com.numericalmethod.suanshu.analysis.interpolation
Class NevilleTable

java.lang.Object
  com.numericalmethod.suanshu.analysis.function.rn2r1.UnivariateRealFunction
      com.numericalmethod.suanshu.analysis.interpolation.NevilleTable

All Implemented Interfaces:

Function, RealScalarFunction, UnivariateRealInterpolator

public class NevilleTable
extends UnivariateRealFunction
implements UnivariateRealInterpolator

Neville's algorithm is an algorithm for polynomial interpolation. Given n + 1 points, there is a unique polynomial of degree ≤ n which associates with them. Neville's algorithm evaluates this polynomial for a given input x.

This implementation is based on filling out the Neville table. This table can be used in two ways.

First, it can be used as a function to compute f(x).

Second, it can be used in an incremental manner by adding a few, say one, data points at a time. The user can examine the values in the table.

See Also:

Wikipedia: Neville's algorithm

Nested Class Summary

static class

NevilleTable.DuplicatedAbscissae RuntimeException thrown when there are duplicated abscissae.

Nested classes/interfaces inherited from interface com.numericalmethod.suanshu.analysis.function.Function

Function.EvaluationException

Constructor Summary

NevilleTable()
Construct an empty Neville Table.

NevilleTable(double[] x, double[] y)
Construct an instance of a Neville Table, initialized with data {(x, y)}.

NevilleTable(int n, double[] x, double[] y)
Construct an instance of a Neville Table with size n, initialized with data {(x, y)}.

Method Summary

void	addData(double[] x, double[] y) Add more data points for interpolation.
double	evaluate(double x) Compute f(x).
double	get(int row, int col) Get the value of a table entry.
int	N() Get the number of data points.
double[][]	table() Get a copy of the Neville table.
double[]	X() Get a copy of the x's.

Methods inherited from class com.numericalmethod.suanshu.analysis.function.rn2r1.UnivariateRealFunction

dimension4Domain, dimension4Range, evaluate

Methods inherited from class java.lang.Object

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

Constructor Detail

NevilleTable

public NevilleTable(int n,
                    double[] x,
                    double[] y)

Construct an instance of a Neville Table with size n, initialized with data {(x, y)}.

The size n is only indicative. If there are more data points than n, the table size will increase accordingly.

Parameters:

n - indicative size; make this big for reservation to add new data points

x - the abscissae

y - the ordinates

NevilleTable

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

Construct an instance of a Neville Table, initialized with data {(x, y)}.

Parameters:

x - the abscissae

y - the ordinates

NevilleTable

public NevilleTable()

Construct an empty Neville Table.

Method Detail

addData

public void addData(double[] x,
                    double[] y)

Add more data points for interpolation.

Specified by:

addData in interface UnivariateRealInterpolator

Parameters:

x - the abscissae

y - the ordinates

N

public int N()

Get the number of data points.

Returns:

the number of data points

table

public double[][] table()

Get a copy of the Neville table.

The returned value is independent and can be modified anyhow.

Returns:

a copy of the table

X

public double[] X()

Get a copy of the x's.

The returned value is independent and can be modified anyhow.

Returns:

a copy of x's

get

public double get(int row,
                  int col)

Get the value of a table entry.

Parameters:

row - row index, counting from 0

col - column index, counting from 0

Returns:

the value of a table entry

evaluate

public double evaluate(double x)

Description copied from class: UnivariateRealFunction

Compute f(x).

Specified by:

evaluate in interface UnivariateRealInterpolator

Specified by:

evaluate in class UnivariateRealFunction

Parameters:

x - x

Returns:

f(x)