The Minimization package*- -* ======================== -* -* This package was originally written in Fortran by Fred James -* and part of PACKLIB (patch D506) -* -* It has been converted to a C++ class by R.Brun -* The current implementation in C++ is a straightforward conversion -* of the original Fortran version: The main changes are: -* -* - The variables in the various Minuit labelled common blocks -* have been changed to the TMinuit class data members. -* - The internal arrays with a maximum dimension depending on the -* maximum number of parameters are now data members arrays with -* a dynamic dimension such that one can fit very large problems -* by simply initialising the TMinuit constructor with the maximum -* number of parameters. -* - The include file Minuit.h has been commented as much as possible -* using existing comments in the code or the printed documentation -* - The original Minuit subroutines are now member functions. -* - Constructors and destructor have been added. -* - Instead of passing the FCN function in the argument -* list, the addresses of this function is stored as pointer -* in the data members of the class. This is by far more elegant -* and flexible in an interactive environment. -* The member function SetFCN can be used to define this pointer. -* - The ROOT static function Printf is provided to replace all -* format statements and to print on currently defined output file. -* - The functions SetObjectFit(TObject *obj)/GetObjectFit() can be -* used inside the FCN function to set/get a referenced object -* instead of using global variables. *
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 = arcsin(2((P -a)/(b- a))-1) P = a+((b- a)/(2))(sinP +1) int ext ext int
so that the internal value P can take on any value, while the external int value P can take on values only between the lower limit a and the ext upper limit b. Since the transformation is necessarily non-linear, it would transform a nice linear problem into a nasty non-linear one, which is the reason why limits should be avoided if not necessary. In addition, the transformation does require some computer time, so it slows down the computation a little bit, and more importantly, it introduces additional numerical inaccuracy into the problem in addition to what is introduced in the numerical calculation of the FCN value. The effects of non-linearity and numerical roundoff both become more important as the external value gets closer to one of the limits (expressed as the distance to nearest limit divided by distance between limits). The user must therefore be aware of the fact that, for example, if they put 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 Pext /partial Pint #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 #((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 Pint is zero no matter what the real derivative partial F/partial Pext is.
((partial F)/(partial P ))= ((partial F)/(partial P ))((partial P )/(partial P )) =((partial F)/(partial P ))= 0 int ext ext int ext
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 discussuion 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:
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 parameterization of the fit contains a linear dependence. If this is the case, then MINUIT (or any other program) cannot solve your problem uniquely, and the error matrix will necessarily be largely meaningless, so the user must remove the underdeterminedness by reformulating the parameterization. MINUIT cannot do this itself.
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.
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 linearization 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.
virtual | ~TMinuit() |
void | TObject::AbstractMethod(const char* method) const |
