NumHask.Data.Range

An Space with no empty, a semigroup based on a convex hull union, and a monoid on a negative space.

Documentation

newtype Range a

A continuous range over type a

>>> let a = Range (-1) 1
>>> a
Range -1 1
>>> fmap (+1) (Range 1 2)
Range 2 3
>>> one :: Range Double
Range -0.5 0.5
>>> zero :: Range Double
Range Infinity -Infinity

as a Field instance

>>> Range 0 1 + zero
Range 0.0 1.0
>>> Range 0 1 + Range 2 3
Range 0.0 3.0
>>> Range 1 1 - one
Range 0.5 1.0
>>> Range 0 1 * one
Range 0.0 1.0
>>> Range 0 1 / one
Range 0.0 1.0
>>> abs (Range 1 0)
Range 0.0 1.0
>>> sign (Range 1 0) == negate one
True

Idempotent

>>> Range 0 2 + Range 0 2
Range 0.0 2.0

as a space instance

>>> NumHask.Space.project (Range 0 1) (Range 1 4) 0.5
2.5
>>> NumHask.Space.grid NumHask.Space.OuterPos (Range 0 10) 5
[0.0,2.0,4.0,6.0,8.0,10.0]
>>> NumHask.Space.gridSpace (Range 0 1) 4
[Range 0.0 0.25,Range 0.25 0.5,Range 0.5 0.75,Range 0.75 1.0]
>>> gridSensible NumHask.Space.OuterPos (Range (-12.0) 23.0) 6
[-10.0,-5.0,0.0,5.0,10.0,15.0,20.0]

Constructors

Range' (a, a)

Instances

Functor Range

Defined in NumHask.Data.Range

Methods

fmap :: (a -> b) -> Range a -> Range b

(<$) :: a -> Range b -> Range a

Applicative Range

Defined in NumHask.Data.Range

Methods

pure :: a -> Range a

(<*>) :: Range (a -> b) -> Range a -> Range b

liftA2 :: (a -> b -> c) -> Range a -> Range b -> Range c

(*>) :: Range a -> Range b -> Range b

(<*) :: Range a -> Range b -> Range a

Foldable Range

Defined in NumHask.Data.Range

Methods

fold :: Monoid m => Range m -> m

foldMap :: Monoid m => (a -> m) -> Range a -> m

foldr :: (a -> b -> b) -> b -> Range a -> b

foldr' :: (a -> b -> b) -> b -> Range a -> b

foldl :: (b -> a -> b) -> b -> Range a -> b

foldl' :: (b -> a -> b) -> b -> Range a -> b

foldr1 :: (a -> a -> a) -> Range a -> a

foldl1 :: (a -> a -> a) -> Range a -> a

toList :: Range a -> [a]

null :: Range a -> Bool

length :: Range a -> Int

elem :: Eq a => a -> Range a -> Bool

maximum :: Ord a => Range a -> a

minimum :: Ord a => Range a -> a

sum :: Num a => Range a -> a

product :: Num a => Range a -> a

Traversable Range

Defined in NumHask.Data.Range

Methods

traverse :: Applicative f => (a -> f b) -> Range a -> f (Range b)

sequenceA :: Applicative f => Range (f a) -> f (Range a)

mapM :: Monad m => (a -> m b) -> Range a -> m (Range b)

sequence :: Monad m => Range (m a) -> m (Range a)

Distributive Range

Defined in NumHask.Data.Range

Methods

distribute :: Functor f => f (Range a) -> Range (f a)

collect :: Functor f => (a -> Range b) -> f a -> Range (f b)

distributeM :: Monad m => m (Range a) -> Range (m a)

collectM :: Monad m => (a -> Range b) -> m a -> Range (m b)

Representable Range

Defined in NumHask.Data.Range

Associated Types

type Rep Range :: Type

Methods

tabulate :: (Rep Range -> a) -> Range a

index :: Range a -> Rep Range -> a

Eq1 Range

Defined in NumHask.Data.Range

Methods

liftEq :: (a -> b -> Bool) -> Range a -> Range b -> Bool

Show1 Range

Defined in NumHask.Data.Range

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Range a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Range a] -> ShowS

Traversable1 Range

Defined in NumHask.Data.Range

Methods

traverse1 :: Apply f => (a -> f b) -> Range a -> f (Range b)

sequence1 :: Apply f => Range (f b) -> f (Range b)

Foldable1 Range

Defined in NumHask.Data.Range

Methods

fold1 :: Semigroup m => Range m -> m

foldMap1 :: Semigroup m => (a -> m) -> Range a -> m

toNonEmpty :: Range a -> NonEmpty a

Apply Range

Defined in NumHask.Data.Range

Methods

(<.>) :: Range (a -> b) -> Range a -> Range b

(.>) :: Range a -> Range b -> Range b

(<.) :: Range a -> Range b -> Range a

liftF2 :: (a -> b -> c) -> Range a -> Range b -> Range c

Eq a => Eq (Range a)

Defined in NumHask.Data.Range

Methods

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

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

Show a => Show (Range a)

Defined in NumHask.Data.Range

Methods

showsPrec :: Int -> Range a -> ShowS

show :: Range a -> String

showList :: [Range a] -> ShowS

Generic (Range a)

