`csa2xs` calculates an approximating cubic spline for
two-dimensional input data.
csa2xs
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
csa2s.

**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 csa2xs( xi[*] : float, yi[*] : float, zi[*] : float, wts[*] : float, knots[2] : integer smth[1] : float nderiv[2] : float xo[*] : float yo[*] : 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. *zi*- A one-dimensional array of the same size as
*xi*and*yi*containing the functional values at the input data coordinates given by*xi*and*yi*.*zi*[k] is the input function value at (*xi*[k],*yi*[k]) for k=0 to dimsizes(*xi*)-1. - wts
- An array containing weights for the
*zi*values at the input*xi*and*yi*values, that is,*wts*(k) is a weight for the value of*zi*(k) for k=0,dimsizes(*xi*)-1. If you do not desire to weight the input*zi*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`csa2xs`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 approximating
surface.
*knots*(0) and*knots*(1) must both be at least 4. The larger the value for*knots*, the closer the approximated surface 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 (=0), first derivative values (=1), or second derivative values (=2) in each of the two coordinate directions.
*xo*- A one-dimensional array containing the X coordinates of the output surface.
*yo*- A one-dimensional array containing the Y coordinates of the output surface.

`csa2xs` is in the
csagrid package
- a software package 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 ; ; Create the input arrays. ; xmin = -1. xmax = 1. ymin = -1. ymax = 1. nx = 29 ny = 25 ndata = 1000 xi = new(ndata,float) yi = new(ndata,float) zi = new(ndata,float) ; ; Generate input data using the function f(x,y) = y**2 - 0.5*y*x**2 ; do i=0,ndata-1 xi(i) = xmin + (xmax-xmin)*rand()/32767. yi(i) = ymin + (ymax-ymin)*rand()/32767. zi(i) = yi(i)*yi(i) - 0.5*xi(i)*xi(i)*yi(i) end do ; ; Set up the output grid. ; xo = fspan(xmin,xmax,nx) yo = fspan(ymin,ymax,ny) knots = (/4,4/) ; ; Calculate the approximated function values. ; wts = -1. smth = 0. nderiv = (/1,2/) yo = csa2xs(xi,yi,zi,wts,knots,smth,nderiv,xo,yo) end

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