Implementation in C++ of the Minuit package written by Fred James.

This 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 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:

\[ P_{\mathrm{int}} = \arcsin \left( 2\: \frac{P_{\mathrm{ext}}-a}{b-a} - 1 \right) P_{\mathrm{ext}} = a + \frac{b - a}{2} \left( \sin P_{\mathrm{int}} + 1 \right) \]

so that the internal value $P_{\mathrm{int}}$ can take on any value, while the external value $P_{\mathrm{ext}}$ can take on values only between the lower limit $a$ and the 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 $(0,10^{10})$ 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 $\partial P_{\mathrm{ext}} / \partial P_{\mathrm{int}} \approx 0$. Therefore, it is 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 $\pm \frac{\pi}{2}$ 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 $\partial F / \partial P_{\mathrm{int}}$ is zero no matter what the real derivative $\partial F / \partial P_{\mathrm{ext}}$ is.

\[ \frac{\partial F}{\partial P_{\mathrm{int}}} = \frac{\partial F}{\partial P_{\mathrm{ext}}} \frac{\partial P_{\mathrm{ext}}}{\partial P_{\mathrm{int}}} = \frac{\partial F}{\partial P_{\mathrm{ext}}} = 0 \]

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 discussion 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 parameterised 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 parameterisation 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 under-determinedness by reformulating the parameterisation. 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.

Minuit parameter errors in the presence of limits

This concerns the way Minuit reports the symmetric (or parabolic) errors on parameters. It does not apply to the errors reported from Minos, which are in general asymmetric.

The symmetric errors reported by Minuit are always calculated from the covariance matrix, assuming that this matrix has been calculated, usually as the result of a Migrad minimization or a direct calculation by Hesse which inverts the second derivative matrix.

When there are no limits on the parameter in question, the error reported by Minuit should therefore be exactly equal to the square root of the corresponding diagonal element of the error matrix reported by Minuit.

However, when there are limits on the parameter, there is a transformation between the internal parameter values seen by Minuit (which are unbounded) and the external parameter values seen by the user in FCN (which remain inside the desired limits). Therefore the internal error matrix kept by Minuit must be transformed to an external error matrix for the user. This is done by multiplying the (I,J)th element by DEXDIN(I)*DEXDIN(J), where DEXDIN is the derivative of the external value with respect to the internal value at the minimum. This is a linearisation of the transformation, and is the only way to produce an error matrix in external coordinates meaningful to the user. But when reporting the individual parabolic errors for limited parameters, Minuit can do a little better, so it does. In this case, Minuit actually transforms the ends of the internal "error bar" to external coordinates and reports the length of this transformed interval. Strictly speaking, it is now asymmetric, but since the origin of the asymmetry is only an artificial transformation it does not make much sense, so the transformed errors are symmetrized.

The result of all the above is that for parameters with limits, the error reported by Minuit is not exactly equal to the square root of the diagonal element of the error matrix. The difference is a measure of how much the limits deform the problem. If possible, it is suggested not to use limits on parameters, and the problem goes away. If for some reason limits are necessary, and you are sensitive to the difference between the two ways of calculating the errors, it is suggested to use Minos errors which take into account the non-linearities much more precisely.

Definition at line 27 of file TMinuit.h.

Public Types
enum	{ kMAXWARN =100 }

Public Member Functions
	TMinuit ()
	Minuit normal constructor. More...

	TMinuit (Int_t maxpar)
	Minuit normal constructor. More...

virtual	~TMinuit ()
	Minuit default destructor. More...

virtual void	BuildArrays (Int_t maxpar=15)
	Create internal Minuit arrays for the maxpar parameters. More...

virtual TObject *	Clone (const char *newname="") const
	Make a clone of an object using the Streamer facility. More...

virtual Int_t	Command (const char *command)
	Execute a Minuit command. More...

virtual TObject *	Contour (Int_t npoints=10, Int_t pa1=0, Int_t pa2=1)
	Creates a TGraph object describing the n-sigma contour of a TMinuit fit. More...

virtual Int_t	DefineParameter (Int_t parNo, const char *name, Double_t initVal, Double_t initErr, Double_t lowerLimit, Double_t upperLimit)
	Define a parameter. More...

virtual void	DeleteArrays ()
	Delete internal Minuit arrays. More...

virtual Int_t	Eval (Int_t npar, Double_t grad, Double_t &fval, Double_t par, Int_t flag)
	Evaluate the minimisation function Input parameters: More...

virtual Int_t	FixParameter (Int_t parNo)
	fix a parameter More...

Int_t	GetMaxIterations () const

TMethodCall *	GetMethodCall () const

virtual Int_t	GetNumFixedPars () const
	returns the number of currently fixed parameters More...

virtual Int_t	GetNumFreePars () const
	returns the number of currently free parameters More...

virtual Int_t	GetNumPars () const
	returns the total number of parameters that have been defined as fixed or free. More...

TObject *	GetObjectFit () const

virtual Int_t	GetParameter (Int_t parNo, Double_t &currentValue, Double_t &currentError) const
	return parameter value and error More...

virtual TObject *	GetPlot () const

Int_t	GetStatus () const

virtual Int_t	Migrad ()
	invokes the MIGRAD minimizer More...

virtual void	mnamin ()
	Initialize AMIN. More...

virtual void	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. More...

virtual void	mncalf (Double_t *pvec, Double_t &ycalf)
	Transform FCN to find further minima. More...

virtual void	mncler ()
	Resets the parameter list to UNDEFINED. More...

virtual void	mncntr (Int_t ke1, Int_t ke2, Int_t &ierrf)
	Print function contours in two variables, on line printer. More...

virtual void	mncomd (const char *crdbin, Int_t &icondn)
	Reads a command string and executes. More...

virtual void	mncont (Int_t ke1, Int_t ke2, Int_t nptu, Double_t xptu, Double_t yptu, Int_t &ierrf)
	Find points along a contour where FCN is minimum. More...

virtual void	mncrck (TString crdbuf, Int_t maxcwd, TString &comand, Int_t &lnc, Int_t mxp, Double_t *plist, Int_t &llist, Int_t &ierr, Int_t isyswr)
	Cracks the free-format input. More...

virtual void	mncros (Double_t &aopt, Int_t &iercr)
	Find point where MNEVAL=AMIN+UP. More...

virtual void	mncuve ()
	Makes sure that the current point is a local minimum. More...

virtual void	mnderi ()
	Calculates the first derivatives of FCN (GRD) More...

virtual void	mndxdi (Double_t pint, Int_t ipar, Double_t &dxdi)
	Calculates the transformation factor between ext/internal values. More...

virtual void	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. More...

