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ROOT 6.07/09 Reference Guide |
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 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.
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:
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:
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.
\[ \frac{\partial F}{\partial P_{\mathrm{int}}} = \frac{\partial F}{\partial P_{\mathrm{ext}}} \frac{\partial P_{\mathrm{ext}}}{\partial P_{\mathrm{int}}} = \frac{\partial F}{\partial P_{\mathrm{ext}}} = 0 \]
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.
There are two kinds of problems that can arise: the reliability of MINUIT's error estimates, and their statistical interpretation, assuming they are accurate.
For discussion of basic concepts, such as the meaning of the elements of the error matrix, or setting of exact confidence levels see:
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:
EDM
too big (estimated Distance to Minimum).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:
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.
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.
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.
For questions of parameter dependence, see the discussion above on positive-definiteness.
Possible other mathematical problems are the following:
Be especially careful of exponential and factorial functions which get big very quickly and lose accuracy.
The function may have unphysical local minima, especially at infinity in some variables.
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.
Public Types | |
enum | { kMAXWARN =100 } |
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enum | { kIsOnHeap = 0x01000000, kNotDeleted = 0x02000000, kZombie = 0x04000000, kBitMask = 0x00ffffff } |
enum | { kSingleKey = BIT(0), kOverwrite = BIT(1), kWriteDelete = BIT(2) } |
enum | EStatusBits { kCanDelete = BIT(0), kMustCleanup = BIT(3), kObjInCanvas = BIT(3), kIsReferenced = BIT(4), kHasUUID = BIT(5), kCannotPick = BIT(6), kNoContextMenu = BIT(8), kInvalidObject = BIT(13) } |
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 ¤tValue, Double_t ¤tError) 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) R__DEPRECATED(6 |
To set the address of the minimization function. 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... | |
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TNamed () | |
TNamed (const char *name, const char *title) | |
TNamed (const TString &name, const TString &title) | |
TNamed (const TNamed &named) | |
TNamed copy ctor. More... | |
virtual | ~TNamed () |
virtual void | Clear (Option_t *option="") |
Set name and title to empty strings (""). More... | |
virtual Int_t | Compare (const TObject *obj) const |
Compare two TNamed objects. More... | |
virtual void | Copy (TObject &named) const |
Copy this to obj. More... | |
virtual void | FillBuffer (char *&buffer) |
Encode TNamed into output buffer. More... | |
virtual const char * | GetName () const |
Returns name of object. More... | |
virtual const char * | GetTitle () const |
Returns title of object. More... | |
virtual ULong_t | Hash () const |
Return hash value for this object. More... | |
virtual Bool_t | IsSortable () const |
virtual void | ls (Option_t *option="") const |
List TNamed name and title. More... | |
TNamed & | operator= (const TNamed &rhs) |
TNamed assignment operator. More... | |
virtual void | Print (Option_t *option="") const |
Print TNamed name and title. More... | |
virtual void | SetName (const char *name) |
Set the name of the TNamed. More... | |
virtual void | SetNameTitle (const char *name, const char *title) |
Set all the TNamed parameters (name and title). More... | |
virtual void | SetTitle (const char *title="") |
Set the title of the TNamed. More... | |
virtual Int_t | Sizeof () const |
Return size of the TNamed part of the TObject. More... | |
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TObject () | |
TObject constructor. More... | |
TObject (const TObject &object) | |
TObject copy ctor. More... | |
virtual | ~TObject () |
TObject destructor. More... | |
void | AbstractMethod (const char *method) const |
Use this method to implement an "abstract" method that you don't want to leave purely abstract. More... | |
virtual void | AppendPad (Option_t *option="") |
Append graphics object to current pad. More... | |
virtual void | Browse (TBrowser *b) |
Browse object. May be overridden for another default action. More... | |
virtual const char * | ClassName () const |
Returns name of class to which the object belongs. More... | |
virtual void | Delete (Option_t *option="") |
Delete this object. More... | |
virtual Int_t | DistancetoPrimitive (Int_t px, Int_t py) |
Computes distance from point (px,py) to the object. More... | |
virtual void | Draw (Option_t *option="") |
Default Draw method for all objects. More... | |
virtual void | DrawClass () const |
Draw class inheritance tree of the class to which this object belongs. More... | |
virtual TObject * | DrawClone (Option_t *option="") const |
Draw a clone of this object in the current pad. More... | |
virtual void | Dump () const |
Dump contents of object on stdout. More... | |
