#!/usr/bin/ruby
## $Id$
-## Copyright (C) 2006 Daigo Moriwaki <daigo at debian dot org>
+## Copyright (C) 2006-2008 Daigo Moriwaki <daigo at debian dot org>
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
#
# Sample:
# $ ./mk_rate . > players.yaml
+# $ ./mk_rate . && ./mk_rate . > players.yaml
#
# The conditions that games and players are rated as following:
# * Rated games, which were played by both rated players.
# * Rated players, who logged in the server with a name followed by a trip:
# "name,trip".
-# * (Rated) players, who played more than $GAMES_LIMIT [ten] (rated) games.
+# * (Rated) players, who played more than $GAMES_LIMIT [15] (rated) games.
+#
+#
+# PREREQUIRE
+# ==========
+#
+# Sample Commands to isntall prerequires will work for Debian.
+#
+# * Rubygems
+# $ sudo aptitude install rubygems
+#
+# * Ruby bindings for the GNU Scientific Library (GSL)
+# $ sudo aptitude install libgsl-ruby1.8
+# Or, download it from http://rb-gsl.rubyforge.org/ .
+#
+# * RGL: Ruby Graph Library
+# $ sudo gem install rgl
+# Or, download it from http://rubyforge.org/projects/rgl/ .
#
require 'yaml'
-require 'matrix'
require 'time'
+require 'gsl'
+require 'rubygems'
+require 'rgl/adjacency'
+require 'rgl/connected_components'
#################################################
# Constants
#
-$GAMES_LIMIT = $DEBUG ? 0 : 10
+
+# Count out players who play less games than $GAMES_LIMIT
+$GAMES_LIMIT = $DEBUG ? 0 : 15
WIN_MARK = "win"
LOSS_MARK = "lose"
-AVERAGE_RATE = 1100
+DRAW_MARK = "draw"
+# Holds players
$players = Hash.new
+# Holds the last time when a player gamed
$players_time = Hash.new { Time.at(0) }
#################################################
-# Calculates rates of every player from a Win Loss Matrix
+# Keeps the value of the lowest key
+#
+class Record
+ def initialize
+ @lowest = []
+ end
+
+ def set(key, value)
+ if @lowest.empty? || key < @lowest[0]
+ @lowest = [key, value]
+ end
+ end
+
+ def get
+ if @lowest.empty?
+ nil
+ else
+ @lowest[1]
+ end
+ end
+end
+
+#################################################
+# Calculates rates of every player from a Win Loss GSL::Matrix
#
class Rating
- include Math
+ include Math
+ # The model of the win possibility is 1/(1 + 10^(-d/400)).
+ # The equation in this class is 1/(1 + e^(-Kd)).
+ # So, K should be calculated like this.
K = Math.log(10.0) / 400.0
- ERROR_LIMIT = 1.0e-5
-
- def Rating.average(vector, mean=0.0)
- sum = Array(vector).inject(0.0) {|sum, n| sum + n}
- vector -= Vector[*Array.new(vector.size, sum/vector.size - mean)]
- vector
- end
-
- def initialize(win_loss_matrix)
- @win_loss_matrix = win_loss_matrix
- @size = @win_loss_matrix.row_size
- end
- attr_reader :rate
-
- def rating
- # 0 is the initial value
- @rate = Vector[*Array.new(@size,0)]
-
- begin
- # the probability that x wins y
- @win_rate_matrix = Matrix[*
- (@rate.collect do |x|
- (@rate.collect do |y|
- # exp(x)
- # ---------------
- # exp(x) + exp(y)
- 1.0/(1.0+exp(K*(y-x)))
- end)
- end)
- ]
-
- # delta in Newton method
- errorVector = Vector[*
- ((0...@size).collect do |k|
-
- numerator = 0.0
- #---------------------
- denominator = 0.0
-
- (0...@size).each do |i|
- next if i == k
- numerator += @win_loss_matrix[k,i] * @win_rate_matrix[i,k] -
- @win_rate_matrix[k,i] * @win_loss_matrix[i,k]
- #------------------------------------------------------
- denominator += @win_rate_matrix[i,k] * @win_rate_matrix[k,i] *
- (@win_loss_matrix[k,i] + @win_loss_matrix[i,k])
- end
-
- # Remained issue: what to do if zero?
