FUMILI minimization package

FUMILI is based on ideas, proposed by I.N. Silin [See NIM A440, 2000 (p431)]. It was converted from FORTRAN to C by Sergey Yaschenko s.yas.nosp@m.chen.nosp@m.ko@fz.nosp@m.-jue.nosp@m.lich..nosp@m.de

FUMILI is used to minimize Chi-square function or to search maximum of likelihood function.

Experimentally measured values \(F_i\) are fitted with theoretical functions \(f_i({\vec x}_i,\vec\theta\,\,)\), where \({\vec x}_i\) are coordinates, and \(\vec\theta\) – vector of parameters.

For better convergence Chi-square function has to be the following form

\[ {\chi^2\over2}={1\over2}\sum^n_{i=1}\left(f_i(\vec x_i,\vec\theta\,\,)-F_i\over\sigma_i\right)^2 \tag{1} \]

where \(\sigma_i\) are errors of measured function.

The minimum condition is

\[ {\partial\chi^2\over\partial\theta_i}=\sum^n_{j=1}{1\over\sigma^2_j}\cdot {\partial f_j\over\partial\theta_i}\left[f_j(\vec x_j,\vec\theta\,\,)-F_j\right]=0,\qquad i=1\ldots m\tag{2} \]

where m is the quantity of parameters.

Expanding left part of (2) over parameter increments and retaining only linear terms one gets

\[ \left(\partial\chi^2\over\theta_i\right)_{\vec\theta={\vec\theta}^0} +\sum_k\left(\partial^2\chi^2\over\partial\theta_i\partial\theta_k\right)_{ \vec\theta={\vec\theta}^0}\cdot(\theta_k-\theta_k^0) = 0\tag{3} \]

Here \({\vec\theta}_0\) is some initial value of parameters. In general case:

\[ {\partial^2\chi^2\over\partial\theta_i\partial\theta_k}= \sum^n_{j=1}{1\over\sigma^2_j}{\partial f_j\over\theta_i} {\partial f_j\over\theta_k} + \sum^n_{j=1}{(f_j - F_j)\over\sigma^2_j}\cdot {\partial^2f_j\over\partial\theta_i\partial\theta_k}\tag{4} \]

In FUMILI algorithm for second derivatives of Chi-square approximate expression is used when last term in (4) is discarded. It is often done, not always wittingly, and sometimes causes troubles, for example, if user wants to limit parameters with positive values by writing down \(\theta_i^2\) instead of \(\theta_i\). FUMILI will fail if one tries minimize \(\chi^2 = g^2(\vec\theta)\) where g is arbitrary function.

Approximate value is:

\[{\partial^2\chi^2\over\partial\theta_i\partial\theta_k}\approx Z_{ik}= \sum^n_{j=1}{1\over\sigma^2_j}{\partial f_j\over\theta_i} {\partial f_j\over\theta_k}\tag{5} \]

Then the equations for parameter increments are

\[\left(\partial\chi^2\over\partial\theta_i\right)_{\vec\theta={\vec\theta}^0} +\sum_k Z_{ik}\cdot(\theta_k-\theta^0_k) = 0, \qquad i=1\ldots m\tag{6} \]

Remarkable feature of algorithm is the technique for step restriction. For an initial value of parameter \({\vec\theta}^0\) a parallelepiped \(P_0\) is built with the center at \({\vec\theta}^0\) and axes parallel to coordinate axes \(\theta_i\). The lengths of parallelepiped sides along i-th axis is \(2b_i\), where \(b_i\) is such a value that the functions \(f_j(\vec\theta)\) are quasi-linear all over the parallelepiped.

FUMILI takes into account simple linear inequalities in the form:

\[ \theta_i^{\rm min}\le\theta_i\le\theta^{\rm max}_i\tag{7} \]

They form parallelepiped \(P\) ( \(P_0\) may be deformed by \(P\)). Very similar step formulae are used in FUMILI for negative logarithm of the likelihood function with the same idea - linearization of function argument.

Definition at line 11 of file TFumili.h.

Public Member Functions
	TFumili (Int_t maxpar=25)

	~TFumili () override
	TFumili destructor.

void	BuildArrays ()
	Allocates memory for internal arrays.

Double_t	Chisquare (Int_t npar, Double_t *params) const override
	return a chisquare equivalent

void	Clear (Option_t *opt="") override
	Resets all parameter names, values and errors to zero.

void	DeleteArrays ()
	Deallocates memory. Called from destructor TFumili::~TFumili.

void	Derivatives (Double_t , Double_t )
	Calculates partial derivatives of theoretical function.

Int_t	Eval (Int_t &npar, Double_t grad, Double_t &fval, Double_t par, Int_t flag)
	Evaluate the minimisation function.

Double_t	EvalTFN (Double_t , Double_t )
	Evaluate theoretical function.

Int_t	ExecuteCommand (const char command, Double_t args, Int_t nargs) override
	Execute MINUIT commands.

Int_t	ExecuteSetCommand (Int_t)
	Called from TFumili::ExecuteCommand in case of "SET xxx" and "SHOW xxx".

virtual void	FitChisquare (Int_t &npar, Double_t gin, Double_t &f, Double_t u, Int_t flag)
	Minimization function for H1s using a Chisquare method.

virtual void	FitChisquareI (Int_t &npar, Double_t gin, Double_t &f, Double_t u, Int_t flag)
	Minimization function for H1s using a Chisquare method.

virtual void	FitLikelihood (Int_t &npar, Double_t gin, Double_t &f, Double_t u, Int_t flag)
	Minimization function for H1s using a Likelihood method.

virtual void	FitLikelihoodI (Int_t &npar, Double_t gin, Double_t &f, Double_t u, Int_t flag)
	Minimization function for H1s using a Likelihood method.

void	FixParameter (Int_t ipar) override
	Fixes parameter number ipar.

Double_t *	GetCovarianceMatrix () const override
	Return a pointer to the covariance matrix.

