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Interpolation[Kriging]

  

procedure_call

  

use the Kriging process to predict the value at one or more points

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

k(coordinates)

k(coordinates, outopt)

Parameters

k

-

a Kriging object

coordinates

-

sequence specifying the coordinates of the point at which the value will be predicted, or a Matrix where each row specifies the coordinates of one point

outopt

-

(optional) keyword option of the form output=format

Description

• 

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.

Examples

withInterpolation:

We generate some data points according to the Spherical1,10,1 variogram.

points,dataKriging:-GenerateSpatialDataSpherical1,10,1

(1)

The next step is to create the Kriging object.

kKrigingpoints,data

kKrⅈgⅈng ⅈntⅇrpolatⅈon obȷⅇct wⅈth 30 samplⅇ poⅈntsVarⅈogram: Sphⅇrⅈcal(1.25259453854485,13.6487615617233,.5525536774)

(2)

We can use this object as is with a variogram estimated purely from the data, but we should expect to get better results if we set the variogram that we know underlies these data.

SetVariogramk,Spherical1,10,1

Krⅈgⅈng ⅈntⅇrpolatⅈon obȷⅇct wⅈth 30 samplⅇ poⅈntsVarⅈogram: Sphⅇrⅈcal(1,10,1)

(3)

We can now find the interpolated value for any point, and the variance at such points, as well.

k0.2,0.3

−2.65388575588638265

(4)

k0.2,0.3,output=variance

2.46857252864955656

(5)

k0.2,0.3,output=both

−2.65388575588638265,2.46857252864955656

(6)

Like any function of two variables, you can plot the interpolated surface with the plot3d command. One can also plot the variance.

plot3dkx,y,x=0..1,y=0..1

plot3dk,0..1,0..1

plot3dkx,y,output=variance,x=0..1,y=0..1

You can even plot the interpolated surface, and use the color to indicate the variance.

plot3dkx,y,x=0..1,y=0..1,color=kx,y,output=variance5,0.8,0.8,colortype=HSV

You can also approximate the area under the surface using numerical integration.

intk,0..1,0..1,numeric,ε=0.1,method=_CubaCuhre

−0.915288153662575

(7)

Compatibility

• 

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

• 

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

See Also

ComputeGrid

Constructor

Kriging

SetVariogram