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.