uk.org.ogsadai.activity.files
Class Sequence

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

public class Sequence

extends java.lang.Object

This class represents a countable, increasing chain in the set of integers under the < relation. Note that since the relation is a strict inequality, the chain may not be eventually constant.

The chain d₁ < d₂ < d₃ < ... is defined by:

d_n =_def P(n)

The seed integers are passed to the constructor of this class, from which the Lagrange interpolating polynomial is generated. This polynomial can then be used to extrapolate the sequence to infinity. The isMember method can be used to test whether a given integer n is a member of this sequence, i.e. whether P(i) = n for any positive integer i.

For example, if the seed integers are p₁ = 2 and p_n = 4, then P(n) = 2n, so isMember will return true when passed any even positive integer.

Note that the indiscriminant use of the Lagrange interpolating polynomial restricts the sequences we can represent. For example, we can represent linear progressions such as 1, 3, 5, ... (with P(n) = 2n - 1); quadratic progressions such as 0, 1, 4, 9 (with P(n) = n² - 2n + 1); etc, but not exponential progressions.

Author:

The OGSA-DAI Project Team

COPYRIGHT_NOTICE

private static final java.lang.String COPYRIGHT_NOTICE

Copyright statement

See Also:

Constant Field Values

mLagrange

private Lagrange mLagrange

Lagrange polynomial

Sequence

public Sequence(int[] items)
         throws NonIncreasingSequenceException

Construct a new Sequence with a provided array of ordered seed integers.

Parameters:

items - The seed integers

Throws:

NonIncreasingSequenceException - If the given sequence is non-increasing.

toString

public java.lang.String toString()

Returns a string representation of this sequence. For debugging purposes only.

Overrides:

toString in class java.lang.Object

Returns:

a string representation

increasing

private boolean increasing(int[] items)

Test to see if the integers in the provided array are strictly increasing. That is, we test whether items[i+1] > items[i] for all integers 0 <= i < items.length-1.

Parameters:

items - The array to test

Returns:

true if the integers are strictly increasing, false otherwise.

isMember

public boolean isMember(int val)
                 throws NonIncreasingSequenceException

Tests to see if a particular integer is a member of the sequence.

Parameters:

val - The integer to test

Returns:

true if the integer is a member of the sequence, false otherwise

Throws:

NonIncreasingSequenceException - If the given sequence is non-increasing.

toInt

private static int toInt(double number)

Return the integer nearest to the given double precision real number.

Parameters:

number - the number to round

Returns:

the rounded number

intArrayToString

static java.lang.String intArrayToString(int[] items)

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

Parameters:

items - The array of integers

Returns:

the textual representation