virtual void	mnemat (Double_t *emat, Int_t ndim)
	Calculates the external error matrix from the internal matrix. More...

virtual void	mnerrs (Int_t number, Double_t &eplus, Double_t &eminus, Double_t &eparab, Double_t &gcc)
	Utility routine to get MINOS errors. More...

virtual void	mneval (Double_t anext, Double_t &fnext, Int_t &ierev)
	Evaluates the function being analysed by MNCROS. More...

virtual void	mnexcm (const char comand, Double_t plist, Int_t llist, Int_t &ierflg)
	Interprets a command and takes appropriate action. More...

virtual void	mnexin (Double_t *pint)
	Transforms the external parameter values U to internal values. More...

virtual void	mnfixp (Int_t iint, Int_t &ierr)
	Removes parameter IINT from the internal parameter list. More...

virtual void	mnfree (Int_t k)
	Restores one or more fixed parameter(s) to variable status. More...

virtual void	mngrad ()
	Interprets the SET GRAD command. More...

virtual void	mnhelp (TString comd)
	HELP routine for MINUIT interactive commands. More...

virtual void	mnhelp (const char *command="")
	interface to Minuit help More...

virtual void	mnhes1 ()
	Calculate first derivatives (GRD) and uncertainties (DGRD) More...

virtual void	mnhess ()
	Calculates the full second-derivative matrix of FCN. More...

virtual void	mnimpr ()
	Attempts to improve on a good local minimum. More...

virtual void	mninex (Double_t *pint)
	Transforms from internal coordinates (PINT) to external (U) More...

virtual void	mninit (Int_t i1, Int_t i2, Int_t i3)
	Main initialization member function for MINUIT. More...

virtual void	mnlims ()
	Interprets the SET LIM command, to reset the parameter limits. More...

virtual void	mnline (Double_t start, Double_t fstart, Double_t step, Double_t slope, Double_t toler)
	Perform a line search from position START. More...

virtual void	mnmatu (Int_t kode)
	Prints the covariance matrix v when KODE=1. More...

virtual void	mnmigr ()
	Performs a local function minimization. More...

virtual void	mnmnos ()
	Performs a MINOS error analysis. More...

virtual void	mnmnot (Int_t ilax, Int_t ilax2, Double_t &val2pl, Double_t &val2mi)
	Performs a MINOS error analysis on one parameter. More...

virtual void	mnparm (Int_t k, TString cnamj, Double_t uk, Double_t wk, Double_t a, Double_t b, Int_t &ierflg)
	Implements one parameter definition. More...

virtual void	mnpars (TString &crdbuf, Int_t &icondn)
	Implements one parameter definition. More...

virtual void	mnpfit (Double_t parx2p, Double_t pary2p, Int_t npar2p, Double_t *coef2p, Double_t &sdev2p)
	To fit a parabola to npar2p points. More...

virtual void	mnpint (Double_t &pexti, Int_t i, Double_t &pinti)
	Calculates the internal parameter value PINTI. More...

virtual void	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. More...

virtual void	mnpout (Int_t iuext, 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. More...

virtual void	mnprin (Int_t inkode, Double_t fval)
	Prints the values of the parameters at the time of the call. More...

virtual void	mnpsdf ()
	Calculates the eigenvalues of v to see if positive-def. More...

virtual void	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. More...

virtual void	mnrn15 (Double_t &val, Int_t &inseed)
	This is a super-portable random number generator. More...

virtual void	mnrset (Int_t iopt)
	Resets function value and errors to UNDEFINED. More...

virtual void	mnsave ()
	Writes current parameter values and step sizes onto file ISYSSA. More...

virtual void	mnscan ()
	Scans the values of FCN as a function of one parameter. More...

virtual void	mnseek ()
	Performs a rough (but global) minimization by monte carlo search. More...

virtual void	mnset ()
	Interprets the commands that start with SET and SHOW. More...

virtual void	mnsimp ()
	Minimization using the simplex method of Nelder and Mead. More...

virtual void	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. More...

virtual void	mntiny (volatile Double_t epsp1, Double_t &epsbak)
	To find the machine precision. More...

Bool_t	mnunpt (TString &cfname)
	Returns .TRUE. More...

virtual void	mnvert (Double_t *a, Int_t l, Int_t m, Int_t n, Int_t &ifail)
	Inverts a symmetric matrix. More...

virtual void	mnwarn (const char copt, const char corg, const char *cmes)
	Prints Warning messages. More...

virtual void	mnwerr ()
	Calculates the WERR, external parameter errors. More...

virtual Int_t	Release (Int_t parNo)
	release a parameter More...

virtual Int_t	SetErrorDef (Double_t up)
	To get the n-sigma contour the error def parameter "up" has to set to n^2. More...

virtual void	SetFCN (void(fcn)(Int_t &, Double_t , Double_t &f, Double_t *, Int_t))
	To set the address of the minimization function. More...

virtual void	SetGraphicsMode (Bool_t mode=kTRUE)

virtual void	SetMaxIterations (Int_t maxiter=500)

virtual void	SetObjectFit (TObject *obj)

virtual Int_t	SetPrintLevel (Int_t printLevel=0)
	set Minuit print level. More...

Public Attributes
Double_t *	fAlim

Double_t	fAmin

Double_t	fApsi

Double_t	fBigedm

Double_t *	fBlim

TString	fCfrom

char *	fChpt

Double_t *	fCOMDplist

Double_t *	fCONTgcc

Double_t *	fCONTw

TString	fCovmes [4]

TString *	fCpnam
	Character to be plotted at the X,Y contour positions. More...

TString	fCstatu

TString	fCtitl

TString	fCundef

TString	fCvrsn

TString	fCword

Double_t	fDcovar

Double_t *	fDgrd

Double_t *	fDirin

Double_t *	fDirins

Double_t	fEDM

Int_t	fEmpty

Double_t	fEpsi

Double_t	fEpsma2

Double_t	fEpsmac

Double_t *	fErn

Double_t *	fErp

void(*	fFCN )(Int_t &npar, Double_t gin, Double_t &f, Double_t u, Int_t flag)

Double_t *	fFIXPyy

Double_t	fFval3

Double_t *	fG2

Double_t *	fG2s

Double_t *	fGin

Double_t *	fGlobcc

Double_t *	fGRADgf

Bool_t	fGraphicsMode

Double_t *	fGrd

Double_t *	fGrds

Double_t *	fGstep

Double_t *	fGsteps

Double_t *	fHESSyy

Int_t	fIcirc [2]

Int_t	fIcomnd

Int_t	fIdbg [11]

