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TFumili Class Reference

### 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)

virtual ~TFumili ()
TFumili destructor.

void BuildArrays ()
Allocates memory for internal arrays.

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

virtual void Clear (Option_t *opt="")
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.

virtual Int_t ExecuteCommand (const char *command, Double_t *args, Int_t nargs)
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.

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

virtual Double_tGetCovarianceMatrix () const
Return a pointer to the covariance matrix.

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

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

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

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

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

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

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

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

Double_tGetPL0 () const

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

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

Double_tGetZ () const

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

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

Int_t Minimize ()
Main minimization procedure.

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

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

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

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

virtual Int_t SetParameter (Int_t ipar, const char *parname, Double_t value, Double_t verr, Double_t vlow, Double_t vhigh)
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.

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

virtual ~TVirtualFitter ()
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

TMethodCallGetMethodCall () const

virtual TObjectGetObjectFit () const

virtual TObjectGetUserFunc () 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

virtual Double_tSetCache (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)

Public Member Functions inherited from TNamed
TNamed ()

TNamed (const char *name, const char *title)

TNamed (const TNamed &named)
TNamed copy ctor.

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

virtual ~TNamed ()
TNamed destructor.

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

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

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

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

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

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

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

virtual Bool_t IsSortable () const

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

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

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

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

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

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

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

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

TObject (const TObject &object)
TObject copy ctor.

virtual ~TObject ()
TObject destructor.

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

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

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

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

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

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

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

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

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

virtual TObjectDrawClone (Option_t *option="") const
Draw a clone of this object in the current selected pad for instance with: gROOT->SetSelectedPad(gPad).

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

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

virtual void Execute (const char *method, const char *params, Int_t *error=0)
Execute method on this object with the given parameter string, e.g.

virtual void Execute (TMethod *method, TObjArray *params, Int_t *error=0)
Execute method on this object with parameters stored in the TObjArray.

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

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

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

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

virtual Option_tGetDrawOption () 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_tGetOption () const

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

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

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

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

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

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

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

void InvertBit (UInt_t f)

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

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

R__ALWAYS_INLINE Bool_t IsOnHeap () const

R__ALWAYS_INLINE Bool_t IsZombie () const

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

virtual Bool_t Notify ()
This method must be overridden to handle object notification.

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

void operator delete (void *ptr)
Operator delete.

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

voidoperator new (size_t sz)

voidoperator new (size_t sz, void *vp)

voidoperator new[] (size_t sz)

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

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

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

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

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

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

void ResetBit (UInt_t f)

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

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

void SetBit (UInt_t f)

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

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

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

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

R__ALWAYS_INLINE Bool_t TestBit (UInt_t f) const

Int_t TestBits (UInt_t f) const

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

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

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

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

## Private Attributes

Double_tfA
[fMaxParam] Fit parameter array

Double_t fAKAPPA

Double_tfAMN
[fMaxParam] Minimum param value

Double_tfAMX
[fMaxParam] Maximum param value

TStringfANames
[fMaxParam] Parameter names

Double_tfCmPar
[fMaxParam] parameters of commands

TString fCword
Command string.

Double_tfDA
[fMaxParam] Parameter step

Bool_t fDEBUG
debug info

Double_tfDF
[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_tfEXDA
[fNED12] experimental data poInt_ter

Double_tfGr
[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_tfParamError
[fMaxParam] Parameter errors

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

Double_tfPL0
[fMaxParam] Step initial bounds

Double_tfR
[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_tfSumLog
[fNlog]

Bool_t fWARN
warnings

Double_tfZ
[fMaxParam2] Invers fZ0 matrix - covariance matrix

Double_tfZ0
[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 = BIT(0) , kOverwrite = BIT(1) , kWriteDelete = BIT(2) }

enum  EDeprecatedStatusBits { kObjInCanvas = BIT(3) }

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

Static Public Member Functions inherited from TVirtualFitter
static TVirtualFitterFitter (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 TVirtualFitterGetFitter ()
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 TObject
static Long_t GetDtorOnly ()
Return destructor only flag.

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

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

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

Protected Types inherited from TObject
enum  { kOnlyPrepStep = BIT(3) }

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

TVirtualFitteroperator= (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_tfCache

Int_t fCacheSize

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

TMethodCallfMethodCall

Int_t fNpoints

TObjectfObjectFit

Foption_t fOption

Int_t fPointSize

TObjectfUserFunc

Int_t fXfirst

Int_t fXlast

Int_t fYfirst

Int_t fYlast

Int_t fZfirst

Int_t fZlast

Protected Attributes inherited from TNamed
TString fName

TString fTitle

#include <TFumili.h>

Inheritance diagram for TFumili:
[legend]

## ◆ TFumili()

 TFumili::TFumili ( Int_t maxpar = 25 )

Definition at line 129 of file TFumili.cxx.

