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