`csa1xs` calculates an approximating cubic spline for one-dimensional
input data. c_csa1xs
is called if you want to
weight
the input data values,
calculate
derivatives,
or
handle data
sparse areas specially.
If you do not
want to do any of these three things, then use
c_csa1s.

**Note:** This function is only available in version 4.1.1 of
NCL. If your site is licensed for version 4.1, then you can get
version 4.1.1 for free. To get version 4.1.1 of NCAR Graphics
software, please contact your site representative. If you don't know
who your site representative is, then send email to ncarginf@ucar.edu or call (303)
497-1201.

function csa1xs( xi[*] : float, yi[*] : float, wts[*] : float, knots[1] : integer smth[1] : float nderiv[1] : float xo[*] : float )

*xi*- A one-dimensional array of any size containing the X coordinates of the input data points.
*yi*- A one-dimensional array of the same size as
*xi*containing the Y coordinates of the input data points. - wts
- An array containing weights for the
*yi*values at the input*xi*values, that is,*wts*(k) is a weight for the value of*yi*(k) for k=0,dimsizes(*xi*)-1. If you do not desire to weight the input*yi*values, then set*wts*to -1, and in that case*wts*can be a scalar. The weights in the*wts*array are relative and may be set to any non-negative value. When`csa1xs`is called, the weights are summed and the individual weights are normalized so that the weight sum is unity. *knots*- The number of knots to be used in constructing the approximation
spline.
*knots*must be at least 4. The larger the value for*knots*, the closer the approximated curve will come to passing through the input function values. *smth*- A parameter that controls extrapolation into data sparse regions.
If
*smth*is zero, then nothing special is done in data sparse regions. A good first choice for*smth*is 1. *nderiv*- Specifies whether you want functional values (
*nderiv*=0), first derivative values (*nderiv*=1), or second derivative values (*nderiv*=2). *xo*- A one-dimensional array containing the X coordinates of the output curve.

`csa1xs` is in the
csagrid package
- a software package in the
ngmath library that
implements a cubic spline approximation algorithm to
fit a function to input data. The input for the approximation is
a set of randomly-spaced data. These data may be one-dimensional,
two-dimensional, or three-dimensional.

The general documentation for csagrid contains several complete examples for entries in the csagrid package.

begin ;----------- Define original data -------------------------------------- xi = (/0.0, 0.1, 0.2, 0.3, 0.5, 0.6, 0.65, 0.8, 0.9, 1./) yi = (/0.0, 0.8, -0.9, -0.9, 0.9, 1.0, 0.90, -0.8, -0.8, 0./) npts = 101 xo = fspan(0.0,1.0,npts) ; Create the output X coordinate array. ;--- Calculate approximated first derivative values. knots = 4 wts = -1. smth = 0. nderiv = 1 yo = csa1xs(xi,yi,wts,knots,smth,nderiv,xo) end

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