Safe Haskell	None
Language	GHC2021

Chart.Data

Contents

Data Primitives
NumHask Exports

Description

Data primitives and utilities

Whilst the library makes use of numhask, it does not re-export, to avoid clashes with Prelude, with the exception of zero, one, angle & abs.

Rect and Point, from numhask-space, make up the base elements of many chart primitives.

Synopsis

newtype Rect a = Rect' (Compose Point Range a)
pattern Rect :: a -> a -> a -> a -> Rect a
mid :: (Space s, Field (Element s)) => s -> Element s
foldRect :: Ord a => [Rect a] -> Maybe (Rect a)
addPoint :: Additive a => Point a -> Rect a -> Rect a
projectOnP :: Rect Double -> Rect Double -> Point Double -> Point Double
projectOnR :: Rect Double -> Rect Double -> Rect Double -> Rect Double
space1 :: (Space s, Traversable f) => f (Element s) -> Maybe s
padRect :: Subtractive a => a -> Rect a -> Rect a
padSingletons :: Rect Double -> Rect Double
isSingleton :: Rect Double -> Bool
data Point a = Point {
- _x :: a
- _y :: a
}
addp :: Point Double -> Point Double -> Point Double
data Range a = Range a a
class Multiplicative a where
- one :: a
class Additive a where
- zero :: a
abs :: Absolute a => a -> a
class (Distributive coord, Distributive (Dir coord)) => Direction coord where
- type Dir coord
- angle :: coord -> Dir coord
- ray :: Dir coord -> coord
class Distributive (Mag a) => Basis a where
- type Mag a
- type Base a
- magnitude :: a -> Mag a
- basis :: a -> Base a

Data Primitives

newtype Rect a #

a rectangular space often representing a finite 2-dimensional or XY plane.

>>> one :: Rect Double
Rect (-0.5) 0.5 (-0.5) 0.5

>>> zero :: Rect Double
Rect 0.0 0.0 0.0 0.0

>>> one + one :: Rect Double
Rect (-1.0) 1.0 (-1.0) 1.0

>>> let a = Rect (-1.0) 1.0 (-2.0) 4.0
>>> a
Rect (-1.0) 1.0 (-2.0) 4.0

>>> a * one
Rect (-1.0) 1.0 (-2.0) 4.0

>>> let (Ranges x y) = a
>>> x
Range -1.0 1.0
>>> y
Range -2.0 4.0
>>> fmap (+1) (Rect 1 2 3 4)
Rect 2 3 4 5

as a Space instance with Points as Elements

>>> project (Rect 0.0 1.0 (-1.0) 0.0) (Rect 1.0 4.0 10.0 0.0) (Point 0.5 1.0)
Point 2.5 (-10.0)
>>> gridSpace (Rect 0.0 10.0 0.0 1.0) (Point (2::Int) (2::Int))
[Rect 0.0 5.0 0.0 0.5,Rect 0.0 5.0 0.5 1.0,Rect 5.0 10.0 0.0 0.5,Rect 5.0 10.0 0.5 1.0]
>>> grid MidPos (Rect 0.0 10.0 0.0 1.0) (Point (2::Int) (2::Int))
[Point 2.5 0.25,Point 2.5 0.75,Point 7.5 0.25,Point 7.5 0.75]

Constructors

Rect' (Compose Point Range a)

Instances

Instances details

Representable Rect

Instance details

Defined in NumHask.Space.Rect

Associated Types

type Rep Rect
Instance details Defined in NumHask.Space.Rect type Rep Rect = (Bool, Bool)

Methods

tabulate :: (Rep Rect -> a) -> Rect a #

index :: Rect a -> Rep Rect -> a #

Foldable Rect

Instance details

Defined in NumHask.Space.Rect

Methods

fold :: Monoid m => Rect m -> m #

foldMap :: Monoid m => (a -> m) -> Rect a -> m #

foldMap' :: Monoid m => (a -> m) -> Rect a -> m #

foldr :: (a -> b -> b) -> b -> Rect a -> b #

foldr' :: (a -> b -> b) -> b -> Rect a -> b #

foldl :: (b -> a -> b) -> b -> Rect a -> b #

foldl' :: (b -> a -> b) -> b -> Rect a -> b #

foldr1 :: (a -> a -> a) -> Rect a -> a #

foldl1 :: (a -> a -> a) -> Rect a -> a #

toList :: Rect a -> [a] #

null :: Rect a -> Bool #

length :: Rect a -> Int #

elem :: Eq a => a -> Rect a -> Bool #

maximum :: Ord a => Rect a -> a #

minimum :: Ord a => Rect a -> a #

sum :: Num a => Rect a -> a #

product :: Num a => Rect a -> a #

Traversable Rect

Instance details

Defined in NumHask.Space.Rect

Methods

traverse :: Applicative f => (a -> f b) -> Rect a -> f (Rect b) #

sequenceA :: Applicative f => Rect (f a) -> f (Rect a) #

mapM :: Monad m => (a -> m b) -> Rect a -> m (Rect b) #

sequence :: Monad m => Rect (m a) -> m (Rect a) #

Applicative Rect

Instance details

Defined in NumHask.Space.Rect

Methods

pure :: a -> Rect a #

(<*>) :: Rect (a -> b) -> Rect a -> Rect b #

liftA2 :: (a -> b -> c) -> Rect a -> Rect b -> Rect c #

(*>) :: Rect a -> Rect b -> Rect b #

(<*) :: Rect a -> Rect b -> Rect a #

Functor Rect

Instance details

Defined in NumHask.Space.Rect

Methods

fmap :: (a -> b) -> Rect a -> Rect b #

(<$) :: a -> Rect b -> Rect a #

Distributive Rect

Instance details

Defined in NumHask.Space.Rect

Methods

distribute :: Functor f => f (Rect a) -> Rect (f a) #

collect :: Functor f => (a -> Rect b) -> f a -> Rect (f b) #

distributeM :: Monad m => m (Rect a) -> Rect (m a) #

collectM :: Monad m => (a -> Rect b) -> m a -> Rect (m b) #

Data a => Data (Rect a)

