The GenerateSpatialData command takes a variogram and generates a set of points and associated data reflective of that variogram model. These points and data can then be used to experiment with, or demonstrate, Kriging interpolation.

If the grid=true option is given, then the points are located in a square $d$-dimensional grid, at coordinates equally spaced between 0 and 1. As a consequence, there will be $k^d$ points in total, for some $k$. Maple chooses $k$ as $⌊n^{\frac{1}{d}}⌋$; consequently, the number of points generated may be smaller than $n$. For example, if $d$ has its default value of 2, then the number of points will be reduced to the largest perfect square that is not greater than n.

If the grid=true option is not given, then the points are uniformly randomly selected from the $d$-dimensional unit cube. In this case, exactly $n$ points are generated.

The data set is returned as an expression sequence of a list of lists representing the points, and a Vector of values at those points.

$\mathrm{points1},\mathrm{data1}≔\mathrm{Interpolation}:-\mathrm{Kriging}:-\mathrm{GenerateSpatialData}\left(\mathrm{Spherical}\left(1\,10\,1\right)\right)$

$\mathrm{k1}≔\mathrm{Interpolation}:-\mathrm{Kriging}\left(\mathrm{points1}\,\mathrm{data1}\right)$

$\mathrm{k1}≔\left(\begin{array}{c}\mathrm{Kriging\; int\ⅇrpolation\; obȷ\ⅇct\; with\; 30\; sampl\ⅇ\; points}\\ \mathrm{Variogram:\; Sph\ⅇrical(1.25259453854486,13.6487615617241,.5525536774)}\end{array}\right)$

$\mathrm{SetVariogram}\left(\mathrm{k1}\,\mathrm{Spherical}\left(1\,10\,1\right)\right)$

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

$\mathrm{ComputeGrid}\left(\mathrm{k1}\,\left[0..1\,0..1\right]\,0.1\,\mathrm{output}=\mathrm{plot}\right)$

$\mathrm{points2},\mathrm{data2}≔\mathrm{Interpolation}:-\mathrm{Kriging}:-\mathrm{GenerateSpatialData}\left(\mathrm{RationalQuadratic}\left(0.1\,10\,4\right)\,216\,\mathrm{dimension}=3\,\mathrm{grid}=\mathrm{true}\right)$

$\mathrm{k2}≔\mathrm{Interpolation}:-\mathrm{Kriging}\left(\mathrm{points2}\,\mathrm{data2}\right)$

$\mathrm{k2}≔\left(\begin{array}{c}\mathrm{Kriging\; int\ⅇrpolation\; obȷ\ⅇct\; with\; 216\; sampl\ⅇ\; points}\\ \mathrm{Variogram:\; Sph\ⅇrical(1.57713557301257,22.6431969077444,.8)}\end{array}\right)$

$\mathrm{SetVariogram}\left(\mathrm{k2}\,\mathrm{RationalQuadratic}\left(0.1\,10\,4\right)\right)$

$\left(\begin{array}{c}\mathrm{Kriging\; int\ⅇrpolation\; obȷ\ⅇct\; with\; 216\; sampl\ⅇ\; points}\\ \mathrm{Variogram:\; RationalQua\ⅆratic(.1,10,4)}\end{array}\right)$

$\mathrm{plots}:-\mathrm{implicitplot3d}\left(\mathrm{k2}\left(x\,y\,z\right)=\mathrm{Statistics}:-\mathrm{Median}\left(\mathrm{data2}\right)\,x=0..1\,y=0..1\,z=0..1\,\mathrm{grid}=\left[8\,8\,8\right]\right)$

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

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