Data.Geometry.Vector.VectorFamilyPeano

Natural number stuff

type One = S Z

type Two = S One

type Three = S Two

type Four = S Three

type Many d = S (S (S (S (S d))))

type family FromPeano (d :: PeanoNum) :: Nat where ...

Equations

FromPeano Z = 0

FromPeano (S d) = 1 + FromPeano d

data SingPeano (d :: PeanoNum) where

Constructors

SZ :: SingPeano Z

SS :: !(SingPeano d) -> SingPeano (S d)

class ImplicitPeano (d :: PeanoNum) where

Minimal complete definition

implicitPeano

Methods

implicitPeano :: SingPeano d

Instances

ImplicitPeano Z

Defined in Data.Geometry.Vector.VectorFamilyPeano

Methods

implicitPeano :: SingPeano Z

ImplicitPeano d => ImplicitPeano (S d)

Defined in Data.Geometry.Vector.VectorFamilyPeano

Methods

implicitPeano :: SingPeano (S d)

d dimensional Vectors

newtype VectorFamily (d :: PeanoNum) (r :: *)

Datatype representing d dimensional vectors. The default implementation is based n VectorFixed. However, for small vectors we automatically select a more efficient representation.

Constructors

VectorFamily

Fields

• _unVF :: VectorFamilyF d r

Instances

ImplicitArity d => Functor (VectorFamily d)

Defined in Data.Geometry.Vector.VectorFamilyPeano

Methods

fmap :: (a -> b) -> VectorFamily d a -> VectorFamily d b

(<$) :: a -> VectorFamily d b -> VectorFamily d a

ImplicitArity d => Applicative (VectorFamily d)

Defined in Data.Geometry.Vector.VectorFamilyPeano

Methods

pure :: a -> VectorFamily d a

(<*>) :: VectorFamily d (a -> b) -> VectorFamily d a -> VectorFamily d b

liftA2 :: (a -> b -> c) -> VectorFamily d a -> VectorFamily d b -> VectorFamily d c

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

(<*) :: VectorFamily d a -> VectorFamily d b -> VectorFamily d a

ImplicitArity d => Foldable (VectorFamily d)

Defined in Data.Geometry.Vector.VectorFamilyPeano

Methods

fold :: Monoid m => VectorFamily d m -> m

foldMap :: Monoid m => (a -> m) -> VectorFamily d a -> m

foldr :: (a -> b -> b) -> b -> VectorFamily d a -> b

foldr' :: (a -> b -> b) -> b -> VectorFamily d a -> b

foldl :: (b -> a -> b) -> b -> VectorFamily d a -> b

foldl' :: (b -> a -> b) -> b -> VectorFamily d a -> b

foldr1 :: (a -> a -> a) -> VectorFamily d a -> a

foldl1 :: (a -> a -> a) -> VectorFamily d a -> a

toList :: VectorFamily d a -> [a]

null :: VectorFamily d a -> Bool

length :: VectorFamily d a -> Int

elem :: Eq a => a -> VectorFamily d a -> Bool

maximum :: Ord a => VectorFamily d a -> a

minimum :: Ord a => VectorFamily d a -> a

sum :: Num a => VectorFamily d a -> a

product :: Num a => VectorFamily d a -> a

ImplicitArity d => Traversable (VectorFamily d)

Defined in Data.Geometry.Vector.VectorFamilyPeano

Methods

traverse :: Applicative f => (a -> f b) -> VectorFamily d a -> f (VectorFamily d b)

sequenceA :: Applicative f => VectorFamily d (f a) -> f (VectorFamily d a)

mapM :: Monad m => (a -> m b) -> VectorFamily d a -> m (VectorFamily d b)

sequence :: Monad m => VectorFamily d (m a) -> m (VectorFamily d a)

ImplicitArity d => Affine (VectorFamily d)

Defined in Data.Geometry.Vector.VectorFamilyPeano

Associated Types

type Diff (VectorFamily d) :: * -> *

Methods

(.-.) :: Num a => VectorFamily d a -> VectorFamily d a -> Diff (VectorFamily d) a

(.+^) :: Num a => VectorFamily d a -> Diff (VectorFamily d) a -> VectorFamily d a

(.-^) :: Num a => VectorFamily d a -> Diff (VectorFamily d) a -> VectorFamily d a

ImplicitArity d => Metric (VectorFamily d)

Defined in Data.Geometry.Vector.VectorFamilyPeano

Methods

dot :: Num a => VectorFamily d a -> VectorFamily d a -> a

quadrance :: Num a => VectorFamily d a -> a

qd :: Num a => VectorFamily d a -> VectorFamily d a -> a

distance :: Floating a => VectorFamily d a -> VectorFamily d a -> a

norm :: Floating a => VectorFamily d a -> a

signorm :: Floating a => VectorFamily d a -> VectorFamily d a

ImplicitArity d => Additive (VectorFamily d)

Defined in Data.Geometry.Vector.VectorFamilyPeano

Methods

zero :: Num a => VectorFamily d a

(^+^) :: Num a => VectorFamily d a -> VectorFamily d a -> VectorFamily d a

(^-^) :: Num a => VectorFamily d a -> VectorFamily d a -> VectorFamily d a

lerp :: Num a => a -> VectorFamily d a -> VectorFamily d a -> VectorFamily d a

liftU2 :: (a -> a -> a) -> VectorFamily d a -> VectorFamily d a -> VectorFamily d a

liftI2 :: (a -> b -> c) -> VectorFamily d a -> VectorFamily d b -> VectorFamily d c