Instance details

Defined in NumHask.Space.Rect

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Rect a -> c (Rect a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Rect a) #

toConstr :: Rect a -> Constr #

dataTypeOf :: Rect a -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Rect a)) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Rect a)) #

gmapT :: (forall b. Data b => b -> b) -> Rect a -> Rect a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Rect a -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Rect a -> r #

gmapQ :: (forall d. Data d => d -> u) -> Rect a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Rect a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Rect a -> m (Rect a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Rect a -> m (Rect a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Rect a -> m (Rect a) #

Ord a => Semigroup (Rect a)

Instance details

Defined in NumHask.Space.Rect

Methods

(<>) :: Rect a -> Rect a -> Rect a #

sconcat :: NonEmpty (Rect a) -> Rect a #

stimes :: Integral b => b -> Rect a -> Rect a #

Generic (Rect a)

Instance details

Defined in NumHask.Space.Rect

Associated Types

type Rep (Rect a)
Instance details Defined in NumHask.Space.Rect type Rep (Rect a) = D1 ('MetaData "Rect" "NumHask.Space.Rect" "numhask-space-0.13.2.0-5EPfNAfsKz84pToaZK4fAB" 'True) (C1 ('MetaCons "Rect'" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Compose Point Range a))))

Methods

from :: Rect a -> Rep (Rect a) x #

to :: Rep (Rect a) x -> Rect a #

(Ord a, Additive a, Show a) => Show (Rect a)

Instance details

Defined in NumHask.Space.Rect

Methods

showsPrec :: Int -> Rect a -> ShowS #

show :: Rect a -> String #

showList :: [Rect a] -> ShowS #

Eq a => Eq (Rect a)

Instance details

Defined in NumHask.Space.Rect

Methods

(==) :: Rect a -> Rect a -> Bool #

(/=) :: Rect a -> Rect a -> Bool #

Additive a => Additive (Rect a)

Numeric algebra based on interval arithmetic for addition and unitRect and projection for multiplication >>> one + one :: Rect Double Rect (-1.0) 1.0 (-1.0) 1.0

Instance details

Defined in NumHask.Space.Rect

Methods

(+) :: Rect a -> Rect a -> Rect a #

zero :: Rect a #

Subtractive a => Subtractive (Rect a)

Instance details

Defined in NumHask.Space.Rect

Methods

negate :: Rect a -> Rect a #

(-) :: Rect a -> Rect a -> Rect a #

(Ord a, Field a) => Basis (Rect a)

Instance details

Defined in NumHask.Space.Rect

Associated Types

type Mag (Rect a)
Instance details Defined in NumHask.Space.Rect type Mag (Rect a) = Rect a
type Base (Rect a)
Instance details Defined in NumHask.Space.Rect type Base (Rect a) = a

Methods

magnitude :: Rect a -> Mag (Rect a) #

basis :: Rect a -> Base (Rect a) #

(Ord a, Field a) => Divisive (Rect a)

Instance details

Defined in NumHask.Space.Rect

Methods

recip :: Rect a -> Rect a #

(/) :: Rect a -> Rect a -> Rect a #

(Ord a, Field a) => Multiplicative (Rect a)

Instance details

Defined in NumHask.Space.Rect

Methods

(*) :: Rect a -> Rect a -> Rect a #

one :: Rect a #

(FromIntegral a Int, Field a, Ord a) => FieldSpace (Rect a)

Instance details

Defined in NumHask.Space.Rect

Associated Types

type Grid (Rect a)
Instance details Defined in NumHask.Space.Rect type Grid (Rect a) = Point Int

Methods

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

gridSpace :: Rect a -> Grid (Rect a) -> [Rect a] #

Ord a => Space (Rect a)

Instance details

Defined in NumHask.Space.Rect

Associated Types

type Element (Rect a)
Instance details Defined in NumHask.Space.Rect type Element (Rect a) = Point a

Methods

lower :: Rect a -> Element (Rect a) #

upper :: Rect a -> Element (Rect a) #

singleton :: Element (Rect a) -> Rect a #

intersection :: Rect a -> Rect a -> Rect a #

union :: Rect a -> Rect a -> Rect a #

normalise :: Rect a -> Rect a #

(...) :: Element (Rect a) -> Element (Rect a) -> Rect a #

(>.<) :: Element (Rect a) -> Element (Rect a) -> Rect a #

(|.|) :: Element (Rect a) -> Rect a -> Bool #

(|>|) :: Rect a -> Rect a -> Bool #

(|<|) :: Rect a -> Rect a -> Bool #

type Rep Rect

Instance details

Defined in NumHask.Space.Rect

type Rep Rect = (Bool, Bool)

type Rep (Rect a)

Instance details

Defined in NumHask.Space.Rect

type Rep (Rect a) = D1 ('MetaData "Rect" "NumHask.Space.Rect" "numhask-space-0.13.2.0-5EPfNAfsKz84pToaZK4fAB" 'True) (C1 ('MetaCons "Rect'" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Compose Point Range a))))

type Base (Rect a)

Instance details

Defined in NumHask.Space.Rect

type Base (Rect a) = a

type Mag (Rect a)

Instance details

Defined in NumHask.Space.Rect

type Mag (Rect a) = Rect a

type Element (Rect a)

Instance details

Defined in NumHask.Space.Rect

type Element (Rect a) = Point a

type Grid (Rect a)

Instance details

Defined in NumHask.Space.Rect

type Grid (Rect a) = Point Int

pattern Rect :: a -> a -> a -> a -> Rect a #

pattern of Rect lowerx upperx lowery uppery

mid :: (Space s, Field (Element s)) => s -> Element s #

middle element of the space

foldRect :: Ord a => [Rect a] -> Maybe (Rect a) #

convex hull union of Rect's

>>> foldRect [Rect 0 1 0 1, one]
Just Rect (-0.5) 1.0 (-0.5) 1.0

addPoint :: Additive a => Point a -> Rect a -> Rect a #

add a Point to a Rect

>>> addPoint (Point 0 1) one
Rect (-0.5) 0.5 0.5 1.5

projectOnP :: Rect Double -> Rect Double -> Point Double -> Point Double #

project a Point from one Rect to another, preserving relative position, with guards for singleton Rects.

