Interpolation[Kriging] - Maple Programming Help

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Interpolation[Kriging]

  

Constructor

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Kriging(points, data)

Parameters

points

-

a list, Vector, listlist, Array, or Matrix containing the coordinates of the points corresponding to data values. If this is a listlist, each inner list must contain n entries, where n is the dimensionality of the data. If this is an Array or Matrix, then there must be n columns, with each row corresponding to one set of coordinates. If it is a plain list or a Vector, then the input points are 1-dimensional.

data

-

a list, Array, or Matrix containing the data, which must be arranged in the same order as the corresponding coordinates appear in points

Description

• 

The Kriging command returns a Kriging object. See this help page for a general mathematical description of the Kriging process.

• 

Input sample points must not contain duplicates. The presence of duplicate points can lead to unexpected results.

• 

The following help pages describe the Kriging object and its methods further:

apply Kriging at a grid of values

Constructor

display the empirical variogram

fit parameters of a variogram

Interpolate at a point

Overview

Set the variogram for a Kriging object

 

Examples

withInterpolation:

Specify some points and some data manually.

points0,0,1,0,3,0,1,1,2,1,3,2,0,3,2,3

points0,0,1,0,3,0,1,1,2,1,3,2,0,3,2,3

(1)

data7.9,7.7,11.4,2.2,3.0,5.7,1.4,4.6

data7.9,7.7,11.4,2.2,3.0,5.7,1.4,4.6

(2)

We can visualize these points and data values as follows.

ptpplotspointplot3dseqoppointsi,datai,i=1..nopspoints:

ptp

Create a Kriging object.

kKrigingpoints,data

kKrⅈgⅈng ⅈntⅇrpolatⅈon obȷⅇct wⅈth 8 samplⅇ poⅈntsVarⅈogram: Sphⅇrⅈcal(4.35,32.49,2.236067977)

(3)

This uses an estimate to set the variogram used. This is often useful if we do not have a model for the variogram, but if we do, we can set the variogram manually.

SetVariogramk,Spherical1,40,4

Krⅈgⅈng ⅈntⅇrpolatⅈon obȷⅇct wⅈth 8 samplⅇ poⅈntsVarⅈogram: Sphⅇrⅈcal(1,40,4)

(4)

If we evaluate k at one of the input points, we get the corresponding value back.

k3,0

11.4000000000000004

(5)

The value at other points is interpolated.

k2,0

7.96736181702214985

(6)

We can visualize the interpolated surface as follows; or we can include the data points, too.

pkplot3dkx,y,x=0..3,y=0..3:

pk

plots:-displayptp,pk

We can also find out what the modeled variance is at various points.

k3,0,output=variance

0.

(7)

k2,0,output=variance

14.8894610336107736

(8)

We can also display this variance, or use the variance to color the visualization of the interpolated surface.

plot3dkx,y,output=variance,x=0..3,y=0..3

pk2plot3dkx,y,x=0..3,y=0..3,color=kx,y,output=variance25,0.8,0.8,colortype=HSV:

plots:-displayptp,pk2

Maple also contains functionality for generating data that is spatially correlated according to a given variogram.

points,dataKrigingGenerateSpatialDataSpherical1,10,1

(9)

Create a Kriging object:

kKrigingpoints,data

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

(10)

Use the Kriging object to interpolate at a given point:

k0.2,0.3

−2.75173577049668650

(11)

Compatibility

• 

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

• 

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

See Also

Interpolating at a point

Kriging

SetVariogram