Double_t	GetCovarianceMatrixElement (Int_t i, Int_t j) const override
	Return element i,j from the covariance matrix.

Int_t	GetErrors (Int_t ipar, Double_t &eplus, Double_t &eminus, Double_t &eparab, Double_t &globcc) const override
	Return errors after MINOs not implemented.

Int_t	GetNumberFreeParameters () const override
	Return the number of free parameters.

Int_t	GetNumberTotalParameters () const override
	Return the total number of parameters (free + fixed)

Double_t	GetParameter (Int_t ipar) const override
	Return current value of parameter ipar.

Int_t	GetParameter (Int_t ipar, char *name, Double_t &value, Double_t &verr, Double_t &vlow, Double_t &vhigh) const override
	Get various ipar parameter attributes:

Double_t	GetParError (Int_t ipar) const override
	Return error of parameter ipar.

const char *	GetParName (Int_t ipar) const override
	Return name of parameter ipar.

Double_t *	GetPL0 () const

Int_t	GetStats (Double_t &amin, Double_t &edm, Double_t &errdef, Int_t &nvpar, Int_t &nparx) const override
	Return global fit parameters.

Double_t	GetSumLog (Int_t) override
	Return Sum(log(i) i=0,n used by log-likelihood fits.

Double_t *	GetZ () const

void	InvertZ (Int_t)
	Inverts packed diagonal matrix Z by square-root method.

TClass *	IsA () const override

Bool_t	IsFixed (Int_t ipar) const override
	Return kTRUE if parameter ipar is fixed, kFALSE otherwise)

Int_t	Minimize ()
	Main minimization procedure.

void	PrintResults (Int_t k, Double_t p) const override
	Prints fit results.

void	ReleaseParameter (Int_t ipar) override
	Releases parameter number ipar.

void	SetData (Double_t *, Int_t, Int_t)
	Sets pointer to data array provided by user.

void	SetFitMethod (const char *name) override
	ret fit method (chisquare or log-likelihood)

Int_t	SetParameter (Int_t ipar, const char *parname, Double_t value, Double_t verr, Double_t vlow, Double_t vhigh) override
	Sets for parameter number ipar initial parameter value, name parname, initial error verr and limits vlow and vhigh.

void	SetParNumber (Int_t ParNum)

Int_t	SGZ ()
	Evaluates objective function ( chi-square ), gradients and Z-matrix using data provided by user via TFumili::SetData.

void	Streamer (TBuffer &) override
	Stream an object of class TObject.

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

Public Member Functions inherited from TVirtualFitter
	TVirtualFitter ()
	Default constructor.

	~TVirtualFitter () override
	Cleanup virtual fitter.

virtual void	GetConfidenceIntervals (Int_t n, Int_t ndim, const Double_t x, Double_t ci, Double_t cl=0.95)
	return confidence intervals in array x of dimension ndim implemented in TFitter and TLinearFitter

virtual void	GetConfidenceIntervals (TObject *obj, Double_t cl=0.95)
	return confidence intervals in TObject obj implemented in TFitter and TLinearFitter

virtual FCNFunc_t	GetFCN ()

virtual Foption_t	GetFitOption () const

TMethodCall *	GetMethodCall () const

virtual TObject *	GetObjectFit () const

virtual TObject *	GetUserFunc () const

virtual Int_t	GetXfirst () const

virtual Int_t	GetXlast () const

virtual Int_t	GetYfirst () const

virtual Int_t	GetYlast () const

virtual Int_t	GetZfirst () const

virtual Int_t	GetZlast () const

TClass *	IsA () const override

virtual Double_t *	SetCache (Int_t npoints, Int_t psize)
	Initialize the cache array npoints is the number of points to be stored (or already stored) in the cache psize is the number of elements per point.

virtual void	SetFCN (void(fcn)(Int_t &, Double_t , Double_t &f, Double_t *, Int_t))
	To set the address of the minimization objective function called by the native compiler (see function below when called by CINT)

virtual void	SetFitOption (Foption_t option)

virtual void	SetObjectFit (TObject *obj)

virtual void	SetUserFunc (TObject *userfunc)

virtual void	SetXfirst (Int_t first)

virtual void	SetXlast (Int_t last)

virtual void	SetYfirst (Int_t first)

virtual void	SetYlast (Int_t last)

virtual void	SetZfirst (Int_t first)

virtual void	SetZlast (Int_t last)

void	Streamer (TBuffer &) override
	Stream an object of class TObject.

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

Public Member Functions inherited from TNamed
	TNamed ()

	TNamed (const char name, const char title)

	TNamed (const TNamed &named)
	TNamed copy ctor.

	TNamed (const TString &name, const TString &title)

virtual	~TNamed ()
	TNamed destructor.

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

Int_t	Compare (const TObject *obj) const override
	Compare two TNamed objects.

void	Copy (TObject &named) const override
	Copy this to obj.

virtual void	FillBuffer (char *&buffer)
	Encode TNamed into output buffer.

const char *	GetName () const override
	Returns name of object.

const char *	GetTitle () const override
	Returns title of object.

ULong_t	Hash () const override
	Return hash value for this object.

Bool_t	IsSortable () const override

void	ls (Option_t *option="") const override
	List TNamed name and title.

TNamed &	operator= (const TNamed &rhs)
	TNamed assignment operator.

void	Print (Option_t *option="") const override
	Print TNamed name and title.

virtual void	SetName (const char *name)
	Set the name of the TNamed.

virtual void	SetNameTitle (const char name, const char title)
	Set all the TNamed parameters (name and title).

virtual void	SetTitle (const char *title="")
	Set the title of the TNamed.

virtual Int_t	Sizeof () const
	Return size of the TNamed part of the TObject.

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

Public Member Functions inherited from TObject
	TObject ()
	TObject constructor.

	TObject (const TObject &object)
	TObject copy ctor.

virtual	~TObject ()
	TObject destructor.

void	AbstractMethod (const char *method) const
	Use this method to implement an "abstract" method that you don't want to leave purely abstract.

virtual void	AppendPad (Option_t *option="")
	Append graphics object to current pad.

virtual void	Browse (TBrowser *b)
	Browse object. May be overridden for another default action.

