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# nngetwtsd

Retrieves natural neighbors and weights for the function values at those neighbors.

## Prototype

```	procedure nngetwtsd (
numw [1] : integer,
nbrs [*] : integer,
wts  [*] : double,
xe   [3] : double,
ye   [3] : double,
ze   [3] : double
)
```

## Arguments

numw

(output)
The number of natural neighbors involved in the most recent call to nnpnt[s|d].

nbrs

(output)
An array of indices of the natural neighbors of the coordinate in the most recent call to nnpnt[s|d]. These indices are for the original input data for nnpntinit[s|d]. For example, if I is an index returned in nbrs, then (X(I),Y(I)) (where the X and Y arrays referred to here are the ones used as arguments to nnpntinit[s|d]) is a neighbor of the input coordinate involved in the most recent call to nnpnt[s|d]. You should probably dimension this array to be the same as the size of your original input data arrays, plus 3 (see the description of xe, ye, and ze, below, for an explanation of the "plus 3").

wts

(output)
The weights used for the input data at the neighbors. For example, if nbrs(N) = M, then wts(N) would be the weight applied to the original function value F(M). The sum of wts(L) for L=1,numw should be unity.

xe
ye
ze

(output)
These are three additional values to be added to the input dataset. The way that Natgrid handles extrapolation is to enclose the coordinates of the original dataset within a large triangle, and to determine function values at the vertices of this triangle by fitting a plane to the original data by least sum of squared distances. So, it is possible that one of these three additional points may be indexed in the list of natural neighbors returned.

## Description

This function is part of the Natgrid package, which implements a natural neighbor interpolation method. Much useful information is available at the above link, including the descriptions of many control parameters that can be modified to materially change its behavior. (The functions nngetp and nnsetp are used to access these parameters.)

nngetwtsd is called to retrieve natural neighbors and weights for the function values at those neighbors. It can be called only after a call to nnpnt[s|d] and before the next call to nnpntend[d].

