Chart.Data

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, norm & abs.

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

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

Functor Rect

Defined in NumHask.Space.Rect

Methods

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

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

Applicative Rect

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

Foldable Rect

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

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)

Distributive Rect

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)

Representable Rect

Defined in NumHask.Space.Rect

Associated Types

type Rep Rect

Methods

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

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

Eq a => Eq (Rect a)

Defined in NumHask.Space.Rect

Methods

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

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

Show a => Show (Rect a)

Defined in NumHask.Space.Rect

Methods

showsPrec :: Int -> Rect a -> ShowS

show :: Rect a -> String

showList :: [Rect a] -> ShowS

Generic (Rect a)

Defined in NumHask.Space.Rect

Associated Types

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

Methods

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

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

Ord a => Semigroup (Rect a)

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

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

Defined in NumHask.Space.Rect

Methods

sign :: Rect a -> Rect a

abs :: Rect a -> Rect a

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

Defined in NumHask.Space.Rect

Methods

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

one :: Rect a

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

Defined in NumHask.Space.Rect

Methods

recip :: Rect a -> Rect a

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

Additive a => Additive (Rect a)

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

Defined in NumHask.Space.Rect

Methods

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

zero :: Rect a

Subtractive a => Subtractive (Rect a)

Defined in NumHask.Space.Rect

Methods

negate :: Rect a -> Rect a

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

Ord a => Space (Rect a)

Defined in NumHask.Space.Rect

Associated Types

type Element (Rect 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

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

Defined in NumHask.Space.Rect

Associated Types

type Grid (Rect a)

Methods

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

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

type Rep Rect

Defined in NumHask.Space.Rect

type Rep Rect = (Bool, Bool)

type Rep (Rect a)

Defined in NumHask.Space.Rect

type Rep (Rect a) = D1 ('MetaData "Rect" "NumHask.Space.Rect" "numhask-space-0.10.0.0-JgyBfnFqS4y76YSUL7WLZz" 'True) (C1 ('MetaCons "Rect'" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Compose Point Range a))))

type Element (Rect a)

Defined in NumHask.Space.Rect

type Element (Rect a) = Point a

type Grid (Rect a)

Defined in NumHask.Space.Rect

type Grid (Rect a) = Point Int

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

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

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

singletonGuard :: Maybe (Rect Double) -> Rect Double

Guard against an upstream Nothing or a singleton dimension

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

Monad Point

Defined in NumHask.Space.Point

Methods

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

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

return :: a -> Point a

Functor Point

Defined in NumHask.Space.Point

Methods

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

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

Applicative Point

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

Foldable Point

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

Traversable Point

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)

Distributive Point

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)

Representable Point

Defined in NumHask.Space.Point

Associated Types

type Rep Point

Methods

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

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

Eq1 Point

Defined in NumHask.Space.Point

Methods

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

Show1 Point

Defined in NumHask.Space.Point

Methods

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

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

Bounded a => Bounded (Point a)

Defined in NumHask.Space.Point

Methods

minBound :: Point a

maxBound :: Point a

Eq a => Eq (Point a)

Defined in NumHask.Space.Point

Methods

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

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

Show a => Show (Point a)

Defined in NumHask.Space.Point

Methods

showsPrec :: Int -> Point a -> ShowS

show :: Point a -> String

showList :: [Point a] -> ShowS

Generic (Point a)

Defined in NumHask.Space.Point

Associated Types

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

Methods

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

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

Semigroup a => Semigroup (Point a)

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

(Semigroup a, Monoid a) => Monoid (Point a)

Defined in NumHask.Space.Point

Methods

mempty :: Point a

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

mconcat :: [Point a] -> Point a

Ord a => JoinSemiLattice (Point a)

Defined in NumHask.Space.Point

Methods

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

Ord a => MeetSemiLattice (Point a)

Defined in NumHask.Space.Point

Methods

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

Field a => Field (Point a)

Defined in NumHask.Space.Point

Signed a => Signed (Point a)

