{-|
Module      : Linear.Simplex.Types
Description : Custom types
Copyright   : (c) Junaid Rasheed, 2020-2022
License     : BSD-3
Maintainer  : jrasheed178@gmail.com
Stability   : experimental
-}
module Linear.Simplex.Types where

-- |List of 'Integer' variables with their 'Rational' coefficients.
-- There is an implicit addition between elements in this list.
-- Users must only provide positive integer variables.
-- 
-- Example: [(2, 3), (6, (-1), (2, 1))] is equivalent to 3x2 + (-x6) + x2.  
type VarConstMap = [(Integer, Rational)]

-- |For specifying constraints in a system.
-- The LHS is a 'VarConstMap', and the RHS, is a 'Rational' number.
-- LEQ [(1, 2), (2, 1)] 3.5 is equivalent to 2x1 + x2 <= 3.5.
-- Users must only provide positive integer variables.
-- 
-- Example: LEQ [(2, 3), (6, (-1), (2, 1))] 12.3 is equivalent to 3x2 + (-x6) + x2 <= 12.3.
data PolyConstraint =
  LEQ VarConstMap Rational      | 
  GEQ VarConstMap Rational      | 
  EQ VarConstMap Rational       deriving (Show, Eq);

-- |Create an objective function.
-- We can either 'Max'imize or 'Min'imize a 'VarConstMap'.
data ObjectiveFunction = Max VarConstMap | Min VarConstMap deriving (Show, Eq)

-- |A 'Tableau' of equations.
-- Each pair in the list is a row. 
-- The first item in the pair specifies which 'Integer' variable is basic in the equation.
-- The second item in the pair is an equation.
-- The 'VarConstMap' in the second equation is a list of variables with their coefficients.
-- The RHS of the equation is a 'Rational' constant.
type Tableau = [(Integer, (VarConstMap, Rational))]

-- |Type representing equations. 
-- Each pair in the list is one equation.
-- The first item of the pair is the basic variable, and is on the LHS of the equation with a coefficient of one.
-- The RHS is represented using a `VarConstMap`.
-- The integer variable -1 is used to represent a 'Rational' on the RHS
type DictionaryForm = [(Integer, VarConstMap)]