-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Very basic simplex implementation.
--   
--   Very basic simplex implementation.
@package simplex-basic
@version 0.0.0.1

module Linear.Simplex.Primal.Types
type Objective = IneqSlack

-- | Standard-form inequality populated with arbitrary slack variables.
data IneqSlack
[IneqSlack] :: IneqStdForm -> [LinVar] -> IneqSlack
[slackIneq] :: IneqSlack -> IneqStdForm
[slackVars] :: IneqSlack -> [LinVar]
instance Eq IneqSlack
instance Show IneqSlack
instance Arbitrary IneqSlack

module Linear.Simplex.Primal

-- | Takes an objective function, a set of constraints, and an operation
--   mode, then returns a substitution. . Objective function should be in
--   the form of <tt>Ax + By + Cz + P = 0</tt>, where <tt>P</tt> is the
--   resule, and free in the constraint set.
simplexPrimal :: IneqStdForm -> [IneqStdForm] -> [(String, Rational)]

-- | Finds next pivot row by the smallest ratio in each row. Note: row list
--   should be non-empty
nextRow :: [IneqSlack] -> Int -> Maybe Int

-- | finds next column index from objective function
nextColumn :: IneqSlack -> Maybe Int

-- | Computes coefficient ratio to constant, based on a column index.
--   Warning: <tt>Int</tt> parameter must be less than the length of the
--   primal variables.
coeffRatio :: IneqSlack -> Int -> Maybe Rational

-- | flattens targeted row to form the identity at it's column coefficient,
--   then reduces each non-zero row at this column, via a multiple of this
--   flattened row. Heart of the simplex method. Also prepends
--   <tt>objective</tt> back on <tt>constrs</tt>.
pivot :: (Int, Int) -> Objective -> [IneqSlack] -> [IneqSlack]

-- | <a>Flattens</a> a row for further processing.
flatten :: IneqSlack -> Int -> IneqSlack

-- | Takes the focal row, the row to affect, and the column in question to
--   facilitate the sum-oriented part of the pivot.
compensate :: IneqSlack -> IneqSlack -> Int -> IneqSlack

-- | Note: Must have identical occurrances of variables, and must be
--   <tt>EquStd</tt>. subtracts rhs from lhs.
diffZip :: IneqSlack -> IneqSlack -> IneqSlack

-- | Extracts resulting data from tableau, excluding junk data
getSubst :: [IneqSlack] -> [(String, Rational)]

-- | Also translates <tt>Ax &gt;= Q</tt> to <tt>-Ax &lt;= -Q</tt>. Ie;
--   result will <b>exclude</b> <tt>GteStd</tt>.
makeSlackVars :: MonadState Integer m => IneqStdForm -> m IneqSlack

-- | Fills missing variables. List of inequalities includes objective
--   function.
populate :: [IneqSlack] -> [IneqSlack]