Defined in NumHask.Space.Point

Methods

sign :: Point a -> Point a

abs :: Point a -> Point a

Distributive a => Distributive (Point a)

Defined in NumHask.Space.Point

Multiplicative a => Multiplicative (Point a)

Defined in NumHask.Space.Point

Methods

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

one :: Point a

Divisive a => Divisive (Point a)

Defined in NumHask.Space.Point

Methods

recip :: Point a -> Point a

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

Additive a => Additive (Point a)

Defined in NumHask.Space.Point

Methods

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

zero :: Point a

Subtractive a => Subtractive (Point a)

Defined in NumHask.Space.Point

Methods

negate :: Point a -> Point a

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

UniformRange a => UniformRange (Point a)

Defined in NumHask.Space.Point

Methods

uniformRM :: StatefulGen g m => (Point a, Point a) -> g -> m (Point a)

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

Defined in NumHask.Space.Point

Methods

norm :: Point a -> a

basis :: Point a -> Point a

TrigField a => Direction (Point a) 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

Defined in NumHask.Space.Point

Methods

angle :: Point a -> a

ray :: a -> Point a

Additive a => AdditiveAction (Point a) a

Defined in NumHask.Space.Point

Methods

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

Subtractive a => SubtractiveAction (Point a) a

Defined in NumHask.Space.Point

Methods

(.-) :: a -> Point a -> Point a

Multiplicative a => MultiplicativeAction (Point a) a

Defined in NumHask.Space.Point

Methods

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

Divisive a => DivisiveAction (Point a) a

Defined in NumHask.Space.Point

Methods

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

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

Defined in NumHask.Space.Point

Methods

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

type Rep Point

Defined in NumHask.Space.Point

type Rep Point = Bool

type Rep (Point a)

Defined in NumHask.Space.Point

type Rep (Point a) = D1 ('MetaData "Point" "NumHask.Space.Point" "numhask-space-0.10.0.0-JgyBfnFqS4y76YSUL7WLZz" 'False) (C1 ('MetaCons "Point" 'PrefixI 'True) (S1 ('MetaSel ('Just "_x") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Just "_y") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedStrict) (Rec0 a)))

addp :: Point Double -> Point Double -> Point Double

add Points, dimension-wise

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

NumHask Exports

Note that (+) and (*) from numhask are not actually re-exported.