- (numerator == 0) ? 0 : numerator / denominator
- end)
- ]
-
- # gets the next value
- @rate += errorVector * (1.0/K)
- $stderr.printf "|error| : %5.2e\n", errorVector.r if $DEBUG
-
- end while (errorVector.r > ERROR_LIMIT * @rate.r)
-
- self
- end
-
+
+ # Convergence limit to stop Newton method.
+ ERROR_LIMIT = 1.0e-3
+ # Stop Newton method after this iterations.
+ COUNT_MAX = 500
+
+ # Average rate among the players
+ AVERAGE_RATE = 1000
+
+
+ ###############
+ # Class methods
+ #
+
+ ##
+ # Calcurates the average of the vector.
+ #
+ def Rating.average(vector, mean=0.0)
+ sum = Array(vector).inject(0.0) {|sum, n| sum + n}
+ vector -= GSL::Vector[*Array.new(vector.size, sum/vector.size - mean)]
+ vector
+ end
+
+ ##################
+ # Instance methods
+ #
+ def initialize(win_loss_matrix)
+ @record = Record.new
+ @n = win_loss_matrix
+ case @n
+ when GSL::Matrix, GSL::Matrix::Int
+ @size = @n.size1
+ when ::Matrix
+ @size = @n.row_size
+ else
+ raise ArgumentError
+ end
+ initial_rate
+ end
+ attr_reader :rate, :n
+
+ def player_vector
+ GSL::Vector[*
+ (0...@size).collect {|k| yield k}
+ ]
+ end
+
+ def each_player
+ (0...@size).each {|k| yield k}
+ end
+
+ ##
+ # The possibility that the player k will beet the player i.
+ #
+ def win_rate(k,i)
+ 1.0/(1.0 + exp(@rate[i]-@rate[k]))
+ end
+
+ ##
+ # Most possible equation
+ #
+ def func_vector
+ player_vector do|k|
+ sum = 0.0
+ each_player do |i|
+ next if i == k
+ sum += @n[k,i] * win_rate(i,k) - @n[i,k] * win_rate(k,i)
+ end
+ sum * 2.0
+ end
+ end
+
+ ##
+ # / f0/R0 f0/R1 f0/R2 ... \
+ # dfk/dRj = | f1/R0 f1/R1 f1/R2 ... |
+ # \ f2/R0 f2/R1 f2/R2 ... /
+ def d_func(k,j)
+ sum = 0.0
+ if k == j
+ each_player do |i|
+ next if i == k
+ sum += win_rate(i,k) * win_rate(k,i) * (@n[k,i] + @n[i,k])
+ end
+ sum *= -2.0
+ else # k != j
+ sum = 2.0 * win_rate(j,k) * win_rate(k,j) * (@n[k,j] + @n[j,k])
+ end
+ sum
+ end
+
+ ##
+ # Jacobi matrix of the func().
+ # m00 m01
+ # m10 m11
+ #
+ def j_matrix
+ GSL::Matrix[*
+ (0...@size).collect do |k|
+ (0...@size).collect do |j|
+ d_func(k,j)
+ end
+ end
+ ]
+ end
+
+ ##
+ # The initial value of the rate, which is of very importance for Newton
+ # method. This is based on my huristics; the higher the win probablity of
+ # a player is, the greater points he takes.
+ #
+ def initial_rate
+ possibility =
+ player_vector do |k|
+ v = GSL::Vector[0, 0]
+ each_player do |i|
+ next if k == i
+ v += GSL::Vector[@n[k,i], @n[i,k]]
+ end
+ v.nrm2 < 1 ? 0 : v[0] / (v[0] + v[1])
+ end
+ rank = possibility.sort_index
+ @rate = player_vector do |k|
+ K*500 * (rank[k]+1) / @size
+ end
+ average!
+ end
+
+ ##
+ # Resets @rate as the higher the current win probablity of a player is,
+ # the greater points he takes.
+ #
+ def initial_rate2
+ @rate = @record.get || @rate
+ rank = @rate.sort_index
+ @rate = player_vector do |k|
+ K*@count*1.5 * (rank[k]+1) / @size
+ end
+ average!
