Linear.Simplex.Types

Documentation

type Var = Int

type SimplexNum = Rational

type SystemRow = PolyConstraint

type System = [SystemRow]

data SystemWithSlackVarRow

Constructors

SystemInStandardFormRow

Fields

• mSlackVar :: Maybe Var

  This is Nothing iff the row does not have a slack variable

• row :: TableauRow

type SystemWithSlackVars = [SystemWithSlackVarRow]

data FeasibleSystem

Constructors

FeasibleSystem

Fields

• dict :: Dict
• slackVars :: [Var]
• artificialVars :: [Var]
• objectiveVar :: Var

Instances

Generic FeasibleSystem

Defined in Linear.Simplex.Types

Associated Types

type Rep FeasibleSystem :: Type -> Type

Methods

from :: FeasibleSystem -> Rep FeasibleSystem x

to :: Rep FeasibleSystem x -> FeasibleSystem

Read FeasibleSystem

Defined in Linear.Simplex.Types

Methods

readsPrec :: Int -> ReadS FeasibleSystem

readList :: ReadS [FeasibleSystem]

readPrec :: ReadPrec FeasibleSystem

readListPrec :: ReadPrec [FeasibleSystem]

Show FeasibleSystem

Defined in Linear.Simplex.Types

Methods

showsPrec :: Int -> FeasibleSystem -> ShowS

show :: FeasibleSystem -> String

showList :: [FeasibleSystem] -> ShowS

Eq FeasibleSystem

Defined in Linear.Simplex.Types

Methods

(==) :: FeasibleSystem -> FeasibleSystem -> Bool

(/=) :: FeasibleSystem -> FeasibleSystem -> Bool

type Rep FeasibleSystem

Defined in Linear.Simplex.Types

type Rep FeasibleSystem = D1 ('MetaData "FeasibleSystem" "Linear.Simplex.Types" "simplex-method-0.2.0.0-DL5Tbu7QSIMBYoeQDIkkgN" 'False) (C1 ('MetaCons "FeasibleSystem" 'PrefixI 'True) ((S1 ('MetaSel ('Just "dict") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Dict) :*: S1 ('MetaSel ('Just "slackVars") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 [Var])) :*: (S1 ('MetaSel ('Just "artificialVars") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 [Var]) :*: S1 ('MetaSel ('Just "objectiveVar") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Var))))

data Result

Constructors

Result

Fields

• objectiveVar :: Var
• varValMap :: VarLitMap

Instances

Generic Result

Defined in Linear.Simplex.Types

Associated Types

type Rep Result :: Type -> Type

Methods

from :: Result -> Rep Result x

to :: Rep Result x -> Result

Read Result

Defined in Linear.Simplex.Types

Methods

readsPrec :: Int -> ReadS Result

readList :: ReadS [Result]

readPrec :: ReadPrec Result

readListPrec :: ReadPrec [Result]

Show Result

Defined in Linear.Simplex.Types

Methods

showsPrec :: Int -> Result -> ShowS

show :: Result -> String

showList :: [Result] -> ShowS

Eq Result

Defined in Linear.Simplex.Types

Methods

(==) :: Result -> Result -> Bool

(/=) :: Result -> Result -> Bool

type Rep Result

Defined in Linear.Simplex.Types

type Rep Result = D1 ('MetaData "Result" "Linear.Simplex.Types" "simplex-method-0.2.0.0-DL5Tbu7QSIMBYoeQDIkkgN" 'False) (C1 ('MetaCons "Result" 'PrefixI 'True) (S1 ('MetaSel ('Just "objectiveVar") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Var) :*: S1 ('MetaSel ('Just "varValMap") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 VarLitMap)))

data SimplexMeta

Constructors

SimplexMeta

Fields

• objective :: ObjectiveFunction
• feasibleSystem :: Maybe FeasibleSystem
• optimisedResult :: Maybe Result

type VarLitMap = Map Var SimplexNum

type VarLitMapSum = VarLitMap

List of variables with their SimplexNum coefficients. There is an implicit addition between elements in this list.

Example: [Var "x" 3, Var "y" -1, Var "z" 1] is equivalent to 3x + (-y) + z.

data PolyConstraint

For specifying constraints in a system. The LHS is a Vars, and the RHS, is a SimplexNum number. LEQ [(1, 2), (2, 1)] 3.5 is equivalent to 2x1 + x2 <= 3.5. Users must only provide positive integer variables.

Example: LEQ [Var "x" 3, Var "y" -1, Var "x" 1] 12.3 is equivalent to 3x + (-y) + x <= 12.3.

