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FITC1

       SUBROUTINE  FITC1 (N, X, Y, SLP1, SLPN, YP, TEMP, SIGMA)
 C$    (Tensioned Spline Fit)
 C$    This subroutine  determines  the  parameters  necessary  to
 C$    compute an  interpolatory spline  under tension  through  a
 C$    sequence of functional values.  The slopes at the two  ends
 C$    of the  curve  may be  specified  or omitted.   For  actual
 C$    computation of points on the curve, it is necessary to call
 C$    the function FITC2.
 C$
 C$    On input--
 C$
 C$    N........is the number of values to be interpolated
 C$             (N.GE.2).
 C$    X........is an array of the N increasing abscissae of the
 C$             functional values.
 C$    Y........is an array of the N ordinates of the values,
 C$             (i.e. Y(K) is  the functional value  corresponding
 C$             to X(K)).
 C$    SLP1 and SLPN......contain the desired values for the first
 C$             derivative  of  the  curve   at  X(1)  and   X(N),
 C$             respectively.  If the quantity SIGMA is  negative,
 C$             these values will be determined internally and the
 C$             user need  only furnish  place-holding  parameters
 C$             for SLP1 and SLPN.  Such place-holding  parameters
 C$             will be ignored but not destroyed.
 C$    YP.......is an array of length at least N
 C$    TEMP.....is an array of length at least N which is used for
 C$             scratch storage.
 C$    SIGMA....contains the tension factor.  This is non-zero and
 C$             indicates the curviness desired.  If ABS(SIGMA) is
 C$             nearly zero (e.g. 0.001),  the resulting curve  is
 C$             approximately a  cubic spline.   If ABS(SIGMA)  is
 C$             large (e.g. 50.0), the resulting curve is nearly a
 C$             polygonal  line.   The  sign  of  SIGMA  indicates
 C$             whether the derivative information has been  input
 C$             or  not.   If  SIGMA  is  negative,  the  endpoint
 C$             derivatives  will  be  determined  internally.   A
 C$             standard value for SIGMA  is approximately 1.0  in
 C$             absolute value.
 C$
 C$    On output--
 C$
 C$    YP......contains values proportional to the second
 C$            derivative of the curve at the given nodes.
 C$    N,X,Y,SLP1,SLPN and SIGMA.....are unaltered.
 C$
 C$    Author:  A.K.  Cline,  "Scalar  and  Planar  Valued   Curve
 C$             Fitting Using Splines Under Tension", Comm. A.C.M.
 C$             17, 218-225 (1974).  (Algorithm 476).
 C$
 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$    (20-JUL-89)