Draw expression varexp for specified entries.
 Returns -1 in case of error or number of selected events in case of success.

  varexp is an expression of the general form
   - "e1"           produces a 1-d histogram (TH1F) of expression "e1"
   - "e1:e2"        produces an unbinned 2-d scatter-plot (TGraph) of "e1" versus "e2"
   - "e1:e2:e3"     produces an unbinned 3-d scatter-plot (TPolyMarker3D) of "e1"
                    versus "e2" versus "e3"
   - "e1:e2:e3:e4"  produces an unbinned 3-d scatter-plot (TPolyMarker3D) of "e1"
                    versus "e2" versus "e3" and "e4" mapped on the color number.
  (to create histograms in the 2, 3, and 4 dimesional case, see section "Saving
  the result of Draw to an histogram")

  Example:
     varexp = x     simplest case: draw a 1-Dim distribution of column named x
            = sqrt(x)            : draw distribution of sqrt(x)
            = x*y/z
            = y:sqrt(x) 2-Dim distribution of y versus sqrt(x)
            = px:py:pz:2.5*E  produces a 3-d scatter-plot of px vs py ps pz
              and the color number of each marker will be 2.5*E.
              If the color number is negative it is set to 0.
              If the color number is greater than the current number of colors
                 it is set to the highest color number.
              The default number of colors is 50.
              see TStyle::SetPalette for setting a new color palette.

  Note that the variables e1, e2 or e3 may contain a selection.
  example, if e1= x*(y<0), the value histogrammed will be x if y<0
  and will be 0 otherwise.

  The expressions can use all the operations and build-in functions
  supported by TFormula (See TFormula::Analyze), including free
  standing function taking numerical arguments (TMath::Bessel).
  In addition, you can call member functions taking numerical
  arguments. For example:
      - "TMath::BreitWigner(fPx,3,2)"
      - "event.GetHistogram().GetXaxis().GetXmax()"
      - "event.GetTrack(fMax).GetPx()

  selection is an expression with a combination of the columns.
  In a selection all the C++ operators are authorized.
  The value corresponding to the selection expression is used as a weight
  to fill the histogram.
  If the expression includes only boolean operations, the result
  is 0 or 1. If the result is 0, the histogram is not filled.
  In general, the expression may be of the form:
      value*(boolean expression)
  if boolean expression is true, the histogram is filled with
  a weight = value.
  Examples:
      selection1 = "x3.2"
      selection2 = "(x+y)*(sqrt(z)>3.2)"
  selection1 returns a weigth = 0 or 1
  selection2 returns a weight = x+y if sqrt(z)>3.2
             returns a weight = 0 otherwise.

  option is the drawing option.
    - See TH1::Draw for the list of all drawing options.
    - If option COL is specified when varexp has three fields:
            tree.Draw("e1:e2:e3","","col");
      a 2D scatter is produced with e1 vs e2, and e3 is mapped on the color
      table.
    - If option contains the string "goff", no graphics is generated.

  nentries is the number of entries to process (default is all)
  first is the first entry to process (default is 0)

  This function returns the number of selected entries. It returns -1
  if an error occurs.

     Drawing expressions using arrays and array elements

 Let assumes, a leaf fMatrix, on the branch fEvent, which is a 3 by 3 array,
 or a TClonesArray.
 In a TTree::Draw expression you can now access fMatrix using the following
 syntaxes:

   String passed    What is used for each entry of the tree

   "fMatrix"       the 9 elements of fMatrix
   "fMatrix[][]"   the 9 elements of fMatrix
   "fMatrix[2][2]" only the elements fMatrix[2][2]
   "fMatrix[1]"    the 3 elements fMatrix[1][0], fMatrix[1][1] and fMatrix[1][2]
   "fMatrix[1][]"  the 3 elements fMatrix[1][0], fMatrix[1][1] and fMatrix[1][2]
   "fMatrix[][0]"  the 3 elements fMatrix[0][0], fMatrix[1][0] and fMatrix[2][0]

   "fEvent.fMatrix...." same as "fMatrix..." (unless there is more than one leaf named fMatrix!).

