Previous: fitc1 Up: ../plot79_f.html Next: fitcf
REAL FUNCTION FITC2 (T, N, X, Y, YP, SIGMA, IT)
C$ (Tensioned Spline Interpolation)
C$ This function interpolates a curve at a given point using a
C$ spline under tension. SUBROUTINE FITC1 should be called
C$ earlier to determine certain necessary parameters.
C$
C$ On input--
C$
C$ T..........contains a REAL value to be mapped onto the
C$ interpolating curve.
C$ N..........contains the number of points which were
C$ interpolated to determine the curve,
C$ X and Y....are arrays containing the ordinates and abcissas
C$ of the interpolated points,
C$ YP.........is an array with values proportional to the
C$ second derivative of the curve at the nodes
C$ SIGMA......contains the tension factor (its sign is
C$ ignored)
C$ IT.........is an INTEGER switch. If IT is not 1, this
C$ indicates that the function has been called
C$ previously (with N, X, Y, YP, and SIGMA
C$ unaltered) and that this value of T exceeds the
C$ previous value. With such information the
C$ function is able to perform the interpolation
C$ much more rapidly. If a user seeks to
C$ interpolate at a sequence of points, efficiency
C$ is gained by ordering the values increasing and
C$ setting IT to the index of the call. If IT is 1
C$ the search for the interval (X(K),X(K+1))
C$ containing T starts with K = 1.
C$
C$ The parameters N,X,Y,YP and SIGMA should be input unaltered
C$ from the output of FITC1.
C$
C$ On Output--
C$
C$ FITC2......contains the interpolated value. For T less
C$ than X(1), FITC2 = Y(1). For T greater than X(N),
C$ FITC2 = Y(N).
C$
C$ None of the input parameters are altered.
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, and to compute SINH(X) more
C$ accurately than 0.5*(EXP(X)-EXP(-X)) for small arguments.
C$ (03-APR-82)