+ end
+
+ # mu is the deaccelrating parameter in Deaccelerated Newton method
+ def deaccelrate(mu, old_rate, a, old_f_nrm2)
+ @rate = old_rate - a * mu
+ if func_vector.nrm2 < (1 - mu / 4.0 ) * old_f_nrm2 then
+ return
+ end
+ if mu < 1e-4
+ @record.set(func_vector.nrm2, @rate)
+ initial_rate2
+ return
+ end
+ $stderr.puts "mu: %f " % [mu] if $DEBUG
+ deaccelrate(mu*0.5, old_rate, a, old_f_nrm2)
+ end
+
+ ##
+ # Main process to calculate ratings.
+ #
+ def rating
+ # Counter to stop the process.
+ # Calulation in Newton method may fall in an infinite loop
+ @count = 0
+
+ # Main loop
+ begin
+ # Solve the equation:
+ # J*a=f
+ # @rate_(n+1) = @rate_(n) - a
+ #
+ # f.nrm2 should approach to zero.
+ f = func_vector
+ j = j_matrix
+
+ # $stderr.puts "j: %s" % [j.inspect] if $DEBUG
+ $stderr.puts "f: %s -> %f" % [f.to_a.inspect, f.nrm2] if $DEBUG
+
+ # GSL::Linalg::LU.solve or GSL::Linalg::HH.solve would be available instead.
+ #a = GSL::Linalg::HH.solve(j, f)
+ a, = GSL::MultiFit::linear(j, f)
+ a = self.class.average(a)
+ # $stderr.puts "a: %s -> %f" % [a.to_a.inspect, a.nrm2] if $DEBUG
+
+ # Deaccelerated Newton method
+ # GSL::Vector object should be immutable.
+ old_rate = @rate
+ old_f = f
+ old_f_nrm2 = old_f.nrm2
+ deaccelrate(1.0, old_rate, a, old_f_nrm2)
+ @record.set(func_vector.nrm2, @rate)
+
+ $stderr.printf "|error| : %5.2e\n", a.nrm2 if $DEBUG
+
+ @count += 1
+ if @count > COUNT_MAX
+ $stderr.puts "Values seem to oscillate. Stopped the process."
+ $stderr.puts "f: %s -> %f" % [func_vector.to_a.inspect, func_vector.nrm2]
+ break
+ end
+
+ end while (a.nrm2 > ERROR_LIMIT * @rate.nrm2)
+
+ @rate = @record.get
+ $stderr.puts "resolved f: %s -> %f" %
+ [func_vector.to_a.inspect, func_vector.nrm2] if $DEBUG
+
+ @rate *= 1.0/K
+ finite!
+ self
+ end
+
+ ##
+ # Make the values of @rate finite.
+ #
+ def finite!
+ @rate = @rate.collect do |a|
+ if a.infinite?
+ a.infinite? * AVERAGE_RATE * 100
+ else
+ a
+ end
+ end
+ end
+
+ ##
+ # Flatten the values of @rate.
+ #
def average!(mean=0.0)
@rate = self.class.average(@rate, mean)
- end
-
- def integer!
- @rate = @rate.map {|a| a.to_i}
- end
+ end
+
+ ##
+ # Make the values of @rate integer.
+ #
+ def integer!
+ @rate = @rate.collect do |a|
+ if a.finite?
+ a.to_i
+ elsif a.nan?
+ 0
+ elsif a.infinite?
+ a.infinite? * AVERAGE_RATE * 100
+ end
+ end
+ end
end
+#################################################
+# Encapsulate a pair of keys and win loss matrix.
+# - keys is an array of player IDs; [gps+123, foo+234, ...]
+# - matrix holds games # where player i (row index) beats player j (column index).
+# The row and column indexes match with the keys.
+#
+# This object should be immutable. If an internal state is being modified, a
+# new object is always returned.