Double_t *	fIMPRdsav

Double_t *	fIMPRy

Int_t *	fIpfix

Int_t	fIstkrd [10]

Int_t	fIstkwr [10]

Int_t	fIstrat

Int_t	fISW [7]

Int_t	fIsysrd

Int_t	fIsyssa

Int_t	fIsyswr

Int_t	fItaur

Int_t	fKe1cr

Int_t	fKe2cr

Bool_t	fLimset

Bool_t	fLnewmn

Bool_t	fLnolim

Bool_t	fLphead

Bool_t	fLrepor

Bool_t	fLwarn

Double_t *	fMATUvline

Int_t	fMaxcpt

Int_t	fMaxext

Int_t	fMaxint

Int_t	fMaxIterations

Int_t	fMaxpar

Int_t	fMaxpar1

Int_t	fMaxpar2

Int_t	fMaxpar5

TMethodCall *	fMethodCall

Double_t *	fMIGRflnu

Double_t *	fMIGRgs

Double_t *	fMIGRstep

Double_t *	fMIGRvg

Double_t *	fMIGRxxs

Double_t *	fMNOTgcc

Double_t *	fMNOTw

Double_t *	fMNOTxdev

Int_t	fNblock

Int_t	fNewpag

Int_t *	fNexofi

Int_t	fNfcn

Int_t	fNfcnfr

Int_t	fNfcnlc

Int_t	fNfcnmx

Int_t	fNfcwar [20]

Int_t *	fNiofex

Int_t	fNpagln

Int_t	fNpagwd

Int_t	fNpar

Int_t	fNpfix

Int_t	fNstkrd

Int_t	fNstkwr

Int_t	fNu

Int_t *	fNvarl

Int_t	fNwrmes [2]

TObject *	fObjectFit

TString	fOrigin [kMAXWARN]

Double_t *	fP

Double_t *	fPARSplist

Double_t *	fPbar

TObject *	fPlot

Double_t *	fPrho

Double_t *	fPSDFs

Double_t *	fPstar

Double_t *	fPstst

Double_t *	fSEEKxbest

Double_t *	fSEEKxmid

Double_t *	fSIMPy

Int_t	fStatus

Double_t *	fU

Double_t	fUndefi

Double_t	fUp

Double_t	fUpdflt

Double_t *	fVERTpp

Double_t *	fVERTq

Double_t *	fVERTs

Double_t *	fVhmat

Double_t	fVlimhi

Double_t	fVlimlo

Double_t *	fVthmat

TString	fWarmes [kMAXWARN]

Double_t *	fWerr

Double_t *	fWord7

Double_t *	fX

Double_t	fXdircr

Double_t	fXmidcr

Double_t *	fXpt

Double_t *	fXs

Double_t *	fXt

Double_t *	fXts

Double_t	fYdircr

Double_t	fYmidcr

Double_t *	fYpt

Private Member Functions
	TMinuit (const TMinuit &m)
	Private TMinuit copy ctor. TMinuit can not be copied. More...

TMinuit &	operator= (const TMinuit &m)

#include <TMinuit.h>

Inheritance diagram for TMinuit:

[legend]

Member Enumeration Documentation

◆ anonymous enum

anonymous enum

Enumerator
kMAXWARN

Definition at line 35 of file TMinuit.h.

Constructor & Destructor Documentation

◆ TMinuit() [1/3]

TMinuit::TMinuit ( const TMinuit & m )

private

Private TMinuit copy ctor. TMinuit can not be copied.

Definition at line 498 of file TMinuit.cxx.

◆ TMinuit() [2/3]

TMinuit::TMinuit ( )

Minuit normal constructor.

Definition at line 356 of file TMinuit.cxx.

◆ TMinuit() [3/3]

TMinuit::TMinuit ( Int_t maxpar )

Minuit normal constructor.

maxpar is the maximum number of parameters used with this TMinuit object.

Definition at line 473 of file TMinuit.cxx.

◆ ~TMinuit()

TMinuit::~TMinuit ( )

virtual

Minuit default destructor.

Definition at line 506 of file TMinuit.cxx.

Member Function Documentation

◆ BuildArrays()

void TMinuit::BuildArrays ( Int_t maxpar = 15 )

virtual

Create internal Minuit arrays for the maxpar parameters.

Definition at line 521 of file TMinuit.cxx.

◆ Clone()

TObject * TMinuit::Clone ( const char * newname = "" ) const

virtual

Make a clone of an object using the Streamer facility.

Function pointer is copied to Clone

Definition at line 605 of file TMinuit.cxx.

◆ Command()

Int_t TMinuit::Command ( const char * command )

virtual

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 See also the complete documentation of all the 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

Definition at line 635 of file TMinuit.cxx.

◆ Contour()

TObject * TMinuit::Contour	(	Int_t	npoints = `10`,
		Int_t	pa1 = `0`,
		Int_t	pa2 = `1`
	)

virtual

Creates a TGraph object describing the n-sigma contour of a TMinuit fit.

The contour of the parameters pa1 and pa2 is calculated using 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*. Note that the TGraph is created with npoints+1 in order to close the contour (setting last point equal to first point).

You can find an example in $ROOTSYS/tutorials/fit/fitcont.C

Definition at line 662 of file TMinuit.cxx.

◆ DefineParameter()

Int_t TMinuit::DefineParameter	(	Int_t	parNo,
		const char *	name,
		Double_t	initVal,
		Double_t	initErr,
		Double_t	lowerLimit,
		Double_t	upperLimit
	)

virtual

Define a parameter.

Definition at line 704 of file TMinuit.cxx.

◆ DeleteArrays()

void TMinuit::DeleteArrays ( )

virtual

Delete internal Minuit arrays.

Definition at line 717 of file TMinuit.cxx.

◆ Eval()

Int_t TMinuit::Eval	(	Int_t	npar,
		Double_t *	grad,
		Double_t &	fval,
		Double_t *	par,
		Int_t	flag
	)

virtual

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 their 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:

Definition at line 809 of file TMinuit.cxx.

◆ FixParameter()

Int_t TMinuit::FixParameter ( Int_t parNo )

virtual

fix a parameter

Definition at line 836 of file TMinuit.cxx.

◆ GetMaxIterations()

Int_t TMinuit::GetMaxIterations ( ) const

inline

Definition at line 195 of file TMinuit.h.

◆ GetMethodCall()

TMethodCall* TMinuit::GetMethodCall ( ) const

inline

Definition at line 193 of file TMinuit.h.

◆ GetNumFixedPars()

Int_t TMinuit::GetNumFixedPars ( ) const

virtual

returns the number of currently fixed parameters

Definition at line 864 of file TMinuit.cxx.

