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.

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

$\mathrm{points1},\mathrm{data1}≔\begin{array}{c}\left[\begin{array}{cc}0.814723686393179& 0.706046088019609\\ 0.905791937075619& 0.0318328463774207\\ 0.126986816293506& 0.276922984960890\\ 0.913375856139019& 0.0461713906311539\\ 0.632359246225410& 0.0971317812358475\\ 0.0975404049994095& 0.823457828327293\\ 0.278498218867048& 0.694828622975817\\ 0.546881519204984& 0.317099480060861\\ 0.957506835434298& 0.950222048838355\\ 0.964888535199277& 0.0344460805029088\\ ⋮& ⋮\end{array}\right]\\ \hfill \text{30 × 2 Matrix}\end{array},\begin{array}{c}\left[\begin{array}{c}\mathrm{-1.31317888309841}\\ 3.78399452938781\\ \mathrm{-4.07906747556730}\\ 2.81033657021080\\ 3.07159908082332\\ 0.128958765233144\\ \mathrm{-3.21737272238246}\\ 0.707245165710619\\ 0.0877877303791926\\ 0.937296621856498\\ ⋮\end{array}\right]\\ \hfill \text{30 element Vector[column]}\end{array}$

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

$\mathrm{k1}≔\left(\begin{array}{c}\mathrm{Kriging\; int\ⅇrpolation\; obȷ\ⅇct\; with\; 30\; sampl\ⅇ\; points}\\ \mathrm{Variogram:\; Sph\ⅇrical(1.25259453854482,13.6487615617247,.5525536774)}\end{array}\right)$

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

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

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

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

$\mathrm{points2},\mathrm{data2}≔\begin{array}{c}\left[\begin{array}{ccc}0.& 0.& 0.\\ 0.200000000000000& 0.& 0.\\ 0.400000000000000& 0.& 0.\\ 0.600000000000000& 0.& 0.\\ 0.800000000000000& 0.& 0.\\ 1.& 0.& 0.\\ 1.& 0.200000000000000& 0.\\ 0.800000000000000& 0.200000000000000& 0.\\ 0.600000000000000& 0.200000000000000& 0.\\ 0.400000000000000& 0.200000000000000& 0.\\ ⋮& ⋮& ⋮\end{array}\right]\\ \hfill \text{216 × 3 Matrix}\end{array},\begin{array}{c}\left[\begin{array}{c}\mathrm{-7.24064444344000}\\ \mathrm{-7.04470706561314}\\ \mathrm{-6.78359898038514}\\ \mathrm{-6.52781963683906}\\ \mathrm{-4.98147399010851}\\ \mathrm{-3.11344813876699}\\ \mathrm{-3.32786898604254}\\ \mathrm{-5.73148375450573}\\ \mathrm{-6.06925765878197}\\ \mathrm{-6.70824019207924}\\ ⋮\end{array}\right]\\ \hfill \text{216 element Vector[column]}\end{array}$

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

$\mathrm{k2}≔\left(\begin{array}{c}\mathrm{Kriging\; int\ⅇrpolation\; obȷ\ⅇct\; with\; 216\; sampl\ⅇ\; points}\\ \mathrm{Variogram:\; Sph\ⅇrical(1.49801816144044,21.6426663001048,.8)}\end{array}\right)$

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

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

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

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

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