library: libFumili
#include "TFumili.h"


class description - source file - inheritance tree (.pdf)

class TFumili : public TVirtualFitter

Inheritance Chart:

TFumili(Int_t maxpar = 25) TFumili(const TFumili&) virtual ~TFumili() void BuildArrays() virtual Double_t Chisquare(Int_t npar, Double_t* params) const static TClass* Class() virtual void Clear(Option_t* opt) void DeleteArrays() void Derivatives(Double_t*, Double_t*) Int_t Eval(Int_t& npar, Double_t* grad, Double_t& fval, Double_t* par, Int_t flag) Double_t EvalTFN(Double_t*, Double_t*) virtual Int_t ExecuteCommand(const char* command, Double_t* args, Int_t nargs) Int_t ExecuteSetCommand(Int_t) virtual void FixParameter(Int_t ipar) virtual Double_t* GetCovarianceMatrix() const virtual Double_t GetCovarianceMatrixElement(Int_t i, Int_t j) const virtual Int_t GetErrors(Int_t ipar, Double_t& eplus, Double_t& eminus, Double_t& eparab, Double_t& globcc) const virtual Int_t GetNumberFreeParameters() const virtual Int_t GetNumberTotalParameters() const virtual Double_t GetParameter(Int_t ipar) const virtual Int_t GetParameter(Int_t ipar, char* name, Double_t& value, Double_t& verr, Double_t& vlow, Double_t& vhigh) const virtual Double_t GetParError(Int_t ipar) const Double_t* GetPL0() const virtual Int_t GetStats(Double_t& amin, Double_t& edm, Double_t& errdef, Int_t& nvpar, Int_t& nparx) const virtual Double_t GetSumLog(Int_t) Double_t* GetZ() const void InvertZ(Int_t) virtual TClass* IsA() const virtual Bool_t IsFixed(Int_t ipar) const Int_t Minimize() TFumili& operator=(const TFumili&) virtual void PrintResults(Int_t k, Double_t p) const virtual void ReleaseParameter(Int_t ipar) void SetData(Double_t*, Int_t, Int_t) virtual void SetFitMethod(const char* name) virtual Int_t SetParameter(Int_t ipar, const char* parname, Double_t value, Double_t verr, Double_t vlow, Double_t vhigh) void SetParNumber(Int_t ParNum) Int_t SGZ() virtual void ShowMembers(TMemberInspector& insp, char* parent) virtual void Streamer(TBuffer& b) void StreamerNVirtual(TBuffer& b)

Data Members

Int_t fMaxParam Int_t fMaxParam2 fMaxParam*fMaxParam Int_t fNlog Int_t fNfcn Number of FCN calls; Int_t fNED1 Number of experimental vectors X=(x1,x2,...xK) Int_t fNED2 K - Length of vector X plus 2 (for chi2) Int_t fNED12 fNED1+fNED2 Int_t fNpar fNpar - number of parameters Int_t fNstepDec fNstepDec - maximum number of step decreasing counter Int_t fNlimMul fNlimMul - after fNlimMul successful iterations permits four-fold increasing of fPL Int_t fNmaxIter fNmaxIter - maximum number of iterations Int_t fLastFixed Last fixed parameter number Int_t fENDFLG End flag of fit Int_t fINDFLG[5] internal flags; Bool_t fGRAD user calculated gradients Bool_t fWARN warnings Bool_t fDEBUG debug info Bool_t fLogLike LogLikelihood flag Bool_t fNumericDerivatives Double_t* fZ0 [fMaxParam2] Matrix of approximate second derivatives of objective function Double_t* fZ [fMaxParam2] Invers fZ0 matrix - covariance matrix Double_t* fGr [fMaxParam] Gradients of objective function Double_t* fParamError [fMaxParam] Parameter errors Double_t* fSumLog [fNlog] Double_t* fEXDA [fNED12] experimental data poInt_ter Double_t* fA [fMaxParam] Fit parameter array Double_t* fPL0 [fMaxParam] Step initial bounds Double_t* fPL [fMaxParam] Limits for parameters step. If <0, then parameter is fixed Double_t* fDA [fMaxParam] Parameter step Double_t* fAMX [fMaxParam] Maximum param value Double_t* fAMN [fMaxParam] Minimum param value Double_t* fR [fMaxParam] Correlation factors Double_t* fDF [fMaxParam] // First derivatives of theoretical function Double_t* fCmPar [fMaxParam] parameters of commands Double_t fS fS - objective function value (return) Double_t fEPS fEPS - required precision of parameters. If fEPS<0 then Double_t fRP Precision of fit ( machine zero on CDC 6000) quite old yeh? Double_t fAKAPPA Double_t fGT Expected function change in next iteration TString* fANames [fMaxParam] Parameter names TString fCword Command string

Class Description

  Based on ideas, proposed by I.N. Silin
    [See NIM A440, 2000 (p431)]
 converted from FORTRAN to C  by
     Sergey Yaschenko <>


FUMILI minimization package

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

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

where $\sigma_i$ are errors of measured function.

