Ruby script to calculate a simple regression curve.(5d)

regression_curve_5d.rb

#! /usr/local/bin/ruby
#*********************************************
# Ruby script to calculate a simple regression curve.
# : y = a + b * x + c * x^2 + d * x^3 + e * x^4 + f * x^5
# : 連立方程式を ガウスの消去法（ピボット選択）で解く方法
#*********************************************
#
class Array
  def reg_curve_5d(y)
    # 以下の場合は例外スロー
    # - 引数の配列が Array クラスでない
    # - 自身配列が空
    # - 配列サイズが異なれば例外
    raise "Argument is not a Array class!"  unless y.class == Array
    raise "Self array is nil!"              if self.size == 0
    raise "Argument array size is invalid!" unless self.size == y.size

    sum_x   = self.inject(0) { |s, a| s += a }
    sum_x2  = self.inject(0) { |s, a| s += a * a }
    sum_x3  = self.inject(0) { |s, a| s += a * a * a }
    sum_x4  = self.inject(0) { |s, a| s += a * a * a * a }
    sum_x5  = self.inject(0) { |s, a| s += a * a * a * a * a }
    sum_x6  = self.inject(0) { |s, a| s += a * a * a * a * a * a }
    sum_x7  = self.inject(0) { |s, a| s += a * a * a * a * a * a * a }
    sum_x8  = self.inject(0) { |s, a| s += a * a * a * a * a * a * a * a }
    sum_x9  = self.inject(0) { |s, a| s += a * a * a * a * a * a * a * a * a }
    sum_x10 = self.inject(0) { |s, a| s += a * a * a * a * a * a * a * a * a * a }
    sum_y   = y.inject(0) { |s, a| s += a }
    sum_xy  = self.zip(y).inject(0) {
      |s, a| s += a[0] * a[1]
    }
    sum_x2y = self.zip(y).inject(0) {
      |s, a| s += a[0] * a[0] * a[1]
    }
    sum_x3y = self.zip(y).inject(0) {
      |s, a| s += a[0] * a[0] * a[0] * a[1]
    }
    sum_x4y = self.zip(y).inject(0) {
      |s, a| s += a[0] * a[0] * a[0] * a[0] * a[1]
    }
    sum_x5y = self.zip(y).inject(0) {
      |s, a| s += a[0] * a[0] * a[0] * a[0] * a[0] * a[1]
    }
    mtx = [
      [self.size,  sum_x, sum_x2, sum_x3, sum_x4, sum_x5,    sum_y],
      [    sum_x, sum_x2, sum_x3, sum_x4, sum_x5, sum_x6,   sum_xy],
      [   sum_x2, sum_x3, sum_x4, sum_x5, sum_x6, sum_x7,  sum_x2y],
      [   sum_x3, sum_x4, sum_x5, sum_x6, sum_x7, sum_x8,  sum_x3y],
      [   sum_x4, sum_x5, sum_x6, sum_x7, sum_x8, sum_x9,  sum_x4y],
      [   sum_x5, sum_x6, sum_x7, sum_x8, sum_x9, sum_x10, sum_x5y]
    ]
    ans = solve_ge(mtx)
    {
      a: ans[0][-1], b: ans[1][-1], c: ans[2][-1],
      d: ans[3][-1], e: ans[4][-1], f: ans[5][-1]
    }
  end

private

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

  # 連立方程式の解（ガウスの消去法（ピボット選択））
  def solve_ge(a)
    n = a.size
    # 前進消去
    (n - 1).times do |k|
      a = pivot(a, k)  # ピボット選択処理
      (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
    return a
  end
end

# 説明変数と目的変数
#ary_x = [107, 336, 233, 82, 61, 378, 129, 313, 142, 428]
#ary_y = [286, 851, 589, 389, 158, 1037, 463, 563, 372, 1020]
ary_x = [83, 71, 64, 69, 69, 64, 68, 59, 81, 91, 57, 65, 58, 62]
ary_y = [183, 168, 171, 178, 176, 172, 165, 158, 183, 182, 163, 175, 164, 175]
puts "説明変数 X = {#{ary_x.join(', ')}}"
puts "目的変数 Y = {#{ary_y.join(', ')}}"
puts "---"

# 単回帰曲線算出
reg_line = ary_x.reg_curve_5d(ary_y)
puts "a = #{reg_line[:a]}"
puts "b = #{reg_line[:b]}"
puts "c = #{reg_line[:c]}"
puts "d = #{reg_line[:d]}"
puts "e = #{reg_line[:e]}"
puts "f = #{reg_line[:f]}"