NAME

       CURVPS - calculate values for a smoothing spline for a periodic function.

SYNOPSIS

       CALL CURVPS (N, X, Y, P, D, ISW, S, EPS, YS, YSP, SIGMA, TEMP, IER)

       This  subroutine  calculates  certain values that are used by CURVP2 in order to compute an interpolatory
       smoothing spline under tension through a sequence of functional  values  for  a  periodic  function.  The
       actual computation of the interpolated values must be done using CURVP2.

       Three parameters are used to control the degree of smoothness -- D, S, and EPS.

       The  parameter  D  is  a  value indicating the degree of confidence in the accuracy of the input function
       values -- it should be an approximation of the standard deviation of error. Effectively the  value  of  D
       controls how close the smoothed curve comes to the input data points. If D is small then the interpolated
       curve will pass close to the input data. The larger the value of D, the more freedom the smooth curve has
       in how close it comes to the input data values.

       S  is  a more subtle global smoothing parameter. S must be non-negative. For small values of S, the curve
       approximates the tension spline and for larger values of S, the curve is smoother. A reasonable value for
       S is REAL(N).

       EPS controls the precision to which S is interpreted;  EPS  must  be  between  0.  and  1.  inclusive.  A
       reasonable value for EPS is SQRT(2./REAL(N)).

DESCRIPTION

       N           (integer, input) The number of input data values. (N > 1)

       X           (integer, input) An array containing the abscissae for the input function.

       Y           (integer,  input) An array containing the functional values for the input function -- Y(K) is
                   the functional value at X(K) for K=1,N.

       P           (real, input) The period of the function.

       D           (integer, input) A user-specified value containing the observed weights. D may be  either  an
                   array or a scalar, depending on the value of ISW (as described below).

       ISW         (integer,  input)  A  switch for interpreting the value of D. If ISW=0, then D is an array of
                   length N (D contains an individual error estimate for each input data value); if ISW=1,  then
                   D is a scalar that serves as an error estimate for every single data item.

       S           (integer, input) Contains the value for smoothing. S must be non-negative.  Larger values for
                   S yield greater smoothing. A reasonable value is REAL(N).

       EPS         (integer,  input)  Contains a tolerance value for the relative precision to which S should be
                   interpreted.  EPS  must  be  between  0.  and  1.   inclusive.    A   reasonable   value   is
                   SQRT(2./REAL(N)).

       YS          (integer, input) An array of length N.

       YSP         (integer, input) An array of length N.

       SIGMA       (integer,  input)  Tension  factor.  Values  near zero result in a cubic spline; large values
                   (e.g. 50) result in nearly a polygonal line. A typical value is 1.

       TEMP        (integer, input) Scratch space.

       IER         (integer, input) An error return value. If  IER  is  returned  as  0,  then  no  errors  were
                   detected.

                   = 1 if N is less than 2.
                   = 2 if S is negative.
                   = 3 if EPS is negative or greater than 1.
                   = 4 if X values are not strictly increasing.
                   = 5 if D is negative.
                   = 6 if P is less than or equal to X(N)-X(1).

ACCESS

       To use CURVPS, load the NCAR Graphics library ngmath.

SEE ALSO

       curvp2, fitgrid_params.

       Complete documentation for Fitgrid is available at URL
       http://ngwww.ucar.edu/ngdoc/ng/ngmath/fitgrid/fithome.html

COPYRIGHT

       Copyright (C) 2000
       University Corporation for Atmospheric Research

       The use of this Software is governed by a License Agreement.

UNIX                                               March 1998                                     CURVPS(3NCARG)