# csa3xs

csa3xs calculates an approximating cubic spline for three-dimensional input data. csa3xs 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 csa3s.

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.

## Synopsis

```    function csa3xs(
xi[*]     : float,
yi[*]     : float,
zi[*]     : float,
ui[*]     : float,
wts[*]    : float,
knots[3]  : integer
smth[1]   : float
nderiv[3] : float
xo[*]     : float
yo[*]     : float
zo[*]     : float
)

```

## Arguments

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 Z coordinates of the input data points.
ui
A one-dimensional array of the same size as xi, yi, and zi containing the functional values at the input data coordinates given by xi, yi, and zi. That is ui[k] is the input function value at (xi[k],yi[k],zi[k]) for k=0 to dimsizes(xi)-1.
wts
An array containing weights for the ui values at the input xi, yi, and zi values. That is, wts(k) is a weight for the value of ui(k) for k=0,dimsizes(xi)-1. If you do not desire to weight the input ui 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 csa3xs 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 spline. knots(0), knots(1), and knots(2) must all 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 three coordinate directions.
xo
A one-dimensional array containing the X coordinates of the approximating spline.
yo
A one-dimensional array containing the Y coordinates of the approximating spline.
zo
A one-dimensional array containing the Z coordinates of the approximating spline.

## Return value

csa3xs returns a three-dimensional array containing the calculated functional values. The first dimension of the returned value has the same size as xo, the second dimension of the returned value has the same size as yo, and the third dimension of the returned value has the same size as zo. If uo is the returned value, then uo(i,j,k) contains the functional value at coordinate (xo(i),yo(j),zo(k)).

## Description

csa3xs 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.

## Example

```begin

;
;  Create the input arrays.
;
xmin = -2.
xmax =  2.
ymin = -2.
ymax =  2.
zmin = -2.
zmax =  2.

nx = 21
ny = 21
nz = 21

ndata = 1000
xi = new(ndata,float)
yi = new(ndata,float)
zi = new(ndata,float)
ui = new(ndata,float)

do i=0,ndata-1
xi(i) = xmin + (xmax-xmin)*rand()/32767.
yi(i) = ymin + (ymax-ymin)*rand()/32767.
zi(i) = zmin + (zmax-zmin)*rand()/32767.
ui(i) = xi(i)*xi(i) + yi(i)*yi(i) + zi(i)*zi(i)
end do

;
;  Set up the output grid.
;
xo = fspan(xmin,xmax,nx)
yo = fspan(ymin,ymax,ny)
zo = fspan(zmin,zmax,nz)

;
;  Calculate the values for the approximating cubic spline for the
;  first partial derivative with respect to Y.
;
knots = (/4,4,4/)
wts = -1.
smth = 0.
nderiv = (/0,1,0/)
uo = csa3xs(xi,yi,zi,ui,wts,knots,smth,nderiv,xo,yo,zo)
end
```

### Reference Manual Control Panel

\$Revision: 1.3 \$ \$Date: 1999/03/18 22:39:00 \$