TMinuit Class Reference

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:

1. Limits on variable parameters should be used only when needed in order to prevent the parameter from taking on unphysical values.
2. 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:

1. F.James. Determining the statistical Significance of experimental Results. Technical Report DD/81/02 and CERN Report 81-03, CERN, 1981.
2. 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:

1. Warning messages produced during the minimization or error analysis.
2. Failure to find new minimum.
3. Value of EDM too big (estimated Distance to Minimum).
4. Correlation coefficients exactly equal to zero, unless some parameters are known to be uncorrelated with the others.
5. 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.
6. 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 aphysical'' 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 Types inherited from TObject
enum	{   kIsOnHeap = 0x01000000 , kNotDeleted = 0x02000000 , kZombie = 0x04000000 , kInconsistent = 0x08000000 ,   kBitMask = 0x00ffffff }
enum	{ kSingleKey = BIT(0) , kOverwrite = BIT(1) , kWriteDelete = BIT(2) }
enum	EDeprecatedStatusBits { kObjInCanvas = BIT(3) }
enum	EStatusBits {   kCanDelete = BIT(0) , kMustCleanup = BIT(3) , kIsReferenced = BIT(4) , kHasUUID = BIT(5) ,   kCannotPick = BIT(6) , kNoContextMenu = BIT(8) , kInvalidObject = BIT(13) }

