TFoam

class TFoam : public TObject

    private:

      Double_t Sqr(Double_t x) const

    public:

                      TFoam()
                      TFoam(const Char_t*)
                      TFoam(const TFoam&)
              virtual ~TFoam()
                 void Carver(Int_t&, Double_t&, Double_t&)
                Int_t CellFill(Int_t, TFoamCell*)
                 void CheckAll(Int_t)
       static TClass* Class()
                Int_t Divide(TFoamCell*)
             Double_t Eval(Double_t*)
                 void Explore(TFoamCell* Cell)
                 void Finalize(Double_t&, Double_t&)
                 void GenerCel2(TFoamCell*&)
                 void GetIntegMC(Double_t&, Double_t&)
                 void GetIntNorm(Double_t&, Double_t&)
                 void GetMCvect(Double_t*)
                 void GetMCwt(Double_t&)
             Double_t GetMCwt()
               Long_t GetnCalls() const
               Long_t GetnEffev() const
             Double_t GetPrimary() const
                 void GetPrimary(Double_t& prime)
             TRandom* GetPseRan() const
      TFoamIntegrand* GetRho()
                Int_t GetTotDim() const
          const char* GetVersion() const
                 void GetWtParams(Double_t, Double_t&, Double_t&, Double_t&)
                 void Grow()
                 void InitCells()
                 void Initialize()
                 void Initialize(TRandom*, TFoamIntegrand*)
      virtual TClass* IsA() const
                 void LinkCells()
                 void MakeActiveList()
                 void MakeAlpha()
                 void MakeEvent()
             Double_t MCgenerate(Double_t* MCvect)
               TFoam& operator=(const TFoam&)
               Long_t PeekMax()
                 void PrintCells()
                 void ResetPseRan(TRandom* PseRan)
                 void ResetRho(TFoamIntegrand* Rho)
                 void RootPlot2dim(Char_t*)
                 void SetChat(Int_t Chat)
                 void SetEvPerBin(Int_t EvPerBin)
                 void SetInhiDiv(Int_t, Int_t)
                 void SetkDim(Int_t kDim)
                 void SetMaxWtRej(Double_t MaxWtRej)
                 void SetnBin(Int_t nBin)
                 void SetnCells(Long_t nCells)
                 void SetnSampl(Long_t nSampl)
                 void SetOptDrive(Int_t OptDrive)
                 void SetOptRej(Int_t OptRej)
                 void SetPseRan(TRandom* PseRan)
                 void SetRho(TFoamIntegrand* Rho)
                 void SetRhoInt(void* Rho)
                 void SetXdivPRD(Int_t, Int_t, Double_t*)
         virtual void ShowMembers(TMemberInspector& insp, char* parent)
         virtual void Streamer(TBuffer& b)
                 void StreamerNVirtual(TBuffer& b)
                 void Varedu(Double_t*, Int_t&, Double_t&, Double_t&)

Data Members

    private:

