BrStatistics

class description - source file - inheritance tree

class BrStatistics : public TObject


    public:

                BrStatistics BrStatistics()
                BrStatistics BrStatistics(Int_t dimension, Bool_t storeData = kFALSE, Int_t size = 100)
                BrStatistics BrStatistics(BrStatistics&)
                virtual void ~BrStatistics()
                 static void AddPoint(Double_t data, UInt_t n, Double_t& average, Double_t& sqvar)
                virtual void AddRow(Double_t* row)
                virtual void Browse(TBrowser* b)
              static TClass* Class()
                 static void CombineSamples(UInt_t n1, Double_t m1, Double_t s1, UInt_t n2, Double_t m2, Double_t s2, Double_t& m, Double_t& s)
                virtual void Draw(Option_t* option)
            virtual Double_t GetAverage(Int_t i) const
      virtual const TArrayD& GetAverageArray() const
            virtual Double_t GetCorrelation(Int_t i, Int_t j) const
            virtual Double_t GetCovariance(Int_t i, Int_t j) const
      virtual const TArrayD& GetCovarianceArray() const
            virtual Double_t GetFluctuation(Int_t i, Int_t j) const
            virtual Double_t GetMax(Int_t i) const
      virtual const TArrayD& GetMaxArray() const
            virtual Double_t GetMin(Int_t i) const
      virtual const TArrayD& GetMinArray() const
           virtual Double_t* GetRow(Int_t i) const
               virtual Int_t GetSampleSize()
            virtual Double_t GetVariance(Int_t i) const
             virtual TClass* IsA() const
              virtual Bool_t IsDataStored() const
                virtual void Print(Option_t* option = "balus") const
                virtual TH1* Project(Int_t i)
                virtual TH1* Project(Int_t i, Int_t j)
                virtual TH1* Project(Int_t i, Int_t j, Int_t k)
                virtual void Set(Int_t n, Bool_t store = kFALSE, Int_t m = 100)
                virtual void ShowMembers(TMemberInspector& insp, char* parent)
                virtual void Streamer(TBuffer& b)
                        void StreamerNVirtual(TBuffer& b)

Data Members

    private:

        Int_t fN           Dimension of sample 
        Int_t fM           Size of sample
      TArrayD fAverage     Average of the sample variables 
      TArrayD fMax         Max of the sample variables 
      TArrayD fMin         Min of the sample variables
      TArrayD fCovariance  Covariance matrix
       Bool_t fDataStored  Store data tuples? 
        Int_t fMmem        Allocated memory 
      TArrayD fData        The sample

Class Description

 Class for low-level statistics



/*


  Given  $M$  input tuples of the form   
  

     $(x$ ₁, ..., x_N)    ,
    
  
  this class will calculate the sample covariance 
  
     $C$ _ij = 1 / M ∑_k^M
      (x_i,k - <x_i>) (x_j,k
      - <x_j>)     ,  
    
  
  and the average (or sample mean) values 
  
     $<x$ _i> = 1 / M ∑_k^M
      x_i,k    , 
    
  
  As well as determind the minimum 
   $x$ _i^min and maximum
   $x$ _i^max of each of
   $N$  variables 
  
     $Forall x$ _i,k in {x_i,1,..., _i,M}
      : x_i^max ≥ x_i,k


      Forall x_i,k in {x_i,1,..., _i,M}
      : x_i^min ≤ x_i,k


    
  


  The algorithms used are the same as in TPrincipal  
  (see the TPrincipal::AddRow
    method), as to minimise rounding errors.  
 

   $N$  can be as large as the underlying OS
  allows (the class contains a  $N×N$ 
  matrix plus 3  $N$  vectors).  The class
  uses double precision variables for optimal precision. 


  This class is usefull to obtains various statistical moments of a
  data sample.  Furhter, the class is persistent.  As far as possible,
  the class methods are inline to improve speed. 


*/

 $Id: BrStatistics.cxx,v 1.7 2002/08/30 20:35:04 videbaek Exp $

BrStatistics()

 Default CTOR, do not use

BrStatistics(Int_t n, Bool_t storeData, Int_t m)

 Create a low-level statistics object for n variables, with
 initial room for m rows.  n must be bigger than 1.  For one
 variable statistics, use the static AddPoint method for
 high-precision statistics.