Defined in NumHask.Data.Range

Associated Types

type Rep (Range a) :: Type -> Type

Methods

from :: Range a -> Rep (Range a) x

to :: Rep (Range a) x -> Range a

BoundedLattice a => Semigroup (Range a)

Monoid based on convex hull union

Defined in NumHask.Data.Range

Methods

(<>) :: Range a -> Range a -> Range a

sconcat :: NonEmpty (Range a) -> Range a

stimes :: Integral b => b -> Range a -> Range a

BoundedLattice a => Monoid (Range a)

Defined in NumHask.Data.Range

Methods

mempty :: Range a

mappend :: Range a -> Range a -> Range a

mconcat :: [Range a] -> Range a

(Multiplicative a, Subtractive a, Lattice a) => Signed (Range a)

Defined in NumHask.Data.Range

Methods

sign :: Range a -> Range a

abs :: Range a -> Range a

JoinSemiLattice a => JoinSemiLattice (Range a)

Defined in NumHask.Data.Range

Methods

(\/) :: Range a -> Range a -> Range a

MeetSemiLattice a => MeetSemiLattice (Range a)

Defined in NumHask.Data.Range

Methods

(/\) :: Range a -> Range a -> Range a

BoundedLattice a => BoundedJoinSemiLattice (Range a)

Defined in NumHask.Data.Range

Methods

bottom :: Range a

BoundedLattice a => BoundedMeetSemiLattice (Range a)

Defined in NumHask.Data.Range

Methods

top :: Range a

(FromInteger a, Lattice a) => FromInteger (Range a)

Defined in NumHask.Data.Range

Methods

fromInteger :: Integer -> Range a

Additive a => AdditiveAction (Range a)

Defined in NumHask.Data.Range

Methods

(.+) :: Range a -> Actor (Range a) -> Range a

(+.) :: Actor (Range a) -> Range a -> Range a

Subtractive a => SubtractiveAction (Range a)

Defined in NumHask.Data.Range

Methods

(.-) :: Range a -> Actor (Range a) -> Range a

(-.) :: Actor (Range a) -> Range a -> Range a

Multiplicative a => MultiplicativeAction (Range a)

Defined in NumHask.Data.Range

Methods

(.*) :: Range a -> Actor (Range a) -> Range a

(*.) :: Actor (Range a) -> Range a -> Range a

Divisive a => DivisiveAction (Range a)

Defined in NumHask.Data.Range

Methods

(./) :: Range a -> Actor (Range a) -> Range a

(/.) :: Actor (Range a) -> Range a -> Range a

(Multiplicative a, Lattice a) => Multiplicative (Range a)

Defined in NumHask.Data.Range

Methods

(*) :: Range a -> Range a -> Range a

one :: Range a

(BoundedLattice a, Epsilon a, Divisive a) => Divisive (Range a)

Defined in NumHask.Data.Range

Methods

recip :: Range a -> Range a

(/) :: Range a -> Range a -> Range a

(Additive a, Lattice a) => Additive (Range a)

Numeric algebra based on Interval arithmetic https://en.wikipedia.org/wiki/Interval_arithmetic

Defined in NumHask.Data.Range

Methods

(+) :: Range a -> Range a -> Range a

zero :: Range a

(Subtractive a, Lattice a) => Subtractive (Range a)

Defined in NumHask.Data.Range

Methods

negate :: Range a -> Range a

(-) :: Range a -> Range a -> Range a

(Lattice a, Field a, Subtractive a, FromInteger a) => FieldSpace (Range a)

Defined in NumHask.Data.Range

Associated Types

type Grid (Range a) :: Type

Methods

grid :: Pos -> Range a -> Grid (Range a) -> [Element (Range a)]

gridSpace :: Range a -> Grid (Range a) -> [Range a]

Lattice a => Space (Range a)

Defined in NumHask.Data.Range

Associated Types

type Element (Range a) :: Type

Methods

lower :: Range a -> Element (Range a)

upper :: Range a -> Element (Range a)

singleton :: Element (Range a) -> Range a

intersection :: Range a -> Range a -> Range a

union :: Range a -> Range a -> Range a

norm :: Range a -> Range a

(...) :: Element (Range a) -> Element (Range a) -> Range a

(>.<) :: Element (Range a) -> Element (Range a) -> Range a

type Rep Range

Defined in NumHask.Data.Range

type Rep Range = Bool

type Rep (Range a)

Defined in NumHask.Data.Range

type Rep (Range a) = D1 (MetaData "Range" "NumHask.Data.Range" "numhask-space-0.1.1-KhD7xYpwLfOGsUJAt0HVyO" True) (C1 (MetaCons "Range'" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (a, a))))

type Actor (Range a)

Defined in NumHask.Data.Range

type Actor (Range a) = a

type Grid (Range a)

Defined in NumHask.Data.Range

type Grid (Range a) = Int

type Element (Range a)

Defined in NumHask.Data.Range

type Element (Range a) = a

pattern Range :: a -> a -> Range a

A tuple is the preferred concrete implementation of a Range, due to many libraries having substantial optimizations for tuples already (eg Vector). 'Pattern Synonyms' allow us to recover a constructor without the need for tuple syntax.

gridSensible :: (Ord a, JoinSemiLattice a, FromInteger a, FromRatio a, QuotientField a Integer, ExpField a, Epsilon a) => Pos -> Bool -> Range a -> Integer -> [a]