              TString fName        Name of a given instance of the FOAM class
              TString fVersion     Actual version of the FOAM like (1.01m)
              TString fDate        Release date of FOAM
                Int_t fDim         Dimension of the integration/simulation space
                Int_t fNCells      Maximum number of cells
                Int_t fRNmax       Maximum No. of the rand. numb. requested at once
                Int_t fOptDrive    Optimization switch =1,2 for variance or maximum weight optimization
                Int_t fChat        Chat=0,1,2 chat level in output, Chat=1 normal level
                Int_t fOptRej      Switch =0 for weighted events; =1 for unweighted events in MC
                Int_t fNBin        No. of bins in the edge histogram for cell MC exploration
                Int_t fNSampl      No. of MC events, when dividing (exploring) cell
                Int_t fEvPerBin    Maximum number of effective (wt=1) events per bin
               Int_t* fMaskDiv     ! [fDim] Dynamic Mask for  cell division
               Int_t* fInhiDiv     ! [fDim] Flags for inhibiting cell division
                Int_t fOptPRD      Option switch for predefined division, for quick check
          TFoamVect** fXdivPRD     ! Lists of division values encoded in one vector per direction
                Int_t fNoAct       Number of active cells
                Int_t fLastCe      Index of the last cell
          TFoamCell** fCells       [fNCells] Array of ALL cells
          TFoamMaxwt* fMCMonit     Monitor of the MC weight for measuring MC efficiency
             Double_t fMaxWtRej    Maximum weight in rejection for getting wt=1 events
           TRefArray* fCellsAct    Array of pointers to active cells, constructed at the end of foam build-up
            Double_t* fPrimAcu     [fNoAct] Array of cumulative probability of all active cells
           TObjArray* fHistEdg     Histograms of wt, one for each cell edge
           TObjArray* fHistDbg     Histograms of wt, for debug
                TH1D* fHistWt      Histogram of the MC wt
            Double_t* fMCvect      [fDim] Generated MC vector for the outside user
             Double_t fMCwt        MC weight
            Double_t* fRvec        [fRNmax] random number vector from r.n. generator fDim+1 maximum elements
      TFoamIntegrand* fRho         Pointer to the user-defined integrand function/distribution
         TMethodCall* fMethodCall  ! ROOT's pointer to user-defined global distribution function
             TRandom* fPseRan      Pointer to user-defined generator of pseudorandom numbers
               Long_t fNCalls      Total number of the function calls
               Long_t fNEffev      Total number of effective events (wt=1) in the foam buildup
             Double_t fSumWt       
             Double_t fSumWt2      Total sum of wt and wt^2
             Double_t fSumOve      Total Sum of overveighted events
             Double_t fNevGen      Total number of the generated MC events
             Double_t fWtMax       
             Double_t fWtMin       Maximum/Minimum MC weight
             Double_t fPrime       Primary integral R' (R=R'<wt>)
             Double_t fMCresult    True Integral R from MC series
             Double_t fMCerror     and its error
            Double_t* fAlpha       [fDim] Internal parameters of the hyperrectangle

Class Description

 FOAM  Version 1.02M
 ===================
 Authors:
   S. Jadach and P.Sawicki
   Institute of Nuclear Physics, Cracow, Poland
   Stanislaw. Jadach@ifj.edu.pl, Pawel.Sawicki@ifj.edu.pl

 What is FOAM for?
 =================
 * Suppose you want to generate randomly points (vectors) according to
   an arbitrary probability distribution  in n dimensions,
   for which you supply your own subprogram. FOAM can do it for you!
   Even if your distributions has quite strong peaks and is discontinuous!
 * FOAM generates random points with weight one or with variable weight.
 * FOAM is capable to integrate using efficient "adaptive" MC method.
   (The distribution does not need to be normalized to one.)
 How does it work?
 =================
 FOAM is the simplified version of the multi-dimensional general purpose
 Monte Carlo event generator (integrator) FOAM.
 It creates hyper-rectangular "foam of cells", which is more dense around its peaks.
 See the following 2-dim. example of the map of 1000 cells for doubly peaked distribution:

 FOAM is now fully integrated with the ROOT package.
 The important bonus of the ROOT use is persistency of the FOAM objects!

 For more sophisticated problems full version of FOAM may be more appropriate:

