Package org.hipparchus.complex

Class RootsOfUnity

java.lang.Object

org.hipparchus.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.

See Also:

• Serialized Form

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method	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 Details

RootsOfUnity

public RootsOfUnity()

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

Method Details

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 MathIllegalArgumentException

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:

MathIllegalArgumentException - if n = 0

getReal

public double getReal(int k)
               throws MathIllegalArgumentException,
MathIllegalStateException

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 MathIllegalArgumentException,
MathIllegalStateException

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

MathIllegalArgumentException - 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