>>> projectOnP one (Rect 0 1 0 1) zero
Point (-0.5) (-0.5)

projectOnR :: Rect Double -> Rect Double -> Rect Double -> Rect Double #

project a Rect from one Rect to another, preserving relative position, with guards for singleton Rects.

>>> projectOnR one (Rect 0 1 0 1) (Rect 0 0.5 0 0.5)
Rect (-0.5) 0.0 (-0.5) 0.0

space1 :: (Space s, Traversable f) => f (Element s) -> Maybe s #

Maybe containing space of a traversable.

padRect :: Subtractive a => a -> Rect a -> Rect a Source #

Additive pad (or frame or buffer) a Rect.

>>> padRect 1 one
Rect (-1.5) 1.5 (-1.5) 1.5

padSingletons :: Rect Double -> Rect Double Source #

Pad a Rect to remove singleton dimensions.

Attempting to scale a singleton dimension of a Rect is a common bug.

Due to the use of scaling, and thus zero dividing, this is a common exception to guard against.

>>> project (Rect 0 0 0 1) one (Point 0 0)
Point NaN (-0.5)

>>> project (padSingletons (Rect 0 0 0 1)) one (Point 0 0)
Point 0.0 (-0.5)

isSingleton :: Rect Double -> Bool Source #

is any dimension singular?

data Point a #

A 2-dimensional Point of a's

In contrast with a tuple, a Point is functorial over both arguments.

>>> let p = Point 1 1
>>> p + p
Point 2 2
>>> (2*) <$> p
Point 2 2

A major reason for this bespoke treatment (compared to just using linear, say) is that Points do not have maximums and minimums but they do form a lattice, and this is useful for folding sets of points to find out the (rectangular) Space they occupy.

>>> Point 0 1 /\ Point 1 0
Point 0 0
>>> Point 0 1 \/ Point 1 0
Point 1 1

This is used extensively in chart-svg to ergonomically obtain chart areas.

unsafeSpace1 [Point 1 0, Point 0 1] :: Rect Double

Rect 0.0 1.0 0.0 1.0

Constructors

Point
Fields _x :: a _y :: a

Instances

Instances details

Representable Point

Instance details

Defined in NumHask.Space.Point

Associated Types

type Rep Point
Instance details Defined in NumHask.Space.Point type Rep Point = Bool

Methods

tabulate :: (Rep Point -> a) -> Point a #

index :: Point a -> Rep Point -> a #

Foldable Point

Instance details

Defined in NumHask.Space.Point

Methods

fold :: Monoid m => Point m -> m #

foldMap :: Monoid m => (a -> m) -> Point a -> m #

foldMap' :: Monoid m => (a -> m) -> Point a -> m #

foldr :: (a -> b -> b) -> b -> Point a -> b #

foldr' :: (a -> b -> b) -> b -> Point a -> b #

foldl :: (b -> a -> b) -> b -> Point a -> b #

foldl' :: (b -> a -> b) -> b -> Point a -> b #

foldr1 :: (a -> a -> a) -> Point a -> a #

foldl1 :: (a -> a -> a) -> Point a -> a #

toList :: Point a -> [a] #

null :: Point a -> Bool #

length :: Point a -> Int #

elem :: Eq a => a -> Point a -> Bool #

maximum :: Ord a => Point a -> a #

minimum :: Ord a => Point a -> a #

sum :: Num a => Point a -> a #

product :: Num a => Point a -> a #

Eq1 Point

Instance details

Defined in NumHask.Space.Point

Methods

liftEq :: (a -> b -> Bool) -> Point a -> Point b -> Bool #

Traversable Point

Instance details

Defined in NumHask.Space.Point

Methods

traverse :: Applicative f => (a -> f b) -> Point a -> f (Point b) #

sequenceA :: Applicative f => Point (f a) -> f (Point a) #

mapM :: Monad m => (a -> m b) -> Point a -> m (Point b) #

sequence :: Monad m => Point (m a) -> m (Point a) #

Applicative Point

Instance details

Defined in NumHask.Space.Point

Methods

pure :: a -> Point a #

(<*>) :: Point (a -> b) -> Point a -> Point b #

liftA2 :: (a -> b -> c) -> Point a -> Point b -> Point c #

(*>) :: Point a -> Point b -> Point b #

(<*) :: Point a -> Point b -> Point a #

Functor Point

Instance details

Defined in NumHask.Space.Point

Methods

fmap :: (a -> b) -> Point a -> Point b #

(<$) :: a -> Point b -> Point a #

Monad Point

Instance details

Defined in NumHask.Space.Point

Methods

(>>=) :: Point a -> (a -> Point b) -> Point b #

(>>) :: Point a -> Point b -> Point b #

return :: a -> Point a #

Distributive Point

Instance details

Defined in NumHask.Space.Point

Methods

distribute :: Functor f => f (Point a) -> Point (f a) #

collect :: Functor f => (a -> Point b) -> f a -> Point (f b) #

distributeM :: Monad m => m (Point a) -> Point (m a) #

collectM :: Monad m => (a -> Point b) -> m a -> Point (m b) #

Data a => Data (Point a)

Instance details

Defined in NumHask.Space.Point

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Point a -> c (Point a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Point a) #

toConstr :: Point a -> Constr #

dataTypeOf :: Point a -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Point a)) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Point a)) #

gmapT :: (forall b. Data b => b -> b) -> Point a -> Point a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Point a -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Point a -> r #

gmapQ :: (forall d. Data d => d -> u) -> Point a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Point a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Point a -> m (Point a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Point a -> m (Point a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Point a -> m (Point a) #

Monoid a => Monoid (Point a)

Instance details

Defined in NumHask.Space.Point

Methods

mempty :: Point a #

mappend :: Point a -> Point a -> Point a #

mconcat :: [Point a] -> Point a #

Semigroup a => Semigroup (Point a)

Instance details

Defined in NumHask.Space.Point

Methods

(<>) :: Point a -> Point a -> Point a #

sconcat :: NonEmpty (Point a) -> Point a #

stimes :: Integral b => b -> Point a -> Point a #

Bounded a => Bounded (Point a)

