Geometry.VertexEnum

Enumeration of the vertices of a convex polytope given by linear inequalities. See README for an example.

Documentation

data Constraint a

Constructors

Constraint (LinearCombination a) Sense (LinearCombination a)

Instances

Show a => Show (Constraint a)

Defined in Geometry.VertexEnum.Constraint

Methods

showsPrec :: Int -> Constraint a -> ShowS

show :: Constraint a -> String

showList :: [Constraint a] -> ShowS

type Var a = LinearCombination a

data Sense

Constructors

Gt

Lt

Instances

Show Sense

Defined in Geometry.VertexEnum.Constraint

Methods

showsPrec :: Int -> Sense -> ShowS

show :: Sense -> String

showList :: [Sense] -> ShowS

Eq Sense

Defined in Geometry.VertexEnum.Constraint

Methods

(==) :: Sense -> Sense -> Bool

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

newtype LinearCombination a

Constructors

LinearCombination (IntMap a)

Instances

Show a => Show (LinearCombination a)

Defined in Geometry.VertexEnum.LinearCombination

Methods

showsPrec :: Int -> LinearCombination a -> ShowS

show :: LinearCombination a -> String

showList :: [LinearCombination a] -> ShowS

Eq a => Eq (LinearCombination a)

Defined in Geometry.VertexEnum.LinearCombination

Methods

(==) :: LinearCombination a -> LinearCombination a -> Bool

(/=) :: LinearCombination a -> LinearCombination a -> Bool

Num a => AdditiveGroup (LinearCombination a)

Defined in Geometry.VertexEnum.LinearCombination

Methods

zeroV :: LinearCombination a

(^+^) :: LinearCombination a -> LinearCombination a -> LinearCombination a

negateV :: LinearCombination a -> LinearCombination a

(^-^) :: LinearCombination a -> LinearCombination a -> LinearCombination a

Num a => VectorSpace (LinearCombination a)

Defined in Geometry.VertexEnum.LinearCombination

Associated Types

type Scalar (LinearCombination a)

Methods

(*^) :: Scalar (LinearCombination a) -> LinearCombination a -> LinearCombination a

type Scalar (LinearCombination a)

Defined in Geometry.VertexEnum.LinearCombination

type Scalar (LinearCombination a) = a

type VarIndex = Int

newVar :: Num a => VarIndex -> Var a

new variable

(.>=.) :: LinearCombination a -> LinearCombination a -> Constraint a infix 4

(.<=.) :: LinearCombination a -> LinearCombination a -> Constraint a infix 4

(.>=) :: LinearCombination a -> a -> Constraint a infix 4

(.<=) :: LinearCombination a -> a -> Constraint a infix 4

linearCombination :: Num a => [(a, Var a)] -> LinearCombination a

linear combination from list of terms

constant :: a -> LinearCombination a

constant linear combination

cst :: a -> LinearCombination a

alias for constant

vertexenum

Arguments

:: Real a

=> [Constraint a]

linear inequalities

-> Maybe [Double]

point satisfying the inequalities, Nothing for automatic point

-> IO [[Double]]

vertices of the polytope defined by the inequalities

Vertex enumeration

checkConstraints

Arguments

:: Real a

=> [Constraint a]

linear inequalities

-> [Double]

point to be tested

-> [(Double, Bool)]

difference and status for each constraint

Checks whether a point fulfills some inequalities; returns the difference between the upper member and the lower member for each inequality, which is positive in case if the inequality is fulfilled.

interiorPoint

Arguments

:: Real a

=> [Constraint a]

linear inequalities

-> IO [Double]

point fulfilling the inequaities

Returns a point fulfilling a list of inequalities