# Imagination is more important than knowledge (지식보다 상상)

## interpolation and derivativesby 바죠

3 차원 그리드 상의 데이터 : interpolation and derivatives

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DB3INK
DB3VAL

http://gams.nist.gov/cgi-bin/serve.cgi/Module/CMLIB/DB3INK/832
http://gams.nist.gov/cgi-bin/serve.cgi/Module/CMLIB/DB3VAL

C***PURPOSE  DOUBLE PRECISION VERSION OF DB3INK
C            DB3INK DETERMINES A PIECEWISE POLYNOMIAL FUNCTION THAT
C            INTERPOLATES THREE-DIMENSIONAL GRIDDED DATA. USERS SPECIFY
C            THE POLYNOMIAL ORDER (DEGREE+1) OF THE INTERPOLANT AND
C            (OPTIONALLY) THE KNOT SEQUENCE.

C   I N P U T
C   ---------
C
C   X       Double precision 1D array (size NX)
C           Array of x abcissae. Must be strictly increasing.
C
C   NX      Integer scalar (.GE. 3)
C           Number of x abcissae.
C
C   Y       Double precision 1D array (size NY)
C           Array of y abcissae. Must be strictly increasing.
C
C   NY      Integer scalar (.GE. 3)
C           Number of y abcissae.
C
C   Z       Double precision 1D array (size NZ)
C           Array of z abcissae. Must be strictly increasing.
C
C   NZ      Integer scalar (.GE. 3)
C           Number of z abcissae.
C
C   FCN     Double precision 3D array (size LDF1 by LDF2 by NY)
C           Array of function values to interpolate. FCN(I,J,K) should
C           contain the function value at the point (X(I),Y(J),Z(K))
C
C   LDF1    Integer scalar (.GE. NX)
C           The actual first dimension of FCN used in the
C           calling program.
C
C   LDF2    Integer scalar (.GE. NY)
C           The actual second dimension of FCN used in the calling
C           program.
C
C   KX      Integer scalar (.GE. 2, .LT. NX)
C           The order of spline pieces in x.
C           (Order = polynomial degree + 1)
C
C   KY      Integer scalar (.GE. 2, .LT. NY)
C           The order of spline pieces in y.
C           (Order = polynomial degree + 1)
C
C   KZ      Integer scalar (.GE. 2, .LT. NZ)
C           The order of spline pieces in z.
C           (Order = polynomial degree + 1)
C
C
C   I N P U T   O R   O U T P U T
C   -----------------------------
C
C   TX      Double precision 1D array (size NX+KX)
C           The knots in the x direction for the spline interpolant.
C           If IFLAG=0 these are chosen by DB3INK.
C           If IFLAG=1 these are specified by the user.
C                      (Must be non-decreasing.)
C
C   TY      Double precision 1D array (size NY+KY)
C           The knots in the y direction for the spline interpolant.
C           If IFLAG=0 these are chosen by DB3INK.
C           If IFLAG=1 these are specified by the user.
C                      (Must be non-decreasing.)
C
C   TZ      Double precision 1D array (size NZ+KZ)
C           The knots in the z direction for the spline interpolant.
C           If IFLAG=0 these are chosen by DB3INK.
C           If IFLAG=1 these are specified by the user.
C                      (Must be non-decreasing.)
C
C
C   O U T P U T
C   -----------
C
C   BCOEF   Double precision 3D array (size NX by NY by NZ)
C           Array of coefficients of the B-spline interpolant.
C           This may be the same array as FCN.
C
C

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