ImplicitArity d => Vector (VectorFamily d) r

Defined in Data.Geometry.Vector.VectorFamilyPeano

Methods

construct :: Fun (Peano (Dim (VectorFamily d))) r (VectorFamily d r)

inspect :: VectorFamily d r -> Fun (Peano (Dim (VectorFamily d))) r b -> b

basicIndex :: VectorFamily d r -> Int -> r

(Eq r, ImplicitArity d) => Eq (VectorFamily d r)

Defined in Data.Geometry.Vector.VectorFamilyPeano

Methods

(==) :: VectorFamily d r -> VectorFamily d r -> Bool

(/=) :: VectorFamily d r -> VectorFamily d r -> Bool

(Ord r, ImplicitArity d) => Ord (VectorFamily d r)

Defined in Data.Geometry.Vector.VectorFamilyPeano

Methods

compare :: VectorFamily d r -> VectorFamily d r -> Ordering

(<) :: VectorFamily d r -> VectorFamily d r -> Bool

(<=) :: VectorFamily d r -> VectorFamily d r -> Bool

(>) :: VectorFamily d r -> VectorFamily d r -> Bool

(>=) :: VectorFamily d r -> VectorFamily d r -> Bool

max :: VectorFamily d r -> VectorFamily d r -> VectorFamily d r

min :: VectorFamily d r -> VectorFamily d r -> VectorFamily d r

(ImplicitArity d, Show r) => Show (VectorFamily d r)

Defined in Data.Geometry.Vector.VectorFamilyPeano

Methods

showsPrec :: Int -> VectorFamily d r -> ShowS

show :: VectorFamily d r -> String

showList :: [VectorFamily d r] -> ShowS

(ToJSON r, ImplicitArity d) => ToJSON (VectorFamily d r)

Defined in Data.Geometry.Vector.VectorFamilyPeano

Methods

toJSON :: VectorFamily d r -> Value

toEncoding :: VectorFamily d r -> Encoding

toJSONList :: [VectorFamily d r] -> Value

toEncodingList :: [VectorFamily d r] -> Encoding

(FromJSON r, ImplicitArity d) => FromJSON (VectorFamily d r)

Defined in Data.Geometry.Vector.VectorFamilyPeano

Methods

parseJSON :: Value -> Parser (VectorFamily d r)

parseJSONList :: Value -> Parser [VectorFamily d r]

(NFData r, ImplicitArity d) => NFData (VectorFamily d r)

Defined in Data.Geometry.Vector.VectorFamilyPeano

Methods

rnf :: VectorFamily d r -> ()

ImplicitArity d => Ixed (VectorFamily d r)

Defined in Data.Geometry.Vector.VectorFamilyPeano

Methods

ix :: Index (VectorFamily d r) -> Traversal' (VectorFamily d r) (IxValue (VectorFamily d r))

type Dim (VectorFamily d)

Defined in Data.Geometry.Vector.VectorFamilyPeano

type Dim (VectorFamily d) = FromPeano d

type Diff (VectorFamily d)

Defined in Data.Geometry.Vector.VectorFamilyPeano

type Diff (VectorFamily d) = VectorFamily d

type Index (VectorFamily d r)

Defined in Data.Geometry.Vector.VectorFamilyPeano

type Index (VectorFamily d r) = Int

type IxValue (VectorFamily d r)

Defined in Data.Geometry.Vector.VectorFamilyPeano

type IxValue (VectorFamily d r) = r

type family VectorFamilyF (d :: PeanoNum) :: * -> * where ...

Mapping between the implementation type, and the actual implementation.

Equations

VectorFamilyF Z = Const ()

VectorFamilyF One = Identity

VectorFamilyF Two = V2

VectorFamilyF Three = V3

VectorFamilyF Four = V4

VectorFamilyF (Many d) = Vector (FromPeano (Many d))

unVF :: Lens (VectorFamily d r) (VectorFamily d t) (VectorFamilyF d r) (VectorFamilyF d t)

type ImplicitArity d = (ImplicitPeano d, Arity (FromPeano d))

element' :: forall d r. ImplicitArity d => Int -> Traversal' (VectorFamily d r) r

elem0 :: Int -> Traversal' (VectorFamily Z r) r

elem1 :: Int -> Traversal' (VectorFamily One r) r

elem2 :: Int -> Traversal' (VectorFamily Two r) r

elem3 :: Int -> Traversal' (VectorFamily Three r) r

elem4 :: Int -> Traversal' (VectorFamily Four r) r

elemD :: Arity (FromPeano (Many d)) => Int -> Traversal' (VectorFamily (Many d) r) r

vectorFromList :: ImplicitArity d => [r] -> Maybe (VectorFamily d r)

vectorFromListUnsafe :: ImplicitArity d => [r] -> VectorFamily d r

destruct :: (ImplicitArity d, ImplicitArity (S d)) => VectorFamily (S d) r -> (r, VectorFamily d r)

Get the head and tail of a vector

snoc :: (ImplicitArity d, ImplicitArity (S d), (1 + FromPeano d) ~ (FromPeano d + 1)) => VectorFamily d r -> r -> VectorFamily (S d) r