virtual void | Error (const char *method, const char *msgfmt,...) const |
Issue error message. More... | |
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. More... | |
virtual void | Execute (TMethod *method, TObjArray *params, Int_t *error=0) |
Execute method on this object with parameters stored in the TObjArray. More... | |
virtual void | ExecuteEvent (Int_t event, Int_t px, Int_t py) |
Execute action corresponding to an event at (px,py). More... | |
virtual void | Fatal (const char *method, const char *msgfmt,...) const |
Issue fatal error message. More... | |
virtual TObject * | FindObject (const char *name) const |
Must be redefined in derived classes. More... | |
virtual TObject * | FindObject (const TObject *obj) const |
Must be redefined in derived classes. More... | |
virtual Option_t * | GetDrawOption () const |
Get option used by the graphics system to draw this object. More... | |
virtual const char * | GetIconName () const |
Returns mime type name of object. More... | |
virtual char * | GetObjectInfo (Int_t px, Int_t py) const |
Returns string containing info about the object at position (px,py). More... | |
virtual Option_t * | GetOption () const |
virtual UInt_t | GetUniqueID () const |
Return the unique object id. More... | |
virtual Bool_t | HandleTimer (TTimer *timer) |
Execute action in response of a timer timing out. More... | |
virtual void | Info (const char *method, const char *msgfmt,...) const |
Issue info message. More... | |
virtual Bool_t | InheritsFrom (const char *classname) const |
Returns kTRUE if object inherits from class "classname". More... | |
virtual Bool_t | InheritsFrom (const TClass *cl) const |
Returns kTRUE if object inherits from TClass cl. More... | |
virtual void | Inspect () const |
Dump contents of this object in a graphics canvas. More... | |
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). More... | |
virtual Bool_t | IsFolder () const |
Returns kTRUE in case object contains browsable objects (like containers or lists of other objects). More... | |
Bool_t | IsOnHeap () const |
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). More... | |
virtual Bool_t | Notify () |
This method must be overridden to handle object notification. More... | |
void | Obsolete (const char *method, const char *asOfVers, const char *removedFromVers) const |
Use this method to declare a method obsolete. More... | |
void | operator delete (void *ptr) |
Operator delete. More... | |
void | operator delete[] (void *ptr) |
Operator delete []. More... | |
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. More... | |
virtual void | Paint (Option_t *option="") |
This method must be overridden if a class wants to paint itself. More... | |
virtual void | Pop () |
Pop on object drawn in a pad to the top of the display list. More... | |
virtual Int_t | Read (const char *name) |
Read contents of object with specified name from the current directory. More... | |
virtual void | RecursiveRemove (TObject *obj) |
Recursively remove this object from a list. More... | |
void | ResetBit (UInt_t f) |
virtual void | SaveAs (const char *filename="", Option_t *option="") const |
Save this object in the file specified by filename. More... | |
virtual void | SavePrimitive (std::ostream &out, Option_t *option="") |
Save a primitive as a C++ statement(s) on output stream "out". More... | |
void | SetBit (UInt_t f, Bool_t set) |
Set or unset the user status bits as specified in f. More... | |
void | SetBit (UInt_t f) |
virtual void | SetDrawOption (Option_t *option="") |
Set drawing option for object. More... | |
virtual void | SetUniqueID (UInt_t uid) |
Set the unique object id. More... | |
virtual void | SysError (const char *method, const char *msgfmt,...) const |
Issue system error message. More... | |
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. More... | |
virtual void | Warning (const char *method, const char *msgfmt,...) const |
Issue warning message. More... | |
virtual Int_t | Write (const char *name=0, Int_t option=0, Int_t bufsize=0) |
Write this object to the current directory. More... | |
virtual Int_t | Write (const char *name=0, Int_t option=0, Int_t bufsize=0) const |
Write this object to the current directory. More... | |
Private Member Functions | |
TMinuit (const TMinuit &m) | |
Private TMinuit copy ctor. TMinuit can not be copied. More... | |
TMinuit & | operator= (const TMinuit &m) |
Additional Inherited Members | |
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static Long_t | GetDtorOnly () |
Return destructor only flag. More... | |
static Bool_t | GetObjectStat () |
Get status of object stat flag. More... | |
static void | SetDtorOnly (void *obj) |
Set destructor only flag. More... | |
static void | SetObjectStat (Bool_t stat) |
Turn on/off tracking of objects in the TObjectTable. More... | |
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virtual void | DoError (int level, const char *location, const char *fmt, va_list va) const |
Interface to ErrorHandler (protected). More... | |
void | MakeZombie () |
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TString | fName |
TString | fTitle |
#include <TMinuit.h>
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Private TMinuit copy ctor. TMinuit can not be copied.
