Class: RubyChem::Equation

Inherits:
Object
  • Object
show all
Defined in:
lib/rubychem/equation.rb

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(equation) ⇒ Equation

Checks if two formulas are balanced. Takes user input.. such as x + y + z = a + b yields @left[Chemical1, Chemical2, Chemical3], @right



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# File 'lib/rubychem/equation.rb', line 10

def initialize(equation)
	@left = Array.new
	@right = Array.new
  
  left_and_right = equation.split(/\=/)
  process_equation_string(left_and_right)
end

Instance Attribute Details

#array ⇒ Object

Returns the value of attribute array.



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# File 'lib/rubychem/equation.rb', line 4

def array
  @array
end

#balanced ⇒ Object

Returns the value of attribute balanced.



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# File 'lib/rubychem/equation.rb', line 4

def balanced
  @balanced
end

#left ⇒ Object

Returns the value of attribute left.



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# File 'lib/rubychem/equation.rb', line 4

def left
  @left
end

#left_system_of_equations ⇒ Object

Returns the value of attribute left_system_of_equations.



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# File 'lib/rubychem/equation.rb', line 4

def left_system_of_equations
  @left_system_of_equations
end

#left_total ⇒ Object

Returns the value of attribute left_total.



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# File 'lib/rubychem/equation.rb', line 4

def left_total
  @left_total
end

#right ⇒ Object

Returns the value of attribute right.



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# File 'lib/rubychem/equation.rb', line 4

def right
  @right
end

#right_system_of_equations ⇒ Object

Returns the value of attribute right_system_of_equations.



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# File 'lib/rubychem/equation.rb', line 4

def right_system_of_equations
  @right_system_of_equations
end

#right_total ⇒ Object

Returns the value of attribute right_total.



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# File 'lib/rubychem/equation.rb', line 4

def right_total
  @right_total
end

#search_order ⇒ Object

Returns the value of attribute search_order.



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# File 'lib/rubychem/equation.rb', line 4

def search_order
  @search_order
end

Instance Method Details

#apply_solved_equivalent_fractions_to_fraction ⇒ Object

Now that we have the whole number from solve_equivalent_fractions we must apply that to each of the fractions to solve for the balanced equation



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# File 'lib/rubychem/equation.rb', line 172

def apply_solved_equivalent_fractions_to_fraction
  int = self.solve_equivalent_fractions
  answer = []
  @reduced_row_echelon_form.each do |row|
    answer << row.last * int
  end
  answer << int
  count = 0
  @balanced = Hash.new
  @left_system_of_equations.each do |x,v|
    answer[count]
    @left_system_of_equations[x] = answer[count].to_i.abs unless answer[count].nil?
    count += 1
  end
  @right_system_of_equations.each do |x,v|
    answer[count]
    @right_system_of_equations[x] = answer[count].to_i.abs unless answer[count].nil?
    count += 1
  end
  answer
  @balanced = {left:@left_system_of_equations,right:@right_system_of_equations}
  self.balanced_string
end

#assign_coeficients_to_part_system_of_equations(part, atom_to_search) ⇒ Object 



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# File 'lib/rubychem/equation.rb', line 108

def assign_coeficients_to_part_system_of_equations(part,atom_to_search)
    chemicals =  part.keys
    chemicals.each do |chemical|
      @search_order << chemical
      # look at the Chemical
      chemical.chem_species.each do |atom|
      # Does the chemical have the atom we are looking for?
      if atom_to_search == atom[0] 
        part[chemical] = atom[1]
      end
    end
  end
end

#assign_coeficients_to_system_of_equations ⇒ Object

  1. determnie instances on left and right of each atom, and assign those to coeficients

C12H26 + O2 = CO2 + H2O O = + 1d” O = “2b=2c+1d”



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# File 'lib/rubychem/equation.rb', line 94

def assign_coeficients_to_system_of_equations
  self.list_atoms
  atom_list = self.left_total.merge(self.right_total)
  # Get the Chemical list
  atom_list.keys.each do |atom|

    self.set_up_system_of_equations
    assign_coeficients_to_part_system_of_equations(@right_system_of_equations,atom)
    assign_coeficients_to_part_system_of_equations(@left_system_of_equations,atom)
    subtract_right_side
    write_matrix
  end
end

#balance ⇒ Object 



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# File 'lib/rubychem/equation.rb', line 145

def balance
  @search_order = Array.new
  @array = Array.new
  @reduced_row_echelon_form = Array.new
  self.assign_coeficients_to_system_of_equations
  @reduced_row_echelon_form = self.reduced_row_echelon_form(@array)
  self.apply_solved_equivalent_fractions_to_fraction
end

#balanced_string ⇒ Object 



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# File 'lib/rubychem/equation.rb', line 196

def balanced_string
  array_of_strings = Array.new
  @balanced[:left].each{|x,y|array_of_strings << (x.chem_species.unshift(y).join);x.chem_species.shift}
  left = array_of_strings.join(" + ")
  array_of_strings = []
  @balanced[:right].each{|x,y|array_of_strings << (x.chem_species.unshift(y).join);x.chem_species.shift}
  right = array_of_strings.join(" + ")
  left + " = " + right
end

#convert_to(ary, type) ⇒ Object

type should be one of :to_s, :to_i, :to_f, :to_r



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# File 'lib/rubychem/equation.rb', line 250

def convert_to(ary, type)
  new = []
  ary.each_index do |row|
    new << ary[row].collect {|elem| elem.send(type)}
  end
  new
end