Instance details

Defined in NumHask.Space.Point

Methods

minBound :: Point a #

maxBound :: Point a #

Generic (Point a)

Instance details

Defined in NumHask.Space.Point

Associated Types

type Rep (Point a)
Instance details Defined in NumHask.Space.Point type Rep (Point a) = D1 ('MetaData "Point" "NumHask.Space.Point" "numhask-space-0.13.2.0-5EPfNAfsKz84pToaZK4fAB" 'False) (C1 ('MetaCons "Point" 'PrefixI 'True) (S1 ('MetaSel ('Just "_x") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Just "_y") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

from :: Point a -> Rep (Point a) x #

to :: Rep (Point a) x -> Point a #

(Ord a, Additive a, Show a) => Show (Point a)

Instance details

Defined in NumHask.Space.Point

Methods

showsPrec :: Int -> Point a -> ShowS #

show :: Point a -> String #

showList :: [Point a] -> ShowS #

Eq a => Eq (Point a)

Instance details

Defined in NumHask.Space.Point

Methods

(==) :: Point a -> Point a -> Bool #

(/=) :: Point a -> Point a -> Bool #

Additive a => AdditiveAction (Point a)

Instance details

Defined in NumHask.Space.Point

Associated Types

type AdditiveScalar (Point a)
Instance details Defined in NumHask.Space.Point type AdditiveScalar (Point a) = a

Methods

(|+) :: Point a -> AdditiveScalar (Point a) -> Point a #

Divisive a => DivisiveAction (Point a)

Instance details

Defined in NumHask.Space.Point

Methods

(|/) :: Point a -> Scalar (Point a) -> Point a #

Multiplicative a => MultiplicativeAction (Point a)

Instance details

Defined in NumHask.Space.Point

Associated Types

type Scalar (Point a)
Instance details Defined in NumHask.Space.Point type Scalar (Point a) = a

Methods

(|*) :: Point a -> Scalar (Point a) -> Point a #

Subtractive a => SubtractiveAction (Point a)

Instance details

Defined in NumHask.Space.Point

Methods

(|-) :: Point a -> AdditiveScalar (Point a) -> Point a #

Additive a => Additive (Point a)

Instance details

Defined in NumHask.Space.Point

Methods

(+) :: Point a -> Point a -> Point a #

zero :: Point a #

Subtractive a => Subtractive (Point a)

Instance details

Defined in NumHask.Space.Point

Methods

negate :: Point a -> Point a #

(-) :: Point a -> Point a -> Point a #

Ord a => JoinSemiLattice (Point a)

Instance details

Defined in NumHask.Space.Point

Methods

(\/) :: Point a -> Point a -> Point a #

Ord a => MeetSemiLattice (Point a)

Instance details

Defined in NumHask.Space.Point

Methods

(/\) :: Point a -> Point a -> Point a #

(ExpField a, Eq a) => Basis (Point a)

Instance details

Defined in NumHask.Space.Point

Associated Types

type Mag (Point a)
Instance details Defined in NumHask.Space.Point type Mag (Point a) = a
type Base (Point a)
Instance details Defined in NumHask.Space.Point type Base (Point a) = Point a

Methods

magnitude :: Point a -> Mag (Point a) #

basis :: Point a -> Base (Point a) #

TrigField a => Direction (Point a)

angle formed by a vector from the origin to a Point and the x-axis (Point 1 0). Note that an angle between two points p1 & p2 is thus angle p2 - angle p1

Instance details

Defined in NumHask.Space.Point

Associated Types

type Dir (Point a)
Instance details Defined in NumHask.Space.Point type Dir (Point a) = a

Methods

angle :: Point a -> Dir (Point a) #

ray :: Dir (Point a) -> Point a #

Divisive a => Divisive (Point a)

Instance details

Defined in NumHask.Space.Point

Methods

recip :: Point a -> Point a #

(/) :: Point a -> Point a -> Point a #

Multiplicative a => Multiplicative (Point a)

Instance details

Defined in NumHask.Space.Point

Methods

(*) :: Point a -> Point a -> Point a #

one :: Point a #

(Multiplicative a, Additive a) => Affinity (Point a) a

Instance details

Defined in NumHask.Space.Point

Methods

transform :: Transform a -> Point a -> Point a #

type Rep Point

Instance details

Defined in NumHask.Space.Point

type Rep Point = Bool

type Rep (Point a)

Instance details

Defined in NumHask.Space.Point

type Rep (Point a) = D1 ('MetaData "Point" "NumHask.Space.Point" "numhask-space-0.13.2.0-5EPfNAfsKz84pToaZK4fAB" 'False) (C1 ('MetaCons "Point" 'PrefixI 'True) (S1 ('MetaSel ('Just "_x") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Just "_y") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

type AdditiveScalar (Point a)

Instance details

Defined in NumHask.Space.Point

type AdditiveScalar (Point a) = a

type Scalar (Point a)

Instance details

Defined in NumHask.Space.Point

type Scalar (Point a) = a

type Base (Point a)

Instance details

Defined in NumHask.Space.Point

type Base (Point a) = Point a

type Dir (Point a)

Instance details

Defined in NumHask.Space.Point

type Dir (Point a) = a

type Mag (Point a)

Instance details

Defined in NumHask.Space.Point

type Mag (Point a) = a

addp :: Point Double -> Point Double -> Point Double Source #

add Points, dimension-wise

>>> Point 1 1 `addp` Point 0 2
Point 1.0 3.0

data Range a #

A continuous range over type a

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

>>> a + a
Range -2 2

>>> a * a
Range -2.0 2.0

>>> (+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 0.0 10.0) 5
[0.0,2.0,4.0,6.0,8.0,10.0]

divide up a Range into equal-sized sections

>>> gridSpace (Range 0.0 1.0) 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

Instances details

Representable Range

Instance details

Defined in NumHask.Space.Range

Associated Types

type Rep Range
Instance details Defined in NumHask.Space.Range type Rep Range = Bool

