class AliTMinuitToolkit: public TNamed

 The AliTMinuitToolkit serves as an easy to use interface for the TMinuit
 package:

 - It allows to fit a curve to one and two dimensional histograms
   (TH2F::Fit() only allows to fit a hyperplane).
 - Or n points can be specified directly via a n x 2 matrix.
 - An option for robust fitting with non-linear functions is implemented.

 A small example illustrating the usage of AliTMinuitToolkit is given in the function
 "AliTMinuitToolkit::Test()".


 1. Setting the formula:

  The formula is simply set via "void SetFitFunction(TFormula * formula)".


 2. Adding the data points

  - In order to fit a histogram, use "void FitHistogram(TH1F * his)" or
    "void FitHistogram(TH2F * his)". The fitter is started automatically
  - Alternatively, the direct specification of the points is possible via
    "void SetPoints(TMatrixD * points)". Note, that the each point
    corresponds to one row in the matrix. The fitter is then started with
    the command "void Fit()". The weight of each point can be specified
    with an n-dimensional vector using "void SetWeights(TVectorD * weights)".


 3. Accessing the fit results

  The N parameters of the formula are stored in a N-dimensional vector which
  is returned by "TVectorD * GetParameters()". In a similar way the covariance
  matrix of the fit is returned via "TMatrixD * GetCovarianceMatrix()" which
  is of the type N x N.


 4. Non-linear robust fitting:

  Even a few outliers can lead to wrong results of a least-squares fitting
  procedure. In this case the use of robust(resistant) methods can be
  helpful, but a stronger dependence on starting values or convergence to
  local minima can occur.

  The robust option becomes active if EnableRobust(true, sigma) is called. It is
  very much recommended that a normalization value (scale variable) corresponding
  to an expected deviation (sigma) is specified via
  "EnableRobust(Bool_t b, Double_t sigma)".

  Performing the fit without knowledge of sigma is also possible if only
  "EnableRobust(true)" is activated, but this is NOT RECOMMENDED.

  The method is based on another estimator instead of chi^2. For small deviations
  the function behaves like x^2 and for larger deviations like |x| - the so
  called Huber estimator:

   h(x) = x^2                              , for x < 2.5*sigma
   h(x) = 2*(2.5*sigma)*x - (2.5*sigma)^2  , for x > 2.5*sigma

  If a weighting function is specified in addition, a second run with the ordinary
  metric is started, but before entering the iteration every point is weighted
  according to its distance to the outcoming function of the first run. The weighting
  function w(x) must be defined on the intervall x in [0,1]. w(0) then
  corresponds to the weight of the closest point and w(1) to the point with the
  largest distance.

  Some standard weighting functions are predefined in
  "SetWeightFunction(Char_t * name, Float_t param1, Float_t param2 = 0)":
   - "BOX" equals to 1 if x < param1 and to 0 if x > param1.
   - "EXPONENTIAL" corresponds to "Math::Exp(-TMath::Log(param1)*x)"
   - "ERRORFUNCTION" corresponds to "TMath::Erfc((x-param1)/param2)"


  REFERENCE for non-linear robust fitting:
  Ekblom H. and Madsen K. (1988), Alogrithms for non-linear Huber estimation,
  BIT Numerical Mathematics 29 (1989) 60-76.
  internet: http://www.springerlink.com/content/m277218542988344


 5. examples:

  A small example illustrating the working principles of AliTMinuitToolkit is given
  in the function "AliTMinuitToolkit::Test()".



 Comments and questions are always welcome: A.Kalweit@gsi.de