DEFINITION MODULE Splines;

   (* EXPORT QUALIFIED Spline, Splint; *)

   FROM NRVect IMPORT Vector;

   PROCEDURE Spline(   X, Y:     Vector; 
                       yp1, ypn: REAL; 
                       Y2:       Vector); 
   (*
     Given arrays X[n] and Y[n] containing a tabulated function, i.e.
     yi = f(xi), with x0 < x1 < ... < x(n-1), and given values yp1 and ypn 
     for the first derivative of the interpolating function at points 0 and n-1,
     respectively, this routine returns an array Y2[n] that contains the second 
     derivatives of the interpolating function at the tabulated points xi. 
     If yp1 and/or ypn are equal to 1 x 10^30 or larger, the routine is signalled
     to set the corresponding boundary condition for a natural spline, with zero 
     second derivative on that boundary.
   *)

   PROCEDURE Splint(    XA, YA, Y2A: Vector; 
                        x:           REAL; 
                    VAR y:           REAL); 
   (*
     Given the arrays XA[n] and YA[n], which tabulate a function (with the XAi's 
     in order), and given the array Y2A[n], which is the output from Spline above, and given
     a value of x, this routine returns a cubic-spline interpolated
     value y.
   *)

END Splines.