class TLinearFitter: public TVirtualFitter

 The Linear Fitter - fitting functions that are LINEAR IN PARAMETERS

 Linear fitter is used to fit a set of data points with a linear
 combination of specified functions. Note, that "linear" in the name
 stands only for the model dependency on parameters, the specified
 functions can be nonlinear.
 The general form of this kind of model is

          y(x) = a[0] + a[1]*f[1](x)+...a[n]*f[n](x)

 Functions f are fixed functions of x. For example, fitting with a
 polynomial is linear fitting in this sense.

                         The fitting method

 The fit is performed using the Normal Equations method with Cholesky
 decomposition.

                         Why should it be used?

 The linear fitter is considerably faster than general non-linear
 fitters and doesn't require to set the initial values of parameters.

                          Using the fitter:

 1.Adding the data points:
  1.1 To store or not to store the input data?
      - There are 2 options in the constructor - to store or not
        store the input data. The advantages of storing the data
        are that you'll be able to reset the fitting model without
        adding all the points again, and that for very large sets
        of points the chisquare is calculated more precisely.
        The obvious disadvantage is the amount of memory used to
        keep all the points.
      - Before you start adding the points, you can change the
        store/not store option by StoreData() method.
  1.2 The data can be added:
      - simply point by point - AddPoint() method
      - an array of points at once:
        If the data is already stored in some arrays, this data
        can be assigned to the linear fitter without physically
        coping bytes, thanks to the Use() method of
        TVector and TMatrix classes - AssignData() method

 2.Setting the formula
  2.1 The linear formula syntax:
      -Additive parts are separated by 2 plus signes "++"
       --for example "1 ++ x" - for fitting a straight line
      -All standard functions, undrestood by TFormula, can be used
       as additive parts
       --TMath functions can be used too
      -Functions, used as additive parts, shouldn't have any parameters,
       even if those parameters are set.
       --for example, if normalizing a sum of a gaus(0, 1) and a
         gaus(0, 2), don't use the built-in "gaus" of TFormula,
         because it has parameters, take TMath::Gaus(x, 0, 1) instead.
      -Polynomials can be used like "pol3", .."polN"
      -If fitting a more than 3-dimensional formula, variables should
       be numbered as follows:
       -- x[0], x[1], x[2]... For example, to fit  "1 ++ x[0] ++ x[1] ++ x[2] ++ x[3]*x[3]"
  2.2 Setting the formula:
    2.2.1 If fitting a 1-2-3-dimensional formula, one can create a
          TF123 based on a linear expression and pass this function
          to the fitter:
          --Example:
            TLinearFitter *lf = new TLinearFitter();
            TF2 *f2 = new TF2("f2", "x ++ y ++ x*x*y*y", -2, 2, -2, 2);
            lf->SetFormula(f2);
          --The results of the fit are then stored in the function,
            just like when the TH1::Fit or TGraph::Fit is used
          --A linear function of this kind is by no means different
            from any other function, it can be drawn, evaluated, etc.

          --For multidimensional fitting, TFormulas of the form:
            x[0]++...++x[n] can be used
    2.2.2 There is no need to create the function if you don't want to,
          the formula can be set by expression:
          --Example:
            // 2 is the number of dimensions
            TLinearFitter *lf = new TLinearFitter(2);
            lf->SetFormula("x ++ y ++ x*x*y*y");

    2.2.3 The fastest functions to compute are polynomials and hyperplanes.
          --Polynomials are set the usual way: "pol1", "pol2",...
          --Hyperplanes are set by expression "hyp3", "hyp4", ...
          ---The "hypN" expressions only work when the linear fitter
             is used directly, not through TH1::Fit or TGraph::Fit.
             To fit a graph or a histogram with a hyperplane, define
             the function as "1++x++y".
          ---A constant term is assumed for a hyperplane, when using
             the "hypN" expression, so "hyp3" is in fact fitting with
             "1++x++y++z" function.
          --Fitting hyperplanes is much faster than fitting other
            expressions so if performance is vital, calculate the
            function values beforehand and give them to the fitter
            as variables
          --Example:
            You want to fit "sin(x)|cos(2*x)" very fast. Calculate
            sin(x) and cos(2*x) beforehand and store them in array *data.
            Then:
            TLinearFitter *lf=new TLinearFitter(2, "hyp2");
            lf->AssignData(npoint, 2, data, y);

  2.3 Resetting the formula
    2.3.1 If the input data is stored (or added via AssignData() function),
          the fitting formula can be reset without re-adding all the points.
          --Example:
            TLinearFitter *lf=new TLinearFitter("1++x++x*x");
            lf->AssignData(n, 1, x, y, e);
            lf->Eval()
            //looking at the parameter significance, you see,
            // that maybe the fit will improve, if you take out
            // the constant term
            lf->SetFormula("x++x*x");
            lf->Eval();

    2.3.2 If the input data is not stored, the fitter will have to be
          cleared and the data will have to be added again to try a
          different formula.

 3.Accessing the fit results
  3.1 There are methods in the fitter to access all relevant information:
      --GetParameters, GetCovarianceMatrix, etc
      --the t-values of parameters and their significance can be reached by
        GetParTValue() and GetParSignificance() methods
  3.2 If fitting with a pre-defined TF123, the fit results are also
      written into this function.


 4.Robust fitting - Least Trimmed Squares regression (LTS)
   Outliers are atypical(by definition), infrequant observations; data points
   which do not appear to follow the characteristic distribution of the rest
   of the data. These may reflect genuine properties of the underlying
   phenomenon(variable), or be due to measurement errors or anomalies which
   shouldn't be modelled. (StatSoft electronic textbook)

   Even a single gross outlier can greatly influence the results of least-
   squares fitting procedure, and in this case use of robust(resistant) methods
   is recommended.

   The method implemented here is based on the article and algorithm:
   "Computing LTS Regression for Large Data Sets" by
   P.J.Rousseeuw and Katrien Van Driessen
   The idea of the method is to find the fitting coefficients for a subset
   of h observations (out of n) with the smallest sum of squared residuals.
   The size of the subset h should lie between (npoints + nparameters +1)/2
   and n, and represents the minimal number of good points in the dataset.
   The default value is set to (npoints + nparameters +1)/2, but of course
   if you are sure that the data contains less outliers it's better to change
   h according to your data.

   To perform a robust fit, call EvalRobust() function instead of Eval() after
   adding the points and setting the fitting function.
   Note, that standard errors on parameters are not computed!