# "name,trip".
# * (Rated) players, who played more than $GAMES_LIMIT [ten] (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 'time'
require 'gsl'
+require 'rubygems'
+require 'rgl/adjacency'
+require 'rgl/connected_components'
#################################################
# Constants
#
+
+# Count out players who play less games than $GAMES_LIMIT
$GAMES_LIMIT = $DEBUG ? 0 : 10
WIN_MARK = "win"
LOSS_MARK = "lose"
+DRAW_MARK = "draw"
+# Holds players
$players = Hash.new
+# Holds the last time when a player gamed
$players_time = Hash.new { Time.at(0) }
#################################################
+# 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
- # 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 like this.
+ # 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
# 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}
# Instance methods
#
def initialize(win_loss_matrix)
+ @record = Record.new
@n = win_loss_matrix
case @n
- when GSL::Matrix
+ when GSL::Matrix, GSL::Matrix::Int
@size = @n.size1
when ::Matrix
@size = @n.row_size
else
raise ArgumentError
end
- # 0 is the initial value
- @rate = initial_rate
+ initial_rate
end
attr_reader :rate, :n
end
##
- # / f0/R0 f0/R1 f0/R2 ... \
- # fk/Rj = | f1/R0 f1/R1 f1/R2 ... |
- # \ f2/R0 f2/R1 f2/R2 ... /
- def d_funk(k,j)
+ # / 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])
- sum *= -2.0
end
+ sum *= -2.0
else # k != j
- sum = win_rate(j,k) * win_rate(k,j) * (@n[k,j] + @n[j,k])
- sum *= 2.0
+ sum = 2.0 * win_rate(j,k) * win_rate(k,j) * (@n[k,j] + @n[j,k])
end
sum
end
GSL::Matrix[*
(0...@size).collect do |k|
(0...@size).collect do |j|
- d_funk(k,j)
+ d_func(k,j)
end
end
]
##
# The initial value of the rate, which is of very importance for Newton method.
- # This is based on my huristics.
+ # 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, 0.0]
+ v = GSL::Vector[0, 0]
each_player do |i|
next if k == i
v += GSL::Vector[@n[k,i], @n[i,k]]
end
- v[0] + v[1] == 0 ? 0.001 : v[0] / (v[0] + v[1])
+ v.nrm2 < 1 ? 0 : v[0] / (v[0] + v[1])
end
rank = possibility.sort_index
- player_vector do |k|
- K*500 * (rank[k]+1) / (@size)
+ @rate = player_vector do |k|
+ K*500 * (rank[k]+1) / @size
end
+ average!
end
##
- # Main method to calculate ratings.
+ # 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
- # Mu parameter in Deaccelerated Newton method
- mu = 1
+ @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
- # f.nrm2 should approach to zero.
+ # $stderr.puts "j: %s" % [j.inspect] if $DEBUG
$stderr.puts "f: %s -> %f" % [f.to_a.inspect, f.nrm2] if $DEBUG
- # LU is not available because J may not be a normal matrix.
- # a = GSL::Linalg::LU.solve(j, f)
+ # 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
- if mu == 1
- old_rate = GSL::Vector.alloc(@rate)
- old_f = GSL::Vector.alloc(f)
- @rate = old_rate - a * mu
- end
- if func_vector.nrm2 < (1.0 - mu / 4.0) * old_f.nrm2
- mu = 1
- break
- else
- mu *= 0.5
- @rate = old_rate - a * mu
- end
+ # 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 > 300
+ @count += 1
+ if @count > COUNT_MAX
$stderr.puts "Values seem to oscillate. Stopped the process."
- $stderr.puts "f: %s -> %f" % [f.to_a.inspect, f.nrm2]
+ $stderr.puts "f: %s -> %f" % [func_vector.to_a.inspect, func_vector.nrm2]
break
end
end while (a.nrm2 > ERROR_LIMIT * @rate.nrm2)
- #end while ( !(0..0.01).include?(func_vector.nrm2) )
+ @rate = @record.get
$stderr.puts "resolved f: %s -> %f" %
[func_vector.to_a.inspect, func_vector.nrm2] if $DEBUG
self
end
+ ##
+ # Make the values of @rate finite.