Methods

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

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

Foldable Range

Instance details

Defined in NumHask.Space.Range

Methods

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

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

Eq1 Range

Instance details

Defined in NumHask.Space.Range

Methods

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

Traversable Range

Instance details

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) #

Applicative Range

Instance details

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 #

Functor Range

Instance details

Defined in NumHask.Space.Range

Methods

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

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

Distributive Range

Instance details

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) #

Apply Range

Instance details

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 #

Data a => Data (Range a)

Instance details

Defined in NumHask.Space.Range

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Range a -> c (Range a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Range a) #

toConstr :: Range a -> Constr #

dataTypeOf :: Range a -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Range a)) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Range a)) #

gmapT :: (forall b. Data b => b -> b) -> Range a -> Range a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Range a -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Range a -> r #

gmapQ :: (forall d. Data d => d -> u) -> Range a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Range a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Range a -> m (Range a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Range a -> m (Range a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Range a -> m (Range a) #

Ord a => Semigroup (Range a)

Monoid based on convex hull union

Instance details

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 #

Generic (Range a)

Instance details

Defined in NumHask.Space.Range

Associated Types

type Rep (Range a)

Instance details

Defined in NumHask.Space.Range

type Rep (Range a) = D1 ('MetaData "Range" "NumHask.Space.Range" "numhask-space-0.13.2.0-5EPfNAfsKz84pToaZK4fAB" '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)))

Methods

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

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

Show a => Show (Range a)

Instance details

Defined in NumHask.Space.Range

Methods

showsPrec :: Int -> Range a -> ShowS #

show :: Range a -> String #

showList :: [Range a] -> ShowS #

Eq a => Eq (Range a)

Instance details

Defined in NumHask.Space.Range

Methods

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

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

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

Instance details

Defined in NumHask.Space.Range

Methods

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

zero :: Range a #

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

Instance details

Defined in NumHask.Space.Range

Methods

negate :: Range a -> Range a #

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

Ord a => JoinSemiLattice (Range a)

Instance details

Defined in NumHask.Space.Range

Methods

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

Ord a => MeetSemiLattice (Range a)

Instance details

Defined in NumHask.Space.Range

Methods

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

(Field a, Ord a) => Basis (Range a)

Instance details

Defined in NumHask.Space.Range

Associated Types

type Mag (Range a)
Instance details Defined in NumHask.Space.Range type Mag (Range a) = Range a
type Base (Range a)
Instance details Defined in NumHask.Space.Range type Base (Range a) = a

Methods

magnitude :: Range a -> Mag (Range a) #

basis :: Range a -> Base (Range a) #

(Ord a, Field a) => Divisive (Range a)

Instance details

Defined in NumHask.Space.Range

Methods

recip :: Range a -> Range a #

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

(Field a, Ord a) => Multiplicative (Range a)

Instance details

Defined in NumHask.Space.Range

Methods

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

one :: Range a #

(Field a, Ord a, FromIntegral a Int) => FieldSpace (Range a)

Instance details

Defined in NumHask.Space.Range

Associated Types

type Grid (Range a)
Instance details Defined in NumHask.Space.Range type Grid (Range a) = Int

Methods

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

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

Ord a => Space (Range a)

Instance details

Defined in NumHask.Space.Range

Associated Types

type Element (Range a)
Instance details Defined in NumHask.Space.Range type Element (Range a) = a

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 #

normalise :: 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

Instance details

Defined in NumHask.Space.Range

type Rep Range = Bool

type Rep (Range a)

Instance details

Defined in NumHask.Space.Range

type Rep (Range a) = D1 ('MetaData "Range" "NumHask.Space.Range" "numhask-space-0.13.2.0-5EPfNAfsKz84pToaZK4fAB" '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 Base (Range a)

Instance details

Defined in NumHask.Space.Range

type Base (Range a) = a

type Mag (Range a)

Instance details

Defined in NumHask.Space.Range

type Mag (Range a) = Range a

type Element (Range a)

Instance details

Defined in NumHask.Space.Range

type Element (Range a) = a

type Grid (Range a)

Instance details

Defined in NumHask.Space.Range

type Grid (Range a) = Int

NumHask Exports

class Multiplicative a where #

or Multiplication

For practical reasons, we begin the class tree with Additive and Multiplicative. Starting with Associative and Unital, or using Semigroup and Monoid from base tends to confuse the interface once you start having to disinguish between (say) monoidal addition and monoidal multiplication.

\a -> one * a == a

\a -> a * one == a

\a b c -> (a * b) * c == a * (b * c)

By convention, (*) is regarded as not necessarily commutative, but this is not universal, and the introduction of another symbol which means commutative multiplication seems a bit dogmatic.

