#!/usr/local/bin/ruby

require 'matrix'

class Matrix
  def []=(i,j,x)
    @rows[i][j]=x
  end
end

DIVIDE = 30
STEP = 10
CFL = 0.5

#Initialize Scheme Matrix
scheme = Matrix.I(DIVIDE)
(1...(DIVIDE-1)).each{|x|
	scheme[x, x-1] = -0.5 * CFL
	scheme[x, x+1] = 0.5 * CFL
}

scheme_inv = scheme.inverse

#Set initiail condition
target = []
(0...DIVIDE).each{|x|
	target << (x < DIVIDE/3 ? 0 : x < 2*DIVIDE/3 ? 1 : 0)
}
target = Vector.elements(target)

#Calc.
(0...STEP).each{|x|
	target = scheme_inv * target
}

#Output
target.to_a.each{|x| printf("%.6f\n", x)}