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SUBROUTINE FITBV (LX,LY, X,Y,Z, NROWZ,N, U,V,W, IERROR)
C$ (Bivariate Interpolation)
C$ This subroutine interpolates, from values of the function
C$ given at input grid points in an X-Y plane and for a given
C$ set of points in the plane, the values of a single-valued
C$ bivariate function Z = Z(X,Y). This function should be
C$ used if a single point, or a single curve, in the X-Y plane
C$ is to be generated. For a full surface, use SUBROUTINE
C$ FITSF. The method is based on a piece-wise function
C$ composed of a set of bicubic polynomials in X and Y. Each
C$ polynomial is applicable to a rectangle of the input grid
C$ in the X-Y plane. Each polynomial is determined locally.
C$
C$ The input arguments are:
C$
C$ LX = Number of input grid points in the X coordinate
C$ (must be 2 or greater)
C$ X = Array of dimension LX storing the X coordinates
C$ of input grid points (in ascending order)
C$ Y = Array of dimension LY storing the Y coordinates
C$ of input grid points (in ascending order)
C$ Z = Doubly-dimensioned array of dimension (NROWZ,LY)
C$ storing the values of the function (Z values)
C$ at input grid points
C$ N = Number of points at which interpolation of the
C$ Z value is desired (must be 1 or greater)
C$ U = Array of dimension N storing the X coordinates
C$ of desired points
C$ v = array of dimension n storing the y coordinates
C$ of desired points
C$
C$ The output arguments are:
C$
C$ W = Array of dimension N where the interpolated Z values
C$ at desired points are to be displayed
C$ IERROR = 0 (Normal return)
C$ = +1 (Abnormal return. A message will be printed
C$ giving all the arguments, and nothing more
C$ will be done)
C$
C$ Some variables internally used are:
C$
C$ ZA = Divided difference of Z with respect to X
C$ ZB = Divided difference of Z with respect to Y
C$ ZAB = Second order divided difference of Z with
C$ respect to X and Y
C$ ZX = Partial derivative of Z with respect to X
C$ ZY = Partial derivative of Z with respect to Y
C$ ZXY = Second order partial derivative of Z with
C$ respect to X and Y
C$
C$ Author: Hiroshi Akima, "Bivariate Interpolation and Smooth
C$ Surface Fitting Based on Local Procedures",
C$ Algorithm 474, Comm. A.C.M. 17, 18-20 (1974).
C$
C$ ***WARNING*** This routine contains non-standard
C$ equivalencing of INTEGER variables with
C$ elements of REAL arrays and may pose problems
C$ on certain computers.
C$
C$ (09-OCT-84)