class TStatToolkit: public TObject

 Default constructor

 Destructor

 Robust estimator in 1D case MI version - (faster than ROOT version)

 For the univariate case
 estimates of location and scatter are returned in mean and sigma parameters
 the algorithm works on the same principle as in multivariate case -
 it finds a subset of size hh with smallest sigma, and then returns mean and
 sigma of this subset

 Modified version of ROOT robust EvaluateUni
 robust estimator in 1D case MI version
 added external factor to include precision of external measurement

  Sort eleements according occurancy
  The size of output array has is 2*n

 LTM : Trimmed mean on histogram - Modified version for binned data

 Robust statistic to estimate properties of the distribution
 See http://en.wikipedia.org/w/index.php?title=Trimmed_estimator&oldid=582847999

 New faster version is under preparation

 Algorithm to filter  histogram
 author:  marian.ivanov@cern.ch
 Details of algorithm:
 http://en.wikipedia.org/w/index.php?title=Median_filter&oldid=582191524
 Input parameters:
    his1D - input histogam - to be modiefied by Medianfilter
    nmendian - number of bins in median filter

 LTM : Trimmed mean on histogram - Modified version for binned data

 Robust statistic to estimate properties of the distribution
 To handle binning error special treatment
 for definition of unbinned data see:
     http://en.wikipedia.org/w/index.php?title=Trimmed_estimator&oldid=582847999

 Function parameters:
     his1D   - input histogram
     params  - vector with parameters
             - 0 - area
             - 1 - mean
             - 2 - rms
             - 3 - error estimate of mean
             - 4 - error estimate of RMS
             - 5 - first accepted bin position
             - 6 - last accepted  bin position

  Fit histogram with gaussian function

  Prameters:
       return value- chi2 - if negative ( not enough points)
       his        -  input histogram
       param      -  vector with parameters
       xmin, xmax -  range to fit - if xmin=xmax=0 - the full histogram range used
  Fitting:
  1. Step - make logarithm
  2. Linear  fit (parabola) - more robust - always converge
  3. In case of small statistic bins are averaged

  Fit histogram with gaussian function

  Prameters:
     nbins: size of the array and number of histogram bins
     xMin, xMax: histogram range
     param: paramters of the fit (0-Constant, 1-Mean, 2-Sigma)
     matrix: covariance matrix -- not implemented yet, pass dummy matrix!!!

  Return values:
    >0: the chi2 returned by TLinearFitter
    -3: only three points have been used for the calculation - no fitter was used
    -2: only two points have been used for the calculation - center of gravity was uesed for calculation
    -1: only one point has been used for the calculation - center of gravity was uesed for calculation
    -4: invalid result!!

  Fitting:
  1. Step - make logarithm
  2. Linear  fit (parabola) - more robust - always converge

  calculate center of gravity rms and sum for array 'arr' with nBins an a x range xMin to xMax
  return COG; in case of failure return xMin

 Test performance of the parabolic - gaussian fit - compare it with
 ROOT gauss fit
  nhistos - number of histograms to be used for test

 delta - number of bins to integrate
 type - 0 - mean value

 function to retrieve the "mean and RMS estimate" of 2D histograms

 Robust statistic to estimate properties of the distribution
 See http://en.wikipedia.org/wiki/Trimmed_estimator

 deltaBin - number of bins to integrate (bin+-deltaBin)
 fraction - fraction of values for the LTM and for the gauss fit
 returnType -
        0 - mean value
        1 - RMS
        2 - LTM mean
        3 - LTM sigma
        4 - Gaus fit mean  - on LTM range
        5 - Gaus fit sigma - on LTM  range

 fit an arbitrary function, specified by formula into the data, specified by drawCommand and cuts
 returns chi2, fitParam and covMatrix
 returns TString with fitted formula

 fit an arbitrary function, specified by formula into the data, specified by drawCommand and cuts
 returns chi2, fitParam and covMatrix
 returns TString with fitted formula

 fit an arbitrary function, specified by formula into the data, specified by drawCommand and cuts
 returns chi2, fitParam and covMatrix
 returns TString with fitted formula

 fitString - ++ separated list of fits
 substring - ++ separated list of the requiered substrings

 return the last occurance of substring in fit string

 Filter fit expression make sub-fit

 Update parameters and covariance - with one measurement
 Input:
 vecXk - input vector - Updated in function
 covXk - covariance matrix - Updated in function
 delta, sigma, s1 - new measurement, rms of new measurement and the index of measurement

 constrain linear fit
 input  - string description of fit function
 filter - string filter to select sub fits
 param,covar - parameters and covariance matrix of the fit
 mean,sigma  - new measurement uning which the fit is updated