virtual void | TObject::AppendPad(Option_t* option = "") |
virtual void | TObject::Browse(TBrowser* b) |
virtual void | BuildArrays(Int_t maxpar = 15) |
static TClass* | Class() |
virtual const char* | TObject::ClassName() const |
virtual void | TNamed::Clear(Option_t* option = "") |
virtual TObject* | Clone(const char* newname = "") const |
virtual Int_t | Command(const char* command) |
virtual Int_t | TNamed::Compare(const TObject* obj) const |
virtual TObject* | Contour(Int_t npoints = 10, Int_t pa1 = 0, Int_t pa2 = 1) |
virtual void | TNamed::Copy(TObject& named) const |
virtual Int_t | DefineParameter(Int_t parNo, const char* name, Double_t initVal, Double_t initErr, Double_t lowerLimit, Double_t upperLimit) |
virtual void | TObject::Delete(Option_t* option = "")MENU |
virtual void | DeleteArrays() |
virtual Int_t | TObject::DistancetoPrimitive(Int_t px, Int_t py) |
virtual void | TObject::Draw(Option_t* option = "") |
virtual void | TObject::DrawClass() constMENU |
virtual TObject* | TObject::DrawClone(Option_t* option = "") constMENU |
virtual void | TObject::Dump() constMENU |
virtual void | TObject::Error(const char* method, const char* msgfmt) const |
virtual Int_t | Eval(Int_t npar, Double_t* grad, Double_t& fval, Double_t* par, Int_t flag) |
virtual void | TObject::Execute(const char* method, const char* params, Int_t* error = 0) |
virtual void | TObject::Execute(TMethod* method, TObjArray* params, Int_t* error = 0) |
virtual void | TObject::ExecuteEvent(Int_t event, Int_t px, Int_t py) |
virtual void | TObject::Fatal(const char* method, const char* msgfmt) const |
virtual void | TNamed::FillBuffer(char*& buffer) |
virtual TObject* | TObject::FindObject(const char* name) const |
virtual TObject* | TObject::FindObject(const TObject* obj) const |
virtual Int_t | FixParameter(Int_t parNo) |
virtual Option_t* | TObject::GetDrawOption() const |
static Long_t | TObject::GetDtorOnly() |
virtual const char* | TObject::GetIconName() const |
Int_t | GetMaxIterations() const |
TMethodCall* | GetMethodCall() const |
virtual const char* | TNamed::GetName() const |
virtual Int_t | GetNumFixedPars() const |
virtual Int_t | GetNumFreePars() const |
virtual Int_t | GetNumPars() const |
TObject* | GetObjectFit() const |
virtual char* | TObject::GetObjectInfo(Int_t px, Int_t py) const |
static Bool_t | TObject::GetObjectStat() |
virtual Option_t* | TObject::GetOption() const |
virtual Int_t | GetParameter(Int_t parNo, Double_t& currentValue, Double_t& currentError) const |
virtual TObject* | GetPlot() const |
Int_t | GetStatus() const |
virtual const char* | TNamed::GetTitle() const |
virtual UInt_t | TObject::GetUniqueID() const |
virtual Bool_t | TObject::HandleTimer(TTimer* timer) |
virtual ULong_t | TNamed::Hash() const |
virtual void | TObject::Info(const char* method, const char* msgfmt) const |
virtual Bool_t | TObject::InheritsFrom(const char* classname) const |
virtual Bool_t | TObject::InheritsFrom(const TClass* cl) const |
virtual void | TObject::Inspect() constMENU |
void | TObject::InvertBit(UInt_t f) |
virtual TClass* | IsA() const |
virtual Bool_t | TObject::IsEqual(const TObject* obj) const |
virtual Bool_t | TObject::IsFolder() const |
Bool_t | TObject::IsOnHeap() const |
virtual Bool_t | TNamed::IsSortable() const |
Bool_t | TObject::IsZombie() const |
virtual void | TNamed::ls(Option_t* option = "") const |
void | TObject::MayNotUse(const char* method) const |
virtual Int_t | Migrad() |
virtual void | mnamin() |
virtual void | mnbins(Double_t a1, Double_t a2, Int_t naa, Double_t& bl, Double_t& bh, Int_t& nb, Double_t& bwid) |
virtual void | mncalf(Double_t* pvec, Double_t& ycalf) |
virtual void | mncler() |
virtual void | mncntr(Int_t ke1, Int_t ke2, Int_t& ierrf) |
virtual void | mncomd(const char* crdbin, Int_t& icondn) |