Constructors

LEQ

Fields

• lhs :: VarLitMapSum
• rhs :: SimplexNum

GEQ

Fields

• lhs :: VarLitMapSum
• rhs :: SimplexNum

EQ

Fields

• lhs :: VarLitMapSum
• rhs :: SimplexNum

Instances

Generic PolyConstraint

Defined in Linear.Simplex.Types

Associated Types

type Rep PolyConstraint :: Type -> Type

Methods

from :: PolyConstraint -> Rep PolyConstraint x

to :: Rep PolyConstraint x -> PolyConstraint

Read PolyConstraint

Defined in Linear.Simplex.Types

Methods

readsPrec :: Int -> ReadS PolyConstraint

readList :: ReadS [PolyConstraint]

readPrec :: ReadPrec PolyConstraint

readListPrec :: ReadPrec [PolyConstraint]

Show PolyConstraint

Defined in Linear.Simplex.Types

Methods

showsPrec :: Int -> PolyConstraint -> ShowS

show :: PolyConstraint -> String

showList :: [PolyConstraint] -> ShowS

Eq PolyConstraint

Defined in Linear.Simplex.Types

Methods

(==) :: PolyConstraint -> PolyConstraint -> Bool

(/=) :: PolyConstraint -> PolyConstraint -> Bool

type Rep PolyConstraint

Defined in Linear.Simplex.Types

type Rep PolyConstraint = D1 ('MetaData "PolyConstraint" "Linear.Simplex.Types" "simplex-method-0.2.0.0-DL5Tbu7QSIMBYoeQDIkkgN" 'False) (C1 ('MetaCons "LEQ" 'PrefixI 'True) (S1 ('MetaSel ('Just "lhs") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 VarLitMapSum) :*: S1 ('MetaSel ('Just "rhs") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 SimplexNum)) :+: (C1 ('MetaCons "GEQ" 'PrefixI 'True) (S1 ('MetaSel ('Just "lhs") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 VarLitMapSum) :*: S1 ('MetaSel ('Just "rhs") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 SimplexNum)) :+: C1 ('MetaCons "EQ" 'PrefixI 'True) (S1 ('MetaSel ('Just "lhs") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 VarLitMapSum) :*: S1 ('MetaSel ('Just "rhs") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 SimplexNum))))

data ObjectiveFunction

Create an objective function. We can either Maximize or Minimize a VarTermSum.

Constructors

Max

Fields

• objective :: VarLitMapSum

Min

Fields

• objective :: VarLitMapSum

Instances

Generic ObjectiveFunction

Defined in Linear.Simplex.Types

Associated Types

type Rep ObjectiveFunction :: Type -> Type

Methods

from :: ObjectiveFunction -> Rep ObjectiveFunction x

to :: Rep ObjectiveFunction x -> ObjectiveFunction

Read ObjectiveFunction

Defined in Linear.Simplex.Types

Methods

readsPrec :: Int -> ReadS ObjectiveFunction

readList :: ReadS [ObjectiveFunction]

readPrec :: ReadPrec ObjectiveFunction

readListPrec :: ReadPrec [ObjectiveFunction]

Show ObjectiveFunction

Defined in Linear.Simplex.Types

Methods

showsPrec :: Int -> ObjectiveFunction -> ShowS

show :: ObjectiveFunction -> String

showList :: [ObjectiveFunction] -> ShowS

Eq ObjectiveFunction

Defined in Linear.Simplex.Types

Methods

(==) :: ObjectiveFunction -> ObjectiveFunction -> Bool

(/=) :: ObjectiveFunction -> ObjectiveFunction -> Bool

type Rep ObjectiveFunction

Defined in Linear.Simplex.Types

type Rep ObjectiveFunction = D1 ('MetaData "ObjectiveFunction" "Linear.Simplex.Types" "simplex-method-0.2.0.0-DL5Tbu7QSIMBYoeQDIkkgN" 'False) (C1 ('MetaCons "Max" 'PrefixI 'True) (S1 ('MetaSel ('Just "objective") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 VarLitMapSum)) :+: C1 ('MetaCons "Min" 'PrefixI 'True) (S1 ('MetaSel ('Just "objective") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 VarLitMapSum)))

data Equation

TODO: Maybe we want this type TODO: A better/alternative name

Constructors

Equation

Fields

• lhs :: VarLitMapSum
• rhs :: SimplexNum

data TableauRow

Value for Tableau. lhs = rhs.