+#
+class WinLossMatrix
+
+ ###############
+ # Class methods
+ #
+
+ def self.mk_matrix(players)
+ keys = players.keys.sort
+ size = keys.size
+ matrix =
+ GSL::Matrix[*
+ ((0...size).collect do |k|
+ p1 = keys[k]
+ p1_hash = players[p1]
+ ((0...size).collect do |j|
+ if k == j
+ 0
+ else
+ p2 = keys[j]
+ v = p1_hash[p2] || Vector[0,0]
+ v[0]
+ end
+ end)
+ end)]
+ return WinLossMatrix.new(keys, matrix)
+ end
+
+ def self.mk_win_loss_matrix(players)
+ obj = mk_matrix(players)
+ return obj.filter
+ end
+
+ ##################
+ # Instance methods
+ #
+
+ # an array of player IDs; [gps+123, foo+234, ...]
+ attr_reader :keys
+
+ # matrix holds games # where player i (row index) beats player j (column index).
+ # The row and column indexes match with the keys.
+ attr_reader :matrix
+
+ def initialize(keys, matrix)
+ @keys = keys
+ @matrix = matrix
+ end
+
+ ##
+ # Returns the size of the keys/matrix
+ #
+ def size
+ if @keys
+ @keys.size
+ else
+ nil
+ end
+ end
+
+ ##
+ # Removes a delete_index'th player and returns a new object.
+ #
+ def delete_row(delete_index)
+ copied_cols = []
+ (0...size).each do |i|
+ next if i == delete_index
+ row = @matrix.row(i).clone
+ row.delete_at(delete_index)
+ copied_cols << row
+ end
+ if copied_cols.size == 0
+ new_matrix = GSL::Matrix.new
+ else
+ new_matrix = GSL::Matrix[*copied_cols]
+ end
+ new_keys = @keys.clone
+ new_keys.delete_at(delete_index)
+ return WinLossMatrix.new(new_keys, new_matrix)
+ end
+
+ ##
+ # Removes players in a rows; [1,3,5]
+ #
+ def delete_rows(rows)
+ obj = self
+ rows.sort.reverse.each do |index|
+ obj = obj.delete_row(index)
+ end
+ obj
+ end
+
+ ##
+ # Removes players who do not pass a criteria to be rated, and returns a
+ # new object.
+ #
+ def filter
+ $stderr.puts @keys.inspect if $DEBUG
+ $stderr.puts @matrix.inspect if $DEBUG
+ delete = []
+ (0...size).each do |i|
+ row = @matrix.row(i)
+ col = @matrix.col(i)
+ win = row.sum
+ loss = col.sum
+ if win < 1 || loss < 1 || win + loss < $GAMES_LIMIT
+ delete << i
+ end
+ end
+
+ # The recursion ends if there is nothing to delete
+ return self if delete.empty?
+
+ new_obj = delete_rows(delete)
+ new_obj.filter
+ end
+
+ ##
+ # Cuts self into connecting groups such as each player in a group has at least
+ # one game with other players in the group. Returns them as an array.
+ #
+ def connected_subsets
+ g = RGL::AdjacencyGraph.new
+ (0...size).each do |k|
+ (0...size).each do |i|
+ next if k == i
+ if @matrix[k,i] > 0
+ g.add_edge(k,i)
+ end
+ end
+ end
+
+ subsets = []
+ g.each_connected_component do |c|
+ new_keys = []
+ c.each do |v|
+ new_keys << keys[v.to_s.to_i]
+ end
+ subsets << new_keys
+ end
+
+ subsets = subsets.sort {|a,b| b.size <=> a.size}
+
+ result = subsets.collect do |keys|
+ matrix =
+ GSL::Matrix[*
+ ((0...keys.size).collect do |k|
+ p1 = @keys.index(keys[k])
+ ((0...keys.size).collect do |j|
+ if k == j
+ 0
+ else
+ p2 = @keys.index(keys[j])
+ @matrix[p1,p2]
+ end
+ end)
+ end)]
+ WinLossMatrix.new(keys, matrix)
+ end
+
+ return result
+ end
+
+ def to_s
+ "size : #{@keys.size}" + "\n" +
+ @keys.inspect + "\n" +
+ @matrix.inspect
+ end
+
+end
#################################################
# Main methods
#
-def mk_win_loss_matrix(players)
- keys = players.keys.sort.reject do |k|
- players[k].values.inject(0) {|sum, v| sum + v[0] + v[1]} < $GAMES_LIMIT
- end
-
- size = keys.size
-
- matrix =
- Matrix[*
- ((0...size).collect do |k|
- ((0...size).collect do |j|
- if k == j
- 0
- else
- v = players[keys[k]][keys[j]]
- v[0]
- end
- end)
- end)]
-
- return matrix, keys
+# Half-life effect
+# After NHAFE_LIFE days value will get half.