ULong_t	CheckedHash ()
	Check and record whether this class has a consistent Hash/RecursiveRemove setup (*) and then return the regular Hash value for this object.

virtual const char *	ClassName () const
	Returns name of class to which the object belongs.

virtual void	Delete (Option_t *option="")
	Delete this object.

virtual Int_t	DistancetoPrimitive (Int_t px, Int_t py)
	Computes distance from point (px,py) to the object.

virtual void	Draw (Option_t *option="")
	Default Draw method for all objects.

virtual void	DrawClass () const
	Draw class inheritance tree of the class to which this object belongs.

virtual TObject *	DrawClone (Option_t *option="") const
	Draw a clone of this object in the current selected pad with: `gROOT->SetSelectedPad(c1)`.

virtual void	Dump () const
	Dump contents of object on stdout.

virtual void	Error (const char method, const char msgfmt,...) const
	Issue error message.

virtual void	Execute (const char method, const char params, Int_t *error=nullptr)
	Execute method on this object with the given parameter string, e.g.

virtual void	Execute (TMethod method, TObjArray params, Int_t *error=nullptr)
	Execute method on this object with parameters stored in the TObjArray.

virtual void	ExecuteEvent (Int_t event, Int_t px, Int_t py)
	Execute action corresponding to an event at (px,py).

virtual void	Fatal (const char method, const char msgfmt,...) const
	Issue fatal error message.

virtual TObject *	FindObject (const char *name) const
	Must be redefined in derived classes.

virtual TObject *	FindObject (const TObject *obj) const
	Must be redefined in derived classes.

virtual Option_t *	GetDrawOption () const
	Get option used by the graphics system to draw this object.

virtual const char *	GetIconName () const
	Returns mime type name of object.

virtual char *	GetObjectInfo (Int_t px, Int_t py) const
	Returns string containing info about the object at position (px,py).

virtual Option_t *	GetOption () const

virtual UInt_t	GetUniqueID () const
	Return the unique object id.

virtual Bool_t	HandleTimer (TTimer *timer)
	Execute action in response of a timer timing out.

Bool_t	HasInconsistentHash () const
	Return true is the type of this object is known to have an inconsistent setup for Hash and RecursiveRemove (i.e.

virtual void	Info (const char method, const char msgfmt,...) const
	Issue info message.

virtual Bool_t	InheritsFrom (const char *classname) const
	Returns kTRUE if object inherits from class "classname".

virtual Bool_t	InheritsFrom (const TClass *cl) const
	Returns kTRUE if object inherits from TClass cl.

virtual void	Inspect () const
	Dump contents of this object in a graphics canvas.

void	InvertBit (UInt_t f)

Bool_t	IsDestructed () const
	IsDestructed.

virtual Bool_t	IsEqual (const TObject *obj) const
	Default equal comparison (objects are equal if they have the same address in memory).

virtual Bool_t	IsFolder () const
	Returns kTRUE in case object contains browsable objects (like containers or lists of other objects).

R__ALWAYS_INLINE Bool_t	IsOnHeap () const

R__ALWAYS_INLINE Bool_t	IsZombie () const

void	MayNotUse (const char *method) const
	Use this method to signal that a method (defined in a base class) may not be called in a derived class (in principle against good design since a child class should not provide less functionality than its parent, however, sometimes it is necessary).

virtual Bool_t	Notify ()
	This method must be overridden to handle object notification (the base implementation is no-op).

void	Obsolete (const char method, const char asOfVers, const char *removedFromVers) const
	Use this method to declare a method obsolete.

void	operator delete (void *ptr)
	Operator delete.

void	operator delete (void ptr, void vp)
	Only called by placement new when throwing an exception.

void	operator delete[] (void *ptr)
	Operator delete [].

void	operator delete[] (void ptr, void vp)
	Only called by placement new[] when throwing an exception.

void *	operator new (size_t sz)

void *	operator new (size_t sz, void *vp)

void *	operator new[] (size_t sz)

void *	operator new[] (size_t sz, void *vp)

TObject &	operator= (const TObject &rhs)
	TObject assignment operator.

virtual void	Paint (Option_t *option="")
	This method must be overridden if a class wants to paint itself.

virtual void	Pop ()
	Pop on object drawn in a pad to the top of the display list.

virtual Int_t	Read (const char *name)
	Read contents of object with specified name from the current directory.

virtual void	RecursiveRemove (TObject *obj)
	Recursively remove this object from a list.

void	ResetBit (UInt_t f)

virtual void	SaveAs (const char filename="", Option_t option="") const
	Save this object in the file specified by filename.

virtual void	SavePrimitive (std::ostream &out, Option_t *option="")
	Save a primitive as a C++ statement(s) on output stream "out".

void	SetBit (UInt_t f)

void	SetBit (UInt_t f, Bool_t set)
	Set or unset the user status bits as specified in f.

virtual void	SetDrawOption (Option_t *option="")
	Set drawing option for object.

virtual void	SetUniqueID (UInt_t uid)
	Set the unique object id.

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

virtual void	SysError (const char method, const char msgfmt,...) const
	Issue system error message.

R__ALWAYS_INLINE Bool_t	TestBit (UInt_t f) const

Int_t	TestBits (UInt_t f) const

virtual void	UseCurrentStyle ()
	Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked.

virtual void	Warning (const char method, const char msgfmt,...) const
	Issue warning message.

virtual Int_t	Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0)
	Write this object to the current directory.

virtual Int_t	Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0) const
	Write this object to the current directory.

