------------------------------------------------------------------------
IMSL Name:  BS2DR/DBS2DR (Single/Double precision version)
 
Revised:    June 10, 1991
 
Purpose:    Evaluate the derivative of a two-dimensional
            tensor-product spline, given its tensor-product
            B-spline representation.
 
Usage:      BS2DR(IXDER, IYDER, X, Y, KXORD, KYORD, XKNOT, YKNOT,
                  NXCOEF, NYCOEF, BSCOEF)
 
Arguments:
   IXDER  - Order of the derivative in the X-direction.  (Input)
   IYDER  - Order of the derivative in the Y-direction.  (Input)
   X      - X-coordinate of the point at which the spline is to be
            evaluated.  (Input)
   Y      - Y-coordinate of the point at which the spline is to be
            evaluated.  (Input)
   KXORD  - Order of the spline in the X-direction.  (Input)
   KYORD  - Order of the spline in the Y-direction.  (Input)
   XKNOT  - Array of length NXCOEF+KXORD containing the knot
            sequence in the X-direction.  (Input)
            XKNOT must be nondecreasing.
   YKNOT  - Array of length NYCOEF+KYORD containing the knot
            sequence in the Y-direction.  (Input)
            YKNOT must be nondecreasing.
   NXCOEF - Number of B-spline coefficients in the X-direction.
            (Input)
   NYCOEF - Number of B-spline coefficients in the Y-direction.
            (Input)
   BSCOEF - Array of length NXCOEF*NYCOEF containing the
            tensor-product B-spline coefficients.  (Input)
            BSCOEF is treated internally as a matrix of size NXCOEF
            by NYCOEF.
   BS2DR  - Value of the (IXDER,IYDER) derivative of the spline at
            (X,Y).  (Output)
 
Remarks:
1. Automatic workspace usage is
            BS2DR    3*MAX(KXORD,KYORD)+KYORD units, or
            DBS2DR   6*MAX(KXORD,KYORD)+2*KYORD units.
   Workspace may be explicitly provided, if desired, by use of
   B22DR/DB22DR.  The reference is
            CALL B22DR(IXDER, IYDER, X, Y, KXORD, KYORD, XKNOT,
                       YKNOT, NXCOEF, NYCOEF, BSCOEF, WK)
   The additional argument is
   WK     - Work array of length 3*MAX(KXORD,KYORD)+KYORD.
 
2. Informational errors
   Type Code
     3   1  The point X does not satisfy
            XKNOT(KXORD).LE.X.LE.XKNOT(NXCOEF+1).
     3   2  The point Y does not satisfy
            YKNOT(KYORD).LE.Y.LE.YKNOT(NYCOEF+1).
 
Keyword:    Differentiate
 
GAMS:       E3a1; E3a2
 
Chapter:    MATH/LIBRARY Interpolation and Approximation
 
Page No.:   MATH/LIBRARY User's Manual page 561