virtual void | mncont(Int_t ke1, Int_t ke2, Int_t nptu, Double_t* xptu, Double_t* yptu, Int_t& ierrf) |
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) |
virtual void | mncros(Double_t& aopt, Int_t& iercr) |
virtual void | mncuve() |
virtual void | mnderi() |
virtual void | mndxdi(Double_t pint, Int_t ipar, Double_t& dxdi) |
virtual void | mneig(Double_t* a, Int_t ndima, Int_t n, Int_t mits, Double_t* work, Double_t precis, Int_t& ifault) |
virtual void | mnemat(Double_t* emat, Int_t ndim) |
virtual void | mnerrs(Int_t number, Double_t& eplus, Double_t& eminus, Double_t& eparab, Double_t& gcc) |
virtual void | mneval(Double_t anext, Double_t& fnext, Int_t& ierev) |
virtual void | mnexcm(const char* comand, Double_t* plist, Int_t llist, Int_t& ierflg) |
virtual void | mnexin(Double_t* pint) |
virtual void | mnfixp(Int_t iint, Int_t& ierr) |
virtual void | mnfree(Int_t k) |
virtual void | mngrad() |
virtual void | mnhelp(TString comd) |
virtual void | mnhelp(const char* command = "") |
virtual void | mnhes1() |
virtual void | mnhess() |
virtual void | mnimpr() |
virtual void | mninex(Double_t* pint) |
virtual void | mninit(Int_t i1, Int_t i2, Int_t i3) |
virtual void | mnlims() |
virtual void | mnline(Double_t* start, Double_t fstart, Double_t* step, Double_t slope, Double_t toler) |
virtual void | mnmatu(Int_t kode) |
virtual void | mnmigr() |
virtual void | mnmnos() |
virtual void | mnmnot(Int_t ilax, Int_t ilax2, Double_t& val2pl, Double_t& val2mi) |
virtual void | mnparm(Int_t k, TString cnamj, Double_t uk, Double_t wk, Double_t a, Double_t b, Int_t& ierflg) |
virtual void | mnpars(TString& crdbuf, Int_t& icondn) |
virtual void | mnpfit(Double_t* parx2p, Double_t* pary2p, Int_t npar2p, Double_t* coef2p, Double_t& sdev2p) |
virtual void | mnpint(Double_t& pexti, Int_t i, Double_t& pinti) |
virtual void | mnplot(Double_t* xpt, Double_t* ypt, char* chpt, Int_t nxypt, Int_t npagwd, Int_t npagln) |
virtual void | mnpout(Int_t iuext, TString& chnam, Double_t& val, Double_t& err, Double_t& xlolim, Double_t& xuplim, Int_t& iuint) const |
virtual void | mnprin(Int_t inkode, Double_t fval) |
virtual void | mnpsdf() |
virtual void | mnrazz(Double_t ynew, Double_t* pnew, Double_t* y, Int_t& jh, Int_t& jl) |
virtual void | mnrn15(Double_t& val, Int_t& inseed) |
virtual void | mnrset(Int_t iopt) |
virtual void | mnsave() |
virtual void | mnscan() |
virtual void | mnseek() |
virtual void | mnset() |
virtual void | mnsimp() |
virtual void | mnstat(Double_t& fmin, Double_t& fedm, Double_t& errdef, Int_t& npari, Int_t& nparx, Int_t& istat) |
virtual void | mntiny(Double_t epsp1, Double_t& epsbak) |
Bool_t | mnunpt(TString& cfname) |
virtual void | mnvert(Double_t* a, Int_t l, Int_t m, Int_t n, Int_t& ifail) |
virtual void | mnwarn(const char* copt, const char* corg, const char* cmes) |
virtual void | mnwerr() |
virtual Bool_t | TObject::Notify() |
void | TObject::Obsolete(const char* method, const char* asOfVers, const char* removedFromVers) const |
void | TObject::operator delete(void* ptr) |
void | TObject::operator delete(void* ptr, void* vp) |
void | TObject::operator delete[](void* ptr) |
void | TObject::operator delete[](void* ptr, void* vp) |
void* | TObject::operator new(size_t sz) |
void* | TObject::operator new(size_t sz, void* vp) |
void* | TObject::operator new[](size_t sz) |
void* | TObject::operator new[](size_t sz, void* vp) |
virtual void | TObject::Paint(Option_t* option = "") |
virtual void | TObject::Pop() |
virtual void | TNamed::Print(Option_t* option = "") const |
virtual Int_t | TObject::Read(const char* name) |
virtual void | TObject::RecursiveRemove(TObject* obj) |
virtual Int_t | Release(Int_t parNo) |
void | TObject::ResetBit(UInt_t f) |
