org.apache.commons.math3.complex

## Class 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:
$Id: RootsOfUnity.java 1416643 2012-12-03 19:37:14Z tn$
Serialized Form
• ### Constructor Summary

Constructors
Constructor and Description
RootsOfUnity()
Build an engine for computing the n-th roots of unity.
• ### Method Summary

Methods
Modifier and Type Method and Description
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
• ### 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