Static Public Member Functions
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

Static Public Member Functions inherited from TVirtualFitter
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

static TVirtualFitter *	Fitter (TObject *obj, Int_t maxpar=25)
	Static function returning a pointer to the current fitter.

static const char *	GetDefaultFitter ()
	static: return the name of the default fitter

static Double_t	GetErrorDef ()
	static: Return the Error Definition

static TVirtualFitter *	GetFitter ()
	static: return the current Fitter

static Int_t	GetMaxIterations ()
	static: Return the maximum number of iterations actually max number of function calls

static Double_t	GetPrecision ()
	static: Return the fit relative precision

static void	SetDefaultFitter (const char *name="")
	static: set name of default fitter

static void	SetErrorDef (Double_t errdef=1)
	static: Set the Error Definition (default=1) For Minuit this is the value passed with the "SET ERR" command (see https://cern-tex.web.cern.ch/cern-tex/minuit/node18.html)

static void	SetFitter (TVirtualFitter *fitter, Int_t maxpar=25)
	Static function to set an alternative fitter.

static void	SetMaxIterations (Int_t niter=5000)
	static: Set the maximum number of function calls for the minimization algorithm For example for MIGRAD this is the maxcalls value passed as first argument (see https://cern-tex.web.cern.ch/cern-tex/minuit/node18.html )

static void	SetPrecision (Double_t prec=1e-6)
	static: Set the tolerance used in the minimization algorithm For example for MIGRAD this is tolerance value passed as second argument (see https://cern-tex.web.cern.ch/cern-tex/minuit/node18.html )

Static Public Member Functions inherited from TNamed
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

Static Public Member Functions inherited from TObject
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

static Longptr_t	GetDtorOnly ()
	Return destructor only flag.

static Bool_t	GetObjectStat ()
	Get status of object stat flag.

static void	SetDtorOnly (void *obj)
	Set destructor only flag.

static void	SetObjectStat (Bool_t stat)
	Turn on/off tracking of objects in the TObjectTable.

Private Attributes
Double_t *	fA
	[fMaxParam] Fit parameter array

Double_t	fAKAPPA

Double_t *	fAMN
	[fMaxParam] Minimum param value

Double_t *	fAMX
	[fMaxParam] Maximum param value

TString *	fANames
	[fMaxParam] Parameter names

Double_t *	fCmPar
	[fMaxParam] parameters of commands

TString	fCword
	Command string.

Double_t *	fDA
	[fMaxParam] Parameter step

Bool_t	fDEBUG
	debug info

Double_t *	fDF
	[fMaxParam] First derivatives of theoretical function

Int_t	fENDFLG
	End flag of fit.

Double_t	fEPS
	fEPS - required precision of parameters. If fEPS<0 then

Double_t *	fEXDA
	[fNED12] experimental data poInt_ter

Double_t *	fGr
	[fMaxParam] Gradients of objective function

Bool_t	fGRAD
	user calculated gradients

Double_t	fGT
	Expected function change in next iteration.

Int_t	fINDFLG [5]
	internal flags;

Int_t	fLastFixed
	Last fixed parameter number.

Bool_t	fLogLike
	LogLikelihood flag.

Int_t	fMaxParam

Int_t	fNED1
	Number of experimental vectors X=(x1,x2,...xK)

Int_t	fNED12
	fNED1+fNED2

Int_t	fNED2
	K - Length of vector X plus 2 (for chi2)

Int_t	fNfcn
	Number of FCN calls;.

Int_t	fNlimMul
	fNlimMul - after fNlimMul successful iterations permits four-fold increasing of fPL

Int_t	fNlog

Int_t	fNmaxIter
	fNmaxIter - maximum number of iterations

Int_t	fNpar
	fNpar - number of parameters

Int_t	fNstepDec
	fNstepDec - maximum number of step decreasing counter

Bool_t	fNumericDerivatives

Double_t *	fParamError
	[fMaxParam] Parameter errors

Double_t *	fPL
	[fMaxParam] Limits for parameters step. If <0, then parameter is fixed

Double_t *	fPL0
	[fMaxParam] Step initial bounds

Double_t *	fR
	[fMaxParam] Correlation factors

Double_t	fRP
	Precision of fit ( machine zero on CDC 6000) quite old yeh?

Double_t	fS
	fS - objective function value (return)

Double_t *	fSumLog
	[fNlog]

Bool_t	fWARN
	warnings

Double_t *	fZ
	[fMaxParam2] Inverse fZ0 matrix - covariance matrix

Double_t *	fZ0
	[fMaxParam2] Matrix of approximate second derivatives of objective function This matrix is diagonal and always contain only variable parameter's derivatives

Additional Inherited Members
Public Types inherited from TVirtualFitter
typedef void(*	FCNFunc_t) (Int_t &npar, Double_t gin, Double_t &f, Double_t u, Int_t flag)

Public Types inherited from TObject
enum	{ kIsOnHeap = 0x01000000 , kNotDeleted = 0x02000000 , kZombie = 0x04000000 , kInconsistent = 0x08000000 , kBitMask = 0x00ffffff }

enum	{ kSingleKey = (1ULL << ( 0 )) , kOverwrite = (1ULL << ( 1 )) , kWriteDelete = (1ULL << ( 2 )) }

enum	EDeprecatedStatusBits { kObjInCanvas = (1ULL << ( 3 )) }

enum	EStatusBits { kCanDelete = (1ULL << ( 0 )) , kMustCleanup = (1ULL << ( 3 )) , kIsReferenced = (1ULL << ( 4 )) , kHasUUID = (1ULL << ( 5 )) , kCannotPick = (1ULL << ( 6 )) , kNoContextMenu = (1ULL << ( 8 )) , kInvalidObject = (1ULL << ( 13 )) }

Protected Types inherited from TObject
enum	{ kOnlyPrepStep = (1ULL << ( 3 )) }

Protected Member Functions inherited from TVirtualFitter
	TVirtualFitter (const TVirtualFitter &tvf)
	copy constructor

TVirtualFitter &	operator= (const TVirtualFitter &tvf)
	assignment operator

Protected Member Functions inherited from TObject
virtual void	DoError (int level, const char location, const char fmt, va_list va) const
	Interface to ErrorHandler (protected).

void	MakeZombie ()

Protected Attributes inherited from TVirtualFitter
Double_t *	fCache
	[fCacheSize] Array of points data (fNpoints*fPointSize < fCacheSize words)

Int_t	fCacheSize
	Size of the fCache array.

