- 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)
+ #@rate -= a # Instead, do not deaccelerate
+ @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
+ $stderr.puts "Count: %d" % [@count] 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.
+ #