The minimum condition is

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

where m is the quantity of parameters.

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

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

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

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

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:

$${\partial^2\chi^2\over\partial\theta_i\partial\theta_k}\approx Z_{ik}= \sum^n_{j=1}{1\over\sigma^2_j}{\partial f_j\over\theta_i} {\partial f_j\over\theta_k}\eqno(5) $$

Then the equations for parameter increments are

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

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: $$ \theta_i^{\rm min}\le\theta_i\le\theta^{\rm max}_i\eqno(7) $$

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 functional argument.


TFumili(Int_t maxpar)
 maxpar is the maximum number of parameters used with TFumili object

void BuildArrays()
   Allocates memory for internal arrays. Called by TFumili::TFumili

 TFumili destructor

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

void Clear(Option_t *)
 Resets all parameter names, values and errors to zero

 Argument opt is ignored

 NB: this procedure doesn't reset parameter limits

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

void Derivatives(Double_t *DF,Double_t *fX)
 Calculates partial derivatives of theoretical function

    fX  - vector of data point
    DF - array of derivatives

 Converted from CERNLIB

Int_t 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 his 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

Double_t EvalTFN(Double_t * /*df*/, Double_t *X)
 Evaluate theoretical function
 df: array of partial derivatives
 X:  vector of theoretical function argument

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

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

void FixParameter(Int_t ipar)
 Fixes parameter number ipar

Double_t* GetCovarianceMatrix() const
 return a pointer to the covariance matrix

Double_t GetCovarianceMatrixElement(Int_t i, Int_t j) const
 return element i,j from the covariance matrix

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

Int_t GetNumberFreeParameters() const
 return the number of free parameters

Double_t GetParError(Int_t ipar) const
 return error of parameter ipar

Double_t GetParameter(Int_t ipar) const
 return current value of parameter ipar

Int_t GetParameter(Int_t ipar,char *cname,Double_t &value,Double_t &verr,Double_t &vlow, Double_t &vhigh) const
 Get various ipar parameter attributs:

 cname:    parameter name
 value:    parameter value
 verr:     parameter error
 vlow:     lower limit
 vhigh:    upper limit
 WARNING! parname must be suitably dimensionned in the calling function.

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

Int_t GetStats(Double_t &amin, Double_t &edm, Double_t &errdef, Int_t &nvpar, Int_t &nparx) const
 return global fit parameters
   amin     : chisquare
   edm      : estimated distance to minimum
   nvpar    : number of variable parameters
   nparx    : total number of parameters

Double_t GetSumLog(Int_t n)
 return Sum(log(i) i=0,n
 used by log likelihood fits

void 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

Bool_t IsFixed(Int_t ipar) const
return kTRUE if parameter ipar is fixed, kFALSE othersise)

Int_t Minimize()
  Based on ideas, proposed by I.N. Silin
    [See NIM A440, 2000 (p431)]
 converted from FORTRAN to C  by
     Sergey Yaschenko <>


 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  - functional is not decreasing (or bad derivatives)
   -3  - error estimations are infinite
   -4  - maximum number of iterations is exceeded

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

 ikode is the type of printing parameters
 p is functional 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

void ReleaseParameter(Int_t ipar)
 Releases parameter number ipar

void 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]

void SetFitMethod(const char *name)
 ret fit method (chisquare or loglikelihood)

Int_t SetParameter(Int_t ipar,const char *parname,Double_t value,Double_t verr,Double_t vlow, Double_t vhigh)
 Sets for prameter 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

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

Inline Functions

          Double_t* GetPL0() const
          Double_t* GetZ() const
               void SetParNumber(Int_t ParNum)
            TClass* Class()
            TClass* IsA() const
               void ShowMembers(TMemberInspector& insp, char* parent)
               void Streamer(TBuffer& b)
               void StreamerNVirtual(TBuffer& b)
            TFumili TFumili(const TFumili&)
           TFumili& operator=(const TFumili&)

Author: Stanislav Nesterov 07/05/2003
Last update: root/fumili:$Name: $:$Id: TFumili.cxx,v 1.20 2004/10/22 21:18:23 brun Exp $

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