Apache Commons Math 3.6.1 · org.apache.commons.math3.complex.RootsOfUnity

Field Summary

Modifier and Type	Field and Description
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 final long	serialVersionUID Serializable version id.

Constructor Summary

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

Method Summary

Modifier and Type	Method and Description
public synchronized void	computeRoots(int the (signed) number of roots of unity to be computed n) Computes the `n`-th roots of unity.
public synchronized double	Returns: imaginary part of the `k`-th `n`-th root of unity getImaginary(int index of the `n`-th root of unity k) Get the imaginary part of the `k`-th `n`-th root of unity.
public synchronized int	Returns: the number of roots of unity currently stored getNumberOfRoots() Returns the number of roots of unity currently stored.
public synchronized double	Returns: real part of the `k`-th `n`-th root of unity getReal(int index of the `n`-th root of unity k) Get the real part of the `k`-th `n`-th root of unity.
public synchronized boolean	Returns: `true` if the roots of unity are stored in counter-clockwise order isCounterClockWise() Returns `true` if `computeRoots(int)` was called with a positive value of its argument `n`.

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

Field Detail

isCounterClockWise	back to summary
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.

omegaCount	back to summary
private int omegaCount Number of roots of unity.

omegaImaginaryClockwise	back to summary
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.

omegaImaginaryCounterClockwise	back to summary
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.

omegaReal	back to summary
private double[] omegaReal Real part of the roots.

serialVersionUID	back to summary
private static final long serialVersionUID Serializable version id.

Constructor Detail

RootsOfUnity	back to summary
public RootsOfUnity() Build an engine for computing the `n`-th roots of unity.

Method Detail

computeRoots back to summary

computeRoots	back to summary
public synchronized 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:int the (signed) number of roots of unity to be computed Exceptions ZeroException: if `n = 0`

public synchronized 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:int: the (signed) number of roots of unity to be computed

Exceptions

ZeroException:: if n = 0

getImaginary back to summary

getImaginary	back to summary
public synchronized double getImaginary(int k) throws MathIllegalStateException, OutOfRangeException Get the imaginary part of the `k`-th `n`-th root of unity. Parameters k:int index of the `n`-th root of unity Returns:double imaginary part of the `k`-th `n`-th root of unity Exceptions MathIllegalStateException: if no roots of unity have been computed yet OutOfRangeException: if `k` is out of range

public synchronized double getImaginary(int k) throws MathIllegalStateException, OutOfRangeException

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

Parameters

k:int: index of the n-th root of unity

Returns:double

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

Exceptions

MathIllegalStateException:: if no roots of unity have been computed yet
OutOfRangeException:: if k is out of range

getNumberOfRoots back to summary

getNumberOfRoots	back to summary
public synchronized 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:int the number of roots of unity currently stored

public synchronized 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:int: the number of roots of unity currently stored

getReal back to summary

getReal	back to summary
public synchronized double getReal(int k) throws MathIllegalStateException, MathIllegalArgumentException Get the real part of the `k`-th `n`-th root of unity. Parameters k:int index of the `n`-th root of unity Returns:double real part of the `k`-th `n`-th root of unity Exceptions MathIllegalStateException: if no roots of unity have been computed yet MathIllegalArgumentException: if `k` is out of range

public synchronized double getReal(int k) throws MathIllegalStateException, MathIllegalArgumentException

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

Parameters

k:int: index of the n-th root of unity

Returns:double

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

Exceptions

MathIllegalStateException:: if no roots of unity have been computed yet
MathIllegalArgumentException:: if k is out of range

isCounterClockWise back to summary

isCounterClockWise	back to summary
public synchronized 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:boolean `true` if the roots of unity are stored in counter-clockwise order Exceptions MathIllegalStateException: if no roots of unity have been computed yet

public synchronized 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:boolean

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

Exceptions

MathIllegalStateException:: if no roots of unity have been computed yet

public Class RootsOfUnity

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