virtual void | TObject::SaveAs(const char* filename = "", Option_t* option = "") constMENU |
virtual void | TObject::SavePrimitive(ostream& out, Option_t* option = "") |
void | TObject::SetBit(UInt_t f) |
void | TObject::SetBit(UInt_t f, Bool_t set) |
virtual void | TObject::SetDrawOption(Option_t* option = "")MENU |
static void | TObject::SetDtorOnly(void* obj) |
virtual Int_t | SetErrorDef(Double_t up) |
virtual void | SetFCN(void* fcn) |
virtual void | SetFCN(void(*)(Int_t&,Double_t*,Double_t&,Double_t*,Int_t) fcn) |
virtual void | SetGraphicsMode(Bool_t mode = kTRUE) |
virtual void | SetMaxIterations(Int_t maxiter = 500) |
virtual void | TNamed::SetName(const char* name)MENU |
virtual void | TNamed::SetNameTitle(const char* name, const char* title) |
virtual void | SetObjectFit(TObject* obj) |
static void | TObject::SetObjectStat(Bool_t stat) |
virtual Int_t | SetPrintLevel(Int_t printLevel = 0) |
virtual void | TNamed::SetTitle(const char* title = "")MENU |
virtual void | TObject::SetUniqueID(UInt_t uid) |
virtual void | ShowMembers(TMemberInspector& insp) const |
virtual Int_t | TNamed::Sizeof() const |
virtual void | Streamer(TBuffer&) |
void | StreamerNVirtual(TBuffer& ClassDef_StreamerNVirtual_b) |
virtual void | TObject::SysError(const char* method, const char* msgfmt) const |
Bool_t | TObject::TestBit(UInt_t f) const |
Int_t | TObject::TestBits(UInt_t f) const |
TMinuit() | |
TMinuit(Int_t maxpar) | |
virtual void | TObject::UseCurrentStyle() |
virtual void | TObject::Warning(const char* method, const char* msgfmt) const |
virtual Int_t | TObject::Write(const char* name = 0, Int_t option = 0, Int_t bufsize = 0) |
virtual Int_t | TObject::Write(const char* name = 0, Int_t option = 0, Int_t bufsize = 0) const |
virtual void | TObject::DoError(int level, const char* location, const char* fmt, va_list va) const |
void | TObject::MakeZombie() |
Double_t* | fAlim | [fMaxpar2] Lower limits for parameters. If zero no limits |
Double_t | fAmin | Minimum value found for FCN |
Double_t | fApsi | |
Double_t | fBigedm | Big EDM = 123456 |
Double_t* | fBlim | [fMaxpar2] Upper limits for parameters |
Double_t* | fCOMDplist | [fMaxpar] array used in mncomd |
Double_t* | fCONTgcc | [fMaxpar] array used in mncont |
Double_t* | fCONTw | [fMaxpar] array used in mncont |
TString | fCfrom | |
char* | fChpt | !Character to be plotted at the X,Y contour positions |
TString | fCovmes[4] | |
TString* | fCpnam | [fMaxpar2] Array of parameters names |
TString | fCstatu | |
TString | fCtitl | |
TString | fCundef | |
TString | fCvrsn | |
TString | fCword | |
Double_t | fDcovar | Relative change in covariance matrix |
Double_t* | fDgrd | [fMaxpar] Uncertainties |
Double_t* | fDirin | [fMaxpar] (Internal) step sizes for current step |
Double_t* | fDirins | [fMaxpar] (Internal) step sizes for current step for fixed params |
Double_t | fEDM | Estimated vertical distance to the minimum |
Int_t | fEmpty | Initialization flag (1 = Minuit initialized) |
Double_t | fEpsi | |
Double_t | fEpsma2 | sqrt(fEpsmac) |
Double_t | fEpsmac | machine precision for floating points: |
Double_t* | fErn | [fMaxpar] Negative Minos errors if calculated |
Double_t* | fErp | [fMaxpar] Positive Minos errors if calculated |
void(*)(Int_t&,Double_t*,Double_t&,Double_t*,Int_t) | fFCN | ! |
Double_t* | fFIXPyy | [fMaxpar] array used in mnfixp |
Double_t | fFval3 | |
Double_t* | fG2 | [fMaxpar] |
Double_t* | fG2s | [fMaxpar] |
Double_t* | fGRADgf | [fMaxpar] array used in mngrad |
Double_t* | fGin | [fMaxpar2] |
Double_t* | fGlobcc | [fMaxpar] Global Correlation Coefficients |
Bool_t | fGraphicsMode | true if graphics mode on (default) |
Double_t* | fGrd | [fMaxpar] First derivatives |
Double_t* | fGrds | [fMaxpar] |
Double_t* | fGstep | [fMaxpar] Step sizes |
Double_t* | fGsteps | [fMaxpar] |