Public Member Functions
	TMinuit ()
	Minuit normal constructor.
	TMinuit (Int_t maxpar)
	Minuit normal constructor.
virtual	~TMinuit ()
	Minuit default destructor.
virtual void	BuildArrays (Int_t maxpar=15)
	Create internal Minuit arrays for the maxpar parameters.
virtual TObject *	Clone (const char *newname="") const
	Make a clone of an object using the Streamer facility.
virtual Int_t	Command (const char *command)
	Execute a Minuit command.
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.
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.
virtual void	DeleteArrays ()
	Delete internal Minuit arrays.
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:
virtual Int_t	FixParameter (Int_t parNo)
	fix a parameter
Int_t	GetMaxIterations () const
TMethodCall *	GetMethodCall () const
virtual Int_t	GetNumFixedPars () const
	returns the number of currently fixed parameters
virtual Int_t	GetNumFreePars () const
	returns the number of currently free parameters
virtual Int_t	GetNumPars () const
	returns the total number of parameters that have been defined as fixed or free.
TObject *	GetObjectFit () const
virtual Int_t	GetParameter (Int_t parNo, Double_t &currentValue, Double_t &currentError) const
	return parameter value and error
virtual TObject *	GetPlot () const
Int_t	GetStatus () const
virtual Int_t	Migrad ()
	invokes the MIGRAD minimizer
virtual void	mnamin ()
	Initialize AMIN.
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.
virtual void	mncalf (Double_t *pvec, Double_t &ycalf)
	Transform FCN to find further minima.
virtual void	mncler ()
	Resets the parameter list to UNDEFINED.
virtual void	mncntr (Int_t ke1, Int_t ke2, Int_t &ierrf)
	Print function contours in two variables, on line printer.
virtual void	mncomd (const char *crdbin, Int_t &icondn)
	Reads a command string and executes.
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.
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.
virtual void	mncros (Double_t &aopt, Int_t &iercr)
	Find point where MNEVAL=AMIN+UP.
virtual void	mncuve ()
	Makes sure that the current point is a local minimum.
virtual void	mnderi ()
	Calculates the first derivatives of FCN (GRD)
virtual void	mndxdi (Double_t pint, Int_t ipar, Double_t &dxdi)
	Calculates the transformation factor between ext/internal values.
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.
virtual void	mnemat (Double_t *emat, Int_t ndim)
	Calculates the external error matrix from the internal matrix.
virtual void	mnerrs (Int_t number, Double_t &eplus, Double_t &eminus, Double_t &eparab, Double_t &gcc)
	Utility routine to get MINOS errors.
virtual void	mneval (Double_t anext, Double_t &fnext, Int_t &ierev)
	Evaluates the function being analysed by MNCROS.
virtual void	mnexcm (const char *comand, Double_t *plist, Int_t llist, Int_t &ierflg)
	Interprets a command and takes appropriate action.
virtual void	mnexin (Double_t *pint)
	Transforms the external parameter values U to internal values.
virtual void	mnfixp (Int_t iint, Int_t &ierr)
	Removes parameter IINT from the internal parameter list.
virtual void	mnfree (Int_t k)
	Restores one or more fixed parameter(s) to variable status.
virtual void	mngrad ()
	Interprets the SET GRAD command.
virtual void	mnhelp (const char *command="")
	interface to Minuit help
virtual void	mnhelp (TString comd)
	HELP routine for MINUIT interactive commands.
virtual void	mnhes1 ()
	Calculate first derivatives (GRD) and uncertainties (DGRD)
virtual void	mnhess ()
	Calculates the full second-derivative matrix of FCN.
virtual void	mnimpr ()
	Attempts to improve on a good local minimum.
virtual void	mninex (Double_t *pint)
	Transforms from internal coordinates (PINT) to external (U)
virtual void	mninit (Int_t i1, Int_t i2, Int_t i3)
	Main initialization member function for MINUIT.
virtual void	mnlims ()
	Interprets the SET LIM command, to reset the parameter limits.
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.
virtual void	mnmatu (Int_t kode)
	Prints the covariance matrix v when KODE=1.
virtual void	mnmigr ()
	Performs a local function minimization.
virtual void	mnmnos ()
	Performs a MINOS error analysis.
virtual void	mnmnot (Int_t ilax, Int_t ilax2, Double_t &val2pl, Double_t &val2mi)
	Performs a MINOS error analysis on one parameter.
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.
virtual void	mnpars (TString &crdbuf, Int_t &icondn)
	Implements one parameter definition.
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.
virtual void	mnpint (Double_t &pexti, Int_t i, Double_t &pinti)
	Calculates the internal parameter value PINTI.
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.
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.
virtual void	mnprin (Int_t inkode, Double_t fval)
	Prints the values of the parameters at the time of the call.
virtual void	mnpsdf ()
	Calculates the eigenvalues of v to see if positive-def.
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.
virtual void	mnrn15 (Double_t &val, Int_t &inseed)
	This is a super-portable random number generator.
virtual void	mnrset (Int_t iopt)
	Resets function value and errors to UNDEFINED.
virtual void	mnsave ()
	Writes current parameter values and step sizes onto file ISYSSA.
virtual void	mnscan ()
	Scans the values of FCN as a function of one parameter.
virtual void	mnseek ()
	Performs a rough (but global) minimization by monte carlo search.
virtual void	mnset ()
	Interprets the commands that start with SET and SHOW.
virtual void	mnsimp ()
	Minimization using the simplex method of Nelder and Mead.
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.
virtual void	mntiny (volatile Double_t epsp1, Double_t &epsbak)
	To find the machine precision.
Bool_t	mnunpt (TString &cfname)
	Returns .TRUE.
virtual void	mnvert (Double_t *a, Int_t l, Int_t m, Int_t n, Int_t &ifail)
	Inverts a symmetric matrix.
virtual void	mnwarn (const char *copt, const char *corg, const char *cmes)
	Prints Warning messages.
virtual void	mnwerr ()
	Calculates the WERR, external parameter errors.
virtual Int_t	Release (Int_t parNo)
	release a parameter
virtual Int_t	SetErrorDef (Double_t up)
	To get the n-sigma contour the error def parameter "up" has to set to n^2.
virtual void	SetFCN (void(*fcn)(Int_t &, Double_t *, Double_t &f, Double_t *, Int_t))
	To set the address of the minimization function.
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.
Public Member Functions inherited from TNamed
	TNamed ()
	TNamed (const char *name, const char *title)
	TNamed (const TNamed &named)
	TNamed copy ctor.
	TNamed (const TString &name, const TString &title)
virtual	~TNamed ()
	TNamed destructor.
virtual void	Clear (Option_t *option="")
	Set name and title to empty strings ("").
virtual Int_t	Compare (const TObject *obj) const
	Compare two TNamed objects.