◆ GetNumFreePars()

Int_t TMinuit::GetNumFreePars ( ) const

virtual

returns the number of currently free parameters

Definition at line 872 of file TMinuit.cxx.

◆ GetNumPars()

Int_t TMinuit::GetNumPars ( ) const

virtual

returns the total number of parameters that have been defined as fixed or free.

The constant parameters are not counted.

Definition at line 881 of file TMinuit.cxx.

◆ GetObjectFit()

TObject* TMinuit::GetObjectFit ( ) const

inline

Definition at line 194 of file TMinuit.h.

◆ GetParameter()

Int_t TMinuit::GetParameter	(	Int_t	parNo,
		Double_t &	currentValue,
		Double_t &	currentError
	)		const

virtual

return parameter value and error

Definition at line 850 of file TMinuit.cxx.

◆ GetPlot()

virtual TObject* TMinuit::GetPlot ( ) const

inlinevirtual

Definition at line 200 of file TMinuit.h.

◆ GetStatus()

Int_t TMinuit::GetStatus ( ) const

inline

Definition at line 201 of file TMinuit.h.

◆ Migrad()

Int_t TMinuit::Migrad ( )

virtual

invokes the MIGRAD minimizer

Definition at line 889 of file TMinuit.cxx.

◆ mnamin()

void TMinuit::mnamin ( )

virtual

Initialize AMIN.

Called from many places. Initializes the value of AMIN by calling the user function. Prints out the function value and parameter values if Print Flag value is high enough.

Definition at line 981 of file TMinuit.cxx.

◆ mnbins()

void TMinuit::mnbins	(	Double_t	a1,
		Double_t	a2,
		Int_t	naa,
		Double_t &	bl,
		Double_t &	bh,
		Int_t &	nb,
		Double_t &	bwid
	)

virtual

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

Definition at line 1006 of file TMinuit.cxx.

◆ mncalf()

void TMinuit::mncalf	(	Double_t *	pvec,
		Double_t &	ycalf
	)

virtual

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)

Definition at line 1079 of file TMinuit.cxx.

◆ mncler()

void TMinuit::mncler ( )

virtual

Resets the parameter list to UNDEFINED.

Called from MINUIT and by option from MNEXCM

Definition at line 1112 of file TMinuit.cxx.

◆ mncntr()

void TMinuit::mncntr	(	Int_t	ike1,
		Int_t	ike2,
		Int_t &	ierrf
	)

virtual

Print function contours in two variables, on line printer.

input arguments: parx, pary, devs, ngrid

Definition at line 1141 of file TMinuit.cxx.

◆ mncomd()

void TMinuit::mncomd	(	const char *	crdbin,
		Int_t &	icondn
	)

virtual

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

Definition at line 1319 of file TMinuit.cxx.

◆ mncont()

void TMinuit::mncont	(	Int_t	ike1,
		Int_t	ike2,
		Int_t	nptu,
		Double_t *	xptu,
		Double_t *	yptu,
		Int_t &	ierrf
	)

virtual

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

Definition at line 1404 of file TMinuit.cxx.

◆ mncrck()

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	isyswr
	)

virtual

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).

Definition at line 1686 of file TMinuit.cxx.

◆ mncros()

void TMinuit::mncros	(	Double_t &	aopt,
		Int_t &	iercr
	)

virtual

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)

Definition at line 1807 of file TMinuit.cxx.

◆ mncuve()

void TMinuit::mncuve ( )

virtual

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

Definition at line 2139 of file TMinuit.cxx.

◆ mnderi()

void TMinuit::mnderi ( )

virtual

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 fISW[2] is zero or one.

Definition at line 2187 of file TMinuit.cxx.

◆ mndxdi()

void TMinuit::mndxdi	(	Double_t	pint,
		Int_t	ipar,
		Double_t &	dxdi
	)

virtual

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.

Definition at line 2302 of file TMinuit.cxx.

◆ mneig()

void TMinuit::mneig	(	Double_t *	a,
		Int_t	ndima,
		Int_t	n,
		Int_t	mits,
		Double_t *	work,
		Double_t	precis,
		Int_t &	ifault
	)

virtual

Compute matrix eigen values.

Definition at line 2314 of file TMinuit.cxx.

◆ mnemat()

void TMinuit::mnemat	(	Double_t *	emat,
		Int_t	ndim
	)

virtual

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);

Definition at line 2510 of file TMinuit.cxx.

◆ mnerrs()

void TMinuit::mnerrs	(	Int_t	number,
		Double_t &	eplus,
		Double_t &	eminus,
		Double_t &	eparab,
		Double_t &	gcc
	)

virtual

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

Definition at line 2587 of file TMinuit.cxx.

◆ mneval()

void TMinuit::mneval	(	Double_t	anext,
		Double_t &	fnext,
		Int_t &	ierev
	)

virtual

Evaluates the function being analysed by MNCROS.

Evaluates the function being analysed 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

Definition at line 2629 of file TMinuit.cxx.

◆ mnexcm()

void TMinuit::mnexcm	(	const char *	command,
		Double_t *	plist,
		Int_t	llist,
		Int_t &	ierflg
	)

virtual

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

Definition at line 2673 of file TMinuit.cxx.

◆ mnexin()

void TMinuit::mnexin ( Double_t * pint )

virtual

Transforms the external parameter values U to internal values.

Transforms the external parameter values U to internal values in the dense array PINT.

Definition at line 3160 of file TMinuit.cxx.

◆ mnfixp()

void TMinuit::mnfixp	(	Int_t	iint1,
		Int_t &	ierr
	)

virtual

Removes parameter IINT from the internal parameter list.

and arranges the rest of the list to fill the hole.

Definition at line 3178 of file TMinuit.cxx.

◆ mnfree()

void TMinuit::mnfree ( Int_t k )

virtual

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

Definition at line 3265 of file TMinuit.cxx.

◆ mngrad()

void TMinuit::mngrad ( )

virtual

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.

Definition at line 3371 of file TMinuit.cxx.

◆ mnhelp() [1/2]

void TMinuit::mnhelp ( TString comd )

virtual

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.

Definition at line 3448 of file TMinuit.cxx.

◆ mnhelp() [2/2]

void TMinuit::mnhelp ( const char * command = "" )

virtual

interface to Minuit help

Definition at line 3431 of file TMinuit.cxx.

◆ mnhes1()

void TMinuit::mnhes1 ( )

virtual

Calculate first derivatives (GRD) and uncertainties (DGRD)

and appropriate step sizes GSTEP Called from MNHESS and MNGRAD

Definition at line 4227 of file TMinuit.cxx.

◆ mnhess()

void TMinuit::mnhess ( )

virtual

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.