 Query a graph errors
 return TGraphErrors specified by expr and cut
 Example  usage TStatToolkit::MakeGraphError(tree,"Y:X:ErrY","X>0", 25,2,0.4)
 tree   - tree with variable
 expr   - examp

 Make a sparse draw of the variables
 Format of expr : Var:Run or Var:Run:ErrorY or Var:Run:ErrorY:ErrorX
 offset : points can slightly be shifted in x for better visibility with more graphs

 Written by Weilin.Yu
 updated & merged with QA-code by Patrick Reichelt

 Add alias using statistical values of a given variable.
 (by MI, Patrick Reichelt)

 tree - input tree
 expr - variable expression
 cut  - selection criteria
 Output - return number of entries used to define variable
 In addition mean, rms, median, and robust mean and rms (choosing fraction of data with smallest RMS)

 Example usage:
     1.) create the robust estimators for variable expr="QA.TPC.CPass1.meanTPCncl" and create a corresponding
     aliases with the prefix alias[0]="ncl", calculated using fraction alias[1]="0.90"

     TStatToolkit::MakeStatAlias(tree,"QA.TPC.CPass1.meanTPCncl","QA.TPC.CPass1.status>0","ncl:0.9");
     root [4] tree->GetListOfAliases().Print()
     OBJ: TNamed    ncl_Median      (130.964333+0)
     OBJ: TNamed    ncl_Mean        (122.120387+0)
     OBJ: TNamed    ncl_RMS         (33.509623+0)
     OBJ: TNamed    ncl_Mean90      (131.503862+0)
     OBJ: TNamed    ncl_RMS90       (3.738260+0)

 Add alias to trending tree using statistical values of a given variable.
 (by MI, Patrick Reichelt)

 format of expr :  varname (e.g. meanTPCncl)
 format of cut  :  char like in TCut
 format of alias:  alias:query:entryFraction(EF) (fraction of entries used for uniformity evaluation)
            e.g.:  varname_Out:(abs(varname-meanEF)>6.*rmsEF):0.8
 available internal variables are: 'varname, Median, Mean, MeanEF, RMS, RMSEF'
 in the alias, 'varname' will be replaced by its content, and 'EF' by the percentage (e.g. MeanEF -> Mean80)

 Example usage:
     1.) Define robust mean (possible, but easier done with TStatToolkit::MakeStatAlias(...))
     TStatToolkit::SetStatusAlias(tree, "meanTPCnclF", "meanTPCnclF>0", "meanTPCnclF_MeanEF:MeanEF:0.80") ;
     root [10] tree->GetListOfAliases()->Print()
               Collection name='TList', class='TList', size=1
               OBJ: TNamed    meanTPCnclF_Mean80      0.899308
     2.) create alias outlyers  - 6 sigma cut
     TStatToolkit::SetStatusAlias(tree, "meanTPCnclF", "meanTPCnclF>0", "meanTPCnclF_Out:(abs(meanTPCnclF-MeanEF)>6.*RMSEF):0.8")
     meanTPCnclF_Out ==> (abs(meanTPCnclF-0.899308)>6.*0.016590)
     3.) the same functionality as in 2.)
     TStatToolkit::SetStatusAlias(tree, "meanTPCnclF", "meanTPCnclF>0", "varname_Out2:(abs(varname-MeanEF)>6.*RMSEF):0.8")
     meanTPCnclF_Out2 ==> (abs(meanTPCnclF-0.899308)>6.*0.016590)

 Compute a trending multigraph that shows for which runs a variable has outliers.
 (by MI, Patrick Reichelt)

 format of expr :  varname:xaxis (e.g. meanTPCncl:run, but 'varname' can be any string that you need for seach-and-replace)
 format of cut  :  char like in TCut
 format of alias:  (1):(statisticOK):(varname_Warning):(varname_Out)[:(varname_PhysAcc):(varname_Extra)]

 function MakeGraphSparse() is called for each alias argument, which will be used as tree expression.
 each alias argument is supposed to be a Boolean statement which can be evaluated as tree expression.
 the order of these criteria should be kept, as the marker styles and colors are chosen to be meaningful this way!
 'statisticOK' could e.g. be an alias for '(meanTPCncl>0)'.
 if you dont need e.g. a 'warning' condition, then just replace it by (0).
 in the alias, 'varname' will be replaced by its content (e.g. varname_Out -> meanTPCncl_Out)
 note: the aliases 'varname_Out' etc have to be defined by function TStatToolkit::SetStatusAlias(...)
 counter igr is used to shift the multigraph in y when filling a TObjArray.


