NAME

       CURVS - calculate values for a smoothing spline

SYNOPSIS

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

       This  subroutine  calculates  certain values that are used by CURV2 in order to compute an
       interpolatory smoothing spline under tension through a sequence of functional values.  The
       actual computation of the interpolated values must be done using CURV2.

       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 interpolated 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.
                   These must be increasing values.

       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.

       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,  output)  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.

ACCESS

       To use CURVS, load the NCAR Graphics library ngmath.

SEE ALSO

       curv2, 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.