org.apache.commons.math.analysis.interpolation
Class DividedDifferenceInterpolator

java.lang.Object
  org.apache.commons.math.analysis.interpolation.DividedDifferenceInterpolator

All Implemented Interfaces:

Serializable, UnivariateRealInterpolator

public class DividedDifferenceInterpolator
extends Object
implements UnivariateRealInterpolator, Serializable

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

Version:

$Revision: 825919 $ $Date: 2009-10-16 16:51:55 +0200 (ven. 16 oct. 2009) $

See Also:

Serialized Form

Constructor Summary

DividedDifferenceInterpolator()

Method Summary

protected static double[]	computeDividedDifference(double[] x, double[] y) Returns a copy of the divided difference array.
PolynomialFunctionNewtonForm	interpolate(double[] x, double[] y) Computes an interpolating function for the data set.

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 DuplicateSampleAbscissaException

Computes an interpolating function for the data set.

Specified by:

interpolate in interface UnivariateRealInterpolator

Parameters:

x - the interpolating points array

y - the interpolating values array

Returns:

a function which interpolates the data set

Throws:

DuplicateSampleAbscissaException - if arguments are invalid

computeDividedDifference

protected static double[] computeDividedDifference(double[] x,
                                                   double[] y)
                                            throws DuplicateSampleAbscissaException

Returns 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).

Parameters:

x - the interpolating points array

y - the interpolating values array

Returns:

a fresh copy of the divided difference array

Throws:

DuplicateSampleAbscissaException - if any abscissas coincide