Definition at line 4002 of file TMinuit.cxx.

◆ mnimpr()

void TMinuit::mnimpr ( )

virtual

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 minimised using the simplex method from several random starting points.

ref. – Goldstein and Price, Math.Comp. 25, 569 (1971)

Definition at line 4304 of file TMinuit.cxx.

◆ mninex()

void TMinuit::mninex ( Double_t * pint )

virtual

Transforms from internal coordinates (PINT) to external (U)

The minimising routines which work in internal coordinates call this routine before calling FCN.

Definition at line 4515 of file TMinuit.cxx.

◆ mninit()

void TMinuit::mninit	(	Int_t	i1,
		Int_t	i2,
		Int_t	i3
	)

virtual

Main initialization member function for MINUIT.

It initializes some constants (including the logical I/O unit nos.),

Definition at line 4535 of file TMinuit.cxx.

◆ mnlims()

void TMinuit::mnlims ( )

virtual

Interprets the SET LIM command, to reset the parameter limits.

Called from MNSET

Definition at line 4625 of file TMinuit.cxx.

◆ mnline()

void TMinuit::mnline	(	Double_t *	start,
		Double_t	fstart,
		Double_t *	step,
		Double_t	slope,
		Double_t	toler
	)

virtual

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.

Definition at line 4745 of file TMinuit.cxx.

◆ mnmatu()

void TMinuit::mnmatu ( Int_t kode )

virtual

Prints the covariance matrix v when KODE=1.

always prints the global correlations, and calculates and prints the individual correlation coefficients

Definition at line 4979 of file TMinuit.cxx.

◆ mnmigr()

void TMinuit::mnmigr ( )

virtual

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"

Definition at line 5059 of file TMinuit.cxx.

◆ mnmnos()

void TMinuit::mnmnos ( )

virtual

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.

Definition at line 5399 of file TMinuit.cxx.

◆ mnmnot()

void TMinuit::mnmnot	(	Int_t	ilax,
		Int_t	ilax2,
		Double_t &	val2pl,
		Double_t &	val2mi
	)

virtual

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.

Definition at line 5474 of file TMinuit.cxx.

◆ mnparm()

void TMinuit::mnparm	(	Int_t	k1,
		TString	cnamj,
		Double_t	uk,
		Double_t	wk,
		Double_t	a,
		Double_t	b,
		Int_t &	ierflg
	)

virtual

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

Definition at line 5674 of file TMinuit.cxx.

◆ mnpars()

void TMinuit::mnpars	(	TString &	crdbuf,
		Int_t &	icondn
	)

virtual

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

Definition at line 5876 of file TMinuit.cxx.

◆ mnpfit()

void TMinuit::mnpfit	(	Double_t *	parx2p,
		Double_t *	pary2p,
		Int_t	npar2p,
		Double_t *	coef2p,
		Double_t &	sdev2p
	)

virtual

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

Definition at line 5965 of file TMinuit.cxx.

◆ mnpint()

void TMinuit::mnpint	(	Double_t &	pexti,
		Int_t	i1,
		Double_t &	pinti
	)

virtual

Calculates the internal parameter value PINTI.

corresponding to the external value PEXTI for parameter I.

Definition at line 6026 of file TMinuit.cxx.

◆ mnplot()

void TMinuit::mnplot	(	Double_t *	xpt,
		Double_t *	ypt,
		char *	chpt,
		Int_t	nxypt,
		Int_t	npagwd,
		Int_t	npagln
	)

virtual

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");

Definition at line 6077 of file TMinuit.cxx.

◆ mnpout()

void TMinuit::mnpout	(	Int_t	iuext1,
		TString &	chnam,
		Double_t &	val,
		Double_t &	err,
		Double_t &	xlolim,
		Double_t &	xuplim,
		Int_t &	iuint
	)		const

virtual

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

Definition at line 6256 of file TMinuit.cxx.

◆ mnprin()

void TMinuit::mnprin	(	Int_t	inkode,
		Double_t	fval
	)

virtual

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 fISW[1]

Definition at line 6313 of file TMinuit.cxx.

◆ mnpsdf()

void TMinuit::mnpsdf ( )

virtual

Calculates the eigenvalues of v to see if positive-def.

if not, adds constant along diagonal to make positive.

Definition at line 6503 of file TMinuit.cxx.

◆ mnrazz()

void TMinuit::mnrazz	(	Double_t	ynew,
		Double_t *	pnew,
		Double_t *	y,
		Int_t &	jh,
		Int_t &	jl
	)

virtual

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.

Definition at line 6577 of file TMinuit.cxx.

◆ mnrn15()

void TMinuit::mnrn15	(	Double_t &	val,
		Int_t &	inseed
	)

virtual

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

Definition at line 6626 of file TMinuit.cxx.

◆ mnrset()

void TMinuit::mnrset ( Int_t iopt )

virtual

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

Definition at line 6668 of file TMinuit.cxx.

◆ mnsave()

void TMinuit::mnsave ( )

virtual

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.

Definition at line 6702 of file TMinuit.cxx.

◆ mnscan()

void TMinuit::mnscan ( )

virtual

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.

Definition at line 6715 of file TMinuit.cxx.

◆ mnseek()

void TMinuit::mnseek ( )

virtual

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).

Definition at line 6825 of file TMinuit.cxx.

◆ mnset()

void TMinuit::mnset ( )

virtual

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

Definition at line 6920 of file TMinuit.cxx.

◆ mnsimp()

void TMinuit::mnsimp ( )

virtual

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)).

Definition at line 7438 of file TMinuit.cxx.

◆ mnstat()

void TMinuit::mnstat	(	Double_t &	fmin,
		Double_t &	fedm,
		Double_t &	errdef,
		Int_t &	npari,
		Int_t &	nparx,
		Int_t &	istat
	)

virtual

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

Definition at line 7645 of file TMinuit.cxx.

◆ mntiny()

void TMinuit::mntiny	(	volatile Double_t	epsp1,
		Double_t &	epsbak
	)

virtual

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 optimiser

Definition at line 7668 of file TMinuit.cxx.

◆ mnunpt()

Bool_t TMinuit::mnunpt ( TString & cfname )

Returns .TRUE.

if CFNAME contains unprintable characters

Definition at line 7677 of file TMinuit.cxx.

◆ mnvert()

void TMinuit::mnvert	(	Double_t *	a,
		Int_t	l,
		Int_t	m,
		Int_t	n,
		Int_t &	ifail
	)

virtual

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.

Definition at line 7703 of file TMinuit.cxx.

