Data.Geometry.Vector.VectorFamily

Implementation of \(d\)-dimensional vectors. The implementation automatically selects an optimized representation for small (up to size 4) vectors.

d dimensional Vectors

newtype Vector (d :: Nat) (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

MKVector

Fields

• _unV :: VectorFamily (Peano d) r

Instances

Arity d => FunctorWithIndex Int (Vector d)

Defined in Data.Geometry.Vector.VectorFamily

Methods

imap :: (Int -> a -> b) -> Vector d a -> Vector d b

Arity d => FoldableWithIndex Int (Vector d)

Defined in Data.Geometry.Vector.VectorFamily

Methods

ifoldMap :: Monoid m => (Int -> a -> m) -> Vector d a -> m

ifoldMap' :: Monoid m => (Int -> a -> m) -> Vector d a -> m

ifoldr :: (Int -> a -> b -> b) -> b -> Vector d a -> b

ifoldl :: (Int -> b -> a -> b) -> b -> Vector d a -> b

ifoldr' :: (Int -> a -> b -> b) -> b -> Vector d a -> b

ifoldl' :: (Int -> b -> a -> b) -> b -> Vector d a -> b

Arity d => TraversableWithIndex Int (Vector d)

Defined in Data.Geometry.Vector.VectorFamily

Methods

itraverse :: Applicative f => (Int -> a -> f b) -> Vector d a -> f (Vector d b)

Arity d => Functor (Vector d)

Defined in Data.Geometry.Vector.VectorFamily

Methods

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

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

Arity d => Applicative (Vector d)

Defined in Data.Geometry.Vector.VectorFamily

Methods

pure :: a -> Vector d a

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

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

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

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

Arity d => Foldable (Vector d)

Defined in Data.Geometry.Vector.VectorFamily

Methods

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

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

foldMap' :: Monoid m => (a -> m) -> Vector d a -> m

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

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

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

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

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

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

toList :: Vector d a -> [a]

null :: Vector d a -> Bool

length :: Vector d a -> Int

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

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

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

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

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

Arity d => Traversable (Vector d)

Defined in Data.Geometry.Vector.VectorFamily

Methods

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

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

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

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

Arity d => Arbitrary1 (Vector d)

Defined in Data.Geometry.Vector

Methods

liftArbitrary :: Gen a -> Gen (Vector d a)

liftShrink :: (a -> [a]) -> Vector d a -> [Vector d a]

Arity d => Eq1 (Vector d)

Defined in Data.Geometry.Vector.VectorFamily

Methods

liftEq :: (a -> b -> Bool) -> Vector d a -> Vector d b -> Bool

Arity d => Read1 (Vector d)

Defined in Data.Geometry.Vector.VectorFamily

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Vector d a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Vector d a]

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Vector d a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Vector d a]

Arity d => Show1 (Vector d)

Defined in Data.Geometry.Vector.VectorFamily

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Vector d a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Vector d a] -> ShowS

Arity d => Affine (Vector d)

Defined in Data.Geometry.Vector.VectorFamily

Associated Types

type Diff (Vector d) :: Type -> Type

Methods

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

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

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

Arity d => Metric (Vector d)

Defined in Data.Geometry.Vector.VectorFamily

Methods

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

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

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

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

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

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

Arity d => Additive (Vector d)

Defined in Data.Geometry.Vector.VectorFamily

Methods

zero :: Num a => Vector d a

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

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

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

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

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

Arity d => Vector (Vector d) r

Defined in Data.Geometry.Vector.VectorFamily

Methods

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

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

basicIndex :: Vector d r -> Int -> r

(Eq r, Arity d) => Eq (Vector d r)

Defined in Data.Geometry.Vector.VectorFamily

Methods

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

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

(Ord r, Arity d) => Ord (Vector d r)

Defined in Data.Geometry.Vector.VectorFamily

Methods

compare :: Vector d r -> Vector d r -> Ordering

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

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

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

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

max :: Vector d r -> Vector d r -> Vector d r

min :: Vector d r -> Vector d r -> Vector d r

(Read r, Arity d) => Read (Vector d r)

Defined in Data.Geometry.Vector.VectorFamily

Methods

readsPrec :: Int -> ReadS (Vector d r)

readList :: ReadS [Vector d r]

readPrec :: ReadPrec (Vector d r)

readListPrec :: ReadPrec [Vector d r]

(Show r, Arity d) => Show (Vector d r)

Defined in Data.Geometry.Vector.VectorFamily

Methods

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

show :: Vector d r -> String

showList :: [Vector d r] -> ShowS

(Random r, Arity d) => Random (Vector d r)

Defined in Data.Geometry.Vector

Methods

randomR :: RandomGen g => (Vector d r, Vector d r) -> g -> (Vector d r, g)

random :: RandomGen g => g -> (Vector d r, g)

randomRs :: RandomGen g => (Vector d r, Vector d r) -> g -> [Vector d r]

randoms :: RandomGen g => g -> [Vector d r]