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

TMethodCall *	fMethodCall
	Pointer to MethodCall in case of interpreted function.

Int_t	fNpoints
	Number of points to fit.

TObject *	fObjectFit
	Pointer to object being fitted.

Foption_t	fOption
	Struct with the fit options.

Int_t	fPointSize
	Number of words per point in the cache.

TObject *	fUserFunc
	Pointer to user theoretical function (a TF1*)

Int_t	fXfirst
	First bin on X axis.

Int_t	fXlast
	Last bin on X axis.

Int_t	fYfirst
	First bin on Y axis.

Int_t	fYlast
	Last bin on Y axis.

Int_t	fZfirst
	First bin on Z axis.

Int_t	fZlast
	Last bin on Z axis.

Protected Attributes inherited from TNamed
TString	fName

TString	fTitle

#include <TFumili.h>

Inheritance diagram for TFumili:

[legend]

Constructor & Destructor Documentation

◆ TFumili()

TFumili::TFumili ( Int_t maxpar = 25 )

Definition at line 129 of file TFumili.cxx.

◆ ~TFumili()

TFumili::~TFumili ( )

override

TFumili destructor.

Definition at line 217 of file TFumili.cxx.

Member Function Documentation

◆ BuildArrays()

void TFumili::BuildArrays ( )

Allocates memory for internal arrays.

Called by TFumili::TFumili

Definition at line 182 of file TFumili.cxx.

◆ Chisquare()

Double_t TFumili::Chisquare	(	Int_t	npar,
		Double_t *	params
	)		const

overridevirtual

return a chisquare equivalent

Implements TVirtualFitter.

Definition at line 227 of file TFumili.cxx.

◆ Class()

static TClass * TFumili::Class ( )

static

Returns: TClass describing this class

◆ Class_Name()

static const char * TFumili::Class_Name ( )

static

Returns: Name of this class

◆ Class_Version()

static constexpr Version_t TFumili::Class_Version ( )

inlinestaticconstexpr

Returns: Version of this class

Definition at line 114 of file TFumili.h.

◆ Clear()

void TFumili::Clear ( Option_t * opt = "" )

overridevirtual

Resets all parameter names, values and errors to zero.

Argument opt is ignored

NB: this procedure doesn't reset parameter limits

Implements TVirtualFitter.

Definition at line 242 of file TFumili.cxx.

◆ DeclFileName()

static const char * TFumili::DeclFileName ( )

inlinestatic

Returns: Name of the file containing the class declaration

Definition at line 114 of file TFumili.h.

◆ DeleteArrays()

void TFumili::DeleteArrays ( )

Deallocates memory. Called from destructor TFumili::~TFumili.

Definition at line 261 of file TFumili.cxx.

◆ Derivatives()

void TFumili::Derivatives	(	Double_t *	df,
		Double_t *	fX
	)

Calculates partial derivatives of theoretical function.

Input:

fX - vector of data point

Output:

DF - array of derivatives

ARITHM.F: Converted from CERNLIB

Definition at line 291 of file TFumili.cxx.

◆ Eval()

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

Evaluate the minimisation function.

Input parameters:

npar: number of currently variable parameters
par: array of (constant and variable) parameters
flag: Indicates what is to be calculated
grad: array of gradients

Output parameters:

fval: The calculated function value.
grad: The 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.

Inside FCN user has to define Z-matrix by means TFumili::GetZ and TFumili::Derivatives, set theoretical function by means of TFumili::SetUserFunc, but first - pass number of parameters by TFumili::SetParNumber

Later values are determined by Fumili as it searches for the minimum or performs whatever analysis is requested by the user.

The default function calls the function specified in SetFCN

Definition at line 350 of file TFumili.cxx.

◆ EvalTFN()

Double_t TFumili::EvalTFN	(	Double_t *	,
		Double_t *	X
	)

Evaluate theoretical function.

df: array of partial derivatives
X: vector of theoretical function argument

Definition at line 362 of file TFumili.cxx.

◆ ExecuteCommand()

Int_t TFumili::ExecuteCommand	(	const char *	command,
		Double_t *	args,
		Int_t	nargs
	)

overridevirtual

Execute MINUIT commands.

MINImize, SIMplex, MIGrad and FUMili all will call TFumili::Minimize method.

For full command list see MINUIT. Reference Manual. CERN Program Library Long Writeup D506.

Improvement and errors calculation are not yet implemented as well as Monte-Carlo seeking and minimization. Contour commands are also unsupported.

command : command string
args : array of arguments
nargs : number of arguments

Implements TVirtualFitter.

Definition at line 391 of file TFumili.cxx.

◆ ExecuteSetCommand()

Int_t TFumili::ExecuteSetCommand ( Int_t nargs )

Called from TFumili::ExecuteCommand in case of "SET xxx" and "SHOW xxx".

Definition at line 558 of file TFumili.cxx.

◆ FitChisquare()

void TFumili::FitChisquare	(	Int_t &	npar,
		Double_t *	gin,
		Double_t &	f,
		Double_t *	u,
		Int_t	flag
	)

virtual

Minimization function for H1s using a Chisquare method.

Default method (function evaluated at center of bin) for each point the cache contains the following info

1D : bc,e,xc (bin content, error, x of center of bin)
2D : bc,e,xc,yc
3D : bc,e,xc,yc,zc

Definition at line 1738 of file TFumili.cxx.

◆ FitChisquareI()

void TFumili::FitChisquareI	(	Int_t &	npar,
		Double_t *	gin,
		Double_t &	f,
		Double_t *	u,
		Int_t	flag
	)

virtual

Minimization function for H1s using a Chisquare method.

