iterative.rb

#!/usr/bin/env ruby1.9

require 'mathn'

A = Matrix[[4,1],
           [2,3]]
b = Vector[6,
           8]

def jacobi(matrix,vector)
  a11 = matrix[0,0]
  a12 = matrix[0,1]
  a21 = matrix[1,0]
  a22 = matrix[1,1]
  b1 = vector[0]
  b2 = vector[1]
  x_1 = ->(x){ b1.fdiv(a11) - (a12.fdiv(a11) * x) }
  x_2 = ->(x){ b2.fdiv(a22) - (a21.fdiv(a22) * x) }
  prev,curr,prev2,curr2,iter = 0,0,0,0,0

  while true
    prev = curr
    prev2 = curr2
    curr = x_1[prev2]
    curr2 = x_2[prev]

    iter += 1
    puts "=== Iteration #{iter} ==="
    puts "x1: (#{b1}/#{a11}) - ((#{a12}/#{a11}) * %.3f) = %.3f" % [prev,curr]
    puts "x2: (#{b2}/#{a22}) - ((#{a21}/#{a22}) * %.3f) = %.3f" % [prev2,curr2]

    break if (curr - prev).abs <= 0.001 && (curr2 - prev2).abs <= 0.001
  end
  puts "result: %.3f %.3f" % [curr,curr2]
end

puts "=================
= Jacobi Method =
================="
jacobi(A,b)

def gauss_seidel(matrix,vector)
  a11 = matrix[0,0]
  a12 = matrix[0,1]
  a21 = matrix[1,0]
  a22 = matrix[1,1]
  b1 = vector[0]
  b2 = vector[1]
  x_1 = ->(x){ b1.fdiv(a11) - (a12.fdiv(a11) * x) }
  x_2 = ->(x){ b2.fdiv(a22) - (a21.fdiv(a22) * x) }
  prev,curr,prev2,curr2,iter = 0,0,0,0,0

  while true
    prev = curr
    prev2 = curr2
    curr = x_1[prev2]
    curr2 = x_2[curr]

    iter += 1
    puts "=== Iteration #{iter} ==="
    puts "x1: (#{b1}/#{a11}) - ((#{a12}/#{a11}) * %.3f) = %.3f" % [prev,curr]
    puts "x2: (#{b2}/#{a22}) - ((#{a21}/#{a22}) * %.3f) = %.3f" % [curr,curr2]

    break if (curr - prev).abs <= 0.001 && (curr2 - prev2).abs <= 0.001
  end
  puts "result: %.3f %.3f" % [curr,curr2]
end


puts "=======================
= Gauss-Seidel Method =
======================="
gauss_seidel(A,b)

#def power_method
#end