virtual void	Copy (TObject &named) const
	Copy this to obj.
virtual void	FillBuffer (char *&buffer)
	Encode TNamed into output buffer.
virtual const char *	GetName () const
	Returns name of object.
virtual const char *	GetTitle () const
	Returns title of object.
virtual ULong_t	Hash () const
	Return hash value for this object.
virtual Bool_t	IsSortable () const
virtual void	ls (Option_t *option="") const
	List TNamed name and title.
TNamed &	operator= (const TNamed &rhs)
	TNamed assignment operator.
virtual void	Print (Option_t *option="") const
	Print TNamed name and title.
virtual void	SetName (const char *name)
	Set the name of the TNamed.
virtual void	SetNameTitle (const char *name, const char *title)
	Set all the TNamed parameters (name and title).
virtual void	SetTitle (const char *title="")
	Set the title of the TNamed.
virtual Int_t	Sizeof () const
	Return size of the TNamed part of the TObject.
Public Member Functions inherited from TObject
	TObject ()
	TObject constructor.
	TObject (const TObject &object)
	TObject copy ctor.
virtual	~TObject ()
	TObject destructor.
void	AbstractMethod (const char *method) const
	Use this method to implement an "abstract" method that you don't want to leave purely abstract.
virtual void	AppendPad (Option_t *option="")
	Append graphics object to current pad.
virtual void	Browse (TBrowser *b)
	Browse object. May be overridden for another default action.
ULong_t	CheckedHash ()
	Check and record whether this class has a consistent Hash/RecursiveRemove setup (*) and then return the regular Hash value for this object.
virtual const char *	ClassName () const
	Returns name of class to which the object belongs.
virtual void	Delete (Option_t *option="")
	Delete this object.
virtual Int_t	DistancetoPrimitive (Int_t px, Int_t py)
	Computes distance from point (px,py) to the object.
virtual void	Draw (Option_t *option="")
	Default Draw method for all objects.
virtual void	DrawClass () const
	Draw class inheritance tree of the class to which this object belongs.
virtual TObject *	DrawClone (Option_t *option="") const
	Draw a clone of this object in the current selected pad for instance with: gROOT->SetSelectedPad(gPad).
virtual void	Dump () const
	Dump contents of object on stdout.
virtual void	Error (const char *method, const char *msgfmt,...) const
	Issue error message.
virtual void	Execute (const char *method, const char *params, Int_t *error=0)
	Execute method on this object with the given parameter string, e.g.
virtual void	Execute (TMethod *method, TObjArray *params, Int_t *error=0)
	Execute method on this object with parameters stored in the TObjArray.
virtual void	ExecuteEvent (Int_t event, Int_t px, Int_t py)
	Execute action corresponding to an event at (px,py).
virtual void	Fatal (const char *method, const char *msgfmt,...) const
	Issue fatal error message.
virtual TObject *	FindObject (const char *name) const
	Must be redefined in derived classes.
virtual TObject *	FindObject (const TObject *obj) const
	Must be redefined in derived classes.
virtual Option_t *	GetDrawOption () const
	Get option used by the graphics system to draw this object.
virtual const char *	GetIconName () const
	Returns mime type name of object.
virtual char *	GetObjectInfo (Int_t px, Int_t py) const
	Returns string containing info about the object at position (px,py).
virtual Option_t *	GetOption () const
virtual UInt_t	GetUniqueID () const
	Return the unique object id.
virtual Bool_t	HandleTimer (TTimer *timer)
	Execute action in response of a timer timing out.
Bool_t	HasInconsistentHash () const
	Return true is the type of this object is known to have an inconsistent setup for Hash and RecursiveRemove (i.e.
virtual void	Info (const char *method, const char *msgfmt,...) const
	Issue info message.
virtual Bool_t	InheritsFrom (const char *classname) const
	Returns kTRUE if object inherits from class "classname".
virtual Bool_t	InheritsFrom (const TClass *cl) const
	Returns kTRUE if object inherits from TClass cl.
virtual void	Inspect () const
	Dump contents of this object in a graphics canvas.
void	InvertBit (UInt_t f)
virtual Bool_t	IsEqual (const TObject *obj) const
	Default equal comparison (objects are equal if they have the same address in memory).
virtual Bool_t	IsFolder () const
	Returns kTRUE in case object contains browsable objects (like containers or lists of other objects).
R__ALWAYS_INLINE Bool_t	IsOnHeap () const
R__ALWAYS_INLINE Bool_t	IsZombie () const
void	MayNotUse (const char *method) const
	Use this method to signal that a method (defined in a base class) may not be called in a derived class (in principle against good design since a child class should not provide less functionality than its parent, however, sometimes it is necessary).
virtual Bool_t	Notify ()
	This method must be overridden to handle object notification.
void	Obsolete (const char *method, const char *asOfVers, const char *removedFromVers) const
	Use this method to declare a method obsolete.
void	operator delete (void *ptr)
	Operator delete.
void	operator delete[] (void *ptr)
	Operator delete [].
void *	operator new (size_t sz)
void *	operator new (size_t sz, void *vp)
void *	operator new[] (size_t sz)
void *	operator new[] (size_t sz, void *vp)
TObject &	operator= (const TObject &rhs)
	TObject assignment operator.
virtual void	Paint (Option_t *option="")
	This method must be overridden if a class wants to paint itself.
virtual void	Pop ()
	Pop on object drawn in a pad to the top of the display list.
virtual Int_t	Read (const char *name)
	Read contents of object with specified name from the current directory.
virtual void	RecursiveRemove (TObject *obj)
	Recursively remove this object from a list.
void	ResetBit (UInt_t f)
virtual void	SaveAs (const char *filename="", Option_t *option="") const
	Save this object in the file specified by filename.
virtual void	SavePrimitive (std::ostream &out, Option_t *option="")
	Save a primitive as a C++ statement(s) on output stream "out".
void	SetBit (UInt_t f)
void	SetBit (UInt_t f, Bool_t set)
	Set or unset the user status bits as specified in f.
virtual void	SetDrawOption (Option_t *option="")
	Set drawing option for object.
virtual void	SetUniqueID (UInt_t uid)
	Set the unique object id.
virtual void	SysError (const char *method, const char *msgfmt,...) const
	Issue system error message.
R__ALWAYS_INLINE Bool_t	TestBit (UInt_t f) const
Int_t	TestBits (UInt_t f) const
virtual void	UseCurrentStyle ()
	Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked.
virtual void	Warning (const char *method, const char *msgfmt,...) const
	Issue warning message.
virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0)
	Write this object to the current directory.
virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0) const
	Write this object to the current directory.

