TF2

class TF2 : public TF1

    public:

                       TF2()
                       TF2(const char* name, const char* formula, Double_t xmin = 0, Double_t xmax = 1, Double_t ymin = 0, Double_t ymax = 1)
                       TF2(const char* name, void* fcn, Double_t xmin = 0, Double_t xmax = 1, Double_t ymin = 0, Double_t ymax = 1, Int_t npar = 0)
                       TF2(const char* name, Double_t (*)(Double_t*, Double_t*) fcn, Double_t xmin = 0, Double_t xmax = 1, Double_t ymin = 0, Double_t ymax = 1, Int_t npar = 0)
                       TF2(const TF2& f2)
               virtual ~TF2()
      virtual Double_t CentralMoment2(Double_t nx, Double_t ax, Double_t bx, Double_t ny, Double_t ay, Double_t by, Double_t epsilon = 0.000001)
        static TClass* Class()
          virtual void Copy(TObject& f2) const
      virtual Double_t Covariance2XY(Double_t ax, Double_t bx, Double_t ay, Double_t by, Double_t epsilon = 0.000001)
         virtual Int_t DistancetoPrimitive(Int_t px, Int_t py)
          virtual void Draw(Option_t* option)
          virtual TF1* DrawCopy(Option_t* option) const
          virtual void DrawDerivative(Option_t* = "al")
          virtual void DrawF2(const char* formula, Double_t xmin, Double_t xmax, Double_t ymin, Double_t ymax, Option_t* option)
          virtual void DrawIntegral(Option_t* = "al")
          virtual void ExecuteEvent(Int_t event, Int_t px, Int_t py)
         virtual Int_t GetContour(Double_t* levels = 0)
      virtual Double_t GetContourLevel(Int_t level) const
                 Int_t GetNpy() const
         virtual char* GetObjectInfo(Int_t px, Int_t py) const
      virtual Double_t GetRandom()
      virtual Double_t GetRandom(Double_t xmin, Double_t xmax)
          virtual void GetRandom2(Double_t& xrandom, Double_t& yrandom)
          virtual void GetRange(Double_t& xmin, Double_t& xmax) const
          virtual void GetRange(Double_t& xmin, Double_t& ymin, Double_t& xmax, Double_t& ymax) const
          virtual void GetRange(Double_t& xmin, Double_t& ymin, Double_t& zmin, Double_t& xmax, Double_t& ymax, Double_t& zmax) const
      virtual Double_t GetSave(const Double_t* x)
      virtual Double_t GetYmax() const
      virtual Double_t GetYmin() const
      virtual Double_t Integral(Double_t a, Double_t b, const Double_t* params = 0, Double_t epsil = 0.000001)
      virtual Double_t Integral(Double_t ax, Double_t bx, Double_t ay, Double_t by, Double_t epsil = 0.000001)
      virtual Double_t Integral(Double_t ax, Double_t bx, Double_t ay, Double_t by, Double_t az, Double_t bz, Double_t epsil = 0.000001)
       virtual TClass* IsA() const
        virtual Bool_t IsInside(const Double_t* x) const
      virtual Double_t Mean2X(Double_t ax, Double_t bx, Double_t ay, Double_t by, Double_t epsilon = 0.000001)
      virtual Double_t Mean2Y(Double_t ax, Double_t bx, Double_t ay, Double_t by, Double_t epsilon = 0.000001)
      virtual Double_t Moment2(Double_t nx, Double_t ax, Double_t bx, Double_t ny, Double_t ay, Double_t by, Double_t epsilon = 0.000001)
                  TF2& operator=(const TF2& rhs)
          virtual void Paint(Option_t* option)
          virtual void Save(Double_t xmin, Double_t xmax, Double_t ymin, Double_t ymax, Double_t zmin, Double_t zmax)
          virtual void SavePrimitive(ofstream& out, Option_t* option)
          virtual void SetContour(Int_t nlevels = 20, const Double_t* levels = 0)
          virtual void SetContourLevel(Int_t level, Double_t value)
          virtual void SetNpy(Int_t npy = 100)
          virtual void SetRange(Double_t xmin, Double_t xmax)
          virtual void SetRange(Double_t xmin, Double_t ymin, Double_t xmax, Double_t ymax)
          virtual void SetRange(Double_t xmin, Double_t ymin, Double_t zmin, Double_t xmax, Double_t ymax, Double_t zmax)
          virtual void ShowMembers(TMemberInspector& insp, char* parent)
          virtual void Streamer(TBuffer& b)
                  void StreamerNVirtual(TBuffer& b)
      virtual Double_t Variance2X(Double_t ax, Double_t bx, Double_t ay, Double_t by, Double_t epsilon = 0.000001)
      virtual Double_t Variance2Y(Double_t ax, Double_t bx, Double_t ay, Double_t by, Double_t epsilon = 0.000001)

