SubHask.Algebra.Metric

This module defines the algebra over various types of balls in metric spaces

Documentation

printTriDistances :: (Show (Scalar m), Metric m) => m -> m -> m -> IO ()

Useful for identifying tree metrics.

printQuadDistances :: (Ord (Scalar t), Show (Scalar t), Metric t) => t -> t -> t -> t -> IO ()

There are three distinct perfect matchings in every complete 4 node graph. A metric is a tree metric iff two of these perfect matchings have the same weight. This is called the 4 points condition. printQuadDistances :: (Ord (Scalar m), Show (Scalar m), Metric m) => m -> m -> m -> m -> IO ()

data Ball v

The closed balls in metric space. Note that since we are not assuming any special structure, addition is rather inefficient.

FIXME: There are several valid ways to perform the addition; which should we use? We could add Lattice instances in a similar way as we could with Box if we added an empty element; should we do this?

Constructors

Ball

Fields

radius :: !(Scalar v)

center :: !v

Instances

(Read v, Read (Scalar v)) => Read (Ball v)

(Show v, Show (Scalar v)) => Show (Ball v)

(Arbitrary v, Arbitrary (Scalar v), HasScalar v) => Arbitrary (Ball v)

(NFData v, NFData (Scalar v)) => NFData (Ball v)

IsMutable (Ball b)

(Metric v, HasScalar v, ClassicalLogic v) => Container (Ball v)

(Metric v, HasScalar v, ClassicalLogic v) => Constructible (Ball v)

(Metric v, HasScalar v, ClassicalLogic v) => Semigroup (Ball v)

(Eq v, HasScalar v) => Eq_ (Ball v)

data Mutable m (Ball b0) = Mutable_AppT__ConT_SubHask_Algebra_Metric_Ball___VarT_b_1627650421_ (PrimRef m (Ball b))

type Elem (Ball v) = v

type Scalar (Ball v) = Scalar v

type Logic (Ball v) = Logic v

type SetElem (Ball v) v' = Ball v'

invar_Ball_radius :: HasScalar v => Ball v -> Logic (Scalar v)

newtype BanachBall v

FIXME: In a Banach space we can make Ball addition more efficient by moving the center to an optimal location.

Constructors

BanachBall (Ball v)