The Kriging command returns a Kriging object. See this help page for a general mathematical description of the Kriging process.

Input sample points must not contain duplicates. The presence of duplicate points can lead to unexpected results.

The following help pages describe the Kriging object and its methods further:

$\mathrm{with}\left(\mathrm{Interpolation}\right)\:$

$\mathrm{points}≔\left[\left[0\,0\right]\,\left[1\,0\right]\,\left[3\,0\right]\,\left[1\,1\right]\,\left[2\,1\right]\,\left[3\,2\right]\,\left[0\,3\right]\,\left[2\,3\right]\right]$

$\mathrm{points}≔\left[\left[0\,0\right]\,\left[1\,0\right]\,\left[3\,0\right]\,\left[1\,1\right]\,\left[2\,1\right]\,\left[3\,2\right]\,\left[0\,3\right]\,\left[2\,3\right]\right]$

$\mathrm{data}≔\left[7.9\,7.7\,11.4\,2.2\,3.0\,5.7\,1.4\,4.6\right]$

$\mathrm{data}≔\left[7.9\,7.7\,11.4\,2.2\,3.0\,5.7\,1.4\,4.6\right]$

$\mathrm{ptp}≔\mathrm{plots}\left[\mathrm{pointplot3d}\right]\left(\left[\mathrm{seq}\left(\left[\mathrm{op}\left(\mathrm{points}\left[i\right]\right)\,\mathrm{data}\left[i\right]\right]\,i=1..\mathrm{nops}\left(\mathrm{points}\right)\right)\right]\right)\:$

$\mathrm{ptp}$

$k≔\mathrm{Kriging}\left(\mathrm{points}\,\mathrm{data}\right)$

$k≔\left(\begin{array}{c}\mathrm{Kriging\; int\ⅇrpolation\; obȷ\ⅇct\; with\; 8\; sampl\ⅇ\; points}\\ \mathrm{Variogram:\; Sph\ⅇrical(4.35,32.49,2.236067977)}\end{array}\right)$

$\mathrm{SetVariogram}\left(k\,\mathrm{Spherical}\left(1\,40\,4\right)\right)$

$\left(\begin{array}{c}\mathrm{Kriging\; int\ⅇrpolation\; obȷ\ⅇct\; with\; 8\; sampl\ⅇ\; points}\\ \mathrm{Variogram:\; Sph\ⅇrical(1,40,4)}\end{array}\right)$

$k\left(3\,0\right)$

$11.4000000000000004$

$k\left(2\,0\right)$

$7.96736181702214896$

$\mathrm{pk}≔\mathrm{plot3d}\left(k\left(x\,y\right)\,x=0..3\,y=0..3\right)\:$

$\mathrm{pk}$

$\mathrm{plots}:-\mathrm{display}\left(\mathrm{ptp}\,\mathrm{pk}\right)$

$k\left(3\,0\,\mathrm{output}=\mathrm{variance}\right)$

$0.$

$k\left(2\,0\,\mathrm{output}=\mathrm{variance}\right)$

$14.8894610336107771$

$\mathrm{plot3d}\left(k\left(x\,y\,\mathrm{output}=\mathrm{variance}\right)\,x=0..3\,y=0..3\right)$

$\mathrm{pk2}≔\mathrm{plot3d}\left(k\left(x\,y\right)\,x=0..3\,y=0..3\,\mathrm{color}=\left[\frac{k\left(x\,y\,\mathrm{output}=\mathrm{variance}\right)}{25}\,0.8\,0.8\,\mathrm{colortype}=\mathrm{HSV}\right]\right)\:$

$\mathrm{plots}:-\mathrm{display}\left(\mathrm{ptp}\,\mathrm{pk2}\right)$

$\mathrm{points},\mathrm{data}≔\mathrm{Kriging}\left[\mathrm{GenerateSpatialData}\right]\left(\mathrm{Spherical}\left(1\,10\,1\right)\right)$

$\mathrm{points},\mathrm{data}≔\begin{array}{c}\left[\begin{array}{cc}0.814723686393179& 0.706046088019609\\ 0.905791937075619& 0.0318328463774207\\ 0.126986816293506& 0.276922984960890\\ 0.913375856139019& 0.0461713906311539\\ 0.632359246225410& 0.0971317812358475\\ 0.0975404049994095& 0.823457828327293\\ 0.278498218867048& 0.694828622975817\\ 0.546881519204984& 0.317099480060861\\ 0.957506835434298& 0.950222048838355\\ 0.964888535199277& 0.0344460805029088\\ ⋮& ⋮\end{array}\right]\\ \hfill \text{30 × 2 Matrix}\end{array},\begin{array}{c}\left[\begin{array}{c}\mathrm{-1.31317888309840}\\ 3.78399452938772\\ \mathrm{-4.07906747556743}\\ 2.81033657021077\\ 3.07159908082336\\ 0.128958765233152\\ \mathrm{-3.21737272238244}\\ 0.707245165710654\\ 0.0877877303791977\\ 0.937296621856632\\ ⋮\end{array}\right]\\ \hfill \text{30 element Vector[column]}\end{array}$

$k≔\mathrm{Kriging}\left(\mathrm{points}\,\mathrm{data}\right)$

$k≔\left(\begin{array}{c}\mathrm{Kriging\; int\ⅇrpolation\; obȷ\ⅇct\; with\; 30\; sampl\ⅇ\; points}\\ \mathrm{Variogram:\; Sph\ⅇrical(1.25259453854473,13.6487615617241,.5525536774)}\end{array}\right)$

$k\left(0.2\,0.3\right)$

$\mathrm{-2.75173577049670470}$

The Interpolation[Kriging]/Constructor command was introduced in Maple 2018.

For more information on Maple 2018 changes, see Updates in Maple 2018.