Class Complex128UniformDisk

java.lang.Object
org.flag4j.rng.distributions.Distribution<Complex128,RandomComplex>
org.flag4j.rng.distributions.Complex128UniformDisk
public class Complex128UniformDisk extends Distribution<Complex128,RandomComplex>

A uniform distribution over an annulus (i.e. washer) on the complex plane.

A uniform distribution over an annulus is defined over the region between two concentric circles with inner radius \( r_{\text{inner}} \) and outer radius \( r_{\text{outer}} \) and centered at \( \left(x, y\right) \).

A complex number \( z = x + yi + re^{i\theta } \) is sampled from this distribution by drawing its modulus \( r \) from a uniform distribution \( \mathcal{U}\left(r_{\text{inner}}, r_{\text{outer}}\right) \) and its argument \( \theta \) from a uniform distribution \( \mathcal{U}(0, 2\pi) \).

The PDF of the joint distribution for a complex value \( z = x + yi + re^{i\theta } \) is given by: \[ f(z) = \begin{cases} \dfrac{1}{\pi \left(r_{\text{outer}}^2 - r_{\text{inner}}^2\right)} & \text{for } r_{\text{inner}} \leq |z - (x + yi)| < r_{\text{outer}} \\ 0 & \text{otherwise}. \end{cases} \]

This distribution ensures that points are uniformly distributed in within the annulus, meaning that the density function accounts for the increasing circumference as \( r \) increases avoiding "bunching" of points close to the inner radius.

See Also:

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    final double
    centerIm
    Imaginary value of the center, y, of the annulus in the complex plane.
    final double
    centerRe
    Real value of the center, x, of the annulus in the complex plane.
    final double
    max
    Outer radius, router , of the annulus (exclusive).
    final double
    min
    Inner radius, rinner , of the annulus (inclusive).

    Fields inherited from class org.flag4j.rng.distributions.Distribution

    rng

  • Constructor Summary

    Constructors
    Constructor
    Description
    Complex128UniformDisk(RandomComplex rng, double min, double max)
    Constructs a complex annular uniform distribution centered at the origin of the complex plane.
    Complex128UniformDisk(RandomComplex rng, double min, double max, double centerRe, double centerIm)
    Constructs a complex annular uniform distribution with specified center on the complex plane.

  • Method Summary

    Modifier and Type
    Method
    Description
    Complex128
    sample()
    Randomly samples this complex annular uniform distribution centered at (centerRe, centerIm) with inner and outer radius min and max respectively.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Field Details

    • min

      public final double min
      Inner radius, rinner , of the annulus (inclusive).

    • max

      public final double max
      Outer radius, router , of the annulus (exclusive).

    • centerRe

      public final double centerRe
      Real value of the center, x, of the annulus in the complex plane.

    • centerIm

      public final double centerIm
      Imaginary value of the center, y, of the annulus in the complex plane.

  • Constructor Details

    • Complex128UniformDisk

      public Complex128UniformDisk(RandomComplex rng, double min, double max)
      Constructs a complex annular uniform distribution centered at the origin of the complex plane. To specify the distribution as a disk, set min=0.0.
      Parameters:
      rng - Pseudorandom number generator to use when randomly sampling from this distribution.
      min - Inner radius of the annulus (inclusive).
      max - Outer radius of the annulus (exclusive).

    • Complex128UniformDisk

      public Complex128UniformDisk(RandomComplex rng, double min, double max, double centerRe, double centerIm)
      Constructs a complex annular uniform distribution with specified center on the complex plane. To specify the distribution as a disk, set min=0.0.
      Parameters:
      rng - Pseudorandom number generator to use when randomly sampling from this distribution.
      min - Inner radius of the annulus (inclusive).
      max - Outer radius of the annulus (exclusive).
      centerRe - Real value of the center of the annulus in the complex plane.
      centerIm - Imaginary value of the center of the annulus in the complex plane.

  • Method Details