Definition at line 496 of file TMinuit.cxx.
TMinuit::TMinuit | ( | ) |
Minuit normal constructor.
Definition at line 354 of file TMinuit.cxx.
TMinuit::TMinuit | ( | Int_t | maxpar | ) |
Minuit normal constructor.
maxpar is the maximum number of parameters used with this TMinuit object.
Definition at line 471 of file TMinuit.cxx.
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Minuit default destructor.
Definition at line 504 of file TMinuit.cxx.
Create internal Minuit arrays for the maxpar parameters.
Definition at line 519 of file TMinuit.cxx.
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Make a clone of an object using the Streamer facility.
Function pointer is copied to Clone
Reimplemented from TNamed.
Definition at line 603 of file TMinuit.cxx.
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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:
Definition at line 633 of file TMinuit.cxx.
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
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 660 of file TMinuit.cxx.
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Define a parameter.
Definition at line 702 of file TMinuit.cxx.
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Delete internal Minuit arrays.
Definition at line 715 of file TMinuit.cxx.
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Evaluate the minimisation function Input parameters:
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 807 of file TMinuit.cxx.
fix a parameter
Definition at line 834 of file TMinuit.cxx.
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returns the number of currently fixed parameters
Definition at line 862 of file TMinuit.cxx.
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returns the number of currently free parameters
Definition at line 870 of file TMinuit.cxx.
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returns the total number of parameters that have been defined as fixed or free.
The constant parameters are not counted.
Definition at line 879 of file TMinuit.cxx.
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return parameter value and error
Definition at line 848 of file TMinuit.cxx.
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invokes the MIGRAD minimizer
Definition at line 887 of file TMinuit.cxx.
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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 994 of file TMinuit.cxx.
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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 1019 of file TMinuit.cxx.
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 1092 of file TMinuit.cxx.
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Resets the parameter list to UNDEFINED.
Called from MINUIT and by option from MNEXCM
Definition at line 1125 of file TMinuit.cxx.
Print function contours in two variables, on line printer.
input arguments: parx, pary, devs, ngrid
Definition at line 1154 of file TMinuit.cxx.
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 =
Definition at line 1332 of file TMinuit.cxx.
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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:
input arguments: parx, pary, devs, ngrid
Definition at line 1417 of file TMinuit.cxx.
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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 :
Definition at line 1699 of file TMinuit.cxx.
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 1820 of file TMinuit.cxx.
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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 2152 of file TMinuit.cxx.
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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 2200 of file TMinuit.cxx.
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 2315 of file TMinuit.cxx.
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Compute matrix eigen values.
Definition at line 2327 of file TMinuit.cxx.
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 2523 of file TMinuit.cxx.
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Utility routine to get MINOS errors.
Called by user.
NUMBER is the parameter number
values returned by MNERRS:
Definition at line 2600 of file TMinuit.cxx.
