NAME

       CURVS1 - calculate values for a smoothing spline for data in the plane.

SYNOPSIS

       CALL CURVS1 (N,X,Y,D,ISW,S,EPS,PARAM,XS,YS,XSP,YSP,
                    SIGMA,TEMP,IERR)

       This  subroutine  calculates  certain values that are used by CURVS2 in order to compute an interpolatory
       smoothing spline under tension through a sequence of data values in the plane.   In  general  this  curve
       will  not  pass through the original data points.  The actual computation of the interpolated values must
       be done using CURVS2.

       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 X-coordinates for the input data.  These need not be
                   increasing.

       Y           (integer, input) An array containing the Y-coordinates for the input data.

       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)).

       PARAM       (integer, output) PARAM(I) is the arc length of  the  curve  up  through  point  (X(I),Y(I)),
                   divided by the total arc length.

       XS          (integer, output) An array of length N.  Contains the smoothed values.

       XSP         (integer,  output)  An  array of length N.  Contains second derivative information for the X-
                   coordinate values.

       YS          (integer, output) An array of length N.  Contains the smoothed values.

       YSP         (integer, output) An array of length N.  Contains second derivative information  for  the  X-
                   coordinate values.

       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 of length at least 19*N.

       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.
                   = 5 if D is negative.

ACCESS

       To use CURVS1, load the NCAR Graphics library ngmath.

SEE ALSO

       curvs2, 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                                               August 2002                                    CURVS1(3NCARG)