Previous: fitsf Up: ../plot79_f.html Next: fittap

FITSM

       SUBROUTINE  FITSM (X,Y, DYINV2, N, S, A,B,C,D, R,R1,R2, T,T1, U,V)
 C$    (Cubic Spline with Smoothing)
 C$    This subroutine implements the evaluation of a cubic spline
 C$    with smoothing through a set of data points (X(K),Y(K))  in
 C$    which  the   ordinate   values  Y(K)   have   uncertainties
 C$    associated with them.  The resulting spline will  generally
 C$    not go  through  the  input  points,  but  will  provide  a
 C$    smoothed curve close to them.
 C$
 C$    The input arguments are:
 C$
 C$    X(*)................Array of abscissa values, arranged in
 C$                        strictly increasing order.
 C$    Y(*)................Array of ordinate values.
 C$    DYINV2(*)...........Array of  the  inverse  square  of  the
 C$                        uncertainties DY(*) in the values Y(*).
 C$                        If available, the  values DY(K)  should
 C$                        be standard  deviations of  the  points
 C$                        Y(K).
 C$    N...................Number of data points.
 C$    S...................A non-negative parameter which controls
 C$                        the extent  of smoothing.   the  spline
 C$                        function is determined such that
 C$
 C$                         N
 C$                        SUM ((F(X(K))-Y(K))/DY(K))**2 .LE. S.
 C$                        K=1
 C$
 C$                        where equality holds unless F describes
 C$                        a straight line.  If S = 0.0, a  normal
 C$                        cubic spline  passing  exactly  through
 C$                        the input points  will be produced.   A
 C$                        natural choice for S will often be (N -
 C$                        SQRT(2N)) .LE. S .LE. (N + SQRT(2N)).
 C$
 C$    The output arguments are:
 C$
 C$    A(*),B(*),C(*),D(*)......Arrays of dimension N collecting
 C$                             the  coefficients  of  the   cubic
 C$                             spline F(T)  such that  with  X(K)
 C$                             .LE. T  .LE. X(K+1)  and H  = T  -
 C$                             X(K), we  have F(T)  = ((D(K)*H  +
 C$                             C(K))*H   +   B(K))*H   +    A(K).
 C$                             Furthermore, A(N)  =  F(X(N))  and
 C$                             C(N)=0, while  B(N) and  D(N)  are
 C$                             left undefined.
 C$
 C$    The remaining arguments  R(*), R1(*),  R2(*), T(*),  T1(*),
 C$    U(*) and  V(*) are  used for  scratch space,  and all  have
 C$    dimension N+2.
 C$
 C$    The method has been published by
 C$
 C$    C. Reinsch,  "Smoothing  by Spline  Functions",  Numerische
 C$    Mathematik 10, 177-183 (1967).
 C$
 C$    This routine  is  a  FORTRAN  version  of  Reinsch's  Algol
 C$    procedure.  Reinsch's  published  Algol procedure  did  not
 C$    initialize A(N) and  C(N) to the  stated values.  This  has
 C$    been corrected in this version.
 C$    (03-APR-82)