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

Additional Inherited Members
Static Public Member Functions inherited from TObject
static Long_t	GetDtorOnly ()
	Return destructor only flag.
static Bool_t	GetObjectStat ()
	Get status of object stat flag.
static void	SetDtorOnly (void *obj)
	Set destructor only flag.
static void	SetObjectStat (Bool_t stat)
	Turn on/off tracking of objects in the TObjectTable.
Protected Types inherited from TObject
enum	{ kOnlyPrepStep = BIT(3) }
Protected Member Functions inherited from TObject
virtual void	DoError (int level, const char *location, const char *fmt, va_list va) const
	Interface to ErrorHandler (protected).
void	MakeZombie ()
Protected Attributes inherited from TNamed
TString	fName
TString	fTitle

#include <TMinuit.h>

Inheritance diagram for TMinuit:

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 488 of file TMinuit.cxx.

TMinuit() [2/3]

TMinuit::TMinuit

(

)

Minuit normal constructor.

Definition at line 346 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 463 of file TMinuit.cxx.

~TMinuit()

TMinuit::~TMinuit ( )

virtual

Minuit default destructor.

Definition at line 496 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 511 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

Reimplemented from TNamed.

Reimplemented in TMVA::MinuitWrapper.

Definition at line 595 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 625 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 652 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 694 of file TMinuit.cxx.

DeleteArrays()

void TMinuit::DeleteArrays ( )

virtual

Delete internal Minuit arrays.

Definition at line 707 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:

Reimplemented in TMVA::MinuitWrapper.

Definition at line 799 of file TMinuit.cxx.

FixParameter()

Int_t TMinuit::FixParameter ( Int_t  parNo )

virtual

fix a parameter

Definition at line 826 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 854 of file TMinuit.cxx.

GetNumFreePars()

Int_t TMinuit::GetNumFreePars ( ) const

virtual

returns the number of currently free parameters

Definition at line 862 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 871 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 840 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 879 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 971 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 996 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 1069 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 1102 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 1131 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 1309 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 1394 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 1676 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 1797 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 2129 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 2177 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 2292 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 2304 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 2500 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 2577 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 2619 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

see also the possible list of all Minuit commands.

Definition at line 2663 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 3150 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 3168 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 3255 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 3361 of file TMinuit.cxx.

mnhelp() [1/2]

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

virtual

interface to Minuit help

Definition at line 3421 of file TMinuit.cxx.

mnhelp() [2/2]

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 3438 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 4217 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 3992 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 4294 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 4505 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 4525 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 4615 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 4735 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 4969 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 5049 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 5389 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 5464 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 5666 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 5868 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 5957 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 6018 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 6069 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 6248 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 6305 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 6495 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 6569 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 6618 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 6660 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 6694 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 6707 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 6817 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 6912 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 7430 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 7637 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 7660 of file TMinuit.cxx.

mnunpt()

Bool_t TMinuit::mnunpt

(

TString &

cfname

)

Returns .TRUE.

if CFNAME contains unprintable characters

Definition at line 7669 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 7695 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 7783 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 7860 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 893 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 907 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 919 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 951 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:

---

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

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