Data Members

    protected:

      Double_t fYmin     Lower bound for the range in y
      Double_t fYmax     Upper bound for the range in y
         Int_t fNpy      Number of points along y used for the graphical representation
       TArrayD fContour  Array to display contour levels

Class Description

 a 2-Dim function with parameters
 TF2 graphics function is via the TH1 drawing functions.

      Example of a function

   TF2 *f2 = new TF2("f2","sin(x)*sin(y)/(x*y)",0,5,0,5);
   f2->Draw();

      See TF1 class for the list of functions formats

*-*-*-*-*-*-*-*-*-*-*F2 default constructor*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
*-*                  ======================

*-*-*-*-*-*-*F2 constructor using a formula definition*-*-*-*-*-*-*-*-*-*-*
*-*          =========================================
*-*
*-*  See TFormula constructor for explanation of the formula syntax.
*-*
*-*
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

*-*-*-*-*-*-*F2 constructor using a pointer to an interpreted function*-*-*
*-*          =========================================================
*-*
*-*   npar is the number of free parameters used by the function
*-*
*-*  Creates a function of type C between xmin and xmax and ymin,ymax.
*-*  The function is defined with npar parameters
*-*  fcn must be a function of type:
*-*     Double_t fcn(Double_t *x, Double_t *params)
*-*
*-*  This constructor is called for functions of type C by CINT.
*-*
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

*-*-*-*-*-*-*F2 constructor using a pointer to a compiled function*-*-*-*-*
*-*          =====================================================
*-*
*-*   npar is the number of free parameters used by the function
*-*
*-*   This constructor creates a function of type C when invoked
*-*   with the normal C++ compiler.
*-*
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

*-*-*-*-*-*-*-*-*-*-*F2 default destructor*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
*-*                  =====================

*-*-*-*-*-*-*-*-*-*-*Copy this F2 to a new F2*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
*-*                  ========================

*-*-*-*-*-*-*-*-*-*-*Compute distance from point px,py to a function*-*-*-*-*
*-*                  ===============================================
*-*  Compute the closest distance of approach from point px,py to this function.
*-*  The distance is computed in pixels units.
*-*
*-*  Algorithm:
*-*
*-*
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

*-*-*-*-*-*-*-*-*-*-*Draw this function with its current attributes*-*-*-*-*
*-*                  ==============================================
*-* NB. You must use DrawCopy if you want to draw several times the same
*-*     function in the current canvas.
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

*-*-*-*-*-*-*-*Draw a copy of this function with its current attributes*-*-*
*-*            ========================================================
*-*
*-*  This function MUST be used instead of Draw when you want to draw
*-*  the same function with different parameters settings in the same canvas.
*-*
*-* Possible option values are:
*-*   "SAME"  superimpose on top of existing picture
*-*   "L"     connect all computed points with a straight line
*-*   "C"     connect all computed points with a smooth curve.
*-*
*-* Note that the default value is "F". Therefore to draw on top
*-* of an existing picture, specify option "SL"
*-*
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

*-*-*-*-*-*-*-*-*-*Draw formula between xmin,ymin and xmax,ymax*-*-*-*-*-*-*-*
*-*                ============================================
*-*

*-*-*-*-*-*-*-*-*-*-*Execute action corresponding to one event*-*-*-*
*-*                  =========================================
*-*  This member function is called when a F2 is clicked with the locator
*-*
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

*-*-*-*-*-*-*-*Return contour values into array levels*-*-*-*-*-*-*-*-*-*
*-*            =======================================
*-*
*-*  The number of contour levels can be returned by getContourLevel
*-*
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

*-*-*-*-*-*-*-*Return the number of contour levels*-*-*-*-*-*-*-*-*-*-*-*-*
*-*            ===================================

   Redefines TObject::GetObjectInfo.
   Displays the function value
   corresponding to cursor position px,py

*-*-*-*-*-*Return a random number following this function shape*-*-*-*-*-*-*
*-*        ====================================================
*-*

