curvs1(3NCARG)
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.
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