smile.interpolation

Class ShepardInterpolation

• java.lang.Object
• smile.interpolation.ShepardInterpolation

• ```public class ShepardInterpolation
extends java.lang.Object```
Shepard interpolation is a special case of normalized radial basis function interpolation if the function φ(r) goes to infinity as r → 0, and is finite for r > 0. In this case, the weights wi are just equal to the respective function values yi. So we need not solve linear equations and thus it works for very large N.

An example of such φ is `φ(r) = r-p` with (typically) `1 < p ≤ 3`.

Shepard interpolation is rarely as accurate as the well-tuned application of other radial basis functions. However, it is simple, fast, and often just the thing for quick and dirty applications.

• Constructor Summary

Constructors
Constructor and Description
```ShepardInterpolation(double[][] x, double[] y)```
Constructor.
```ShepardInterpolation(double[][] x, double[] y, double p)```
Constructor.
• Method Summary

All Methods
Modifier and Type Method and Description
`double` `interpolate(double... x)`
Interpolate the function at given point.
`java.lang.String` `toString()`
• Methods inherited from class java.lang.Object

`clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait`
• Constructor Detail

• ShepardInterpolation

```public ShepardInterpolation(double[][] x,
double[] y)```
Constructor. By default p = 2.
Parameters:
`x` - the point set.
`y` - the function values at given points.
• ShepardInterpolation

```public ShepardInterpolation(double[][] x,
double[] y,
double p)```
Constructor.
Parameters:
`x` - the point set.
`y` - the function values at given points.
`p` - the parameter in the radial basis function φ(r) = r-p.
• Method Detail

• interpolate

`public double interpolate(double... x)`
Interpolate the function at given point.
• toString

`public java.lang.String toString()`
Overrides:
`toString` in class `java.lang.Object`