>>> one * 2
2

>>> 2 * 3
6

Minimal complete definition

(*), one

Methods

one :: a #

Instances

Instances details

Multiplicative Int16
Instance details Defined in NumHask.Algebra.Multiplicative Methods (*) :: Int16 -> Int16 -> Int16 # one :: Int16 #
Multiplicative Int32
Instance details Defined in NumHask.Algebra.Multiplicative Methods (*) :: Int32 -> Int32 -> Int32 # one :: Int32 #
Multiplicative Int64
Instance details Defined in NumHask.Algebra.Multiplicative Methods (*) :: Int64 -> Int64 -> Int64 # one :: Int64 #
Multiplicative Int8
Instance details Defined in NumHask.Algebra.Multiplicative Methods (*) :: Int8 -> Int8 -> Int8 # one :: Int8 #
Multiplicative Word16
Instance details Defined in NumHask.Algebra.Multiplicative Methods (*) :: Word16 -> Word16 -> Word16 # one :: Word16 #
Multiplicative Word32
Instance details Defined in NumHask.Algebra.Multiplicative Methods (*) :: Word32 -> Word32 -> Word32 # one :: Word32 #
Multiplicative Word64
Instance details Defined in NumHask.Algebra.Multiplicative Methods (*) :: Word64 -> Word64 -> Word64 # one :: Word64 #
Multiplicative Word8
Instance details Defined in NumHask.Algebra.Multiplicative Methods (*) :: Word8 -> Word8 -> Word8 # one :: Word8 #
Multiplicative Integer
Instance details Defined in NumHask.Algebra.Multiplicative Methods (*) :: Integer -> Integer -> Integer # one :: Integer #
Multiplicative Natural
Instance details Defined in NumHask.Algebra.Multiplicative Methods (*) :: Natural -> Natural -> Natural # one :: Natural #
Multiplicative Bool
Instance details Defined in NumHask.Algebra.Multiplicative Methods (*) :: Bool -> Bool -> Bool # one :: Bool #
Multiplicative Double
Instance details Defined in NumHask.Algebra.Multiplicative Methods (*) :: Double -> Double -> Double # one :: Double #
Multiplicative Float
Instance details Defined in NumHask.Algebra.Multiplicative Methods (*) :: Float -> Float -> Float # one :: Float #
Multiplicative Int
Instance details Defined in NumHask.Algebra.Multiplicative Methods (*) :: Int -> Int -> Int # one :: Int #
Multiplicative Word
Instance details Defined in NumHask.Algebra.Multiplicative Methods (*) :: Word -> Word -> Word # one :: Word #
Multiplicative a => Multiplicative (EuclideanPair a)
Instance details Defined in NumHask.Algebra.Metric Methods (*) :: EuclideanPair a -> EuclideanPair a -> EuclideanPair a # one :: EuclideanPair a #
(Subtractive a, Multiplicative a) => Multiplicative (Complex a)
Instance details Defined in NumHask.Data.Complex Methods (*) :: Complex a -> Complex a -> Complex a # one :: Complex a #
Multiplicative a => Multiplicative (Positive a)
Instance details Defined in NumHask.Data.Positive Methods (*) :: Positive a -> Positive a -> Positive a # one :: Positive a #
(Ord a, EndoBased a, Integral a, Ring a) => Multiplicative (Ratio a)
Instance details Defined in NumHask.Data.Rational Methods (*) :: Ratio a -> Ratio a -> Ratio a # one :: Ratio a #
Multiplicative a => Multiplicative (Wrapped a)
Instance details Defined in NumHask.Data.Wrapped Methods (*) :: Wrapped a -> Wrapped a -> Wrapped a # one :: Wrapped a #
Multiplicative a => Multiplicative (Point a)
Instance details Defined in NumHask.Space.Point Methods (*) :: Point a -> Point a -> Point a # one :: Point a #
(Field a, Ord a) => Multiplicative (Range a)
Instance details Defined in NumHask.Space.Range Methods (*) :: Range a -> Range a -> Range a # one :: Range a #
(Ord a, Field a) => Multiplicative (Rect a)
Instance details Defined in NumHask.Space.Rect Methods (*) :: Rect a -> Rect a -> Rect a # one :: Rect a #
Multiplicative b => Multiplicative (a -> b)
Instance details Defined in NumHask.Algebra.Multiplicative Methods (*) :: (a -> b) -> (a -> b) -> a -> b # one :: a -> b #

class Additive a where #

or Addition

For practical reasons, we begin the class tree with Additive. Starting with Associative and Unital, or using Semigroup and Monoid from base tends to confuse the interface once you start having to disinguish between (say) monoidal addition and monoidal multiplication.

\a -> zero + a == a

\a -> a + zero == a

\a b c -> (a + b) + c == a + (b + c)

\a b -> a + b == b + a

By convention, (+) is regarded as commutative, but this is not universal, and the introduction of another symbol which means non-commutative addition seems a bit dogmatic.

>>> zero + 1
1

>>> 1 + 1
2

Minimal complete definition

(+), zero

Methods

zero :: a #

Instances

Instances details

Additive Int16
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Int16 -> Int16 -> Int16 # zero :: Int16 #
Additive Int32
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Int32 -> Int32 -> Int32 # zero :: Int32 #
Additive Int64
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Int64 -> Int64 -> Int64 # zero :: Int64 #
Additive Int8
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Int8 -> Int8 -> Int8 # zero :: Int8 #
Additive Word16
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Word16 -> Word16 -> Word16 # zero :: Word16 #
Additive Word32
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Word32 -> Word32 -> Word32 # zero :: Word32 #
Additive Word64
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Word64 -> Word64 -> Word64 # zero :: Word64 #
Additive Word8
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Word8 -> Word8 -> Word8 # zero :: Word8 #
Additive Integer
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Integer -> Integer -> Integer # zero :: Integer #
Additive Natural
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Natural -> Natural -> Natural # zero :: Natural #
Additive Bool
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Bool -> Bool -> Bool # zero :: Bool #
Additive Double
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Double -> Double -> Double # zero :: Double #
Additive Float
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Float -> Float -> Float # zero :: Float #
Additive Int
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Int -> Int -> Int # zero :: Int #
Additive Word
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Word -> Word -> Word # zero :: Word #
Additive a => Additive (Sum a)
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: Sum a -> Sum a -> Sum a # zero :: Sum a #
Additive a => Additive (EuclideanPair a)
Instance details Defined in NumHask.Algebra.Metric Methods (+) :: EuclideanPair a -> EuclideanPair a -> EuclideanPair a # zero :: EuclideanPair a #
Additive a => Additive (Complex a)
Instance details Defined in NumHask.Data.Complex Methods (+) :: Complex a -> Complex a -> Complex a # zero :: Complex a #
Additive a => Additive (Positive a)
Instance details Defined in NumHask.Data.Positive Methods (+) :: Positive a -> Positive a -> Positive a # zero :: Positive a #
(Ord a, EndoBased a, Integral a, Ring a) => Additive (Ratio a)
Instance details Defined in NumHask.Data.Rational Methods (+) :: Ratio a -> Ratio a -> Ratio a # zero :: Ratio a #
Additive a => Additive (Wrapped a)
Instance details Defined in NumHask.Data.Wrapped Methods (+) :: Wrapped a -> Wrapped a -> Wrapped a # zero :: Wrapped a #
Additive a => Additive (Point a)
Instance details Defined in NumHask.Space.Point Methods (+) :: Point a -> Point a -> Point a # zero :: Point a #
(Additive a, Ord a) => Additive (Range a)
Instance details Defined in NumHask.Space.Range Methods (+) :: Range a -> Range a -> Range a # zero :: Range a #
Additive a => Additive (Rect a)	Numeric algebra based on interval arithmetic for addition and unitRect and projection for multiplication >>> one + one :: Rect Double Rect (-1.0) 1.0 (-1.0) 1.0
Instance details Defined in NumHask.Space.Rect Methods (+) :: Rect a -> Rect a -> Rect a # zero :: Rect a #
Additive b => Additive (a -> b)
Instance details Defined in NumHask.Algebra.Additive Methods (+) :: (a -> b) -> (a -> b) -> a -> b # zero :: a -> b #

abs :: Absolute a => a -> a #

The absolute value of a number.

