| library: libFumili #include "TFumili.h" |
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public:
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)
private:
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
FUMILI
Based on ideas, proposed by I.N. Silin
[See NIM A440, 2000 (p431)]
converted from FORTRAN to C by
Sergey Yaschenko <s.yaschenko@fz-juelich.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
$$ {\chi^2\over2}={1\over2}\sum^n_{i=1}\left(f_i(\vec x_i,\vec\theta\,\,)-F_i\over\sigma_i\right)^2 \eqno(1) $$
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.
______________________________________________________________________________
maxpar is the maximum number of parameters used with TFumili object
Allocates memory for internal arrays. Called by TFumili::TFumili
TFumili destructor
return a chisquare equivalent
Resets all parameter names, values and errors to zero Argument opt is ignored NB: this procedure doesn't reset parameter limits
Deallocates memory. Called from destructor TFumili::~TFumili
Calculates partial derivatives of theoretical function
Input:
fX - vector of data point
Output:
DF - array of derivatives
ARITHM.F
Converted from CERNLIB
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
Evaluate theoretical function df: array of partial derivatives X: vector of theoretical function argument
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
Called from TFumili::ExecuteCommand in case of "SET xxx" and "SHOW xxx".
Fixes parameter number ipar
return a pointer to the covariance matrix
return element i,j from the covariance matrix
return the total number of parameters (free + fixed)
return the number of free parameters
return error of parameter ipar
return current value of parameter ipar
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.
Return errors after MINOs not implemented
return global fit parameters amin : chisquare edm : estimated distance to minimum errdef nvpar : number of variable parameters nparx : total number of parameters
return Sum(log(i) i=0,n used by log likelihood fits
Inverts packed diagonal matrix Z by square-root method. Matrix elements corresponding to fix parameters are removed. n: number of variable parameters
return kTRUE if parameter ipar is fixed, kFALSE othersise)
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
FUMILI
Based on ideas, proposed by I.N. Silin
[See NIM A440, 2000 (p431)]
converted from FORTRAN to C by
Sergey Yaschenko <s.yaschenko@fz-juelich.de>
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
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
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
Releases parameter number ipar
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]
ret fit method (chisquare or loglikelihood)
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
Evaluates objective function ( chi-square ), gradients and Z-matrix using data provided by user via TFumili::SetData
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&)