NumHask.Space.Range

A Space containing numerical elements

Documentation

data Range a

A continuous range over type a

>>> let a = Range (-1) 1
>>> a
Range -1 1

Num instance based on interval arithmetic (with Ranges normalising to lower ... upper)

>>> a + a
Range -2 2
>>> a * a
Range -1 1
>>> (+1) <$> (Range 1 2)
Range 2 3

Ranges are very useful in shifting a bunch of numbers from one Range to another. eg project 0.5 from the range 0 to 1 to the range 1 to 4

>>> project (Range 0 1) (Range 1 4) 0.5
2.5

Create an equally spaced grid including outer bounds over a Range

>>> grid OuterPos (Range 0 10) 5
[0.0,2.0,4.0,6.0,8.0,10.0]

divide up a Range into equal-sized sections

>>> 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]

Constructors

Range a a

Instances

Functor Range

Defined in NumHask.Space.Range

Methods

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

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

Applicative Range

Defined in NumHask.Space.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.Space.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.Space.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.Space.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.Space.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.Space.Range

Methods

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

Show1 Range

Defined in NumHask.Space.Range

Methods

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

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

Apply Range

Defined in NumHask.Space.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

Foldable1 Range

Defined in NumHask.Space.Range

Methods

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

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

toNonEmpty :: Range a -> NonEmpty a

Traversable1 Range

Defined in NumHask.Space.Range

Methods

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

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

Eq a => Eq (Range a)

Defined in NumHask.Space.Range

Methods

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

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

(Num a, Eq a, Ord a) => Num (Range a)

Numeric algebra based on Interval arithmetic

Defined in NumHask.Space.Range

Methods

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

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

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

negate :: Range a -> Range a

abs :: Range a -> Range a

signum :: Range a -> Range a

fromInteger :: Integer -> Range a

Show a => Show (Range a)

Defined in NumHask.Space.Range

Methods

showsPrec :: Int -> Range a -> ShowS

show :: Range a -> String

showList :: [Range a] -> ShowS

Generic (Range a)

Defined in NumHask.Space.Range

Associated Types

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

Methods

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

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

(Eq a, Ord a) => Semigroup (Range a)

Monoid based on convex hull union

Defined in NumHask.Space.Range

Methods

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

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

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

Ord a => Lattice (Range a)

Defined in NumHask.Space.Range

Methods

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

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

(Ord a, Fractional a) => FieldSpace (Range a)

Defined in NumHask.Space.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]

(Eq a, Ord a) => Space (Range a)

Defined in NumHask.Space.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

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

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

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

type Rep Range

Defined in NumHask.Space.Range

type Rep Range = Bool

type Rep (Range a)

Defined in NumHask.Space.Range

type Rep (Range a) = D1 (MetaData "Range" "NumHask.Space.Range" "numhask-space-0.3.0-GM7MUIaWR8l8Uregq0MgYU" False) (C1 (MetaCons "Range" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

type Grid (Range a)

Defined in NumHask.Space.Range

type Grid (Range a) = Int

type Element (Range a)

Defined in NumHask.Space.Range

type Element (Range a) = a

gridSensible :: (Ord a, RealFrac a, Floating a, Integral b) => Pos -> Bool -> Range a -> b -> [a]

a grid with human sensible (rounded) values

>>> gridSensible OuterPos False (Range (-12.0) 23.0) 6
[-15.0,-10.0,-5.0,0.0,5.0,10.0,15.0,20.0,25.0]