Code to generate Gaussian (normally distributed) random numbers in Ruby

Question

What is some code to generate normally distributed random numbers in ruby?

(Note: I answered my own question, but I'll wait a few days before accepting to see if anyone has a better answer.)

EDIT:

Searching for this, I looked at all pages on SO resulting from the two searches:

+"normal distribution" ruby

and

+gaussian +random ruby

Answer 1

Python's random.gauss() and Boost's normal_distribution both use the Box-Muller transform, so that should be good enough for Ruby too.

def gaussian(mean, stddev, rand)
  theta = 2 * Math::PI * rand.call
  rho = Math.sqrt(-2 * Math.log(1 - rand.call))
  scale = stddev * rho
  x = mean + scale * Math.cos(theta)
  y = mean + scale * Math.sin(theta)
  return x, y
end

The method can be wrapped up in a class that returns the samples one by one.

class RandomGaussian
  def initialize(mean, stddev, rand_helper = lambda { Kernel.rand })
    @rand_helper = rand_helper
    @mean = mean
    @stddev = stddev
    @valid = false
    @next = 0
  end

  def rand
    if @valid then
      @valid = false
      return @next
    else
      @valid = true
      x, y = self.class.gaussian(@mean, @stddev, @rand_helper)
      @next = y
      return x
    end
  end

  private
  def self.gaussian(mean, stddev, rand)
    theta = 2 * Math::PI * rand.call
    rho = Math.sqrt(-2 * Math.log(1 - rand.call))
    scale = stddev * rho
    x = mean + scale * Math.cos(theta)
    y = mean + scale * Math.sin(theta)
    return x, y
  end
end

(CC0)

To the extent possible under law, antonakos has waived all copyright and related or neighboring rights to the RandomGaussian Ruby class. This work is published from: Denmark.

---

The license statement does not mean I care about this code. On the contrary, I don't use the code, I haven't tested it, and I don't program in Ruby.

Answer 2

The original question asked for code, but the author's followup comment implied an interest in using existing libraries. I was interested in the same, and my searches turned up these two ruby gems:

gsl - "Ruby interface to the GNU Scientific Library" (requires you to install GSL). The calling sequence for normally distributed random numbers with mean = 0 and a given standard deviation is

 rng = GSL::Rng.alloc
 rng.gaussian(sd)      # a single random sample
 rng.gaussian(sd, 100) # 100 random samples

rubystats - "a port of the statistics libraries from PHPMath" (pure ruby). The calling sequence for normally distributed random numbers with a given mean and standard deviation is

 gen = Rubystats::NormalDistribution.new(mean, sd)
 gen.rng               # a single random sample
 gen.rng(100)          # 100 random samples

Answer 3

+1 on @antonakos's answer. Here's the implementation of Box-Muller that I've been using; it's essentially identical but slightly tighter code:

class RandomGaussian
  def initialize(mean = 0.0, sd = 1.0, rng = lambda { Kernel.rand })
    @mean, @sd, @rng = mean, sd, rng
    @compute_next_pair = false
  end

  def rand
    if (@compute_next_pair = !@compute_next_pair)
      # Compute a pair of random values with normal distribution.
      # See http://en.wikipedia.org/wiki/Box-Muller_transform
      theta = 2 * Math::PI * @rng.call
      scale = @sd * Math.sqrt(-2 * Math.log(1 - @rng.call))
      @g1 = @mean + scale * Math.sin(theta)
      @g0 = @mean + scale * Math.cos(theta)
    else
      @g1
    end
  end
end

Of course, if you really cared about speed, you should implement the Ziggurat Algorithm :).

Answer 4

Another option, this one using the distribution gem, written by one of the SciRuby fellows.

It is a little simpler to use, I think.

require 'distribution'
normal = Distribution::Normal.rng(1)
norm_distribution = 1_000.times.map {normal.call}