 In summary, if a specific index is not specified for a dimension, TTree::Draw
 will loop through all the indices along this dimension.  Leaving off the
 last (right most) dimension of specifying then with the two characters '[]'
 is equivalent.  For variable size arrays (and TClonesArray) the range
 of the first dimension is recalculated for each entry of the tree.

 TTree::Draw also now properly handling operations involving 2 or more arrays.

 Let assume a second matrix fResults[5][2], here are a sample of some
 of the possible combinations, the number of elements they produce and
 the loop used:

  expression                       element(s)  Loop

  "fMatrix[2][1] - fResults[5][2]"   one     no loop
  "fMatrix[2][]  - fResults[5][2]"   three   on 2nd dim fMatrix
  "fMatrix[2][]  - fResults[5][]"    two     on both 2nd dimensions
  "fMatrix[][2]  - fResults[][1]"    three   on both 1st dimensions
  "fMatrix[][2]  - fResults[][]"     six     on both 1st and 2nd dimensions of
                                             fResults
  "fMatrix[][2]  - fResults[3][]"    two     on 1st dim of fMatrix and 2nd of
                                             fResults (at the same time)
  "fMatrix[][]   - fResults[][]"     six     on 1st dim then on  2nd dim


 In summary, TTree::Draw loops through all un-specified dimensions.  To
 figure out the range of each loop, we match each unspecified dimension
 from left to right (ignoring ALL dimensions for which an index has been
 specified), in the equivalent loop matched dimensions use the same index
 and are restricted to the smallest range (of only the matched dimensions).
 When involving variable arrays, the range can of course be different
 for each entry of the tree.

 So the loop equivalent to "fMatrix[][2] - fResults[3][]" is:

    for (Int_t i0; i < min(3,2); i++) {
       use the value of (fMatrix[i0][2] - fMatrix[3][i0])
    }

 So the loop equivalent to "fMatrix[][2] - fResults[][]" is:

    for (Int_t i0; i < min(3,5); i++) {
       for (Int_t i1; i1 < 2; i1++) {
          use the value of (fMatrix[i0][2] - fMatrix[i0][i1])
       }
    }

 So the loop equivalent to "fMatrix[][] - fResults[][]" is:

    for (Int_t i0; i < min(3,5); i++) {
       for (Int_t i1; i1 < min(3,2); i1++) {
          use the value of (fMatrix[i0][i1] - fMatrix[i0][i1])
       }
    }

     Retrieving the result of Draw


  By default the temporary histogram created is called "htemp", but only in
  the one dimensional Draw("e1") it contains the TTree's data points. For
  a two dimensional Draw, the data is filled into a TGraph which is named
  "Graph". They can be retrieved by calling
    TH1F *htemp = (TH1F*)gPad->GetPrimitive("htemp"); // 1D
    TGraph *graph = (TGraph*)gPad->GetPrimitive("Graph"); // 2D

  For a three and four dimensional Draw the TPloyMarker3D is unnamed, and
  cannot be retrieved.

  gPad always contains a TH1 derived object called "htemp" which allows to
  access the axes:
    TGraph *graph = (TGraph*)gPad->GetPrimitive("Graph"); // 2D
    TH2F   *htemp = (TH2F*)gPad->GetPrimitive("htemp"); // empty, but has axes
    TAxis  *xaxis = htemp->GetXaxis();

     Saving the result of Draw to an histogram


  If varexp0 contains >>hnew (following the variable(s) name(s),
  the new histogram created is called hnew and it is kept in the current
  directory (and also the current pad). This works for all dimensions.
  Example:
    tree.Draw("sqrt(x)>>hsqrt","y>0")
    will draw sqrt(x) and save the histogram as "hsqrt" in the current
    directory.  To retrieve it do:
    TH1F *hsqrt = (TH1F*)gDirectory->Get("hsqrt");

  The binning information is taken from the environment variables

     Hist.Binning.?D.?

