Module org.cicirello.rho_mu
Package org.cicirello.math.rand

Class PolarGaussian

  • public final class PolarGaussian
extends Object

    This class provides methods for generating pseudorandom numbers from a Gaussian distribution using the classic Polar Method. Other methods exist that are faster than Polar, and with superior statistical properties over the Polar method. One such algorithm is the Ziggurat method, implemented in the ZigguratGaussian class. The Polar method implementation provided in the PolarGaussian class was originally implemented as part of an experimental study comparing the effects of different Gaussian algorithms on the performance of a genetic algorithm. It is included here in this repository, however, if you are looking for a fast algorithm for generating Gaussian distributed random numbers, we suggest you consider the ZigguratGaussian class instead.

    It should be noted that the Java API includes a polar method implementation in both the Random and ThreadLocalRandom classes. However, the experimental study mentioned above also included the use of SplittableRandom which does not provide any methods for generating Gaussian distributed random numbers. The SplittableRandom class is also declared final, so extending to add such a method was not an option. Our solution was a static method in this class with a parameter for the underlying pseudorandom number generator (PRNG). We chose to do the same for Random and ThreadLocalRandom so that our approach was consistent across all 3 PRNGs used in the study.

    You can find some experimental data comparing the performance of a sequential genetic algorithm (GA) using this implementation of the Polar method for Gaussian mutation vs using the faster Ziggurat method, as well as experimental data for the same comparison but with a Parallel GA, in the following paper:

    • Method Summary

      All Methods Static Methods Concrete Methods 
      Modifier and Type Method Description
      static double nextGaussian()
      Generates a random number from a Gaussian distribution with mean 0 and standard deviation 1.
      static double nextGaussian​(double sigma)
      Generates a random number from a Gaussian distribution with mean 0 and standard deviation, sigma, or your choosing.
      static double nextGaussian​(double sigma, Random r)
      Generates a random number from a Gaussian distribution with mean 0 and standard deviation, sigma, or your choosing.
      static double nextGaussian​(double sigma, SplittableRandom r)
      Generates a random number from a Gaussian distribution with mean 0 and standard deviation, sigma, or your choosing.
      static double nextGaussian​(Random r)
      Generates a random number from a Gaussian distribution with mean 0 and standard deviation 1.
      static double nextGaussian​(SplittableRandom r)
      Generates a random number from a Gaussian distribution with mean 0 and standard deviation 1.

    • Method Detail

      • nextGaussian

        public static double nextGaussian​(double sigma)
        Generates a random number from a Gaussian distribution with mean 0 and standard deviation, sigma, or your choosing. ThreadLocalRandom is used as the pseudorandom number generator for the source of randomness.
        Parameters:
        sigma - The standard deviation of the Gaussian.
        Returns:
        A random number from a Gaussian distribution with mean 0 and standard deviation sigma.

      • nextGaussian

        public static double nextGaussian​(double sigma,
                                  Random r)
        Generates a random number from a Gaussian distribution with mean 0 and standard deviation, sigma, or your choosing.
        Parameters:
        sigma - The standard deviation of the Gaussian.
        r - The pseudorandom number generator to use for the source of randomness.
        Returns:
        A random number from a Gaussian distribution with mean 0 and standard deviation sigma.

      • nextGaussian

        public static double nextGaussian​(double sigma,
                                  SplittableRandom r)
        Generates a random number from a Gaussian distribution with mean 0 and standard deviation, sigma, or your choosing.
        Parameters:
        sigma - The standard deviation of the Gaussian.
        r - The pseudorandom number generator to use for the source of randomness.
        Returns:
        A random number from a Gaussian distribution with mean 0 and standard deviation sigma.

      • nextGaussian

        public static double nextGaussian()
        Generates a random number from a Gaussian distribution with mean 0 and standard deviation 1. ThreadLocalRandom is used as the pseudorandom number generator for the source of randomness.
        Returns:
        A random number from a Gaussian distribution with mean 0 and standard deviation 1.

      • nextGaussian

        public static double nextGaussian​(Random r)
        Generates a random number from a Gaussian distribution with mean 0 and standard deviation 1.
        Parameters:
        r - The pseudorandom number generator to use for the source of randomness.
        Returns:
        A random number from a Gaussian distribution with mean 0 and standard deviation 1.

      • nextGaussian

        public static double nextGaussian​(SplittableRandom r)
        Generates a random number from a Gaussian distribution with mean 0 and standard deviation 1.
        Parameters:
        r - The pseudorandom number generator to use for the source of randomness.
        Returns:
        A random number from a Gaussian distribution with mean 0 and standard deviation 1.