◆ mnwarn()

void TMinuit::mnwarn	(	const char *	copt1,
		const char *	corg1,
		const char *	cmes1
	)

virtual

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 kMAXMES.
- If called with CORG=CMES='SHO', it prints the messages in the circular buffer, FIFO, and empties the buffer.

Definition at line 7791 of file TMinuit.cxx.

◆ mnwerr()

void TMinuit::mnwerr ( )

virtual

Calculates the WERR, external parameter errors.

and the global correlation coefficients, to be called whenever a new covariance matrix is available.

Definition at line 7868 of file TMinuit.cxx.

◆ operator=()

TMinuit& TMinuit::operator= ( const TMinuit & m )

private

◆ Release()

Int_t TMinuit::Release ( Int_t parNo )

virtual

release a parameter

Definition at line 903 of file TMinuit.cxx.

◆ SetErrorDef()

Int_t TMinuit::SetErrorDef ( Double_t up )

virtual

To get the n-sigma contour the error def parameter "up" has to set to n^2.

Definition at line 917 of file TMinuit.cxx.

◆ SetFCN()

void TMinuit::SetFCN ( void(*)(Int_t &, Double_t *, Double_t &f, Double_t *, Int_t) fcn )

virtual

To set the address of the minimization function.

Definition at line 929 of file TMinuit.cxx.

◆ SetGraphicsMode()

virtual void TMinuit::SetGraphicsMode ( Bool_t mode = kTRUE )

inlinevirtual

Definition at line 263 of file TMinuit.h.

◆ SetMaxIterations()

virtual void TMinuit::SetMaxIterations ( Int_t maxiter = 500 )

inlinevirtual

Definition at line 264 of file TMinuit.h.

◆ SetObjectFit()

virtual void TMinuit::SetObjectFit ( TObject * obj )

inlinevirtual

Definition at line 265 of file TMinuit.h.

◆ SetPrintLevel()

Int_t TMinuit::SetPrintLevel ( Int_t printLevel = 0 )

virtual

set Minuit print level.

printlevel:

= -1 quiet (also suppress all warnings)
= 0 normal
= 1 verbose

Definition at line 961 of file TMinuit.cxx.

Member Data Documentation

◆ fAlim

Double_t* TMinuit::fAlim

Definition at line 69 of file TMinuit.h.

◆ fAmin

Double_t TMinuit::fAmin

Definition at line 49 of file TMinuit.h.

◆ fApsi

Double_t TMinuit::fApsi

Definition at line 54 of file TMinuit.h.

◆ fBigedm

Double_t TMinuit::fBigedm

Definition at line 61 of file TMinuit.h.

◆ fBlim

Double_t* TMinuit::fBlim

Definition at line 70 of file TMinuit.h.

◆ fCfrom

TString TMinuit::fCfrom

Definition at line 166 of file TMinuit.h.

◆ fChpt

char* TMinuit::fChpt

Definition at line 164 of file TMinuit.h.

◆ fCOMDplist

Double_t* TMinuit::fCOMDplist

Definition at line 123 of file TMinuit.h.

◆ fCONTgcc

Double_t* TMinuit::fCONTgcc

Definition at line 100 of file TMinuit.h.

◆ fCONTw

Double_t* TMinuit::fCONTw

Definition at line 101 of file TMinuit.h.

◆ fCovmes

TString TMinuit::fCovmes[4]

Definition at line 172 of file TMinuit.h.

◆ fCpnam

TString* TMinuit::fCpnam

Character to be plotted at the X,Y contour positions.

Definition at line 165 of file TMinuit.h.

◆ fCstatu

TString TMinuit::fCstatu

Definition at line 167 of file TMinuit.h.

◆ fCtitl

TString TMinuit::fCtitl

Definition at line 168 of file TMinuit.h.

◆ fCundef

TString TMinuit::fCundef

Definition at line 170 of file TMinuit.h.

◆ fCvrsn

TString TMinuit::fCvrsn

Definition at line 171 of file TMinuit.h.

◆ fCword

TString TMinuit::fCword

Definition at line 169 of file TMinuit.h.

◆ fDcovar

Double_t TMinuit::fDcovar

Definition at line 55 of file TMinuit.h.

◆ fDgrd

Double_t* TMinuit::fDgrd

Definition at line 85 of file TMinuit.h.

◆ fDirin

Double_t* TMinuit::fDirin

Definition at line 77 of file TMinuit.h.

◆ fDirins

Double_t* TMinuit::fDirins

Definition at line 80 of file TMinuit.h.

◆ fEDM

Double_t TMinuit::fEDM

Definition at line 51 of file TMinuit.h.

◆ fEmpty

Int_t TMinuit::fEmpty

Definition at line 38 of file TMinuit.h.

◆ fEpsi

Double_t TMinuit::fEpsi

Definition at line 53 of file TMinuit.h.

◆ fEpsma2

Double_t TMinuit::fEpsma2

Definition at line 57 of file TMinuit.h.

◆ fEpsmac

Double_t TMinuit::fEpsmac

Definition at line 56 of file TMinuit.h.

◆ fErn

Double_t* TMinuit::fErn

Definition at line 72 of file TMinuit.h.

◆ fErp

Double_t* TMinuit::fErp

Definition at line 71 of file TMinuit.h.

◆ fFCN

void(* TMinuit::fFCN) (Int_t &npar, Double_t *gin, Double_t &f, Double_t *u, Int_t flag)

Definition at line 178 of file TMinuit.h.

◆ fFIXPyy

Double_t* TMinuit::fFIXPyy

Definition at line 102 of file TMinuit.h.

◆ fFval3

Double_t TMinuit::fFval3

Definition at line 52 of file TMinuit.h.

◆ fG2

Double_t* TMinuit::fG2

Definition at line 82 of file TMinuit.h.

◆ fG2s

Double_t* TMinuit::fG2s

Definition at line 87 of file TMinuit.h.

◆ fGin

Double_t* TMinuit::fGin

Definition at line 84 of file TMinuit.h.

◆ fGlobcc

Double_t* TMinuit::fGlobcc

Definition at line 74 of file TMinuit.h.

◆ fGRADgf

Double_t* TMinuit::fGRADgf

Definition at line 103 of file TMinuit.h.

◆ fGraphicsMode

Bool_t TMinuit::fGraphicsMode

Definition at line 163 of file TMinuit.h.

◆ fGrd

Double_t* TMinuit::fGrd

Definition at line 81 of file TMinuit.h.

◆ fGrds

Double_t* TMinuit::fGrds

Definition at line 86 of file TMinuit.h.

◆ fGstep

Double_t* TMinuit::fGstep

Definition at line 83 of file TMinuit.h.

◆ fGsteps

Double_t* TMinuit::fGsteps

Definition at line 88 of file TMinuit.h.

