Package ca.cgjennings.math

Class Interpolation.InterpolatedFunction

java.lang.Object

ca.cgjennings.math.Interpolation.InterpolatedFunction

All Implemented Interfaces:

Fn

Direct Known Subclasses:

Interpolation.CubicSpline, Interpolation.LinearRegression, Interpolation.QuadraticRegression

Enclosing class:

Interpolation

public abstract static class Interpolation.InterpolatedFunction
extends java.lang.Object
implements Fn

This is a base class for interpolated functions. An interpolated function is given a set of points. It then creates a function for a curve that passes through or near those points, interpolating "smoothly" between them.

One way to think of this is that you have a mystery curve that you don't have a function for, but that you have some (possibly noisy) points which are on or near the curve. An InterpolatedFunction will create a function for your mystery curve, allowing you to evaluate the function for any point instead of just your sample points. Depending on the kind of interpolation, the data may be assumed to be noisy (the interpolator finds a curve of best fit, effectively adjusting the points to fit an idealized curve) or it may assume that the data are perfect (the interpolator passes through each points, adjusting the curve as needed). It may also fall between these extremes, coming close to each point but not necessarily passing through it.

Field Summary

Fields inherited from interface ca.cgjennings.math.Fn

IDENTITY

Constructor Summary

Constructors

Constructor	Description
InterpolatedFunction(double[] x, double[] y)	Creates an interpolated function for the points (x[0],y[0]), (x[1],y[1]), ..., (x[x.length-1],y[y.length-1).

Method Summary

Modifier and Type	Method	Description
protected void	checkPoints(double[] x, double[] y)	Checks that the set of sample points satisfy any criteria for using the interpolator.
abstract double	f(double x)	Returns the y-value of the interpolation function given an x-value.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

InterpolatedFunction

public InterpolatedFunction(double[] x,
                            double[] y)

Creates an interpolated function for the points (x[0],y[0]), (x[1],y[1]), ..., (x[x.length-1],y[y.length-1). The nature of the interpolation is determined by the concrete implementation.

The base class calls checkPoints(double[], double[]) in order to validate the input, but does nothing else.

Parameters:

x - an array of x-values for the points

y - an array of y-values for the points

Throws:

java.lang.NullPointerException - if either array is null

java.lang.IllegalArgumentException - if the data point criteria are not met

Method Detail

checkPoints

protected void checkPoints(double[] x,
                           double[] y)

Checks that the set of sample points satisfy any criteria for using the interpolator. The base class checks the following:

• x and y must be non-null and have the same length
• there must be at least one point (note that the concrete subclass may require more than one point; check the specific class for details)
• the values of x must be strictly increasing (for all j in 1 to x.length-1, x[j-1] < x[j]); this simply means that the x values must be sorted from lowest to highest and must not contain any repeats

Subclasses should call the superclass implementation and then perform any additional checks specific to the interpolator.

Parameters:

x - an array of x-values for the points

y - an array of y-values for the points

Throws:

java.lang.NullPointerException - if either array is null

java.lang.IllegalArgumentException - if the criteria above are not met

f

public abstract double f(double x)

Returns the y-value of the interpolation function given an x-value.

Specified by:

f in interface Fn

Parameters:

x - the value to evaluate the curve function at

Returns:

f(x), where f is a function for the interpolating curve