit, or it may be because the minimizer has become ``blocked'' at a limit. This may normally happen only if the parameter is so close to a limit (internal value at an odd multiple of #((pi)/(2)) that MINUIT prints a warning to this effect when it prints the parameter values. The minimizer can become blocked at a limit, because at a limit the derivative seen by the minimizer partial F/partial P is zero no matter int what the real derivative partial F/partial P is. ext
((partial F)/(partial P ))= ((partial F)/(partial P ))((partial P )/(partial P )) =((partial F)/(partial P ))= 0 int ext ext int ext
Getting the right parameter errors with limits.
In the best case, where the minimum is far from any limits, MINUIT will correctly transform the error matrix, and the parameter errors it reports should be accurate and very close to those you would have got without limits. In other cases (which should be more common, since otherwise you wouldn't need limits), the very meaning of parameter errors becomes problematic. Mathematically, since the limit is an absolute constraint on the parameter, a parameter at its limit has no error, at least in one direction. The error matrix, which can assign only symmetric errors, then becomes essentially meaningless.
Interpretation of Parameter Errors:
There are two kinds of problems that can arise: the reliability of MINUIT's error estimates, and their statistical interpretation, assuming they are accurate.
Statistical interpretation:
For discussuion of basic concepts, such as the meaning of the elements of the error matrix, or setting of exact confidence levels see:
- F.James. Determining the statistical Significance of experimental Results. Technical Report DD/81/02 and CERN Report 81-03, CERN, 1981.
- W.T.Eadie, D.Drijard, F.James, M.Roos, and B.Sadoulet. Statistical Methods in Experimental Physics. North-Holland, 1971.
Reliability of MINUIT error estimates.
MINUIT always carries around its own current estimates of the parameter errors, which it will print out on request, no matter how accurate they are at any given point in the execution. For example, at initialization, these estimates are just the starting step sizes as specified by the user. After a HESSE step, the errors are usually quite accurate, unless there has been a problem. MINUIT, when it prints out error values, also gives some indication of how reliable it thinks they are. For example, those marked CURRENT GUESS ERROR are only working values not to be believed, and APPROXIMATE ERROR means that they have been calculated but there is reason to believe that they may not be accurate.
If no mitigating adjective is given, then at least MINUIT believes the errors are accurate, although there is always a small chance that MINUIT has been fooled. Some visible signs that MINUIT may have been fooled are:
- Warning messages produced during the minimization or error analysis.
- Failure to find new minimum.
- Value of EDM too big (estimated Distance to Minimum).
- Correlation coefficients exactly equal to zero, unless some parameters are known to be uncorrelated with the others.
- Correlation coefficients very close to one (greater than 0.99). This indicates both an exceptionally difficult problem, and one which has been badly parameterized so that individual errors are not very meaningful because they are so highly correlated.
- Parameter at limit. This condition, signalled by a MINUIT warning message, may make both the function minimum and parameter errors unreliable. See the discussion above ``Getting the right parameter errors with limits''.
The best way to be absolutely sure of the errors, is to use ``independent'' calculations and compare them, or compare the calculated errors with a picture of the function. Theoretically, the covariance matrix for a ``physical'' function must be positive-definite at the minimum, although it may not be so for all points far away from the minimum, even for a well-determined physical problem. Therefore, if MIGRAD reports that it has found a non-positive-definite covariance matrix, this may be a sign of one or more of the following:
A non-physical region:
On its way to the minimum, MIGRAD may have traversed a region which has unphysical behaviour, which is of course not a serious problem as long as it recovers and leaves such a region.
An underdetermined problem:
If the matrix is not positive-definite even at the minimum, this may mean that the solution is not well-defined, for example that there are more unknowns than there are data points, or that the parameterization of the fit contains a linear dependence. If this is the case, then MINUIT (or any other program) cannot solve your problem uniquely, and the error matrix will necessarily be largely meaningless, so the user must remove the underdeterminedness by reformulating the parameterization. MINUIT cannot do this itself.
Numerical inaccuracies:
It is possible that the apparent lack of positive-definiteness is in fact only due to excessive roundoff errors in numerical calculations in the user function or not enough precision. This is unlikely in general, but becomes more likely if the number of free parameters is very large, or if the parameters are badly scaled (not all of the same order of magnitude), and correlations are also large. In any case, whether the non-positive-definiteness is real or only numerical is largely irrelevant, since in both cases the error matrix will be unreliable and the minimum suspicious.
An ill-posed problem:
For questions of parameter dependence, see the discussion above on positive-definiteness.
Possible other mathematical problems are the following:
Excessive numerical roundoff:
Be especially careful of exponential and factorial functions which get big very quickly and lose accuracy.
Starting too far from the solution:
The function may have unphysical local minima, especially at infinity in some variables. */ // #include <stdlib.h> #include <stdio.h> #include "TROOT.h" #include "TMinuit.h" #include "TMath.h" #include "TError.h" #include "TPluginManager.h" #include "TClass.h" #include "Api.h" TMinuit *gMinuit; const char charal[29] = " .ABCDEFGHIJKLMNOPQRSTUVWXYZ"; ClassImp(TMinuit) //______________________________________________________________________________ TMinuit::TMinuit(): TNamed("MINUIT","The Minimization package") { //*-*-*-*-*-*-*-*-*-*-*Minuit normal constructor*-*-*-*-*-*-*-*-*-*-*-*-*-*-* //*-* ======================== if (TMinuit::Class()->IsCallingNew()) { //preset all pointers to null fCpnam = 0; fU = 0; fAlim = 0; fBlim = 0; fPstar = 0; fGin = 0; fNvarl = 0; fNiofex = 0; fNexofi = 0; fIpfix = 0; fErp = 0; fErn = 0; fWerr = 0; fGlobcc = 0; fX = 0; fXt = 0; fDirin = 0; fXs = 0; fXts = 0; fDirins = 0; fGrd = 0; fG2 = 0; fGstep = 0; fDgrd = 0; fGrds = 0; fG2s = 0; fGsteps = 0; fPstst = 0; fPbar = 0; fPrho = 0; fWord7 = 0; fVhmat = 0; fVthmat = 0; fP = 0; fXpt = 0; fYpt = 0; fChpt = 0; fCONTgcc = 0; fCONTw = 0; fFIXPyy = 0; fGRADgf = 0; fHESSyy = 0; fIMPRdsav = 0; fIMPRy = 0; fMATUvline = 0; fMIGRflnu = 0; fMIGRstep = 0; fMIGRgs = 0; fMIGRvg = 0; fMIGRxxs = 0; fMNOTxdev = 0; fMNOTw = 0; fMNOTgcc = 0; fPSDFs = 0; fSEEKxmid = 0; fSEEKxbest = 0; fSIMPy = 0; fVERTq = 0; fVERTs = 0; fVERTpp = 0; fCOMDplist = 0; fPARSplist = 0; } else { BuildArrays(25); fStatus = 0; fEmpty = 0; fMethodCall = 0; fGraphicsMode = kTRUE; fPlot = 0; SetMaxIterations(); mninit(5,6,7); } gMinuit = this; gROOT->GetListOfSpecials()->Add(gMinuit); } //______________________________________________________________________________ TMinuit::TMinuit(Int_t maxpar): TNamed("MINUIT","The Minimization package") { //*-*-*-*-*-*-*-*-*-*-*Minuit normal constructor*-*-*-*-*-*-*-*-*-*-*-*-*-*-* //*-* ======================== // // maxpar is the maximum number of parameters used with this TMinuit object. BuildArrays(maxpar); fStatus = 0; fEmpty = 0; fMethodCall = 0; fGraphicsMode = kTRUE; fPlot = 0; SetMaxIterations(); mninit(5,6,7); gMinuit = this; gROOT->GetListOfSpecials()->Add(gMinuit); } //______________________________________________________________________________ TMinuit::TMinuit(const TMinuit &minuit) : TNamed(minuit) { // Private TMinuit copy ctor. TMinuit can not be copied. Error("TMinuit", "can not copy construct TMinuit"); } //______________________________________________________________________________ TMinuit::~TMinuit() { //*-*-*-*-*-*-*-*-*-*-*Minuit default destructor*-*-*-*-*-*-*-*-*-*-*-*-*-*-* //*-* ========================= DeleteArrays(); delete fPlot; delete fMethodCall; gROOT->GetListOfSpecials()->Remove(this); if (gMinuit == this) gMinuit = 0; } //______________________________________________________________________________ void TMinuit::BuildArrays(Int_t maxpar) { //*-*-*-*-*-*-*Create internal Minuit arrays for the maxpar parameters*-*-*-* //*-* ======================================================= fMaxpar = 25; if (maxpar > 10) fMaxpar = maxpar; fMaxpar1= fMaxpar*(fMaxpar+1); fMaxpar2= 2*fMaxpar; fMaxpar5= fMaxpar1/2; fMaxcpt = 101; fCpnam = new TString[fMaxpar2]; fU = new Double_t[fMaxpar2]; fAlim = new Double_t[fMaxpar2]; fBlim = new Double_t[fMaxpar2]; fPstar = new Double_t[fMaxpar2]; fGin = new Double_t[fMaxpar2]; fNvarl = new Int_t[fMaxpar2]; fNiofex = new Int_t[fMaxpar2]; fNexofi = new Int_t[fMaxpar]; fIpfix = new Int_t[fMaxpar]; fErp = new Double_t[fMaxpar]; fErn = new Double_t[fMaxpar]; fWerr = new Double_t[fMaxpar]; fGlobcc = new Double_t[fMaxpar]; fX = new Double_t[fMaxpar]; fXt = new Double_t[fMaxpar]; fDirin = new Double_t[fMaxpar]; fXs = new Double_t[fMaxpar]; fXts = new Double_t[fMaxpar]; fDirins = new Double_t[fMaxpar]; fGrd = new Double_t[fMaxpar]; fG2 = new Double_t[fMaxpar]; fGstep = new Double_t[fMaxpar]; fDgrd = new Double_t[fMaxpar]; fGrds = new Double_t[fMaxpar]; fG2s = new Double_t[fMaxpar]; fGsteps = new Double_t[fMaxpar]; fPstst = new Double_t[fMaxpar]; fPbar = new Double_t[fMaxpar]; fPrho = new Double_t[fMaxpar]; fWord7 = new Double_t[fMaxpar]; fVhmat = new Double_t[fMaxpar5]; fVthmat = new Double_t[fMaxpar5]; fP = new Double_t[fMaxpar1]; fXpt = new Double_t[fMaxcpt]; fYpt = new Double_t[fMaxcpt]; fChpt = new char[fMaxcpt+1]; // initialisation of dynamic arrays used internally in some functions // these arrays had a fix dimension in Minuit fCONTgcc = new Double_t[fMaxpar]; fCONTw = new Double_t[fMaxpar]; fFIXPyy = new Double_t[fMaxpar]; fGRADgf = new Double_t[fMaxpar]; fHESSyy = new Double_t[fMaxpar]; fIMPRdsav = new Double_t[fMaxpar]; fIMPRy = new Double_t[fMaxpar]; fMATUvline = new Double_t[fMaxpar]; fMIGRflnu = new Double_t[fMaxpar]; fMIGRstep = new Double_t[fMaxpar]; fMIGRgs = new Double_t[fMaxpar]; fMIGRvg = new Double_t[fMaxpar]; fMIGRxxs = new Double_t[fMaxpar]; fMNOTxdev = new Double_t[fMaxpar]; fMNOTw = new Double_t[fMaxpar]; fMNOTgcc = new Double_t[fMaxpar]; fPSDFs = new Double_t[fMaxpar]; fSEEKxmid = new Double_t[fMaxpar]; fSEEKxbest = new Double_t[fMaxpar]; fSIMPy = new Double_t[fMaxpar]; fVERTq = new Double_t[fMaxpar]; fVERTs = new Double_t[fMaxpar]; fVERTpp = new Double_t[fMaxpar]; fCOMDplist = new Double_t[fMaxpar]; fPARSplist = new Double_t[fMaxpar]; for (int i = 0; i < fMaxpar; i++) { fErp[i] = 0; fErn[i] = 0; } } //______________________________________________________________________________ TObject *TMinuit::Clone(const char *newname) const { // Make a clone of an object using the Streamer facility. // Function pointer is copied to Clone TMinuit *named = (TMinuit*)TNamed::Clone(newname); named->fFCN=fFCN; return named; } //______________________________________________________________________________ Int_t TMinuit::Command(const char *command) { // execute a Minuit command // Equivalent to MNEXCM except that the command is given as a // character string. // See TMinuit::mnhelp for the full list of available commands // // Returns the status of the execution: // = 0: command executed normally // 1: command is blank, ignored // 2: command line unreadable, ignored // 3: unknown command, ignored // 4: abnormal termination (e.g., MIGRAD not converged) // 5: command is a request to read PARAMETER definitions // 6: 'SET INPUT' command // 7: 'SET TITLE' command // 8: 'SET COVAR' command // 9: reserved // 10: END command // 11: EXIT or STOP command // 12: RETURN command // //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Int_t status = 0; mncomd(command,status); return status; } //______________________________________________________________________________ TObject *TMinuit::Contour(Int_t npoints, Int_t pa1, Int_t pa2) { // Creates a TGraph object describing the n-sigma contour of a // TMinuit fit. The contour of the parameters pa1 and pa2 is calculated // unsing npoints (>=4) points. The TMinuit status will be // 0 on success and // -1 if errors in the calling sequence (pa1, pa2 not variable) // 1 if less than four points can be found // 2 if npoints<4 // n>3 if only n points can be found (n < npoints) // The status can be obtained via TMinuit::GetStatus(). // // To get the n-sigma contour the ERRDEF parameter in Minuit has to set // to n^2. The fcn function has to be set before the routine is called. // // The TGraph object is created via the interpreter. The user must cast it // to a TGraph* // // You can find an example in $ROOTSYS/tutorials/fitcont.C if (npoints<4) { // we need at least 4 points fStatus= 2; return (TObject *)0; } Int_t error; Double_t *xcoor = new Double_t[npoints+1]; Double_t *ycoor = new Double_t[npoints+1]; mncont(pa1,pa2,npoints,xcoor,ycoor,error); if (error!=npoints) { // mncont did go wrong fStatus= (error==0 ? 1 : error); delete [] xcoor; delete [] ycoor; return (TObject *)0; } fStatus=0; // create graph via the PluginManager xcoor[npoints] = xcoor[0]; // add first point at end to get closed polyline ycoor[npoints] = ycoor[0]; TObject *gr = 0; TPluginHandler *h; if ((h = gROOT->GetPluginManager()->FindHandler("TMinuitGraph"))) { if (h->LoadPlugin() != -1) gr = (TObject*)h->ExecPlugin(3,npoints,xcoor,ycoor); } delete [] xcoor; delete [] ycoor; return gr; } //______________________________________________________________________________ Int_t TMinuit::DefineParameter( Int_t parNo, const char *name, Double_t initVal, Double_t initErr, Double_t lowerLimit, Double_t upperLimit ) { // Define a parameter Int_t err; TString sname = name; mnparm( parNo, sname, initVal, initErr, lowerLimit, upperLimit, err); return err; } //______________________________________________________________________________ void TMinuit::DeleteArrays() { //*-*-*-*-*-*-*-*-*-*-*-*Delete internal Minuit arrays*-*-*-*-*-*-*-*-* //*-* ============================= if (fEmpty) return; delete [] fCpnam; delete [] fU; delete [] fAlim; delete [] fBlim; delete [] fErp; delete [] fErn; delete [] fWerr; delete [] fGlobcc; delete [] fNvarl; delete [] fNiofex; delete [] fNexofi; delete [] fX; delete [] fXt; delete [] fDirin; delete [] fXs; delete [] fXts; delete [] fDirins; delete [] fGrd; delete [] fG2; delete [] fGstep; delete [] fGin; delete [] fDgrd; delete [] fGrds; delete [] fG2s; delete [] fGsteps; delete [] fIpfix; delete [] fVhmat; delete [] fVthmat; delete [] fP; delete [] fPstar; delete [] fPstst; delete [] fPbar; delete [] fPrho; delete [] fWord7; delete [] fXpt; delete [] fYpt; delete [] fChpt; delete [] fCONTgcc; delete [] fCONTw; delete [] fFIXPyy; delete [] fGRADgf; delete [] fHESSyy; delete [] fIMPRdsav; delete [] fIMPRy; delete [] fMATUvline; delete [] fMIGRflnu; delete [] fMIGRstep; delete [] fMIGRgs; delete [] fMIGRvg; delete [] fMIGRxxs; delete [] fMNOTxdev; delete [] fMNOTw; delete [] fMNOTgcc; delete [] fPSDFs; delete [] fSEEKxmid; delete [] fSEEKxbest; delete [] fSIMPy; delete [] fVERTq; delete [] fVERTs; delete [] fVERTpp; delete [] fCOMDplist; delete [] fPARSplist; fEmpty = 1; } //______________________________________________________________________________ Int_t TMinuit::Eval(Int_t npar, Double_t *grad, Double_t &fval, Double_t *par, Int_t flag) { // Evaluate the minimisation function // Input parameters: // npar: number of currently variable parameters // par: array of (constant and variable) parameters // flag: Indicates what is to be calculated (see example below) // grad: array of gradients // Output parameters: // fval: The calculated function value. // grad: The (optional) vector of first derivatives). // // The meaning of the parameters par is of course defined by the user, // who uses the values of those parameters to calculate his function value. // The starting values must be specified by the user. // Later values are determined by Minuit as it searches for the minimum // or performs whatever analysis is requested by the user. // // Note that this virtual function may be redefined in a class derived from TMinuit. // The default function calls the function specified in SetFCN // // Example of Minimisation function: /* if (flag == 1) { read input data, calculate any necessary constants, etc. } if (flag == 2) { calculate GRAD, the first derivatives of FVAL (this is optional) } Always calculate the value of the function, FVAL, which is usually a chisquare or log likelihood. if (iflag == 3) { will come here only after the fit is finished. Perform any final calculations, output fitted data, etc. } */ // See concrete examples in TH1::H1FitChisquare, H1FitLikelihood if (fFCN) (*fFCN)(npar,grad,fval,par,flag); return 0; } //______________________________________________________________________________ Int_t TMinuit::FixParameter( Int_t parNo) { // fix a parameter Int_t err; Double_t tmp = parNo+1; //set internal Minuit nuumbering mnexcm( "FIX", &tmp, 1, err ); return err; } //______________________________________________________________________________ Int_t TMinuit::GetParameter( Int_t parNo, Double_t ¤tValue, Double_t ¤tError ) const { // return parameter value and error Int_t err; TString name; // ignored Double_t bnd1, bnd2; // ignored mnpout( parNo, name, currentValue, currentError, bnd1, bnd2, err ); return err; } //______________________________________________________________________________ Int_t TMinuit::GetNumFixedPars() const { // returns the number of currently fixed parameters return fNpfix; } //______________________________________________________________________________ Int_t TMinuit::GetNumFreePars() const { // returns the number of currently free parameters return fNpar; } //______________________________________________________________________________ Int_t TMinuit::GetNumPars() const { // returns the total number of parameters that have been defined. // (fixed and free) return fNpar + fNpfix; } //______________________________________________________________________________ Int_t TMinuit::Migrad() { // invokes the MIGRAD minimizer Int_t err; Double_t tmp = 0; mnexcm( "MIGRAD", &tmp, 0, err ); return err; } //______________________________________________________________________________ Int_t TMinuit::Release( Int_t parNo) { // release a parameter Int_t err; Double_t tmp = parNo+1; //set internal Minuit numbering mnexcm( "RELEASE", &tmp, 1, err ); return err; } //______________________________________________________________________________ Int_t TMinuit::SetErrorDef( Double_t up ) { Int_t err; mnexcm( "SET ERRDEF", &up, 1, err ); return err; } //______________________________________________________________________________ void TMinuit::SetFCN(void (*fcn)(Int_t &, Double_t *, Double_t &f, Double_t *, Int_t)) { //*-*-*-*-*-*-*To set the address of the minimization function*-*-*-*-*-*-*-* //*-* =============================================== //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* fFCN = fcn; } //______________________________________________________________________________ void InteractiveFCNm(Int_t &npar, Double_t *gin, Double_t &f, Double_t *u, Int_t flag) { //*-*-*-*-*-*-*Static function called when SetFCN is called in interactive mode //*-* =============================================== TMethodCall *m = gMinuit->GetMethodCall(); if (!m) return; Long_t args[5]; args[0] = (Long_t)∦ args[1] = (Long_t)gin; args[2] = (Long_t)&f; args[3] = (Long_t)u; args[4] = (Long_t)flag; m->SetParamPtrs(args); Double_t result; m->Execute(result); } //______________________________________________________________________________ void TMinuit::SetFCN(void *fcn) { //*-*-*-*-*-*-*To set the address of the minimization function*-*-*-*-*-*-*-* //*-* =============================================== // this function is called by CINT instead of the function above //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* if (!fcn) return; char *funcname = G__p2f2funcname(fcn); if (funcname) { fMethodCall = new TMethodCall(); fMethodCall->InitWithPrototype(funcname,"Int_t&,Double_t*,Double_t&,Double_t*,Int_t"); } fFCN = InteractiveFCNm; } //______________________________________________________________________________ Int_t TMinuit::SetPrintLevel( Int_t printLevel ) { Int_t err; Double_t tmp = printLevel; mnexcm( "SET PRINT", &tmp, 1, err ); return err; } //______________________________________________________________________________ void TMinuit::mnamin() { //*-*-*-*-*-*-*-*-*-*-*-*-*Initialize AMIN*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* //*-* =============== //*-*C Called from many places. Initializes the value of AMIN by //*-*C calling the user function. Prints out the function value and //*-*C parameter values if Print Flag value is high enough. //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t fnew; Int_t nparx; nparx = fNpar; if (fISW[4] >= 1) { Printf(" FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4."); } mnexin(fX); Eval(nparx, fGin, fnew, fU, 4); ++fNfcn; fAmin = fnew; fEDM = fBigedm; } /* mnamin_ */ //______________________________________________________________________________ void TMinuit::mnbins(Double_t a1, Double_t a2, Int_t naa, Double_t &bl, Double_t &bh, Int_t &nb, Double_t &bwid) { //*-*-*-*-*-*-*-*-*-*-*Compute reasonable histogram intervals*-*-*-*-*-*-*-*-* //*-* ====================================== //*-* Function TO DETERMINE REASONABLE HISTOGRAM INTERVALS //*-* GIVEN ABSOLUTE UPPER AND LOWER BOUNDS A1 AND A2 //*-* AND DESIRED MAXIMUM NUMBER OF BINS NAA //*-* PROGRAM MAKES REASONABLE BINNING FROM BL TO BH OF WIDTH BWID //*-* F. JAMES, AUGUST, 1974 , stolen for Minuit, 1988 //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t awid,ah, al, sigfig, sigrnd, alb; Int_t kwid, lwid, na=0, log_; al = TMath::Min(a1,a2); ah = TMath::Max(a1,a2); if (al == ah) ah = al + 1; //*-*- IF NAA .EQ. -1 , PROGRAM USES BWID INPUT FROM CALLING ROUTINE if (naa == -1) goto L150; L10: na = naa - 1; if (na < 1) na = 1; //*-*- GET NOMINAL BIN WIDTH IN EXPON FORM L20: awid = (ah-al) / Double_t(na); log_ = Int_t(TMath::Log10(awid)); if (awid <= 1) --log_; sigfig = awid*TMath::Power(10, -log_); //*-*- ROUND MANTISSA UP TO 2, 2.5, 5, OR 10 if (sigfig > 2) goto L40; sigrnd = 2; goto L100; L40: if (sigfig > 2.5) goto L50; sigrnd = 2.5; goto L100; L50: if (sigfig > 5) goto L60; sigrnd = 5; goto L100; L60: sigrnd = 1; ++log_; L100: bwid = sigrnd*TMath::Power(10, log_); goto L200; //*-*- GET NEW BOUNDS FROM NEW WIDTH BWID L150: if (bwid <= 0) goto L10; L200: alb = al / bwid; lwid = Int_t(alb); if (alb < 0) --lwid; bl = bwid*Double_t(lwid); alb = ah / bwid + 1; kwid = Int_t(alb); if (alb < 0) --kwid; bh = bwid*Double_t(kwid); nb = kwid - lwid; if (naa > 5) goto L240; if (naa == -1) return; //*-*- REQUEST FOR ONE BIN IS DIFFICULT CASE if (naa > 1 || nb == 1) return; bwid *= 2; nb = 1; return; L240: if (nb << 1 != naa) return; ++na; goto L20; } /* mnbins_ */ //______________________________________________________________________________ void TMinuit::mncalf(Double_t *pvec, Double_t &ycalf) { //*-*-*-*-*-*-*-*-*-*Transform FCN to find further minima*-*-*-*-*-*-*-*-*-* //*-* ==================================== //*-* Called only from MNIMPR. Transforms the function FCN //*-* by dividing out the quadratic part in order to find further //*-* minima. Calculates ycalf = (f-fmin)/(x-xmin)*v*(x-xmin) //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Int_t ndex, i, j, m, n, nparx; Double_t denom, f; nparx = fNpar; mninex(&pvec[0]); Eval(nparx, fGin, f, fU, 4); ++fNfcn; for (i = 1; i <= fNpar; ++i) { fGrd[i-1] = 0; for (j = 1; j <= fNpar; ++j) { m = TMath::Max(i,j); n = TMath::Min(i,j); ndex = m*(m-1) / 2 + n; fGrd[i-1] += fVthmat[ndex-1]*(fXt[j-1] - pvec[j-1]); } } denom = 0; for (i = 1; i <= fNpar; ++i) {denom += fGrd[i-1]*(fXt[i-1] - pvec[i-1]); } if (denom <= 0) { fDcovar = 1; fISW[1] = 0; denom = 1; } ycalf = (f - fApsi) / denom; } /* mncalf_ */ //______________________________________________________________________________ void TMinuit::mncler() { //*-*-*-*-*-*-*-*-*-*-*Resets the parameter list to UNDEFINED*-*-*-*-*-*-*-* //*-* ====================================== //*-* Called from MINUIT and by option from MNEXCM //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Int_t i; fNpfix = 0; fNu = 0; fNpar = 0; fNfcn = 0; fNwrmes[0] = 0; fNwrmes[1] = 0; for (i = 1; i <= fMaxext; ++i) { fU[i-1] = 0; fCpnam[i-1] = fCundef; fNvarl[i-1] = -1; fNiofex[i-1] = 0; } mnrset(1); fCfrom = "CLEAR "; fNfcnfr = fNfcn; fCstatu = "UNDEFINED "; fLnolim = kTRUE; fLphead = kTRUE; } /* mncler_ */ //______________________________________________________________________________ void TMinuit::mncntr(Int_t ike1, Int_t ike2, Int_t &ierrf) { //*-*-*-*-*Print function contours in two variables, on line printer*-*-*-*-* //*-* ========================================================= //*-* //*-* input arguments: parx, pary, devs, ngrid //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* static TString clabel = "0123456789ABCDEFGHIJ"; /* Local variables */ Double_t d__1, d__2; Double_t fcna[115], fcnb[115], contur[20]; Double_t ylabel, fmn, fmx, xlo, ylo, xup, yup; Double_t devs, xsav, ysav, bwidx, bwidy, unext, ff, xb4; Int_t i, ngrid, ixmid, nparx, ix, nx, ny, ki1, ki2, ixzero, iy, ics; TString chmid, chln, chzero; Int_t ke1 = ike1+1; Int_t ke2 = ike2+1; if (ke1 <= 0 || ke2 <= 0) goto L1350; if (ke1 > fNu || ke2 > fNu) goto L1350; ki1 = fNiofex[ke1-1]; ki2 = fNiofex[ke2-1]; if (ki1 <= 0 || ki2 <= 0) goto L1350; if (ki1 == ki2) goto L1350; if (fISW[1] < 1) { mnhess(); mnwerr(); } nparx = fNpar; xsav = fU[ke1-1]; ysav = fU[ke2-1]; devs = fWord7[2]; if (devs <= 0) devs = 2; xlo = fU[ke1-1] - devs*fWerr[ki1-1]; xup = fU[ke1-1] + devs*fWerr[ki1-1]; ylo = fU[ke2-1] - devs*fWerr[ki2-1]; yup = fU[ke2-1] + devs*fWerr[ki2-1]; ngrid = Int_t(fWord7[3]); if (ngrid <= 0) { ngrid = 25; //*-* Computing MIN nx = TMath::Min(fNpagwd - 15,ngrid); //*-* Computing MIN ny = TMath::Min(fNpagln - 7,ngrid); } else { nx = ngrid; ny = ngrid; } if (nx < 11) nx = 11; if (ny < 11) ny = 11; if (nx >= 115) nx = 114; //*-*- ask if parameter outside limits if (fNvarl[ke1-1] > 1) { if (xlo < fAlim[ke1-1]) xlo = fAlim[ke1-1]; if (xup > fBlim[ke1-1]) xup = fBlim[ke1-1]; } if (fNvarl[ke2-1] > 1) { if (ylo < fAlim[ke2-1]) ylo = fAlim[ke2-1]; if (yup > fBlim[ke2-1]) yup = fBlim[ke2-1]; } bwidx = (xup - xlo) / Double_t(nx); bwidy = (yup - ylo) / Double_t(ny); ixmid = Int_t(((xsav - xlo)*Double_t(nx) / (xup - xlo)) + 1); if (fAmin == fUndefi) mnamin(); for (i = 1; i <= 20; ++i) { contur[i-1] = fAmin + fUp*(i-1)*(i-1); } contur[0] += fUp*.01; //*-*- fill FCNB to prepare first row, and find column zero/ fU[ke2-1] = yup; ixzero = 0; xb4 = 1; //TH chmid.Resize(nx+1); chzero.Resize(nx+1); chln.Resize(nx+1); for (ix = 1; ix <= nx + 1; ++ix) { fU[ke1-1] = xlo + Double_t(ix-1)*bwidx; Eval(nparx, fGin, ff, fU, 4); fcnb[ix-1] = ff; if (xb4 < 0 && fU[ke1-1] > 0) ixzero = ix - 1; xb4 = fU[ke1-1]; chmid[ix-1] = '*'; chzero[ix-1] = '-'; } Printf(" Y-AXIS: PARAMETER %3d: %s",ke2,(const char*)fCpnam[ke2-1]); if (ixzero > 0) { chzero[ixzero-1] = '+'; chln = " "; Printf(" X=0"); } //*-*- loop over rows for (iy = 1; iy <= ny; ++iy) { unext = fU[ke2-1] - bwidy; //*-*- prepare this line background pattern for contour chln = " "; // TH chln.Resize(nx+1); chln[ixmid-1] = '*'; if (ixzero != 0) chln[ixzero-1] = ':'; if (fU[ke2-1] > ysav && unext < ysav) chln = chmid; if (fU[ke2-1] > 0 && unext < 0) chln = chzero; fU[ke2-1] = unext; ylabel = fU[ke2-1] + bwidy*.5; //*-*- move FCNB to FCNA and fill FCNB with next row for (ix = 1; ix <= nx + 1; ++ix) { fcna[ix-1] = fcnb[ix-1]; fU[ke1-1] = xlo + Double_t(ix-1)*bwidx; Eval(nparx, fGin, ff, fU, 4); fcnb[ix-1] = ff; } //*-*- look for contours crossing the FCNxy squares for (ix = 1; ix <= nx; ++ix) { d__1 = TMath::Max(fcna[ix-1],fcnb[ix-1]), d__2 = TMath::Max(fcna[ix],fcnb[ix]); fmx = TMath::Max(d__1,d__2); d__1 = TMath::Min(fcna[ix-1],fcnb[ix-1]), d__2 = TMath::Min(fcna[ix],fcnb[ix]); fmn = TMath::Min(d__1,d__2); for (ics = 1; ics <= 20; ++ics) { if (contur[ics-1] > fmn) goto L240; } continue; L240: if (contur[ics-1] < fmx) chln[ix-1] = clabel[ics-1]; } //*-*- print a row of the contour plot Printf(" %12.4g %s",ylabel,(const char*)chln); } //*-*- contours printed, label x-axis chln = " "; chln(0,1) = 'I'; chln(ixmid-1,1) = 'I'; chln(nx-1,1) = 'I'; Printf(" %s",(const char*)chln); //*-*- the hardest of all: print x-axis scale! chln = " "; if (nx <= 26) { Printf(" %12.4g%s%12.4g",xlo,(const char*)chln,xup); Printf(" %s%12.4g",(const char*)chln,xsav); } else { Printf(" %12.4g%s%12.4g%s%12.4g",xlo,(const char*)chln,xsav,(const char*)chln,xup); } Printf(" X-AXIS: PARAMETER%3d: %s ONE COLUMN=%12.4g" ,ke1,(const char*)fCpnam[ke1-1],bwidx); Printf(" FUNCTION VALUES: F(I)=%12.4g +%12.4g *I**2",fAmin,fUp); //*-*- finished. reset input values fU[ke1-1] = xsav; fU[ke2-1] = ysav; ierrf = 0; return; L1350: Printf(" INVALID PARAMETER NUMBER(S) REQUESTED. IGNORED."); ierrf = 1; } /* mncntr_ */ //______________________________________________________________________________ void TMinuit::mncomd(const char *crdbin, Int_t &icondn) { //*-*-*-*-*-*-*-*-*-*-*Reads a command string and executes*-*-*-*-*-*-*-*-*-* //*-* =================================== //*-* Called by user. 'Reads' a command string and executes. //*-* Equivalent to MNEXCM except that the command is given as a //*-* character string. //*-* //*-* ICONDN = 0: command executed normally //*-* 1: command is blank, ignored //*-* 2: command line unreadable, ignored //*-* 3: unknown command, ignored //*-* 4: abnormal termination (e.g., MIGRAD not converged) //*-* 5: command is a request to read PARAMETER definitions //*-* 6: 'SET INPUT' command //*-* 7: 'SET TITLE' command //*-* 8: 'SET COVAR' command //*-* 9: reserved //*-* 10: END command //*-* 11: EXIT or STOP command //*-* 12: RETURN command //*-* //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Int_t ierr, ipos, i, llist, lenbuf, lnc; Bool_t leader; TString comand, crdbuf, ctemp; crdbuf = crdbin; crdbuf.ToUpper(); lenbuf = crdbuf.Length(); icondn = 0; //*-*- record not case-sensitive, get upper case, strip leading blanks leader = kTRUE; ipos = 1; for (i = 1; i <= TMath::Min(20,lenbuf); ++i) { if (crdbuf[i-1] == ''') break; if (crdbuf[i-1] == ' ') { if (leader) ++ipos; continue; } leader = kFALSE; } //*-*- blank or null command if (ipos > lenbuf) { Printf(" BLANK COMMAND IGNORED."); icondn = 1; return; } //*-*- . . preemptive commands //*-*- if command is 'PARAMETER' if (crdbuf(ipos-1,3) == "PAR") { icondn = 5; fLphead = kTRUE; return; } //*-*- if command is 'SET INPUT' if (crdbuf(ipos-1,3) == "SET INP") { icondn = 6; fLphead = kTRUE; return; } //*-*- if command is 'SET TITLE' if (crdbuf(ipos-1,7) == "SET TIT") { icondn = 7; fLphead = kTRUE; return; } //*-*- if command is 'SET COVARIANCE' if (crdbuf(ipos-1,7) == "SET COV") { icondn = 8; fLphead = kTRUE; return; } //*-*- crack the command . . . . . . . . . . . . . . . . ctemp = crdbuf(ipos-1,lenbuf-ipos+1); mncrck(ctemp, 20, comand, lnc, fMaxpar, fCOMDplist, llist, ierr, fIsyswr); if (ierr > 0) { Printf(" COMMAND CANNOT BE INTERPRETED"); icondn = 2; return; } mnexcm(comand.Data(), fCOMDplist, llist, ierr); icondn = ierr; } /* mncomd_ */ //______________________________________________________________________________ void TMinuit::mncont(Int_t ike1, Int_t ike2, Int_t nptu, Double_t *xptu, Double_t *yptu, Int_t &ierrf) { //*-*-*-*-*-*-*Find points along a contour where FCN is minimum*-*-*-*-*-*-* //*-* ================================================ //*-* Find NPTU points along a contour where the function //*-* FMIN (X(KE1),X(KE2)) = AMIN+UP //*-* where FMIN is the minimum of FCN with respect to all //*-* the other NPAR-2 variable parameters (if any). //*-* IERRF on return will be equal to the number of points found: //*-* NPTU if normal termination with NPTU points found //*-* -1 if errors in the calling sequence (KE1, KE2 not variable) //*-* 0 if less than four points can be found (using MNMNOT) //*-* n>3 if only n points can be found (n < NPTU) //*-* //*-* input arguments: parx, pary, devs, ngrid //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* System generated locals */ Int_t i__1; /* Local variables */ Double_t d__1, d__2; Double_t dist, xdir, ydir, aopt, u1min, u2min; Double_t abest, scalx, scaly; Double_t a1, a2, val2mi, val2pl, dc, sclfac, bigdis, sigsav; Int_t nall, iold, line, mpar, ierr, inew, move, next, i, j, nfcol, iercr; Int_t idist=0, npcol, kints, i2, i1, lr, nfcnco=0, ki1, ki2, ki3, ke3; Int_t nowpts, istrav, nfmxin, isw2, isw4; Bool_t ldebug; /* Function Body */ Int_t ke1 = ike1+1; Int_t ke2 = ike2+1; ldebug = fIdbg[6] >= 1; if (ke1 <= 0 || ke2 <= 0) goto L1350; if (ke1 > fNu || ke2 > fNu) goto L1350; ki1 = fNiofex[ke1-1]; ki2 = fNiofex[ke2-1]; if (ki1 <= 0 || ki2 <= 0) goto L1350; if (ki1 == ki2) goto L1350; if (nptu < 4) goto L1400; nfcnco = fNfcn; fNfcnmx = (nptu + 5)*100*(fNpar + 1); //*-*- The minimum mncuve(); u1min = fU[ke1-1]; u2min = fU[ke2-1]; ierrf = 0; fCfrom = "MNContour "; fNfcnfr = nfcnco; if (fISW[4] >= 0) { Printf(" START MNCONTOUR CALCULATION OF%4d POINTS ON CONTOUR.",nptu); if (fNpar > 2) { if (fNpar == 3) { ki3 = 6 - ki1 - ki2; ke3 = fNexofi[ki3-1]; Printf(" EACH POINT IS A MINIMUM WITH RESPECT TO PARAMETER %3d %s",ke3,(const char*)fCpnam[ke3-1]); } else { Printf(" EACH POINT IS A MINIMUM WITH RESPECT TO THE OTHER%3d VARIABLE PARAMETERS.",fNpar - 2); } } } //*-*- Find the first four points using MNMNOT //*-*- ........................ first two points mnmnot(ke1, ke2, val2pl, val2mi); if (fErn[ki1-1] == fUndefi) { xptu[0] = fAlim[ke1-1]; mnwarn("W", "MNContour ", "Contour squeezed by parameter limits."); } else { if (fErn[ki1-1] >= 0) goto L1500; xptu[0] = u1min + fErn[ki1-1]; } yptu[0] = val2mi; if (fErp[ki1-1] == fUndefi) { xptu[2] = fBlim[ke1-1]; mnwarn("W", "MNContour ", "Contour squeezed by parameter limits."); } else { if (fErp[ki1-1] <= 0) goto L1500; xptu[2] = u1min + fErp[ki1-1]; } yptu[2] = val2pl; scalx = 1 / (xptu[2] - xptu[0]); //*-*- ........................... next two points mnmnot(ke2, ke1, val2pl, val2mi); if (fErn[ki2-1] == fUndefi) { yptu[1] = fAlim[ke2-1]; mnwarn("W", "MNContour ", "Contour squeezed by parameter limits."); } else { if (fErn[ki2-1] >= 0) goto L1500; yptu[1] = u2min + fErn[ki2-1]; } xptu[1] = val2mi; if (fErp[ki2-1] == fUndefi) { yptu[3] = fBlim[ke2-1]; mnwarn("W", "MNContour ", "Contour squeezed by parameter limits."); } else { if (fErp[ki2-1] <= 0) goto L1500; yptu[3] = u2min + fErp[ki2-1]; } xptu[3] = val2pl; scaly = 1 / (yptu[3] - yptu[1]); nowpts = 4; next = 5; if (ldebug) { Printf(" Plot of four points found by MINOS"); fXpt[0] = u1min; fYpt[0] = u2min; fChpt[0] = ' '; //*-* Computing MIN nall = TMath::Min(nowpts + 1,101); for (i = 2; i <= nall; ++i) { fXpt[i-1] = xptu[i-2]; fYpt[i-1] = yptu[i-2]; } sprintf(fChpt,"%s"," ABCD"); mnplot(fXpt, fYpt, fChpt, nall, fNpagwd, fNpagln); } //*-*- ..................... save some values before fixing isw2 = fISW[1]; isw4 = fISW[3]; sigsav = fEDM; istrav = fIstrat; dc = fDcovar; fApsi = fEpsi*.5; abest = fAmin; mpar = fNpar; nfmxin = fNfcnmx; for (i = 1; i <= mpar; ++i) { fXt[i-1] = fX[i-1]; } i__1 = mpar*(mpar + 1) / 2; for (j = 1; j <= i__1; ++j) { fVthmat[j-1] = fVhmat[j-1]; } for (i = 1; i <= mpar; ++i) { fCONTgcc[i-1] = fGlobcc[i-1]; fCONTw[i-1] = fWerr[i-1]; } //*-*- fix the two parameters in question kints = fNiofex[ke1-1]; mnfixp(kints-1, ierr); kints = fNiofex[ke2-1]; mnfixp(kints-1, ierr); //*-*- ......................Fill in the rest of the points for (inew = next; inew <= nptu; ++inew) { //*-* find the two neighbouring points with largest separation bigdis = 0; for (iold = 1; iold <= inew - 1; ++iold) { i2 = iold + 1; if (i2 == inew) i2 = 1; d__1 = scalx*(xptu[iold-1] - xptu[i2-1]); d__2 = scaly*(yptu[iold-1] - yptu[i2-1]); dist = d__1*d__1 + d__2*d__2; if (dist > bigdis) { bigdis = dist; idist = iold; } } i1 = idist; i2 = i1 + 1; if (i2 == inew) i2 = 1; //*-*- next point goes between I1 and I2 a1 = .5; a2 = .5; L300: fXmidcr = a1*xptu[i1-1] + a2*xptu[i2-1]; fYmidcr = a1*yptu[i1-1] + a2*yptu[i2-1]; xdir = yptu[i2-1] - yptu[i1-1]; ydir = xptu[i1-1] - xptu[i2-1]; sclfac = TMath::Max(TMath::Abs(xdir*scalx),TMath::Abs(ydir*scaly)); fXdircr = xdir / sclfac; fYdircr = ydir / sclfac; fKe1cr = ke1; fKe2cr = ke2; //*-*- Find the contour crossing point along DIR fAmin = abest; mncros(aopt, iercr); if (iercr > 1) { //*-*- If cannot find mid-point, try closer to point 1 if (a1 > .5) { if (fISW[4] >= 0) { Printf(" MNCONT CANNOT FIND NEXT POINT ON CONTOUR. ONLY%3d POINTS FOUND.",nowpts); } goto L950; } mnwarn("W", "MNContour ", "Cannot find midpoint, try closer."); a1 = .75; a2 = .25; goto L300; } //*-*- Contour has been located, insert new point in list for (move = nowpts; move >= i1 + 1; --move) { xptu[move] = xptu[move-1]; yptu[move] = yptu[move-1]; } ++nowpts; xptu[i1] = fXmidcr + fXdircr*aopt; yptu[i1] = fYmidcr + fYdircr*aopt; } L950: ierrf = nowpts; fCstatu = "SUCCESSFUL"; if (nowpts < nptu) fCstatu = "INCOMPLETE"; //*-*- make a lineprinter plot of the contour if (fISW[4] >= 0) { fXpt[0] = u1min; fYpt[0] = u2min; fChpt[0] = ' '; nall = TMath::Min(nowpts + 1,101); for (i = 2; i <= nall; ++i) { fXpt[i-1] = xptu[i-2]; fYpt[i-1] = yptu[i-2]; fChpt[i-1] = 'X'; } fChpt[nall] = 0; Printf(" Y-AXIS: PARAMETER %3d %s",ke2,(const char*)fCpnam[ke2-1]); mnplot(fXpt, fYpt, fChpt, nall, fNpagwd, fNpagln); Printf(" X-AXIS: PARAMETER %3d %s",ke1,(const char*)fCpnam[ke1-1]); } //*-*- print out the coordinates around the contour if (fISW[4] >= 1) { npcol = (nowpts + 1) / 2; nfcol = nowpts / 2; Printf("%5d POINTS ON CONTOUR. FMIN=%13.5e ERRDEF=%11.3g",nowpts,abest,fUp); Printf(" %s%s%s%s",(const char*)fCpnam[ke1-1], (const char*)fCpnam[ke2-1], (const char*)fCpnam[ke1-1], (const char*)fCpnam[ke2-1]); for (line = 1; line <= nfcol; ++line) { lr = line + npcol; 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]); } if (nfcol < npcol) { Printf(" %5d%13.5e%13.5e",npcol,xptu[npcol-1],yptu[npcol-1]); } } //*-*- . . contour finished. reset v fItaur = 1; mnfree(1); mnfree(1); i__1 = mpar*(mpar + 1) / 2; for (j = 1; j <= i__1; ++j) { fVhmat[j-1] = fVthmat[j-1]; } for (i = 1; i <= mpar; ++i) { fGlobcc[i-1] = fCONTgcc[i-1]; fWerr[i-1] = fCONTw[i-1]; fX[i-1] = fXt[i-1]; } mninex(fX); fEDM = sigsav; fAmin = abest; fISW[1] = isw2; fISW[3] = isw4; fDcovar = dc; fItaur = 0; fNfcnmx = nfmxin; fIstrat = istrav; fU[ke1-1] = u1min; fU[ke2-1] = u2min; goto L2000; //*-*- Error returns L1350: Printf(" INVALID PARAMETER NUMBERS."); goto L1450; L1400: Printf(" LESS THAN FOUR POINTS REQUESTED."); L1450: ierrf = -1; fCstatu = "USER ERROR"; goto L2000; L1500: Printf(" MNCONT UNABLE TO FIND FOUR POINTS."); fU[ke1-1] = u1min; fU[ke2-1] = u2min; ierrf = 0; fCstatu = "FAILED"; L2000: fCfrom = "MNContour "; fNfcnfr = nfcnco; } /* mncont_ */ //______________________________________________________________________________ void TMinuit::mncrck(TString cardbuf, Int_t maxcwd, TString &comand, Int_t &lnc, Int_t mxp, Double_t *plist, Int_t &llist, Int_t &ierr, Int_t) { //*-*-*-*-*-*-*-*-*-*-*-*Cracks the free-format input*-*-*-*-*-*-*-*-*-*-*-*-* //*-* ============================ //*-* Cracks the free-format input, expecting zero or more //*-* alphanumeric fields (which it joins into COMAND(1:LNC)) //*-* followed by one or more numeric fields separated by //*-* blanks and/or one comma. The numeric fields are put into //*-* the LLIST (but at most MXP) elements of PLIST. //*-* IERR = 0 if no errors, //*-* = 1 if error(s). //*-* //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Initialized data */ char *cnull = 0; const char *cnumer = "123456789-.0+"; /* Local variables */ Int_t ifld, iend, lend, left, nreq, ipos, kcmnd, nextb, ic, ibegin, ltoadd; Int_t ielmnt, lelmnt[25], nelmnt; TString ctemp; char *celmnt[25]; char command[25]; /* Function Body */ char *crdbuf = (char*)cardbuf.Data(); lend = cardbuf.Length(); ielmnt = 0; nextb = 1; ierr = 0; //*-*- . . . . loop over words CELMNT L10: for (ipos = nextb; ipos <= lend; ++ipos) { ibegin = ipos; if (crdbuf[ipos-1] == ' ') continue; if (crdbuf[ipos-1] == ',') goto L250; goto L150; } goto L300; L150: //*-*- found beginning of word, look for end for (ipos = ibegin + 1; ipos <= lend; ++ipos) { if (crdbuf[ipos-1] == ' ') goto L250; if (crdbuf[ipos-1] == ',') goto L250; } ipos = lend + 1; L250: iend = ipos - 1; ++ielmnt; if (iend >= ibegin) celmnt[ielmnt-1] = &crdbuf[ibegin-1]; else celmnt[ielmnt-1] = cnull; lelmnt[ielmnt-1] = iend - ibegin + 1; if (lelmnt[ielmnt-1] > 19) { Printf(" MINUIT WARNING: INPUT DATA WORD TOO LONG."); ctemp = cardbuf(ibegin-1,iend-ibegin+1); Printf(" ORIGINAL:%s",ctemp.Data()); Printf(" TRUNCATED TO:%s",celmnt[ielmnt-1]); lelmnt[ielmnt-1] = 19; } if (ipos >= lend) goto L300; if (ielmnt >= 25) goto L300; //*-*- look for comma or beginning of next word for (ipos = iend + 1; ipos <= lend; ++ipos) { if (crdbuf[ipos-1] == ' ') continue; nextb = ipos; if (crdbuf[ipos-1] == ',') nextb = ipos + 1; goto L10; } //*-*- All elements found, join the alphabetic ones to //*-*- form a command L300: nelmnt = ielmnt; command[0] = ' '; command[1] = 0; lnc = 1; plist[0] = 0; llist = 0; if (ielmnt == 0) goto L900; kcmnd = 0; for (ielmnt = 1; ielmnt <= nelmnt; ++ielmnt) { if ( celmnt[ielmnt-1] == cnull) goto L450; for (ic = 1; ic <= 13; ++ic) { if (*celmnt[ielmnt-1] == cnumer[ic-1]) goto L450; } if (kcmnd >= maxcwd) continue; left = maxcwd - kcmnd; ltoadd = lelmnt[ielmnt-1]; if (ltoadd > left) ltoadd = left; strncpy(&command[kcmnd],celmnt[ielmnt-1],ltoadd); kcmnd += ltoadd; if (kcmnd == maxcwd) continue; command[kcmnd] = ' '; ++kcmnd; command[kcmnd] = 0; } lnc = kcmnd; goto L900; L450: lnc = kcmnd; //*-*- . . . . we have come to a numeric field llist = 0; for (ifld = ielmnt; ifld <= nelmnt; ++ifld) { ++llist; if (llist > mxp) { nreq = nelmnt - ielmnt + 1; Printf(" MINUIT WARNING IN MNCRCK: "); Printf(" COMMAND HAS INPUT%5d NUMERIC FIELDS, BUT MINUIT CAN ACCEPT ONLY%3d",nreq,mxp); goto L900; } if (celmnt[ifld-1] == cnull) plist[llist-1] = 0; else { sscanf(celmnt[ifld-1],"%lf",&plist[llist-1]); } } //*-*- end loop over numeric fields L900: if (lnc <= 0) lnc = 1; comand = command; } /* mncrck_ */ //______________________________________________________________________________ void TMinuit::mncros(Double_t &aopt, Int_t &iercr) { //*-*-*-*-*-*-*-*-*-*-*Find point where MNEVAL=AMIN+UP*-*-*-*-*-*-*-*-*-*-*-* //*-* =============================== //*-* Find point where MNEVAL=AMIN+UP, along the line through //*-* XMIDCR,YMIDCR with direction XDIRCR,YDIRCR, where X and Y //*-* are parameters KE1CR and KE2CR. If KE2CR=0 (from MINOS), //*-* only KE1CR is varied. From MNCONT, both are varied. //*-* Crossing point is at //*-* (U(KE1),U(KE2)) = (XMID,YMID) + AOPT*(XDIR,YDIR) //*-* //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t alsb[3], flsb[3], bmin, bmax, zmid, sdev, zdir, zlim; Double_t coeff[3], aleft, aulim, fdist, adist, aminsv; Double_t anext, fnext, slope, s1, s2, x1, x2, ecarmn, ecarmx; Double_t determ, rt, smalla, aright, aim, tla, tlf, dfda,ecart; Int_t iout=0, i, ileft, ierev, maxlk, ibest, ik, it; Int_t noless, iworst=0, iright, itoohi, kex, ipt; Bool_t ldebug; const char *chsign; x2 = 0; ldebug = fIdbg[6] >= 1; aminsv = fAmin; //*-*- convergence when F is within TLF of AIM and next prediction //*-*- of AOPT is within TLA of previous value of AOPT aim = fAmin + fUp; tlf = fUp*.01; tla = .01; fXpt[0] = 0; fYpt[0] = aim; fChpt[0] = ' '; ipt = 1; if (fKe2cr == 0) { fXpt[1] = -1; fYpt[1] = fAmin; fChpt[1] = '.'; ipt = 2; } //*-*- find the largest allowed A aulim = 100; for (ik = 1; ik <= 2; ++ik) { if (ik == 1) { kex = fKe1cr; zmid = fXmidcr; zdir = fXdircr; } else { if (fKe2cr == 0) continue; kex = fKe2cr; zmid = fYmidcr; zdir = fYdircr; } if (fNvarl[kex-1] <= 1) continue; if (zdir == 0) continue; zlim = fAlim[kex-1]; if (zdir > 0) zlim = fBlim[kex-1]; aulim = TMath::Min(aulim,(zlim - zmid) / zdir); } //*-*- LSB = Line Search Buffer //*-*- first point anext = 0; aopt = anext; fLimset = kFALSE; if (aulim < aopt + tla) fLimset = kTRUE; mneval(anext, fnext, ierev); //*-* debug printout: if (ldebug) { Printf(" MNCROS: calls=%8d AIM=%10.5f F,A=%10.5f%10.5f",fNfcn,aim,fnext,aopt); } if (ierev > 0) goto L900; if (fLimset && fnext <= aim) goto L930; ++ipt; fXpt[ipt-1] = anext; fYpt[ipt-1] = fnext; fChpt[ipt-1] = charal[ipt-1]; alsb[0] = anext; flsb[0] = fnext; fnext = TMath::Max(fnext,aminsv + fUp*.1); aopt = TMath::Sqrt(fUp / (fnext - aminsv)) - 1; if (TMath::Abs(fnext - aim) < tlf) goto L800; if (aopt < -.5)aopt = -.5; if (aopt > 1) aopt = 1; fLimset = kFALSE; if (aopt > aulim) { aopt = aulim; fLimset = kTRUE; } mneval(aopt, fnext, ierev); //*-* debug printout: if (ldebug) { Printf(" MNCROS: calls=%8d AIM=%10.5f F,A=%10.5f%10.5f",fNfcn,aim,fnext,aopt); } if (ierev > 0) goto L900; if (fLimset && fnext <= aim) goto L930; alsb[1] = aopt; ++ipt; fXpt[ipt-1] = alsb[1]; fYpt[ipt-1] = fnext; fChpt[ipt-1] = charal[ipt-1]; flsb[1] = fnext; dfda = (flsb[1] - flsb[0]) / (alsb[1] - alsb[0]); //*-*- DFDA must be positive on the contour if (dfda > 0) goto L460; L300: mnwarn("D", "MNCROS ", "Looking for slope of the right sign"); maxlk = 15 - ipt; for (it = 1; it <= maxlk; ++it) { alsb[0] = alsb[1]; flsb[0] = flsb[1]; aopt = alsb[0] + Double_t(it)*.2; fLimset = kFALSE; if (aopt > aulim) { aopt = aulim; fLimset = kTRUE; } mneval(aopt, fnext, ierev); //*-* debug printout: if (ldebug) { Printf(" MNCROS: calls=%8d AIM=%10.5f F,A=%10.5f%10.5f",fNfcn,aim,fnext,aopt); } if (ierev > 0) goto L900; if (fLimset && fnext <= aim) goto L930; alsb[1] = aopt; ++ipt; fXpt[ipt-1] = alsb[1]; fYpt[ipt-1] = fnext; fChpt[ipt-1] = charal[ipt-1]; flsb[1] = fnext; dfda = (flsb[1] - flsb[0]) / (alsb[1] - alsb[0]); if (dfda > 0) goto L450; } mnwarn("W", "MNCROS ", "Cannot find slope of the right sign"); goto L950; L450: //*-*- we have two points with the right slope L460: aopt = alsb[1] + (aim - flsb[1]) / dfda; fdist = TMath::Min(TMath::Abs(aim - flsb[0]),TMath::Abs(aim - flsb[1])); adist = TMath::Min(TMath::Abs(aopt - alsb[0]),TMath::Abs(aopt - alsb[1])); tla = .01; if (TMath::Abs(aopt) > 1) tla = TMath::Abs(aopt)*.01; if (adist < tla && fdist < tlf) goto L800; if (ipt >= 15) goto L950; bmin = TMath::Min(alsb[0],alsb[1]) - 1; if (aopt < bmin) aopt = bmin; bmax = TMath::Max(alsb[0],alsb[1]) + 1; if (aopt > bmax) aopt = bmax; //*-*- Try a third point fLimset = kFALSE; if (aopt > aulim) { aopt = aulim; fLimset = kTRUE; } mneval(aopt, fnext, ierev); //*-* debug printout: if (ldebug) { Printf(" MNCROS: calls=%8d AIM=%10.5f F,A=%10.5f%10.5f",fNfcn,aim,fnext,aopt); } if (ierev > 0) goto L900; if (fLimset && fnext <= aim) goto L930; alsb[2] = aopt; ++ipt; fXpt[ipt-1] = alsb[2]; fYpt[ipt-1] = fnext; fChpt[ipt-1] = charal[ipt-1]; flsb[2] = fnext; //*-*- now we have three points, ask how many <AIM ecarmn = TMath::Abs(fnext-aim); ibest = 3; ecarmx = 0; noless = 0; for (i = 1; i <= 3; ++i) { ecart = TMath::Abs(flsb[i-1] - aim); if (ecart > ecarmx) { ecarmx = ecart; iworst = i; } if (ecart < ecarmn) { ecarmn = ecart; ibest = i; } if (flsb[i-1] < aim) ++noless; } //*-*- if at least one on each side of AIM, fit a parabola if (noless == 1 || noless == 2) goto L500; //*-*- if all three are above AIM, third must be closest to AIM if (noless == 0 && ibest != 3) goto L950; //*-*- if all three below, and third is not best, then slope //*-*- has again gone negative, look for positive slope. if (noless == 3 && ibest != 3) { alsb[1] = alsb[2]; flsb[1] = flsb[2]; goto L300; } //*-*- in other cases, new straight line thru last two points alsb[iworst-1] = alsb[2]; flsb[iworst-1] = flsb[2]; dfda = (flsb[1] - flsb[0]) / (alsb[1] - alsb[0]); goto L460; //*-*- parabola fit L500: mnpfit(alsb, flsb, 3, coeff, sdev); if (coeff[2] <= 0) { mnwarn("D", "MNCROS ", "Curvature is negative near contour line."); } determ = coeff[1]*coeff[1] - coeff[2]*4*(coeff[0] - aim); if (determ <= 0) { mnwarn("D", "MNCROS ", "Problem 2, impossible determinant"); goto L950; } //*-*- Find which root is the right one rt = TMath::Sqrt(determ); x1 = (-coeff[1] + rt) / (coeff[2]*2); x2 = (-coeff[1] - rt) / (coeff[2]*2); s1 = coeff[1] + x1*2*coeff[2]; s2 = coeff[1] + x2*2*coeff[2]; if (s1*s2 > 0) { Printf(" MNCONTour problem 1"); } aopt = x1; slope = s1; if (s2 > 0) { aopt = x2; slope = s2; } //*-*- ask if converged tla = .01; if (TMath::Abs(aopt) > 1) tla = TMath::Abs(aopt)*.01; if (TMath::Abs(aopt - alsb[ibest-1]) < tla && TMath::Abs(flsb[ibest-1] - aim) < tlf) { goto L800; } if (ipt >= 15) goto L950; //*-*- see if proposed point is in acceptable zone between L and R //*-*- first find ILEFT, IRIGHT, IOUT and IBEST ileft = 0; iright = 0; ibest = 1; ecarmx = 0; ecarmn = TMath::Abs(aim - flsb[0]); for (i = 1; i <= 3; ++i) { ecart = TMath::Abs(flsb[i-1] - aim); if (ecart < ecarmn) { ecarmn = ecart; ibest = i; } if (ecart > ecarmx) { ecarmx = ecart; } if (flsb[i-1] > aim) { if (iright == 0) iright = i; else if (flsb[i-1] > flsb[iright-1]) iout = i; else { iout = iright; iright = i; } } else if (ileft == 0) ileft = i; else if (flsb[i-1] < flsb[ileft-1]) iout = i; else { iout = ileft; ileft = i; } } //*-*- avoid keeping a very bad point next time around if (ecarmx > TMath::Abs(flsb[iout-1] - aim)*10) { aopt = aopt*.5 + (alsb[iright-1] + alsb[ileft-1])*.25; } //*-*- knowing ILEFT and IRIGHT, get acceptable window smalla = tla*.1; if (slope*smalla > tlf) smalla = tlf / slope; aleft = alsb[ileft-1] + smalla; aright = alsb[iright-1] - smalla; //*-*- move proposed point AOPT into window if necessary if (aopt < aleft) aopt = aleft; if (aopt > aright) aopt = aright; if (aleft > aright) aopt = (aleft + aright)*.5; //*-*- see if proposed point outside limits (should be impossible!) fLimset = kFALSE; if (aopt > aulim) { aopt = aulim; fLimset = kTRUE; } //*-*- Evaluate function at new point AOPT mneval(aopt, fnext, ierev); //*-* debug printout: if (ldebug) { Printf(" MNCROS: calls=%8d AIM=%10.5f F,A=%10.5f%10.5f",fNfcn,aim,fnext,aopt); } if (ierev > 0) goto L900; if (fLimset && fnext <= aim) goto L930; ++ipt; fXpt[ipt-1] = aopt; fYpt[ipt-1] = fnext; fChpt[ipt-1] = charal[ipt-1]; //*-*- Replace odd point by new one alsb[iout-1] = aopt; flsb[iout-1] = fnext; //*-*- the new point may not be the best, but it is the only one //*-*- which could be good enough to pass convergence criteria ibest = iout; goto L500; //*-*- Contour has been located, return point to MNCONT OR MINOS L800: iercr = 0; goto L1000; //*-*- error in the minimization L900: if (ierev == 1) goto L940; goto L950; //*-*- parameter up against limit L930: iercr = 1; goto L1000; //*-*- too many calls to FCN L940: iercr = 2; goto L1000; //*-*- cannot find next point L950: iercr = 3; //*-*- in any case L1000: if (ldebug) { itoohi = 0; for (i = 1; i <= ipt; ++i) { if (fYpt[i-1] > aim + fUp) { fYpt[i-1] = aim + fUp; fChpt[i-1] = '+'; itoohi = 1; } } fChpt[ipt] = 0; chsign = "POSI"; if (fXdircr < 0) chsign = "NEGA"; if (fKe2cr == 0) { Printf(" %sTIVE MINOS ERROR, PARAMETER %3d",chsign,fKe1cr); } if (itoohi == 1) { Printf("POINTS LABELLED '+' WERE TOO HIGH TO PLOT."); } if (iercr == 1) { Printf("RIGHTMOST POINT IS UP AGAINST LIMIT."); } mnplot(fXpt, fYpt, fChpt, ipt, fNpagwd, fNpagln); } } /* mncros_ */ //______________________________________________________________________________ void TMinuit::mncuve() { //*-*-*-*-*-*-*-*Makes sure that the current point is a local minimum*-*-*-*-* //*-* ==================================================== //*-* Makes sure that the current point is a local //*-* minimum and that the error matrix exists, //*-* or at least something good enough for MINOS and MNCONT //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t dxdi, wint; Int_t ndex, iext, i, j; if (fISW[3] < 1) { Printf(" FUNCTION MUST BE MINIMIZED BEFORE CALLING %s",(const char*)fCfrom); fApsi = fEpsi; mnmigr(); } if (fISW[1] < 3) { mnhess(); if (fISW[1] < 1) { mnwarn("W", fCfrom, "NO ERROR MATRIX. WILL IMPROVISE."); for (i = 1; i <= fNpar; ++i) { ndex = i*(i-1) / 2; for (j = 1; j <= i-1; ++j) { ++ndex; fVhmat[ndex-1] = 0; } ++ndex; if (fG2[i-1] <= 0) { wint = fWerr[i-1]; iext = fNexofi[i-1]; if (fNvarl[iext-1] > 1) { mndxdi(fX[i-1], i-1, dxdi); if (TMath::Abs(dxdi) < .001) wint = .01; else wint /= TMath::Abs(dxdi); } fG2[i-1] = fUp / (wint*wint); } fVhmat[ndex-1] = 2 / fG2[i-1]; } fISW[1] = 1; fDcovar = 1; } else mnwerr(); } } /* mncuve_ */ //______________________________________________________________________________ void TMinuit::mnderi() { //*-*-*-*-*-*-*-*Calculates the first derivatives of FCN (GRD)*-*-*-*-*-*-*-* //*-* ============================================= //*-* Calculates the first derivatives of FCN (GRD), //*-* either by finite differences or by transforming the user- //*-* supplied derivatives to internal coordinates, //*-* according to whether ISW(3) is zero or one. //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t step, dfmin, stepb4, dd, df, fs1; Double_t tlrstp, tlrgrd, epspri, optstp, stpmax, stpmin, fs2, grbfor=0, d1d2, xtf; Int_t icyc, ncyc, iint, iext, i, nparx; Bool_t ldebug; nparx = fNpar; ldebug = fIdbg[2] >= 1; if (fAmin == fUndefi) mnamin(); if (fISW[2] == 1) goto L100; if (ldebug) { //*-*- make sure starting at the right place mninex(fX); nparx = fNpar; Eval(nparx, fGin, fs1, fU, 4); ++fNfcn; if (fs1 != fAmin) { df = fAmin - fs1; mnwarn("D", "MNDERI", Form("function value differs from AMIN by %12.3g",df)); fAmin = fs1; } Printf(" FIRST DERIVATIVE DEBUG PRINTOUT. MNDERI"); Printf(" PAR DERIV STEP MINSTEP OPTSTEP D1-D2 2ND DRV"); } dfmin = fEpsma2*8*(TMath::Abs(fAmin) + fUp); if (fIstrat <= 0) { ncyc = 2; tlrstp = .5; tlrgrd = .1; } else if (fIstrat == 1) { ncyc = 3; tlrstp = .3; tlrgrd = .05; } else { ncyc = 5; tlrstp = .1; tlrgrd = .02; } //*-*- loop over variable parameters for (i = 1; i <= fNpar; ++i) { epspri = fEpsma2 + TMath::Abs(fGrd[i-1]*fEpsma2); //*-*- two-point derivatives always assumed necessary //*-*- maximum number of cycles over step size depends on strategy xtf = fX[i-1]; stepb4 = 0; //*-*- loop as little as possible here!