◆ fHESSyy

Double_t* TMinuit::fHESSyy

Definition at line 104 of file TMinuit.h.

◆ fIcirc

Int_t TMinuit::fIcirc[2]

Definition at line 153 of file TMinuit.h.

◆ fIcomnd

Int_t TMinuit::fIcomnd

Definition at line 144 of file TMinuit.h.

◆ fIdbg

Int_t TMinuit::fIdbg[11]

Definition at line 142 of file TMinuit.h.

◆ fIMPRdsav

Double_t* TMinuit::fIMPRdsav

Definition at line 105 of file TMinuit.h.

◆ fIMPRy

Double_t* TMinuit::fIMPRy

Definition at line 106 of file TMinuit.h.

◆ fIpfix

Int_t* TMinuit::fIpfix

Definition at line 129 of file TMinuit.h.

◆ fIstkrd

Int_t TMinuit::fIstkrd[10]

Definition at line 137 of file TMinuit.h.

◆ fIstkwr

Int_t TMinuit::fIstkwr[10]

Definition at line 139 of file TMinuit.h.

◆ fIstrat

Int_t TMinuit::fIstrat

Definition at line 150 of file TMinuit.h.

◆ fISW

Int_t TMinuit::fISW[7]

Definition at line 141 of file TMinuit.h.

◆ fIsysrd

Int_t TMinuit::fIsysrd

Definition at line 131 of file TMinuit.h.

◆ fIsyssa

Int_t TMinuit::fIsyssa

Definition at line 133 of file TMinuit.h.

◆ fIsyswr

Int_t TMinuit::fIsyswr

Definition at line 132 of file TMinuit.h.

◆ fItaur

Int_t TMinuit::fItaur

Definition at line 149 of file TMinuit.h.

◆ fKe1cr

Int_t TMinuit::fKe1cr

Definition at line 155 of file TMinuit.h.

◆ fKe2cr

Int_t TMinuit::fKe2cr

Definition at line 156 of file TMinuit.h.

◆ fLimset

Bool_t TMinuit::fLimset

Definition at line 159 of file TMinuit.h.

◆ fLnewmn

Bool_t TMinuit::fLnewmn

Definition at line 161 of file TMinuit.h.

◆ fLnolim

Bool_t TMinuit::fLnolim

Definition at line 160 of file TMinuit.h.

◆ fLphead

Bool_t TMinuit::fLphead

Definition at line 162 of file TMinuit.h.

◆ fLrepor

Bool_t TMinuit::fLrepor

Definition at line 158 of file TMinuit.h.

◆ fLwarn

Bool_t TMinuit::fLwarn

Definition at line 157 of file TMinuit.h.

◆ fMATUvline

Double_t* TMinuit::fMATUvline

Definition at line 107 of file TMinuit.h.

◆ fMaxcpt

Int_t TMinuit::fMaxcpt

Definition at line 45 of file TMinuit.h.

◆ fMaxext

Int_t TMinuit::fMaxext

Definition at line 42 of file TMinuit.h.

◆ fMaxint

Int_t TMinuit::fMaxint

Definition at line 40 of file TMinuit.h.

◆ fMaxIterations

Int_t TMinuit::fMaxIterations

Definition at line 43 of file TMinuit.h.

◆ fMaxpar

Int_t TMinuit::fMaxpar

Definition at line 39 of file TMinuit.h.

◆ fMaxpar1

Int_t TMinuit::fMaxpar1

Definition at line 47 of file TMinuit.h.

◆ fMaxpar2

Int_t TMinuit::fMaxpar2

Definition at line 46 of file TMinuit.h.

◆ fMaxpar5

Int_t TMinuit::fMaxpar5

Definition at line 44 of file TMinuit.h.

◆ fMethodCall

TMethodCall* TMinuit::fMethodCall

Definition at line 177 of file TMinuit.h.

◆ fMIGRflnu

Double_t* TMinuit::fMIGRflnu

Definition at line 108 of file TMinuit.h.

◆ fMIGRgs

Double_t* TMinuit::fMIGRgs

Definition at line 110 of file TMinuit.h.

◆ fMIGRstep

Double_t* TMinuit::fMIGRstep

Definition at line 109 of file TMinuit.h.

◆ fMIGRvg

Double_t* TMinuit::fMIGRvg

Definition at line 111 of file TMinuit.h.

◆ fMIGRxxs

Double_t* TMinuit::fMIGRxxs

Definition at line 112 of file TMinuit.h.

◆ fMNOTgcc

Double_t* TMinuit::fMNOTgcc

Definition at line 115 of file TMinuit.h.

◆ fMNOTw

Double_t* TMinuit::fMNOTw

Definition at line 114 of file TMinuit.h.

◆ fMNOTxdev

Double_t* TMinuit::fMNOTxdev

Definition at line 113 of file TMinuit.h.

◆ fNblock

Int_t TMinuit::fNblock

Definition at line 143 of file TMinuit.h.

◆ fNewpag

Int_t TMinuit::fNewpag

Definition at line 136 of file TMinuit.h.

◆ fNexofi

Int_t* TMinuit::fNexofi

Definition at line 128 of file TMinuit.h.

◆ fNfcn

Int_t TMinuit::fNfcn

Definition at line 145 of file TMinuit.h.

◆ fNfcnfr

Int_t TMinuit::fNfcnfr

Definition at line 148 of file TMinuit.h.

◆ fNfcnlc

Int_t TMinuit::fNfcnlc

Definition at line 147 of file TMinuit.h.

◆ fNfcnmx

Int_t TMinuit::fNfcnmx

Definition at line 146 of file TMinuit.h.

◆ fNfcwar

Int_t TMinuit::fNfcwar[20]

Definition at line 152 of file TMinuit.h.

◆ fNiofex

Int_t* TMinuit::fNiofex

Definition at line 127 of file TMinuit.h.

◆ fNpagln

Int_t TMinuit::fNpagln

Definition at line 135 of file TMinuit.h.

◆ fNpagwd

Int_t TMinuit::fNpagwd

Definition at line 134 of file TMinuit.h.

◆ fNpar

Int_t TMinuit::fNpar

Definition at line 41 of file TMinuit.h.

◆ fNpfix

Int_t TMinuit::fNpfix

Definition at line 37 of file TMinuit.h.

◆ fNstkrd

Int_t TMinuit::fNstkrd

Definition at line 138 of file TMinuit.h.

◆ fNstkwr

Int_t TMinuit::fNstkwr

Definition at line 140 of file TMinuit.h.

◆ fNu

Int_t TMinuit::fNu

Definition at line 130 of file TMinuit.h.