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

Multiplicative Bool

Defined in NumHask.Algebra.Multiplicative

Methods

(*) :: Bool -> Bool -> Bool

one :: Bool

Multiplicative Double

Defined in NumHask.Algebra.Multiplicative

Methods

(*) :: Double -> Double -> Double

one :: Double

Multiplicative Float

Defined in NumHask.Algebra.Multiplicative

Methods

(*) :: Float -> Float -> Float

one :: Float

Multiplicative Int

Defined in NumHask.Algebra.Multiplicative

Methods

(*) :: Int -> Int -> Int

one :: Int

Multiplicative Int8

Defined in NumHask.Algebra.Multiplicative

Methods

(*) :: Int8 -> Int8 -> Int8

one :: Int8

Multiplicative Int16

Defined in NumHask.Algebra.Multiplicative

Methods

(*) :: Int16 -> Int16 -> Int16

one :: Int16

Multiplicative Int32

Defined in NumHask.Algebra.Multiplicative

Methods

(*) :: Int32 -> Int32 -> Int32

one :: Int32

Multiplicative Int64

Defined in NumHask.Algebra.Multiplicative

Methods

(*) :: Int64 -> Int64 -> Int64

one :: Int64

Multiplicative Integer

Defined in NumHask.Algebra.Multiplicative

Methods

(*) :: Integer -> Integer -> Integer

one :: Integer

Multiplicative Natural

Defined in NumHask.Algebra.Multiplicative

Methods

(*) :: Natural -> Natural -> Natural

one :: Natural

Multiplicative Word

Defined in NumHask.Algebra.Multiplicative

Methods

(*) :: Word -> Word -> Word

one :: Word

Multiplicative Word8

Defined in NumHask.Algebra.Multiplicative

Methods

(*) :: Word8 -> Word8 -> Word8

one :: Word8

Multiplicative Word16

Defined in NumHask.Algebra.Multiplicative

Methods

(*) :: Word16 -> Word16 -> Word16

one :: Word16

Multiplicative Word32

Defined in NumHask.Algebra.Multiplicative

Methods

(*) :: Word32 -> Word32 -> Word32

one :: Word32

Multiplicative Word64

Defined in NumHask.Algebra.Multiplicative

Methods

(*) :: Word64 -> Word64 -> Word64

one :: Word64

(Ord a, Signed a, Integral a, Ring a, Multiplicative a) => Multiplicative (Ratio a)

Defined in NumHask.Data.Rational

Methods

(*) :: Ratio a -> Ratio a -> Ratio a

one :: Ratio a

(Subtractive a, Multiplicative a) => Multiplicative (Complex a)

Defined in NumHask.Data.Complex

Methods

(*) :: Complex a -> Complex a -> Complex a

one :: Complex a

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

Defined in NumHask.Space.Rect

Methods

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

one :: Rect a

Multiplicative a => Multiplicative (Point a)

Defined in NumHask.Space.Point

Methods

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

one :: Point a

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

Defined in NumHask.Space.Range

Methods

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

one :: Range a

Multiplicative b => Multiplicative (a -> b)

Defined in NumHask.Algebra.Multiplicative

Methods

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

one :: a -> b

(Multiplicative a, Distributive a, Subtractive a, KnownNat m, HasShape '[m, m]) => Multiplicative (Matrix m m a)

Defined in NumHask.Array.Fixed

Methods

(*) :: Matrix m m a -> Matrix m m a -> Matrix m m a

one :: Matrix m m a

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

Additive Bool

Defined in NumHask.Algebra.Additive

Methods

(+) :: Bool -> Bool -> Bool

zero :: Bool

Additive Double

Defined in NumHask.Algebra.Additive

Methods

(+) :: Double -> Double -> Double

zero :: Double

Additive Float

Defined in NumHask.Algebra.Additive

Methods

(+) :: Float -> Float -> Float

zero :: Float

Additive Int

Defined in NumHask.Algebra.Additive

Methods

(+) :: Int -> Int -> Int

zero :: Int

Additive Int8

Defined in NumHask.Algebra.Additive

Methods

(+) :: Int8 -> Int8 -> Int8

zero :: Int8

Additive Int16

Defined in NumHask.Algebra.Additive

Methods

(+) :: Int16 -> Int16 -> Int16

zero :: Int16

Additive Int32

Defined in NumHask.Algebra.Additive

Methods

(+) :: Int32 -> Int32 -> Int32

zero :: Int32

Additive Int64

Defined in NumHask.Algebra.Additive

Methods

(+) :: Int64 -> Int64 -> Int64

zero :: Int64

Additive Integer

Defined in NumHask.Algebra.Additive

Methods

(+) :: Integer -> Integer -> Integer

zero :: Integer

Additive Natural

Defined in NumHask.Algebra.Additive

Methods

(+) :: Natural -> Natural -> Natural

zero :: Natural

Additive Word

Defined in NumHask.Algebra.Additive

Methods

(+) :: Word -> Word -> Word

zero :: Word

Additive Word8

Defined in NumHask.Algebra.Additive

Methods

(+) :: Word8 -> Word8 -> Word8

zero :: Word8

Additive Word16

Defined in NumHask.Algebra.Additive

Methods

(+) :: Word16 -> Word16 -> Word16

zero :: Word16

Additive Word32

Defined in NumHask.Algebra.Additive

Methods

(+) :: Word32 -> Word32 -> Word32

zero :: Word32

Additive Word64

Defined in NumHask.Algebra.Additive

Methods

(+) :: Word64 -> Word64 -> Word64

zero :: Word64

(Ord a, Signed a, Integral a, Ring a) => Additive (Ratio a)