\a -> abs a * signum a ~= a

>>> abs (-1)
1

class (Distributive coord, Distributive (Dir coord)) => Direction coord where #

Convert between a "co-ordinated" or "higher-kinded" number and a direction.

ray . angle == basis
magnitude (ray x) == one

Since: numhask-0.7

Associated Types

type Dir coord #

Methods

angle :: coord -> Dir coord #

ray :: Dir coord -> coord #

Instances

Instances details

TrigField a => Direction (EuclideanPair a)

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Dir (EuclideanPair a)
Instance details Defined in NumHask.Algebra.Metric type Dir (EuclideanPair a) = a

Methods

angle :: EuclideanPair a -> Dir (EuclideanPair a) #

ray :: Dir (EuclideanPair a) -> EuclideanPair a #

TrigField a => Direction (Complex a)

Instance details

Defined in NumHask.Data.Complex

Associated Types

type Dir (Complex a)
Instance details Defined in NumHask.Data.Complex type Dir (Complex a) = Dir (EuclideanPair a)

Methods

angle :: Complex a -> Dir (Complex a) #

ray :: Dir (Complex a) -> Complex a #

Direction a => Direction (Positive a)

Instance details

Defined in NumHask.Data.Positive

Associated Types

type Dir (Positive a)
Instance details Defined in NumHask.Data.Positive type Dir (Positive a) = Dir (Wrapped a)

Methods

angle :: Positive a -> Dir (Positive a) #

ray :: Dir (Positive a) -> Positive a #

Direction a => Direction (Wrapped a)

Instance details

Defined in NumHask.Data.Wrapped

Associated Types

type Dir (Wrapped a)
Instance details Defined in NumHask.Data.Wrapped type Dir (Wrapped a) = Dir a

Methods

angle :: Wrapped a -> Dir (Wrapped a) #

ray :: Dir (Wrapped a) -> Wrapped a #

TrigField a => Direction (Point a)

angle formed by a vector from the origin to a Point and the x-axis (Point 1 0). Note that an angle between two points p1 & p2 is thus angle p2 - angle p1

Instance details

Defined in NumHask.Space.Point

Associated Types

type Dir (Point a)
Instance details Defined in NumHask.Space.Point type Dir (Point a) = a

Methods

angle :: Point a -> Dir (Point a) #

ray :: Dir (Point a) -> Point a #

class Distributive (Mag a) => Basis a where #

Basis encapsulates the notion of magnitude (intuitively the quotienting of a higher-kinded number to a scalar one) and the basis on which the magnitude quotienting was performed. An instance needs to satisfy these laws:

\a -> magnitude a >= zero
\a -> magnitude zero == zero
\a -> a == magnitude a *| basis a
\a -> magnitude (basis a) == one

The names chosen are meant to represent the spiritual idea of a basis rather than a specific mathematics. See https://en.wikipedia.org/wiki/Basis_(linear_algebra) & https://en.wikipedia.org/wiki/Norm_(mathematics) for some mathematical motivations.

>>> magnitude (-0.5 :: Double)
0.5

>>> basis (-0.5 :: Double)
-1.0

Since: numhask-0.11

Associated Types

type Mag a #

type Base a #

Methods

magnitude :: a -> Mag a #

or length, or ||v||

basis :: a -> Base a #

or direction, or v-hat

Instances

Instances details

Basis Int16

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Int16
Instance details Defined in NumHask.Algebra.Metric type Mag Int16 = Int16
type Base Int16
Instance details Defined in NumHask.Algebra.Metric type Base Int16 = Int16

Methods

magnitude :: Int16 -> Mag Int16 #

basis :: Int16 -> Base Int16 #

Basis Int32

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Int32
Instance details Defined in NumHask.Algebra.Metric type Mag Int32 = Int32
type Base Int32
Instance details Defined in NumHask.Algebra.Metric type Base Int32 = Int32

Methods

magnitude :: Int32 -> Mag Int32 #

basis :: Int32 -> Base Int32 #

Basis Int64

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Int64
Instance details Defined in NumHask.Algebra.Metric type Mag Int64 = Int64
type Base Int64
Instance details Defined in NumHask.Algebra.Metric type Base Int64 = Int64

Methods

magnitude :: Int64 -> Mag Int64 #

basis :: Int64 -> Base Int64 #

Basis Int8

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Int8
Instance details Defined in NumHask.Algebra.Metric type Mag Int8 = Int8
type Base Int8
Instance details Defined in NumHask.Algebra.Metric type Base Int8 = Int8

Methods

magnitude :: Int8 -> Mag Int8 #

basis :: Int8 -> Base Int8 #

Basis Word16

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Word16
Instance details Defined in NumHask.Algebra.Metric type Mag Word16 = Word16
type Base Word16
Instance details Defined in NumHask.Algebra.Metric type Base Word16 = Word16

Methods

magnitude :: Word16 -> Mag Word16 #

basis :: Word16 -> Base Word16 #

Basis Word32

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Word32
Instance details Defined in NumHask.Algebra.Metric type Mag Word32 = Word32
type Base Word32
Instance details Defined in NumHask.Algebra.Metric type Base Word32 = Word32

Methods

magnitude :: Word32 -> Mag Word32 #

basis :: Word32 -> Base Word32 #

Basis Word64

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Word64
Instance details Defined in NumHask.Algebra.Metric type Mag Word64 = Word64
type Base Word64
Instance details Defined in NumHask.Algebra.Metric type Base Word64 = Word64

Methods

magnitude :: Word64 -> Mag Word64 #

basis :: Word64 -> Base Word64 #

Basis Word8

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Word8
Instance details Defined in NumHask.Algebra.Metric type Mag Word8 = Word8
type Base Word8
Instance details Defined in NumHask.Algebra.Metric type Base Word8 = Word8

