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REAL FUNCTION FITDS (T, N, X, A, B, C, D, IT)
C$ (First Derivative of Cubic Spline)
C$ This function interpolates the derivative of a curve at a
C$ given point using a cubic spline. SUBROUTINE FITSM should
C$ be called earlier to determine certain necessary
C$ parameters. For best results, it is recommended that this
C$ function to used to evaluate the derivatives at the
C$ original data points, and then to call SUBROUTINE FITSM to
C$ obtain a new spline function for the derivatives. The
C$ splined derivatives then obtained from FUNCTION FITCS will
C$ generally be much less oscillatory than the derivatives of
C$ the spline computed here.
C$
C$ On input--
C$
C$ T...........ordinate value for which the cubic spline
C$ interpolant is to be evaluated.
C$ N...........number of points in X(*).
C$ X(*)........original ordinate values used to determine
C$ the spline.
C$ A(*),B(*),C(*),D(*).....spline polynomial coefficients.
C$ IT.......... .EQ. 1 - first call.
C$ .NE. 1 - subsequent call (with N, X, A, B, C,
C$ D unchanged), and this value of T
C$ larger than the previous value. In
C$ such a case, the search for the
C$ interval in which T lies can be
C$ greatly speeded. Thus IT can
C$ frequently be a loop index in the
C$ calling program if the values of T
C$ are incremented successively.
C$
C$ The parameters N, X, A, B, C, and D should be input
C$ unaltered from the output of SUBROUTINE FITSM.
C$
C$ On output--
C$
C$ FITDS......contains the interpolated derivative. For T less
C$ than X(1), FITDS = YPRIME(1). For T greater than
C$ X(N), FITDS = YPRIME(N).
C$
C$ None of the input parameters are altered. Adapted from
C$ FUNCTION FITC2 published by
C$
C$ Author: A.K. Cline, "Scalar and Planar Valued Curve Fitting
C$ Using Splines Under Tension", Comm. A.C.M. 17,
C$ 218-225 (1974). (Algorithm 476).
C$
C$ Modifications by Nelson H.F. Beebe, Department of Chemistry
C$ Aarhus University, Aarhus, Denmark, to provide a more
C$ transportable program.
C$ (03-APR-82)