  In addition, the name of the histogram can be followed by up to 9
  numbers between '(' and ')', where the numbers describe the
  following:

   1 - bins in x-direction
   2 - lower limit in x-direction
   3 - upper limit in x-direction
   4-6 same for y-direction
   7-9 same for z-direction

   When a new binning is used the new value will become the default.
   Values can be skipped.
  Example:
    tree.Draw("sqrt(x)>>hsqrt(500,10,20)")
          // plot sqrt(x) between 10 and 20 using 500 bins
    tree.Draw("sqrt(x):sin(y)>>hsqrt(100,10,60,50,.1,.5)")
          // plot sqrt(x) against sin(y)
          // 100 bins in x-direction; lower limit on x-axis is 10; upper limit is 60
          //  50 bins in y-direction; lower limit on y-axis is .1; upper limit is .5

  By default, the specified histogram is reset.
  To continue to append data to an existing histogram, use "+" in front
  of the histogram name.
  A '+' in front of the histogram name is ignored, when the name is followed by
  binning information as described in the previous paragraph.
    tree.Draw("sqrt(x)>>+hsqrt","y>0")
      will not reset hsqrt, but will continue filling.
  This works for 1-D, 2-D and 3-D histograms.

     Accessing collection objects


  TTree::Draw default's handling of collections is to assume that any
  request on a collection pertain to it content.  For example, if fTracks
  is a collection of Track objects, the following:
      tree->Draw("event.fTracks.fPx");
  will plot the value of fPx for each Track objects inside the collection.
  Also
     tree->Draw("event.fTracks.size()");
  would plot the result of the member function Track::size() for each
  Track object inside the collection.
  To access information about the collection itself, TTree::Draw support
  the '@' notation.  If a variable which points to a collection is prefixed
  or postfixed with '@', the next part of the expression will pertain to
  the collection object.  For example:
     tree->Draw("event.@fTracks.size()");
  will plot the size of the collection refered to by fTracks (i.e the number
  of Track objects).

     Drawing 'objects'


  When a class has a member function named AsDouble or AsString, requesting
  to directly draw the object will imply a call to one of the 2 functions.
  If both AsDouble and AsString are present, AsDouble will be used.
  AsString can return either a char*, a std::string or a TString.s
  For example, the following
     tree->Draw("event.myTTimeStamp");
  will draw the same histogram as
     tree->Draw("event.myTTimeStamp.AsDouble()");
  In addition, when the object is a type TString or std::string, TTree::Draw
  will call respectively TString::Data and std::string::c_str()

  If the object is a TBits, the histogram will contain the index of the bit
  that are turned on.

     Retrieving  information about the tree itself.


  You can refer to the tree (or chain) containing the data by using the
  string 'This'.
  You can then could any TTree methods.  For example:
     tree->Draw("This->GetReadEntry()");
  will display the local entry numbers be read.
     tree->Draw("This->GetUserInfo()->At(0)->GetName()");
  will display the name of the first 'user info' object.

     Special functions and variables


  Entry$:  A TTree::Draw formula can use the special variable Entry$
  to access the entry number being read.  For example to draw every
  other entry use:
    tree.Draw("myvar","Entry$%2==0");

  Entry$      : return the current entry number (== TTree::GetReadEntry())
  LocalEntry$ : return the current entry number in the current tree of a
                chain (== GetTree()->GetReadEntry())
  Entries$    : return the total number of entries (== TTree::GetEntries())
  Length$     : return the total number of element of this formula for this
                 entry (==TTreeFormula::GetNdata())
  Iteration$: return the current iteration over this formula for this
                 entry (i.e. varies from 0 to Length$).

  Length$(formula): return the total number of element of the formula given as a
                    parameter.
  Sum$(formula): return the sum of the value of the elements of the formula given
                    as a parameter.  For example the mean for all the elements in
                    one entry can be calculated with:
                Sum$(formula)/Length$(formula)
  Min$(formula): return the minimun (within one TTree entry) of the value of the
                    elements of the formula given as a parameter.
  Max$(formula): return the maximum (within one TTree entry) of the value of the
                    elements of the formula given as a parameter.
  MinIf$(formula,condition)
  MaxIf$(formula,condition): return the minimum (maximum) (within one TTree entry)
                    of the value of the elements of the formula given as a parameter
                    if they match the condition. If not element match the condition, the result is zero.  To avoid the
                    the result is zero.  To avoid the consequent peak a zero, use the
                    pattern:
    tree->Draw("MinIf$(formula,condition)","condition");
                    which will avoid calculation MinIf$ for the entries that have no match
                    for the condition.