(Arbitrary r, Arity d) => Arbitrary (Vector d r)

Defined in Data.Geometry.Vector

Methods

arbitrary :: Gen (Vector d r)

shrink :: Vector d r -> [Vector d r]

(Arity d, Hashable r) => Hashable (Vector d r)

Defined in Data.Geometry.Vector.VectorFamily

Methods

hashWithSalt :: Int -> Vector d r -> Int

hash :: Vector d r -> Int

(ToJSON r, Arity d) => ToJSON (Vector d r)

Defined in Data.Geometry.Vector.VectorFamily

Methods

toJSON :: Vector d r -> Value

toEncoding :: Vector d r -> Encoding

toJSONList :: [Vector d r] -> Value

toEncodingList :: [Vector d r] -> Encoding

(FromJSON r, Arity d) => FromJSON (Vector d r)

Defined in Data.Geometry.Vector.VectorFamily

Methods

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

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

(NFData r, Arity d) => NFData (Vector d r)

Defined in Data.Geometry.Vector.VectorFamily

Methods

rnf :: Vector d r -> ()

Arity d => Ixed (Vector d r)

Defined in Data.Geometry.Vector.VectorFamily

Methods

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

(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (Vector d r)

Defined in Data.Geometry.Transformation

Methods

transformBy :: Transformation (Dimension (Vector d r)) (NumType (Vector d r)) -> Vector d r -> Vector d r

type Dim (Vector d)

Defined in Data.Geometry.Vector.VectorFamily

type Dim (Vector d) = FromPeano (Peano d)

type Diff (Vector d)

Defined in Data.Geometry.Vector.VectorFamily

type Diff (Vector d) = Vector d

type Index (Vector d r)

Defined in Data.Geometry.Vector.VectorFamily

type Index (Vector d r) = Int

type IxValue (Vector d r)

Defined in Data.Geometry.Vector.VectorFamily

type IxValue (Vector d r) = r

type NumType (Vector d r)

Defined in Data.Geometry.Vector

type NumType (Vector d r) = r

type Dimension (Vector d r)

Defined in Data.Geometry.Vector

type Dimension (Vector d r) = d

unV :: Iso (Vector d r) (Vector d s) (VectorFamily (Peano d) r) (VectorFamily (Peano d) s)

Vectors are isomorphic to a definition determined by VectorFamily.

class (ImplicitArity (Peano d), KnownNat d) => Arity d

Instances

(ImplicitArity (Peano d), KnownNat d) => Arity d

Defined in Data.Geometry.Vector.VectorFamily

Convenience "constructors"

pattern Vector :: VectorFamilyF (Peano d) r -> Vector d r

Constant sized vector with d elements.

pattern Vector1 :: r -> Vector 1 r

Constant sized vector with 1 element.

pattern Vector2 :: r -> r -> Vector 2 r

Constant sized vector with 2 elements.

pattern Vector3 :: r -> r -> r -> Vector 3 r

Constant sized vector with 3 elements.

pattern Vector4 :: r -> r -> r -> r -> Vector 4 r

Constant sized vector with 4 elements.

vectorFromList :: Arity d => [r] -> Maybe (Vector d r)

\( O(n) \) Convert from a list to a non-empty vector.

vectorFromListUnsafe :: Arity d => [r] -> Vector d r

\( O(n) \) Convert from a list to a non-empty vector.

destruct :: (Arity d, Arity (d + 1)) => Vector (d + 1) r -> (r, Vector d r)

\( O(n) \) Pop the first element off a vector.

head :: (Arity d, 1 <= d) => Vector d r -> r

\( O(1) \) First element. Since arity is at least 1, this function is total.

Indexing vectors

element :: forall proxy i d r. (Arity d, KnownNat i, (i + 1) <= d) => proxy i -> Lens' (Vector d r) r

Lens into the i th element

element' :: forall d r. Arity d => Int -> Traversal' (Vector d r) r

Similar to element above. Except that we don't have a static guarantee that the index is in bounds. Hence, we can only return a Traversal

Snoccing and consindg

cons :: (Arity d, Arity (d + 1)) => r -> Vector d r -> Vector (d + 1) r

\( O(n) \) Prepend an element.

snoc :: (Arity (d + 1), Arity d) => Vector d r -> r -> Vector (d + 1) r

Add an element at the back of the vector

init :: (Arity d, Arity (d + 1)) => Vector (d + 1) r -> Vector d r

Get a vector of the first d - 1 elements.

last :: forall d r. (KnownNat d, Arity (d + 1)) => Vector (d + 1) r -> r

\( O(1) \) Last element. Since the vector is non-empty, runtime bounds checks are bypassed.

prefix :: forall i d r. (Arity d, Arity i, i <= d) => Vector d r -> Vector i r

Get a prefix of i elements of a vector

Specific on 3-dimensional vectors

cross :: Num r => Vector 3 r -> Vector 3 r -> Vector 3 r

Cross product of two three-dimensional vectors