NumHask.Range

representation of a continuous range of a type

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
>>> P.singleton 2.3 :: Range Double
Range 2.3 2.3
>>> 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

>>> project (Range 0 1) (Range 1 4) 0.5
2.5
>>> grid OuterPos (Range 0 10) 5
[0.0,2.0,4.0,6.0,8.0,10.0]
>>> 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 OuterPos (Range (-12) 23) 6
[-10.0,-5.0,0.0,5.0,10.0,15.0,20.0]

Constructors

Range' (a, a)

Instances

Monad Range

Methods

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

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

return :: a -> Range a

fail :: String -> Range a

Functor Range

Methods

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

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

Applicative 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

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

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

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

Associated Types

type Rep (Range :: * -> *) :: *

Methods

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

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

Eq1 Range

Methods

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

Show1 Range

Methods

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

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

Singleton Range

Methods

singleton :: a -> Range a

Traversable1 Range

Methods

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

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

Foldable1 Range

Methods

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

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

toNonEmpty :: Range a -> NonEmpty a

Apply 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

Additive a => AdditiveModule Range a

Methods

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

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

AdditiveGroup a => AdditiveGroupModule Range a

Methods

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

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

Multiplicative a => MultiplicativeModule Range a

Methods

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

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

MultiplicativeGroup a => MultiplicativeGroupModule Range a

Methods

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

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

Additive a => AdditiveBasis Range a

Methods

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

AdditiveGroup a => AdditiveGroupBasis Range a

Methods

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

Multiplicative a => MultiplicativeBasis Range a

Methods

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

MultiplicativeGroup a => MultiplicativeGroupBasis Range a

Methods

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

Eq a => Eq (Range a)

Methods

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

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

(Ord a, BoundedField a, FromInteger a) => Ord (Range a)

Methods

compare :: Range a -> Range a -> Ordering

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

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

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

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

max :: Range a -> Range a -> Range a

min :: Range a -> Range a -> Range a

Show a => Show (Range a)

Methods

showsPrec :: Int -> Range a -> ShowS

show :: Range a -> String

showList :: [Range a] -> ShowS

Generic (Range a)

Associated Types

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

Methods

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

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

(Ord a, BoundedField a, FromInteger a) => Semigroup (Range a)

Methods

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

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

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

(Ord a, BoundedField a, FromInteger a) => Monoid (Range a)

Methods

mempty :: Range a

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

mconcat :: [Range a] -> Range a

Arbitrary a => Arbitrary (Range a)

Methods

arbitrary :: Gen (Range a)

shrink :: Range a -> [Range a]

NFData a => NFData (Range a)

Methods

rnf :: Range a -> ()

(FromInteger a, AdditiveInvertible a, BoundedField a, Ord a) => Signed (Range a)

Methods

sign :: Range a -> Range a

abs :: Range a -> Range a

(BoundedField a, Ord a, Epsilon a) => Epsilon (Range a)

Methods

nearZero :: Range a -> Bool

aboutEqual :: Range a -> Range a -> Bool

positive :: Range a -> Bool

veryPositive :: Range a -> Bool

veryNegative :: Range a -> Bool

(FromInteger a, Ord a, BoundedField a) => MultiplicativeMagma (Range a)

times may well be some sort of affine projection lurking under the hood

Methods

times :: Range a -> Range a -> Range a

(FromInteger a, Ord a, BoundedField a) => MultiplicativeUnital (Range a)

The unital object (Range -0.5 0.5) satisfies:

width one = one
mid zero = zero

Methods

one :: Range a

(FromInteger a, Ord a, BoundedField a) => MultiplicativeAssociative (Range a)

(FromInteger a, Ord a, BoundedField a) => MultiplicativeCommutative (Range a)

(FromInteger a, Ord a, BoundedField a) => MultiplicativeInvertible (Range a)

Methods

recip :: Range a -> Range a

(FromInteger a, Ord a, BoundedField a) => Multiplicative (Range a)

Methods

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

(FromInteger a, Ord a, BoundedField a) => MultiplicativeGroup (Range a)

Methods

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

Ord a => AdditiveMagma (Range a)

convex hull union

Methods

plus :: Range a -> Range a -> Range a

(Ord a, BoundedField a) => AdditiveUnital (Range a)

Methods

zero :: Range a

Ord a => AdditiveAssociative (Range a)

Ord a => AdditiveCommutative (Range a)

Ord a => AdditiveInvertible (Range a)

Methods

negate :: Range a -> Range a

(Ord a, BoundedField a) => Additive (Range a)

Methods

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

(Ord a, BoundedField a) => AdditiveGroup (Range a)

Methods

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

(FromInteger a, Ord a, BoundedField a) => Space (Range a)

Associated Types

type Element (Range a) :: *

type Grid (Range a) :: *

Methods

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

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

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

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

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

singular :: Range a -> Bool

element :: Element (Range a) -> Range a -> Bool

contains :: Range a -> Range a -> Bool

disjoint :: Range a -> Range a -> Bool

intersects :: Range a -> Range a -> Bool

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

nul :: Range a

space :: Foldable f => f (Element (Range a)) -> Range a

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

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

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

AdditiveGroup a => Normed (Range a) a

Methods

normL1 :: Range a -> a

normL2 :: Range a -> a

normLp :: a -> Range a -> a

(Ord a, AdditiveGroup a) => Metric (Range a) a

Methods

distanceL1 :: Range a -> Range a -> a

distanceL2 :: Range a -> Range a -> a

distanceLp :: a -> Range a -> Range a -> a

type Rep Range

type Rep Range = Bool

type Rep (Range a)

type Rep (Range a) = D1 * (MetaData "Range" "NumHask.Range" "numhask-range-0.2.2.1-CuiYZN34Lwi4movg2vrydE" True) (C1 * (MetaCons "Range'" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (a, a))))

type Element (Range a)

type Element (Range a) = a

type Grid (Range a)

type Grid (Range a) = Int

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 :: (FromInteger a, Fractional a, QuotientField a Integer, ExpField a) => Pos -> Range a -> Integer -> [a]

turn a range into n as pleasing to human sense and sensibility the as may well lie outside the original range as a result