/ for (icyc = 1; icyc <= ncyc; ++icyc) { //*-*- ........ theoretically best step optstp = TMath::Sqrt(dfmin / (TMath::Abs(fG2[i-1]) + epspri)); //*-*- step cannot decrease by more than a factor of ten step = TMath::Max(optstp,TMath::Abs(fGstep[i-1]*.1)); //*-*- but if parameter has limits, max step size = 0.5 if (fGstep[i-1] < 0 && step > .5) step = .5; //*-*- and not more than ten times the previous step stpmax = TMath::Abs(fGstep[i-1])*10; if (step > stpmax) step = stpmax; //*-*- minimum step size allowed by machine precision stpmin = TMath::Abs(fEpsma2*fX[i-1])*8; if (step < stpmin) step = stpmin; //*-*- end of iterations if step change less than factor 2 if (TMath::Abs((step - stepb4) / step) < tlrstp) goto L50; //*-*- take step positive stepb4 = step; if (fGstep[i-1] > 0) fGstep[i-1] = TMath::Abs(step); else fGstep[i-1] = -TMath::Abs(step); stepb4 = step; fX[i-1] = xtf + step; mninex(fX); Eval(nparx, fGin, fs1, fU, 4); ++fNfcn; //*-*- take step negative fX[i-1] = xtf - step; mninex(fX); Eval(nparx, fGin, fs2, fU, 4); ++fNfcn; grbfor = fGrd[i-1]; fGrd[i-1] = (fs1 - fs2) / (step*2); fG2[i-1] = (fs1 + fs2 - fAmin*2) / (step*step); fX[i-1] = xtf; if (ldebug) { d1d2 = (fs1 + fs2 - fAmin*2) / step; Printf("%4d%11.3g%11.3g%10.2g%10.2g%10.2g%10.2g%10.2g",i,fGrd[i-1],step,stpmin,optstp,d1d2,fG2[i-1]); } //*-*- see if another iteration is necessary if (TMath::Abs(grbfor - fGrd[i-1]) / (TMath::Abs(fGrd[i-1]) + dfmin/step) < tlrgrd) goto L50; } //*-*- end of ICYC loop. too many iterations if (ncyc == 1) goto L50; mnwarn("D", "MNDERI", Form("First derivative not converged. %g%g",fGrd[i-1],grbfor)); L50: ; } mninex(fX); return; //*-*- . derivatives calc by fcn L100: for (iint = 1; iint <= fNpar; ++iint) { iext = fNexofi[iint-1]; if (fNvarl[iext-1] <= 1) { fGrd[iint-1] = fGin[iext-1]; } else { dd = (fBlim[iext-1] - fAlim[iext-1])*.5*TMath::Cos(fX[iint-1]); fGrd[iint-1] = fGin[iext-1]*dd; } } } /* mnderi_ */ //______________________________________________________________________________ void TMinuit::mndxdi(Double_t pint, Int_t ipar, Double_t &dxdi) { //*-*-*-*Calculates the transformation factor between ext/internal values*-* //*-* ===================================================================== //*-* calculates the transformation factor between external and //*-* internal parameter values. this factor is one for //*-* parameters which are not limited. called from MNEMAT. //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Int_t i = fNexofi[ipar]; dxdi = 1; if (fNvarl[i-1] > 1) { dxdi = TMath::Abs((fBlim[i-1] - fAlim[i-1])*TMath::Cos(pint))*.5; } } /* mndxdi_ */ //______________________________________________________________________________ void TMinuit::mneig(Double_t *a, Int_t ndima, Int_t n, Int_t mits, Double_t *work, Double_t precis, Int_t &ifault) { //*-*-*-*-*-*-*-*-*-*-*-*Compute matrix eigen values*-*-*-*-*-*-*-*-*-*-*-*-* //*-* =========================== /* System generated locals */ Int_t a_offset; Double_t d__1; /* Local variables */ Double_t b, c, f, h, r, s, hh, gl, pr, pt; Int_t i, j, k, l, m=0, i0, i1, j1, m1, n1; //*-*- PRECIS is the machine precision EPSMAC /* Parameter adjustments */ a_offset = ndima + 1; a -= a_offset; --work; /* Function Body */ ifault = 1; i = n; for (i1 = 2; i1 <= n; ++i1) { l = i-2; f = a[i + (i-1)*ndima]; gl = 0; if (l < 1) goto L25; for (k = 1; k <= l; ++k) { d__1 = a[i + k*ndima]; gl += d__1*d__1; } L25: h = gl + f*f; if (gl > 1e-35) goto L30; work[i] = 0; work[n + i] = f; goto L65; L30: ++l; gl = TMath::Sqrt(h); if (f >= 0) gl = -gl; work[n + i] = gl; h -= f*gl; a[i + (i-1)*ndima] = f - gl; f = 0; for (j = 1; j <= l; ++j) { a[j + i*ndima] = a[i + j*ndima] / h; gl = 0; for (k = 1; k <= j; ++k) { gl += a[j + k*ndima]*a[i + k*ndima]; } if (j >= l) goto L47; j1 = j + 1; for (k = j1; k <= l; ++k) { gl += a[k + j*ndima]*a[i + k*ndima]; } L47: work[n + j] = gl / h; f += gl*a[j + i*ndima]; } hh = f / (h + h); for (j = 1; j <= l; ++j) { f = a[i + j*ndima]; gl = work[n + j] - hh*f; work[n + j] = gl; for (k = 1; k <= j; ++k) { a[j + k*ndima] = a[j + k*ndima] - f*work[n + k] - gl*a[i + k*ndima]; } } work[i] = h; L65: --i; } work[1] = 0; work[n + 1] = 0; for (i = 1; i <= n; ++i) { l = i-1; if (work[i] == 0 || l == 0) goto L100; for (j = 1; j <= l; ++j) { gl = 0; for (k = 1; k <= l; ++k) { gl += a[i + k*ndima]*a[k + j*ndima]; } for (k = 1; k <= l; ++k) { a[k + j*ndima] -= gl*a[k + i*ndima]; } } L100: work[i] = a[i + i*ndima]; a[i + i*ndima] = 1; if (l == 0) continue; for (j = 1; j <= l; ++j) { a[i + j*ndima] = 0; a[j + i*ndima] = 0; } } n1 = n - 1; for (i = 2; i <= n; ++i) { i0 = n + i-1; work[i0] = work[i0 + 1]; } work[n + n] = 0; b = 0; f = 0; for (l = 1; l <= n; ++l) { j = 0; h = precis*(TMath::Abs(work[l]) + TMath::Abs(work[n + l])); if (b < h) b = h; for (m1 = l; m1 <= n; ++m1) { m = m1; if (TMath::Abs(work[n + m]) <= b) goto L150; } L150: if (m == l) goto L205; L160: if (j == mits) return; ++j; pt = (work[l + 1] - work[l]) / (work[n + l]*2); r = TMath::Sqrt(pt*pt + 1); pr = pt + r; if (pt < 0) pr = pt - r; h = work[l] - work[n + l] / pr; for (i = l; i <= n; ++i) { work[i] -= h; } f += h; pt = work[m]; c = 1; s = 0; m1 = m - 1; i = m; for (i1 = l; i1 <= m1; ++i1) { j = i; --i; gl = c*work[n + i]; h = c*pt; if (TMath::Abs(pt) >= TMath::Abs(work[n + i])) goto L180; c = pt / work[n + i]; r = TMath::Sqrt(c*c + 1); work[n + j] = s*work[n + i]*r; s = 1 / r; c /= r; goto L190; L180: c = work[n + i] / pt; r = TMath::Sqrt(c*c + 1); work[n + j] = s*pt*r; s = c / r; c = 1 / r; L190: pt = c*work[i] - s*gl; work[j] = h + s*(c*gl + s*work[i]); for (k = 1; k <= n; ++k) { h = a[k + j*ndima]; a[k + j*ndima] = s*a[k + i*ndima] + c*h; a[k + i*ndima] = c*a[k + i*ndima] - s*h; } } work[n + l] = s*pt; work[l] = c*pt; if (TMath::Abs(work[n + l]) > b) goto L160; L205: work[l] += f; } for (i = 1; i <= n1; ++i) { k = i; pt = work[i]; i1 = i + 1; for (j = i1; j <= n; ++j) { if (work[j] >= pt) continue; k = j; pt = work[j]; } if (k == i) continue; work[k] = work[i]; work[i] = pt; for (j = 1; j <= n; ++j) { pt = a[j + i*ndima]; a[j + i*ndima] = a[j + k*ndima]; a[j + k*ndima] = pt; } } ifault = 0; } /* mneig_ */ //______________________________________________________________________________ void TMinuit::mnemat(Double_t *emat, Int_t ndim) { // Calculates the external error matrix from the internal matrix // // Note that if the matrix is declared like Double_t matrix[5][5] // in the calling program, one has to call mnemat with, eg // gMinuit->mnemat(&matrix[0][0],5); /* System generated locals */ Int_t emat_dim1, emat_offset; /* Local variables */ Double_t dxdi, dxdj; Int_t i, j, k, npard, k2, kk, iz, nperln, kga, kgb; TString ctemp; /* Parameter adjustments */ emat_dim1 = ndim; emat_offset = emat_dim1 + 1; emat -= emat_offset; /* Function Body */ if (fISW[1] < 1) return; if (fISW[4] >= 2) { Printf(" EXTERNAL ERROR MATRIX. NDIM=%4d NPAR=%3d ERR DEF=%g",ndim,fNpar,fUp); } //*-*- size of matrix to be printed npard = fNpar; if (ndim < fNpar) { npard = ndim; if (fISW[4] >= 0) { Printf(" USER-DIMENSIONED ARRAY EMAT NOT BIG ENOUGH. REDUCED MATRIX CALCULATED."); } } //*-*- NPERLN is the number of elements that fit on one line nperln = (fNpagwd - 5) / 10; nperln = TMath::Min(nperln,13); if (fISW[4] >= 1 && npard > nperln) { Printf(" ELEMENTS ABOVE DIAGONAL ARE NOT PRINTED."); } //*-*- I counts the rows of the matrix for (i = 1; i <= npard; ++i) { mndxdi(fX[i-1], i-1, dxdi); kga = i*(i-1) / 2; for (j = 1; j <= i; ++j) { mndxdi(fX[j-1], j-1, dxdj); kgb = kga + j; emat[i + j*emat_dim1] = dxdi*fVhmat[kgb-1]*dxdj*fUp; emat[j + i*emat_dim1] = emat[i + j*emat_dim1]; } } //*-*- IZ is number of columns to be printed in row I if (fISW[4] >= 2) { for (i = 1; i <= npard; ++i) { iz = npard; if (npard >= nperln) iz = i; ctemp = " "; for (k = 1; nperln < 0 ? k >= iz : k <= iz; k += nperln) { k2 = k + nperln - 1; if (k2 > iz) k2 = iz; for (kk = k; kk <= k2; ++kk) { ctemp += Form("%10.3e ",emat[i + kk*emat_dim1]); } Printf("%s",(const char*)ctemp); } } } } /* mnemat_ */ //______________________________________________________________________________ void TMinuit::mnerrs(Int_t number, Double_t &eplus, Double_t &eminus, Double_t &eparab, Double_t &gcc) { //*-*-*-*-*-*-*-*-*-*Utility routine to get MINOS errors*-*-*-*-*-*-*-*-*-*-* //*-* =================================== //*-* Called by user. //*-* NUMBER is the parameter number //*-* values returned by MNERRS: //*-* EPLUS, EMINUS are MINOS errors of parameter NUMBER, //*-* EPARAB is 'parabolic' error (from error matrix). //*-* (Errors not calculated are set = 0) //*-* GCC is global correlation coefficient from error matrix //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Double_t dxdi; Int_t ndiag, iin, iex; iex = number+1; if (iex > fNu || iex <= 0) goto L900; iin = fNiofex[iex-1]; if (iin <= 0) goto L900; //*-*- IEX is external number, IIN is internal number eplus = fErp[iin-1]; if (eplus == fUndefi) eplus = 0; eminus = fErn[iin-1]; if (eminus == fUndefi) eminus = 0; mndxdi(fX[iin-1], iin-1, dxdi); ndiag = iin*(iin + 1) / 2; eparab = TMath::Abs(dxdi*TMath::Sqrt(TMath::Abs(fUp*fVhmat[ndiag- 1]))); //*-*- global correlation coefficient gcc = 0; if (fISW[1] < 2) return; gcc = fGlobcc[iin-1]; return; //*-*- ERROR. parameter number not valid L900: eplus = 0; eminus = 0; eparab = 0; gcc = 0; } /* mnerrs_ */ //______________________________________________________________________________ void TMinuit::mneval(Double_t anext, Double_t &fnext, Int_t &ierev) { //*-*-*-*-*-*-*Evaluates the function being analyzed by MNCROS*-*-*-*-*-*-*-* //*-* =============================================== //*-* Evaluates the function being analyzed by MNCROS, which is //*-* generally the minimum of FCN with respect to all remaining //*-* variable parameters. The class data members contains the //*-* data necessary to know the values of U(KE1CR) and U(KE2CR) //*-* to be used, namely U(KE1CR) = XMIDCR + ANEXT*XDIRCR //*-* and (if KE2CR .NE. 0) U(KE2CR) = YMIDCR + ANEXT*YDIRCR //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Int_t nparx; fU[fKe1cr-1] = fXmidcr + anext*fXdircr; if (fKe2cr != 0) fU[fKe2cr-1] = fYmidcr + anext*fYdircr; mninex(fX); nparx = fNpar; Eval(nparx, fGin, fnext, fU, 4); ++fNfcn; ierev = 0; if (fNpar > 0) { fItaur = 1; fAmin = fnext; fISW[0] = 0; mnmigr(); fItaur = 0; fnext = fAmin; if (fISW[0] >= 1) ierev = 1; if (fISW[3] < 1) ierev = 2; } } /* mneval_ */ //______________________________________________________________________________ void TMinuit::mnexcm(const char *command, Double_t *plist, Int_t llist, Int_t &ierflg) { //*-*-*-*-*-*Interprets a command and takes appropriate action*-*-*-*-*-*-*-* //*-* ================================================= //*-* either directly by skipping to the corresponding code in //*-* MNEXCM, or by setting up a call to a function //*-* //*-* recognized MINUIT commands: //*-* obsolete commands: //*-* IERFLG is now (94.5) defined the same as ICONDN in MNCOMD //*-* = 0: command executed normally //*-* 1: command is blank, ignored //*-* 2: command line unreadable, ignored //*-* 3: unknown command, ignored //*-* 4: abnormal termination (e.g., MIGRAD not converged) //*-* 9: reserved //*-* 10: END command //*-* 11: EXIT or STOP command //*-* 12: RETURN command //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Initialized data */ TString comand = command; static TString clower = "abcdefghijklmnopqrstuvwxyz"; static TString cupper = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"; const char *cname[40] = { "MINImize ", "SEEk ", "SIMplex ", "MIGrad ", "MINOs ", "SET xxx ", "SHOw xxx ", "TOP of pag", "FIX ", "REStore ", "RELease ", "SCAn ", "CONtour ", "HESse ", "SAVe ", "IMProve ", "CALl fcn ", "STAndard ", "END ", "EXIt ", "RETurn ", "CLEar ", "HELP ", "MNContour ", "STOp ", "JUMp ", " ", " ", " ", " ", " ", " ", " ", "COVARIANCE", "PRINTOUT ", "GRADIENT ", "MATOUT ", "ERROR DEF ", "LIMITS ", "PUNCH "}; Int_t nntot = 40; /* Local variables */ Double_t step, xptu[101], yptu[101], f, rno; Int_t icol, kcol, ierr, iint, iext, lnow, nptu, i, iflag, ierrf; Int_t ilist, nparx, izero, nf, lk, it, iw, inonde, nsuper; Int_t it2, ke1, ke2, nowprt, kll, krl; TString chwhy, c26, cvblnk, cneway, comd; TString ctemp; Bool_t lfreed, ltofix, lfixed; //*-* alphabetical order of command names! /* Function Body */ lk = comand.Length(); if (lk > 20) lk = 20; fCword = comand; fCword.ToUpper(); //*-*- Copy the first MAXP arguments into WORD7, making //*-*- sure that WORD7(1)=0 if LLIST=0 for (iw = 1; iw <= fMaxpar; ++iw) { fWord7[iw-1] = 0; if (iw <= llist) fWord7[iw-1] = plist[iw-1]; } ++fIcomnd; fNfcnlc = fNfcn; if (fCword(0,7) != "SET PRI" || fWord7[0] >= 0) { if (fISW[4] >= 0) { lnow = llist; if (lnow > 4) lnow = 4; Printf(" **********"); ctemp = Form(" **%5d **%s",fIcomnd,(const char*)fCword); for (i = 1; i <= lnow; ++i) { ctemp += Form("%12.4g",plist[i-1]); } Printf("%s",(const char*)ctemp); inonde = 0; if (llist > lnow) { kll = llist; if (llist > fMaxpar) { inonde = 1; kll = fMaxpar; } Printf(" ***********"); for (i = lnow + 1; i <= kll; ++i) { Printf("%12.4g",plist[i-1]); } } Printf(" **********"); if (inonde > 0) { Printf(" ERROR: ABOVE CALL TO MNEXCM TRIED TO PASS MORE THAN %d PARAMETERS.", fMaxpar); } } } fNfcnmx = Int_t(fWord7[0]); if (fNfcnmx <= 0) { fNfcnmx = fNpar*100 + 200 + fNpar*fNpar*5; } fEpsi = fWord7[1]; if (fEpsi <= 0) { fEpsi = fUp*.1; } fLnewmn = kFALSE; fLphead = kTRUE; fISW[0] = 0; ierflg = 0; //*-*- look for command in list CNAME . . . . . . . . . . ctemp = fCword(0,3); for (i = 1; i <= nntot; ++i) { if (strncmp(ctemp.Data(),cname[i-1],3) == 0) goto L90; } Printf("UNKNOWN COMMAND IGNORED:%s", comand.Data()); ierflg = 3; return; //*-*- normal case: recognized MINUIT command . . . . . . . L90: if (fCword(0,4) == "MINO") i = 5; if (i != 6 && i != 7 && i != 8 && i != 23) { fCfrom = cname[i-1]; fNfcnfr = fNfcn; } //*-*- 1 2 3 4 5 6 7 8 9 10 switch (i) { case 1: goto L400; case 2: goto L200; case 3: goto L300; case 4: goto L400; case 5: goto L500; case 6: goto L700; case 7: goto L700; case 8: goto L800; case 9: goto L900; case 10: goto L1000; case 11: goto L1100; case 12: goto L1200; case 13: goto L1300; case 14: goto L1400; case 15: goto L1500; case 16: goto L1600; case 17: goto L1700; case 18: goto L1800; case 19: goto L1900; case 20: goto L1900; case 21: goto L1900; case 22: goto L2200; case 23: goto L2300; case 24: goto L2400; case 25: goto L1900; case 26: goto L2600; case 27: goto L3300; case 28: goto L3300; case 29: goto L3300; case 30: goto L3300; case 31: goto L3300; case 32: goto L3300; case 33: goto L3300; case 34: goto L3400; case 35: goto L3500; case 36: goto L3600; case 37: goto L3700; case 38: goto L3800; case 39: goto L3900; case 40: goto L4000; } //*-*- . . . . . . . . . . seek L200: mnseek(); return; //*-*- . . . . . . . . . . simplex L300: mnsimp(); if (fISW[3] < 1) ierflg = 4; return; //*-*- . . . . . . migrad, minimize L400: nf = fNfcn; fApsi = fEpsi; mnmigr(); mnwerr(); if (fISW[3] >= 1) return; ierflg = 4; if (fISW[0] == 1) return; if (fCword(0,3) == "MIG") return; fNfcnmx = fNfcnmx + nf - fNfcn; nf = fNfcn; mnsimp(); if (fISW[0] == 1) return; fNfcnmx = fNfcnmx + nf - fNfcn; mnmigr(); if (fISW[3] >= 1) ierflg = 0; mnwerr(); return; //*-*- . . . . . . . . . . minos L500: nsuper = fNfcn + (fNpar + 1 << 1)*fNfcnmx; //*-*- possible loop over new minima fEpsi = fUp*.1; L510: mncuve(); mnmnos(); if (! fLnewmn) return; mnrset(0); mnmigr(); mnwerr(); if (fNfcn < nsuper) goto L510; Printf(" TOO MANY FUNCTION CALLS. MINOS GIVES UP"); ierflg = 4; return; //*-*- . . . . . . . . . .set, show L700: mnset(); return; //*-*- . . . . . . . . . . top of page L800: Printf("1"); return; //*-*- . . . . . . . . . . fix L900: ltofix = kTRUE; //*-*- . . (also release) .... L901: lfreed = kFALSE; lfixed = kFALSE; if (llist == 0) { Printf("%s: NO PARAMETERS REQUESTED ",(const char*)fCword); return; } for (ilist = 1; ilist <= llist; ++ilist) { iext = Int_t(plist[ilist-1]); chwhy = " IS UNDEFINED."; if (iext <= 0) goto L930; if (iext > fNu) goto L930; if (fNvarl[iext-1] < 0) goto L930; chwhy = " IS CONSTANT. "; if (fNvarl[iext-1] == 0) goto L930; iint = fNiofex[iext-1]; if (ltofix) { chwhy = " ALREADY FIXED."; if (iint == 0) goto L930; mnfixp(iint-1, ierr); if (ierr == 0) lfixed = kTRUE; else ierflg = 4; } else { chwhy = " ALREADY VARIABLE."; if (iint > 0) goto L930; krl = -abs(iext); mnfree(krl); lfreed = kTRUE; } continue; L930: Printf(" PARAMETER%4d %s IGNORED.",iext,(const char*)chwhy); } if (lfreed || lfixed) mnrset(0); if (lfreed) { fISW[1] = 0; fDcovar = 1; fEDM = fBigedm; fISW[3] = 0; } mnwerr(); if (fISW[4] > 1) mnprin(5, fAmin); return; //*-*- . . . . . . . . . . restore L1000: it = Int_t(fWord7[0]); if (it > 1 || it < 0) goto L1005; lfreed = fNpfix > 0; mnfree(it); if (lfreed) { mnrset(0); fISW[1] = 0; fDcovar = 1; fEDM = fBigedm; } return; L1005: Printf(" IGNORED. UNKNOWN ARGUMENT:%4d",it); ierflg = 3; return; //*-*- . . . . . . . . . . release L1100: ltofix = kFALSE; goto L901; //*-*- . . . . . . . . . . scan . . . L1200: iext = Int_t(fWord7[0]); if (iext <= 0) goto L1210; it2 = 0; if (iext <= fNu) it2 = fNiofex[iext-1]; if (it2 <= 0) goto L1250; L1210: mnscan(); return; L1250: Printf(" PARAMETER%4d NOT VARIABLE.",iext); ierflg = 3; return; //*-*- . . . . . . . . . . contour L1300: ke1 = Int_t(fWord7[0]); ke2 = Int_t(fWord7[1]); if (ke1 == 0) { if (fNpar == 2) { ke1 = fNexofi[0]; ke2 = fNexofi[1]; } else { Printf("%s: NO PARAMETERS REQUESTED ",(const char*)fCword); ierflg = 3; return; } } fNfcnmx = 1000; mncntr(ke1-1, ke2-1, ierrf); if (ierrf > 0) ierflg = 3; return; //*-*- . . . . . . . . . . hesse L1400: mnhess(); mnwerr(); if (fISW[4] >= 0) mnprin(2, fAmin); if (fISW[4] >= 1) mnmatu(1); return; //*-*- . . . . . . . . . . save L1500: mnsave(); return; //*-*- . . . . . . . . . . improve L1600: mncuve(); mnimpr(); if (fLnewmn) goto L400; ierflg = 4; return; //*-*- . . . . . . . . . . call fcn L1700: iflag = Int_t(fWord7[0]); nparx = fNpar; f = fUndefi; Eval(nparx, fGin, f, fU, iflag); ++fNfcn; nowprt = 0; if (f != fUndefi) { if (fAmin == fUndefi) { fAmin = f; nowprt = 1; } else if (f < fAmin) { fAmin = f; nowprt = 1; } if (fISW[4] >= 0 && iflag <= 5 && nowprt == 1) { mnprin(5, fAmin); } if (iflag == 3) fFval3 = f; } if (iflag > 5) mnrset(1); return; //*-*- . . . . . . . . . . standard L1800: // stand(); return; //*-*- . . . return, stop, end, exit L1900: it = Int_t(fWord7[0]); if (fFval3 != fAmin && it == 0) { iflag = 3; Printf(" CALL TO USER FUNCTION WITH IFLAG = 3"); nparx = fNpar; Eval(nparx, fGin, f, fU, iflag); ++fNfcn; } ierflg = 11; if (fCword(0,3) == "END") ierflg = 10; if (fCword(0,3) == "RET") ierflg = 12; return; //*-*- . . . . . . . . . . clear L2200: mncler(); if (fISW[4] >= 1) { Printf(" MINUIT MEMORY CLEARED. NO PARAMETERS NOW DEFINED."); } return; //*-*- . . . . . . . . . . help L2300: kcol = 0; for (icol = 5; icol <= lk; ++icol) { if (fCword[icol-1] == ' ') continue; kcol = icol; goto L2320; } L2320: if (kcol == 0) comd = "* "; else comd = fCword(kcol-1,lk-kcol+1); mnhelp(comd); return; //*-*- . . . . . . . . . . MNContour L2400: fEpsi = fUp*.05; ke1 = Int_t(fWord7[0]); ke2 = Int_t(fWord7[1]); if (ke1 == 0 && fNpar == 2) { ke1 = fNexofi[0]; ke2 = fNexofi[1]; } nptu = Int_t(fWord7[2]); if (nptu <= 0) nptu = 20; if (nptu > 101) nptu = 101; fNfcnmx = (nptu + 5)*100*(fNpar + 1); mncont(ke1-1, ke2-1, nptu, xptu, yptu, ierrf); if (ierrf < nptu) ierflg = 4; if (ierrf == -1) ierflg = 3; return; //*-*- . . . . . . . . . . jump L2600: step = fWord7[0]; if (step <= 0) step = 2; rno = 0; izero = 0; for (i = 1; i <= fNpar; ++i) { mnrn15(rno, izero); rno = rno*2 - 1; fX[i-1] += rno*step*fWerr[i-1]; } mninex(fX); mnamin(); mnrset(0); return; //*-*- . . . . . . . . . . blank line L3300: Printf(" BLANK COMMAND IGNORED."); ierflg = 1; return; //*-* . . . . . . . . obsolete commands . . . . . . . . . . . . . . //*-*- . . . . . . . . . . covariance L3400: 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*"); ierflg = 3; return; //*-*- . . . . . . . . . . printout L3500: cneway = "SET PRInt "; goto L3100; //*-*- . . . . . . . . . . gradient L3600: cneway = "SET GRAd "; goto L3100; //*-*- . . . . . . . . . . matout L3700: cneway = "SHOW COVar"; goto L3100; //*-*- . . . . . . . . . error def L3800: cneway = "SET ERRdef"; goto L3100; //*-*- . . . . . . . . . . limits L3900: cneway = "SET LIMits"; goto L3100; //*-*- . . . . . . . . . . punch L4000: cneway = "SAVE "; //*-*- ....... come from obsolete commands L3100: Printf(" OBSOLETE COMMAND:%s PLEASE USE: %s",(const char*)fCword ,(const char*)cneway); fCword = cneway; if (fCword == "SAVE ") goto L1500; goto L700; //*-* . . . . . . . . . . . . . . . . . . } /* mnexcm_ */ //______________________________________________________________________________ void TMinuit::mnexin(Double_t *pint) { //*-*-*-*-*Transforms the external parameter values U to internal values*-*-* //*-* ============================================================= //*-* Transforms the external parameter values U to internal //*-* values in the dense array PINT. //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Double_t pinti; Int_t iint, iext; fLimset = kFALSE; for (iint = 1; iint <= fNpar; ++iint) { iext = fNexofi[iint-1]; mnpint(fU[iext-1], iext-1, pinti); pint[iint-1] = pinti; } } /* mnexin_ */ //______________________________________________________________________________ void TMinuit::mnfixp(Int_t iint1, Int_t &ierr) { //*-*-*-*-*-*-*Removes parameter IINT from the internal parameter list*-*-* //*-* ======================================================= //*-* and arranges the rest of the list to fill the hole. //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t yyover; Int_t kold, nold, ndex, knew, iext, i, j, m, n, lc, ik; //*-*- first see if it can be done ierr = 0; Int_t iint = iint1+1; if (iint > fNpar || iint <= 0) { ierr = 1; Printf(" MINUIT ERROR. ARGUMENT TO MNFIXP=%4d",iint); return; } iext = fNexofi[iint-1]; if (fNpfix >= fMaxpar) { ierr = 1; Printf(" MINUIT CANNOT FIX PARAMETER%4d MAXIMUM NUMBER THAT CAN BE FIXED IS %d",iext,fMaxpar); return; } //*-*- reduce number of variable parameters by one fNiofex[iext-1] = 0; nold = fNpar; --fNpar; //*-*- save values in case parameter is later restored ++fNpfix; fIpfix[fNpfix-1] = iext; lc = iint; fXs[fNpfix-1] = fX[lc-1]; fXts[fNpfix-1] = fXt[lc-1]; fDirins[fNpfix-1] = fWerr[lc-1]; fGrds[fNpfix-1] = fGrd[lc-1]; fG2s[fNpfix-1] = fG2[lc-1]; fGsteps[fNpfix-1] = fGstep[lc-1]; //*-*- shift values for other parameters to fill hole for (ik = iext + 1; ik <= fNu; ++ik) { if (fNiofex[ik-1] > 0) { lc = fNiofex[ik-1] - 1; fNiofex[ik-1] = lc; fNexofi[lc-1] = ik; fX[lc-1] = fX[lc]; fXt[lc-1] = fXt[lc]; fDirin[lc-1] = fDirin[lc]; fWerr[lc-1] = fWerr[lc]; fGrd[lc-1] = fGrd[lc]; fG2[lc-1] = fG2[lc]; fGstep[lc-1] = fGstep[lc]; } } if (fISW[1] <= 0) return; //*-*- remove one row and one column from variance matrix if (fNpar <= 0) return; for (i = 1; i <= nold; ++i) { m = TMath::Max(i,iint); n = TMath::Min(i,iint); ndex = m*(m-1) / 2 + n; fFIXPyy[i-1] = fVhmat[ndex-1]; } yyover = 1 / fFIXPyy[iint-1]; knew = 0; kold = 0; for (i = 1; i <= nold; ++i) { for (j = 1; j <= i; ++j) { ++kold; if (j == iint || i == iint) continue; ++knew; fVhmat[knew-1] = fVhmat[kold-1] - fFIXPyy[j-1]*fFIXPyy[i-1]*yyover; } } } /* mnfixp_ */ //______________________________________________________________________________ void TMinuit::mnfree(Int_t k) { //*-*-*-*Restores one or more fixed parameter(s) to variable status*-*-*-*-*-* //*-* ========================================================== //*-* Restores one or more fixed parameter(s) to variable status //*-* by inserting it into the internal parameter list at the //*-* appropriate place. //*-* //*-* K = 0 means restore all parameters //*-* K = 1 means restore the last parameter fixed //*-* K = -I means restore external parameter I (if possible) //*-* IQ = fix-location where internal parameters were stored //*-* IR = external number of parameter being restored //*-* IS = internal number of parameter being restored //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t grdv, xv, dirinv, g2v, gstepv, xtv; Int_t i, ipsav, ka, lc, ik, iq, ir, is; if (k > 1) { Printf(" CALL TO MNFREE IGNORED. ARGUMENT GREATER THAN ONE"); } if (fNpfix < 1) { Printf(" CALL TO MNFREE IGNORED. THERE ARE NO FIXED PARAMETERS"); } if (k == 1 || k == 0) goto L40; //*-*- release parameter with specified external number ka = abs(k); if (fNiofex[ka-1] == 0) goto L15; Printf(" IGNORED. PARAMETER SPECIFIED IS ALREADY VARIABLE."); return; L15: if (fNpfix < 1) goto L21; for (ik = 1; ik <= fNpfix; ++ik) { if (fIpfix[ik-1] == ka) goto L24; } L21: Printf(" PARAMETER%4d NOT FIXED. CANNOT BE RELEASED.",ka); return; L24: if (ik == fNpfix) goto L40; //*-*- move specified parameter to end of list ipsav = ka; xv = fXs[ik-1]; xtv = fXts[ik-1]; dirinv = fDirins[ik-1]; grdv = fGrds[ik-1]; g2v = fG2s[ik-1]; gstepv = fGsteps[ik-1]; for (i = ik + 1; i <= fNpfix; ++i) { fIpfix[i-2] = fIpfix[i-1]; fXs[i-2] = fXs[i-1]; fXts[i-2] = fXts[i-1]; fDirins[i-2] = fDirins[i-1]; fGrds[i-2] = fGrds[i-1]; fG2s[i-2] = fG2s[i-1]; fGsteps[i-2] = fGsteps[i-1]; } fIpfix[fNpfix-1] = ipsav; fXs[fNpfix-1] = xv; fXts[fNpfix-1] = xtv; fDirins[fNpfix-1] = dirinv; fGrds[fNpfix-1] = grdv; fG2s[fNpfix-1] = g2v; fGsteps[fNpfix-1] = gstepv; //*-*- restore last parameter in fixed list -- IPFIX(NPFIX) L40: if (fNpfix < 1) goto L300; ir = fIpfix[fNpfix-1]; is = 0; for (ik = fNu; ik >= ir; --ik) { if (fNiofex[ik-1] > 0) { lc = fNiofex[ik-1] + 1; is = lc - 1; fNiofex[ik-1] = lc; fNexofi[lc-1] = ik; fX[lc-1] = fX[lc-2]; fXt[lc-1] = fXt[lc-2]; fDirin[lc-1] = fDirin[lc-2]; fWerr[lc-1] = fWerr[lc-2]; fGrd[lc-1] = fGrd[lc-2]; fG2[lc-1] = fG2[lc-2]; fGstep[lc-1] = fGstep[lc-2]; } } ++fNpar; if (is == 0) is = fNpar; fNiofex[ir-1] = is; fNexofi[is-1] = ir; iq = fNpfix; fX[is-1] = fXs[iq-1]; fXt[is-1] = fXts[iq-1]; fDirin[is-1] = fDirins[iq-1]; fWerr[is-1] = fDirins[iq-1]; fGrd[is-1] = fGrds[iq-1]; fG2[is-1] = fG2s[iq-1]; fGstep[is-1] = fGsteps[iq-1]; --fNpfix; fISW[1] = 0; fDcovar = 1; if (fISW[4] - fItaur >= 1) { Printf(" PARAMETER%4d %s RESTORED TO VARIABLE.",ir, (const char*)fCpnam[ir-1]); } if (k == 0) goto L40; L300: //*-*- if different from internal, external values are taken mnexin(fX); } /* mnfree_ */ //______________________________________________________________________________ void TMinuit::mngrad() { //*-*-*-*-*-*-*-*-*-*Interprets the SET GRAD command*-*-*-*-*-*-*-*-*-*-*-*-* //*-* =============================== //*-* Called from MNSET //*-* Interprets the SET GRAD command, which informs MINUIT whether //*-* the first derivatives of FCN will be calculated by the user //*-* inside FCN. It can check the user derivative calculation //*-* by comparing it with a finite difference approximation. //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t fzero, err; Int_t i, nparx, lc, istsav; Bool_t lnone; static TString cwd = " "; fISW[2] = 1; nparx = fNpar; if (fWord7[0] > 0) goto L2000; //*-*- get user-calculated first derivatives from FCN for (i = 1; i <= fNu; ++i) { fGin[i-1] = fUndefi; } mninex(fX); Eval(nparx, fGin, fzero, fU, 2); ++fNfcn; mnderi(); for (i = 1; i <= fNpar; ++i) { fGRADgf[i-1] = fGrd[i-1]; } //*-*- get MINUIT-calculated first derivatives fISW[2] = 0; istsav = fIstrat; fIstrat = 2; mnhes1(); fIstrat = istsav; Printf(" CHECK OF GRADIENT CALCULATION IN FCN"); Printf(" PARAMETER G(IN FCN) G(MINUIT) DG(MINUIT) AGREEMENT"); fISW[2] = 1; lnone = kFALSE; for (lc = 1; lc <= fNpar; ++lc) { i = fNexofi[lc-1]; cwd = "GOOD"; err = fDgrd[lc-1]; if (TMath::Abs(fGRADgf[lc-1] - fGrd[lc-1]) > err) cwd = " BAD"; if (fGin[i-1] == fUndefi) { cwd = "NONE"; lnone = kTRUE; fGRADgf[lc-1] = 0; } if (cwd != "GOOD") fISW[2] = 0; Printf(" %5d %10s%12.4e%12.4e%12.4e %s",i ,(const char*)fCpnam[i-1] ,fGRADgf[lc-1],fGrd[lc-1],err,(const char*)cwd); } if (lnone) { Printf(" AGREEMENT=NONE MEANS FCN DID NOT CALCULATE THE DERIVATIVE"); } if (fISW[2] == 0) { Printf(" MINUIT DOES NOT ACCEPT DERIVATIVE CALCULATIONS BY FCN"); Printf(" TO FORCE ACCEPTANCE, ENTER *SET GRAD 1*"); } L2000: return; } /* mngrad_ */ //______________________________________________________________________________ void TMinuit::mnhelp(const char *command) { TString comd = command; mnhelp(comd); } //______________________________________________________________________________ void TMinuit::mnhelp(TString comd) { //*-*-*-*-*-*-*-*HELP routine for MINUIT interactive commands*-*-*-*-*-*-*-*-* //*-* ============================================ //*-* //*-* COMD ='*' or "" prints a global help for all commands //*-* COMD =Command_name: print detailed help for one command. //*-* Note that at least 3 characters must be given for the command //*-* name. //*-* //*-* Author: Rene Brun //*-* comments extracted from the MINUIT documentation file. //*-* //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* //*-*....................................................................... //*-* //*-* Global HELP: Summary of all commands //*-* ==================================== //*-* comd.ToUpper(); if( comd.Length() == 0 || comd[0] == '*' || comd[0] == '?' || comd[0] == 0 || comd=="HELP" ) { Printf(" ==>List of MINUIT Interactive commands:"); Printf(" CLEar Reset all parameter names and values undefined"); Printf(" CONtour Make contour map of the user function"); Printf(" EXIT Exit from Interactive Minuit"); Printf(" FIX Cause parameter(s) to remain constant"); Printf(" HESse Calculate the Hessian or error matrix."); Printf(" IMPROVE Search for a new minimum around current minimum"); Printf(" MIGrad Minimize by the method of Migrad"); Printf(" MINImize MIGRAD + SIMPLEX method if Migrad fails"); Printf(" MINOs Exact (non-linear) parameter error analysis"); Printf(" MNContour Calculate one MINOS function contour"); Printf(" PARameter Define or redefine new parameters and values"); Printf(" RELease Make previously FIXed parameters variable again"); Printf(" REStore Release last parameter fixed"); Printf(" SAVe Save current parameter values on a file"); Printf(" SCAn Scan the user function by varying parameters"); Printf(" SEEk Minimize by the method of Monte Carlo"); Printf(" SET Set various MINUIT constants or conditions"); Printf(" SHOw Show values of current constants or conditions"); Printf(" SIMplex Minimize by the method of Simplex"); goto L99; } //*-* __________________________________________________________________ //*-* //*-* -- Command CLEAR //*-* -- ============= //*-* if( !strncmp(comd.Data(),"CLE",3) ) { Printf(" ***>CLEAR"); Printf(" Resets all parameter names and values to undefined."); Printf(" Must normally be followed by a PARameters command or "); Printf(" equivalent, in order to define parameter values."); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command CONTOUR //*-* -- =============== //*-* . if( !strncmp(comd.Data(),"CON",3) ) { Printf(" ***>CONTOUR <par1> <par2> [devs] [ngrid]"); Printf(" Instructs Minuit to trace contour lines of the user function"); Printf(" with respect to the two parameters whose external numbers"); Printf(" are <par1> and <par2>."); Printf(" Other variable parameters of the function, if any, will have"); Printf(" their values fixed at the current values during the contour"); Printf(" tracing. The optional parameter [devs] (default value 2.)"); Printf(" gives the number of standard deviations in each parameter"); Printf(" which should lie entirely within the plotting area."); Printf(" Optional parameter [ngrid] (default value 25 unless page"); Printf(" size is too small) determines the resolution of the plot,"); Printf(" i.e. the number of rows and columns of the grid at which the"); Printf(" function will be evaluated. [See also MNContour.]"); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command END //*-* -- =========== //*-* . if( !strncmp(comd.Data(),"END",3) ) { Printf(" ***>END"); Printf(" Signals the end of a data block (i.e., the end of a fit),"); Printf(" and implies that execution should continue, because another"); Printf(" Data Block follows. A Data Block is a set of Minuit data"); Printf(" consisting of"); Printf(" (1) A Title,"); Printf(" (2) One or more Parameter Definitions,"); Printf(" (3) A blank line, and"); Printf(" (4) A set of Minuit Commands."); Printf(" The END command is used when more than one Data Block is to"); Printf(" be used with the same FCN function. It first causes Minuit"); Printf(" to issue a CALL FCN with IFLAG=3, in order to allow FCN to"); Printf(" perform any calculations associated with the final fitted"); Printf(" parameter values, unless a CALL FCN 3 command has already"); Printf(" been executed at the current FCN value."); goto L99; } //*-* __________________________________________________________________ //*-* . //*-* -- //*-* -- Command EXIT //*-* -- ============ if( !strncmp(comd.Data(),"EXI",3) ) { Printf(" ***>EXIT"); Printf(" Signals the end of execution."); Printf(" The EXIT command first causes Minuit to issue a CALL FCN"); Printf(" with IFLAG=3, to allow FCN to perform any calculations"); Printf(" associated with the final fitted parameter values, unless a"); Printf(" CALL FCN 3 command has already been executed."); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command FIX //*-* -- =========== //*-* . if( !strncmp(comd.Data(),"FIX",3) ) { Printf(" ***>FIX} <parno> [parno] ... [parno]"); Printf(" Causes parameter(s) <parno> to be removed from the list of"); Printf(" variable parameters, and their value(s) will remain constant"); Printf(" during subsequent minimizations, etc., until another command"); Printf(" changes their value(s) or status."); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command HESSE //*-* -- ============= //*-* . if( !strncmp(comd.Data(),"HES",3) ) { Printf(" ***>HESse [maxcalls]"); Printf(" Calculate, by finite differences, the Hessian or error matrix."); Printf(" That is, it calculates the full matrix of second derivatives"); Printf(" of the function with respect to the currently variable"); Printf(" parameters, and inverts it, printing out the resulting error"); Printf(" matrix. The optional argument [maxcalls] specifies the"); Printf(" (approximate) maximum number of function calls after which"); Printf(" the calculation will be stopped."); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command IMPROVE //*-* -- =============== //*-* . if( !strncmp(comd.Data(),"IMP",3) ) { Printf(" ***>IMPROVE [maxcalls]"); Printf(" If a previous minimization has converged, and the current"); Printf(" values of the parameters therefore correspond to a local"); Printf(" minimum of the function, this command requests a search for"); Printf(" additional distinct local minima."); Printf(" The optional argument [maxcalls] specifies the (approximate"); Printf(" maximum number of function calls after which the calculation"); Printf(" will be stopped."); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command MIGRAD //*-* -- ============== //*-* . if( !strncmp(comd.Data(),"MIG",3) ) { Printf(" ***>MIGrad [maxcalls] [tolerance]"); Printf(" Causes minimization of the function by the method of Migrad,"); Printf(" the most efficient and complete single method, recommended"); Printf(" for general functions (see also MINImize)."); Printf(" The minimization produces as a by-product the error matrix"); Printf(" of the parameters, which is usually reliable unless warning"); Printf(" messages are produced."); Printf(" The optional argument [maxcalls] specifies the (approximate)"); Printf(" maximum number of function calls after which the calculation"); Printf(" will be stopped even if it has not yet converged."); Printf(" The optional argument [tolerance] specifies required tolerance"); Printf(" on the function value at the minimum."); Printf(" The default tolerance is 0.1, and the minimization will stop"); Printf(" when the estimated vertical distance to the minimum (EDM) is"); Printf(" less than 0.001*[tolerance]*UP (see [SET ERRordef])."); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command MINIMIZE //*-* -- ================ //*-* . if( !strncmp(comd.Data(),"MINI",4) ) { Printf(" ***>MINImize [maxcalls] [tolerance]"); Printf(" Causes minimization of the function by the method of Migrad,"); Printf(" as does the MIGrad command, but switches to the SIMplex method"); Printf(" if Migrad fails to converge. Arguments are as for MIGrad."); Printf(" Note that command requires four characters to be unambiguous."); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command MINOS //*-* -- ============= //*-* . if( !strncmp(comd.Data(),"MIN0",4) ) { Printf(" ***>MINOs [maxcalls] [parno] [parno] ..."); Printf(" Causes a Minos error analysis to be performed on the parameters"); Printf(" whose numbers [parno] are specified. If none are specified,"); Printf(" Minos errors are calculated for all variable parameters."); Printf(" Minos errors may be expensive to calculate, but are very"); Printf(" reliable since they take account of non-linearities in the"); Printf(" problem as well as parameter correlations, and are in general"); Printf(" asymmetric."); Printf(" The optional argument [maxcalls] specifies the (approximate)"); Printf(" maximum number of function calls per parameter requested,"); Printf(" after which the calculation will stop for that parameter."); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command MNCONTOUR //*-* -- ================= //*-* . if( !strncmp(comd.Data(),"MNC",3) ) { Printf(" ***>MNContour <par1> <par2> [npts]"); Printf(" Calculates one function contour of FCN with respect to"); Printf(" parameters par1 and par2, with FCN minimized always with"); Printf(" respect to all other NPAR-2 variable parameters (if any)."); Printf(" Minuit will try to find npts points on the contour (default 20)"); Printf(" If only two parameters are variable at the time, it is not"); Printf(" necessary to specify their numbers. To calculate more than"); Printf(" one contour, it is necessary to SET ERRordef to the appropriate"); Printf(" value and issue the MNContour command for each contour."); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command PARAMETER //*-* -- ================= //*-* . if( !strncmp(comd.Data(),"PAR",3) ) { Printf(" ***>PARameters"); Printf(" followed by one or more parameter definitions."); Printf(" Parameter definitions are of the form:"); Printf(" <number> ''name'' <value> <step> [lolim] [uplim] "); Printf(" for example:"); Printf(" 3 ''K width'' 1.2 0.1"); Printf(" the last definition is followed by a blank line or a zero."); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command RELEASE //*-* -- =============== //*-* . if( !strncmp(comd.Data(),"REL",3) ) { Printf(" ***>RELease <parno> [parno] ... [parno]"); Printf(" If <parno> is the number of a previously variable parameter"); Printf(" which has been fixed by a command: FIX <parno>, then that"); Printf(" parameter will return to variable status. Otherwise a warning"); Printf(" message is printed and the command is ignored."); Printf(" Note that this command operates only on parameters which were"); Printf(" at one time variable and have been FIXed. It cannot make"); Printf(" constant parameters variable; that must be done by redefining"); Printf(" the parameter with a PARameters command."); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command RESTORE //*-* -- =============== //*-* . if( !strncmp(comd.Data(),"RES",3) ) { Printf(" ***>REStore [code]"); Printf(" If no [code] is specified, this command restores all previously"); Printf(" FIXed parameters to variable status. If [code]=1, then only"); Printf(" the last parameter FIXed is restored to variable status."); Printf(" If code is neither zero nor one, the command is ignored."); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command RETURN //*-* -- ============== //*-* . if( !strncmp(comd.Data(),"RET",3) ) { Printf(" ***>RETURN"); Printf(" Signals the end of a data block, and instructs Minuit to return"); Printf(" to the program which called it. The RETurn command first"); Printf(" causes Minuit to CALL FCN with IFLAG=3, in order to allow FCN"); Printf(" to perform any calculations associated with the final fitted"); Printf(" parameter values, unless a CALL FCN 3 command has already been"); Printf(" executed at the current FCN value."); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command SAVE //*-* -- ============ //*-* . if( !strncmp(comd.Data(),"SAV",3) ) { Printf(" ***>SAVe"); Printf(" Causes the current parameter values to be saved on a file in"); Printf(" such a format that they can be read in again as Minuit"); Printf(" parameter definitions. If the covariance matrix exists, it is"); Printf(" also output in such a format. The unit number is by default 7,"); Printf(" or that specified by the user in his call to MINTIO or"); Printf(" MNINIT. The user is responsible for opening the file previous"); Printf(" to issuing the [SAVe] command (except where this can be done"); Printf(" interactively)."); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command SCAN //*-* -- ============ //*-* . if( !strncmp(comd.Data(),"SCA",3) ) { Printf(" ***>SCAn [parno] [numpts] [from] [to]"); Printf(" Scans the value of the user function by varying parameter"); Printf(" number [parno], leaving all other parameters fixed at the"); Printf(" current value. If [parno] is not specified, all variable"); Printf(" parameters are scanned in sequence."); Printf(" The number of points [numpts] in the scan is 40 by default,"); Printf(" and cannot exceed 100. The range of the scan is by default"); Printf(" 2 standard deviations on each side of the current best value,"); Printf(" but can be specified as from [from] to [to]."); Printf(" After each scan, if a new minimum is found, the best parameter"); Printf(" values are retained as start values for future scans or"); Printf(" minimizations. The curve resulting from each scan is plotted"); Printf(" on the output unit in order to show the approximate behaviour"); Printf(" of the function."); Printf(" This command is not intended for minimization, but is sometimes"); Printf(" useful for debugging the user function or finding a"); Printf(" reasonable starting point."); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command SEEK //*-* -- ============ //*-* . if( !strncmp(comd.Data(),"SEE",3) ) { Printf(" ***>SEEk [maxcalls] [devs]"); Printf(" Causes a Monte Carlo minimization of the function, by choosing"); Printf(" random values of the variable parameters, chosen uniformly"); Printf(" over a hypercube centered at the current best value."); Printf(" The region size is by default 3 standard deviations on each"); Printf(" side, but can be changed by specifying the value of [devs]."); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command SET //*-* -- =========== //*-* . if( !strncmp(comd.Data(),"SET",3) ) { Printf(" ***>SET <option_name>"); Printf(" SET BATch"); Printf(" Informs Minuit that it is running in batch mode."); Printf(" "); Printf(" SET EPSmachine <accuracy>"); Printf(" Informs Minuit that the relative floating point arithmetic"); Printf(" precision is <accuracy>. Minuit determines the nominal"); Printf(" precision itself, but the SET EPSmachine command can be"); Printf(" used to override Minuit own determination, when the user"); Printf(" knows that the FCN function value is not calculated to"); Printf(" the nominal machine accuracy. Typical values of <accuracy>"); Printf(" are between 10**-5 and 10**-14."); Printf(" "); Printf(" SET ERRordef <up>"); Printf(" Sets the value of UP (default value= 1.), defining parameter"); Printf(" errors. Minuit defines parameter errors as the change"); Printf(" in parameter value required to change the function value"); Printf(" by UP. Normally, for chisquared fits UP=1, and for negative"); Printf(" log likelihood, UP=0.5."); Printf(" "); Printf(" SET GRAdient [force]"); Printf(" Informs Minuit that the user function is prepared to"); Printf(" calculate its own first derivatives and return their values"); Printf(" in the array GRAD when IFLAG=2 (see specs of FCN)."); Printf(" If [force] is not specified, Minuit will calculate"); Printf(" the FCN derivatives by finite differences at the current"); Printf(" point and compare with the user calculation at that point,"); Printf(" accepting the user values only if they agree."); Printf(" If [force]=1, Minuit does not do its own derivative"); Printf(" calculation, and uses the derivatives calculated in FCN."); Printf(" "); Printf(" SET INPut [unitno] [filename]"); Printf(" Causes Minuit, in data-driven mode only, to read subsequent"); Printf(" commands (or parameter definitions) from a different input"); Printf(" file. If no [unitno] is specified, reading reverts to the"); Printf(" previous input file, assuming that there was one."); Printf(" If [unitno] is specified, and that unit has not been opened,"); Printf(" then Minuit attempts to open the file [filename]} if a"); Printf(" name is specified. If running in interactive mode and"); Printf(" [filename] is not specified and [unitno] is not opened,"); Printf(" Minuit prompts the user to enter a file name."); Printf(" If the word REWIND is added to the command (note:no blanks"); Printf(" between INPUT and REWIND), the file is rewound before"); Printf(" reading. Note that this command is implemented in standard"); Printf(" Fortran 77 and the results may depend on the system;"); Printf(" for example, if a filename is given under VM/CMS, it must"); Printf(" be preceeded by a slash."); Printf(" "); Printf(" SET INTeractive"); Printf(" Informs Minuit that it is running interactively."); Printf(" "); Printf(" SET LIMits [parno] [lolim] [uplim]"); Printf(" Allows the user to change the limits on one or all"); Printf(" parameters. If no arguments are specified, all limits are"); Printf(" removed from all parameters. If [parno] alone is specified,"); Printf(" limits are removed from parameter [parno]."); Printf(" If all arguments are specified, then parameter [parno] will"); Printf(" be bounded between [lolim] and [uplim]."); Printf(" Limits can be specified in either order, Minuit will take"); Printf(" the smaller as [lolim] and the larger as [uplim]."); Printf(" However, if [lolim] is equal to [uplim], an error condition"); Printf(" results."); Printf(" "); Printf(" SET LINesperpage"); Printf(" Sets the number of lines for one page of output."); Printf(" Default value is 24 for interactive mode"); Printf(" "); Printf(" SET NOGradient"); Printf(" The inverse of SET GRAdient, instructs Minuit not to"); Printf(" use the first derivatives calculated by the user in FCN."); Printf(" "); Printf(" SET NOWarnings"); Printf(" Supresses Minuit warning messages."); Printf(" "); Printf(" SET OUTputfile <unitno>"); Printf(" Instructs Minuit to write further output to unit <unitno>."); Printf(" "); Printf(" SET PAGethrow <integer>"); Printf(" Sets the carriage control character for ``new page'' to"); Printf(" <integer>. Thus the value 1 produces a new page, and 0"); Printf(" produces a blank line, on some devices (see TOPofpage)"); Printf(" "); Printf(" SET PARameter <parno> <value>"); Printf(" Sets the value of parameter <parno> to <value>."); Printf(" The parameter in question may be variable, fixed, or"); Printf(" constant, but must be defined."); Printf(" "); Printf(" SET PRIntout <level>"); Printf(" Sets the print level, determining how much output will be"); Printf(" produced. Allowed values and their meanings are displayed"); Printf(" after a SHOw PRInt command, and are currently <level>=:"); Printf(" [-1] no output except from SHOW commands"); Printf(" [0] minimum output"); Printf(" [1] default value, normal output"); Printf(" [2] additional output giving intermediate results."); Printf(" [3] maximum output, showing progress of minimizations."); Printf(" Note: See also the SET WARnings command."); Printf(" "); Printf(" SET RANdomgenerator <seed>"); Printf(" Sets the seed of the random number generator used in SEEk."); Printf(" This can be any integer between 10000 and 900000000, for"); Printf(" example one which was output from a SHOw RANdom command of"); Printf(" a previous run."); Printf(" "); Printf(" SET STRategy <level>"); Printf(" Sets the strategy to be used in calculating first and second"); Printf(" derivatives and in certain minimization methods."); Printf(" In general, low values of <level> mean fewer function calls"); Printf(" and high values mean more reliable minimization."); Printf(" Currently allowed values are 0, 1 (default), and 2."); Printf(" "); Printf(" SET TITle"); Printf(" Informs Minuit that the next input line is to be considered"); Printf(" the (new) title for this task or sub-task. This is for"); Printf(" the convenience of the user in reading his output."); Printf(" "); Printf(" SET WARnings"); Printf(" Instructs Minuit to output warning messages when suspicious"); Printf(" conditions arise which may indicate unreliable results."); Printf(" This is the default."); Printf(" "); Printf(" SET WIDthpage"); Printf(" Informs