## Examples

```begin
nxyz = 171
x = new(nxyz+3,double)
y = new(nxyz+3,double)
z = new(nxyz+3,double)
;
;  Coordinate data are defined as random numbers between -0.2
;  and 1.2 and are explicitly defined here for uniformity
;  across platforms.
;
x(0:nxyz-1) = (/ \
1.16,  0.47,  0.29,  0.72,  0.52,  1.12,  0.33,  0.20,  0.30, \
0.78,  0.92,  0.52,  0.44,  0.22, -0.10,  0.11,  0.59,  1.13, \
0.68,  1.11,  0.93,  0.29,  0.74,  0.43,  0.87,  0.87, -0.10, \
0.26,  0.85,  0.00, -0.02,  1.01, -0.12,  0.65,  0.39,  0.96, \
0.39,  0.38,  0.94, -0.03, -0.17,  0.00,  0.03,  0.67, -0.06, \
0.82, -0.03,  1.08,  0.37,  1.02, -0.11, -0.13,  1.03,  0.61, \
0.26,  0.18,  0.62,  0.42,  1.03,  0.72,  0.97,  0.08,  1.18, \
0.00,  0.69,  0.10,  0.80,  0.06,  0.82,  0.20,  0.46,  0.37, \
1.16,  0.93,  1.09,  0.96,  1.00,  0.80,  0.01,  0.12,  1.01, \
0.48,  0.79,  0.04,  0.42,  0.48, -0.18,  1.16,  0.85,  0.97, \
0.14,  0.40,  0.78,  1.12,  1.19,  0.68,  0.65,  0.41,  0.90, \
0.84, -0.11, -0.01, -0.02, -0.10,  1.04,  0.58,  0.61,  0.12, \
-0.02, -0.03,  0.27,  1.17,  1.02,  0.16, -0.17,  1.03,  0.13, \
0.04, -0.03,  0.15,  0.00, -0.01,  0.91,  1.20,  0.54, -0.14, \
1.03,  0.93,  0.42,  0.36, -0.10,  0.57,  0.22,  0.74,  1.15, \
0.40,  0.82,  0.96,  1.09,  0.42,  1.13,  0.24,  0.51,  0.60, \
0.06,  0.38,  0.15,  0.59,  0.76,  1.16,  0.02,  0.86,  1.14, \
0.37,  0.38,  0.26,  0.26,  0.07,  0.87,  0.90,  0.83,  0.09, \
0.03,  0.56, -0.19,  0.51,  1.07, -0.13,  0.99,  0.84,  0.22 /)

y(0:nxyz-1) = (/ \
-0.11,  1.07,  1.11, -0.17,  0.08,  0.09,  0.91,  0.17, -0.02, \
0.83,  1.08,  0.87,  0.46,  0.66,  0.50, -0.14,  0.78,  1.08, \
0.65,  0.00,  1.03,  0.06,  0.69, -0.16,  0.02,  0.59,  0.19, \
0.54,  0.68,  0.95,  0.30,  0.77,  0.94,  0.76,  0.56,  0.12, \
0.05, -0.07,  1.01,  0.61,  1.04, -0.07,  0.46,  1.07,  0.87, \
0.11,  0.63,  0.06,  0.53,  0.95,  0.78,  0.48,  0.45,  0.77, \
0.78,  0.29,  0.38,  0.85, -0.10,  1.17,  0.35,  1.14, -0.04, \
0.34, -0.18,  0.78,  0.17,  0.63,  0.88, -0.12,  0.58, -0.12, \
1.00,  0.99,  0.45,  0.86, -0.15,  0.97,  0.99,  0.90,  0.42, \
0.61,  0.74,  0.41,  0.44,  1.08,  1.06,  1.18,  0.89,  0.74, \
0.74, -0.06,  0.00,  0.99,  0.03,  1.00, -0.04,  0.24,  0.65, \
0.12,  0.13, -0.09, -0.05,  1.03,  1.07, -0.02,  1.18,  0.19, \
0.03, -0.03,  0.86,  1.12,  0.38,  0.72, -0.20, -0.08, -0.18, \
0.32,  0.13, -0.19,  0.93,  0.81,  0.31,  1.09, -0.03,  1.01, \
-0.17,  0.84, -0.11,  0.45,  0.18,  0.23,  0.81,  0.39,  1.09, \
-0.05,  0.58,  0.53,  0.96,  0.43,  0.48,  0.96, -0.03,  1.13, \
1.16,  0.16,  1.15,  0.57,  0.13,  0.71,  0.35,  1.04,  0.62, \
1.03,  0.98,  0.31,  0.70,  0.97,  0.87,  1.14,  0.08,  1.19, \
0.88,  1.00,  0.51,  0.03,  0.17,  1.01,  0.44,  0.17, -0.11 /)

z = (x-0.25)*(x-0.25) + (y-0.50)*(y-0.50)

;
; Define an output grid.
;
numxout = 21
xmin = new(1,double)
xmax = new(1,double)
xmin = -0.2
xmax =  1.2
xinc = (xmax-xmin)/(numxout-1.)
xi = xmin + ispan(0,numxout-1,1) * xinc

numyout = 21
ymin = new(1,double)
ymax = new(1,double)
ymin =  -0.2
ymax =   1.2
yinc = (ymax-ymin)/(numyout-1.)
yi = ymin + ispan(0,numyout-1,1) * yinc

zi = new((/numxout,numyout/),double)
;
; Enter single point mode.
;
nnpntinitd(x(0:nxyz-1),y(0:nxyz-1),z(0:nxyz-1))

;
;  Calculate the interpolated values at the desired points.
;
nbrs = new(nxyz+3,integer)
wts  = new(nxyz+3,double)
numw = new(1,integer)
do i=0,numxout-1
do j=0,numyout-1
zi(i,j) = nnpntd(xi(i),yi(j))
;
;  Get the indices for the neighbors and the associated weights.
;
nngetwtsd(numw,nbrs,wts,x(nxyz:nxyz+2),y(nxyz:nxyz+2),z(nxyz:nxyz+2))
;
;  Calculate the interpolated function value at (xi(i),yi(j))
;  using the retrieved neighbors and weights and compare this
;  with the value returned from nnpnts.
;
zp = sum(wts(0:numw-1)*z(nbrs(0:numw-1)))
difference = (zp-zi(i,j))/zp
if (difference .gt. 0.000001) then
print("i = " + i + " j = " + j + " zp = " + zp + "zi = " + zi(i,j))
end if
end do
end do

;
;  Release space allocated by "nnpntinitd" call, above.
;
nnpntendd()

end
```