 Simple example of the use of FOAM:
 ==================================
 Int_t kanwa(){
   gSystem->Load("libFoam.so");
   TH2D  *hst_xy = new TH2D("hst_xy" ,  "x-y plot", 50,0,1.0, 50,0,1.0);
   Double_t *MCvect =new Double_t[2]; // 2-dim vector generated in the MC run
   TRandom3  *PseRan   = new TRandom3();  // Create random number generator
   PseRan->SetSeed(4357);                // Set seed
   TFoam   *FoamX    = new TFoam("FoamX");   // Create Simulator
   FoamX->SetkDim(2);          // No. of dimensions, obligatory!
   FoamX->SetnCells(500);      // No. of cells, can be omitted, default=2000
   FoamX->SetRhoInt(Camel2);   // Set 2-dim distribution, included below
   FoamX->SetPseRan(PseRan);   // Set random number generator
   FoamX->Initialize();        // Initialize simulator, takes a few seconds...
   // From now on FoamX is ready to generate events according to Camel2(x,y)
   for(Long_t loop=0; loop<100000; loop++){
     FoamX->MakeEvent();          // generate MC event
     FoamX->GetMCvect( MCvect);   // get generated vector (x,y)
     Double_t x=MCvect[0];
     Double_t y=MCvect[1];
     if(loop<10) cout<<"(x,y) =  ( "<< x <<", "<< y <<" )"<<endl;
     hst_xy->Fill(x,y);           // fill scattergram
   }// loop
   Double_t mcResult, mcError;
   FoamX->GetIntegMC( mcResult, mcError);  // get MC integral, should be one
   cout << " mcResult= " << mcResult << " +- " << mcError <<endl;
   // now hst_xy will be plotted visualizing generated distribution
   TCanvas *cKanwa = new TCanvas("cKanwa","Canvas for plotting",600,600);
   cKanwa->cd();
   hst_xy->Draw("lego2");
 }//kanwa
 Double_t sqr(Double_t x){return x*x;};
 Double_t Camel2(Int_t nDim, Double_t *Xarg){
 // 2-dimensional distribution for FOAM, normalized to one (within 1e-5)
   Double_t x=Xarg[0];
   Double_t y=Xarg[1];
   Double_t GamSq= sqr(0.100e0);
   Double_t Dist=exp(-(sqr(x-1./3) +sqr(y-1./3))/GamSq)/GamSq/TMath::Pi();
   Dist        +=exp(-(sqr(x-2./3) +sqr(y-2./3))/GamSq)/GamSq/TMath::Pi();
   return 0.5*Dist;
 }// Camel2
 Two-dim. histogram of the MC points generated with the above program looks as follows:

 Canonical nine steering parameters of FOAM
 ===========================================
------------------------------------------------------------------------------
  Name     | default  | Description
------------------------------------------------------------------------------
  kDim     | 0        | Dimension of the integration space. Must be redefined!
  nCells   | 1000     | No of allocated number of cells,
  nSampl   | 200      | No. of MC events in the cell MC exploration
  nBin     | 8        | No. of bins in edge-histogram in cell exploration
  OptRej   | 1        | OptRej = 0, weighted; OptRej=1, wt=1 MC events
  OptDrive | 2        | Maximum weight reduction, =1 for variance reduction
  EvPerBin | 25       | Maximum number of the effective wt=1 events/bin,
           |          | EvPerBin=0 deactivates this option
  Chat     | 1        | =0,1,2 is the ``chat level'' in the standard output
  MaxWtRej | 1.1      | Maximum weight used to get w=1 MC events
------------------------------------------------------------------------------
 The above can be redefined before calling 'Initialize()' method,
 for instance FoamObject->SetkDim(15) sets dimension of the distribution to 15.
 Only kDim HAS TO BE redefined, the other parameters may be left at their defaults.
 nCell may be increased up to about million cells for wildly peaked distributions.
 Increasing nSampl sometimes helps, but it may cost CPU time.
 MaxWtRej may need to be increased for wild a distribution, while using OptRej=0.

 --------------------------------------------------------------------
 Past versions of FOAM: August 2003, v.1.00; September 2003 v.1.01
 Adopted starting from FOAM-2.06 by P. Sawicki
 --------------------------------------------------------------------
 Users of FOAM are kindly requested to cite the following work:
 S. Jadach, Computer Physics Communications 152 (2003) 55.

______________________________________________________________________________

 Default constructor for streamer, user should not use it.