~BrStatistics()

 Destructor

void CombineSamples(UInt_t n1, Double_t m1, Double_t s1, UInt_t n2, Double_t m2, Double_t s2, Double_t& m, Double_t& s)

 Static method.
 Given the two partial sample of the same stocastic variable, of
 size n1 and n2, with averages m1 and m2, and square variances,
 s1 and s2, calculate the full sample average and square variance,
 and return them in m and s.  The formulas used are:

       n1 * m1 + n2 * m2
   m = -----------------
           n1 + n2

       n1 * s1 + n2 * s2   n1 * n2 * (m1 - m2)^2
   s = ----------------- + ---------------------
           n1 + n2              (n1 + n2)^2

void AddPoint(Double_t data, UInt_t n, Double_t& average, Double_t& sqvar)

 Static method to add a point to a 1D statistics. The arguments
 are:

    data       the n'th data point
    n          number of data point (must be in [1,M])
    average    on input this must be the average after n-1 data
               points. On output this contains the new average
    sqvar      on input this must be the sqyare variance after n-1
               data points. On output this contains the new square
               variance

 The algorithm is the one used in TPrincipal::AddRow.

void AddRow(Double_t* row)

 Add one row (observation) to the statisical sample. Values are
 stored internally. Average, Max, Min, and the covariance matrix
 is calculated on the fly (It actually improves accuary).  See
 also TPrincipal::AddRow.

void Draw(Option_t* option)

 Draw variables as given by option. The form of the option is
   <option> ::= <var list><option list>
 where
   <var list>    ::= <quantity>
                  |  <var number>
                  |  <var number>:<var number>
                  |  <var number>:<var number>:<var number>

   <option list> ::=
                  |  ::<histogram draw option>

   <quantity>    ::= one of A, S, C, L, U

 where <histogram draw option> is any valid histogram option for
 the type of histogram drawn (1D, 2D, or 3D). See TH1::Draw.

 The <quantity>'s corresponds to

    A           Average in each variable (1D)
    S           Spread in each varaible (1D)
    C           Covariance matrix (2D)
    L           Mimimum in each varaible (1D)
    U           Maximum in each variable (1D)
    F           Spread^2 / average in each variable  (1D)
    G           Spread^2 / average^2 in each variable (1D)
    W           Covariance / sqrt(average * average) in each cell (2D)
    X           Covariance / (average * average) in each cell (2D)
    K           Correlation matrix (2D)
    V           Alias for S
    M           Alias for A

Double_t* GetRow(Int_t i) const

 Get a pointer into internal data, starting at row i

TH1* Project(Int_t i)

 Project variable i into a 1D histogram (TH1D).  User
 need to store the histogram immediately

TH1* Project(Int_t i, Int_t j)

 Project variables i and j into a 2D histogram (TH2D).  User need
 to cast the returned histogram to a TH2D pointer. User need to
 store the histogram immediately

TH1* Project(Int_t i, Int_t j, Int_t k)

 Project variables i, j and k into a 3D histogram (TH3D). User
 need to store the histogram immediately

void Print(Option_t* option) const

 Print the statistics
 Options:
    B            Basic information
    A            Average (a.k.a. sample mean)
    L            Minimum
    U            Maximum
    S            Spread
    C            Covariance matrix
    F            Fluctuation matrix
    K            Kovariance matrix
    D            Data
 Default is BALUS

void Set(Int_t n, Bool_t store, Int_t m)

   Set the dimension and initial size of the sample storage, if
   store is true. All arrays are reset

Inline Functions

                  void Browse(TBrowser* b)
                 Int_t GetSampleSize()
              Double_t GetMax(Int_t i) const
        const TArrayD& GetMaxArray() const
              Double_t GetCovariance(Int_t i, Int_t j) const
        const TArrayD& GetCovarianceArray() const
              Double_t GetAverage(Int_t i) const
        const TArrayD& GetAverageArray() const
              Double_t GetMin(Int_t i) const
        const TArrayD& GetMinArray() const
              Double_t GetVariance(Int_t i) const
              Double_t GetFluctuation(Int_t i, Int_t j) const
              Double_t GetCorrelation(Int_t i, Int_t j) const
                Bool_t IsDataStored() const
               TClass* Class()
               TClass* IsA() const
                  void ShowMembers(TMemberInspector& insp, char* parent)
                  void Streamer(TBuffer& b)
                  void StreamerNVirtual(TBuffer& b)
          BrStatistics BrStatistics(BrStatistics&)

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