Minuit of the output page width."); Printf(" Default values are 80 for interactive jobs"); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command SHOW //*-* -- ============ //*-* . if( !strncmp(comd.Data(),"SHO",3) ) { Printf(" ***>SHOw <option_name>"); Printf(" All SET XXXX commands have a corresponding SHOw XXXX command."); Printf(" In addition, the SHOw commands listed starting here have no"); Printf(" corresponding SET command for obvious reasons."); Printf(" "); Printf(" SHOw CORrelations"); Printf(" Calculates and prints the parameter correlations from the"); Printf(" error matrix."); Printf(" "); Printf(" SHOw COVariance"); Printf(" Prints the (external) covariance (error) matrix."); Printf(" "); Printf(" SHOw EIGenvalues"); Printf(" Calculates and prints the eigenvalues of the covariance"); Printf(" matrix."); Printf(" "); Printf(" SHOw FCNvalue"); Printf(" Prints the current value of FCN."); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command SIMPLEX //*-* -- =============== //*-* . if( !strncmp(comd.Data(),"SIM",3) ) { Printf(" ***>SIMplex [maxcalls] [tolerance]"); Printf(" Performs a function minimization using the simplex method of"); Printf(" Nelder and Mead. Minimization terminates either when the"); Printf(" function has been called (approximately) [maxcalls] times,"); Printf(" or when the estimated vertical distance to minimum (EDM) is"); Printf(" less than [tolerance]."); Printf(" The default value of [tolerance] is 0.1*UP(see SET ERRordef)."); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command STANDARD //*-* -- ================ //*-* . if( !strncmp(comd.Data(),"STA",3) ) { Printf(" ***>STAndard"); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command STOP //*-* -- ============ //*-* . if( !strncmp(comd.Data(),"STO",3) ) { Printf(" ***>STOP"); Printf(" Same as EXIT."); goto L99; } //*-* __________________________________________________________________ //*-* -- //*-* -- Command TOPOFPAGE //*-* -- ================= //*-* . if( !strncmp(comd.Data(),"TOP",3) ) { Printf(" ***>TOPofpage"); Printf(" Causes Minuit to write the character specified in a"); Printf(" SET PAGethrow command (default = 1) to column 1 of the output"); Printf(" file, which may or may not position your output medium to"); Printf(" the top of a page depending on the device and system."); goto L99; } //*-* __________________________________________________________________ Printf(" Unknown MINUIT command. Type HELP for list of commands."); L99: return; } /* mnhelp_ */ //______________________________________________________________________________ void TMinuit::mnhess() { //*-*-*-*-*-*Calculates the full second-derivative matrix of FCN*-*-*-*-*-*-*-* //*-* =================================================== //*-* by taking finite differences. When calculating diagonal //*-* elements, it may iterate so that step size is nearly that //*-* which gives function change= UP/10. The first derivatives //*-* of course come as a free side effect, but with a smaller //*-* step size in order to obtain a known accuracy. //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t dmin_, dxdi, elem, wint, tlrg2, d, dlast, ztemp, g2bfor; Double_t df, aimsag, fs1, tlrstp, fs2, stpinm, g2i, sag=0, xtf, xti, xtj; Int_t icyc, ncyc, ndex, idrv, iext, npar2, i, j, ifail, npard, nparx, id, multpy; Bool_t ldebug; ldebug = fIdbg[3] >= 1; if (fAmin == fUndefi) { mnamin(); } if (fIstrat <= 0) { ncyc = 3; tlrstp = .5; tlrg2 = .1; } else if (fIstrat == 1) { ncyc = 5; tlrstp = .3; tlrg2 = .05; } else { ncyc = 7; tlrstp = .1; tlrg2 = .02; } if (fISW[4] >= 2 || ldebug) { Printf(" START COVARIANCE MATRIX CALCULATION."); } fCfrom = "HESSE "; fNfcnfr = fNfcn; fCstatu = "OK "; npard = fNpar; //*-*- make sure starting at the right place mninex(fX); nparx = fNpar; Eval(nparx, fGin, fs1, fU, 4); ++fNfcn; if (fs1 != fAmin) { df = fAmin - fs1; mnwarn("D", "MNHESS", Form("function value differs from AMIN by %g",df)); } fAmin = fs1; if (ldebug) { Printf(" PAR D GSTEP D G2 GRD SAG "); } //*-*- . . . . . . diagonal elements . //*-*- ISW(2) = 1 if approx, 2 if not posdef, 3 if ok //*-*- AIMSAG is the sagitta we are aiming for in second deriv calc. aimsag = TMath::Sqrt(fEpsma2)*(TMath::Abs(fAmin) + fUp); //*-*- Zero the second derivative matrix npar2 = fNpar*(fNpar + 1) / 2; for (i = 1; i <= npar2; ++i) { fVhmat[i-1] = 0; } //*-*- Loop over variable parameters for second derivatives idrv = 2; for (id = 1; id <= npard; ++id) { i = id + fNpar - npard; iext = fNexofi[i-1]; if (fG2[i-1] == 0) { mnwarn("W", "HESSE", Form("Second derivative enters zero, param %d",iext)); wint = fWerr[i-1]; if (fNvarl[iext-1] > 1) { mndxdi(fX[i-1], i-1, dxdi); if (TMath::Abs(dxdi) < .001) wint = .01; else wint /= TMath::Abs(dxdi); } fG2[i-1] = fUp / (wint*wint); } xtf = fX[i-1]; dmin_ = fEpsma2*8*TMath::Abs(xtf); //*-*- find step which gives sagitta = AIMSAG d = TMath::Abs(fGstep[i-1]); int skip50 = 0; for (icyc = 1; icyc <= ncyc; ++icyc) { //*-*- loop here only if SAG=0 for (multpy = 1; multpy <= 5; ++multpy) { //*-*- take two steps fX[i-1] = xtf + d; mninex(fX); nparx = fNpar; Eval(nparx, fGin, fs1, fU, 4); ++fNfcn; fX[i-1] = xtf - d; mninex(fX); Eval(nparx, fGin, fs2, fU, 4); ++fNfcn; fX[i-1] = xtf; sag = (fs1 + fs2 - fAmin*2)*.5; if (sag != 0) goto L30; if (fGstep[i-1] < 0) { if (d >= .5) goto L26; d *= 10; if (d > .5) d = .51; continue; } d *= 10; } L26: mnwarn("W", "HESSE", Form("Second derivative zero for parameter%d",iext)); goto L390; //*-*- SAG is not zero L30: g2bfor = fG2[i-1]; fG2[i-1] = sag*2 / (d*d); fGrd[i-1] = (fs1 - fs2) / (d*2); if (ldebug) { Printf("%4d%2d%12.5g%12.5g%12.5g%12.5g%12.5g%12.5g",i,idrv,fGstep[i-1],fG2[i-1],fGrd[i-1],sag); } if (fGstep[i-1] > 0) fGstep[i-1] = TMath::Abs(d); else fGstep[i-1] = -TMath::Abs(d); fDirin[i-1] = d; fHESSyy[i-1]= fs1; dlast = d; d = TMath::Sqrt(aimsag*2 / TMath::Abs(fG2[i-1])); //*-*- if parameter has limits, max int step size = 0.5 stpinm = .5; if (fGstep[i-1] < 0) d = TMath::Min(d,stpinm); if (d < dmin_) d = dmin_; //*-*- see if converged if (TMath::Abs((d - dlast) / d) < tlrstp || TMath::Abs((fG2[i-1] - g2bfor) / fG2[i-1]) < tlrg2) { skip50 = 1; break; } d = TMath::Min(d,dlast*102); d = TMath::Max(d,dlast*.1); } //*-*- end of step size loop if (!skip50) mnwarn("D", "MNHESS", Form("Second Deriv. SAG,AIM= %d%g%g",iext,sag,aimsag)); ndex = i*(i + 1) / 2; fVhmat[ndex-1] = fG2[i-1]; } //*-*- end of diagonal second derivative loop mninex(fX); //*-*- refine the first derivatives if (fIstrat > 0) mnhes1(); fISW[1] = 3; fDcovar = 0; //*-*- . . . . off-diagonal elements if (fNpar == 1) goto L214; for (i = 1; i <= fNpar; ++i) { for (j = 1; j <= i-1; ++j) { xti = fX[i-1]; xtj = fX[j-1]; fX[i-1] = xti + fDirin[i-1]; fX[j-1] = xtj + fDirin[j-1]; mninex(fX); Eval(nparx, fGin, fs1, fU, 4); ++fNfcn; fX[i-1] = xti; fX[j-1] = xtj; elem = (fs1 + fAmin - fHESSyy[i-1] - fHESSyy[j-1]) / ( fDirin[i-1]*fDirin[j-1]); ndex = i*(i-1) / 2 + j; fVhmat[ndex-1] = elem; } } L214: mninex(fX); //*-*- verify matrix positive-definite mnpsdf(); for (i = 1; i <= fNpar; ++i) { for (j = 1; j <= i; ++j) { ndex = i*(i-1) / 2 + j; fP[i + j*fMaxpar - fMaxpar-1] = fVhmat[ndex-1]; fP[j + i*fMaxpar - fMaxpar-1] = fP[i + j*fMaxpar - fMaxpar-1]; } } mnvert(fP, fMaxint, fMaxint, fNpar, ifail); if (ifail > 0) { mnwarn("W", "HESSE", "Matrix inversion fails."); goto L390; } //*-*- . . . . . . . calculate e d m fEDM = 0; for (i = 1; i <= fNpar; ++i) { //*-*- off-diagonal elements ndex = i*(i-1) / 2; for (j = 1; j <= i-1; ++j) { ++ndex; ztemp = fP[i + j*fMaxpar - fMaxpar-1]*2; fEDM += fGrd[i-1]*ztemp*fGrd[j-1]; fVhmat[ndex-1] = ztemp; } //*-*- diagonal elements ++ndex; fVhmat[ndex-1] = fP[i + i*fMaxpar - fMaxpar-1]*2; fEDM += fP[i + i*fMaxpar - fMaxpar-1]*(fGrd[i-1]*fGrd[i-1]); } if (fISW[4] >= 1 && fISW[1] == 3 && fItaur == 0) { Printf(" COVARIANCE MATRIX CALCULATED SUCCESSFULLY"); } goto L900; //*-*- failure to invert 2nd deriv matrix L390: fISW[1] = 1; fDcovar = 1; fCstatu = "FAILED "; if (fISW[4] >= 0) { Printf(" MNHESS FAILS AND WILL RETURN DIAGONAL MATRIX. "); } for (i = 1; i <= fNpar; ++i) { ndex = i*(i-1) / 2; for (j = 1; j <= i-1; ++j) { ++ndex; fVhmat[ndex-1] = 0; } ++ndex; g2i = fG2[i-1]; if (g2i <= 0) g2i = 1; fVhmat[ndex-1] = 2 / g2i; } L900: return; } /* mnhess_ */ //______________________________________________________________________________ void TMinuit::mnhes1() { //*-*-*-*Calculate first derivatives (GRD) and uncertainties (DGRD)*-*-*-*-*-* //*-* ========================================================== //*-* and appropriate step sizes GSTEP //*-* Called from MNHESS and MNGRAD //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t dmin_, d, dfmin, dgmin=0, change, chgold, grdold=0, epspri; Double_t fs1, optstp, fs2, grdnew=0, sag, xtf; Int_t icyc, ncyc=0, idrv, i, nparx; Bool_t ldebug; ldebug = fIdbg[5] >= 1; if (fIstrat <= 0) ncyc = 1; if (fIstrat == 1) ncyc = 2; if (fIstrat > 1) ncyc = 6; idrv = 1; nparx = fNpar; dfmin = fEpsma2*4*(TMath::Abs(fAmin) + fUp); //*-*- main loop over parameters for (i = 1; i <= fNpar; ++i) { xtf = fX[i-1]; dmin_ = fEpsma2*4*TMath::Abs(xtf); epspri = fEpsma2 + TMath::Abs(fGrd[i-1]*fEpsma2); optstp = TMath::Sqrt(dfmin / (TMath::Abs(fG2[i-1]) + epspri)); d = TMath::Abs(fGstep[i-1])*.2; if (d > optstp) d = optstp; if (d < dmin_) d = dmin_; chgold = 1e4; //*-*- iterate reducing step size for (icyc = 1; icyc <= ncyc; ++icyc) { fX[i-1] = xtf + d; mninex(fX); Eval(nparx, fGin, fs1, fU, 4); ++fNfcn; fX[i-1] = xtf - d; mninex(fX); Eval(nparx, fGin, fs2, fU, 4); ++fNfcn; fX[i-1] = xtf; //*-*- check if step sizes appropriate sag = (fs1 + fs2 - fAmin*2)*.5; grdold = fGrd[i-1]; grdnew = (fs1 - fs2) / (d*2); dgmin = fEpsmac*(TMath::Abs(fs1) + TMath::Abs(fs2)) / d; if (ldebug) { Printf("%4d%2d%12.5g%12.5g%12.5g%12.5g%12.5g%12.5g",i,idrv,fGstep[i-1],d,fG2[i-1],grdnew,sag); } if (grdnew == 0) goto L60; change = TMath::Abs((grdold - grdnew) / grdnew); if (change > chgold && icyc > 1) goto L60; chgold = change; fGrd[i-1] = grdnew; if (fGstep[i-1] > 0) fGstep[i-1] = TMath::Abs(d); else fGstep[i-1] = -TMath::Abs(d); //*-*- decrease step until first derivative changes by <5% if (change < .05) goto L60; if (TMath::Abs(grdold - grdnew) < dgmin) goto L60; if (d < dmin_) { mnwarn("D", "MNHES1", "Step size too small for 1st drv."); goto L60; } d *= .2; } //*-*- loop satisfied = too many iter mnwarn("D", "MNHES1", Form("Too many iterations on D1.%g%g",grdold,grdnew)); L60: fDgrd[i-1] = TMath::Max(dgmin,TMath::Abs(grdold - grdnew)); } //*-*- end of first deriv. loop mninex(fX); } /* mnhes1_ */ //______________________________________________________________________________ void TMinuit::mnimpr() { //*-*-*-*-*-*-*Attempts to improve on a good local minimum*-*-*-*-*-*-*-*-*-* //*-* =========================================== //*-* Attempts to improve on a good local minimum by finding a //*-* better one. The quadratic part of FCN is removed by MNCALF //*-* and this transformed function is minimized using the simplex //*-* method from several random starting points. //*-* ref. -- Goldstein and Price, Math.Comp. 25, 569 (1971) //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Initialized data */ static Double_t rnum = 0; /* Local variables */ Double_t amax, ycalf, ystar, ystst; Double_t pb, ep, wg, xi, sigsav, reg, sig2; Int_t npfn, ndex, loop=0, i, j, ifail, iseed; Int_t jhold, nloop, nparx, nparp1, jh, jl, iswtr; if (fNpar <= 0) return; if (fAmin == fUndefi) mnamin(); fCstatu = "UNCHANGED "; fItaur = 1; fEpsi = fUp*.1; npfn = fNfcn; nloop = Int_t(fWord7[1]); if (nloop <= 0) nloop = fNpar + 4; nparx = fNpar; nparp1 = fNpar + 1; wg = 1 / Double_t(fNpar); sigsav = fEDM; fApsi = fAmin; iswtr = fISW[4] - 2*fItaur; for (i = 1; i <= fNpar; ++i) { fXt[i-1] = fX[i-1]; fIMPRdsav[i-1] = fWerr[i-1]; for (j = 1; j <= i; ++j) { ndex = i*(i-1) / 2 + j; fP[i + j*fMaxpar - fMaxpar-1] = fVhmat[ndex-1]; fP[j + i*fMaxpar - fMaxpar-1] = fP[i + j*fMaxpar - fMaxpar-1]; } } mnvert(fP, fMaxint, fMaxint, fNpar, ifail); if (ifail >= 1) goto L280; //*-*- Save inverted matrix in VT for (i = 1; i <= fNpar; ++i) { ndex = i*(i-1) / 2; for (j = 1; j <= i; ++j) { ++ndex; fVthmat[ndex-1] = fP[i + j*fMaxpar - fMaxpar-1]; } } loop = 0; L20: for (i = 1; i <= fNpar; ++i) { fDirin[i-1] = fIMPRdsav[i-1]*2; mnrn15(rnum, iseed); fX[i-1] = fXt[i-1] + fDirin[i-1]*2*(rnum - .5); } ++loop; reg = 2; if (fISW[4] >= 0) { Printf("START ATTEMPT NO.%2d TO FIND NEW MINIMUM",loop); } L30: mncalf(fX, ycalf); fAmin = ycalf; //*-*- . . . . set up random simplex jl = nparp1; jh = nparp1; fIMPRy[nparp1-1] = fAmin; amax = fAmin; for (i = 1; i <= fNpar; ++i) { xi = fX[i-1]; mnrn15(rnum, iseed); fX[i-1] = xi - fDirin[i-1]*(rnum - .5); mncalf(fX, ycalf); fIMPRy[i-1] = ycalf; if (fIMPRy[i-1] < fAmin) { fAmin = fIMPRy[i-1]; jl = i; } else if (fIMPRy[i-1] > amax) { amax = fIMPRy[i-1]; jh = i; } for (j = 1; j <= fNpar; ++j) { fP[j + i*fMaxpar - fMaxpar-1] = fX[j-1]; } fP[i + nparp1*fMaxpar - fMaxpar-1] = xi; fX[i-1] = xi; } fEDM = fAmin; sig2 = fEDM; //*-*- . . . . . . . start main loop L50: if (fAmin < 0) goto L95; if (fISW[1] <= 2) goto L280; ep = fAmin*.1; if (sig2 < ep && fEDM < ep) goto L100; sig2 = fEDM; if (fNfcn - npfn > fNfcnmx) goto L300; //*-*- calculate new point * by reflection for (i = 1; i <= fNpar; ++i) { pb = 0; for (j = 1; j <= nparp1; ++j) { pb += wg*fP[i + j*fMaxpar - fMaxpar-1]; } fPbar[i-1] = pb - wg*fP[i + jh*fMaxpar - fMaxpar-1]; fPstar[i-1] = fPbar[i-1]*2 - fP[i + jh*fMaxpar - fMaxpar-1]*1; } mncalf(fPstar, ycalf); ystar = ycalf; if (ystar >= fAmin) goto L70; //*-*- point * better than jl, calculate new point ** for (i = 1; i <= fNpar; ++i) { fPstst[i-1] = fPstar[i-1]*2 + fPbar[i- 1]*-1; } mncalf(fPstst, ycalf); ystst = ycalf; if (ystst < fIMPRy[jl-1]) goto L67; mnrazz(ystar, fPstar, fIMPRy, jh, jl); goto L50; L67: mnrazz(ystst, fPstst, fIMPRy, jh, jl); goto L50; //*-*- point * is not as good as jl L70: if (ystar >= fIMPRy[jh-1]) goto L73; jhold = jh; mnrazz(ystar, fPstar, fIMPRy, jh, jl); if (jhold != jh) goto L50; //*-*- calculate new point ** L73: for (i = 1; i <= fNpar; ++i) { fPstst[i-1] = fP[i + jh*fMaxpar - fMaxpar-1]*.5 + fPbar[i-1]*.5; } mncalf(fPstst, ycalf); ystst = ycalf; if (ystst > fIMPRy[jh-1]) goto L30; //*-*- point ** is better than jh if (ystst < fAmin) goto L67; mnrazz(ystst, fPstst, fIMPRy, jh, jl); goto L50; //*-*- . . . . . . end main loop L95: if (fISW[4] >= 0) { Printf(" AN IMPROVEMENT ON THE PREVIOUS MINIMUM HAS BEEN FOUND"); } reg = .1; //*-*- . . . . . ask if point is new L100: mninex(fX); Eval(nparx, fGin, fAmin, fU, 4); ++fNfcn; for (i = 1; i <= fNpar; ++i) { fDirin[i-1] = reg*fIMPRdsav[i-1]; if (TMath::Abs(fX[i-1] - fXt[i-1]) > fDirin[i-1]) goto L150; } goto L230; L150: fNfcnmx = fNfcnmx + npfn - fNfcn; npfn = fNfcn; mnsimp(); if (fAmin >= fApsi) goto L325; for (i = 1; i <= fNpar; ++i) { fDirin[i-1] = fIMPRdsav[i-1]*.1; if (TMath::Abs(fX[i-1] - fXt[i-1]) > fDirin[i-1]) goto L250; } L230: if (fAmin < fApsi) goto L350; goto L325; /* . . . . . . truly new minimum */ L250: fLnewmn = kTRUE; if (fISW[1] >= 1) { fISW[1] = 1; fDcovar = TMath::Max(fDcovar,.5); } else fDcovar = 1; fItaur = 0; fNfcnmx = fNfcnmx + npfn - fNfcn; fCstatu = "NEW MINIMU"; if (fISW[4] >= 0) { Printf(" IMPROVE HAS FOUND A TRULY NEW MINIMUM"); Printf(" *************************************"); } return; //*-*- . . . return to previous region L280: if (fISW[4] > 0) { Printf(" COVARIANCE MATRIX WAS NOT POSITIVE-DEFINITE"); } goto L325; L300: fISW[0] = 1; L325: for (i = 1; i <= fNpar; ++i) { fDirin[i-1] = fIMPRdsav[i-1]*.01; fX[i-1] = fXt[i-1]; } fAmin = fApsi; fEDM = sigsav; L350: mninex(fX); if (fISW[4] > 0) { Printf(" IMPROVE HAS RETURNED TO REGION OF ORIGINAL MINIMUM"); } fCstatu = "UNCHANGED "; mnrset(0); if (fISW[1] < 2) goto L380; if (loop < nloop && fISW[0] < 1) goto L20; L380: if (iswtr >= 0) mnprin(5, fAmin); fItaur = 0; } /* mnimpr_ */ //______________________________________________________________________________ void TMinuit::mninex(Double_t *pint) { //*-*-*-*-*Transforms from internal coordinates (PINT) to external (U)*-*-*-* //*-* =========================================================== //*-* The minimizing routines which work in //*-* internal coordinates call this routine before calling FCN. //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Int_t i, j; for (j = 1; j <= fNpar; ++j) { i = fNexofi[j-1]; if (fNvarl[i-1] == 1) { fU[i-1] = pint[j-1]; } else { fU[i-1] = fAlim[i-1] + (TMath::Sin(pint[j-1]) + 1)*.5*(fBlim[i-1] - fAlim[i-1]); } } } /* mninex_ */ //______________________________________________________________________________ void TMinuit::mninit(Int_t i1, Int_t i2, Int_t i3) { //*-*-*-*-*-*Main initialization member function for MINUIT*-*-*-*-*-*-*-*-* //*-* ============================================== //*-* It initializes some constants //*-* (including the logical I/O unit nos.), //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t piby2, epsp1, epsbak, epstry, distnn; Int_t i, idb; //*-*- I/O unit numbers fIsysrd = i1; fIsyswr = i2; fIstkwr[0] = fIsyswr; fNstkwr = 1; fIsyssa = i3; fNstkrd = 0; //*-*- version identifier fCvrsn = "95.03++ "; //*-*- some CONSTANT fMaxint = fMaxpar; fMaxext = 2*fMaxpar; fUndefi = -54321; fBigedm = 123456; fCundef = ")UNDEFINED"; fCovmes[0] = "NO ERROR MATRIX "; fCovmes[1] = "ERR MATRIX APPROXIMATE"; fCovmes[2] = "ERR MATRIX NOT POS-DEF"; fCovmes[3] = "ERROR MATRIX ACCURATE "; //*-*- some starting values fNblock = 0; fIcomnd = 0; fCtitl = fCundef; fCfrom = "INPUT "; fNfcn = 0; fNfcnfr = fNfcn; fCstatu = "INITIALIZE"; fISW[2] = 0; fISW[3] = 0; fISW[4] = 1; //*-*- ISW(6)=0 for batch jobs, =1 for interactive jobs //*-*- =-1 for originally interactive temporarily batch fISW[5] = 0; // if (intrac(&dummy)) fISW[5] = 1; //*-*- DEBUG options set to default values for (idb = 0; idb <= 10; ++idb) { fIdbg[idb] = 0; } fLrepor = kFALSE; fLwarn = kTRUE; fLimset = kFALSE; fLnewmn = kFALSE; fIstrat = 1; fItaur = 0; //*-*- default page dimensions and 'new page' carriage control integer fNpagwd = 120; fNpagln = 56; fNewpag = 1; if (fISW[5] > 0) { fNpagwd = 80; fNpagln = 30; fNewpag = 0; } fUp = 1; fUpdflt = fUp; //*-*- determine machine accuracy epsmac epstry = .5; for (i = 1; i <= 100; ++i) { epstry *= .5; epsp1 = epstry + 1; mntiny(epsp1, epsbak); if (epsbak < epstry) goto L35; } epstry = 1e-7; fEpsmac = epstry*4; Printf(" MNINIT UNABLE TO DETERMINE ARITHMETIC PRECISION. WILL ASSUME:%g",fEpsmac); L35: fEpsmac = epstry*8; fEpsma2 = TMath::Sqrt(fEpsmac)*2; //*-*- the vlims are a non-negligible distance from pi/2 //*-*- used by MNPINT to set variables "near" the physical limits piby2 = TMath::ATan(1)*2; distnn = TMath::Sqrt(fEpsma2)*8; fVlimhi = piby2 - distnn; fVlimlo = -piby2 + distnn; mncler(); // Printf(" MINUIT RELEASE %s INITIALIZED. DIMENSIONS 100/50 EPSMAC=%g",(const char*)fCvrsn,fEpsmac); } /* mninit_ */ //______________________________________________________________________________ void TMinuit::mnlims() { //*-*-*-*Interprets the SET LIM command, to reset the parameter limits*-*-*-* //*-* ============================================================= //*-* Called from MNSET //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t dxdi, snew; Int_t kint, i2, newcod, ifx=0, inu; fCfrom = "SET LIM "; fNfcnfr = fNfcn; fCstatu = "NO CHANGE "; i2 = Int_t(fWord7[0]); if (i2 > fMaxext || i2 < 0) goto L900; if (i2 > 0) goto L30; //*-*- set limits on all parameters newcod = 4; if (fWord7[1] == fWord7[2]) newcod = 1; for (inu = 1; inu <= fNu; ++inu) { if (fNvarl[inu-1] <= 0) continue; if (fNvarl[inu-1] == 1 && newcod == 1) continue; kint = fNiofex[inu-1]; //*-*- see if parameter has been fixed if (kint <= 0) { if (fISW[4] >= 0) { Printf(" LIMITS NOT CHANGED FOR FIXED PARAMETER:%4d",inu); } continue; } if (newcod == 1) { //*-*- remove limits from parameter if (fISW[4] > 0) { Printf(" LIMITS REMOVED FROM PARAMETER :%3d",inu); } fCstatu = "NEW LIMITS"; mndxdi(fX[kint-1], kint-1, dxdi); snew = fGstep[kint-1]*dxdi; fGstep[kint-1] = TMath::Abs(snew); fNvarl[inu-1] = 1; } else { //*-*- put limits on parameter fAlim[inu-1] = TMath::Min(fWord7[1],fWord7[2]); fBlim[inu-1] = TMath::Max(fWord7[1],fWord7[2]); if (fISW[4] > 0) { Printf(" PARAMETER %3d LIMITS SET TO %15.5g%15.5g",inu,fAlim[inu-1],fBlim[inu-1]); } fNvarl[inu-1] = 4; fCstatu = "NEW LIMITS"; fGstep[kint-1] = -.1; } } goto L900; //*-*- set limits on one parameter L30: if (fNvarl[i2-1] <= 0) { Printf(" PARAMETER %3d IS NOT VARIABLE.", i2); goto L900; } kint = fNiofex[i2-1]; //*-*- see if parameter was fixed if (kint == 0) { Printf(" REQUEST TO CHANGE LIMITS ON FIXED PARAMETER:%3d",i2); for (ifx = 1; ifx <= fNpfix; ++ifx) { if (i2 == fIpfix[ifx-1]) goto L92; } Printf(" MINUIT BUG IN MNLIMS. SEE F. JAMES"); L92: ; } if (fWord7[1] != fWord7[2]) goto L235; //*-*- remove limits if (fNvarl[i2-1] != 1) { if (fISW[4] > 0) { Printf(" LIMITS REMOVED FROM PARAMETER %2d",i2); } fCstatu = "NEW LIMITS"; if (kint <= 0) { fGsteps[ifx-1] = TMath::Abs(fGsteps[ifx-1]); } else { mndxdi(fX[kint-1], kint-1, dxdi); if (TMath::Abs(dxdi) < .01) dxdi = .01; fGstep[kint-1] = TMath::Abs(fGstep[kint-1]*dxdi); fGrd[kint-1] *= dxdi; } fNvarl[i2-1] = 1; } else { Printf(" NO LIMITS SPECIFIED. PARAMETER %3d IS ALREADY UNLIMITED. NO CHANGE.",i2); } goto L900; //*-*- put on limits L235: fAlim[i2-1] = TMath::Min(fWord7[1],fWord7[2]); fBlim[i2-1] = TMath::Max(fWord7[1],fWord7[2]); fNvarl[i2-1] = 4; if (fISW[4] > 0) { Printf(" PARAMETER %3d LIMITS SET TO %15.5g%15.5g",i2,fAlim[i2-1],fBlim[i2-1]); } fCstatu = "NEW LIMITS"; if (kint <= 0) fGsteps[ifx-1] = -.1; else fGstep[kint-1] = -.1; L900: if (fCstatu != "NO CHANGE ") { mnexin(fX); mnrset(1); } } /* mnlims_ */ //______________________________________________________________________________ void TMinuit::mnline(Double_t *start, Double_t fstart, Double_t *step, Double_t slope, Double_t toler) { //*-*-*-*-*-*-*-*-*-*Perform a line search from position START*-*-*-*-*-*-*-* //*-* ========================================= //*-* along direction STEP, where the length of vector STEP //*-* gives the expected position of minimum. //*-* FSTART is value of function at START //*-* SLOPE (if non-zero) is df/dx along STEP at START //*-* TOLER is initial tolerance of minimum in direction STEP //*-* //*-* SLAMBG and ALPHA control the maximum individual steps allowed. //*-* The first step is always =1. The max length of second step is SLAMBG. //*-* The max size of subsequent steps is the maximum previous successful //*-* step multiplied by ALPHA + the size of most recent successful step, //*-* but cannot be smaller than SLAMBG. //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t xpq[12], ypq[12], slam, sdev, coeff[3], denom, flast; Double_t fvals[3], xvals[3], f1, fvmin, xvmin, ratio, f2, f3, fvmax; Double_t toler8, toler9, overal, undral, slamin, slamax, slopem; Int_t i, nparx=0, nvmax=0, nxypt, kk, ipt; Bool_t ldebug; TString cmess; char chpq[13]; int l65, l70, l80; /* Function Body */ l65 = 0; l70 = 0; l80 = 0; ldebug = fIdbg[1] >= 1; //*-*- starting values for overall limits on total step SLAM overal = 1e3; undral = -100; //*-*- debug check if start is ok if (ldebug) { mninex(&start[0]); Eval(nparx, fGin, f1, fU, 4); ++fNfcn; if (f1 != fstart) { Printf(" MNLINE start point not consistent, F values, parameters="); for (kk = 1; kk <= fNpar; ++kk) { Printf(" %14.5e",fX[kk-1]); } } } //*-*- . set up linear search along STEP fvmin = fstart; xvmin = 0; nxypt = 1; chpq[0] = charal[0]; xpq[0] = 0; ypq[0] = fstart; //*-*- SLAMIN = smallest possible value of ABS(SLAM) slamin = 0; for (i = 1; i <= fNpar; ++i) { if (step[i-1] != 0) { ratio = TMath::Abs(start[i-1] / step[i-1]); if (slamin == 0) slamin = ratio; if (ratio < slamin) slamin = ratio; } fX[i-1] = start[i-1] + step[i-1]; } if (slamin == 0) slamin = fEpsmac; slamin *= fEpsma2; nparx = fNpar; mninex(fX); Eval(nparx, fGin, f1, fU, 4); ++fNfcn; ++nxypt; chpq[nxypt-1] = charal[nxypt-1]; xpq[nxypt-1] = 1; ypq[nxypt-1] = f1; if (f1 < fstart) { fvmin = f1; xvmin = 1; } //*-*- . quadr interp using slope GDEL and two points slam = 1; toler8 = toler; slamax = 5; flast = f1; //*-*- can iterate on two-points (cut) if no imprvmnt do { denom = (flast - fstart - slope*slam)*2 / (slam*slam); slam = 1; if (denom != 0) slam = -slope / denom; if (slam < 0) slam = slamax; if (slam > slamax) slam = slamax; if (slam < toler8) slam = toler8; if (slam < slamin) { l80 = 1; break; } if (TMath::Abs(slam - 1) < toler8 && f1 < fstart) { l70 = 1; break; } if (TMath::Abs(slam - 1) < toler8) slam = toler8 + 1; if (nxypt >= 12) { l65 = 1; break; } for (i = 1; i <= fNpar; ++i) { fX[i-1] = start[i-1] + slam*step[i-1]; } mninex(fX); nparx = fNpar; Eval(nparx, fGin, f2, fU, 4); ++fNfcn; ++nxypt; chpq[nxypt-1] = charal[nxypt-1]; xpq[nxypt-1] = slam; ypq[nxypt-1] = f2; if (f2 < fvmin) { fvmin = f2; xvmin = slam; } if (fstart == fvmin) { flast = f2; toler8 = toler*slam; overal = slam - toler8; slamax = overal; } } while (fstart == fvmin); if (!l65 && !l70 && !l80) { //*-*- . quadr interp using 3 points xvals[0] = xpq[0]; fvals[0] = ypq[0]; xvals[1] = xpq[nxypt-2]; fvals[1] = ypq[nxypt-2]; xvals[2] = xpq[nxypt-1]; fvals[2] = ypq[nxypt-1]; //*-*- begin iteration, calculate desired step do { slamax = TMath::Max(slamax,TMath::Abs(xvmin)*2); mnpfit(xvals, fvals, 3, coeff, sdev); if (coeff[2] <= 0) { slopem = coeff[2]*2*xvmin + coeff[1]; if (slopem <= 0) slam = xvmin + slamax; else slam = xvmin - slamax; } else { slam = -coeff[1] / (coeff[2]*2); if (slam > xvmin + slamax) slam = xvmin + slamax; if (slam < xvmin - slamax) slam = xvmin - slamax; } if (slam > 0) if (slam > overal) slam = overal; else if (slam < undral) slam = undral; //*-*- come here if step was cut below do { toler9 = TMath::Max(toler8,TMath::Abs(toler8*slam)); for (ipt = 1; ipt <= 3; ++ipt) { if (TMath::Abs(slam - xvals[ipt-1]) < toler9) { l70 = 1; break; } } if (l70) break; //*-*- take the step if (nxypt >= 12) { l65 = 1; break; } for (i = 1; i <= fNpar; ++i) { fX[i-1] = start[i-1] + slam*step[i-1]; } mninex(fX); Eval(nparx, fGin, f3, fU, 4); ++fNfcn; ++nxypt; chpq[nxypt-1] = charal[nxypt-1]; xpq[nxypt-1] = slam; ypq[nxypt-1] = f3; //*-*- find worst previous point out of three fvmax = fvals[0]; nvmax = 1; if (fvals[1] > fvmax) { fvmax = fvals[1]; nvmax = 2; } if (fvals[2] > fvmax) { fvmax = fvals[2]; nvmax = 3; } //*-*- if latest point worse than all three previous, cut step if (f3 >= fvmax) { if (nxypt >= 12) { l65 = 1; break; } if (slam > xvmin) overal = TMath::Min(overal,slam - toler8); if (slam < xvmin) undral = TMath::Max(undral,slam + toler8); slam = (slam + xvmin)*.5; } } while (f3 >= fvmax); //*-*- prepare another iteration, replace worst previous point if (l65 || l70) break; xvals[nvmax-1] = slam; fvals[nvmax-1] = f3; if (f3 < fvmin) { fvmin = f3; xvmin = slam; } else { if (slam > xvmin) overal = TMath::Min(overal,slam - toler8); if (slam < xvmin) undral = TMath::Max(undral,slam + toler8); } } while (nxypt < 12); } //*-*- . . end of iteration . . . //*-*- stop because too many iterations if (!l70 && !l80) { cmess = " LINE SEARCH HAS EXHAUSTED THE LIMIT OF FUNCTION CALLS "; if (ldebug) { Printf(" MNLINE DEBUG: steps="); for (kk = 1; kk <= fNpar; ++kk) { Printf(" %12.4g",step[kk-1]); } } } //*-*- stop because within tolerance if (l70) cmess = " LINE SEARCH HAS ATTAINED TOLERANCE "; if (l80) cmess = " STEP SIZE AT ARITHMETICALLY ALLOWED MINIMUM"; fAmin = fvmin; for (i = 1; i <= fNpar; ++i) { fDirin[i-1] = step[i-1]*xvmin; fX[i-1] = start[i-1] + fDirin[i-1]; } mninex(fX); if (xvmin < 0) { mnwarn("D", "MNLINE", " LINE MINIMUM IN BACKWARDS DIRECTION"); } if (fvmin == fstart) { mnwarn("D", "MNLINE", " LINE SEARCH FINDS NO IMPROVEMENT "); } if (ldebug) { Printf(" AFTER%3d POINTS,%s",nxypt,(const char*)cmess); mnplot(xpq, ypq, chpq, nxypt, fNpagwd, fNpagln); } } /* mnline_ */ //______________________________________________________________________________ void TMinuit::mnmatu(Int_t kode) { //*-*-*-*-*-*-*-*Prints the covariance matrix v when KODE=1*-*-*-*-*-*-*-*-* //*-* ========================================== //*-* always prints the global correlations, and //*-* calculates and prints the individual correlation coefficients //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Int_t ndex, i, j, m, n, ncoef, nparm, id, it, ix; Int_t nsofar, ndi, ndj, iso, isw2, isw5; TString ctemp; isw2 = fISW[1]; if (isw2 < 1) { Printf("%s",(const char*)fCovmes[isw2]); return; } if (fNpar == 0) { Printf(" MNMATU: NPAR=0"); return; } //*-*- . . . . .external error matrix if (kode == 1) { isw5 = fISW[4]; fISW[4] = 2; mnemat(fP, fMaxint); if (isw2 < 3) { Printf("%s",(const char*)fCovmes[isw2]); } fISW[4] = isw5; } //*-*- . . . . . correlation coeffs. . if (fNpar <= 1) return; mnwerr(); //*-*- NCOEF is number of coeff. that fit on one line, not to exceed 20 ncoef = (fNpagwd - 19) / 6; ncoef = TMath::Min(ncoef,20); nparm = TMath::Min(fNpar,ncoef); Printf(" PARAMETER CORRELATION COEFFICIENTS "); ctemp = " NO. GLOBAL"; for (id = 1; id <= nparm; ++id) { ctemp += Form(" %6d",fNexofi[id-1]); } Printf("%s",(const char*)ctemp); for (i = 1; i <= fNpar; ++i) { ix = fNexofi[i-1]; ndi = i*(i + 1) / 2; for (j = 1; j <= fNpar; ++j) { m = TMath::Max(i,j); n = TMath::Min(i,j); ndex = m*(m-1) / 2 + n; ndj = j*(j + 1) / 2; fMATUvline[j-1] = fVhmat[ndex-1] / TMath::Sqrt(TMath::Abs(fVhmat[ndi-1]*fVhmat[ndj-1])); } nparm = TMath::Min(fNpar,ncoef); ctemp = Form(" %3d %7.5f ",ix,fGlobcc[i-1]); for (it = 1; it <= nparm; ++it) { ctemp += Form(" %6.3f",fMATUvline[it-1]); } Printf("%s",(const char*)ctemp); if (i <= nparm) continue; ctemp = " "; for (iso = 1; iso <= 10; ++iso) { nsofar = nparm; nparm = TMath::Min(fNpar,nsofar + ncoef); for (it = nsofar + 1; it <= nparm; ++it) { ctemp = ctemp + Form(" %6.3f",fMATUvline[it-1]); } Printf("%s",(const char*)ctemp); if (i <= nparm) break; } } if (isw2 < 3) { Printf(" %s",(const char*)fCovmes[isw2]); } } /* mnmatu_ */ //______________________________________________________________________________ void TMinuit::mnmigr() { //*-*-*-*-*-*-*-*-*Performs a local function minimization*-*-*-*-*-*-*-*-*-* //*-* ====================================== //*-* Performs a local function minimization using basically the //*-* method of Davidon-Fletcher-Powell as modified by Fletcher //*-* ref. -- Fletcher, Comp.J. 13,317 (1970) "switching method" //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t gdel, gami, vlen, dsum, gssq, vsum, d; Double_t fzero, fs, ri, delgam, rhotol; Double_t gdgssq, gvg, vgi; Int_t npfn, ndex, iext, i, j, m, n, npsdf, nparx; Int_t iswtr, lined2, kk, nfcnmg, nrstrt,iter; Bool_t ldebug; Double_t toler = 0.05; if (fNpar <= 0) return; if (fAmin == fUndefi) mnamin(); ldebug = kFALSE; if ( fIdbg[4] >= 1) ldebug = kTRUE; fCfrom = "MIGRAD "; fNfcnfr = fNfcn; nfcnmg = fNfcn; fCstatu = "INITIATE "; iswtr = fISW[4] - 2*fItaur; npfn = fNfcn; nparx = fNpar; vlen = (Double_t) (fNpar*(fNpar + 1) / 2); nrstrt = 0; npsdf = 0; lined2 = 0; fISW[3] = -1; rhotol = fApsi*.001; if (iswtr >= 1) { Printf(" START MIGRAD MINIMIZATION. STRATEGY%2d. CONVERGENCE WHEN EDM .LT.%9.2e",fIstrat,rhotol); } //*-*- initialization strategy if (fIstrat < 2 || fISW[1] >= 3) goto L2; //*-*- come (back) here to restart completely L1: if (nrstrt > fIstrat) { fCstatu = "FAILED "; fISW[3] = -1; goto L230; } //*-*- . get full covariance and gradient mnhess(); mnwerr(); npsdf = 0; if (fISW[1] >= 1) goto L10; //*-*- . get gradient at start point L2: mninex(fX); if (fISW[2] == 1) { Eval(nparx, fGin, fzero, fU, 2); ++fNfcn; } mnderi(); if (fISW[1] >= 1) goto L10; //*-*- sometimes start with diagonal matrix for (i = 1; i <= fNpar; ++i) { fMIGRxxs[i-1] = fX[i-1]; fMIGRstep[i-1] = 0; } //*-*- do line search if second derivative negative ++lined2; if (lined2 < (fIstrat + 1)*fNpar) { for (i = 1; i <= fNpar; ++i) { if (fG2[i-1] > 0) continue; if (fGrd[i-1] > 0) fMIGRstep[i-1] = -TMath::Abs(fGstep[i-1]); else fMIGRstep[i-1] = TMath::Abs(fGstep[i-1]); gdel = fMIGRstep[i-1]*fGrd[i-1]; fs = fAmin; mnline(fMIGRxxs, fs, fMIGRstep, gdel, toler); mnwarn("D", "MNMIGR", "Negative G2 line search"); iext = fNexofi[i-1]; if (ldebug) { Printf(" Negative G2 line search, param %3d %13.3g%13.3g",iext,fs,fAmin); } goto L2; } } //*-*- make diagonal error matrix for (i = 1; i <= fNpar; ++i) { ndex = i*(i-1) / 2; for (j = 1; j <= i-1; ++j) { ++ndex; fVhmat[ndex-1] = 0; } ++ndex; if (fG2[i-1] <= 0) fG2[i-1] = 1; fVhmat[ndex-1] = 2 / fG2[i-1]; } fDcovar = 1; if (ldebug) { Printf(" DEBUG MNMIGR, STARTING MATRIX DIAGONAL, VHMAT="); for (kk = 1; kk <= Int_t(vlen); ++kk) { Printf(" %10.2g",fVhmat[kk-1]); } } //*-*- ready to start first iteration L10: ++nrstrt; if (nrstrt > fIstrat + 1) { fCstatu = "FAILED "; goto L230; } fs = fAmin; //*-*- . . . get EDM and set up loop fEDM = 0; for (i = 1; i <= fNpar; ++i) { fMIGRgs[i-1] = fGrd[i-1]; fMIGRxxs[i-1] = fX[i-1]; ndex = i*(i-1) / 2; for (j = 1; j <= i-1; ++j) { ++ndex; fEDM += fMIGRgs[i-1]*fVhmat[ndex-1]*fMIGRgs[j-1]; } ++ndex; fEDM += fMIGRgs[i-1]*fMIGRgs[i-1]*.5*fVhmat[ndex-1]; } fEDM = fEDM*.5*(fDcovar*3 + 1); if (fEDM < 0) { mnwarn("W", "MIGRAD", "STARTING MATRIX NOT POS-DEFINITE."); fISW[1] = 0; fDcovar = 1; goto L2; } if (fISW[1] == 0) fEDM = fBigedm; iter = 0; mninex(fX); mnwerr(); if (iswtr >= 1) mnprin(3, fAmin); if (iswtr >= 2) mnmatu(0); //*-*- . . . . . start main loop L24: if (fNfcn - npfn >= fNfcnmx) goto L190; gdel = 0; gssq = 0; for (i = 1; i <= fNpar; ++i) { ri = 0; gssq += fMIGRgs[i-1]*fMIGRgs[i-1]; for (j = 1; j <= fNpar; ++j) { m = TMath::Max(i,j); n = TMath::Min(i,j); ndex = m*(m-1) / 2 + n; ri += fVhmat[ndex-1]*fMIGRgs[j-1]; } fMIGRstep[i-1] = ri*-.5; gdel += fMIGRstep[i-1]*fMIGRgs[i-1]; } if (gssq == 0) { mnwarn("D", "MIGRAD", " FIRST DERIVATIVES OF FCN ARE ALL ZERO"); goto L300; } //*-*- if gdel positive, V not posdef if (gdel >= 0) { mnwarn("D", "MIGRAD", " NEWTON STEP NOT DESCENT."); if (npsdf == 1) goto L1; mnpsdf(); npsdf = 1; goto L24; } //*-*- . . . . do line search mnline(fMIGRxxs, fs, fMIGRstep, gdel, toler); if (fAmin == fs) goto L200; fCfrom = "MIGRAD "; fNfcnfr = nfcnmg; fCstatu = "PROGRESS "; //*-*- . get gradient at new point mninex(fX); if (fISW[2] == 1) { Eval(nparx, fGin, fzero, fU, 2); ++fNfcn; } mnderi(); //*-*- . calculate new EDM npsdf = 0; L81: fEDM = 0; gvg = 0; delgam = 0; gdgssq = 0; for (i = 1; i <= fNpar; ++i) { ri = 0; vgi = 0; for (j = 1; j <= fNpar; ++j) { m = TMath::Max(i,j); n = TMath::Min(i,j); ndex = m*(m-1) / 2 + n; vgi += fVhmat[ndex-1]*(fGrd[j-1] - fMIGRgs[j-1]); ri += fVhmat[ndex-1]*fGrd[j-1]; } fMIGRvg[i-1] = vgi*.5; gami = fGrd[i-1] - fMIGRgs[i-1]; gdgssq += gami*gami; gvg += gami*fMIGRvg[i-1]; delgam += fDirin[i-1]*gami; fEDM += fGrd[i-1]*ri*.5; } fEDM = fEDM*.5*(fDcovar*3 + 1); //*-*- . if EDM negative, not positive-definite if (fEDM < 0 || gvg <= 0) { mnwarn("D", "MIGRAD", "NOT POS-DEF. EDM OR GVG NEGATIVE."); fCstatu = "NOT POSDEF"; if (npsdf == 1) goto L230; mnpsdf(); npsdf = 1; goto L81; } //*-*- print information about this iteration ++iter; if (iswtr >= 3 || iswtr == 2 && iter % 10 == 1) { mnwerr(); mnprin(3, fAmin); } if (gdgssq == 0) { mnwarn("D", "MIGRAD", "NO CHANGE IN FIRST DERIVATIVES OVER LAST STEP"); } if (delgam < 0) { mnwarn("D", "MIGRAD", "FIRST DERIVATIVES INCREASING ALONG SEARCH LINE"); } //*-*- . update covariance matrix fCstatu = "IMPROVEMNT"; if (ldebug) { Printf(" VHMAT 1 ="); for (kk = 1; kk <= 10; ++kk) { Printf(" %10.2g",fVhmat[kk-1]); } } dsum = 0; vsum = 0; for (i = 1; i <= fNpar; ++i) { for (j = 1; j <= i; ++j) { d = fDirin[i-1]*fDirin[j-1] / delgam - fMIGRvg[i-1]*fMIGRvg[j-1] / gvg; dsum += TMath::Abs(d); ndex = i*(i-1) / 2 + j; fVhmat[ndex-1] += d*2; vsum += TMath::Abs(fVhmat[ndex-1]); } } //*-*- smooth local fluctuations by averaging DCOVAR fDcovar = (fDcovar + dsum / vsum)*.5; if (iswtr >= 3 || ldebug) { Printf(" RELATIVE CHANGE IN COV. MATRIX=%5.1f per cent",fDcovar*100); } if (ldebug) { Printf(" VHMAT 2 ="); for (kk = 1; kk <= 10; ++kk) { Printf(" %10.3g",fVhmat[kk-1]); } } if (delgam <= gvg) goto L135; for (i = 1; i <= fNpar; ++i) { fMIGRflnu[i-1] = fDirin[i-1] / delgam - fMIGRvg[i-1] / gvg; } for (i = 1; i <= fNpar; ++i) { for (j = 1; j <= i; ++j) { ndex = i*(i-1) / 2 + j; fVhmat[ndex-1] += gvg*2*fMIGRflnu[i-1]*fMIGRflnu[j-1]; } } L135: //*-*- and see if converged if (fEDM < rhotol*.1) goto L300; //*-*- if not, prepare next iteration for (i = 1; i <= fNpar; ++i) { fMIGRxxs[i-1] = fX[i-1]; fMIGRgs[i-1] = fGrd[i-1]; } fs = fAmin; if (fISW[1] == 0 && fDcovar < .5) fISW[1] = 1; if (fISW[1] == 3 && fDcovar > .1) fISW[1] = 1; if (fISW[1] == 1 && fDcovar < .05) fISW[1] = 3; goto L24; //*-*- . . . . . end main loop //*-*- . . call limit in MNMIGR L190: fISW[0] = 1; if (fISW[4] >= 0) { Printf(" CALL LIMIT EXCEEDED IN MIGRAD."); } fCstatu = "CALL LIMIT"; goto L230; //*-*- . . fails to improve . . L200: if (iswtr >= 1) { Printf(" MIGRAD FAILS TO FIND IMPROVEMENT"); } for (i = 1; i <= fNpar; ++i) { fX[i-1] = fMIGRxxs[i-1]; } if (fEDM < rhotol) goto L300; if (fEDM < TMath::Abs(fEpsma2*fAmin)) { if (iswtr >= 0) { Printf(" MACHINE ACCURACY LIMITS FURTHER IMPROVEMENT."); } goto L300; } if (fIstrat < 1) { if (fISW[4] >= 0) { Printf(" MIGRAD FAILS WITH STRATEGY=0. WILL TRY WITH STRATEGY=1."); } fIstrat = 1; } goto L1; //*-*- . . fails to converge L230: if (iswtr >= 0) { Printf(" MIGRAD TERMINATED WITHOUT CONVERGENCE."); } if (fISW[1] == 3) fISW[1] = 1; fISW[3] = -1; goto L400; //*-*- . . apparent convergence L300: if (iswtr >= 0) { Printf(" MIGRAD MINIMIZATION HAS CONVERGED."); } if (fItaur == 0) { if (fIstrat >= 2 || (fIstrat == 1 && fISW[1] < 3)) { if (fISW[4] >= 0) { Printf(" MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX."); } mnhess(); mnwerr(); npsdf = 0; if (fEDM > rhotol) goto L10; } } fCstatu = "CONVERGED "; fISW[3] = 1; //*-*- come here in any case L400: fCfrom = "MIGRAD "; fNfcnfr = nfcnmg; mninex(fX); mnwerr(); if (iswtr >= 0) mnprin(3, fAmin); if (iswtr >= 1) mnmatu(1); } /* mnmigr_ */ //______________________________________________________________________________ void TMinuit::mnmnos() { //*-*-*-*-*-*-*-*-*-*-*Performs a MINOS error analysis*-*-*-*-*-*-*-*-*-*-*-* //*-* =============================== //*-* Performs a MINOS error analysis on those parameters for //*-* which it is requested on the MINOS command by calling //*-* MNMNOT for each parameter requested. //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t val2mi, val2pl; Int_t nbad, ilax, ilax2, ngood, nfcnmi, iin, knt; if (fNpar <= 0) goto L700; ngood = 0; nbad = 0; nfcnmi = fNfcn; //*-*- . loop over parameters requested for (knt = 1; knt <= fNpar; ++knt) { if (Int_t(fWord7[1]) == 0) { ilax = fNexofi[knt-1]; } else { if (knt >= 7) break; ilax = Int_t(fWord7[knt]); if (ilax == 0) break; if (ilax > 0 && ilax <= fNu) { if (fNiofex[ilax-1] > 0) goto L565; } Printf(" PARAMETER NUMBER %3d NOT VARIABLE. IGNORED.",ilax); continue; } L565: //*-*- calculate one pair of M E s ilax2 = 0; mnmnot(ilax, ilax2, val2pl, val2mi); if (fLnewmn) goto L650; //*-*- update NGOOD and NBAD iin = fNiofex[ilax-1]; if (fErp[iin-1] > 0) ++ngood; else ++nbad; if (fErn[iin-1] < 0) ++ngood; else ++nbad; } //*-*- end of loop . . . . . . . //*-*- . . . . printout final values . fCfrom = "MINOS "; fNfcnfr = nfcnmi; fCstatu = "UNCHANGED "; if (ngood == 0 && nbad == 0) goto L700; if (ngood > 0 && nbad == 0) fCstatu = "SUCCESSFUL"; if (ngood == 0 && nbad > 0) fCstatu = "FAILURE "; if (ngood > 0 && nbad > 0) fCstatu = "PROBLEMS "; if (fISW[4] >= 0) mnprin(4, fAmin); if (fISW[4] >= 2) mnmatu(0); return; //*-*- . . . new minimum found . . . . L650: fCfrom = "MINOS "; fNfcnfr = nfcnmi; fCstatu = "NEW MINIMU"; if (fISW[4] >= 0) mnprin(4, fAmin); Printf(" NEW MINIMUM FOUND. GO BACK TO MINIMIZATION STEP."); Printf(" ================================================="); Printf(" V"); Printf(" V"); Printf(" V"); Printf(" VVVVVVV"); Printf(" VVVVV"); Printf(" VVV"); Printf(" V"); Printf(""); return; L700: Printf(" THERE ARE NO MINOS ERRORS TO CALCULATE."); } /* mnmnos_ */ //______________________________________________________________________________ void TMinuit::mnmnot(Int_t ilax, Int_t ilax2, Double_t &val2pl, Double_t &val2mi) { //*-*-*-*-*-*Performs a MINOS error analysis on one parameter*-*-*-*-*-*-*-*-* //*-* ================================================ //*-* The parameter ILAX is varied, and the minimum of the //*-* function with respect to the other parameters is followed //*-* until it crosses the value FMIN+UP. //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* System generated locals */ Int_t i__1; /* Local variables */ Double_t delu, aopt, eros; Double_t abest, xunit, dc, ut, sigsav, du1; Double_t fac, sig, sav; Int_t marc, isig, mpar, ndex, imax, indx, ierr, i, j; Int_t iercr, it, istrav, nfmxin, nlimit, isw2, isw4; TString csig; //*-*- . . save and prepare start vals isw2 = fISW[1]; isw4 = fISW[3]; sigsav = fEDM; istrav = fIstrat; dc = fDcovar; fLnewmn = kFALSE; fApsi = fEpsi*.5; abest = fAmin; mpar = fNpar; nfmxin = fNfcnmx; for (i = 1; i <= mpar; ++i) { fXt[i-1] = fX[i-1]; } i__1 = mpar*(mpar + 1) / 2; for (j = 1; j <= i__1; ++j) { fVthmat[j-1] = fVhmat[j-1]; } for (i = 1; i <= mpar; ++i) { fMNOTgcc[i-1] = fGlobcc[i-1]; fMNOTw[i-1] = fWerr[i-1]; } it = fNiofex[ilax-1]; fErp[it-1] = 0; fErn[it-1] = 0; mninex(fXt); ut = fU[ilax-1]; if (fNvarl[ilax-1] == 1) { fAlim[ilax-1] = ut - fMNOTw[it-1]*100; fBlim[ilax-1] = ut + fMNOTw[it-1]*100; } ndex = it*(it + 1) / 2; xunit = TMath::Sqrt(fUp / fVthmat[ndex-1]); marc = 0; for (i = 1; i <= mpar; ++i) { if (i == it) continue; ++marc; imax = TMath::Max(it,i); indx = imax*(imax-1) / 2 + TMath::Min(it,i); fMNOTxdev[marc-1] = xunit*fVthmat[indx-1]; } //*-*- fix the parameter in question mnfixp(it-1, ierr); if (ierr > 0) { Printf(" MINUIT ERROR. CANNOT FIX PARAMETER%4d INTERNAL%3d",ilax,it); goto L700; } //*-*- . . . . . Nota Bene: from here on, NPAR=MPAR-1 //*-*- Remember: MNFIXP squeezes IT out of X, XT, WERR, and VHMAT, //*-*- not W, VTHMAT for (isig = 1; isig <= 2; ++isig) { if (isig == 1) { sig = 1; csig = "POSI"; } else { sig = -1; csig = "NEGA"; } //*-*- . sig=sign of error being calcd if (fISW[4] > 1) { Printf(" DETERMINATION OF %sTIVE MINOS ERROR FOR PARAMETER%d" ,(const char*)csig,ilax ,(const char*)fCpnam[ilax-1]); } if (fISW[1] <= 0) { mnwarn("D", "MINOS", "NO COVARIANCE MATRIX."); } nlimit = fNfcn + nfmxin; fIstrat = TMath::Max(istrav-1,0); du1 = fMNOTw[it-1]; fU[ilax-1] = ut + sig*du1; fU[ilax-1] = TMath::Min(fU[ilax-1],fBlim[ilax-1]); fU[ilax-1] = TMath::Max(fU[ilax-1],fAlim[ilax-1]); delu = fU[ilax-1] - ut; //*-*- stop if already at limit with negligible step size if (TMath::Abs(delu) / (TMath::Abs(ut) + TMath::Abs(fU[ilax-1])) < fEpsmac) goto L440; fac = delu / fMNOTw[it-1]; for (i = 1; i <= fNpar; ++i) { fX[i-1] = fXt[i-1] + fac*fMNOTxdev[i-1]; } if (fISW[4] > 1) { Printf(" PARAMETER%4d SET TO%11.3e + %10.3e = %12.3e",ilax,ut,delu,fU[ilax-1]); } //*-*- loop to hit AMIN+UP fKe1cr = ilax; fKe2cr = 0; fXmidcr = fU[ilax-1]; fXdircr = delu; fAmin = abest; fNfcnmx = nlimit - fNfcn; mncros(aopt, iercr); if (abest - fAmin > fUp*.01) goto L650; if (iercr == 1) goto L440; if (iercr == 2) goto L450; if (iercr == 3) goto L460; //*-*- . error successfully calculated eros = fXmidcr - ut + aopt*fXdircr; if (fISW[4] > 1) { Printf(" THE %4sTIVE MINOS ERROR OF PARAMETER%3d %10s, IS %12.4e" ,(const char*)csig,ilax ,(const char*)fCpnam[ilax-1],eros); } goto L480; //*-*- . . . . . . . . failure returns L440: if (fISW[4] >= 1) { Printf(" THE %4sTIVE MINOS ERROR OF PARAMETER%3d, %s EXCEEDS ITS LIMIT." ,(const char*)csig,ilax ,(const char*)fCpnam[ilax-1]); } eros = fUndefi; goto L480; L450: if (fISW[4] >= 1) { Printf(" THE %4sTIVE MINOS ERROR%4d REQUIRES MORE THAN%5d FUNCTION CALLS." ,(const char*)csig,ilax,nfmxin); } eros = 0; goto L480; L460: if (fISW[4] >= 1) { Printf(" %4sTIVE MINOS ERROR NOT CALCULATED FOR PARAMETER%d" ,(const char*)csig,ilax); } eros = 0; L480: if (fISW[4] > 1) { Printf(" **************************************************************************"); } if (sig < 0) { fErn[it-1] = eros; if (ilax2 > 0 && ilax2 <= fNu) val2mi = fU[ilax2-1]; } else { fErp[it-1] = eros; if (ilax2 > 0 && ilax2 <= fNu) val2pl = fU[ilax2-1]; } } //*-*- . . parameter finished. reset v //*-*- normal termination */ fItaur = 1; mnfree(1); i__1 = mpar*(mpar + 1) / 2; for (j = 1; j <= i__1; ++j) { fVhmat[j-1] = fVthmat[j-1]; } for (i = 1; i <= mpar; ++i) { fWerr[i-1] = fMNOTw[i-1]; fGlobcc[i-1] = fMNOTgcc[i-1]; fX[i-1] = fXt[i-1]; } mninex(fX); fEDM = sigsav; fAmin = abest; fISW[1] = isw2; fISW[3] = isw4; fDcovar = dc; goto L700; //*-*- new minimum L650: fLnewmn = kTRUE; fISW[1] = 0; fDcovar = 1; fISW[3] = 0; sav = fU[ilax-1]; fItaur = 1; mnfree(1); fU[ilax-1] = sav; mnexin(fX); fEDM = fBigedm; //*-*- in any case L700: fItaur = 0; fNfcnmx = nfmxin; fIstrat = istrav; } /* mnmnot_ */ //______________________________________________________________________________ void TMinuit::mnparm(Int_t k1, TString cnamj, Double_t uk, Double_t wk, Double_t a, Double_t b, Int_t &ierflg) { //*-*-*-*-*-*-*-*-*Implements one parameter definition*-*-*-*-*-*-*-*-*-*-*-* //*-* =================================== //*-* Called from MNPARS and user-callable //*-* Implements one parameter definition, that is: //*-* K (external) parameter number //*-* CNAMK parameter name //*-* UK starting value //*-* WK starting step size or uncertainty //*-* A, B lower and upper physical parameter limits //*-* and sets up (updates) the parameter lists. //*-* Output: IERFLG=0 if no problems //*-* >0 if MNPARM unable to implement definition //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t vplu, a_small, gsmin, pinti, vminu, danger, sav, sav2; Int_t ierr, kint, in, ix, ktofix, lastin, kinfix, nvl; TString cnamk, chbufi; Int_t k = k1+1; cnamk = cnamj; kint = fNpar; if (k < 1 || k > fMaxext) { //*-*- parameter number exceeds allowed maximum value Printf(" MINUIT USER ERROR. PARAMETER NUMBER IS %3d ALLOWED RANGE IS ONE TO %4d",k,fMaxext); goto L800; } //*-*- normal parameter request ktofix = 0; if (fNvarl[k-1] < 0) goto L50; //*-*- previously defined parameter is being redefined //*-*- find if parameter was fixed for (ix = 1; ix <= fNpfix; ++ix) { if (fIpfix[ix-1] == k) ktofix = k; } if (ktofix > 0) { mnwarn("W", "PARAM DEF", "REDEFINING A FIXED PARAMETER."); if (kint >= fMaxint) { Printf(" CANNOT RELEASE. MAX NPAR EXCEEDED."); goto L800; } mnfree(-k); } //*-*- if redefining previously variable parameter if (fNiofex[k-1] > 0) kint = fNpar - 1; L50: //*-*- . . .print heading if (fLphead && fISW[4] >= 0) { Printf(" PARAMETER DEFINITIONS:"); Printf(" NO. NAME VALUE STEP SIZE LIMITS"); fLphead = kFALSE; } if (wk > 0) goto L122; //*-*- . . .constant parameter . . . . if (fISW[4] >= 0) { Printf(" %5d %-10s %13.5e constant",k,(const char*)cnamk,uk); } nvl = 0; goto L200; L122: if (a == 0 && b == 0) { //*-*- variable parameter without limits nvl = 1; if (fISW[4] >= 0) { Printf(" %5d %-10s %13.5e%13.5e no limits",k,(const char*)cnamk,uk,wk); } } else { //*-*- variable parameter with limits nvl = 4; fLnolim = kFALSE; if (fISW[4] >= 0) { Printf(" %5d %-10s %13.5e%13.5e %13.5e%13.5e",k,(const char*)cnamk,uk,wk,a,b); } } //*-*- . . request for another variable parameter ++kint; if (kint > fMaxint) { Printf(" MINUIT USER ERROR. TOO MANY VARIABLE PARAMETERS."); goto L800; } if (nvl == 1) goto L200; if (a == b) { Printf(" USER ERROR IN MINUIT PARAMETER"); Printf(" DEFINITION"); Printf(" UPPER AND LOWER LIMITS EQUAL."); goto L800; } if (b < a) { sav = b; b = a; a = sav; mnwarn("W", "PARAM DEF", "PARAMETER LIMITS WERE REVERSED."); if (fLwarn) fLphead = kTRUE; } if (b - a > 1e7) { mnwarn("W", "PARAM DEF", Form("LIMITS ON PARAM%d TOO FAR APART.",k)); if (fLwarn) fLphead = kTRUE; } danger = (b - uk)*(uk - a); if (danger < 0) { mnwarn("W", "PARAM DEF", "STARTING VALUE OUTSIDE LIMITS."); } if (danger == 0) { mnwarn("W", "PARAM DEF", "STARTING VALUE IS AT LIMIT."); } L200: //*-*- . . . input OK, set values, arrange lists, //*-*- calculate step sizes GSTEP, DIRIN fCfrom = "PARAMETR"; fNfcnfr = fNfcn; fCstatu = "NEW VALUES"; fNu = TMath::Max(fNu,k); fCpnam[k-1] = cnamk; fU[k-1] = uk; fAlim[k-1] = a; fBlim[k-1] = b; fNvarl[k-1] = nvl; mnrset(1); //*-*- K is external number of new parameter //*-*- LASTIN is the number of var. params with ext. param. no.