Double_t* | fHESSyy | [fMaxpar] array used in mnhess |
Double_t* | fIMPRdsav | [fMaxpar] array used in mnimpr |
Double_t* | fIMPRy | [fMaxpar] array used in mnimpr |
Int_t | fISW[7] | Array of switches |
Int_t | fIcirc[2] | |
Int_t | fIcomnd | Number of commands |
Int_t | fIdbg[11] | Array of internal debug switches |
Int_t* | fIpfix | [fMaxpar] List of fixed parameters |
Int_t | fIstkrd[10] | |
Int_t | fIstkwr[10] | |
Int_t | fIstrat | |
Int_t | fIsysrd | standardInput unit |
Int_t | fIsyssa | |
Int_t | fIsyswr | standard output unit |
Int_t | fItaur | |
Int_t | fKe1cr | |
Int_t | fKe2cr | |
Bool_t | fLimset | true if a parameter is up against limits (for MINOS) |
Bool_t | fLnewmn | true if the previous process has unexpectedly improved FCN |
Bool_t | fLnolim | true if there are no limits on any parameters (not yet used) |
Bool_t | fLphead | true if a heading should be put out for the next parameter definition |
Bool_t | fLrepor | true if exceptional conditions are put out (default=false) |
Bool_t | fLwarn | true if warning messges are to be put out (default=true) |
Double_t* | fMATUvline | [fMaxpar] array used in mnmatu |
Double_t* | fMIGRflnu | [fMaxpar] array used in mnmigr |
Double_t* | fMIGRgs | [fMaxpar] array used in mnmigr |
Double_t* | fMIGRstep | [fMaxpar] array used in mnmigr |
Double_t* | fMIGRvg | [fMaxpar] array used in mnmigr |
Double_t* | fMIGRxxs | [fMaxpar] array used in mnmigr |
Double_t* | fMNOTgcc | [fMaxpar] array used in mnmnot |
Double_t* | fMNOTw | [fMaxpar] array used in mnmnot |
Double_t* | fMNOTxdev | [fMaxpar] array used in mnmnot |
Int_t | fMaxIterations | Maximum number of iterations |
Int_t | fMaxcpt | |
Int_t | fMaxext | Maximum number of external parameters |
Int_t | fMaxint | Maximum number of internal parameters |
Int_t | fMaxpar | Maximum number of parameters |
Int_t | fMaxpar1 | fMaxpar*(fMaxpar+1) |
Int_t | fMaxpar2 | fMaxpar*fMaxpar |
Int_t | fMaxpar5 | fMaxpar*(fMaxpar+1)/2 |
TMethodCall* | fMethodCall | Pointer to MethodCall in case of interpreted function |
Int_t | fNblock | Number of Minuit data blocks |
Int_t | fNewpag | |
Int_t* | fNexofi | [fMaxpar] External parameters number for currently variable parameters |
Int_t | fNfcn | Number of calls to FCN |
Int_t | fNfcnfr | |
Int_t | fNfcnlc | |
Int_t | fNfcnmx | Maximum number of calls to FCN |
Int_t | fNfcwar[20] | |
Int_t* | fNiofex | [fMaxpar2] Internal parameters number, or zero if not currently variable |
Int_t | fNpagln | Number of lines per page |
Int_t | fNpagwd | Page width |
Int_t | fNpar | Number of free parameters (total number of pars = fNpar + fNfix) |
Int_t | fNpfix | Number of fixed parameters |
Int_t | fNstkrd | |
Int_t | fNstkwr | |
Int_t | fNu | |
Int_t* | fNvarl | [fMaxpar2] parameters flag (-1=undefined, 0=constant..) |
Int_t | fNwrmes[2] | |
TObject* | fObjectFit | Pointer to object being fitted |
TString | fOrigin[100] | |
Double_t* | fP | [fMaxpar1] |
Double_t* | fPARSplist | [fMaxpar] array used in mnpars |
Double_t* | fPSDFs | [fMaxpar] array used in mnpsdf |
Double_t* | fPbar | [fMaxpar] |
TObject* | fPlot | Pointer to TGraph object created by mncont |
Double_t* | fPrho | [fMaxpar] Minimum point of parabola |
Double_t* | fPstar | [fMaxpar2] |
Double_t* | fPstst | [fMaxpar] |
Double_t* | fSEEKxbest | [fMaxpar] array used in mnseek |
Double_t* | fSEEKxmid | [fMaxpar] array used in mnseek |
Double_t* | fSIMPy | [fMaxpar] array used in mnsimp |
Int_t | fStatus | Status flag for the last called Minuit function |
Double_t* | fU | [fMaxpar2] External (visible to user in FCN) value of parameters |
Double_t | fUndefi | Undefined number = -54321 |
Double_t | fUp | FCN+-UP defines errors (for chisquare fits UP=1) |
Double_t | fUpdflt | |
Double_t* | fVERTpp | [fMaxpar] array used in mnvert |
Double_t* | fVERTq | [fMaxpar] array used in mnvert |