+ #
def finite!
@rate = @rate.collect do |a|
if a.infinite?
end
end
+ ##
+ # Flatten the values of @rate.
+ #
def average!(mean=0.0)
@rate = self.class.average(@rate, mean)
end
+ ##
+ # Make the values of @rate integer.
+ #
def integer!
@rate = @rate.collect do |a|
if a.finite?
end
end
-
-
#################################################
-# Main methods
+# 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 =
+ 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 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
+ def self.mk_win_loss_matrix(players)
+ obj = mk_matrix(players)
+ return obj.filter
end
- size = keys.size
+ ##################
+ # Instance methods
+ #
- 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]
+ # 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.get_row(i) # get_row returns a copy of the row
+ row.delete_at(delete_index)
+ copied_cols << row
+ end
+ new_matrix = Matrix[*copied_cols]
+ 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)
- end)]
-
- return matrix, keys
+ 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 =
+ 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
+#
+
+# 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)
+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]
- $players[loser][winner] += GSL::Vector[0,1]
+ $players[winner][loser] += GSL::Vector[1.0*half_life(how_long_days),0]
+ $players[loser][winner] += GSL::Vector[0,1.0*half_life(how_long_days)]
end
def _add_time(player, time)
def add(black_mark, black_name, white_name, white_mark, time)
if black_mark == WIN_MARK && white_mark == LOSS_MARK
- _add_win_loss(black_name, white_name)
+ _add_win_loss(black_name, white_name, time)
elsif black_mark == LOSS_MARK && white_mark == WIN_MARK
- _add_win_loss(white_name, black_name)
+ _add_win_loss(white_name, black_name, time)
+ elsif black_mark == DRAW_MARK && white_mark == DRAW_MARK
+ return
else
raise "Never reached!"
end
_add_time(white_name, time)
end
+def identify_id(id)
+ if /@NORATE\+/ =~ id # the player having @NORATE in the name should not be rated
+ return nil
+ end
+ id.gsub(/@.*?\+/,"+")
+end
+
def grep(file)
str = File.open(file).read
if /^N\-(.*)$/ =~ str then white_name = $1.strip end
if /^'summary:(.*)$/ =~ str
- dummy, p1, p2 = $1.split(":").map {|a| a.strip}
+ state, p1, p2 = $1.split(":").map {|a| a.strip}
+ return if state == "abnormal"
p1_name, p1_mark = p1.split(" ")
p2_name, p2_mark = p2.split(" ")
if p1_name == black_name
black_name, black_mark = p2_name, p2_mark
white_name, white_mark = p1_name, p1_mark
else
- raise "Never reach!: #{black} #{white} #{p1} #{p2}"
+ raise "Never reach!: #{black} #{white} #{p3} #{p2}"
end
end
if /^'\$END_TIME:(.*)$/ =~ str
end
if /^'rating:(.*)$/ =~ str
black_id, white_id = $1.split(":").map {|a| a.strip}
- add(black_mark, black_id, white_id, white_mark, time)
+ black_id = identify_id(black_id)
+ white_id = identify_id(white_id)
+ if black_id && white_id && (black_id != white_id)
+ add(black_mark, black_id, white_id, white_mark, time)
+ end
end
end
Dir.glob( File.join(dir, "**", "*.csa") ) {|f| grep(f)}
end
- win_loss_matrix, keys = mk_win_loss_matrix($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!(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]}
+ yaml = {}
+ yaml["players"] = {}
+ if $players.size > 0
+ obj = WinLossMatrix::mk_win_loss_matrix($players)
+ rating_group = 0
+ 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
puts yaml.to_yaml
end
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