public class RootsOfUnity
extends java.lang.Object
implements java.io.Serializable
n-th roots of
unity.| Modifier and Type | Field and Description |
|---|---|
private boolean |
isCounterClockWise
|
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 and Description |
|---|
RootsOfUnity()
Build an engine for computing the
n-th roots of unity. |
| 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()
|
private static final long serialVersionUID
private int omegaCount
private double[] omegaReal
private double[] omegaImaginaryCounterClockwise
n-th roots of unity, for positive values
of n. In this array, the roots are stored in counter-clockwise
order.private double[] omegaImaginaryClockwise
n-th roots of unity, for negative values
of n. In this array, the roots are stored in clockwise order.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.public RootsOfUnity()
n-th roots of unity.public boolean isCounterClockWise()
throws MathIllegalStateException
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.true if the roots of unity are stored in
counter-clockwise orderMathIllegalStateException - if no roots of unity have been computed
yetpublic 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.n > 0, then the roots are stored in counter-clockwise order.n < 0, then the roots are stored in clockwise order.
n - the (signed) number of roots of unity to be computedZeroException - if n = 0public double getReal(int k)
throws MathIllegalStateException,
MathIllegalArgumentException
k-th n-th root of unity.k - index of the n-th root of unityk-th n-th root of unityMathIllegalStateException - if no roots of unity have been
computed yetMathIllegalArgumentException - if k is out of rangepublic double getImaginary(int k)
throws MathIllegalStateException,
OutOfRangeException
k-th n-th root of unity.k - index of the n-th root of unityk-th n-th root of unityMathIllegalStateException - if no roots of unity have been
computed yetOutOfRangeException - if k is out of rangepublic int getNumberOfRoots()
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.Copyright (c) 2003-2017 Apache Software Foundation