The "I"ntegral method is used for each point the cache contains the following info

1D : bc,e,xc,xw (bin content, error, x of center of bin, x bin width of bin)
2D : bc,e,xc,xw,yc,yw
3D : bc,e,xc,xw,yc,yw,zc,zw

Definition at line 1809 of file TFumili.cxx.

◆ FitLikelihood()

void TFumili::FitLikelihood	(	Int_t &	npar,
		Double_t *	gin,
		Double_t &	f,
		Double_t *	u,
		Int_t	flag
	)

virtual

Minimization function for H1s using a Likelihood method.

Basically, it forms the likelihood by determining the Poisson probability that given a number of entries in a particular bin, the fit would predict it's value. This is then done for each bin, and the sum of the logs is taken as the likelihood.

Default method (function evaluated at center of bin) for each point the cache contains the following info

1D : bc,e,xc (bin content, error, x of center of bin)
2D : bc,e,xc,yc
3D : bc,e,xc,yc,zc

Definition at line 1884 of file TFumili.cxx.

◆ FitLikelihoodI()

void TFumili::FitLikelihoodI	(	Int_t &	npar,
		Double_t *	gin,
		Double_t &	f,
		Double_t *	u,
		Int_t	flag
	)

virtual

Minimization function for H1s using a Likelihood method.

Basically, it forms the likelihood by determining the Poisson probability that given a number of entries in a particular bin, the fit would predict it's value. This is then done for each bin, and the sum of the logs is taken as the likelihood.

The "I"ntegral method is used for each point the cache contains the following info

1D : bc,e,xc,xw (bin content, error, x of center of bin, x bin width of bin)
2D : bc,e,xc,xw,yc,yw
3D : bc,e,xc,xw,yc,yw,zc,zw

Definition at line 1972 of file TFumili.cxx.

◆ FixParameter()

void TFumili::FixParameter ( Int_t ipar )

overridevirtual

Fixes parameter number ipar.

Implements TVirtualFitter.

Definition at line 774 of file TFumili.cxx.

◆ GetCovarianceMatrix()

Double_t * TFumili::GetCovarianceMatrix ( ) const

overridevirtual

Return a pointer to the covariance matrix.

Implements TVirtualFitter.

Definition at line 784 of file TFumili.cxx.

◆ GetCovarianceMatrixElement()

Double_t TFumili::GetCovarianceMatrixElement	(	Int_t	i,
		Int_t	j
	)		const

overridevirtual

Return element i,j from the covariance matrix.

Implements TVirtualFitter.

Definition at line 793 of file TFumili.cxx.

◆ GetErrors()

Int_t TFumili::GetErrors	(	Int_t	ipar,
		Double_t &	eplus,
		Double_t &	eminus,
		Double_t &	eparab,
		Double_t &	globcc
	)		const

overridevirtual

Return errors after MINOs not implemented.

Implements TVirtualFitter.

Definition at line 882 of file TFumili.cxx.

◆ GetNumberFreeParameters()

Int_t TFumili::GetNumberFreeParameters ( ) const

overridevirtual

Return the number of free parameters.

Implements TVirtualFitter.

Definition at line 814 of file TFumili.cxx.

◆ GetNumberTotalParameters()

Int_t TFumili::GetNumberTotalParameters ( ) const

overridevirtual

Return the total number of parameters (free + fixed)

Implements TVirtualFitter.

Definition at line 806 of file TFumili.cxx.

◆ GetParameter() [1/2]

Double_t TFumili::GetParameter ( Int_t ipar ) const

overridevirtual

Return current value of parameter ipar.

Implements TVirtualFitter.

Definition at line 835 of file TFumili.cxx.

◆ GetParameter() [2/2]

Int_t TFumili::GetParameter	(	Int_t	ipar,
		char *	cname,
		Double_t &	value,
		Double_t &	verr,
		Double_t &	vlow,
		Double_t &	vhigh
	)		const

overridevirtual

Get various ipar parameter attributes:

cname: parameter name
value: parameter value
verr: parameter error
vlow: lower limit
vhigh: upper limit

WARNING! parname must be suitably dimensioned in the calling function.

Implements TVirtualFitter.

Definition at line 852 of file TFumili.cxx.

◆ GetParError()

Double_t TFumili::GetParError ( Int_t ipar ) const

overridevirtual

Return error of parameter ipar.

Implements TVirtualFitter.

Definition at line 826 of file TFumili.cxx.

◆ GetParName()

const char * TFumili::GetParName ( Int_t ipar ) const

overridevirtual

Return name of parameter ipar.

Implements TVirtualFitter.

Definition at line 872 of file TFumili.cxx.

◆ GetPL0()

Double_t * TFumili::GetPL0 ( ) const

inline

Definition at line 95 of file TFumili.h.

◆ GetStats()

Int_t TFumili::GetStats	(	Double_t &	amin,
		Double_t &	edm,
		Double_t &	errdef,
		Int_t &	nvpar,
		Int_t &	nparx
	)		const

overridevirtual

Return global fit parameters.

amin : chisquare
edm : estimated distance to minimum
errdef
nvpar : number of variable parameters
nparx : total number of parameters

Implements TVirtualFitter.

Definition at line 904 of file TFumili.cxx.

◆ GetSumLog()

Double_t TFumili::GetSumLog ( Int_t n )

overridevirtual

Return Sum(log(i) i=0,n used by log-likelihood fits.

Implements TVirtualFitter.

Definition at line 921 of file TFumili.cxx.

◆ GetZ()

Double_t * TFumili::GetZ ( ) const

inline

Definition at line 102 of file TFumili.h.

◆ InvertZ()

void TFumili::InvertZ ( Int_t n )

Inverts packed diagonal matrix Z by square-root method.

Matrix elements corresponding to fix parameters are removed.

n: number of variable parameters

Definition at line 945 of file TFumili.cxx.

◆ IsA()

TClass * TFumili::IsA ( ) const

inlineoverridevirtual

Returns: TClass describing current object

Reimplemented from TObject.

Definition at line 114 of file TFumili.h.

