DEFINITION MODULE CubicSplines;
(*
This Module implements the cubic splines. See "Numerical Methods for
Scientists and Engineers" by R. W. Hamming, page 349. Currently, a set
of 100 data points can spline fitted. This limitation will be removed 
in the future.
*)

EXPORT QUALIFIED Spline,MakeSpline,EvalSpline,DerivSpline;

TYPE Spline;   (* hidden *)

PROCEDURE MakeSpline(
        x : ARRAY OF REAL (* in *);
        y : ARRAY OF REAL (* in *);
        un: CARDINAL      (* in *);
    VAR S : Spline        (* out *) ) : BOOLEAN;
    (*
    This procedure takes the user x,y data and creates a cubic spline S.
    The x values must be increasing either in the direction x[1]..x[un] or
    x[un]..x[1] but must never be such that two x values overlap or cross.
    *)
    
PROCEDURE EvalSpline(
          x : REAL   (* in *);
          S : Spline (* in *);
    VAR val : REAL   (* out *) ) : BOOLEAN;
    (*
    Evaluate spline S at x and return value in "val". If trouble, e.g,
    x is out of range, RETURN FALSE.
    *)

PROCEDURE DerivSpline(
            x : REAL     (* in *);
            S : Spline   (* in *);
    VAR Deriv : REAL     (* out *) ): BOOLEAN;
    (*
    Evaluates the derivative of the spline "S" at x. The function value
    returned is TRUE if ok, otherwise if x is out of range or if other
    problems occur, FALSE is returned.
    *)

END CubicSplines.