Methods

magnitude :: Word8 -> Mag Word8 #

basis :: Word8 -> Base Word8 #

Basis Integer

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Integer
Instance details Defined in NumHask.Algebra.Metric type Mag Integer = Integer
type Base Integer
Instance details Defined in NumHask.Algebra.Metric type Base Integer = Integer

Methods

magnitude :: Integer -> Mag Integer #

basis :: Integer -> Base Integer #

Basis Natural

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Natural
Instance details Defined in NumHask.Algebra.Metric type Mag Natural = Natural
type Base Natural
Instance details Defined in NumHask.Algebra.Metric type Base Natural = Natural

Methods

magnitude :: Natural -> Mag Natural #

basis :: Natural -> Base Natural #

Basis Double

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Double
Instance details Defined in NumHask.Algebra.Metric type Mag Double = Double
type Base Double
Instance details Defined in NumHask.Algebra.Metric type Base Double = Double

Methods

magnitude :: Double -> Mag Double #

basis :: Double -> Base Double #

Basis Float

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Float
Instance details Defined in NumHask.Algebra.Metric type Mag Float = Float
type Base Float
Instance details Defined in NumHask.Algebra.Metric type Base Float = Float

Methods

magnitude :: Float -> Mag Float #

basis :: Float -> Base Float #

Basis Int

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Int
Instance details Defined in NumHask.Algebra.Metric type Mag Int = Int
type Base Int
Instance details Defined in NumHask.Algebra.Metric type Base Int = Int

Methods

magnitude :: Int -> Mag Int #

basis :: Int -> Base Int #

Basis Word

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Word
Instance details Defined in NumHask.Algebra.Metric type Mag Word = Word
type Base Word
Instance details Defined in NumHask.Algebra.Metric type Base Word = Word

Methods

magnitude :: Word -> Mag Word #

basis :: Word -> Base Word #

(ExpField a, Eq a) => Basis (EuclideanPair a)

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag (EuclideanPair a)
Instance details Defined in NumHask.Algebra.Metric type Mag (EuclideanPair a) = a
type Base (EuclideanPair a)
Instance details Defined in NumHask.Algebra.Metric type Base (EuclideanPair a) = EuclideanPair a

Methods

magnitude :: EuclideanPair a -> Mag (EuclideanPair a) #

basis :: EuclideanPair a -> Base (EuclideanPair a) #

(Additive a, Multiplicative a) => Basis (Polar a)

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag (Polar a)
Instance details Defined in NumHask.Algebra.Metric type Mag (Polar a) = a
type Base (Polar a)
Instance details Defined in NumHask.Algebra.Metric type Base (Polar a) = a

Methods

magnitude :: Polar a -> Mag (Polar a) #

basis :: Polar a -> Base (Polar a) #

(ExpField a, Eq a) => Basis (Complex a)

Instance details

Defined in NumHask.Data.Complex

Associated Types

type Mag (Complex a)
Instance details Defined in NumHask.Data.Complex type Mag (Complex a) = Mag (EuclideanPair a)
type Base (Complex a)
Instance details Defined in NumHask.Data.Complex type Base (Complex a) = Base (EuclideanPair a)

Methods

magnitude :: Complex a -> Mag (Complex a) #

basis :: Complex a -> Base (Complex a) #

Basis a => Basis (Positive a)

Instance details

Defined in NumHask.Data.Positive

Associated Types

type Mag (Positive a)
Instance details Defined in NumHask.Data.Positive type Mag (Positive a) = Mag (Wrapped a)
type Base (Positive a)
Instance details Defined in NumHask.Data.Positive type Base (Positive a) = Base (Wrapped a)

Methods

magnitude :: Positive a -> Mag (Positive a) #

basis :: Positive a -> Base (Positive a) #

(Ord a, EndoBased a, Integral a, Ring a) => Basis (Ratio a)

Instance details

Defined in NumHask.Data.Rational

Associated Types

type Mag (Ratio a)
Instance details Defined in NumHask.Data.Rational type Mag (Ratio a) = Ratio a
type Base (Ratio a)
Instance details Defined in NumHask.Data.Rational type Base (Ratio a) = Ratio a

Methods

magnitude :: Ratio a -> Mag (Ratio a) #

basis :: Ratio a -> Base (Ratio a) #

Basis a => Basis (Wrapped a)

Instance details

Defined in NumHask.Data.Wrapped

Associated Types

type Mag (Wrapped a)
Instance details Defined in NumHask.Data.Wrapped type Mag (Wrapped a) = Mag a
type Base (Wrapped a)
Instance details Defined in NumHask.Data.Wrapped type Base (Wrapped a) = Base a

Methods

magnitude :: Wrapped a -> Mag (Wrapped a) #

basis :: Wrapped a -> Base (Wrapped a) #

(ExpField a, Eq a) => Basis (Point a)

Instance details

Defined in NumHask.Space.Point

Associated Types

type Mag (Point a)
Instance details Defined in NumHask.Space.Point type Mag (Point a) = a
type Base (Point a)
Instance details Defined in NumHask.Space.Point type Base (Point a) = Point a

Methods

magnitude :: Point a -> Mag (Point a) #

basis :: Point a -> Base (Point a) #

(Field a, Ord a) => Basis (Range a)

Instance details

Defined in NumHask.Space.Range

Associated Types

type Mag (Range a)
Instance details Defined in NumHask.Space.Range type Mag (Range a) = Range a
type Base (Range a)
Instance details Defined in NumHask.Space.Range type Base (Range a) = a

Methods

magnitude :: Range a -> Mag (Range a) #

basis :: Range a -> Base (Range a) #

(Ord a, Field a) => Basis (Rect a)

Instance details

Defined in NumHask.Space.Rect

Associated Types

type Mag (Rect a)
Instance details Defined in NumHask.Space.Rect type Mag (Rect a) = Rect a
type Base (Rect a)
Instance details Defined in NumHask.Space.Rect type Base (Rect a) = a

Methods

magnitude :: Rect a -> Mag (Rect a) #

basis :: Rect a -> Base (Rect a) #