◆ IsFixed()

Bool_t TFumili::IsFixed ( Int_t ipar ) const

overridevirtual

Return kTRUE if parameter ipar is fixed, kFALSE otherwise)

Implements TVirtualFitter.

Definition at line 1060 of file TFumili.cxx.

◆ Minimize()

Int_t TFumili::Minimize ( )

Main minimization procedure.

This function is called after setting theoretical function by means of TFumili::SetUserFunc and initializing parameters. Optionally one can set FCN function (see TFumili::SetFCN and TFumili::Eval) If FCN is undefined then user has to provide data arrays by calling TFumili::SetData procedure.

TFumili::Minimize return following values:

0 - fit is converged
-2 - function is not decreasing (or bad derivatives)
-3 - error estimations are infinite
-4 - maximum number of iterations is exceeded

Definition at line 1085 of file TFumili.cxx.

◆ PrintResults()

void TFumili::PrintResults	(	Int_t	ikode,
		Double_t	p
	)		const

overridevirtual

Prints fit results.

ikode is the type of printing parameters p is function value

ikode = 1 - print values, errors and limits
ikode = 2 - print values, errors and steps
ikode = 3 - print values, errors, steps and derivatives
ikode = 4 - print only values and errors

Implements TVirtualFitter.

Definition at line 1483 of file TFumili.cxx.

◆ ReleaseParameter()

void TFumili::ReleaseParameter ( Int_t ipar )

overridevirtual

Releases parameter number ipar.

Implements TVirtualFitter.

Definition at line 1586 of file TFumili.cxx.

◆ SetData()

void TFumili::SetData	(	Double_t *	exdata,
		Int_t	numpoints,
		Int_t	vecsize
	)

Sets pointer to data array provided by user.

Necessary if SetFCN is not called.

numpoints: number of experimental points
vecsize: size of data point vector + 2 (for N-dimensional fit vecsize=N+2)
exdata: data array with following format
- exdata[0] = ExpValue_0 - experimental data value number 0
- exdata[1] = ExpSigma_0 - error of value number 0
- exdata[2] = X_0[0]
- exdata[3] = X_0[1]
- exdata[vecsize-1] = X_0[vecsize-3]
- exdata[vecsize] = ExpValue_1
- exdata[vecsize+1] = ExpSigma_1
- exdata[vecsize+2] = X_1[0]
- exdata[vecsize*(numpoints-1)] = ExpValue_(numpoints-1)
- exdata[vecsize*numpoints-1] = X_(numpoints-1)[vecsize-3]

Definition at line 1616 of file TFumili.cxx.

◆ SetFitMethod()

void TFumili::SetFitMethod ( const char * name )

overridevirtual

ret fit method (chisquare or log-likelihood)

Implements TVirtualFitter.

Definition at line 1628 of file TFumili.cxx.

◆ SetParameter()

Int_t TFumili::SetParameter	(	Int_t	ipar,
		const char *	parname,
		Double_t	value,
		Double_t	verr,
		Double_t	vlow,
		Double_t	vhigh
	)

overridevirtual

Sets for parameter number ipar initial parameter value, name parname, initial error verr and limits vlow and vhigh.

If vlow = vhigh but not equal to zero, parameter will be fixed.
If vlow = vhigh = 0, parameter is released and its limits are discarded

Implements TVirtualFitter.

Definition at line 1641 of file TFumili.cxx.

◆ SetParNumber()

void TFumili::SetParNumber ( Int_t ParNum )

Definition at line 168 of file TFumili.cxx.

◆ SGZ()

Int_t TFumili::SGZ ( )

Evaluates objective function ( chi-square ), gradients and Z-matrix using data provided by user via TFumili::SetData.

Definition at line 1670 of file TFumili.cxx.

◆ Streamer()

void TFumili::Streamer ( TBuffer & R__b )

overridevirtual

Stream an object of class TObject.

Reimplemented from TObject.

◆ StreamerNVirtual()

void TFumili::StreamerNVirtual ( TBuffer & ClassDef_StreamerNVirtual_b )

inline

Definition at line 114 of file TFumili.h.

Member Data Documentation

◆ fA

Double_t* TFumili::fA

private

[fMaxParam] Fit parameter array

Definition at line 44 of file TFumili.h.

◆ fAKAPPA

Double_t TFumili::fAKAPPA

private

Definition at line 60 of file TFumili.h.

◆ fAMN

Double_t* TFumili::fAMN

private

[fMaxParam] Minimum param value

Definition at line 51 of file TFumili.h.

◆ fAMX

Double_t* TFumili::fAMX

private

[fMaxParam] Maximum param value

Definition at line 50 of file TFumili.h.

◆ fANames

TString* TFumili::fANames

private

[fMaxParam] Parameter names

Definition at line 62 of file TFumili.h.

◆ fCmPar

Double_t* TFumili::fCmPar

private

[fMaxParam] parameters of commands

Definition at line 55 of file TFumili.h.

◆ fCword

TString TFumili::fCword

private

Command string.

Definition at line 63 of file TFumili.h.

◆ fDA

Double_t* TFumili::fDA

private

[fMaxParam] Parameter step

Definition at line 49 of file TFumili.h.

◆ fDEBUG

Bool_t TFumili::fDEBUG

private

debug info

Definition at line 30 of file TFumili.h.

◆ fDF

Double_t* TFumili::fDF

private

[fMaxParam] First derivatives of theoretical function

Definition at line 54 of file TFumili.h.

◆ fENDFLG

Int_t TFumili::fENDFLG

private

End flag of fit.

Definition at line 24 of file TFumili.h.

◆ fEPS

Double_t TFumili::fEPS

private

fEPS - required precision of parameters. If fEPS<0 then

Definition at line 58 of file TFumili.h.

◆ fEXDA

Double_t* TFumili::fEXDA

private

[fNED12] experimental data poInt_ter

Definition at line 41 of file TFumili.h.

◆ fGr

Double_t* TFumili::fGr

private

[fMaxParam] Gradients of objective function

Definition at line 38 of file TFumili.h.