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 2642 of file TMinuit.cxx.
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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 =
see also the possible list of all Minuit commands.
Definition at line 2686 of file TMinuit.cxx.
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 3173 of file TMinuit.cxx.
Removes parameter IINT from the internal parameter list.
and arranges the rest of the list to fill the hole.
Definition at line 3191 of file TMinuit.cxx.
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 3278 of file TMinuit.cxx.
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Interprets the SET GRAD command.
Definition at line 3384 of file TMinuit.cxx.
HELP routine for MINUIT interactive 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 3459 of file TMinuit.cxx.
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interface to Minuit help
Definition at line 3442 of file TMinuit.cxx.
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Calculate first derivatives (GRD) and uncertainties (DGRD)
and appropriate step sizes GSTEP Called from MNHESS and MNGRAD
Definition at line 4238 of file TMinuit.cxx.
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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 4013 of file TMinuit.cxx.
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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 4315 of file TMinuit.cxx.
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 4526 of file TMinuit.cxx.
Main initialization member function for MINUIT.
It initializes some constants (including the logical I/O unit nos.),
Definition at line 4546 of file TMinuit.cxx.
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Interprets the SET LIM command, to reset the parameter limits.
Called from MNSET
Definition at line 4636 of file TMinuit.cxx.
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Perform a line search from position START.
along direction STEP, where the length of vector STEP gives the expected position of minimum.
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 4756 of file TMinuit.cxx.
Prints the covariance matrix v when KODE=1.
always prints the global correlations, and calculates and prints the individual correlation coefficients
Definition at line 4990 of file TMinuit.cxx.
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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 5070 of file TMinuit.cxx.
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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 5410 of file TMinuit.cxx.
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 5485 of file TMinuit.cxx.
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Implements one parameter definition.
Called from MNPARS and user-callable Implements one parameter definition, that is:
Definition at line 5685 of file TMinuit.cxx.
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:
Definition at line 5887 of file TMinuit.cxx.
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To fit a parabola to npar2p points.
Definition at line 5976 of file TMinuit.cxx.
Calculates the internal parameter value PINTI.
corresponding to the external value PEXTI for parameter I.
Definition at line 6037 of file TMinuit.cxx.
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Plots points in array xypt onto one page with labelled axes.
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:
Definition at line 6088 of file TMinuit.cxx.
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Provides the user with information concerning the current status.
of parameter number IUEXT. Namely, it returns:
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 6270 of file TMinuit.cxx.
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=
when INKODE=5, MNPRIN chooses IKODE=1,2, or 3, according to fISW[1]
Definition at line 6327 of file TMinuit.cxx.
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Calculates the eigenvalues of v to see if positive-def.
if not, adds constant along diagonal to make positive.
Definition at line 6517 of file TMinuit.cxx.
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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 6591 of file TMinuit.cxx.
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 6640 of file TMinuit.cxx.
Resets function value and errors to UNDEFINED.
Definition at line 6668 of file TMinuit.cxx.
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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.
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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.
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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.
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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.
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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.
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Returns concerning the current status of the minimization.
User-called Namely, it returns:
Definition at line 7645 of file TMinuit.cxx.
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.
Returns .TRUE.
if CFNAME contains unprintable characters
Definition at line 7677 of file TMinuit.cxx.
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.
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Prints Warning messages.
Definition at line 7791 of file TMinuit.cxx.
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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.
release a parameter
Definition at line 901 of file TMinuit.cxx.
To get the n-sigma contour the error def parameter "up" has to set to n^2.
Definition at line 915 of file TMinuit.cxx.
To set the address of the minimization function.
this function is called by the interpretor instead of the function above
Definition at line 956 of file TMinuit.cxx.
To set the address of the minimization function.
Definition at line 927 of file TMinuit.cxx.
set Minuit print level.
printlevel:
Definition at line 974 of file TMinuit.cxx.
TString* TMinuit::fCpnam |
TMethodCall* TMinuit::fMethodCall |