TSpline3

 Third spline creator given an array of
 arbitrary knots in increasing abscissa order and
 possibly end point conditions

 Third spline creator given an array of
 arbitrary function values on equidistant n abscissa
 values from xmin to xmax and possibly end point conditions

 Third spline creator given an array of
 arbitrary abscissas in increasing order and a function
 to interpolate and possibly end point conditions

 Third spline creator given a function to be
 evaluated on n equidistand abscissa points between xmin
 and xmax and possibly end point conditions

 Third spline creator given a TGraph with
 abscissa in increasing order and possibly end
 point conditions

copy constructor

assignment operator

 Check the boundary conditions

 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.

 Find X

 Eval this spline at x

 Derivative

 write this spline as a C++ function that can be executed without ROOT
 the name of the function is the name of the file up to the "." if any

      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.

 Stream an object of class TSpline3.