Ruby script to solve simultaneous equations with Gauss elimination method(pivot).

gauss_elimination_pivot.rb

#! /usr/local/bin/ruby
#*********************************************
# 連立方程式の解法 ( ガウスの消去法（ピボット選択） )
#*********************************************
#
class GaussElimination
  def initialize
    # 係数
    @a = [
      [1.0, 2.0, 7.0, 6.0,  6.0],
      [2.0, 4.0, 4.0, 2.0,  2.0],
      [1.0, 8.0, 5.0, 2.0, 12.0],
      [2.0, 4.0, 3.0, 3.0,  5.0]
    ]
    # 次元の数
    @n = @a.size
  end

  # 計算・結果出力
  def exec
    # 元の連立方程式をコンソール出力
    display_equations
    # 前進消去
    (@n - 1).times do |k|
      raise unless pivot(k)
      (k + 1).upto(@n - 1) do |i|
        d = @a[i][k] / @a[k][k].to_f
        (k + 1).upto(@n) do |j|
          @a[i][j] -= @a[k][j] * d
        end
      end
    end
    # 後退代入
    (@n - 1).downto(0) do |i|
      d = @a[i][@n]
      (i + 1).upto(@n - 1) do |j|
        d -= @a[i][j] * @a[j][@n]
      end
      @a[i][@n] = d / @a[i][i].to_f
    end
    # 結果出力
    display_answers
  rescue => e
    raise
  end

private

  # ピボット選択
  def pivot(k)
    pv = k
    v_max = @a[k][k].abs
    (k + 1).upto(@n - 1) do |i|
      if @a[i][k].abs > v_max
        pv = i
        v_max = @a[i][k]
      end
    end
    if k != pv
      dummy   = @a[k]
      @a[k]  = @a[pv]
      @a[pv] = dummy
    end
    return true
  rescue => e
    return false
  end

  # 元の連立方程式をコンソール出力
  def display_equations
    @n.times do |i|
      @n.times { |j| printf("%+dx%d ", @a[i][j], j + 1) }
      puts "= %+d" % @a[i][@n]
    end
  rescue => e
    raise
  end

  # 結果出力
  def display_answers
    0.upto(@n - 1) { |k| puts "x%d = %f" % [k + 1, @a[k][@n]] }
  rescue => e
    raise
  end
end

if __FILE__ == $0
  begin
    obj = GaussElimination.new
    obj.exec
  rescue => e
    $stderr.puts "[#{e.class}] #{e.message}"
    e.backtrace.each{ |tr| $stderr.puts "\t#{tr}" }
  end
end