Math.ExpPairs.LinearForm

Provides types for rational forms (to hold objective functions in Math.ExpPairs) and linear contraints (to hold constraints of optimization). Both of them are built atop of projective linear forms.

Documentation

data LinearForm t

Define an affine linear form of two variables: a*k + b*l + c*m. First argument of LinearForm stands for a, second for b and third for c. Linear forms form a monoid by addition.

Constructors

LinearForm t t t

Instances

Eq t => Eq (LinearForm t)

Num t => Num (LinearForm t)

(Num t, Eq t, Show t) => Show (LinearForm t)

Num t => Monoid (LinearForm t)

evalLF :: Num t => (t, t, t) -> LinearForm t -> t

Evaluate a linear form a*k + b*l + c*m for given k, l and m.

substituteLF :: (Eq t, Num t) => (LinearForm t, LinearForm t, LinearForm t) -> LinearForm t -> LinearForm t

Substitute linear forms k, l and m into a given linear form a*k + b*l + c*m to obtain a new linear form.

data RationalForm t

Define a rational form of two variables, equal to the ratio of two LinearForm.

Constructors

RationalForm (LinearForm t) (LinearForm t)

Instances

Num t => Fractional (RationalForm t)

Num t => Num (RationalForm t)

(Eq t, Num t, Show t) => Show (RationalForm t)

evalRF :: (Real t, Num t) => (Integer, Integer, Integer) -> RationalForm t -> RationalInf

Evaluate a rational form (a*k + b*l + c*m) / (a'*k + b'*l + c'*m) for given k, l and m.

data IneqType

Constants to specify the strictness of Constraint.

Constructors

Strict

Strict inequality (>0).

NonStrict

Non-strict inequality (≥0).

Instances

Eq IneqType

Show IneqType

data Constraint t

A linear constraint of two variables.

Constructors

Constraint (LinearForm t) IneqType

Instances

(Eq t, Num t, Show t) => Show (Constraint t)

checkConstraint :: (Num t, Eq t) => (Integer, Integer, Integer) -> Constraint t -> Bool

Evaluate a rational form of constraint and compare its value with 0. Strictness depends on the given IneqType.