Double_t* | fVERTs | [fMaxpar] array used in mnvert |
Double_t* | fVhmat | [fMaxpar5] (Internal) error matrix stored as Half MATrix, since it is symmetric |
Double_t | fVlimhi | |
Double_t | fVlimlo | |
Double_t* | fVthmat | [fMaxpar5] VHMAT is sometimes saved in VTHMAT, especially in MNMNOT |
TString | fWarmes[100] | |
Double_t* | fWerr | [fMaxpar] External parameters error (standard deviation, defined by UP) |
Double_t* | fWord7 | [fMaxpar] |
Double_t* | fX | [fMaxpar] Internal parameters values |
Double_t | fXdircr | |
Double_t | fXmidcr | |
Double_t* | fXpt | [fMaxcpt] X array of points for contours |
Double_t* | fXs | [fMaxpar] Internal parameters values saved for fixed params |
Double_t* | fXt | [fMaxpar] Internal parameters values X saved as Xt |
Double_t* | fXts | [fMaxpar] Internal parameters values X saved as Xt for fixed params |
Double_t | fYdircr | |
Double_t | fYmidcr | |
Double_t* | fYpt | [fMaxcpt] Y array of points for contours |
static TObject::<anonymous> | TObject::kBitMask | |
static TObject::EStatusBits | TObject::kCanDelete | |
static TObject::EStatusBits | TObject::kCannotPick | |
static TObject::EStatusBits | TObject::kHasUUID | |
static TObject::EStatusBits | TObject::kInvalidObject | |
static TObject::<anonymous> | TObject::kIsOnHeap | |
static TObject::EStatusBits | TObject::kIsReferenced | |
static TMinuit::<anonymous> | kMAXWARN | |
static TObject::EStatusBits | TObject::kMustCleanup | |
static TObject::EStatusBits | TObject::kNoContextMenu | |
static TObject::<anonymous> | TObject::kNotDeleted | |
static TObject::EStatusBits | TObject::kObjInCanvas | |
static TObject::<anonymous> | TObject::kOverwrite | |
static TObject::<anonymous> | TObject::kSingleKey | |
static TObject::<anonymous> | TObject::kWriteDelete | |
static TObject::<anonymous> | TObject::kZombie |
TString | TNamed::fName | object identifier |
TString | TNamed::fTitle | object title |
Minuit normal constructor*-*-*-*- *-* ======================== maxpar is the maximum number of parameters used with this TMinuit object.
-*-*-*Create internal Minuit arrays for the maxpar parameters *-* =======================================================
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 http://wwwasdoc.web.cern.ch/wwwasdoc/minuit/node18.html for a 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 *
Creates a TGraph object describing the n-sigma contour of a TMinuit fit. The contour of the parameters pa1 and pa2 is calculated unsing npoints (>=4) points. The TMinuit status will be 0 on success and -1 if errors in the calling sequence (pa1, pa2 not variable) 1 if less than four points can be found 2 if npoints<4 n>3 if only n points can be found (n < npoints) The status can be obtained via TMinuit::GetStatus(). To get the n-sigma contour the ERRDEF parameter in Minuit has to set to n^2. The fcn function has to be set before the routine is called. The TGraph object is created via the interpreter. The user must cast it to a TGraph*. 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
Define a parameter
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: if (flag == 1) { read input data, calculate any necessary constants, etc. } if (flag == 2) { calculate GRAD, the first derivatives of FVAL (this is optional) } Always calculate the value of the function, FVAL, which is usually a chisquare or log likelihood. if (iflag == 3) { will come here only after the fit is finished. Perform any final calculations, output fitted data, etc. } See concrete examples in TH1::H1FitChisquare, H1FitLikelihood
return parameter value and error
returns the total number of parameters that have been defined as fixed or free. The constant parameters are not counted.
To get the n-sigma contour the error def parameter "up" has to set to n^2.
