## Class DividedDifferenceInterpolator

• java.lang.Object
• org.apache.commons.math4.legacy.analysis.interpolation.DividedDifferenceInterpolator
• All Implemented Interfaces:
UnivariateInterpolator

public class DividedDifferenceInterpolator
extends Object
implements UnivariateInterpolator
Implements the Divided Difference Algorithm for interpolation of real univariate functions. For reference, see Introduction to Numerical Analysis, ISBN 038795452X, chapter 2.

The actual code of Neville's evaluation is in PolynomialFunctionLagrangeForm, this class provides an easy-to-use interface to it.

Since:
1.2
• ### Constructor Summary

Constructors
Constructor Description
DividedDifferenceInterpolator()
• ### Method Summary

All Methods
Modifier and Type Method Description
protected static double[] computeDividedDifference​(double[] x, double[] y)
Return a copy of the divided difference array.
PolynomialFunctionNewtonForm interpolate​(double[] x, double[] y)
Compute an interpolating function for the dataset.
• ### Methods inherited from class java.lang.Object

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

• #### DividedDifferenceInterpolator

public DividedDifferenceInterpolator()
• ### Method Detail

• #### interpolate

public PolynomialFunctionNewtonForm interpolate​(double[] x,
double[] y)
throws DimensionMismatchException,
NumberIsTooSmallException,
NonMonotonicSequenceException
Compute an interpolating function for the dataset.
Specified by:
interpolate in interface UnivariateInterpolator
Parameters:
x - Interpolating points array.
y - Interpolating values array.
Returns:
a function which interpolates the dataset.
Throws:
DimensionMismatchException - if the array lengths are different.
NumberIsTooSmallException - if the number of points is less than 2.
NonMonotonicSequenceException - if x is not sorted in strictly increasing order.
• #### computeDividedDifference

protected static double[] computeDividedDifference​(double[] x,
double[] y)
throws DimensionMismatchException,
NumberIsTooSmallException,
NonMonotonicSequenceException
Return a copy of the divided difference array.

The divided difference array is defined recursively by

 f[x0] = f(x0)
f[x0,x1,...,xk] = (f[x1,...,xk] - f[x0,...,x[k-1]]) / (xk - x0)


The computational complexity is $$O(n^2)$$ where $$n$$ is the common length of x and y.

Parameters:
x - Interpolating points array.
y - Interpolating values array.
Returns:
a fresh copy of the divided difference array.
Throws:
DimensionMismatchException - if the array lengths are different.
NumberIsTooSmallException - if the number of points is less than 2.
NonMonotonicSequenceException - if x is not sorted in strictly increasing order.