mk_rate

#!/usr/bin/ruby
# $Id$
#
# Author:: Daigo Moriwaki
# Homepage:: http://sourceforge.jp/projects/shogi-server/
#
#--
# Copyright (C) 2006-2009 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
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software
# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
#++
#
# == Synopsis
#
# mk_rate reads CSA files, calculates rating scores of each player, and then
# outputs a yaml file (players.yaml) that Shogi-server can recognize.
#
# == Usage
#
# ./mk_rate [options] DIR..
# 
# DIR::
#   CSA files are recursively looked up the directories.
#
# --base-date::
#   a base time point for this calicuration (default now). Ex. '2009-10-31'
#
# --half-life::
#   n [days] (default 60)
#   
# --half-life-ignore::
#   m [days] (default  7)
#   after m days, the half-life effect works
#
# --fixed-rate-player::
#   player whose rate is fixed at the rate
#
# --fixed-rate::
#   rate 
#
# --skip-draw-games::
#   skip draw games. [default: draw games are counted in as 0.5 win and 0.5
#   lost.]
#
# --help::
#   show this message
#
# == PREREQUIRE
#
# Sample Command lines that isntall prerequires will work on Debian.
#
# * Ruby 1.8.7
#
#   $ sudo aptitude install ruby1.8
#
# * Rubygems
#
#   $ sudo aptitude install rubygems
#
# * Ruby bindings for the GNU Scientific Library (GSL[http://rb-gsl.rubyforge.org/])
#
#   $ sudo aptitude install libgsl-ruby1.8
#
# * RGL: {Ruby Graph Library}[http://rubyforge.org/projects/rgl/]
#
#   $ sudo gem install rgl
#
# == Run
#
#   $ ./mk_rate . > players.yaml
#
# or, if you do not want the file to be update in case of errors, 
#
#   $ ./mk_rate . && ./mk_rate . > players.yaml
#
# == How players are rated
#
# 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 [15] (rated) games. 
#

require 'yaml'
require 'time'
require 'getoptlong'
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 : 15
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 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}
    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

  ##
  # Translate by value
  #
  def translate!(value)
    @rate += value
  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 players in a rows such as [1,3,5], and then returns a new
  # object.
  #
  def delete_rows(rows)
    rows = rows.sort.reverse

    copied_cols = []
    (0...size).each do |i|
      next if rows.include?(i)
      row = @matrix.row(i).clone
      rows.each do |j|
        row.delete_at(j)
      end
      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
    rows.each do |j|
      new_keys.delete_at(j)
    end

    return WinLossMatrix.new(new_keys, new_matrix)
  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
#

# Half-life effect
# After NHAFE_LIFE days value will get half.
# 0.693 is constant, where exp(0.693) ~ 0.5
def half_life(days)
  if days < $options["half-life-ignore"]
    return 1.0
  else
    Math::exp(-0.693/$options["half-life"]*(days-$options["half-life-ignore"]))
  end
end

def _add_win_loss(winner, loser, time)
  how_long_days = ($options["base-date"] - 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_draw(player1, player2, time)
  how_long_days = ($options["base-date"] - time)/(3600*24)
  $players[player1] ||= Hash.new { GSL::Vector[0,0] }
  $players[player2] ||= Hash.new { GSL::Vector[0,0] }
  $players[player1][player2] += GSL::Vector[0.5*half_life(how_long_days),0.5*half_life(how_long_days)]
  $players[player2][player1] += GSL::Vector[0.5*half_life(how_long_days),0.5*half_life(how_long_days)]
end

def _add_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, 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
    if $options["skip-draw-games"]
      return
    else
      _add_draw(black_name, white_name, time)
    end
  else
    raise "Never reached!"
  end
  _add_time(black_name, time)
  _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

# Parse a game result line
#
def parse(line)
  time, state, black_mark, black_id, white_id, white_mark, file = line.split("\t")
  unless time && state && black_mark && black_id &&
         white_id && white_mark && file
    $stderr.puts "Failed to parse the line : #{line}"
    return
  end

  return if state == "abnormal"
  time = Time.parse(time)
  return if $options["base-date"] < time
  black_id = identify_id(black_id)
  white_id = identify_id(white_id)

  if black_id && white_id && (black_id != white_id) &&
     black_mark && white_mark
    add(black_mark, black_id, white_id, white_mark, time)
  end
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 usage(io)
    io.puts <<EOF
USAGE: #{$0} [options] DIR..
  DIR                where CSA files are looked up recursively
OPTOINS:
  --base-date         a base time point for this calicuration (default now). Ex. '2009-10-31'
  --half-life         n [days] (default 60)
  --half-life-ignore  m [days] (default  7)
                      after m days, half-life effect works
  --fixed-rate-player player whose rate is fixed at the rate
  --fixed-rate        rate 
  --skip-draw-games   skip draw games. [default: draw games are counted in
                      as 0.5 win and 0.5 lost]
  --help              show this message
EOF
end

def main
  $options = Hash::new
  parser = GetoptLong.new(
    ["--base-date",         GetoptLong::REQUIRED_ARGUMENT],
    ["--half-life",         GetoptLong::REQUIRED_ARGUMENT],
    ["--half-life-ignore",  GetoptLong::REQUIRED_ARGUMENT],
    ["--help", "-h",        GetoptLong::NO_ARGUMENT],
    ["--fixed-rate-player", GetoptLong::REQUIRED_ARGUMENT],
    ["--fixed-rate",        GetoptLong::REQUIRED_ARGUMENT],
    ["--skip-draw-games",   GetoptLong::NO_ARGUMENT])
  parser.quiet = true
  begin
    parser.each_option do |name, arg|
      name.sub!(/^--/, '')
      $options[name] = arg.dup
    end
    if ( $options["fixed-rate-player"] && !$options["fixed-rate"]) ||
       (!$options["fixed-rate-player"] &&  $options["fixed-rate"]) ||
       ( $options["fixed-rate-player"] &&  $options["fixed-rate"].to_i <= 0) 
      usage($stderr)
      exit 1
    end
  rescue
    usage($stderr)
    raise parser.error_message
  end
  if $options["help"]
    usage($stdout) 
    exit 0
  end
  if $options["base-date"]
    $options["base-date"] = Time::parse $options["base-date"]
  else
    $options["base-date"] = Time.now
  end
  $options["half-life"] ||= 60
  $options["half-life"] = $options["half-life"].to_i
  $options["half-life-ignore"] ||= 7
  $options["half-life-ignore"] = $options["half-life-ignore"].to_i
  $options["fixed-rate"] = $options["fixed-rate"].to_i if $options["fixed-rate"]

  if ARGV.empty?
    while line = $stdin.gets do
      parse line.strip
    end
  else
    while file = ARGV.shift do
      File.open(file) do |f|
        f.each_line do |line|
          parse line.strip
        end
      end 
    end
  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!

      if $options["fixed-rate-player"]
        # first, try exact match
        index = win_loss_matrix.keys.index($options["fixed-rate-player"])
        # second, try regular match
        unless index
          win_loss_matrix.keys.each_with_index do |p, i|
            if %r!#{$options["fixed-rate-player"]}! =~ p
              index = i
            end
          end
        end
        if index
          the_rate = rating.rate[index]
          rating.translate!($options["fixed-rate"] - the_rate)
        end
      end

      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
end

# vim: ts=2 sw=2 sts=0