TSpline3


class description - source file - inheritance tree

class TSpline3 : public TSpline

    private:
virtual void BuildCoeff() void SetCond(const char* opt) protected:
public:
TSpline3 TSpline3() TSpline3 TSpline3(const char* title, Double_t* x, Double_t* y, Int_t n, const char* opt = 0, Double_t valbeg = 0, Double_t valend = 0) TSpline3 TSpline3(const char* title, Double_t xmin, Double_t xmax, Double_t* y, Int_t n, const char* opt = 0, Double_t valbeg = 0, Double_t valend = 0) TSpline3 TSpline3(const char* title, Double_t* x, TF1* func, Int_t n, const char* opt = 0, Double_t valbeg = 0, Double_t valend = 0) TSpline3 TSpline3(const char* title, Double_t xmin, Double_t xmax, TF1* func, Int_t n, const char* opt = 0, Double_t valbeg = 0, Double_t valend = 0) TSpline3 TSpline3(const char* title, TGraph* g, const char* opt = 0, Double_t valbeg = 0, Double_t valend = 0) TSpline3 TSpline3(TSpline3&) virtual void ~TSpline3() static TClass* Class() virtual Double_t Eval(Double_t x) const void GetCoeff(Int_t i, Double_t& x, Double_t& y, Double_t& b, Double_t& c, Double_t& d) virtual void GetKnot(Int_t i, Double_t& x, Double_t& y) const virtual TClass* IsA() const virtual void ShowMembers(TMemberInspector& insp, char* parent) virtual void Streamer(TBuffer& b) void StreamerNVirtual(TBuffer& b) static void Test()

Data Members

    private:
TSplinePoly3* fPoly [fNp] Array of polynomial terms Double_t fValBeg Initial value of first or second derivative Double_t fValEnd End value of first or second derivative Int_t fBegCond 0=no beg cond, 1=first derivative, 2=second derivative Int_t fEndCond 0=no end cond, 1=first derivative, 2=second derivative protected:
public:

Class Description

                                                                      
 TSpline                                                              
                                                                      
 Base class for spline implementation containing the Draw/Paint       
 methods                                                              
                                                                      


TSpline3(const char *title, Double_t x[], Double_t y[], Int_t n, const char *opt, Double_t valbeg, Double_t valend) : TSpline(title,-1,x[0],x[n-1],n,kFALSE), fValBeg(valbeg), fValEnd(valend), fBegCond(0), fEndCond(0)
 Third spline creator given an array of
 arbitrary knots in increasing abscissa order and
 possibly end point conditions


TSpline3(const char *title, Double_t xmin, Double_t xmax, Double_t y[], Int_t n, const char *opt, Double_t valbeg, Double_t valend) : TSpline(title,(xmax-xmin)/(n-1), xmin, xmax, n, kTRUE), fValBeg(valbeg), fValEnd(valend), fBegCond(0), fEndCond(0)
 Third spline creator given an array of
 arbitrary function values on equidistant n abscissa
 values from xmin to xmax and possibly end point conditions


TSpline3(const char *title, Double_t x[], TF1 *func, Int_t n, const char *opt, Double_t valbeg, Double_t valend) : TSpline(title,-1, x[0], x[n-1], n, kFALSE), fValBeg(valbeg), fValEnd(valend), fBegCond(0), fEndCond(0)
 Third spline creator given an array of
 arbitrary abscissas in increasing order and a function
 to interpolate and possibly end point conditions


TSpline3(const char *title, Double_t xmin, Double_t xmax, TF1 *func, Int_t n, const char *opt, Double_t valbeg, Double_t valend) : TSpline(title,(xmax-xmin)/(n-1), xmin, xmax, n, kTRUE), fValBeg(valbeg), fValEnd(valend), fBegCond(0), fEndCond(0)
 Third spline creator given a function to be
 evaluated on n equidistand abscissa points between xmin
 and xmax and possibly end point conditions


TSpline3(const char *title, TGraph *g, const char *opt, Double_t valbeg, Double_t valend) : TSpline(title,-1,0,0,g->GetN(),kFALSE), fValBeg(valbeg), fValEnd(valend), fBegCond(0), fEndCond(0)
 Third spline creator given a TGraph with
 abscissa in increasing order and possibly end
 point conditions


void SetCond(const char *opt)
 Check the boundary conditions


void Test()
 Test method for TSpline5

   n          number of data points.
   m          2*m-1 is order of spline.
                 m = 2 always for third spline.
   nn,nm1,mm,
   mm1,i,k,
   j,jj       temporary integer variables.
   z,p        temporary double precision variables.
   x[n]       the sequence of knots.
   y[n]       the prescribed function values at the knots.
   a[200][4]  two dimensional array whose columns are
                 the computed spline coefficients
   diff[3]    maximum values of differences of values and
                 derivatives to right and left of knots.
   com[3]     maximum values of coefficients.


   test of TSpline3 with nonequidistant knots and
      equidistant knots follows.



Double_t Eval(Double_t x) const
 Evaluate spline polynomial


void BuildCoeff()
      subroutine cubspl ( tau, c, n, ibcbeg, ibcend )
  from  * a practical guide to splines *  by c. de boor
     ************************  input  ***************************
     n = number of data points. assumed to be .ge. 2.
     (tau(i), c(1,i), i=1,...,n) = abscissae and ordinates of the
        data points. tau is assumed to be strictly increasing.
     ibcbeg, ibcend = boundary condition indicators, and
     c(2,1), c(2,n) = boundary condition information. specifically,
        ibcbeg = 0  means no boundary condition at tau(1) is given.
           in this case, the not-a-knot condition is used, i.e. the
           jump in the third derivative across tau(2) is forced to
           zero, thus the first and the second cubic polynomial pieces
           are made to coincide.)
        ibcbeg = 1  means that the slope at tau(1) is made to equal
           c(2,1), supplied by input.
        ibcbeg = 2  means that the second derivative at tau(1) is
           made to equal c(2,1), supplied by input.
        ibcend = 0, 1, or 2 has analogous meaning concerning the
           boundary condition at tau(n), with the additional infor-
           mation taken from c(2,n).
     ***********************  output  **************************
     c(j,i), j=1,...,4; i=1,...,l (= n-1) = the polynomial coefficients
        of the cubic interpolating spline with interior knots (or
        joints) tau(2), ..., tau(n-1). precisely, in the interval
        (tau(i), tau(i+1)), the spline f is given by
           f(x) = c(1,i)+h*(c(2,i)+h*(c(3,i)+h*c(4,i)/3.)/2.)
        where h = x - tau(i). the function program *ppvalu* may be
        used to evaluate f or its derivatives from tau,c, l = n-1,
        and k=4.

void Streamer(TBuffer &R__b)
 Stream an object of class TSpline3.



Inline Functions


           TSpline3 TSpline3(const char* title, TGraph* g, const char* opt = 0, Double_t valbeg = 0, Double_t valend = 0)
               void GetCoeff(Int_t i, Double_t& x, Double_t& y, Double_t& b, Double_t& c, Double_t& d)
               void GetKnot(Int_t i, Double_t& x, Double_t& y) const
            TClass* Class()
            TClass* IsA() const
               void ShowMembers(TMemberInspector& insp, char* parent)
               void StreamerNVirtual(TBuffer& b)
           TSpline3 TSpline3(TSpline3&)
               void ~TSpline3()


Author: Federico Carminati 28/02/2000
Last update: root/graf:$Name: $:$Id: TSpline.cxx,v 1.5 2001/02/07 20:54:01 brun Exp $
Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. *


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