Class Complex128UniformRect

java.lang.Object
org.flag4j.rng.distributions.Distribution<Complex128,RandomComplex>
org.flag4j.rng.distributions.Complex128UniformRect
public class Complex128UniformRect extends Distribution<Complex128,RandomComplex>

A rectangular uniform distribution on the complex plane.

A rectangular uniform distribution on the complex plane is equivalent to combining two 1D uniform distributions over the real and imaginary axes: \(\mathcal{U}(a, b) \) and \(\mathcal{U}(c, d) \) respectively.

The PDF of the joint distribution of the real component \( x \sim \mathcal{U}(a, b) \) and the complex component \( y \sim \mathcal{U}(c, d) \) for a complex value \( z = x + iy \) is given by: \[ f(z) = \begin{cases} \frac{1}{(b - a)(d - c)} & \text{for } \Re(z) \in [a, b), \Im(z) \in [c, d) \\ 0 & \text{otherwise}. \end{cases} \]

See Also:

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    final double
    maxIm
    Upper bound, \( d \), of the imaginary component of the uniform distribution (exclusive).
    final double
    maxRe
    Upper bound, \( b \), of the real component of the uniform distribution (exclusive).
    final double
    minIm
    Lower bound, \( c \), of the imaginary component of the uniform distribution (inclusive).
    final double
    minRe
    Lower bound, \( a \), of the real component of the uniform distribution (inclusive).

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

    rng

  • Constructor Summary

    Constructors
    Constructor
    Description
    Complex128UniformRect(RandomComplex rng, double minRe, double maxRe, double minIm, double maxIm)
    Constructs a complex rectangular uniform distribution.

  • Method Summary

    Modifier and Type
    Method
    Description
    Complex128
    sample()
    Randomly samples this complex rectangular uniform distribution.

    Methods inherited from class java.lang.Object

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

  • Field Details

    • minRe

      public final double minRe
      Lower bound, \( a \), of the real component of the uniform distribution (inclusive).

    • maxRe

      public final double maxRe
      Upper bound, \( b \), of the real component of the uniform distribution (exclusive).

    • minIm

      public final double minIm
      Lower bound, \( c \), of the imaginary component of the uniform distribution (inclusive).

    • maxIm

      public final double maxIm
      Upper bound, \( d \), of the imaginary component of the uniform distribution (exclusive).

  • Constructor Details

    • Complex128UniformRect

      public Complex128UniformRect(RandomComplex rng, double minRe, double maxRe, double minIm, double maxIm)
      Constructs a complex rectangular uniform distribution.
      Parameters:
      rng - Pseudorandom number generator to use when randomly sampling from this distribution.
      minRe - Lower bound of the real component of the uniform distribution (inclusive).
      maxRe - Upper bound of the real component of the uniform distribution (exclusive).
      minIm - Lower bound of the imaginary component of the uniform distribution (inclusive).
      maxIm - Upper bound of the imaginary component of the uniform distribution (exclusive).

  • Method Details

    • sample

      public Complex128 sample()
      Randomly samples this complex rectangular uniform distribution.
      Specified by:
      sample in class Distribution<Complex128,RandomComplex>
      Returns:
      A random value distributed according to this complex rectangular uniform distribution.