rewrite based on the F# program by microsoft: http://blogs.technet.co…

…m/apg/archive/2008/06/16/trueskill-in-f.aspx

lib/saulabs/gauss.rb

@@ -0,0 +1,3 @@
+require "#{File.dirname(__FILE__)}/gauss/functions.rb"
+require "#{File.dirname(__FILE__)}/gauss/distribution.rb"
+require "#{File.dirname(__FILE__)}/gauss/factor_graph.rb"

lib/saulabs/gauss/distribution.rb

@@ -0,0 +1,81 @@
+module Saulabs
+  module Gauss
+    class Distribution
+
+      # gaussian normal distribution values
+      attr_accessor :mean, :deviation, :variance, :precision, :precision_mean
+
+      def initialize
+        @mean = 0.0
+        @deviation = 0.0
+        @variance = 0.0
+        @precision = 0.0
+        @precision_mean = 0.0
+      end
+
+      class << self
+
+        def with_deviation(mean, deviation)
+          dist = Distribution.new
+          dist.mean = mean
+          dist.deviation = deviation
+          dist.variance = deviation * deviation
+          dist.precision = 1 / dist.variance.to_f
+          dist.precision_mean = dist.precision * mean
+          return dist
+        end
+
+        def with_precision(mean, precision)
+          Distribution.with_deviation(mean / precision, Math.sqrt(1 / precision))
+        end
+
+        def absolute_difference(x, y)
+          [(x.precision_mean - y.precision_mean).abs, Math.sqrt((x.precision - y.precision).abs)].max
+        end
+
+        def log_product_normalisation(x, y)
+          return 0.0 if x.precision == 0.0 || y.precision == 0.0
+          vsum = x.variance + y.variance
+          mdiff = x.mean - y.mean
+          -0.91893853320467267 - Math.log(vsum) / 2.0 - mdiff * mdiff / 2.0 * vsum
+        end
+
+        def log_ratio_normalisation(x, y)
+          return 0.0 if x.precision == 0.0 || y.precision == 0.0
+          v2 = y.variance
+          vdiff = v2 - x.variance
+          return 0.0 if vdiff == 0.0
+          mdiff = x.mean - y.mean
+          Math.log(v2) + 0.91893853320467267 - Math.log(vdiff) / 2.0 + mdiff * mdiff / 2.0 * vdiff
+        end
+
+      end
+
+      def *(other)
+        Rating.with_precision(self.precision_mean + other.precision_mean, self.precision + other.precision)
+      end
+
+      def /(other)
+        Rating.with_precision(self.precision_mean - other.precision_mean, self.precision - other.precision)
+      end
+
+      # absolute difference
+      def -(other)
+        Distribution.absolute_difference(self, other)
+      end
+
+      def +(other)
+
+      end
+
+      def ==(other)
+        self.mean == other.mean && self.variance == other.variance
+      end
+
+      def equals(other)
+        self == other
+      end
+
+    end
+  end
+end

lib/saulabs/gauss/factor_graph.rb

@@ -0,0 +1,7 @@
+module Saulabs
+  module Gauss
+    class FactorGraph
+
+    end
+  end
+end

lib/saulabs/gauss/functions.rb

@@ -0,0 +1,32 @@
+module Saulabs
+  module Gauss    
+    class Functions
+
+      SQRT2 = Math.sqrt(2).freeze
+      INV_SQRT_2PI = (1 / Math.sqrt(2 * Math::PI)).freeze
+
+      class << self
+
+        # Computes the cummulative Gaussian distribution at a specified point of interest
+        def cumulative_distribution_function(x)
+          0.5 * (1 + Math.erf(x / SQRT2))
+        end
+        alias_method :cdf, :cumulative_distribution_function
+
+        # Computes the Gaussian density at a specified point of interest
+        def probability_density_function(x)
+          INV_SQRT_2PI * Math.exp(-0.5 * (x**2))
+        end
+        alias_method :pdf, :probability_density_function
+
+        # The inverse of the cummulative Gaussian distribution function
+        def quantile_function(x)
+          -SQRT2 * Math.erfc(2.0 * x)
+        end
+        alias_method :inv_cdf, :quantile_function
+
+      end
+
+    end
+  end
+end

lib/saulabs/trueskill.rb

@@ -0,0 +1,22 @@
+require "#{File.dirname(__FILE__)}/gauss.rb"
+
+module Saulabs
+
+  module TrueSkill
+
+    # tau: uncertainty of the skill’s standard deviation TODO: interval???
+    # beta: chance factor (low for low-chance games like go and chess) TODO: interval???
+    # draw_prob: probalility of a draw game - [0,1(
+    # skills: the current skills of the participating players
+    # 
+    def self.update_skills(tau, beta, draw_prob, skills)
+      tau2 = tau**2
+      beta2 = beta**2
+      num_players = skills.size
+      epsilon = -Math.sqrt(2.0 * beta2) * Gauss::Functions.inv_cdf((1.0 - draw_prob) / 2.0)
+      factors = []
+    end
+
+  end
+
+end

spec/saulabs/gauss_distribution_spec.rb

@@ -0,0 +1,73 @@
+require File.dirname(__FILE__) + '/../spec_helper'
+
+describe Saulabs::Gauss::Distribution, "#with_deviation" do
+
+  before :each do 
+    @dist = Saulabs::Gauss::Distribution.with_deviation(25.0, 8.333333)
+  end
+
+  it "should have a default mean value of 25.0" do
+    @dist.mean.should == 25.0
+  end
+
+  it "should have a default deviation of 8.333333" do
+    @dist.deviation.should be_close(8.333333, 0.000001)
+  end
+
+  it "should set the variance to 69.444438" do
+    @dist.variance.should be_close(69.4444, 0.0001)
+  end
+
+  it "should set the precision to 0.0144" do
+    @dist.precision.should be_close(0.0144, 0.0001)
+  end
+
+  it "should set the precision_mean to 0.36" do
+    @dist.precision_mean.should be_close(0.36, 0.0001)
+  end
+
+end
+
+describe Saulabs::Gauss::Distribution, "#with_precision" do
+
+  before :each do 
+    @dist = Saulabs::Gauss::Distribution.with_precision(0.36, 0.0144)
+  end
+
+  it "should have a default mean value of 25.0" do
+    @dist.mean.should == 25.0
+  end
+
+  it "should have a default deviation of 8.333333" do
+    @dist.deviation.should be_close(8.333333, 0.000001)
+  end
+
+  it "should set the variance to 69.444438" do
+    @dist.variance.should be_close(69.4444, 0.0001)
+  end
+
+  it "should set the precision to 0.0144" do
+    @dist.precision.should be_close(0.0144, 0.0001)
+  end
+
+  it "should set the precision_mean to 0.36" do
+    @dist.precision_mean.should be_close(0.36, 0.0001)
+  end
+
+end
+
+describe Saulabs::Gauss::Distribution, "absolute difference (-)" do
+
+  before :each do 
+    @dist = Saulabs::Gauss::Distribution.with_deviation(25.0, 8.333333)
+  end
+
+  it "should be 0.0 for the same distribution" do
+    (@dist - @dist).should == 0.0
+  end
+
+  it "should equal the precision mean if the 0-distribution is subtracted" do
+    (@dist - Saulabs::Gauss::Distribution.new).should == @dist.precision_mean
+  end
+
+end