uk.org.ogsadai.activity.files
Class Lagrange

java.lang.Object
  |
  +--uk.org.ogsadai.activity.files.Lagrange

public class Lagrange

extends java.lang.Object

A class which generates Lagrange interpolating polynomials interpolating the co-ordinates (p_n, n), given an array of integers {p_n}.

The generated polynomial is defined to be of degree n-1 if there are n co-ordinates.

Author:

The OGSA-DAI Project Team

Field Summary

private static java.lang.String	COPYRIGHT_NOTICE Copyright statement
private int	mN
private int[]	mX
private int[]	mY

Constructor Summary

Lagrange(int[] vals)
Generate a new polynomial based on the given "seed integers" {p_n}.

Method Summary

double	p(int x) The function representing the Lagrange interpolating polynomial.
double	p(int j, int x) The function representing one part of the Lagrange interpolating polynomial, used by the function P(int x).
java.lang.String	toString() Return a textual representation of the array of seed integers.

Methods inherited from class java.lang.Object

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

Field Detail

COPYRIGHT_NOTICE

private static final java.lang.String COPYRIGHT_NOTICE

Copyright statement

See Also:

Constant Field Values

mX

private int[] mX

mY

private int[] mY

mN

private int mN

Constructor Detail

Lagrange

public Lagrange(int[] vals)

Generate a new polynomial based on the given "seed integers" {p_n}.

Parameters:

vals - The seed integers

Method Detail

toString

public java.lang.String toString()

Return a textual representation of the array of seed integers. For debugging purposes only.

Overrides:

toString in class java.lang.Object

Returns:

the textual representation

p

public double p(int x)

The function representing the Lagrange interpolating polynomial.

P(x) =_def Sum of (P_j(x)), for j = 1 to n.

Parameters:

x - The abscissa

Returns:

the ordinate

p

public double p(int j,
                int x)

The function representing one part of the Lagrange interpolating polynomial, used by the function P(int x).

P_j(x) =_def y_j * Product of ((x - x_k) / (x_j - x_k)), for k = 1 to n and k != j.

Parameters:

j - The index j of the function P_j

x - The abscissa

Returns:

the ordinate