ComputeGrid - Maple Help

Interpolation[Kriging]

 ComputeGrid
 uses the Kriging process to compute values

 Calling Sequence ComputeGrid(k, bounds, spacing, options)

Parameters

 k - a Kriging object bounds - a list of $n$ ranges specifying the space over which values should be computed, where $n$ is the dimension of the data stored in k spacing - a single numeric value or a list of $n$ numeric values specifying how large the interval between computed values should be along each dimension of the data options - (optional) keyword option of the form variogram=model and/or output=format

Description

 • The ComputeGrid command takes a set of data values contained in the Kriging object. It then uses the same code as for interpolating at a point repeatedly over the specified space at the specified intervals and returns the list of computed values.
 • The predictions are returned as a list of $n+1$-dimensional points, where $n$ is the dimension of the data, and the last coordinate contains the computed value.
 • If the spacing parameter is a list, then each value specifies the spacing of predicted values in its corresponding dimension.  If the spacing parameter is a single value, this value is used for the spacing of all dimensions.
 • By default, the variogram set in the Kriging object is used. This can be overridden by specifying the variogram = model option. model can be given with its nugget, sill, and range parameters specified or without specifying them. If they are not specified, they will be set automatically by calling FitVariogramParameters.
 • By using the output = format keyword option, you can select an alternative output if the data is 2-dimensional. In particular, you can specify output = plot to obtain a plot of the computed values. The default is output = points.

Examples

 > $\mathrm{points},\mathrm{data}≔\mathrm{Interpolation}:-\mathrm{Kriging}:-\mathrm{GenerateSpatialData}\left(\mathrm{Spherical}\left(1,10,1\right)\right)$
 ${\mathrm{points}}{,}{\mathrm{data}}{≔}\begin{array}{c}\left[\begin{array}{cc}{0.814723686393179}& {0.706046088019609}\\ {0.905791937075619}& {0.0318328463774207}\\ {0.126986816293506}& {0.276922984960890}\\ {0.913375856139019}& {0.0461713906311539}\\ {0.632359246225410}& {0.0971317812358475}\\ {0.0975404049994095}& {0.823457828327293}\\ {0.278498218867048}& {0.694828622975817}\\ {0.546881519204984}& {0.317099480060861}\\ {0.957506835434298}& {0.950222048838355}\\ {0.964888535199277}& {0.0344460805029088}\\ {⋮}& {⋮}\end{array}\right]\\ \hfill {\text{30 × 2 Matrix}}\end{array}{,}\begin{array}{c}\left[\begin{array}{c}{-1.31317888309841}\\ {3.78399452938781}\\ {-4.07906747556730}\\ {2.81033657021080}\\ {3.07159908082332}\\ {0.128958765233144}\\ {-3.21737272238246}\\ {0.707245165710619}\\ {0.0877877303791926}\\ {0.937296621856498}\\ {⋮}\end{array}\right]\\ \hfill {\text{30 element Vector[column]}}\end{array}$ (1)
 > $k≔\mathrm{Interpolation}:-\mathrm{Kriging}\left(\mathrm{points},\mathrm{data}\right)$
 ${k}{≔}\left(\begin{array}{c}{Kriging intⅇrpolation obȷⅇct with 30 samplⅇ points}\\ {Variogram: Sphⅇrical\left(1.25259453854482,13.6487615617247,.5525536774\right)}\end{array}\right)$ (2)
 > $\mathrm{SetVariogram}\left(k,\mathrm{Spherical}\left(1,10,1\right)\right)$
 $\left(\begin{array}{c}{Kriging intⅇrpolation obȷⅇct with 30 samplⅇ points}\\ {Variogram: Sphⅇrical\left(1,10,1\right)}\end{array}\right)$ (3)
 > $\mathrm{ComputeGrid}\left(k,\left[0..5,0..5\right],0.1,\mathrm{output}=\mathrm{plot}\right)$

Compatibility

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