DEFINITION MODULE Inter2;

   (* EXPORT QUALIFIED BCuCof, BCuInt, PolIn2, Splie2, Splin2; *)

   FROM NRMatr IMPORT Matrix;
   FROM NRVect IMPORT Vector;

   TYPE
      RealArray4 = ARRAY [0..3] OF REAL;
      RealArray4by4 = ARRAY [0..3],[0..3] OF REAL;

   PROCEDURE BCuCof(    y, y1, y2, y12: RealArray4; 
                        d1, d2:         REAL; 
                    VAR c:              RealArray4by4); 
   (*
     Given arrays y[4], y1[4], y2[4], and y12[4], containing the function, 
     gradients, and cross derivative at the four grid points of a rectangular 
     grid cell (numbered counterclockwise from the lower left), and given d1 
     and d2, the length of the grid cell in the 1- and 2-directions, this 
     routine returns the table c[4, 4] that is used by BCuInt for bicubic 
     interpolation.
   *)

   PROCEDURE BCuInt(    y, y1, y2, y12:             RealArray4; 
                        x1l, x1u, x2l, x2u, x1, x2: REAL; 
                    VAR ansy, ansy1, ansy2:         REAL); 
   (*
     Bicubic interpolation within a grid square. Input quantities are 
     y, y1, y2, y12 (as described in BCuCof); x1l and x1u, the lower and 
     upper coordinates of the grid square in the 1-direction; x2l and x2u 
     likewise for the 2-direction; and x1,x2, the coordinates of the desired 
     point for the interpolation.
     The interpolated function value is returned as ansy, and the interpolated
     gradient values as ansy1 and ansy2. This routine calls BCuCof.
   *)

   PROCEDURE PolIn2(    X1A, X2A: Vector; 
                        YA:       Matrix; 
                        x1, x2:   REAL; 
                    VAR y, dy:    REAL); 
   (*
     Given arrays X1A[0, m-1] and X2A[0, n-1] of independent variables, and a
     submatrix of function values YA[m, n], tabulated at the grid points defined
     by X1A and X2A; and given values x1 and x2 of the independent variables;
     this routine returns an interpolated function value y, and
     an accuracy indication dy (based only on the interpolation in the x1 
     direction, however).
   *)

   PROCEDURE Splie2(X1A, X2A: Vector; 
                    YA, Y2A:  Matrix); 
   (*
     Given the tabulated independent variables X1A[0, m-1] and X2A[0, n-1],
     and a tabulated function YA[m, n], this routine constructs one-dimensional 
     natural cubic splines of the rows of YA and returns the second-derivatives 
     in the array Y2A[m, n].
   *)

   PROCEDURE Splin2(    X1A, X2A: Vector; 
                        YA, Y2A:  Matrix; 
                        x1, x2:   REAL; 
                    VAR y:        REAL); 
   (*
     Given X1A, X2A, YA, m, n as described in SPLIE2 and Y2A as produced 
     by that routine; and given a desired interpolating point x1, x2; 
     this routine returns an interpolated function value y by bicubic 
     spline interpolation.
   *)

END Inter2.