Defined in NumHask.Data.Rational

Methods

(+) :: Ratio a -> Ratio a -> Ratio a

zero :: Ratio a

Additive a => Additive (Complex a)

Defined in NumHask.Data.Complex

Methods

(+) :: Complex a -> Complex a -> Complex a

zero :: Complex a

Additive a => Additive (Rect a)

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

Defined in NumHask.Space.Rect

Methods

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

zero :: Rect a

Additive a => Additive (Point a)

Defined in NumHask.Space.Point

Methods

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

zero :: Point a

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

Defined in NumHask.Space.Range

Methods

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

zero :: Range a

Additive b => Additive (a -> b)

Defined in NumHask.Algebra.Additive

Methods

(+) :: (a -> b) -> (a -> b) -> a -> b

zero :: a -> b

(Additive a, HasShape s) => Additive (Array s a)

Defined in NumHask.Array.Fixed

Methods

(+) :: Array s a -> Array s a -> Array s a

zero :: Array s a

class (Additive coord, Multiplicative coord, Additive dir, Multiplicative dir) => Direction coord dir | coord -> dir where

Convert between a "co-ordinated" or "higher-kinded" number and representations of an angle. Typically thought of as polar co-ordinate conversion.

See Polar coordinate system

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

Methods

angle :: coord -> dir

ray :: dir -> coord

Instances

TrigField a => Direction (Complex a) a

Defined in NumHask.Data.Complex

Methods

angle :: Complex a -> a

ray :: a -> Complex a

TrigField a => Direction (Point a) 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

Defined in NumHask.Space.Point

Methods

angle :: Point a -> a

ray :: a -> Point a

class (Additive a, Multiplicative b, Additive b) => Norm a b | a -> b where

Norm is a slight generalisation of Signed. The class has the same shape but allows the codomain to be different to the domain.

\a -> norm a >= zero
\a -> norm zero == zero
\a -> a == norm a .* basis a
\a -> norm (basis a) == one

>>> norm (-0.5 :: Double) :: Double
0.5

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

Methods

norm :: a -> b

or length, or ||v||

basis :: a -> a

or direction, or v-hat

Instances

Norm Double Double

Defined in NumHask.Algebra.Metric

Methods

norm :: Double -> Double

basis :: Double -> Double

Norm Float Float

Defined in NumHask.Algebra.Metric

Methods

norm :: Float -> Float

basis :: Float -> Float

Norm Int Int

Defined in NumHask.Algebra.Metric

Methods

norm :: Int -> Int

basis :: Int -> Int

Norm Int8 Int8

Defined in NumHask.Algebra.Metric

Methods

norm :: Int8 -> Int8

basis :: Int8 -> Int8

Norm Int16 Int16

Defined in NumHask.Algebra.Metric

Methods

norm :: Int16 -> Int16

basis :: Int16 -> Int16

Norm Int32 Int32

Defined in NumHask.Algebra.Metric

Methods

norm :: Int32 -> Int32

basis :: Int32 -> Int32

Norm Int64 Int64

Defined in NumHask.Algebra.Metric

Methods

norm :: Int64 -> Int64

basis :: Int64 -> Int64

Norm Integer Integer

Defined in NumHask.Algebra.Metric

Methods

norm :: Integer -> Integer

basis :: Integer -> Integer

Norm Natural Natural

Defined in NumHask.Algebra.Metric

Methods

norm :: Natural -> Natural

basis :: Natural -> Natural

Norm Word Word

Defined in NumHask.Algebra.Metric

Methods

norm :: Word -> Word

basis :: Word -> Word

Norm Word8 Word8

Defined in NumHask.Algebra.Metric

Methods

norm :: Word8 -> Word8

basis :: Word8 -> Word8

Norm Word16 Word16

Defined in NumHask.Algebra.Metric

Methods

norm :: Word16 -> Word16

basis :: Word16 -> Word16

Norm Word32 Word32

Defined in NumHask.Algebra.Metric

Methods

norm :: Word32 -> Word32

basis :: Word32 -> Word32

Norm Word64 Word64

Defined in NumHask.Algebra.Metric

Methods

norm :: Word64 -> Word64

basis :: Word64 -> Word64

ExpField a => Norm (Complex a) a

A euclidean-style norm is strong convention for Complex.

