Package org.apache.commons.math3.complex

Class RootsOfUnity

java.lang.Object
org.apache.commons.math3.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.
Since:
3.0
See Also:

  • Field Details

    • serialVersionUID

      private static final long serialVersionUID
      Serializable version id.
      See Also:

    • omegaCount

      private int omegaCount
      Number of roots of unity.

    • omegaReal

      private double[] omegaReal
      Real part of the roots.

    • omegaImaginaryCounterClockwise

      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.

    • omegaImaginaryClockwise

      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.

    • isCounterClockWise

      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.

  • 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 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