  Alt$(primary,alternate) : return the value of "primary" if it is available
                 for the current iteration otherwise return the value of "alternate".
                 For example, with arr1[3] and arr2[2]
    tree->Draw("arr1+Alt$(arr2,0)");
                 will draw arr1[0]+arr2[0] ; arr1[1]+arr2[1] and arr1[2]+0
                 Or with a variable size array arr3
    tree->Draw("Alt$(arr3[0],0)+Alt$(arr3[1],0)+Alt$(arr3[2],0)");
                 will draw the sum arr3 for the index 0 to min(2,actual_size_of_arr3-1)
                 As a comparison
    tree->Draw("arr3[0]+arr3[1]+arr3[2]");
                 will draw the sum arr3 for the index 0 to 2 only if the
                 actual_size_of_arr3 is greater or equal to 3.
                 Note that the array in 'primary' is flatened/linearilized thus using
                 Alt$ with multi-dimensional arrays of different dimensions in unlikely
                 to yield the expected results.  To visualize a bit more what elements
                 would be matched by TTree::Draw, TTree::Scan can be used:
    tree->Scan("arr1:Alt$(arr2,0)");
                 will print on one line the value of arr1 and (arr2,0) that will be
                 matched by
    tree->Draw("arr1-Alt$(arr2,0)");

  The ternary operator is not directly support in TTree::Draw however, to plot the
  equivalent of 'var2<20 ? -99 : var1', you can use:
     tree->Draw("(var2<20)*99+(var2>=20)*var1","");

     Drawing a user function accessing the TTree data directly


  If the formula contains  a file name, TTree::MakeProxy will be used
  to load and execute this file.   In particular it will draw the
  result of a function with the same name as the file.  The function
  will be executed in a context where the name of the branches can
  be used as a C++ variable.

  For example draw px using the file hsimple.root (generated by the
  hsimple.C tutorial), we need a file named hsimple.cxx:

     double hsimple() {
        return px;
     }

  MakeProxy can then be used indirectly via the TTree::Draw interface
  as follow:
     new TFile("hsimple.root")
     ntuple->Draw("hsimple.cxx");

  A more complete example is available in the tutorials directory:
    h1analysisProxy.cxx , h1analysProxy.h and h1analysisProxyCut.C
  which reimplement the selector found in h1analysis.C

  The main features of this facility are:

    * on-demand loading of branches
    * ability to use the 'branchname' as if it was a data member
    * protection against array out-of-bound
    * ability to use the branch data as object (when the user code is available)

  See TTree::MakeProxy for more details.

     Making a Profile histogram

  In case of a 2-Dim expression, one can generate a TProfile histogram
  instead of a TH2F histogram by specyfying option=prof or option=profs.
  The option=prof is automatically selected in case of y:x>>pf
  where pf is an existing TProfile histogram.

     Making a parallel coordinates plot.

  In case of a 2-Dim or more expression with the option=para, one can generate
  a parallel coordinates plot. With that option, the number of dimensions is
  arbitrary. Giving more than 4 variables without the option=para or
  option=candle or option=goff will produce an error.

     Making a candle sticks chart.

  In case of a 2-Dim or more expression with the option=candle, one can generate
  a candle sticks chart. With that option, the number of dimensions is
  arbitrary. Giving more than 4 variables without the option=para or
  option=candle or option=goff will produce an error.

     Saving the result of Draw to a TEventList or a TEntryList

  TTree::Draw can be used to fill a TEventList object (list of entry numbers)
  instead of histogramming one variable.
  If varexp0 has the form >>elist , a TEventList object named "elist"
  is created in the current directory. elist will contain the list
  of entry numbers satisfying the current selection.
  If option "entrylist" is used, a TEntryList object is created
  Example:
    tree.Draw(">>yplus","y>0")
    will create a TEventList object named "yplus" in the current directory.
    In an interactive session, one can type (after TTree::Draw)
       yplus.Print("all")
    to print the list of entry numbers in the list.
    tree.Draw(">>yplus", "y>0", "entrylist")
    will create a TEntryList object names "yplus" in the current directory

  By default, the specified entry list is reset.
  To continue to append data to an existing list, use "+" in front
  of the list name;
    tree.Draw(">>+yplus","y>0")
      will not reset yplus, but will enter the selected entries at the end
      of the existing list.