Defined in NumHask.Data.Complex

Methods

norm :: Complex a -> a

basis :: Complex a -> Complex a

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

Defined in NumHask.Space.Point

Methods

norm :: Point a -> a

basis :: Point a -> Point a

(Ord a, Signed a, Integral a, Ring a) => Norm (Ratio a) (Ratio a)

Defined in NumHask.Data.Rational

Methods

norm :: Ratio a -> Ratio a

basis :: Ratio a -> Ratio a

class (Additive a, Multiplicative a) => Signed a where

signum from base is not an operator name in numhask and is replaced by sign. Compare with Norm where there is a change in codomain.

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

abs zero == zero, so any value for sign zero is ok. We choose lawful neutral:

>>> sign zero == zero
True

>>> abs (-1)
1

>>> sign (-1)
-1

Methods

sign :: a -> a

abs :: a -> a

Instances

Signed Double

Defined in NumHask.Algebra.Metric

Methods

sign :: Double -> Double

abs :: Double -> Double

Signed Float

Defined in NumHask.Algebra.Metric

Methods

sign :: Float -> Float

abs :: Float -> Float

Signed Int

Defined in NumHask.Algebra.Metric

Methods

sign :: Int -> Int

abs :: Int -> Int

Signed Int8

Defined in NumHask.Algebra.Metric

Methods

sign :: Int8 -> Int8

abs :: Int8 -> Int8

Signed Int16

Defined in NumHask.Algebra.Metric

Methods

sign :: Int16 -> Int16

abs :: Int16 -> Int16

Signed Int32

Defined in NumHask.Algebra.Metric

Methods

sign :: Int32 -> Int32

abs :: Int32 -> Int32

Signed Int64

Defined in NumHask.Algebra.Metric

Methods

sign :: Int64 -> Int64

abs :: Int64 -> Int64

Signed Integer

Defined in NumHask.Algebra.Metric

Methods

sign :: Integer -> Integer

abs :: Integer -> Integer

Signed Natural

Defined in NumHask.Algebra.Metric

Methods

sign :: Natural -> Natural

abs :: Natural -> Natural

Signed Word

Defined in NumHask.Algebra.Metric

Methods

sign :: Word -> Word

abs :: Word -> Word

Signed Word8

Defined in NumHask.Algebra.Metric

Methods

sign :: Word8 -> Word8

abs :: Word8 -> Word8

Signed Word16

Defined in NumHask.Algebra.Metric

Methods

sign :: Word16 -> Word16

abs :: Word16 -> Word16

Signed Word32

Defined in NumHask.Algebra.Metric

Methods

sign :: Word32 -> Word32

abs :: Word32 -> Word32

Signed Word64

Defined in NumHask.Algebra.Metric

Methods

sign :: Word64 -> Word64

abs :: Word64 -> Word64

(Ord a, Signed a, Integral a, Ring a) => Signed (Ratio a)

Defined in NumHask.Data.Rational

Methods

sign :: Ratio a -> Ratio a

abs :: Ratio a -> Ratio a

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

Defined in NumHask.Space.Rect

Methods

sign :: Rect a -> Rect a

abs :: Rect a -> Rect a

Signed a => Signed (Point a)

Defined in NumHask.Space.Point

Methods

sign :: Point a -> Point a

abs :: Point a -> Point a

(Field a, Subtractive a, Eq a, Ord a) => Signed (Range a)

Defined in NumHask.Space.Range

Methods

sign :: Range a -> Range a

abs :: Range a -> Range a

Re-exports

module NumHask.Space