To set the address of the minimization function*- *-* =============================================== *
To set the address of the minimization function*- *-* =============================================== this function is called by CINT instead of the function above *
set Minuit print level printlevel = -1 quiet (also suppresse all warnings) = 0 normal = 1 verbose
Initialize AMIN*-*-*-*- *-* =============== *-*C Called from many places. Initializes the value of AMIN by *-*C calling the user function. Prints out the function value and *-*C parameter values if Print Flag value is high enough. *
-*-*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 *
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) *
-*-*-*Resets the parameter list to UNDEFINED *-* ====================================== *-* Called from MINUIT and by option from MNEXCM *
Print function contours in two variables, on line printer *-* ========================================================= - *-* input arguments: parx, pary, devs, ngrid *
-*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 - *
Find points along a contour where FCN is minimum *-* ================================================ *-* Find NPTU points along a contour where the function *-* FMIN (X(KE1),X(KE2)) = AMIN+UP *-* where FMIN is the minimum of FCN with respect to all *-* the other NPAR-2 variable parameters (if any). *-* IERRF on return will be equal to the number of points found: *-* NPTU if normal termination with NPTU points found *-* -1 if errors in the calling sequence (KE1, KE2 not variable) *-* 0 if less than four points can be found (using MNMNOT) *-* n>3 if only n points can be found (n < NPTU) - *-* input arguments: parx, pary, devs, ngrid * System generated locals
Cracks the free-format input*- *-* ============================ *-* Cracks the free-format input, expecting zero or more *-* alphanumeric fields (which it joins into COMAND(1:LNC)) *-* followed by one or more numeric fields separated by *-* blanks and/or one comma. The numeric fields are put into *-* the LLIST (but at most MXP) elements of PLIST. *-* IERR = 0 if no errors, *-* = 1 if error(s). - * Initialized data
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) - *
-*-*-*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 *
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. *
-*-*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. *
Compute matrix eigen values*- *-* =========================== System generated locals
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 *
Evaluates the function being analyzed by MNCROS*- *-* =============================================== *-* Evaluates the function being analyzed by MNCROS, which is *-* generally the minimum of FCN with respect to all remaining *-* variable parameters. The class data members contains the *-* data necessary to know the values of U(KE1CR) and U(KE2CR) *-* to be used, namely U(KE1CR) = XMIDCR + ANEXT*XDIRCR *-* and (if KE2CR .NE. 0) U(KE2CR) = YMIDCR + ANEXT*YDIRCR *
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 http://wwwasdoc.web.cern.ch/wwwasdoc/minuit/node18.html for the possible list *-* of all Minuit commands - *
-*-*Transforms the external parameter values U to internal values *-* ============================================================= *-* Transforms the external parameter values U to internal *-* values in the dense array PINT. *
-*-*-*-*Removes parameter IINT from the internal parameter list *-* ======================================================= *-* and arranges the rest of the list to fill the hole. *
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 *
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. *
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. - *
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. *
Calculate first derivatives (GRD) and uncertainties (DGRD)*-*- *-* ========================================================== *-* and appropriate step sizes GSTEP *-* Called from MNHESS and MNGRAD *
Attempts to improve on a good local minimum*-*-*- *-* =========================================== *-* Attempts to improve on a good local minimum by finding a *-* better one. The quadratic part of FCN is removed by MNCALF *-* and this transformed function is minimized using the simplex *-* method from several random starting points. *-* ref. -- Goldstein and Price, Math.Comp. 25, 569 (1971) *
-*Transforms from internal coordinates (PINT) to external (U) *-* =========================================================== *-* The minimizing routines which work in *-* internal coordinates call this routine before calling FCN. *
Main initialization member function for MINUIT*-*-*- *-* ============================================== *-* It initializes some constants *-* (including the logical I/O unit nos.), *
Interprets the SET LIM command, to reset the parameter limits *-* ============================================================= *-* Called from MNSET *
-*-*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. *
Prints the covariance matrix v when KODE=1*- *-* ========================================== *-* always prints the global correlations, and *-* calculates and prints the individual correlation coefficients *
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"
*
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. *
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. *
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 *
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 *
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 *
Calculates the internal parameter value PINTI*- *-* ============================================= *-* corresponding to the external value PEXTI for parameter I. *
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"); - *
-*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 *
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] *
-*Calculates the eigenvalues of v to see if positive-def *-* ====================================================== *-* if not, adds constant along diagonal to make positive. *
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. *
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 *
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 *
-*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. *
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. *
-*-*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). *
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 *
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)). *
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 *
To find the machine precision*-*-*-*-*-*-*- *-* ============================= *-* Compares its argument with the value 1.0, and returns *-* the value .TRUE. if they are equal. To find EPSMAC *-* safely by foiling the Fortran optimizer *
-*-*Returns .TRUE. if CFNAME contains unprintable characters *-* ======================================================== *
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. *
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. *
-*Calculates the WERR, external parameter errors *-* ============================================== *-* and the global correlation coefficients, to be called *-* whenever a new covariance matrix is available. *