      Using a TEventList or a TEntryList as Input

  Once a TEventList or a TEntryList object has been generated, it can be used as input
  for TTree::Draw. Use TTree::SetEventList or TTree::SetEntryList to set the
  current event list
  Example1:
     TEventList *elist = (TEventList*)gDirectory->Get("yplus");
     tree->SetEventList(elist);
     tree->Draw("py");
  Example2:
     TEntryList *elist = (TEntryList*)gDirectory->Get("yplus");
     tree->SetEntryList(elist);
     tree->Draw("py");
  If a TEventList object is used as input, a new TEntryList object is created
  inside the SetEventList function. In case of a TChain, all tree headers are loaded
  for this transformation. This new object is owned by the chain and is deleted
  with it, unless the user extracts it by calling GetEntryList() function.
  See also comments to SetEventList() function of TTree and TChain.

  If arrays are used in the selection critera, the entry entered in the
  list are all the entries that have at least one element of the array that
  satisfy the selection.
  Example:
      tree.Draw(">>pyplus","fTracks.fPy>0");
      tree->SetEventList(pyplus);
      tree->Draw("fTracks.fPy");
  will draw the fPy of ALL tracks in event with at least one track with
  a positive fPy.

  To select only the elements that did match the original selection
  use TEventList::SetReapplyCut or TEntryList::SetReapplyCut.
  Example:
      tree.Draw(">>pyplus","fTracks.fPy>0");
      pyplus->SetReapplyCut(kTRUE);
      tree->SetEventList(pyplus);
      tree->Draw("fTracks.fPy");
  will draw the fPy of only the tracks that have a positive fPy.

  Note: Use tree->SetEventList(0) if you do not want use the list as input.

      How to obtain more info from TTree::Draw


  Once TTree::Draw has been called, it is possible to access useful
  information still stored in the TTree object via the following functions:
    -GetSelectedRows()    // return the number of entries accepted by the
                          //selection expression. In case where no selection
                          //was specified, returns the number of entries processed.
    -GetV1()              //returns a pointer to the double array of V1
    -GetV2()              //returns a pointer to the double array of V2
    -GetV3()              //returns a pointer to the double array of V3
    -GetW()               //returns a pointer to the double array of Weights
                          //where weight equal the result of the selection expression.
   where V1,V2,V3 correspond to the expressions in
   TTree::Draw("V1:V2:V3",selection);

   Example:
    Root > ntuple->Draw("py:px","pz>4");
    Root > TGraph *gr = new TGraph(ntuple->GetSelectedRows(),
                                   ntuple->GetV2(), ntuple->GetV1());
    Root > gr->Draw("ap"); //draw graph in current pad
    creates a TGraph object with a number of points corresponding to the
    number of entries selected by the expression "pz>4", the x points of the graph
    being the px values of the Tree and the y points the py values.

   Important note: By default TTree::Draw creates the arrays obtained
    with GetV1, GetV2, GetV3, GetW with a length corresponding to the
    parameter fEstimate. By default fEstimate=1000000 and can be modified
    via TTree::SetEstimate. A possible recipee is to do
       tree->SetEstimate(tree->GetEntries());
    You must call SetEstimate if the expected number of selected rows
    is greater than 1000000.

    You can use the option "goff" to turn off the graphics output
    of TTree::Draw in the above example.

           Automatic interface to TTree::Draw via the TTreeViewer


    A complete graphical interface to this function is implemented
    in the class TTreeViewer.
    To start the TTreeViewer, three possibilities:
       - select TTree context menu item "StartViewer"
       - type the command  "TTreeViewer TV(treeName)"
       - execute statement "tree->StartViewer();"

-- SeoKonKang - 20 Apr 2010