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.\"	$Id: curvps.m,v 1.4 2008-07-27 03:35:39 haley Exp $
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.TH CURVPS 3NCARG "March 1998" UNIX "NCAR GRAPHICS"
.SH NAME
CURVPS - calculate values for a smoothing spline for a periodic function.
.SH SYNOPSIS
CALL CURVPS (N, X, Y, P, D, ISW, S, EPS, YS, YSP, SIGMA, TEMP, IER) 
.sp
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. 
.sp
Three parameters are used to control the degree of smoothness -- D,
S, and EPS. 
.sp
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. 
.sp
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). 
.sp
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)). 
.SH DESCRIPTION
.IP N 12
(integer, input) The number of input data values. (N > 1) 
.IP X 12
(integer, input) An array containing the abscissae for the input function. 
.IP Y 12
(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. 
.IP P 12
(real, input) The period of the function. 
.IP D 12
(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). 
.IP ISW 12
(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. 
.IP S 12
(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). 
.IP EPS 12
(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)). 
.IP YS 12
(integer, input) An array of length N. 
.IP YSP 12
(integer, input) An array of length N. 
.IP SIGMA 12
(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. 
.IP TEMP 12
(integer, input) Scratch space. 
.IP IER 12
(integer, input) An error return value. If IER is returned as 0, then no errors
were detected. 
.sp
= 1 if N is less than 2. 
.br
= 2 if S is negative. 
.br
= 3 if EPS is negative or greater than 1. 
.br
= 4 if X values are not strictly increasing. 
.br
= 5 if D is negative. 
.br
= 6 if P is less than or equal to X(N)-X(1). 
.SH ACCESS
To use CURVPS, load the NCAR Graphics library ngmath.
.SH SEE ALSO
curvp2,
fitgrid_params.
.sp
Complete documentation for Fitgrid is available at URL
.br
http://ngwww.ucar.edu/ngdoc/ng/ngmath/fitgrid/fithome.html
.SH COPYRIGHT
Copyright (C) 2000
.br
University Corporation for Atmospheric Research
.br

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