◆ fGRAD

Bool_t TFumili::fGRAD

private

user calculated gradients

Definition at line 28 of file TFumili.h.

◆ fGT

Double_t TFumili::fGT

private

Expected function change in next iteration.

Definition at line 61 of file TFumili.h.

◆ fINDFLG

Int_t TFumili::fINDFLG[5]

private

internal flags;

Definition at line 25 of file TFumili.h.

◆ fLastFixed

Int_t TFumili::fLastFixed

private

Last fixed parameter number.

Definition at line 23 of file TFumili.h.

◆ fLogLike

Bool_t TFumili::fLogLike

private

LogLikelihood flag.

Definition at line 31 of file TFumili.h.

◆ fMaxParam

Int_t TFumili::fMaxParam

private

Definition at line 13 of file TFumili.h.

◆ fNED1

Int_t TFumili::fNED1

private

Number of experimental vectors X=(x1,x2,...xK)

Definition at line 16 of file TFumili.h.

◆ fNED12

Int_t TFumili::fNED12

private

fNED1+fNED2

Definition at line 18 of file TFumili.h.

◆ fNED2

Int_t TFumili::fNED2

private

K - Length of vector X plus 2 (for chi2)

Definition at line 17 of file TFumili.h.

◆ fNfcn

Int_t TFumili::fNfcn

private

Number of FCN calls;.

Definition at line 15 of file TFumili.h.

◆ fNlimMul

Int_t TFumili::fNlimMul

private

fNlimMul - after fNlimMul successful iterations permits four-fold increasing of fPL

Definition at line 21 of file TFumili.h.

◆ fNlog

Int_t TFumili::fNlog

private

Definition at line 14 of file TFumili.h.

◆ fNmaxIter

Int_t TFumili::fNmaxIter

private

fNmaxIter - maximum number of iterations

Definition at line 22 of file TFumili.h.

◆ fNpar

Int_t TFumili::fNpar

private

fNpar - number of parameters

Definition at line 19 of file TFumili.h.

◆ fNstepDec

Int_t TFumili::fNstepDec

private

fNstepDec - maximum number of step decreasing counter

Definition at line 20 of file TFumili.h.

◆ fNumericDerivatives

Bool_t TFumili::fNumericDerivatives

private

Definition at line 32 of file TFumili.h.

◆ fParamError

Double_t* TFumili::fParamError

private

[fMaxParam] Parameter errors

Definition at line 39 of file TFumili.h.

◆ fPL

Double_t* TFumili::fPL

private

[fMaxParam] Limits for parameters step. If <0, then parameter is fixed

Definition at line 46 of file TFumili.h.

◆ fPL0

Double_t* TFumili::fPL0

private

[fMaxParam] Step initial bounds

Definition at line 45 of file TFumili.h.

◆ fR

Double_t* TFumili::fR

private

[fMaxParam] Correlation factors

Definition at line 52 of file TFumili.h.

◆ fRP

Double_t TFumili::fRP

private

Precision of fit ( machine zero on CDC 6000) quite old yeh?

Definition at line 59 of file TFumili.h.

◆ fS

Double_t TFumili::fS

private

fS - objective function value (return)

Definition at line 57 of file TFumili.h.

◆ fSumLog

Double_t* TFumili::fSumLog

private

[fNlog]

Definition at line 40 of file TFumili.h.

◆ fWARN

Bool_t TFumili::fWARN

private

warnings

Definition at line 29 of file TFumili.h.

◆ fZ

Double_t* TFumili::fZ

private

[fMaxParam2] Inverse fZ0 matrix - covariance matrix

Definition at line 37 of file TFumili.h.

◆ fZ0

Double_t* TFumili::fZ0

private

[fMaxParam2] Matrix of approximate second derivatives of objective function This matrix is diagonal and always contain only variable parameter's derivatives

Definition at line 34 of file TFumili.h.

Libraries for TFumili:

[legend]

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

math/fumili/inc/TFumili.h
math/fumili/src/TFumili.cxx

FUMILI minimization package

Public Member Functions

Static Public Member Functions

Private Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ TFumili()

◆ ~TFumili()

Member Function Documentation

◆ BuildArrays()

◆ Chisquare()

◆ Class()

◆ Class_Name()

◆ Class_Version()

◆ Clear()

◆ DeclFileName()

◆ DeleteArrays()

◆ Derivatives()

◆ Eval()

◆ EvalTFN()

◆ ExecuteCommand()

◆ ExecuteSetCommand()

◆ FitChisquare()

◆ FitChisquareI()

◆ FitLikelihood()

◆ FitLikelihoodI()

◆ FixParameter()

◆ GetCovarianceMatrix()

◆ GetCovarianceMatrixElement()

◆ GetErrors()

◆ GetNumberFreeParameters()

◆ GetNumberTotalParameters()

◆ GetParameter() [1/2]

◆ GetParameter() [2/2]

◆ GetParError()

◆ GetParName()

◆ GetPL0()

◆ GetStats()

◆ GetSumLog()

◆ GetZ()

◆ InvertZ()

◆ IsA()

◆ IsFixed()

◆ Minimize()

◆ PrintResults()

◆ ReleaseParameter()

◆ SetData()

◆ SetFitMethod()

◆ SetParameter()

◆ SetParNumber()

◆ SGZ()

◆ Streamer()

◆ StreamerNVirtual()

Member Data Documentation

◆ fA

◆ fAKAPPA

◆ fAMN

◆ fAMX

◆ fANames

◆ fCmPar

◆ fCword

◆ fDA

◆ fDEBUG

◆ fDF

◆ fENDFLG

◆ fEPS

◆ fEXDA

◆ fGr

◆ fGRAD

◆ fGT

◆ fINDFLG

◆ fLastFixed

◆ fLogLike

◆ fMaxParam

◆ fNED1

◆ fNED12

◆ fNED2

◆ fNfcn

◆ fNlimMul

◆ fNlog