 To create the Status Bar, the following is done in principle.
    ( example current usage in $ALICE_ROOT/PWGPP/TPC/macros/drawPerformanceTPCQAMatchTrends.C and ./qaConfig.C. )

  TStatToolkit::SetStatusAlias(tree, "meanTPCncl",    "", "varname_Out:(abs(varname-MeanEF)>6.*RMSEF):0.8");
  TStatToolkit::SetStatusAlias(tree, "tpcItsMatchA",  "", "varname_Out:(abs(varname-MeanEF)>6.*RMSEF):0.8");
  TStatToolkit::SetStatusAlias(tree, "meanTPCncl",    "", "varname_Warning:(abs(varname-MeanEF)>3.*RMSEF):0.8");
  TStatToolkit::SetStatusAlias(tree, "tpcItsMatchA",  "", "varname_Warning:(abs(varname-MeanEF)>3.*RMSEF):0.8");
  TObjArray* oaMultGr = new TObjArray(); int igr=0;
  oaMultGr->Add( TStatToolkit::MakeStatusMultGr(tree, "tpcItsMatchA:run",  "", "(1):(meanTPCncl>0):(varname_Warning):(varname_Outlier):", igr) ); igr++;
  oaMultGr->Add( TStatToolkit::MakeStatusMultGr(tree, "meanTPCncl:run",    "", "(1):(meanTPCncl>0):(varname_Warning):(varname_Outlier):", igr) ); igr++;
  TCanvas *c1 = new TCanvas("c1","c1");
  TStatToolkit::AddStatusPad(c1, 0.30, 0.40);
  TStatToolkit::DrawStatusGraphs(oaMultGr);

 add pad to bottom of canvas for Status graphs (by Patrick Reichelt)
 call function "DrawStatusGraphs(...)" afterwards

 draw Status graphs into active pad of canvas (by MI, Patrick Reichelt)
 ...into bottom pad, if called after "AddStatusPad(...)"

 Create Tree with Integers for each status variable flag (warning, outlier, physacc).
 (by Patrick Reichelt)

 input: either a TMultiGraph with status of single variable, which
        was computed by TStatToolkit::MakeStatusMultGr(),
        or a TObjArray which contains up to 10 of such variables.
        example: TTree* statusTree = WriteStatusToTree( TStatToolkit::MakeStatusMultGr(tree, "tpcItsMatch:run",  "", sCriteria.Data(), 0) );
        or     : TTree* statusTree = TStatToolkit::WriteStatusToTree(oaMultGr);

 output tree: 1=flag is true, 0=flag is false, -1=flag was not computed.
 To be rewritten to the pcstream

 Make a  summary tree for the input tree
 For the moment statistic works only for the primitive branches (Float/Double/Int)
 Extension recursive version planned for graphs a and histograms

 Following statistics are exctracted:
   - Standard: mean, meadian, rms
   - LTM robust statistic: mean60, rms60, mean90, rms90
 Parameters:
    treeIn    - input tree
    pctream   - Output redirector
    sumID     - ID as will be used in output tree
    selection - selection criteria define the set of entries used to evaluat statistic

 Create status lines for trending using MakeGraphSparse(), very similar to MakeStatusMultGr().
 (by Patrick Reichelt)

 format of expr :  varname:xaxis (e.g. meanTPCncl:run, but 'varname' can be any string that you need for seach-and-replace)
 format of cut  :  char like in TCut
 format of alias:  varname_OutlierMin:varname_OutlierMax:varname_WarningMin:varname_WarningMax:varname_PhysAccMin:varname_PhysAccMax:varname_RobustMean

 Draw histogram from TTree with robust range
 Only for 1D so far!

 Parameters:
 - histoname:  name of histogram
 - histotitle: title of histgram
 - fraction:   fraction of data to define the robust mean
 - nsigma:     nsigma value for range

 Check consistency of tree aliases