## ◆ ~TFumili()

 TFumili::~TFumili ( )
virtual

TFumili destructor.

Definition at line 209 of file TFumili.cxx.

## ◆ BuildArrays()

 void TFumili::BuildArrays ( )

Allocates memory for internal arrays.

Called by TFumili::TFumili

Definition at line 174 of file TFumili.cxx.

## ◆ Chisquare()

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

return a chisquare equivalent

Implements TVirtualFitter.

Definition at line 219 of file TFumili.cxx.

## ◆ Clear()

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

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 234 of file TFumili.cxx.

## ◆ DeleteArrays()

 void TFumili::DeleteArrays ( )

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

Definition at line 253 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 283 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 342 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 354 of file TFumili.cxx.

## ◆ ExecuteCommand()

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

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 383 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 550 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 1730 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 1801 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 1876 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 1964 of file TFumili.cxx.

## ◆ FixParameter()

 void TFumili::FixParameter ( Int_t ipar )
virtual

Fixes parameter number ipar.

Implements TVirtualFitter.

Definition at line 766 of file TFumili.cxx.

## ◆ GetCovarianceMatrix()

 Double_t * TFumili::GetCovarianceMatrix ( ) const
virtual

Return a pointer to the covariance matrix.

Implements TVirtualFitter.

Definition at line 776 of file TFumili.cxx.

## ◆ GetCovarianceMatrixElement()

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

Return element i,j from the covariance matrix.

Implements TVirtualFitter.

Definition at line 785 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
virtual

Return errors after MINOs not implemented.

Implements TVirtualFitter.

Definition at line 874 of file TFumili.cxx.

## ◆ GetNumberFreeParameters()

 Int_t TFumili::GetNumberFreeParameters ( ) const
virtual

Return the number of free parameters.

Implements TVirtualFitter.

Definition at line 806 of file TFumili.cxx.

## ◆ GetNumberTotalParameters()

 Int_t TFumili::GetNumberTotalParameters ( ) const
virtual

Return the total number of parameters (free + fixed)

Implements TVirtualFitter.

Definition at line 798 of file TFumili.cxx.

## ◆ GetParameter() [1/2]

 Double_t TFumili::GetParameter ( Int_t ipar ) const
virtual

Return current value of parameter ipar.

Implements TVirtualFitter.

Definition at line 827 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
virtual

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 844 of file TFumili.cxx.

## ◆ GetParError()

 Double_t TFumili::GetParError ( Int_t ipar ) const
virtual

Return error of parameter ipar.

Implements TVirtualFitter.

Definition at line 818 of file TFumili.cxx.

## ◆ GetParName()

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

Return name of parameter ipar.

Implements TVirtualFitter.

Definition at line 864 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
virtual

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 896 of file TFumili.cxx.

## ◆ GetSumLog()

 Double_t TFumili::GetSumLog ( Int_t n )
virtual

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

Implements TVirtualFitter.

Definition at line 913 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 937 of file TFumili.cxx.

## ◆ IsFixed()

 Bool_t TFumili::IsFixed ( Int_t ipar ) const
virtual

Return kTRUE if parameter ipar is fixed, kFALSE otherwise)

Implements TVirtualFitter.

Definition at line 1052 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 1077 of file TFumili.cxx.

## ◆ PrintResults()

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

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 1475 of file TFumili.cxx.

## ◆ ReleaseParameter()

 void TFumili::ReleaseParameter ( Int_t ipar )
virtual

Releases parameter number ipar.

Implements TVirtualFitter.

Definition at line 1578 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 1608 of file TFumili.cxx.

## ◆ SetFitMethod()

 void TFumili::SetFitMethod ( const char * name )
virtual

ret fit method (chisquare or log-likelihood)

Implements TVirtualFitter.

Definition at line 1620 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 )
virtual

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

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

Implements TVirtualFitter.

Definition at line 1633 of file TFumili.cxx.

## ◆ SetParNumber()

 void TFumili::SetParNumber ( Int_t ParNum )
inline

Definition at line 112 of file TFumili.h.

## ◆ 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 1662 of file TFumili.cxx.

## ◆ 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] Invers 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:

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