A Kriging object can be used in a function call. Used in this way, the function call makes use of the data stored in the Kriging object to predict the value at the point of the given coordinates.

The variogram set in the Kriging object is used to carry out the prediction. This can be set by using the SetVariogram procedure.

By default, the predicted value is returned. This is equivalent to the behavior if output=value. If output=variance then the variance associated with the predicted value is returned, which can be used as a measure of the uncertainty in the prediction. If output=both, then the sequence val, var is returned, where val is the predicted value and var is the associated variance.

coordinates can be an $m$-by-$n$ dimensional matrix, where $n$ is the dimensionality of the point data stored in the Kriging object. Each of the $m$ rows is treated as the coordinates of a point where the Kriging interpolation will be performed. If output=both then an $m$-by-2 matrix will be returned, with the first column corresponding to the predicted values and the second column corresponding to the variances. Otherwise, a column vector will be returned containing either the predicted values or variances as specified.

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

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

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

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

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

$\mathrm{SetVariogram}\left(k\,\mathrm{Spherical}\left(1\,10\,1\right)\right)$

$\left(\begin{array}{c}\mathrm{Kriging\; int\ⅇrpolation\; obȷ\ⅇct\; with\; 30\; sampl\ⅇ\; points}\\ \mathrm{Variogram:\; Sph\ⅇrical(1,10,1)}\end{array}\right)$

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

$\mathrm{-2.65388575588639997}$

$k\left(0.2\,0.3\,\mathrm{output}=\mathrm{variance}\right)$

$2.46857252864955568$

$k\left(0.2\,0.3\,\mathrm{output}=\mathrm{both}\right)$

$\mathrm{-2.65388575588639997},2.46857252864955568$

$\mathrm{plot3d}\left(k\left(x\,y\right)\,x=0..1\,y=0..1\right)$

$\mathrm{plot3d}\left(k\,0..1\,0..1\right)$

$\mathrm{plot3d}\left(k\left(x\,y\,\mathrm{output}=\mathrm{variance}\right)\,x=0..1\,y=0..1\right)$

$\mathrm{plot3d}\left(k\left(x\,y\right)\,x=0..1\,y=0..1\,\mathrm{color}=\left[\frac{k\left(x\,y\,\mathrm{output}=\mathrm{variance}\right)}{5}\,0.8\,0.8\,\mathrm{colortype}=\mathrm{HSV}\right]\right)$

$\mathrm{int}\left(k\,0..1\,0..1\,\mathrm{numeric}\,\mathrm{\epsilon }=0.1\,\mathrm{method}=\mathrm{\_CubaCuhre}\right)$

$\mathrm{-0.915288153662587}$

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

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