< K lastin = 0; for (ix = 1; ix <= k-1; ++ix) { if (fNiofex[ix-1] > 0) ++lastin; } //*-*- KINT is new number of variable params, NPAR is old if (kint == fNpar) goto L280; if (kint > fNpar) { //*-*- insert new variable parameter in list for (in = fNpar; in >= lastin + 1; --in) { ix = fNexofi[in-1]; fNiofex[ix-1] = in + 1; fNexofi[in] = ix; fX[in] = fX[in-1]; fXt[in] = fXt[in-1]; fDirin[in] = fDirin[in-1]; fG2[in] = fG2[in-1]; fGstep[in] = fGstep[in-1]; } } else { //*-*- remove variable parameter from list for (in = lastin + 1; in <= kint; ++in) { ix = fNexofi[in]; fNiofex[ix-1] = in; fNexofi[in-1] = ix; fX[in-1] = fX[in]; fXt[in-1] = fXt[in]; fDirin[in-1] = fDirin[in]; fG2[in-1] = fG2[in]; fGstep[in-1] = fGstep[in]; } } L280: ix = k; fNiofex[ix-1] = 0; fNpar = kint; //*-*- lists are now arranged . . . . if (nvl > 0) { in = lastin + 1; fNexofi[in-1] = ix; fNiofex[ix-1] = in; sav = fU[ix-1]; mnpint(sav, ix-1, pinti); fX[in-1] = pinti; fXt[in-1] = fX[in-1]; fWerr[in-1] = wk; sav2 = sav + wk; mnpint(sav2, ix-1, pinti); vplu = pinti - fX[in-1]; sav2 = sav - wk; mnpint(sav2, ix-1, pinti); vminu = pinti - fX[in-1]; fDirin[in-1] = (TMath::Abs(vplu) + TMath::Abs(vminu))*.5; fG2[in-1] = fUp*2 / (fDirin[in-1]*fDirin[in-1]); gsmin = fEpsma2*8*TMath::Abs(fX[in-1]); fGstep[in-1] = TMath::Max(gsmin,fDirin[in-1]*.1); if (fAmin != fUndefi) { a_small = TMath::Sqrt(fEpsma2*(fAmin + fUp) / fUp); fGstep[in-1] = TMath::Max(gsmin,a_small*fDirin[in-1]); } fGrd[in-1] = fG2[in-1]*fDirin[in-1]; //*-*- if parameter has limits if (fNvarl[k-1] > 1) { if (fGstep[in-1] > .5) fGstep[in-1] = .5; fGstep[in-1] = -fGstep[in-1]; } } if (ktofix > 0) { kinfix = fNiofex[ktofix-1]; if (kinfix > 0) mnfixp(kinfix-1, ierr); if (ierr > 0) goto L800; } ierflg = 0; return; //*-*- error on input, unable to implement request . . . . L800: ierflg = 1; } /* mnparm_ */ //______________________________________________________________________________ void TMinuit::mnpars(TString &crdbuf, Int_t &icondn) { //*-*-*-*-*-*-*-*Implements one parameter definition*-*-*-*-*-*-*-*-*-*-*-*-* //*-* =========== ======================= //*-* Called from MNREAD and user-callable //*-* Implements one parameter definition, that is: //*-* parses the string CRDBUF and calls MNPARM //*-* //*-* output conditions: //*-* ICONDN = 0 all OK //*-* ICONDN = 1 error, attempt to define parameter is ignored //*-* ICONDN = 2 end of parameter definitions //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t a=0, b=0, fk=0, uk=0, wk=0, xk=0; Int_t ierr, kapo1, kapo2; Int_t k, llist, ibegin, lenbuf, istart, lnc, icy; TString cnamk, comand, celmnt, ctemp; char stmp[128]; lenbuf = strlen((const char*)crdbuf); //*-*- find out whether fixed or free-field format kapo1 = strspn((const char*)crdbuf, "'"); if (kapo1 == 0) goto L150; kapo2 = strspn((const char*)crdbuf + kapo1, "'"); if (kapo2 == 0) goto L150; //*-*- new (free-field) format kapo2 += kapo1; //*-*- skip leading blanks if any for (istart = 1; istart <= kapo1-1; ++istart) { if (crdbuf(istart-1,1) != ' ') goto L120; } goto L210; L120: //*-*- parameter number integer celmnt = crdbuf(istart-1, kapo1-istart); scanf((const char*)celmnt,fk); k = Int_t(fk); if (k <= 0) goto L210; cnamk = "PARAM " + celmnt; if (kapo2 - kapo1 > 1) { cnamk = crdbuf(kapo1, kapo2-1-kapo1); } //*-* special handling if comma or blanks and a comma follow 'name' for (icy = kapo2 + 1; icy <= lenbuf; ++icy) { if (crdbuf(icy-1,1) == ',') goto L139; if (crdbuf(icy-1,1) != ' ') goto L140; } uk = 0; wk = 0; a = 0; b = 0; goto L170; L139: ++icy; L140: ibegin = icy; ctemp = crdbuf(ibegin-1,lenbuf-ibegin); mncrck(ctemp, 20, comand, lnc, fMaxpar, fPARSplist, llist, ierr, fIsyswr); if (ierr > 0) goto L180; uk = fPARSplist[0]; wk = 0; if (llist >= 2) wk = fPARSplist[1]; a = 0; if (llist >= 3) a = fPARSplist[2]; b = 0; if (llist >= 4) b = fPARSplist[3]; goto L170; //*-*- old (fixed-field) format L150: scanf((const char*)crdbuf,xk,stmp,uk,wk,a,b); cnamk = stmp; k = Int_t(xk); if (k == 0) goto L210; //*-*- parameter format cracked, implement parameter definition L170: mnparm(k-1, cnamk, uk, wk, a, b, ierr); icondn = ierr; return; //*-*- format or other error L180: icondn = 1; return; //*-*- end of data L210: icondn = 2; } /* mnpars_ */ //______________________________________________________________________________ void TMinuit::mnpfit(Double_t *parx2p, Double_t *pary2p, Int_t npar2p, Double_t *coef2p, Double_t &sdev2p) { //*-*-*-*-*-*-*-*-*-*To fit a parabola to npar2p points*-*-*-*-*-*-*-*-*-*-* //*-* ================================== //*-* npar2p no. of points //*-* parx2p(i) x value of point i //*-* pary2p(i) y value of point i //*-* //*-* coef2p(1...3) coefficients of the fitted parabola //*-* y=coef2p(1) + coef2p(2)*x + coef2p(3)*x**2 //*-* sdev2p= variance //*-* method : chi**2 = min equation solved explicitly //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t a, f, s, t, y, s2, x2, x3, x4, y2, cz[3], xm, xy, x2y; x2 = x3 = 0; Int_t i; /* Parameter adjustments */ --coef2p; --pary2p; --parx2p; /* Function Body */ for (i = 1; i <= 3; ++i) { cz[i-1] = 0; } sdev2p = 0; if (npar2p < 3) goto L10; f = (Double_t) (npar2p); //*-* --- center x values for reasons of machine precision xm = 0; for (i = 1; i <= npar2p; ++i) { xm += parx2p[i]; } xm /= f; x2 = 0; x3 = 0; x4 = 0; y = 0; y2 = 0; xy = 0; x2y = 0; for (i = 1; i <= npar2p; ++i) { s = parx2p[i] - xm; t = pary2p[i]; s2 = s*s; x2 += s2; x3 += s*s2; x4 += s2*s2; y += t; y2 += t*t; xy += s*t; x2y += s2*t; } a = (f*x4 - x2*x2)*x2 - f*(x3*x3); if (a == 0) goto L10; cz[2] = (x2*(f*x2y - x2*y) - f*x3*xy) / a; cz[1] = (xy - x3*cz[2]) / x2; cz[0] = (y - x2*cz[2]) / f; if (npar2p == 3) goto L6; sdev2p = y2 - (cz[0]*y + cz[1]*xy + cz[2]*x2y); if (sdev2p < 0) sdev2p = 0; sdev2p /= f - 3; L6: cz[0] += xm*(xm*cz[2] - cz[1]); cz[1] -= xm*2*cz[2]; L10: for (i = 1; i <= 3; ++i) { coef2p[i] = cz[i-1]; } } /* mnpfit_ */ //______________________________________________________________________________ void TMinuit::mnpint(Double_t &pexti, Int_t i1, Double_t &pinti) { //*-*-*-*-*-*-*Calculates the internal parameter value PINTI*-*-*-*-*-*-*-* //*-* ============================================= //*-* corresponding to the external value PEXTI for parameter I. //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t a, alimi, blimi, yy, yy2; Int_t igo; TString chbuf2, chbufi; Int_t i = i1+1; pinti = pexti; igo = fNvarl[i-1]; if (igo == 4) { //*-* -- there are two limits alimi = fAlim[i-1]; blimi = fBlim[i-1]; yy = (pexti - alimi)*2 / (blimi - alimi) - 1; yy2 = yy*yy; if (yy2 >= 1 - fEpsma2) { if (yy < 0) { a = fVlimlo; chbuf2 = " IS AT ITS LOWER ALLOWED LIMIT."; } else { a = fVlimhi; chbuf2 = " IS AT ITS UPPER ALLOWED LIMIT."; } pinti = a; pexti = alimi + (blimi - alimi)*.5*(TMath::Sin(a) + 1); fLimset = kTRUE; if (yy2 > 1) chbuf2 = " BROUGHT BACK INSIDE LIMITS."; mnwarn("W", fCfrom, Form("VARIABLE%d%s",i,chbuf2.Data())); } else { pinti = TMath::ASin(yy); } } } /* mnpint_ */ //______________________________________________________________________________ void TMinuit::mnplot(Double_t *xpt, Double_t *ypt, char *chpt, Int_t nxypt, Int_t npagwd, Int_t npagln) { //*-*-*-*Plots points in array xypt onto one page with labelled axes*-*-*-*-* //*-* =========================================================== //*-* NXYPT is the number of points to be plotted //*-* XPT(I) = x-coord. of ith point //*-* YPT(I) = y-coord. of ith point //*-* CHPT(I) = character to be plotted at this position //*-* the input point arrays XPT, YPT, CHPT are destroyed. //*-* //*-* //*-* If fGraphicsmode is true (default), a TGraph object is produced //*-* via the Plug-in handler. To get the plot, you can do: //*-* TGraph *gr = (TGraph*)gMinuit->GetPlot(); //*-* gr->Draw("al"); //*-* //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* if (fGraphicsMode) { TPluginHandler *h; if ((h = gROOT->GetPluginManager()->FindHandler("TMinuitGraph"))) { //remove the first two points if (h->LoadPlugin() != -1) fPlot = (TObject*)h->ExecPlugin(3,nxypt-2,&xpt[2],&ypt[2]); } return; } static TString cdot = "."; static TString cslash = "/"; /* Local variables */ Double_t xmin, ymin, xmax, ymax, savx, savy, yprt; Double_t bwidx, bwidy, xbest, ybest, ax, ay, bx, by; Double_t xvalus[12], any, dxx, dyy; Int_t iten, i, j, k, maxnx, maxny, iquit, ni, linodd; Int_t nxbest, nybest, km1, ibk, isp1, nx, ny, ks, ix; TString chmess, ctemp; Bool_t overpr; char cline[120]; char chsav, chbest; /* Function Body */ //*-* Computing MIN maxnx = TMath::Min(npagwd-20,100); if (maxnx < 10) maxnx = 10; maxny = npagln; if (maxny < 10) maxny = 10; if (nxypt <= 1) return; xbest = xpt[0]; ybest = ypt[0]; chbest = chpt[0]; //*-*- order the points by decreasing y km1 = nxypt - 1; for (i = 1; i <= km1; ++i) { iquit = 0; ni = nxypt - i; for (j = 1; j <= ni; ++j) { if (ypt[j-1] > ypt[j]) continue; savx = xpt[j-1]; xpt[j-1] = xpt[j]; xpt[j] = savx; savy = ypt[j-1]; ypt[j-1] = ypt[j]; ypt[j] = savy; chsav = chpt[j-1]; chpt[j-1]= chpt[j]; chpt[j] = chsav; iquit = 1; } if (iquit == 0) break; } //*-*- find extreme values xmax = xpt[0]; xmin = xmax; for (i = 1; i <= nxypt; ++i) { if (xpt[i-1] > xmax) xmax = xpt[i-1]; if (xpt[i-1] < xmin) xmin = xpt[i-1]; } dxx = (xmax - xmin)*.001; xmax += dxx; xmin -= dxx; mnbins(xmin, xmax, maxnx, xmin, xmax, nx, bwidx); ymax = ypt[0]; ymin = ypt[nxypt-1]; if (ymax == ymin) ymax = ymin + 1; dyy = (ymax - ymin)*.001; ymax += dyy; ymin -= dyy; mnbins(ymin, ymax, maxny, ymin, ymax, ny, bwidy); any = (Double_t) ny; //*-*- if first point is blank, it is an 'origin' if (chbest == ' ') goto L50; xbest = (xmax + xmin)*.5; ybest = (ymax + ymin)*.5; L50: //*-*- find scale constants ax = 1 / bwidx; ay = 1 / bwidy; bx = -ax*xmin + 2; by = -ay*ymin - 2; //*-*- convert points to grid positions for (i = 1; i <= nxypt; ++i) { xpt[i-1] = ax*xpt[i-1] + bx; ypt[i-1] = any - ay*ypt[i-1] - by; } nxbest = Int_t((ax*xbest + bx)); nybest = Int_t((any - ay*ybest - by)); //*-*- print the points ny += 2; nx += 2; isp1 = 1; linodd = 1; overpr = kFALSE; for (i = 1; i <= ny; ++i) { for (ibk = 1; ibk <= nx; ++ibk) { cline[ibk-1] = ' '; } cline[nx] = '0'; cline[nx+1] = '0'; cline[0] = '.'; cline[nx-1] = '.'; cline[nxbest-1] = '.'; if (i != 1 && i != nybest && i != ny) goto L320; for (j = 1; j <= nx; ++j) { cline[j-1] = '.'; } L320: yprt = ymax - Double_t(i-1)*bwidy; if (isp1 > nxypt) goto L350; //*-*- find the points to be plotted on this line for (k = isp1; k <= nxypt; ++k) { ks = Int_t(ypt[k-1]); if (ks > i) goto L345; ix = Int_t(xpt[k-1]); if (cline[ix-1] == '.') goto L340; if (cline[ix-1] == ' ') goto L340; if (cline[ix-1] == chpt[k-1]) continue; overpr = kTRUE; //*-*- OVERPR is true if one or more positions contains more than //*-*- one point cline[ix-1] = '&'; continue; L340: cline[ix-1] = chpt[k-1]; } isp1 = nxypt + 1; goto L350; L345: isp1 = k; L350: if (linodd == 1 || i == ny) goto L380; linodd = 1; ctemp = cline; Printf(" %s",(const char*)ctemp); goto L400; L380: ctemp = cline; Printf(" %14.7g ..%s",yprt,(const char*)ctemp); linodd = 0; L400: ; } //*-*- print labels on x-axis every ten columns for (ibk = 1; ibk <= nx; ++ibk) { cline[ibk-1] = ' '; if (ibk % 10 == 1) cline[ibk-1] = '/'; } Printf(" %s",cline); for (ibk = 1; ibk <= 12; ++ibk) { xvalus[ibk-1] = xmin + Double_t(ibk-1)*10*bwidx; } printf(" "); iten = (nx + 9) / 10; for (ibk = 1; ibk <= iten; ++ibk) { printf(" %9.4g", xvalus[ibk-1]); } chmess = " "; if (overpr) chmess = " Overprint character is &"; Printf(" ONE COLUMN=%13.7g%s",bwidx,(const char*)chmess); } /* mnplot_ */ //______________________________________________________________________________ void TMinuit::mnpout(Int_t iuext1, TString &chnam, Double_t &val, Double_t &err, Double_t &xlolim, Double_t &xuplim, Int_t &iuint) const { //*-*-*-*Provides the user with information concerning the current status*-*-* //*-* ================================================================ //*-* of parameter number IUEXT. Namely, it returns: //*-* CHNAM: the name of the parameter //*-* VAL: the current (external) value of the parameter //*-* ERR: the current estimate of the parameter uncertainty //*-* XLOLIM: the lower bound (or zero if no limits) //*-* XUPLIM: the upper bound (or zero if no limits) //*-* IUINT: the internal parameter number (or zero if not variable, //*-* or negative if undefined). //*-* Note also: If IUEXT is negative, then it is -internal parameter //*-* number, and IUINT is returned as the EXTERNAL number. //*-* Except for IUINT, this is exactly the inverse of MNPARM //*-* User-called //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Int_t iint, iext, nvl; Int_t iuext = iuext1 + 1; xlolim = 0; xuplim = 0; err = 0; if (iuext == 0) goto L100; if (iuext < 0) { //*-*- internal parameter number specified iint = -(iuext); if (iint > fNpar) goto L100; iext = fNexofi[iint-1]; iuint = iext; } else { //*-*- external parameter number specified iext = iuext; if (iext == 0) goto L100; if (iext > fNu) goto L100; iint = fNiofex[iext-1]; iuint = iint; } //*-*- in both cases nvl = fNvarl[iext-1]; if (nvl < 0) goto L100; chnam = fCpnam[iext-1]; val = fU[iext-1]; if (iint > 0) err = fWerr[iint-1]; if (nvl == 4) { xlolim = fAlim[iext-1]; xuplim = fBlim[iext-1]; } return; //*-*- parameter is undefined L100: iuint = -1; chnam = "undefined"; val = 0; } /* mnpout_ */ //______________________________________________________________________________ void TMinuit::mnprin(Int_t inkode, Double_t fval) { //*-*-*-*Prints the values of the parameters at the time of the call*-*-*-*-* //*-* =========================================================== //*-* also prints other relevant information such as function value, //*-* estimated distance to minimum, parameter errors, step sizes. //*-* //*-* According to the value of IKODE, the printout is:/ //*-* IKODE=INKODE= 0 only info about function value //*-* 1 parameter values, errors, limits //*-* 2 values, errors, step sizes, internal values //*-* 3 values, errors, step sizes, first derivs. //*-* 4 values, parabolic errors, MINOS errors //*-* when INKODE=5, MNPRIN chooses IKODE=1,2, or 3, according to ISW(2) //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Initialized data */ static TString cblank = " "; static TString cnambf = " "; /* Local variables */ Double_t dcmax, x1, x2, x3, dc; x2 = x3 = 0; Int_t nadd, i, k, l, m, ikode, ic, nc, ntrail, lbl; TString chedm; TString colhdl[6], colhdu[6], cx2, cx3, cheval; if (fNu == 0) { Printf(" THERE ARE CURRENTLY NO PARAMETERS DEFINED"); return; } //*-*- get value of IKODE based in INKODE, ISW(2) ikode = inkode; if (inkode == 5) { ikode = fISW[1] + 1; if (ikode > 3) ikode = 3; } //*-*- set 'default' column headings for (k = 1; k <= 6; ++k) { colhdu[k-1] = "UNDEFINED"; colhdl[k-1] = "COLUMN HEAD"; } //*-*- print title if Minos errors, and title exists. if (ikode == 4 && fCtitl != fCundef) { Printf(" MINUIT TASK: %s",(const char*)fCtitl); } //*-*- report function value and status if (fval == fUndefi) cheval = " unknown "; else cheval = Form("%g",fval); if (fEDM == fBigedm) chedm = " unknown "; else chedm = Form("%g",fEDM); nc = fNfcn - fNfcnfr; Printf(" FCN=%s FROM %8s STATUS=%10s %6d CALLS %9d TOTAL" ,(const char*)cheval ,(const char*)fCfrom ,(const char*)fCstatu,nc,fNfcn); m = fISW[1]; if (m == 0 || m == 2 || fDcovar == 0) { Printf(" EDM=%s STRATEGY=%2d %s" ,(const char*)chedm,fIstrat ,(const char*)fCovmes[m]); } else { dcmax = 1; dc = TMath::Min(fDcovar,dcmax)*100; Printf(" EDM=%s STRATEGY=%2d ERROR MATRIX UNCERTAINTY %5.1f per cent" ,(const char*)chedm,fIstrat,dc); } if (ikode == 0) return; //*-*- find longest name (for Rene!) ntrail = 10; for (i = 1; i <= fNu; ++i) { if (fNvarl[i-1] < 0) continue; for (ic = 10; ic >= 1; --ic) { if (fCpnam[i-1](ic-1,1) != " ") goto L16; } ic = 1; L16: lbl = 10 - ic; if (lbl < ntrail) ntrail = lbl; } nadd = ntrail / 2 + 1; if (ikode == 1) { colhdu[0] = " "; colhdl[0] = " ERROR "; colhdu[1] = " PHYSICAL"; colhdu[2] = " LIMITS "; colhdl[1] = " NEGATIVE "; colhdl[2] = " POSITIVE "; } if (ikode == 2) { colhdu[0] = " "; colhdl[0] = " ERROR "; colhdu[1] = " INTERNAL "; colhdl[1] = " STEP SIZE "; colhdu[2] = " INTERNAL "; colhdl[2] = " VALUE "; } if (ikode == 3) { colhdu[0] = " "; colhdl[0] = " ERROR "; colhdu[1] = " STEP "; colhdl[1] = " SIZE "; colhdu[2] = " FIRST "; colhdl[2] = " DERIVATIVE "; } if (ikode == 4) { colhdu[0] = " PARABOLIC "; colhdl[0] = " ERROR "; colhdu[1] = " MINOS "; colhdu[2] = "ERRORS "; colhdl[1] = " NEGATIVE "; colhdl[2] = " POSITIVE "; } if (ikode != 4) { if (fISW[1] < 3) colhdu[0] = " APPROXIMATE "; if (fISW[1] < 1) colhdu[0] = " CURRENT GUESS"; } Printf(" EXT PARAMETER %-14s%-14s%-14s",(const char*)colhdu[0] ,(const char*)colhdu[1] ,(const char*)colhdu[2]); Printf(" NO. NAME VALUE %-14s%-14s%-14s",(const char*)colhdl[0] ,(const char*)colhdl[1] ,(const char*)colhdl[2]); //*-*- . . . loop over parameters . . for (i = 1; i <= fNu; ++i) { if (fNvarl[i-1] < 0) continue; l = fNiofex[i-1]; cnambf = cblank(0,nadd) + fCpnam[i-1]; if (l == 0) goto L55; //*-*- variable parameter. x1 = fWerr[l-1]; cx2 = "PLEASE GET X.."; cx3 = "PLEASE GET X.."; if (ikode == 1) { if (fNvarl[i-1] <= 1) { Printf("%4d %-11s%14.5e%14.5e",i,(const char*)cnambf,fU[i-1],x1); continue; } else { x2 = fAlim[i-1]; x3 = fBlim[i-1]; } } if (ikode == 2) { x2 = fDirin[l-1]; x3 = fX[l-1]; } if (ikode == 3) { x2 = fDirin[l-1]; x3 = fGrd[l-1]; if (fNvarl[i-1] > 1 && TMath::Abs(TMath::Cos(fX[l-1])) < .001) { cx3 = "** at limit **"; } } if (ikode == 4) { x2 = fErn[l-1]; if (x2 == 0) cx2 = " "; if (x2 == fUndefi) cx2 = " at limit "; x3 = fErp[l-1]; if (x3 == 0) cx3 = " "; if (x3 == fUndefi) cx3 = " at limit "; } if (cx2 == "PLEASE GET X..") cx2 = Form("%14.5e",x2); if (cx3 == "PLEASE GET X..") cx3 = Form("%14.5e",x3); Printf("%4d %-11s%14.5e%14.5e%-14s%-14s",i ,(const char*)cnambf,fU[i-1],x1 ,(const char*)cx2,(const char*)cx3); //*-*- check if parameter is at limit if (fNvarl[i-1] <= 1 || ikode == 3) continue; if (TMath::Abs(TMath::Cos(fX[l-1])) < .001) { Printf(" WARNING - - ABOVE PARAMETER IS AT LIMIT."); } continue; //*-*- print constant or fixed parameter. L55: colhdu[0] = " constant "; if (fNvarl[i-1] > 0) colhdu[0] = " fixed "; if (fNvarl[i-1] == 4 && ikode == 1) { Printf("%4d %-11s%14.5e%-14s%14.5e%14.5e",i ,(const char*)cnambf,fU[i-1] ,(const char*)colhdu[0],fAlim[i-1],fBlim[i-1]); } else { Printf("%4d %-11s%14.5e%s",i ,(const char*)cnambf,fU[i-1],(const char*)colhdu[0]); } } if (fUp != fUpdflt) { Printf(" ERR DEF= %g",fUp); } return; } /* mnprin_ */ //______________________________________________________________________________ void TMinuit::mnpsdf() { //*-*-*-*-*-*Calculates the eigenvalues of v to see if positive-def*-*-*-*-* //*-* ====================================================== //*-* if not, adds constant along diagonal to make positive. //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t dgmin, padd, pmin, pmax, dg, epspdf, epsmin; Int_t ndex, i, j, ndexd, ip, ifault; TString chbuff, ctemp; epsmin = 1e-6; epspdf = TMath::Max(epsmin,fEpsma2); dgmin = fVhmat[0]; //*-*- Check if negative or zero on diagonal for (i = 1; i <= fNpar; ++i) { ndex = i*(i + 1) / 2; if (fVhmat[ndex-1] <= 0) { mnwarn("W", fCfrom, Form("Negative diagonal element %d in Error Matrix",i)); } if (fVhmat[ndex-1] < dgmin) dgmin = fVhmat[ndex-1]; } if (dgmin <= 0) { dg = epspdf + 1 - dgmin; mnwarn("W", fCfrom, Form("%g added to diagonal of error matrix",dg)); } else { dg = 0; } //*-*- Store VHMAT in P, make sure diagonal pos. for (i = 1; i <= fNpar; ++i) { ndex = i*(i-1) / 2; ndexd = ndex + i; fVhmat[ndexd-1] += dg; fPSDFs[i-1] = 1 / TMath::Sqrt(fVhmat[ndexd-1]); for (j = 1; j <= i; ++j) { ++ndex; fP[i + j*fMaxpar - fMaxpar-1] = fVhmat[ndex-1]*fPSDFs[i-1]*fPSDFs[j-1]; } } //*-*- call eigen (p,p,maxint,npar,pstar,-npar) mneig(fP, fMaxint, fNpar, fMaxint, fPstar, epspdf, ifault); pmin = fPstar[0]; pmax = fPstar[0]; for (ip = 2; ip <= fNpar; ++ip) { if (fPstar[ip-1] < pmin) pmin = fPstar[ip-1]; if (fPstar[ip-1] > pmax) pmax = fPstar[ip-1]; } pmax = TMath::Max(TMath::Abs(pmax),Double_t(1)); if (pmin <= 0 && fLwarn || fISW[4] >= 2) { Printf(" EIGENVALUES OF SECOND-DERIVATIVE MATRIX:"); ctemp = " "; for (ip = 1; ip <= fNpar; ++ip) { ctemp += Form(" %11.4e",fPstar[ip-1]); } Printf((const char*)ctemp); } if (pmin > epspdf*pmax) return; if (fISW[1] == 3) fISW[1] = 2; padd = pmax*.001 - pmin; for (ip = 1; ip <= fNpar; ++ip) { ndex = ip*(ip + 1) / 2; fVhmat[ndex-1] *= padd + 1; } fCstatu = "NOT POSDEF"; mnwarn("W", fCfrom, Form("MATRIX FORCED POS-DEF BY ADDING %f TO DIAGONAL.",padd)); } /* mnpsdf_ */ //______________________________________________________________________________ void TMinuit::mnrazz(Double_t ynew, Double_t *pnew, Double_t *y, Int_t &jh, Int_t &jl) { //*-*-*-*-*Called only by MNSIMP (and MNIMPR) to add a new point*-*-*-*-*-*-* //*-* ===================================================== //*-* and remove an old one from the current simplex, and get the //*-* estimated distance to minimum. //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t pbig, plit; Int_t i, j, nparp1; /* Function Body */ for (i = 1; i <= fNpar; ++i) { fP[i + jh*fMaxpar - fMaxpar-1] = pnew[i-1]; } y[jh-1] = ynew; if (ynew < fAmin) { for (i = 1; i <= fNpar; ++i) { fX[i-1] = pnew[i-1]; } mninex(fX); fAmin = ynew; fCstatu = "PROGRESS "; jl = jh; } jh = 1; nparp1 = fNpar + 1; for (j = 2; j <= nparp1; ++j) { if (y[j-1] > y[jh-1]) jh = j; } fEDM = y[jh-1] - y[jl-1]; if (fEDM <= 0) goto L45; for (i = 1; i <= fNpar; ++i) { pbig = fP[i-1]; plit = pbig; for (j = 2; j <= nparp1; ++j) { if (fP[i + j*fMaxpar - fMaxpar-1] > pbig) pbig = fP[i + j*fMaxpar - fMaxpar-1]; if (fP[i + j*fMaxpar - fMaxpar-1] < plit) plit = fP[i + j*fMaxpar - fMaxpar-1]; } fDirin[i-1] = pbig - plit; } L40: return; L45: Printf(" FUNCTION VALUE DOES NOT SEEM TO DEPEND ON ANY OF THE%d VARIABLE PARAMETERS.",fNpar); Printf(" VERIFY THAT STEP SIZES ARE BIG ENOUGH AND CHECK FCN LOGIC."); Printf(" *******************************************************************************"); Printf(" *******************************************************************************"); goto L40; } /* mnrazz_ */ //______________________________________________________________________________ void TMinuit::mnrn15(Double_t &val, Int_t &inseed) { //*-*-*-*-*-*-*This is a super-portable random number generator*-*-*-*-*-*-* //*-* ================================================ //*-* It should not overflow on any 32-bit machine. //*-* The cycle is only ~10**9, so use with care! //*-* Note especially that VAL must not be undefined on input. //*-* Set Default Starting Seed //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Initialized data */ static Int_t iseed = 12345; Int_t k; if (val == 3) goto L100; inseed = iseed; k = iseed / 53668; iseed = (iseed - k*53668)*40014 - k*12211; if (iseed < 0) iseed += 2147483563; val = Double_t(iseed*4.656613e-10); return; //*-* "entry" to set seed, flag is VAL=3 L100: iseed = inseed; } /* mnrn15_ */ //______________________________________________________________________________ void TMinuit::mnrset(Int_t iopt) { //*-*-*-*-*-*-*-*Resets function value and errors to UNDEFINED*-*-*-*-*-*-*-* //*-* ============================================= //*-* If IOPT=1, //*-* If IOPT=0, sets only MINOS errors to undefined //*-* Called from MNCLER and whenever problem changes, for example //*-* after SET LIMITS, SET PARAM, CALL FCN 6 //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Int_t iext, i; fCstatu = "RESET "; if (iopt >= 1) { fAmin = fUndefi; fFval3 = TMath::Abs(fAmin)*2 + 1; fEDM = fBigedm; fISW[3] = 0; fISW[1] = 0; fDcovar = 1; fISW[0] = 0; } fLnolim = kTRUE; for (i = 1; i <= fNpar; ++i) { iext = fNexofi[i-1]; if (fNvarl[iext-1] >= 4) fLnolim = kFALSE; fErp[i-1] = 0; fErn[i-1] = 0; fGlobcc[i-1] = 0; } if (fISW[1] >= 1) { fISW[1] = 1; fDcovar = TMath::Max(fDcovar,.5); } } /* mnrset_ */ //______________________________________________________________________________ void TMinuit::mnsave() { //*-*-*-*Writes current parameter values and step sizes onto file ISYSSA*-*-* //*-* =============================================================== //*-* in format which can be reread by Minuit for restarting. //*-* The covariance matrix is also output if it exists. //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Printf("mnsave is dummy in the base class TMinuit: Use TMinuitOld"); } /* mnsave_ */ //______________________________________________________________________________ void TMinuit::mnscan() { //*-*-*-*-*Scans the values of FCN as a function of one parameter*-*-*-*-*-* //*-* ====================================================== //*-* and plots the resulting values as a curve using MNPLOT. //*-* It may be called to scan one parameter or all parameters. //*-* retains the best function and parameter values found. //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t step, uhigh, xhreq, xlreq, ubest, fnext, unext, xh, xl; Int_t ipar, iint, icall, ncall, nbins, nparx; Int_t nxypt, nccall, iparwd; xlreq = TMath::Min(fWord7[2],fWord7[3]); xhreq = TMath::Max(fWord7[2],fWord7[3]); ncall = Int_t((fWord7[1] + .01)); if (ncall <= 1) ncall = 41; if (ncall > 101) ncall = 101; nccall = ncall; if (fAmin == fUndefi) mnamin(); iparwd = Int_t((fWord7[0] + .1)); ipar = TMath::Max(iparwd,0); iint = fNiofex[ipar-1]; fCstatu = "NO CHANGE"; if (iparwd > 0) goto L200; //*-*- equivalent to a loop over parameters requested L100: ++ipar; if (ipar > fNu) goto L900; iint = fNiofex[ipar-1]; if (iint <= 0) goto L100; //*-*- set up range for parameter IPAR L200: ubest = fU[ipar-1]; fXpt[0] = ubest; fYpt[0] = fAmin; fChpt[0] = ' '; fXpt[1] = ubest; fYpt[1] = fAmin; fChpt[1] = 'X'; nxypt = 2; if (fNvarl[ipar-1] > 1) goto L300; //*-*- no limits on parameter if (xlreq == xhreq) goto L250; unext = xlreq; step = (xhreq - xlreq) / Double_t(ncall-1); goto L500; L250: xl = ubest - fWerr[iint-1]; xh = ubest + fWerr[iint-1]; mnbins(xl, xh, ncall, unext, uhigh, nbins, step); nccall = nbins + 1; goto L500; //*-*- limits on parameter L300: if (xlreq == xhreq) goto L350; //*-* Computing MAX xl = TMath::Max(xlreq,fAlim[ipar-1]); //*-* Computing MIN xh = TMath::Min(xhreq,fBlim[ipar-1]); if (xl >= xh) goto L700; unext = xl; step = (xh - xl) / Double_t(ncall-1); goto L500; L350: unext = fAlim[ipar-1]; step = (fBlim[ipar-1] - fAlim[ipar-1]) / Double_t(ncall-1); //*-*- main scanning loop over parameter IPAR L500: for (icall = 1; icall <= nccall; ++icall) { fU[ipar-1] = unext; nparx = fNpar; Eval(nparx, fGin, fnext, fU, 4); ++fNfcn; ++nxypt; fXpt[nxypt-1] = unext; fYpt[nxypt-1] = fnext; fChpt[nxypt-1] = '*'; if (fnext < fAmin) { fAmin = fnext; ubest = unext; fCstatu = "IMPROVED "; } unext += step; } fChpt[nccall] = 0; //*-*- finished with scan of parameter IPAR fU[ipar-1] = ubest; mnexin(fX); Printf("%dSCAN OF PARAMETER NO. %d, %s" ,fNewpag,ipar,(const char*)fCpnam[ipar-1]); mnplot(fXpt, fYpt, fChpt, nxypt, fNpagwd, fNpagln); goto L800; L700: Printf(" REQUESTED RANGE OUTSIDE LIMITS FOR PARAMETER %d",ipar); L800: if (iparwd <= 0) goto L100; //*-*- finished with all parameters L900: mnprin(5, fAmin); } /* mnscan_ */ //______________________________________________________________________________ void TMinuit::mnseek() { //*-*-*-*Performs a rough (but global) minimization by monte carlo search*-* //*-* ================================================================ //*-* Each time a new minimum is found, the search area is shifted //*-* to be centered at the best value. Random points are chosen //*-* uniformly over a hypercube determined by current step sizes. //*-* The Metropolis algorithm accepts a worse point with probability //*-* exp(-d/UP), where d is the degradation. Improved points //*-* are of course always accepted. Actual steps are random //*-* multiples of the nominal steps (DIRIN). //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Local variables */ Double_t dxdi, rnum, ftry, rnum1, rnum2, alpha; Double_t flast, bar; Int_t ipar, iext, j, ifail, iseed, nparx, istep, ib, mxfail, mxstep; mxfail = Int_t(fWord7[0]); if (mxfail <= 0) mxfail = fNpar*20 + 100; mxstep = mxfail*10; if (fAmin == fUndefi) mnamin(); alpha = fWord7[1]; if (alpha <= 0) alpha = 3; if (fISW[4] >= 1) { Printf(" MNSEEK: MONTE CARLO MINIMIZATION USING METROPOLIS ALGORITHM"); Printf(" TO STOP AFTER %6d SUCCESSIVE FAILURES, OR %7d STEPS",mxfail,mxstep); Printf(" MAXIMUM STEP SIZE IS %9.3f ERROR BARS.",alpha); } fCstatu = "INITIAL "; if (fISW[4] >= 2) mnprin(2, fAmin); fCstatu = "UNCHANGED "; ifail = 0; rnum = 0; rnum1 = 0; rnum2 = 0; nparx = fNpar; flast = fAmin; //*-*- set up step sizes, starting values for (ipar = 1; ipar <= fNpar; ++ipar) { iext = fNexofi[ipar-1]; fDirin[ipar-1] = alpha*2*fWerr[ipar-1]; if (fNvarl[iext-1] > 1) { //*-*- parameter with limits mndxdi(fX[ipar-1], ipar-1, dxdi); if (dxdi == 0) dxdi = 1; fDirin[ipar-1] = alpha*2*fWerr[ipar-1] / dxdi; if (TMath::Abs(fDirin[ipar-1]) > 6.2831859999999997) { fDirin[ipar-1] = 6.2831859999999997; } } fSEEKxmid[ipar-1] = fX[ipar-1]; fSEEKxbest[ipar-1] = fX[ipar-1]; } //*-*- search loop for (istep = 1; istep <= mxstep; ++istep) { if (ifail >= mxfail) break; for (ipar = 1; ipar <= fNpar; ++ipar) { mnrn15(rnum1, iseed); mnrn15(rnum2, iseed); fX[ipar-1] = fSEEKxmid[ipar-1] + (rnum1 + rnum2 - 1)*.5*fDirin[ipar-1]; } mninex(fX); Eval(nparx, fGin, ftry, fU, 4); ++fNfcn; if (ftry < flast) { if (ftry < fAmin) { fCstatu = "IMPROVEMNT"; fAmin = ftry; for (ib = 1; ib <= fNpar; ++ib) { fSEEKxbest[ib-1] = fX[ib-1]; } ifail = 0; if (fISW[4] >= 2) mnprin(2, fAmin); } goto L300; } else { ++ifail; //*-*- Metropolis algorithm bar = (fAmin - ftry) / fUp; mnrn15(rnum, iseed); if (bar < TMath::Log(rnum)) continue; } //*-*- Accept new point, move there L300: for (j = 1; j <= fNpar; ++j) { fSEEKxmid[j-1] = fX[j-1]; } flast = ftry; } //*-*- end search loop if (fISW[4] > 1) { Printf(" MNSEEK: %5d SUCCESSIVE UNSUCCESSFUL TRIALS.",ifail); } for (ib = 1; ib <= fNpar; ++ib) { fX[ib-1] = fSEEKxbest[ib-1]; } mninex(fX); if (fISW[4] >= 1) mnprin(2, fAmin); if (fISW[4] == 0) mnprin(0, fAmin); } /* mnseek_ */ //______________________________________________________________________________ void TMinuit::mnset() { //*-*-*-*-*Interprets the commands that start with SET and SHOW*-*-*-*-*-*-* //*-* ==================================================== //*-* Called from MNEXCM //*-* file characteristics for SET INPUT //*-* 'SET ' or 'SHOW', 'ON ' or 'OFF', 'SUPPRESSED' or 'REPORTED ' //*-* explanation of print level numbers -1:3 and strategies 0:2 //*-* identification of debug options //*-* things that can be set or shown //*-* options not intended for normal users //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Initialized data */ const char *cname[30] = { "FCN value ", "PARameters", "LIMits ", "COVariance", "CORrelatio", "PRInt levl", "NOGradient", "GRAdient ", "ERRor def ", "INPut file", "WIDth page", "LINes page", "NOWarnings", "WARnings ", "RANdom gen", "TITle ", "STRategy ", "EIGenvalue", "PAGe throw", "MINos errs", "EPSmachine", "OUTputfile", "BATch ", "INTeractiv", "VERsion ", "reserve ", "NODebug ", "DEBug ", "SHOw ", "SET "}; static Int_t nname = 25; static Int_t nntot = 30; static TString cprlev[5] = { "-1: NO OUTPUT EXCEPT FROM SHOW ", " 0: REDUCED OUTPUT ", " 1: NORMAL OUTPUT ", " 2: EXTRA OUTPUT FOR PROBLEM CASES", " 3: MAXIMUM OUTPUT "}; static TString cstrat[3] = { " 0: MINIMIZE THE NUMBER OF CALLS TO FUNCTION", " 1: TRY TO BALANCE SPEED AGAINST RELIABILITY", " 2: MAKE SURE MINIMUM TRUE, ERRORS CORRECT "}; static TString cdbopt[7] = { "REPORT ALL EXCEPTIONAL CONDITIONS ", "MNLINE: LINE SEARCH MINIMIZATION ", "MNDERI: FIRST DERIVATIVE CALCULATIONS ", "MNHESS: SECOND DERIVATIVE CALCULATIONS ", "MNMIGR: COVARIANCE MATRIX UPDATES ", "MNHES1: FIRST DERIVATIVE UNCERTAINTIES ", "MNCONT: MNCONTOUR PLOT (MNCROS SEARCH) "}; /* System generated locals */ Int_t f_inqu(); /* Local variables */ Double_t val; Int_t iset, iprm, i, jseed, kname, iseed, iunit, id, ii, kk; Int_t ikseed, idbopt, igrain, iswsav, isw2; TString cfname, cmode, ckind, cwarn, copt, ctemp, ctemp2; Bool_t lname=kFALSE; for (i = 1; i <= nntot; ++i) { ctemp = cname[i-1]; ckind = ctemp(0,3); ctemp2 = fCword(4,6); if (strstr(ctemp2.Data(),ckind.Data())) goto L5; } i = 0; L5: kname = i; //*-*- Command could be SET xxx, SHOW xxx, HELP SET or HELP SHOW ctemp2 = fCword(0,3); if ( ctemp2.Contains("HEL")) goto L2000; if ( ctemp2.Contains("SHO")) goto L1000; if (!ctemp2.Contains("SET")) goto L1900; //*-*- --- ckind = "SET "; //*-*- . . . . . . . . . . set unknown if (kname <= 0) goto L1900; //*-*- . . . . . . . . . . set known switch ((int)kname) { case 1: goto L3000; case 2: goto L20; case 3: goto L30; case 4: goto L40; case 5: goto L3000; case 6: goto L60; case 7: goto L70; case 8: goto L80; case 9: goto L90; case 10: goto L100; case 11: goto L110; case 12: goto L120; case 13: goto L130; case 14: goto L140; case 15: goto L150; case 16: goto L160; case 17: goto L170; case 18: goto L3000; case 19: goto L190; case 20: goto L3000; case 21: goto L210; case 22: goto L220; case 23: goto L230; case 24: goto L240; case 25: goto L3000; case 26: goto L1900; case 27: goto L270; case 28: goto L280; case 29: goto L290; case 30: goto L300; } //*-*- . . . . . . . . . . set param L20: iprm = Int_t(fWord7[0]); if (iprm > fNu) goto L25; if (iprm <= 0) goto L25; if (fNvarl[iprm-1] < 0) goto L25; fU[iprm-1] = fWord7[1]; mnexin(fX); isw2 = fISW[1]; mnrset(1); //*-*- Keep approximate covariance matrix, even if new param value fISW[1] = TMath::Min(isw2,1); fCfrom = "SET PARM"; fNfcnfr = fNfcn; fCstatu = "NEW VALUES"; return; L25: Printf(" UNDEFINED PARAMETER NUMBER. IGNORED."); return; //*-*- . . . . . . . . . . set limits L30: mnlims(); return; //*-*- . . . . . . . . . . set covar L40: //*-* this command must be handled by MNREAD, and is not Fortran-callable goto L3000; //*-*- . . . . . . . . . . set print L60: fISW[4] = Int_t(fWord7[0]); return; //*-*- . . . . . . . . . . set nograd L70: fISW[2] = 0; return; //*-*- . . . . . . . . . . set grad L80: mngrad(); return; //*-*- . . . . . . . . . . set errdef L90: if (fWord7[0] == fUp) return; if (fWord7[0] <= 0) { if (fUp == fUpdflt) return; fUp = fUpdflt; } else { fUp = fWord7[0]; } for (i = 1; i <= fNpar; ++i) { fErn[i-1] = 0; fErp[i-1] = 0; } mnwerr(); return; //*-*- . . . . . . . . . . set input //*-* This command must be handled by MNREAD. If it gets this far, //*-*- it is illegal. L100: goto L3000; //*-*- . . . . . . . . . . set width L110: fNpagwd = Int_t(fWord7[0]); fNpagwd = TMath::Max(fNpagwd,50); return; L120: fNpagln = Int_t(fWord7[0]); return; //*-*- . . . . . . . . . . set nowarn L130: fLwarn = kFALSE; return; //*-*- . . . . . . . . . . set warn L140: fLwarn = kTRUE; mnwarn("W", "SHO", "SHO"); return; //*-*- . . . . . . . . . . set random L150: jseed = Int_t(fWord7[0]); val = 3; mnrn15(val, jseed); if (fISW[4] > 0) { Printf(" MINUIT RANDOM NUMBER SEED SET TO %d",jseed); } return; //*-*- . . . . . . . . . . set title L160: //*-* this command must be handled by MNREAD, and is not Fortran-callable goto L3000; //*-*- . . . . . . . . . set strategy L170: fIstrat = Int_t(fWord7[0]); fIstrat = TMath::Max(fIstrat,0); fIstrat = TMath::Min(fIstrat,2); if (fISW[4] > 0) goto L1172; return; //*-*- . . . . . . . . . set page throw L190: fNewpag = Int_t(fWord7[0]); goto L1190; //*-*- . . . . . . . . . . set epsmac L210: if (fWord7[0] > 0 && fWord7[0] < .1) { fEpsmac = fWord7[0]; } fEpsma2 = TMath::Sqrt(fEpsmac); goto L1210; //*-*- . . . . . . . . . . set outputfile L220: iunit = Int_t(fWord7[0]); fIsyswr = iunit; fIstkwr[0] = iunit; if (fISW[4] >= 0) goto L1220; return; //*-*- . . . . . . . . . . set batch L230: fISW[5] = 0; if (fISW[4] >= 0) goto L1100; return; //*-*- . . . . . . . . . . set interactive L240: fISW[5] = 1; if (fISW[4] >= 0) goto L1100; return; //*-*- . . . . . . . . . . set nodebug L270: iset = 0; goto L281; //*-*- . . . . . . . . . . set debug L280: iset = 1; L281: idbopt = Int_t(fWord7[0]); if (idbopt > 6) goto L288; if (idbopt >= 0) { fIdbg[idbopt] = iset; if (iset == 1) fIdbg[0] = 1; } else { //*-*- SET DEBUG -1 sets all debug options for (id = 0; id <= 6; ++id) { fIdbg[id] = iset; } } fLrepor = fIdbg[0] >= 1; mnwarn("D", "SHO", "SHO"); return; L288: Printf(" UNKNOWN DEBUG OPTION %d REQUESTED. IGNORED",idbopt); return; //*-*- . . . . . . . . . . set show L290: //*-*- . . . . . . . . . . set set L300: goto L3000; //*-*- ----------------------------------------------------- L1000: //*-*- at this point, CWORD must be 'SHOW' ckind = "SHOW"; if (kname <= 0) goto L1900; switch ((int)kname) { case 1: goto L1010; case 2: goto L1020; case 3: goto L1030; case 4: goto L1040; case 5: goto L1050; case 6: goto L1060; case 7: goto L1070; case 8: goto L1070; case 9: goto L1090; case 10: goto L1100; case 11: goto L1110; case 12: goto L1120; case 13: goto L1130; case 14: goto L1130; case 15: goto L1150; case 16: goto L1160; case 17: goto L1170; case 18: goto L1180; case 19: goto L1190; case 20: goto L1200; case 21: goto L1210; case 22: goto L1220; case 23: goto L1100; case 24: goto L1100; case 25: goto L1250; case 26: goto L1900; case 27: goto L1270; case 28: goto L1270; case 29: goto L1290; case 30: goto L1300; } //*-*- . . . . . . . . . . show fcn L1010: if (fAmin == fUndefi) mnamin(); mnprin(0, fAmin); return; //*-*- . . . . . . . . . . show param L1020: if (fAmin == fUndefi) mnamin(); mnprin(5, fAmin); return; //*-*- . . . . . . . . . . show limits L1030: if (fAmin == fUndefi) mnamin(); mnprin(1, fAmin); return; //*-*- . . . . . . . . . . show covar L1040: mnmatu(1); return; //*-*- . . . . . . . . . . show corre L1050: mnmatu(0); return; //*-*- . . . . . . . . . . show print L1060: if (fISW[4] < -1) fISW[4] = -1; if (fISW[4] > 3) fISW[4] = 3; Printf(" ALLOWED PRINT LEVELS ARE:"); Printf(" %s",cprlev[0].Data()); Printf(" %s",cprlev[1].Data()); Printf(" %s",cprlev[2].Data()); Printf(" %s",cprlev[3].Data()); Printf(" %s",cprlev[4].Data()); Printf(" CURRENT PRINTOUT LEVEL IS %s",cprlev[fISW[4]+1].Data()); return; //*-*- . . . . . . . show nograd, grad L1070: if (fISW[2] <= 0) { Printf(" NOGRAD IS SET. DERIVATIVES NOT COMPUTED IN FCN."); } else { Printf(" GRAD IS SET. USER COMPUTES DERIVATIVES IN FCN."); } return; //*-*- . . . . . . . . . . show errdef L1090: Printf(" ERRORS CORRESPOND TO FUNCTION CHANGE OF %g",fUp); return; //*-*- . . . . . . . . . . show input, //*-*- batch, or interactive L1100: // ioin__1.inerr = 0; // ioin__1.inunit = fIsysrd; // ioin__1.infile = 0; // ioin__1.inex = 0; // ioin__1.inopen = 0; // ioin__1.innum = 0; // ioin__1.innamed = &lname; // ioin__1.innamlen = 64; // ioin__1.inname = cfname; // ioin__1.inacc = 0; // ioin__1.inseq = 0; // ioin__1.indir = 0; // ioin__1.infmt = 0; // ioin__1.inform = 0; // ioin__1.inunf = 0; // ioin__1.inrecl = 0; // ioin__1.innrec = 0; // ioin__1.inblank = 0; // f_inqu(&ioin__1); cmode = "BATCH MODE "; if (fISW[5] == 1) cmode = "INTERACTIVE MODE"; if (! lname) cfname = "unknown"; Printf(" INPUT NOW BEING READ IN %s FROM UNIT NO. %d FILENAME: %s" ,(const char*)cmode,fIsysrd,(const char*)cfname); return; //*-*- . . . . . . . . . . show width L1110: Printf(" PAGE WIDTH IS SET TO %d COLUMNS",fNpagwd); return; //*-*- . . . . . . . . . . show lines L1120: Printf(" PAGE LENGTH IS SET TO %d LINES",fNpagln); return; //*-*- . . . . . . .show nowarn, warn L1130: cwarn = "SUPPRESSED"; if (fLwarn) cwarn = "REPORTED "; Printf("%s",(const char*)cwarn); if (! fLwarn) mnwarn("W", "SHO", "SHO"); return; //*-*- . . . . . . . . . . show random L1150: val = 0; mnrn15(val, igrain); ikseed = igrain; Printf(" MINUIT RNDM SEED IS CURRENTLY=",ikseed); val = 3; iseed = ikseed; mnrn15(val, iseed); return; //*-*- . . . . . . . . . show title L1160: Printf(" TITLE OF CURRENT TASK IS:%s",(const char*)fCtitl); return; //*-*- . . . . . . . show strategy L1170: Printf(" ALLOWED STRATEGIES ARE:"); Printf(" %s",cstrat[0].Data()); Printf(" %s",cstrat[1].Data()); Printf(" %s",cstrat[2].Data()); L1172: Printf(" NOW USING STRATEGY %s",(const char*)cstrat[fIstrat]); return; //*-*- . . . . . show eigenvalues L1180: iswsav = fISW[4]; fISW[4] = 3; if (fISW[1] < 1) { Printf("%s",(const char*)fCovmes[0]); } else { mnpsdf(); } fISW[4] = iswsav; return; //*-*- . . . . . show page throw L1190: Printf(" PAGE THROW CARRIAGE CONTROL = %d",fNewpag); if (fNewpag == 0) { Printf(" NO PAGE THROWS IN MINUIT OUTPUT"); } return; //*-*- . . . . . . show minos errors L1200: for (ii = 1; ii <= fNpar; ++ii) { if (fErp[ii-1] > 0 || fErn[ii-1] < 0) goto L1204; } Printf(" THERE ARE NO MINOS ERRORS CURRENTLY VALID."); return; L1204: mnprin(4, fAmin); return; //*-*- . . . . . . . . . show epsmac L1210: Printf(" FLOATING-POINT NUMBERS ASSUMED ACCURATE TO %g",fEpsmac); return; //*-*- . . . . . . show outputfiles L1220: Printf(" MINUIT PRIMARY OUTPUT TO UNIT %d",fIsyswr); return; //*-*- . . . . . . show version L1250: Printf(" THIS IS MINUIT VERSION:%s",(const char*)fCvrsn); return; //*-*- . . . . . . show nodebug, debug L1270: for (id = 0; id <= 6; ++id) { copt = "OFF"; if (fIdbg[id] >= 1) copt = "ON "; Printf(" DEBUG OPTION %3d IS %3s :%s" ,id,(const char*)copt,(const char*)cdbopt[id]); } if (! fLrepor) mnwarn("D", "SHO", "SHO"); return; //*-*- . . . . . . . . . . show show L1290: ckind = "SHOW"; goto L2100; //*-*- . . . . . . . . . . show set L1300: ckind = "SET "; goto L2100; //*-*- ----------------------------------------------------- //*-*- UNKNOWN COMMAND L1900: Printf(" THE COMMAND:%10s IS UNKNOWN.",(const char*)fCword); goto L2100; //*-*- ----------------------------------------------------- //*-*- HELP SHOW, HELP SET, SHOW SET, or SHOW SHOW L2000: ckind = "SET "; ctemp2 = fCword(3,7); if (strcmp(ctemp2.Data(), "SHO")) ckind = "SHOW"; L2100: Printf(" THE FORMAT OF THE %4s COMMAND IS:",(const char*)ckind); Printf(" %s xxx [numerical arguments if any]",(const char*)ckind); Printf(" WHERE xxx MAY BE ONE OF THE FOLLOWING:"); for (kk = 1; kk <= nname; ++kk) { Printf(" %s",cname[kk-1]); } return; //*-*- ----------------------------------------------------- //*-*- ILLEGAL COMMAND L3000: Printf(" ABOVE COMMAND IS ILLEGAL. IGNORED"); } /* mnset_ */ //______________________________________________________________________________ void TMinuit::mnsimp() { //*-*-*-*-*Minimization using the simplex method of Nelder and Mead*-*-*-*-* //*-* ======================================================== //*-* Performs a minimization using the simplex method of Nelder //*-* and Mead (ref. -- Comp. J. 7,308 (1965)). //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* Initialized data */ static Double_t alpha = 1; static Double_t beta = .5; static Double_t gamma = 2; static Double_t rhomin = 4; static Double_t rhomax = 8; /* Local variables */ Double_t dmin_, dxdi, yrho, f, ynpp1, aming, ypbar; Double_t bestx, ystar, y1, y2, ystst, pb, wg; Double_t absmin, rho, sig2, rho1, rho2; Int_t npfn, i, j, k, jhold, ncycl, nparx; Int_t nparp1, kg, jh, nf, jl, ns; if (fNpar <= 0) return; if (fAmin == fUndefi) mnamin(); fCfrom = "SIMPLEX "; fNfcnfr = fNfcn; fCstatu = "UNCHANGED "; npfn = fNfcn; nparp1 = fNpar + 1; nparx = fNpar; rho1 = alpha + 1; rho2 = rho1 + alpha*gamma; wg = 1 / Double_t(fNpar); if (fISW[4] >= 0) { Printf(" START SIMPLEX MINIMIZATION. CONVERGENCE WHEN EDM .LT. %g",fEpsi); } for (i = 1; i <= fNpar; ++i) { fDirin[i-1] = fWerr[i-1]; mndxdi(fX[i-1], i-1, dxdi); if (dxdi != 0) fDirin[i-1] = fWerr[i-1] / dxdi; dmin_ = fEpsma2*TMath::Abs(fX[i-1]); if (fDirin[i-1] < dmin_) fDirin[i-1] = dmin_; } //*-* ** choose the initial simplex using single-parameter searches L1: ynpp1 = fAmin; jl = nparp1; fSIMPy[nparp1-1] = fAmin; absmin = fAmin; for (i = 1; i <= fNpar; ++i) { aming = fAmin; fPbar[i-1] = fX[i-1]; bestx = fX[i-1]; kg = 0; ns = 0; nf = 0; L4: fX[i-1] = bestx + fDirin[i-1]; mninex(fX); Eval(nparx, fGin, f, fU, 4); ++fNfcn; if (f <= aming) goto L6; //*-*- failure if (kg == 1) goto L8; kg = -1; ++nf; fDirin[i-1] *= -.4; if (nf < 3) goto L4; ns = 6; //*-*- success L6: bestx = fX[i-1]; fDirin[i-1] *= 3; aming = f; fCstatu = "PROGRESS "; kg = 1; ++ns; if (ns < 6) goto L4; //*-*- local minimum found in ith direction L8: fSIMPy[i-1] = aming; if (aming < absmin) jl = i; if (aming < absmin) absmin = aming; fX[i-1] = bestx; for (k = 1; k <= fNpar; ++k) { fP[k + i*fMaxpar - fMaxpar-1] = fX[k-1]; } } jh = nparp1; fAmin = fSIMPy[jl-1]; mnrazz(ynpp1, fPbar, fSIMPy, jh, jl); for (i = 1; i <= fNpar; ++i) { fX[i-1] = fP[i + jl*fMaxpar - fMaxpar-1]; } mninex(fX); fCstatu = "PROGRESS "; if (fISW[4] >= 1) mnprin(5, fAmin); fEDM = fBigedm; sig2 = fEDM; ncycl = 0; //*-*- . . . . . start main loop L50: if (sig2 < fEpsi && fEDM < fEpsi) goto L76; sig2 = fEDM; if (fNfcn - npfn > fNfcnmx) goto L78; //*-*- calculate new point * by reflection for (i = 1; i <= fNpar; ++i) { pb = 0; for (j = 1; j <= nparp1; ++j) { pb += wg*fP[i + j*fMaxpar - fMaxpar-1]; } fPbar[i-1] = pb - wg*fP[i + jh*fMaxpar - fMaxpar-1]; fPstar[i-1] = (alpha + 1)*fPbar[i-1] - alpha*fP[i + jh*fMaxpar - fMaxpar-1]; } mninex(fPstar); Eval(nparx, fGin, ystar, fU, 4); ++fNfcn; if (ystar >= fAmin) goto L70; //*-*- point * better than jl, calculate new point ** for (i = 1; i <= fNpar; ++i) { fPstst[i-1] = gamma*fPstar[i-1] + (1 - gamma)*fPbar[i-1]; } mninex(fPstst); Eval(nparx, fGin, ystst, fU, 4); ++fNfcn; //*-*- try a parabola through ph, pstar, pstst. min = prho y1 = (ystar - fSIMPy[jh-1])*rho2; y2 = (ystst - fSIMPy[jh-1])*rho1; rho = (rho2*y1 - rho1*y2)*.5 / (y1 - y2); if (rho < rhomin) goto L66; if (rho > rhomax) rho = rhomax; for (i = 1; i <= fNpar; ++i) { fPrho[i-1] = rho*fPbar[i-1] + (1 - rho)*fP[i + jh*fMaxpar - fMaxpar-1]; } mninex(fPrho); Eval(nparx, fGin, yrho, fU, 4); ++fNfcn; if (yrho < fSIMPy[jl-1] && yrho < ystst) goto L65; if (ystst < fSIMPy[jl-1]) goto L67; if (yrho > fSIMPy[jl-1]) goto L66; //*-*- accept minimum point of parabola, PRHO L65: mnrazz(yrho, fPrho, fSIMPy, jh, jl); goto L68; L66: if (ystst < fSIMPy[jl-1]) goto L67; mnrazz(ystar, fPstar, fSIMPy, jh, jl); goto L68; L67: mnrazz(ystst, fPstst, fSIMPy, jh, jl); L68: ++ncycl; if (fISW[4] < 2) goto L50; if (fISW[4] >= 3 || ncycl % 10 == 0) { mnprin(5, fAmin); } goto L50; //*-*- point * is not as good as jl L70: if (ystar >= fSIMPy[jh-1]) goto L73; jhold = jh; mnrazz(ystar, fPstar, fSIMPy, jh, jl); if (jhold != jh) goto L50; //*-*- calculate new point ** L73: for (i = 1; i <= fNpar; ++i) { fPstst[i-1] = beta*fP[i + jh*fMaxpar - fMaxpar-1] + (1 - beta)*fPbar[i-1]; } mninex(fPstst); Eval(nparx, fGin, ystst, fU, 4); ++fNfcn; if (ystst > fSIMPy[jh-1]) goto L1; //*-*- point ** is better than jh if (ystst < fAmin) goto L67; mnrazz(ystst, fPstst, fSIMPy, jh, jl); goto L50; //*-*- . . . . . . end main loop L76: if (fISW[4] >= 0) { Printf(" SIMPLEX MINIMIZATION HAS CONVERGED."); } fISW[3] = 1; goto L80; L78: if (fISW[4] >= 0) { Printf(" SIMPLEX TERMINATES WITHOUT CONVERGENCE."); } fCstatu = "CALL LIMIT"; fISW[3] = -1; fISW[0] = 1; L80: for (i = 1; i <= fNpar; ++i) { pb = 0; for (j = 1; j <= nparp1; ++j) { pb += wg*fP[i + j*fMaxpar - fMaxpar-1]; } fPbar[i-1] = pb - wg*fP[i + jh*fMaxpar - fMaxpar-1]; } mninex(fPbar); Eval(nparx, fGin, ypbar, fU, 4); ++fNfcn; if (ypbar < fAmin) mnrazz(ypbar, fPbar, fSIMPy, jh, jl); mninex(fX); if (fNfcnmx + npfn - fNfcn < fNpar*3) goto L90; if (fEDM > fEpsi*2) goto L1; L90: if (fISW[4] >= 0) mnprin(5, fAmin); } /* mnsimp_ */ //______________________________________________________________________________ void TMinuit::mnstat(Double_t &fmin, Double_t &fedm, Double_t &errdef, Int_t &npari, Int_t &nparx, Int_t &istat) { //*-*-*-*-*Returns concerning the current status of the minimization*-*-*-*-* //*-* ========================================================= //*-* User-called //*-* Namely, it returns: //*-* FMIN: the best function value found so far //*-* FEDM: the estimated vertical distance remaining to minimum //*-* ERRDEF: the value of UP defining parameter uncertainties //*-* NPARI: the number of currently variable parameters //*-* NPARX: the highest (external) parameter number defined by user //*-* ISTAT: a status integer indicating how good is the covariance //*-* matrix: 0= not calculated at all //*-* 1= approximation only, not accurate //*-* 2= full matrix, but forced positive-definite //*-* 3= full accurate covariance matrix //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* fmin = fAmin; fedm = fEDM; errdef = fUp; npari = fNpar; nparx = fNu; istat = fISW[1]; if (fEDM == fBigedm) fedm = fUp; if (fAmin == fUndefi) { fmin = 0; fedm = fUp; istat = 0; } } /* mnstat_ */ //______________________________________________________________________________ void TMinuit::mntiny(Double_t epsp1, Double_t &epsbak) { //*-*-*-*-*-*-*-*To find the machine precision*-*-*-*-*-*-*-*-*-*-*-*-*-*-* //*-* ============================= //*-* Compares its argument with the value 1.0, and returns //*-* the value .TRUE. if they are equal. To find EPSMAC //*-* safely by foiling the Fortran optimizer //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* epsbak = epsp1 - 1; } /* mntiny_ */ //______________________________________________________________________________ Bool_t TMinuit::mnunpt(TString &cfname) { //*-*-*-*-*-*Returns .TRUE. if CFNAME contains unprintable characters*-*-*-* //*-* ======================================================== //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Int_t i, l, ic; Bool_t ret_val; static TString cpt = " ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz1234567890./;:[]$%*_!@#&+()"; ret_val = kFALSE; l = strlen((const char*)cfname); for (i = 1; i <= l; ++i) { for (ic = 1; ic <= 80; ++ic) { if (cfname[i-1] == cpt[ic-1]) goto L100; } return kTRUE; L100: ; } return ret_val; } /* mnunpt_ */ //______________________________________________________________________________ void TMinuit::mnvert(Double_t *a, Int_t l, Int_t, Int_t n, Int_t &ifail) { //*-*-*-*-*-*-*-*-*-*-*-*Inverts a symmetric matrix*-*-*-*-*-*-*-*-*-*-*-*-* //*-* ========================== //*-* inverts a symmetric matrix. matrix is first scaled to //*-* have all ones on the diagonal (equivalent to change of units) //*-* but no pivoting is done since matrix is positive-definite. //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* /* System generated locals */ Int_t a_offset; /* Local variables */ Double_t si; Int_t i, j, k, kp1, km1; /* Parameter adjustments */ a_offset = l + 1; a -= a_offset; /* Function Body */ ifail = 0; if (n < 1) goto L100; if (n > fMaxint) goto L100; //*-*- scale matrix by sqrt of diag elements for (i = 1; i <= n; ++i) { si = a[i + i*l]; if (si <= 0) goto L100; fVERTs[i-1] = 1 / TMath::Sqrt(si); } for (i = 1; i <= n; ++i) { for (j = 1; j <= n; ++j) { a[i + j*l] = a[i + j*l]*fVERTs[i-1]*fVERTs[j-1]; } } //*-*- . . . start main loop . . . . for (i = 1; i <= n; ++i) { k = i; //*-*- preparation for elimination step1 if (a[k + k*l] != 0) fVERTq[k-1] = 1 / a[k + k*l]; else goto L100; fVERTpp[k-1] = 1; a[k + k*l] = 0; kp1 = k + 1; km1 = k - 1; if (km1 < 0) goto L100; else if (km1 == 0) goto L50; else goto L40; L40: for (j = 1; j <= km1; ++j) { fVERTpp[j-1] = a[j + k*l]; fVERTq[j-1] = a[j + k*l]*fVERTq[k-1]; a[j + k*l] = 0; } L50: if (k - n < 0) goto L51; else if (k - n == 0) goto L60; else goto L100; L51: for (j = kp1; j <= n; ++j) { fVERTpp[j-1] = a[k + j*l]; fVERTq[j-1] = -a[k + j*l]*fVERTq[k-1]; a[k + j*l] = 0; } //*-*- elimination proper L60: for (j = 1; j <= n; ++j) { for (k = j; k <= n; ++k) { a[j + k*l] += fVERTpp[j-1]*fVERTq[k-1]; } } } //*-*- elements of left diagonal and unscaling for (j = 1; j <= n; ++j) { for (k = 1; k <= j; ++k) { a[k + j*l] = a[k + j*l]*fVERTs[k-1]*fVERTs[j-1]; a[j + k*l] = a[k + j*l]; } } return; //*-*- failure return L100: ifail = 1; } /* mnvert_ */ //______________________________________________________________________________ void TMinuit::mnwarn(const char *copt1, const char *corg1, const char *cmes1) { //*-*-*-*-*-*-*-*-*-*-*-*Prints Warning messages*-*-*-*-*-*-*-*-*-*-*-*-*-* //*-* ======================= //*-* If COPT='W', CMES is a WARning message from CORG. //*-* If COPT='D', CMES is a DEBug message from CORG. //*-* If SET WARnings is in effect (the default), this routine //*-* prints the warning message CMES coming from CORG. //*-* If SET NOWarnings is in effect, the warning message is //*-* stored in a circular buffer of length MAXMES. //*-* If called with CORG=CMES='SHO', it prints the messages in //*-* the circular buffer, FIFO, and empties the buffer. //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* TString copt = copt1; TString corg = corg1; TString cmes = cmes1; const Int_t MAXMES = 10; Int_t ityp, i, ic, nm; TString englsh, ctyp; if (corg(0,3) != "SHO" || cmes(0,3) != "SHO") { //*-*- Either print warning or put in buffer if (copt == "W") { ityp = 1; if (fLwarn) { Printf(" MINUIT WARNING IN %s",(const char*)corg); Printf(" ============== %s",(const char*)cmes); return; } } else { ityp = 2; if (fLrepor) { Printf(" MINUIT DEBUG FOR %s",(const char*)corg); Printf(" =============== %s ",(const char*)cmes); return; } } //*-*- if appropriate flag is off, fill circular buffer if (fNwrmes[ityp-1] == 0) fIcirc[ityp-1] = 0; ++fNwrmes[ityp-1]; ++fIcirc[ityp-1]; if (fIcirc[ityp-1] > 10) fIcirc[ityp-1] = 1; ic = fIcirc[ityp-1]; fOrigin[ic] = corg; fWarmes[ic] = cmes; fNfcwar[ic] = fNfcn; return; } //*-*- 'SHO WARnings', ask if any suppressed mess in buffer if (copt == "W") { ityp = 1; ctyp = "WARNING"; } else { ityp = 2; ctyp = "*DEBUG*"; } if (fNwrmes[ityp-1] > 0) { englsh = " WAS SUPPRESSED. "; if (fNwrmes[ityp-1] > 1) englsh = "S WERE SUPPRESSED."; Printf(" %5d MINUIT %s MESSAGE%s",fNwrmes[ityp-1] ,(const char*)ctyp,(const char*)englsh); nm = fNwrmes[ityp-1]; ic = 0; if (nm > MAXMES) { Printf(" ONLY THE MOST RECENT 10 WILL BE LISTED BELOW."); nm = MAXMES; ic = fIcirc[ityp-1]; } Printf(" CALLS ORIGIN MESSAGE"); for (i = 1; i <= nm; ++i) { ++ic; if (ic > MAXMES) ic = 1; Printf(" %6d %s %s", fNfcwar[ic],fOrigin[ic].Data(),fWarmes[ic].Data()); } fNwrmes[ityp-1] = 0; Printf(" "); } } /* mnwarn_ */ //______________________________________________________________________________ void TMinuit::mnwerr() { //*-*-*-*-*-*-*-*Calculates the WERR, external parameter errors*-*-*-*-*-*-* //*-* ============================================== //*-* and the global correlation coefficients, to be called //*-* whenever a new covariance matrix is available. //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Double_t denom, ba, al, dx, du1, du2; Int_t ndex, ierr, i, j, k, l, ndiag, k1, iin; //*-*- calculate external error if v exists if (fISW[1] >= 1) { for (l = 1; l <= fNpar; ++l) { ndex = l*(l + 1) / 2; dx = TMath::Sqrt(TMath::Abs(fVhmat[ndex-1]*fUp)); i = fNexofi[l-1]; if (fNvarl[i-1] > 1) { al = fAlim[i-1]; ba = fBlim[i-1] - al; du1 = al + 0.5*(TMath::Sin(fX[l-1] + dx) + 1)*ba - fU[i-1]; du2 = al + 0.5*(TMath::Sin(fX[l-1] - dx) + 1)*ba - fU[i-1]; if (dx > 1) du1 = ba; dx = 0.5*(TMath::Abs(du1) + TMath::Abs(du2)); } fWerr[l-1] = dx; } } //*-*- global correlation coefficients if (fISW[1] >= 1) { for (i = 1; i <= fNpar; ++i) { fGlobcc[i-1] = 0; k1 = i*(i-1) / 2; for (j = 1; j <= i; ++j) { k = k1 + j; fP[i + j*fMaxpar - fMaxpar-1] = fVhmat[k-1]; fP[j + i*fMaxpar - fMaxpar-1] = fP[i + j*fMaxpar - fMaxpar-1]; } } mnvert(fP, fMaxint, fMaxint, fNpar, ierr); if (ierr == 0) { for (iin = 1; iin <= fNpar; ++iin) { ndiag = iin*(iin + 1) / 2; denom = fP[iin + iin*fMaxpar - fMaxpar-1]*fVhmat[ndiag-1]; if (denom <= 1 && denom >= 0) fGlobcc[iin-1] = 0; else fGlobcc[iin-1] = TMath::Sqrt(1 - 1 / denom); } } } } /* mnwerr_ */