◆ fNvarl

Int_t* TMinuit::fNvarl

Definition at line 126 of file TMinuit.h.

◆ fNwrmes

Int_t TMinuit::fNwrmes[2]

Definition at line 151 of file TMinuit.h.

◆ fObjectFit

TObject* TMinuit::fObjectFit

Definition at line 175 of file TMinuit.h.

◆ fOrigin

TString TMinuit::fOrigin[kMAXWARN]

Definition at line 173 of file TMinuit.h.

◆ fP

Double_t* TMinuit::fP

Definition at line 91 of file TMinuit.h.

◆ fPARSplist

Double_t* TMinuit::fPARSplist

Definition at line 124 of file TMinuit.h.

◆ fPbar

Double_t* TMinuit::fPbar

Definition at line 94 of file TMinuit.h.

◆ fPlot

TObject* TMinuit::fPlot

Definition at line 176 of file TMinuit.h.

◆ fPrho

Double_t* TMinuit::fPrho

Definition at line 95 of file TMinuit.h.

◆ fPSDFs

Double_t* TMinuit::fPSDFs

Definition at line 116 of file TMinuit.h.

◆ fPstar

Double_t* TMinuit::fPstar

Definition at line 92 of file TMinuit.h.

◆ fPstst

Double_t* TMinuit::fPstst

Definition at line 93 of file TMinuit.h.

◆ fSEEKxbest

Double_t* TMinuit::fSEEKxbest

Definition at line 118 of file TMinuit.h.

◆ fSEEKxmid

Double_t* TMinuit::fSEEKxmid

Definition at line 117 of file TMinuit.h.

◆ fSIMPy

Double_t* TMinuit::fSIMPy

Definition at line 119 of file TMinuit.h.

◆ fStatus

Int_t TMinuit::fStatus

Definition at line 154 of file TMinuit.h.

◆ fU

Double_t* TMinuit::fU

Definition at line 68 of file TMinuit.h.

◆ fUndefi

Double_t TMinuit::fUndefi

Definition at line 60 of file TMinuit.h.

◆ fUp

Double_t TMinuit::fUp

Definition at line 50 of file TMinuit.h.

◆ fUpdflt

Double_t TMinuit::fUpdflt

Definition at line 62 of file TMinuit.h.

◆ fVERTpp

Double_t* TMinuit::fVERTpp

Definition at line 122 of file TMinuit.h.

◆ fVERTq

Double_t* TMinuit::fVERTq

Definition at line 120 of file TMinuit.h.

◆ fVERTs

Double_t* TMinuit::fVERTs

Definition at line 121 of file TMinuit.h.

◆ fVhmat

Double_t* TMinuit::fVhmat

Definition at line 89 of file TMinuit.h.

◆ fVlimhi

Double_t TMinuit::fVlimhi

Definition at line 59 of file TMinuit.h.

◆ fVlimlo

Double_t TMinuit::fVlimlo

Definition at line 58 of file TMinuit.h.

◆ fVthmat

Double_t* TMinuit::fVthmat

Definition at line 90 of file TMinuit.h.

◆ fWarmes

TString TMinuit::fWarmes[kMAXWARN]

Definition at line 174 of file TMinuit.h.

◆ fWerr

Double_t* TMinuit::fWerr

Definition at line 73 of file TMinuit.h.

◆ fWord7

Double_t* TMinuit::fWord7

Definition at line 96 of file TMinuit.h.

◆ fX

Double_t* TMinuit::fX

Definition at line 75 of file TMinuit.h.

◆ fXdircr

Double_t TMinuit::fXdircr

Definition at line 65 of file TMinuit.h.

◆ fXmidcr

Double_t TMinuit::fXmidcr

Definition at line 63 of file TMinuit.h.

◆ fXpt

Double_t* TMinuit::fXpt

Definition at line 97 of file TMinuit.h.

◆ fXs

Double_t* TMinuit::fXs

Definition at line 78 of file TMinuit.h.

◆ fXt

Double_t* TMinuit::fXt

Definition at line 76 of file TMinuit.h.

◆ fXts

Double_t* TMinuit::fXts

Definition at line 79 of file TMinuit.h.

◆ fYdircr

Double_t TMinuit::fYdircr

Definition at line 66 of file TMinuit.h.

◆ fYmidcr

Double_t TMinuit::fYmidcr

Definition at line 64 of file TMinuit.h.

◆ fYpt

Double_t* TMinuit::fYpt

Definition at line 98 of file TMinuit.h.

Libraries for TMinuit:

[legend]

The documentation for this class was generated from the following files:

math/minuit/inc/TMinuit.h
math/minuit/src/TMinuit.cxx

Basic concepts of MINUIT

Basic concepts - The transformation for parameters with limits.

How to get the right answer from MINUIT.

Getting the right minimum with limits.

Getting the right parameter errors with limits.

Interpretation of Parameter Errors:

Statistical interpretation:

Reliability of MINUIT error estimates.

A non-physical region:

An underdetermined problem:

Numerical inaccuracies:

An ill-posed problem:

Excessive numerical roundoff:

Starting too far from the solution:

Minuit parameter errors in the presence of limits

Public Types

Public Member Functions

Public Attributes

Private Member Functions

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ TMinuit() [1/3]

◆ TMinuit() [2/3]

◆ TMinuit() [3/3]

◆ ~TMinuit()

Member Function Documentation

◆ BuildArrays()

◆ Clone()

◆ Command()

◆ Contour()

◆ DefineParameter()

◆ DeleteArrays()

◆ Eval()

◆ FixParameter()

◆ GetMaxIterations()

◆ GetMethodCall()

◆ GetNumFixedPars()

◆ GetNumFreePars()

◆ GetNumPars()

◆ GetObjectFit()

◆ GetParameter()

◆ GetPlot()

◆ GetStatus()

◆ Migrad()

◆ mnamin()

◆ mnbins()

◆ mncalf()

◆ mncler()

◆ mncntr()

◆ mncomd()

◆ mncont()

◆ mncrck()

◆ mncros()

◆ mncuve()

◆ mnderi()

◆ mndxdi()

◆ mneig()

◆ mnemat()

◆ mnerrs()

◆ mneval()

◆ mnexcm()

◆ mnexin()

◆ mnfixp()

◆ mnfree()

◆ mngrad()

◆ mnhelp() [1/2]

◆ mnhelp() [2/2]

◆ mnhes1()

◆ mnhess()

◆ mnimpr()

◆ mninex()

◆ mninit()

◆ mnlims()

◆ mnline()

◆ mnmatu()

◆ mnmigr()

◆ mnmnos()

◆ mnmnot()

◆ mnparm()