algebra.rb

module Algebra

  class MaximumIterationsReached < Exception
  end

  class NewtonsMethod

    def self.calculate(function, x)
      x - function.evaluated_at(x) / function.derivative_at(x)
    end

  end

  class NewtonsDifferenceQuotient

    def self.calculate(function, x, delta=0.1)
      (function.evaluated_at(x + delta) - function.evaluated_at(x) ).to_f / delta
    end

  end

  class Function

    attr_accessor :differentiation_method, :root_method, :maximum_iterations, :tolerance

    def initialize(differentiation_method=NewtonsDifferenceQuotient, root_method=NewtonsMethod, &block)
      @definition = block
      @differentiation_method, @root_method = differentiation_method, root_method
      @maximum_iterations = 1000
      @tolerance = 0.0001
    end

    def evaluated_at(x)
      @definition.call(x)
    end

    def derivative_at(x)
      differentiation_method.calculate(self, x)
    end

    def zero(initial_value=0)
      recursive_zero(initial_value, 1)
    end

    private

    def recursive_zero(guess, iteration)
      raise MaximumIterationsReached if iteration >= @maximum_iterations

      better_guess = @root_method.calculate(self, guess)

      if (better_guess - guess).abs <= @tolerance
        better_guess
      else
        recursive_zero(better_guess, iteration + 1)
      end
    end

  end

end