 User constructor, to be employed by the user

 Default destructor
  cout<<" DESTRUCTOR entered "<<endl;

 Copy Constructor  NOT IMPLEMENTED (NEVER USED)

 Basic initialization of FOAM invoked by the user. Mandatory!
 ============================================================
 This method starts the process of the cell build-up.
 User must invoke Initialize with two arguments or Initialize without arguments.
 This is done BEFORE generating first MC event and AFTER allocating FOAM object
 and reseting (optionally) its internal parameters/switches.
 The overall operational scheme of the FOAM is the following:

 This method invokes several other methods:
 ==========================================
 InitCells initializes memory storage for cells and begins exploration process
 from the root cell. The empty cells are allocated/filled using  CellFill.
 The procedure Grow which loops over cells, picks up the cell with the biggest
 ``driver integral'', see Comp. Phys. Commun. 152 152 (2003) 55 for explanations,
 with the help of PeekMax procedure. The chosen cell is split using Divide.
 Subsequently, the procedure Explore called by the Divide
 (and by InitCells for the root cell) does the most important
 job in the FOAM object build-up: it performs a small MC run for each
 newly allocated daughter cell.
 Explore calculates how profitable the future split of the cell will be
 and defines the optimal cell division geometry with the help of Carver or Varedu
 procedures, for maximum weight or variance optimization respectively.
 All essential results of the exploration are written into
 the explored cell object. At the very end of the foam build-up,
 Finally, MakeActiveList is invoked to create a list of pointers to
 all active cells, for the purpose of the quick access during the MC generation.
 The procedure Explore employs MakeAlpha to generate random coordinates
 inside a given cell with the uniform distribution.
 The above sequence of the procedure calls is depicted in the following figure:

 Basic initialization of FOAM invoked by the user.
 IMPORTANT: Random number generator and the distribution object has to be
 provided using SetPseRan and SetRho prior to invoking this initializator!

 Internal subprogram used by Initialize.
 It initializes "root part" of the FOAM of the tree of cells.

 Internal subprogram used by Initialize.
 It initializes content of the newly allocated active cell.

 Internal subprogram used by Initialize.
 It explores newly defined cell with help of special short MC sampling.
 As a result, estimates of true and drive volume is defined/determined
 Average and dispersion of the weight distribution will is found along
 each edge and the best edge (minimum dispersion, best maximum weight)
 is memorized for future use.
 The optimal division point for eventual future cell division is
 determined/recorded. Recorded are also minimum and maximum weight etc.
 The volume estimate in all (inactive) parent cells is updated.
 Note that links to parents and initial volume = 1/2 parent has to be
 already defined prior to calling this routine.

 Internal subrogram used by Initialize.
 In determines the best edge candidate and the position of the cell division plane
 in case of the variance reduction for future cell division,
 using results of the MC exploration run stored in fHistEdg

 Internal subrogram used by Initialize.
 Determines the best edge-candidate and the position of the division plane
 for the future cell division, in the case of the optimization of the maximum weight.
 It exploits results of the cell MC exploration run stored in fHistEdg.

 Internal subrogram used by Initialize.
 Provides random vector Alpha  0< Alpha(i) < 1

 Internal subrogram used by Initialize.
 It grow new cells by the binary division process.

 Internal subprogram used by Initialize.
 It finds cell with maximal driver integral for the purpose of the division.

 Internal subrogram used by Initialize.
 It divides cell iCell into two daughter cells.
 The iCell is retained and tagged as inactive, daughter cells are appended
 at the end of the buffer.
 New vertex is added to list of vertices.
 List of active cells is updated, iCell removed, two daughters added
 and their properties set with help of MC sampling (TFoam_Explore)
 Returns Code RC=-1 of buffer limit is reached,  fLastCe=fnBuf.

 Internal subrogram used by Initialize.
 It finds out number of active cells fNoAct,
 creates list of active cell fCellsAct and primary cumulative fPrimAcu.
 They are used during the MC generation to choose randomly an active cell.

 User may optionally reset random number generator using this method
 Usually it is done when FOAM object is restored from the disk.
 IMPORTANT: this method deletes existing  random number generator registered in the FOAM object.
 In particular such an object is created by the streamer during the disk-read operation.

