# "name,trip".
# * (Rated) players, who played more than $GAMES_LIMIT [ten] (rated) games.
#
+#
+# PREREQUIRE
+# ==========
+#
+# Ruby bindings for the GNU Scientific Library (GSL) is required.
+# You can download it from http://rb-gsl.rubyforge.org/
+# Or, if you use Debian,
+# $ sudo aptitude install libgsl-ruby1.8
+#
require 'yaml'
-require 'matrix'
require 'time'
+require 'gsl'
#################################################
# Constants
#
+
+# Count out players who play less games than $GAMES_LIMIT
$GAMES_LIMIT = $DEBUG ? 0 : 10
WIN_MARK = "win"
LOSS_MARK = "lose"
-AVERAGE_RATE = 1100
+# 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|
- # 1
- # --------------
- # 1 + exp(y-x)
- 1.0/(1.0+exp(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
- $stderr.printf "|error| : %5.2e\n", errorVector.r if $DEBUG
-
- end while (errorVector.r > ERROR_LIMIT * @rate.r)
-
+
+ # 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
+ @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::SV.solve(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
- self
- end
+ 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
#
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
+ 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 =
+ GSL::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
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]
+ $players[winner] ||= Hash.new { GSL::Vector[0,0] }
+ $players[loser] ||= Hash.new { GSL::Vector[0,0] }
+ $players[winner][loser] += GSL::Vector[1,0]
+ $players[loser][winner] += GSL::Vector[0,1]
end
def _add_time(player, time)
- $players_time[player] = time if $players_time[player] < time
+ $players_time[player] = time if $players_time[player] < time
end
def add(black_mark, black_name, white_name, white_mark, time)
- if black_mark == WIN_MARK && white_mark == LOSS_MARK
- _add_win_loss(black_name, white_name)
- elsif black_mark == LOSS_MARK && white_mark == WIN_MARK
- _add_win_loss(white_name, black_name)
- else
- raise "Never reached!"
- end
- _add_time(black_name, time)
- _add_time(white_name, time)
+ if black_mark == WIN_MARK && white_mark == LOSS_MARK
+ _add_win_loss(black_name, white_name)
+ elsif black_mark == LOSS_MARK && white_mark == WIN_MARK
+ _add_win_loss(white_name, black_name)
+ else
+ raise "Never reached!"
+ end
+ _add_time(black_name, time)
+ _add_time(white_name, time)
end
def grep(file)
- str = File.open(file).read
+ str = File.open(file).read
if /^N\+(.*)$/ =~ str then black_name = $1.strip end
if /^N\-(.*)$/ =~ str then white_name = $1.strip end
- if /^'summary:(.*)$/ =~ str
- dummy, p1, p2 = $1.split(":").map {|a| a.strip}
+ if /^'summary:(.*)$/ =~ str
+ dummy, p1, p2 = $1.split(":").map {|a| a.strip}
p1_name, p1_mark = p1.split(" ")
p2_name, p2_mark = p2.split(" ")
if p1_name == black_name
else
raise "Never reach!: #{black} #{white} #{p1} #{p2}"
end
- end
- if /^'\$END_TIME:(.*)$/ =~ str
+ end
+ if /^'\$END_TIME:(.*)$/ =~ str
time = Time.parse($1.strip)
- end
- if /^'rating:(.*)$/ =~ str
- black_id, white_id = $1.split(":").map {|a| a.strip}
- add(black_mark, black_id, white_id, white_mark, time)
- end
+ end
+ if /^'rating:(.*)$/ =~ str
+ black_id, white_id = $1.split(":").map {|a| a.strip}
+ add(black_mark, black_id, white_id, white_mark, time)
+ end
end
def usage
- $stderr.puts <<-EOF
+ $stderr.puts <<-EOF
USAGE: #{$0} dir [...]
- EOF
- exit 1
+ EOF
+ exit 1
end
def main
- usage if ARGV.empty?
- while dir = ARGV.shift do
- Dir.glob( File.join(dir, "**", "*.csa") ) {|f| grep(f)}
- end
+ usage if ARGV.empty?
+ while dir = ARGV.shift do
+ Dir.glob( File.join(dir, "**", "*.csa") ) {|f| grep(f)}
+ end
- win_loss_matrix, keys = mk_win_loss_matrix($players)
+ win_loss_matrix, keys = mk_win_loss_matrix($players)
$stderr.puts keys.inspect if $DEBUG
$stderr.puts win_loss_matrix.inspect if $DEBUG
- 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}
+ rating = Rating.new(win_loss_matrix)
+ rating.rating
+ rating.average!(Rating::AVERAGE_RATE)
+ rating.integer!
+
+ yaml = {}
+ keys.each_with_index do |p, i| # player_id, index#
+ win_loss = $players[p].values.inject(GSL::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].dup,
- 'win' => win_loss[0],
- 'loss' => win_loss[1]}
- end
- puts yaml.to_yaml
+ yaml[p] =
+ { 'name' => p.split("+")[0],
+ 'rate' => rating.rate[i],
+ 'last_modified' => $players_time[p].dup,
+ 'win' => win_loss[0],
+ 'loss' => win_loss[1]}
+ end
+ puts yaml.to_yaml
end
if __FILE__ == $0
- main
+ main
end
# vim: ts=2 sw=2 sts=0
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