+# 0.693 is constant, where exp(0.693) ~ 0.5
+NHALF_LIFE=60
+def half_life(days)
+ if days < 7
+ return 1.0
+ else
+ Math::exp(-0.693/NHALF_LIFE*(days-7))
+ end
end
-def _add_win_loss(winner, loser)
- $players[winner] ||= Hash.new { Vector[0,0] }
- $players[loser] ||= Hash.new { Vector[0,0] }
- $players[winner][loser] += Vector[1,0]
- $players[loser][winner] += Vector[0,1]
+def _add_win_loss(winner, loser, time)
+ how_long_days = (Time.now - time)/(3600*24)
+ $players[winner] ||= Hash.new { GSL::Vector[0,0] }
+ $players[loser] ||= Hash.new { GSL::Vector[0,0] }
+ $players[winner][loser] += GSL::Vector[1.0*half_life(how_long_days),0]
+ $players[loser][winner] += GSL::Vector[0,1.0*half_life(how_long_days)]
end
def _add_time(player, time)
- $players_time[player] = time if $players_time[player] < time
+ $players_time[player] = time if $players_time[player] < time
end
def add(black_mark, black_name, white_name, white_mark, time)
- if black_mark == WIN_MARK && white_mark == LOSS_MARK
- _add_win_loss(black_name, white_name)
- elsif black_mark == LOSS_MARK && white_mark == WIN_MARK
- _add_win_loss(white_name, black_name)
- else
- raise "Never reached!"
- end
- _add_time(black_name, time)
- _add_time(white_name, time)
+ if black_mark == WIN_MARK && white_mark == LOSS_MARK
+ _add_win_loss(black_name, white_name, time)
+ elsif black_mark == LOSS_MARK && white_mark == WIN_MARK
+ _add_win_loss(white_name, black_name, time)
+ elsif black_mark == DRAW_MARK && white_mark == DRAW_MARK
+ return
+ else
+ raise "Never reached!"
+ end
+ _add_time(black_name, time)
+ _add_time(white_name, time)
end
-def grep(file)
- str = File.open(file).read
-
- black_mark = ""; white_mark = ""
- time = nil
+def identify_id(id)
+ if /@NORATE\+/ =~ id # the player having @NORATE in the name should not be rated
+ return nil
+ end
+ id.gsub(/@.*?\+/,"+")
+end
- str.gsub(/^'summary:(.*)$/) do |line|
- dummy, sente, gote = $1.split(":").map {|a| a.strip}
- black_mark, white_mark = [sente,gote].map {|p| p.split(" ")[1]}
- end
- str.gsub(/^'\$END_TIME:(.*)$/) do |line|
+def grep(file)
+ str = File.open(file).read
+
+ if /^N\+(.*)$/ =~ str then black_name = $1.strip end
+ if /^N\-(.*)$/ =~ str then white_name = $1.strip end
+
+ if /^'summary:(.*)$/ =~ str
+ state, p1, p2 = $1.split(":").map {|a| a.strip}
+ return if state == "abnormal"
+ p1_name, p1_mark = p1.split(" ")
+ p2_name, p2_mark = p2.split(" ")
+ if p1_name == black_name
+ black_name, black_mark = p1_name, p1_mark
+ white_name, white_mark = p2_name, p2_mark
+ elsif p2_name == black_name
+ black_name, black_mark = p2_name, p2_mark
+ white_name, white_mark = p1_name, p1_mark
+ else
+ raise "Never reach!: #{black} #{white} #{p3} #{p2}"
+ end
+ end
+ if /^'\$END_TIME:(.*)$/ =~ str
time = Time.parse($1.strip)
- end
- if /^'rating:(.*)$/ =~ str
- black_name, white_name = $1.split(":").map {|a| a.strip}
- add(black_mark, black_name, white_name, white_mark, time)
- end
+ end
+ if /^'rating:(.*)$/ =~ str
+ black_id, white_id = $1.split(":").map {|a| a.strip}
+ black_id = identify_id(black_id)
+ white_id = identify_id(white_id)
+ if black_id && white_id && (black_id != white_id)
+ add(black_mark, black_id, white_id, white_mark, time)
+ end
+ end
end
def usage
- $stderr.puts <<-EOF
+ $stderr.puts <<-EOF
USAGE: #{$0} dir [...]