 User may use this method to set (register) random number generator used by
 the given instance of the FOAM event generator. Note that single r.n. generator
 may serve several FOAM objects.

 User may optionally reset the distribution using this method
 Usually it is done when FOAM object is restored from the disk.
 IMPORTANT: this method deletes existing  distribution object registered in the FOAM object.
 In particular such an object is created by the streamer diring the disk-read operation.
 This method is used only in very special cases, because the distribution in most cases
 should be "owned" by the FOAM object and should not be replaced by another one after initialization.

 User may use this to set pointer to the global function (not descending
 from TFoamIntegrand) serving as a distribution for FOAM.
 It is useful for simple interactive applications.
 Note that persistency for FOAM object will not work in the case of such
 a distribution.

 Internal subprogram.
 Evaluates distribution to be generated.

 Internal subprogram.
 Return randomly chosen active cell with probability equal to its
 contribution into total driver integral using interpolation search.

 User subprogram.
 It generates randomly point/vector according to user-defined distribution.
 Prior initialization with help of Initialize() is mandatory.
 Generated MC point/vector is available using GetMCvect and the MC weight with GetMCwt.
 MC point is generated with wt=1 or with variable weight, see OptRej switch.

 User may get generated MC point/vector with help of this method

 User may get weight MC weight using this method

 User may get weight MC weight using this method

 User subprogram which generates MC event and returns MC weight

 User subprogram.
 It provides the value of the integral calculated from the averages of the MC run
 May be called after (or during) the MC run.

 User subprogram.
 It returns NORMALIZATION integral to be combined with the average weights
 and content of the histograms in order to get proper absolute normalization
 of the integrand and distributions.
 It can be called after initialization, before or during the MC run.

 May be called optionally after the MC run.
 Returns various parameters of the MC weight for efficiency evaluation

 May be called optionally by the user after the MC run.
 It provides normalization and also prints some information/statistics on the MC run.

 This can be called before Initialize, after setting kDim
 It defines which variables are excluded in the process of the cell division.
 For example 'FoamX->SetInhiDiv(1, 1);' inhibits division of y-variable.
 The resulting map of cells in 2-dim. case will look as follows:

 This should be called before Initialize, after setting  kDim
 It predefines values of the cell division for certain variable iDim.
 For example setting 3 predefined division lines using:
     xDiv[0]=0.30; xDiv[1]=0.40; xDiv[2]=0.65;
     FoamX->SetXdivPRD(0,3,xDiv);
 results in the following 2-dim. pattern of the cells:

  User utility, miscellaneous and debug.
  Checks all pointers in the tree of cells. This is useful autodiagnostic.
  level=0, no printout, failures causes STOP
  level=1, printout, failures lead to WARNINGS only

 Prints geometry of ALL cells of the FOAM

 Debugging tool which plots 2-dimensional cells as rectangles
 in C++ format readable for root

 Void function for backward compatibility

Inline Functions

        TFoamIntegrand* GetRho()
               TRandom* GetPseRan() const
                   void SetPseRan(TRandom* PseRan)
                   void SetkDim(Int_t kDim)
                   void SetnCells(Long_t nCells)
                   void SetnSampl(Long_t nSampl)
                   void SetnBin(Int_t nBin)
                   void SetChat(Int_t Chat)
                   void SetOptRej(Int_t OptRej)
                   void SetOptDrive(Int_t OptDrive)
                   void SetEvPerBin(Int_t EvPerBin)
                   void SetMaxWtRej(Double_t MaxWtRej)
            const char* GetVersion() const
                  Int_t GetTotDim() const
               Double_t GetPrimary() const
                   void GetPrimary(Double_t& prime)
                 Long_t GetnCalls() const
                 Long_t GetnEffev() const
               Double_t Sqr(Double_t x) const
                TClass* Class()
                TClass* IsA() const
                   void ShowMembers(TMemberInspector& insp, char* parent)
                   void Streamer(TBuffer& b)
                   void StreamerNVirtual(TBuffer& b)
                 TFoam& operator=(const TFoam&)