org.apache.commons.math3.complex
Class RootsOfUnity

java.lang.Object
  org.apache.commons.math3.complex.RootsOfUnity

All Implemented Interfaces:

Serializable

public class RootsOfUnity
extends Object
implements Serializable

A helper class for the computation and caching of the n-th roots of unity.

Since:

3.0

Version:

$Id: RootsOfUnity.java 1416643 2012-12-03 19:37:14Z tn $

See Also:

Serialized Form

Field Summary

private boolean	isCounterClockWise true if computeRoots(int) was called with a positive value of its argument n.
private int	omegaCount Number of roots of unity.
private double[]	omegaImaginaryClockwise Imaginary part of the n-th roots of unity, for negative values of n.
private double[]	omegaImaginaryCounterClockwise Imaginary part of the n-th roots of unity, for positive values of n.
private double[]	omegaReal Real part of the roots.
private static long	serialVersionUID Serializable version id.

Constructor Summary

RootsOfUnity()
Build an engine for computing the n-th roots of unity.

Method Summary

void	computeRoots(int n) Computes the n-th roots of unity.
double	getImaginary(int k) Get the imaginary part of the k-th n-th root of unity.
int	getNumberOfRoots() Returns the number of roots of unity currently stored.
double	getReal(int k) Get the real part of the k-th n-th root of unity.
boolean	isCounterClockWise() Returns true if computeRoots(int) was called with a positive value of its argument n.

Methods inherited from class java.lang.Object

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

Field Detail

serialVersionUID

private static final long serialVersionUID

Serializable version id.

See Also:

Constant Field Values

omegaCount

private int omegaCount

Number of roots of unity.

omegaReal

private double[] omegaReal

Real part of the roots.

omegaImaginaryCounterClockwise

private double[] omegaImaginaryCounterClockwise

Imaginary part of the n-th roots of unity, for positive values of n. In this array, the roots are stored in counter-clockwise order.

omegaImaginaryClockwise

private double[] omegaImaginaryClockwise

Imaginary part of the n-th roots of unity, for negative values of n. In this array, the roots are stored in clockwise order.

isCounterClockWise

private boolean isCounterClockWise

true if computeRoots(int) was called with a positive value of its argument n. In this case, counter-clockwise ordering of the roots of unity should be used.

Constructor Detail

RootsOfUnity

public RootsOfUnity()

Build an engine for computing the n-th roots of unity.

Method Detail

isCounterClockWise

public boolean isCounterClockWise()
                           throws MathIllegalStateException

Returns true if computeRoots(int) was called with a positive value of its argument n. If true, then counter-clockwise ordering of the roots of unity should be used.

Returns:

true if the roots of unity are stored in counter-clockwise order

Throws:

MathIllegalStateException - if no roots of unity have been computed yet

computeRoots

public void computeRoots(int n)
                  throws ZeroException

Computes the n-th roots of unity. The roots are stored in omega[], such that omega[k] = w ^ k, where k = 0, ..., n - 1, w = exp(2 * pi * i / n) and i = sqrt(-1).

Note that n can be positive of negative

• abs(n) is always the number of roots of unity.
• If n > 0, then the roots are stored in counter-clockwise order.
• If n < 0, then the roots are stored in clockwise order.

Parameters:

n - the (signed) number of roots of unity to be computed

Throws:

ZeroException - if n = 0

getReal

public double getReal(int k)
               throws MathIllegalStateException,
                      MathIllegalArgumentException

Get the real part of the k-th n-th root of unity.

Parameters:

k - index of the n-th root of unity

Returns:

real part of the k-th n-th root of unity

Throws:

MathIllegalStateException - if no roots of unity have been computed yet

MathIllegalArgumentException - if k is out of range

getImaginary

public double getImaginary(int k)
                    throws MathIllegalStateException,
                           OutOfRangeException

Get the imaginary part of the k-th n-th root of unity.

Parameters:

k - index of the n-th root of unity

Returns:

imaginary part of the k-th n-th root of unity

Throws:

MathIllegalStateException - if no roots of unity have been computed yet

OutOfRangeException - if k is out of range

getNumberOfRoots

public int getNumberOfRoots()

Returns the number of roots of unity currently stored. If computeRoots(int) was called with n, then this method returns abs(n). If no roots of unity have been computed yet, this method returns 0.

Returns:

the number of roots of unity currently stored