- EOF
- exit 1
+ EOF
+ exit 1
+end
+
+def validate(yaml)
+ yaml["players"].each do |group_key, group|
+ group.each do |player_key, player|
+ rate = player['rate']
+ next unless rate
+ if rate > 10000 || rate < -10000
+ return false
+ end
+ end
+ end
+ return true
end
def main
- usage if ARGV.empty?
- while dir = ARGV.shift do
- Dir.glob( File.join(dir, "**", "*.csa") ) {|f| grep(f)}
- end
-
- win_loss_matrix, keys = mk_win_loss_matrix($players)
- rating = Rating.new(win_loss_matrix)
- rating.rating
- rating.average!(AVERAGE_RATE)
- rating.integer!
-
- yaml = {}
- keys.each_with_index do |p, i| # player_id, index#
- win_loss = $players[p].values.inject(Vector[0,0]) {|sum, v| sum + v}
- win = win_loss_matrix
- yaml[p] =
- { 'name' => p.split("+")[0],
- 'rate' => rating.rate[i],
- 'last_modified' => $players_time[p],
- 'win' => win_loss[0],
- 'loss' => win_loss[1]}
- end
- puts yaml.to_yaml
+ usage if ARGV.empty?
+ while dir = ARGV.shift do
+ Dir.glob( File.join(dir, "**", "*.csa") ) {|f| grep(f)}
+ end
+
+ yaml = {}
+ yaml["players"] = {}
+ rating_group = 0
+ if $players.size > 0
+ obj = WinLossMatrix::mk_win_loss_matrix($players)
+ obj.connected_subsets.each do |win_loss_matrix|
+ yaml["players"][rating_group] = {}
+
+ rating = Rating.new(win_loss_matrix.matrix)
+ rating.rating
+ rating.average!(Rating::AVERAGE_RATE)
+ rating.integer!
+
+ win_loss_matrix.keys.each_with_index do |p, i| # player_id, index#
+ win = win_loss_matrix.matrix.row(i).sum
+ loss = win_loss_matrix.matrix.col(i).sum
+
+ yaml["players"][rating_group][p] =
+ { 'name' => p.split("+")[0],
+ 'rating_group' => rating_group,
+ 'rate' => rating.rate[i],
+ 'last_modified' => $players_time[p].dup,
+ 'win' => win,
+ 'loss' => loss}
+ end
+ rating_group += 1
+ end
+ end
+ rating_group -= 1
+ non_rated_group = 999 # large enough
+ yaml["players"][non_rated_group] = {}
+ $players.each_key do |id|
+ # skip players who have already been rated
+ found = false
+ (0..rating_group).each do |i|
+ found = true if yaml["players"][i][id]
+ break if found
+ end
+ next if found
+
+ v = GSL::Vector[0, 0]
+ $players[id].each_value {|value| v += value}
+ next if v[0] < 1 && v[1] < 1
+
+ yaml["players"][non_rated_group][id] =
+ { 'name' => id.split("+")[0],
+ 'rating_group' => non_rated_group,
+ 'rate' => 0,
+ 'last_modified' => $players_time[id].dup,
+ 'win' => v[0],
+ 'loss' => v[1]}
+ end
+ unless validate(yaml)
+ $stderr.puts "Aborted. It did not result in valid ratings."
+ $stderr.puts yaml.to_yaml if $DEBUG
+ exit 10
+ end
+ puts yaml.to_yaml
end
if __FILE__ == $0
- main
+ main
end
# vim: ts=2 sw=2 sts=0