Overview of the Interpolation Package - Maple Programming Help

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Overview of the Interpolation Package

 

Description

List of Interpolation Package Commands

List of Kriging Commands

Comparing the Interpolation Package to Similar Functionality in Other Packages

Compatibility

Description

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The Interpolation package contains functions for interpolation.

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It includes methods that support interpolation of irregularly spaced data and a method for kriging interpolation using variograms.

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Each command in the Interpolation package can be accessed by using either the long form or the short form of the command name in the calling sequence.

  

As the underlying implementation of the Interpolation package is a module, it is also possible to use the form Interpolation:-command to access a command from the package. For more information, see Module Members.

List of Interpolation Package Commands

CubicInterpolation

HighestNeighborInterpolation

Interpolate

InverseDistanceWeightedInterpolation

LinearInterpolation

LinearTriangularInterpolation

LowestNeighborInterpolation

NaturalNeighborInterpolation

NearestNeighborInterpolation

RadialBasisFunctionInterpolation

SplineInterpolation

 

List of Kriging Commands

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

 

Comparing the Interpolation Package to Similar Functionality in Other Packages

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The CurveFitting package also supports various interpolation methods. This section compares the interpolation functionality in both packages. There are many concrete examples on the Interpolation and Smoothing example help page.

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The interpolation methods available in the Interpolation package all work as follows. First, the user calls one of the commands in the package, submitting the input points and the values at these points. This returns an object encapsulating all the data and options submitted. This object can then be used like a normal mathematical function, e.g. for plotting, integration, or just to evaluate at a given point. This feature makes this package a little easier to use than similar functionality in the CurveFitting package.

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Additionally, the Interpolation package supports some methods of interpolation not supported by the CurveFitting package - in particular, the CurveFitting package only supports interpolation with more than one independent dimension if the input points form a grid; this is not needed for Radial Basis Function Interpolation, Inverse Distance Weighted Interpolation, Kriging Interpolation, Natural Neighbor Interpolation, or Linear Triangular Interpolation available in the Interpolation package.

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On the other hand, the CurveFitting package supports some functionality not supported by the Interpolation package:

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The Lowess command applies smoothing to the given data points; it performs approximation rather than interpolation. There is some similar functionality in the CurveFitting[LeastSquares] command, in various commands in the Statistics package, and in the TimeSeriesAnalysis package.

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The BSpline and BSplineCurve commands define arbitrary curves in the plane, rather than functional relationship with an input and output.

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The PolynomialInterpolation, RationalInterpolation, Spline, and Thiele commands allow for symbolic expressions as the results.

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Consequently, use of the Interpolation package is recommended whenever you want to do interpolation and get floating-point answers, or if you want to do interpolation with more than one independent dimension.

Compatibility

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The Interpolation package was introduced in Maple 2018.

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