#convert_to_rational(ary) ⇒ Object 



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# File 'lib/rubychem/equation.rb', line 241

def convert_to_rational(ary)
  new = []
  ary.each_index do |row|
    new << ary[row].collect {|elem| Rational(elem)}
  end
  new
end

#instantiate_chemical_object_from_string(equation, side) ⇒ Object 



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# File 'lib/rubychem/equation.rb', line 23

def instantiate_chemical_object_from_string(equation, side)	
 if side == "left"
   equation.split(/\+/).each do |chemical|
     @left << RubyChem::Chemical.new(chemical.strip)     
    end
  else
  	equation.split(/\+/).each do |chemical|
     @right << RubyChem::Chemical.new(chemical.strip)     
    end
  end  
end

#is_balanced? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/rubychem/equation.rb', line 58

def is_balanced?
   @right_total.each_key do |key|
    @balanced = @right_total[key] == @left_total[key]
   end
   @balanced
end

#list_atoms ⇒ Object

add up all atoms, on each side left = Na:1,Cl:2 right = Na:2,Cl:4



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# File 'lib/rubychem/equation.rb', line 39

def list_atoms
  @left_total = Hash.new
  @right_total = Hash.new
  list_part(@left, @left_total)
  list_part(@right, @right_total)
end

#list_part(part, total) ⇒ Object 



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# File 'lib/rubychem/equation.rb', line 46

def list_part(part, total)
  part.each do |chemical|
    chemical.chem_species.each do |atom|
      if total[atom[0]].nil?
        total[atom[0]] = atom[1]
      else
        total[atom[0]] += atom[1]
      end
    end
  end
end

#part_set_up_system_of_equations(part, total) ⇒ Object 



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# File 'lib/rubychem/equation.rb', line 83

def part_set_up_system_of_equations(part,total)
  part.each do |key|
    total[key] = 0
  end
end

#print_matrix(m) ⇒ Object 



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# File 'lib/rubychem/equation.rb', line 258

def print_matrix(m)
  max = m[0].collect {-1}
  m.each {|row| row.each_index {|i| max[i] = [max[i], row[i].to_s.length].max}}
  m.each {|row| row.each_index {|i| print "%#{max[i]}s " % row[i].to_s}; puts ""}
end

#process_equation_string(left_and_right) ⇒ Object 



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# File 'lib/rubychem/equation.rb', line 18

def process_equation_string(left_and_right)
  instantiate_chemical_object_from_string(left_and_right[0], "left")
  instantiate_chemical_object_from_string(left_and_right[1], "right")
end

#reduced_row_echelon_form(ary) ⇒ Object

returns an 2-D array where each element is a Rational



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# File 'lib/rubychem/equation.rb', line 207

def reduced_row_echelon_form(ary)
  lead = 0
  rows = ary.size
  cols = ary[0].size
  rary = convert_to_rational(ary)  # use rational arithmetic
  catch :done  do
    rows.times do |r|
    throw :done  if cols <= lead
      i = r
      while rary[i][lead] == 0
        i += 1
        if rows == i
          i = r
          lead += 1
          throw :done  if cols == lead
        end
      end
      # swap rows i and r 
      rary[i], rary[r] = rary[r], rary[i]
      # normalize row r
      v = rary[r][lead]
      rary[r].collect! {|x| x /= v}
      # reduce other rows
      rows.times do |i|
        next if i == r
        v = rary[i][lead]
        rary[i].each_index {|j| rary[i][j] -= v * rary[r][j]}
      end
      lead += 1
    end
  end
  rary
end

#set_up_system_of_equations ⇒ Object

System of Equations setup

  1. Assign unknown coeficients

C12H26 + O2 = CO2 + H2O aC12H26 + bO2 = cCO2 + dH2O



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# File 'lib/rubychem/equation.rb', line 76

def set_up_system_of_equations
  @right_system_of_equations = Hash.new
  @left_system_of_equations = Hash.new
  part_set_up_system_of_equations(@right,@right_system_of_equations)
  part_set_up_system_of_equations(@left,@left_system_of_equations)
end

#solve_equivalent_fractions ⇒ Object

from the reduced row echelon form we are left with a set of equivalent fractions to transform into a whole number we do this by using the gcdlcm method



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# File 'lib/rubychem/equation.rb', line 158

def solve_equivalent_fractions
  last = 0
  array = Array.new
  @reduced_row_echelon_form.each do |x|
     array = last.gcdlcm(x.last.denominator)
     last = x.last.denominator
  end
  array.max
end

#subtract_right_side ⇒ Object 



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# File 'lib/rubychem/equation.rb', line 122

def subtract_right_side
  self.right_system_of_equations.each do |k,v|
    self.right_system_of_equations[k] = v *= -1
  end
end

#write_matrix ⇒ Object

  1. Rearrange the system of equations and write it in a matrix

a   b   c  d

O 0 2 -2 -1

[0,2,-2,-1] 


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# File 'lib/rubychem/equation.rb', line 133

def write_matrix
  array = Array.new
  @left_system_of_equations.keys.each do |key|
    array << @left_system_of_equations[key]
  end
  @right_system_of_equations.keys.each do |key|
    array  <<  @right_system_of_equations[key]
  end
   @array << array
end