library: libFoam #include "TFoam.h"

# TFoam

class description - source file - inheritance tree (.pdf)

## class TFoam : public TObject

| Inheritance Chart:
`TObject`
| <- | `TFoam` |

        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:

See full version of FOAM

     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.

    ______________________________________________________________________________

TFoam()

     Default constructor for streamer, user should not use it.

TFoam(const Char_t* Name)

     User constructor, to be employed by the user

~TFoam()

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

TFoam(const TFoam &From): TObject(From)

     Copy Constructor  NOT IMPLEMENTED (NEVER USED)

void Initialize(TRandom *PseRan, TFoamIntegrand *fun )

     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:

void Initialize()

     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!

void InitCells()

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

Int_t CellFill(Int_t Status, TFoamCell *Parent)

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

void Explore(TFoamCell *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.

void Varedu(Double_t CeSum[5], Int_t &kBest, Double_t &xBest, Double_t &yBest)

     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

void Carver(Int_t &kBest, Double_t &xBest, Double_t &yBest)

     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.

void MakeAlpha()

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

void Grow()

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

Long_t PeekMax()

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

Int_t Divide(TFoamCell *Cell)

     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.

void MakeActiveList()

     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.

void ResetPseRan(TRandom *PseRan)

     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.

void SetRho(TFoamIntegrand *fun)

     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.

void ResetRho(TFoamIntegrand *fun)

     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.

void SetRhoInt(void *fun)

     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.

Double_t Eval(Double_t *xRand)

     Internal subprogram.
     Evaluates distribution to be generated.

void GenerCel2(TFoamCell *&pCell)

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

void MakeEvent(void)

     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.

void GetMCvect(Double_t *MCvect)

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

Double_t GetMCwt(void)

     User may get weight MC weight using this method

void GetMCwt(Double_t &MCwt)

     User may get weight MC weight using this method

Double_t MCgenerate(Double_t *MCvect)

     User subprogram which generates MC event and returns MC weight

void GetIntegMC(Double_t &MCresult, Double_t &MCerror)

     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.

void GetIntNorm(Double_t& IntNorm, Double_t& Errel )

     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.

void GetWtParams(Double_t eps, Double_t &AveWt, Double_t &WtMax, Double_t &Sigma)

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

void Finalize(Double_t& IntNorm, Double_t& Errel)

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

void SetInhiDiv(Int_t iDim, Int_t InhiDiv)

     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:

void SetXdivPRD(Int_t iDim, Int_t len, Double_t xDiv[])

     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:

void CheckAll(Int_t level)

      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

void PrintCells(void)

     Prints geometry of ALL cells of the FOAM

void RootPlot2dim(Char_t *filename)

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

void LinkCells()

     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&)

Author: S. Jadach, P.Sawicki
Last update: root/foam:$Name: $:$Id: TFoam.cxx,v 1.11 2005/05/18 12:31:08 brun Exp $