*-*-*-*-*-*Return a random number following this function shape*-*-*-*-*-*-*
*-*        ====================================================
*-*

*-*-*-*-*-*Return 2 random numbers following this function shape*-*-*-*-*-*
*-*        =====================================================
*-*
*-*   The distribution contained in this TF2 function is integrated
*-*   over the cell contents.
*-*   It is normalized to 1.
*-*   Getting the two random numbers implies:
*-*     - Generating a random number between 0 and 1 (say r1)
*-*     - Look in which cell in the normalized integral r1 corresponds to
*-*     - make a linear interpolation in the returned cell
*-*
*-*
*-*  IMPORTANT NOTE
*-*  The integral of the function is computed at fNpx * fNpy points.
*-*  If the function has sharp peaks, you should increase the number of
*-*  points (SetNpx, SetNpy) such that the peak is correctly tabulated
*-*  at several points.

*-*-*-*-*-*-*-*-*-*-*Return range of a 2-D function*-*-*-*-*-*-*-*-*-*-*-*-*
*-*                  ==============================

*-*-*-*-*-*-*-*-*-*-*Return range of function*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
*-*                  ========================

 Get value corresponding to X in array of fSave values

 Return Integral of a 2d function in range [ax,bx],[ay,by]

 Return kTRUE is the point is inside the function range

*-*-*-*-*-*-*-*-*Paint this 2-D function with its current attributes*-*-*-*-*
*-*              ===================================================

 Save values of function in array fSave

 Save primitive as a C++ statement(s) on output stream out

*-*-*-*-*-*-*-*Set the number and values of contour levels*-*-*-*-*-*-*-*-*
*-*            ===========================================

  By default the number of contour levels is set to 20.

  if argument levels = 0 or missing, equidistant contours are computed

*-*-*-*-*-*-*-*-*-*-*Set value for one contour level*-*-*-*-*-*-*-*-*-*-*-*
*-*                  ===============================

 Set the number of points used to draw the function

 The default number of points along x is 30 for 2-d/3-d functions.
 You can increase this value to get a better resolution when drawing
 pictures with sharp peaks or to get a better result when using TF2::GetRandom2
 the minimum number of points is 4, the maximum is 10000 for 2-d/3-d functions

*-*-*-*-*-*Initialize the upper and lower bounds to draw the function*-*-*-*
*-*        ==========================================================

 Stream an object of class TF2.

 Return x^nx * y^ny moment of a 2d function in range [ax,bx],[ay,by]
   Author: Gene Van Buren <gene@bnl.gov>

 Return x^nx * y^ny central moment of a 2d function in range [ax,bx],[ay,by]
   Author: Gene Van Buren <gene@bnl.gov>

Inline Functions

               TF2& operator=(const TF2& rhs)
               void DrawDerivative(Option_t* = "al")
               void DrawIntegral(Option_t* = "al")
              Int_t GetNpy() const
               void GetRange(Double_t& xmin, Double_t& ymin, Double_t& zmin, Double_t& xmax, Double_t& ymax, Double_t& zmax) const
           Double_t GetYmin() const
           Double_t GetYmax() const
           Double_t Integral(Double_t ax, Double_t bx, Double_t ay, Double_t by, Double_t epsil = 0.000001)
           Double_t Integral(Double_t ax, Double_t bx, Double_t ay, Double_t by, Double_t az, Double_t bz, Double_t epsil = 0.000001)
               void SetRange(Double_t xmin, Double_t ymin, Double_t xmax, Double_t ymax)
               void SetRange(Double_t xmin, Double_t ymin, Double_t zmin, Double_t xmax, Double_t ymax, Double_t zmax)
           Double_t Mean2X(Double_t ax, Double_t bx, Double_t ay, Double_t by, Double_t epsilon = 0.000001)
           Double_t Mean2Y(Double_t ax, Double_t bx, Double_t ay, Double_t by, Double_t epsilon = 0.000001)
           Double_t Variance2X(Double_t ax, Double_t bx, Double_t ay, Double_t by, Double_t epsilon = 0.000001)
           Double_t Variance2Y(Double_t ax, Double_t bx, Double_t ay, Double_t by, Double_t epsilon = 0.000001)
           Double_t Covariance2XY(Double_t ax, Double_t bx, Double_t ay, Double_t by, Double_t epsilon = 0.000001)
            TClass* Class()
            TClass* IsA() const
               void ShowMembers(TMemberInspector& insp, char* parent)
               void StreamerNVirtual(TBuffer& b)