Kriging - Maple Help

Interpolation

 Kriging
 an overview of Kriging objects

Description

 • Kriging is a method for unstructured spatial interpolation. It is based upon a variogram function which models the variance between two data points as a function of their distance. Typically, this is an increasing function, since points closer together are likely to have more similar values (less variance). Based on the variogram and the distances from the evaluation point to all input points, a weight for each input value is computed, and these weights are used to compute a weighted average which is the predicted value.  The variograms supported by Maple, such as the Spherical and Exponential variograms, are detailed in the SetVariogram help page.
 • The following help pages describe the Kriging object and its methods further:

Examples

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

Create some data that is spatially correlated:

 > $\mathrm{points},\mathrm{data}≔\mathrm{Kriging}\left[\mathrm{GenerateSpatialData}\right]\left(\mathrm{Spherical}\left(1,10,1\right)\right)$
 ${\mathrm{points}}{,}{\mathrm{data}}{≔}\begin{array}{c}\left[\begin{array}{cc}{0.814723686393179}& {0.706046088019609}\\ {0.905791937075619}& {0.0318328463774207}\\ {0.126986816293506}& {0.276922984960890}\\ {0.913375856139019}& {0.0461713906311539}\\ {0.632359246225410}& {0.0971317812358475}\\ {0.0975404049994095}& {0.823457828327293}\\ {0.278498218867048}& {0.694828622975817}\\ {0.546881519204984}& {0.317099480060861}\\ {0.957506835434298}& {0.950222048838355}\\ {0.964888535199277}& {0.0344460805029088}\\ {⋮}& {⋮}\end{array}\right]\\ \hfill {\text{30 × 2 Matrix}}\end{array}{,}\begin{array}{c}\left[\begin{array}{c}{-1.31317888309841}\\ {3.78399452938781}\\ {-4.07906747556730}\\ {2.81033657021080}\\ {3.07159908082332}\\ {0.128958765233144}\\ {-3.21737272238246}\\ {0.707245165710619}\\ {0.0877877303791926}\\ {0.937296621856498}\\ {⋮}\end{array}\right]\\ \hfill {\text{30 element Vector[column]}}\end{array}$ (1)

Create a Kriging object:

 > $k≔\mathrm{Kriging}\left(\mathrm{points},\mathrm{data}\right)$
 ${k}{≔}\left(\begin{array}{c}{Kriging intⅇrpolation obȷⅇct with 30 samplⅇ points}\\ {Variogram: Sphⅇrical\left(1.25259453854482,13.6487615617247,.5525536774\right)}\end{array}\right)$ (2)

Use the Kriging object to interpolate at a given point:

 > $k\left(0.2,0.3\right)$
 ${-2.75173577049670337}$ (3)

Compatibility

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