Constructors

TableauRow

Fields

• lhs :: VarLitMapSum
• rhs :: SimplexNum

Instances

Generic TableauRow

Defined in Linear.Simplex.Types

Associated Types

type Rep TableauRow :: Type -> Type

Methods

from :: TableauRow -> Rep TableauRow x

to :: Rep TableauRow x -> TableauRow

Read TableauRow

Defined in Linear.Simplex.Types

Methods

readsPrec :: Int -> ReadS TableauRow

readList :: ReadS [TableauRow]

readPrec :: ReadPrec TableauRow

readListPrec :: ReadPrec [TableauRow]

Show TableauRow

Defined in Linear.Simplex.Types

Methods

showsPrec :: Int -> TableauRow -> ShowS

show :: TableauRow -> String

showList :: [TableauRow] -> ShowS

Eq TableauRow

Defined in Linear.Simplex.Types

Methods

(==) :: TableauRow -> TableauRow -> Bool

(/=) :: TableauRow -> TableauRow -> Bool

type Rep TableauRow

Defined in Linear.Simplex.Types

type Rep TableauRow = D1 ('MetaData "TableauRow" "Linear.Simplex.Types" "simplex-method-0.2.0.0-DL5Tbu7QSIMBYoeQDIkkgN" 'False) (C1 ('MetaCons "TableauRow" 'PrefixI 'True) (S1 ('MetaSel ('Just "lhs") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 VarLitMapSum) :*: S1 ('MetaSel ('Just "rhs") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 SimplexNum)))

type Tableau = Map Var TableauRow

A simplex Tableu of equations. Each entry in the map is a row.

data DictValue

Values for a Dict.

Constructors

DictValue

Fields

• varMapSum :: VarLitMapSum
• constant :: SimplexNum

Instances

Generic DictValue

Defined in Linear.Simplex.Types

Associated Types

type Rep DictValue :: Type -> Type

Methods

from :: DictValue -> Rep DictValue x

to :: Rep DictValue x -> DictValue

Read DictValue

Defined in Linear.Simplex.Types

Methods

readsPrec :: Int -> ReadS DictValue

readList :: ReadS [DictValue]

readPrec :: ReadPrec DictValue

readListPrec :: ReadPrec [DictValue]

Show DictValue

Defined in Linear.Simplex.Types

Methods

showsPrec :: Int -> DictValue -> ShowS

show :: DictValue -> String

showList :: [DictValue] -> ShowS

Eq DictValue

Defined in Linear.Simplex.Types

Methods

(==) :: DictValue -> DictValue -> Bool

(/=) :: DictValue -> DictValue -> Bool

type Rep DictValue

Defined in Linear.Simplex.Types

type Rep DictValue = D1 ('MetaData "DictValue" "Linear.Simplex.Types" "simplex-method-0.2.0.0-DL5Tbu7QSIMBYoeQDIkkgN" 'False) (C1 ('MetaCons "DictValue" 'PrefixI 'True) (S1 ('MetaSel ('Just "varMapSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 VarLitMapSum) :*: S1 ('MetaSel ('Just "constant") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 SimplexNum)))

type Dict = Map Var DictValue

A simplex Dict One quation represents the objective function. Each pair in the list is one equation in the system we're working with. data Dict = Dict { objective :: DictObjective , entries :: DictEntries } deriving (Show, Read, Eq, Generic)

data PivotObjective

Constructors

PivotObjective

Fields

• variable :: Var
• function :: VarLitMapSum
• constant :: SimplexNum

Instances

Generic PivotObjective

Defined in Linear.Simplex.Types

Associated Types

type Rep PivotObjective :: Type -> Type

Methods

from :: PivotObjective -> Rep PivotObjective x

to :: Rep PivotObjective x -> PivotObjective

Read PivotObjective

Defined in Linear.Simplex.Types

Methods

readsPrec :: Int -> ReadS PivotObjective

readList :: ReadS [PivotObjective]

readPrec :: ReadPrec PivotObjective

readListPrec :: ReadPrec [PivotObjective]

Show PivotObjective

Defined in Linear.Simplex.Types

Methods

showsPrec :: Int -> PivotObjective -> ShowS

show :: PivotObjective -> String

showList :: [PivotObjective] -> ShowS

Eq PivotObjective

Defined in Linear.Simplex.Types

Methods

(==) :: PivotObjective -> PivotObjective -> Bool

(/=) :: PivotObjective -> PivotObjective -> Bool

type Rep PivotObjective

Defined in Linear.Simplex.Types

type Rep PivotObjective = D1 ('MetaData "PivotObjective" "Linear.Simplex.Types" "simplex-method-0.2.0.0-DL5Tbu7QSIMBYoeQDIkkgN" 'False) (C1 ('MetaCons "PivotObjective" 'PrefixI 'True) (S1 ('MetaSel ('Just "variable") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Var) :*: (S1 ('MetaSel ('Just "function") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 VarLitMapSum) :*: S1 ('MetaSel ('Just "constant") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 SimplexNum))))