Linear.V1

1-D Vectors

Documentation

newtype V1 a

A 1-dimensional vector

>>> pure 1 :: V1 Int
V1 1

>>> V1 2 + V1 3
V1 5

>>> V1 2 * V1 3
V1 6

>>> sum (V1 2)
2

Constructors

V1 a

Instances

Monad V1

Methods

(>>=) :: V1 a -> (a -> V1 b) -> V1 b

(>>) :: V1 a -> V1 b -> V1 b

return :: a -> V1 a

fail :: String -> V1 a

Functor V1

Methods

fmap :: (a -> b) -> V1 a -> V1 b

(<$) :: a -> V1 b -> V1 a

MonadFix V1

Methods

mfix :: (a -> V1 a) -> V1 a

Applicative V1

Methods

pure :: a -> V1 a

(<*>) :: V1 (a -> b) -> V1 a -> V1 b

(*>) :: V1 a -> V1 b -> V1 b

(<*) :: V1 a -> V1 b -> V1 a

Foldable V1

Methods

fold :: Monoid m => V1 m -> m

foldMap :: Monoid m => (a -> m) -> V1 a -> m

foldr :: (a -> b -> b) -> b -> V1 a -> b

foldr' :: (a -> b -> b) -> b -> V1 a -> b

foldl :: (b -> a -> b) -> b -> V1 a -> b

foldl' :: (b -> a -> b) -> b -> V1 a -> b

foldr1 :: (a -> a -> a) -> V1 a -> a

foldl1 :: (a -> a -> a) -> V1 a -> a

toList :: V1 a -> [a]

null :: V1 a -> Bool

length :: V1 a -> Int

elem :: Eq a => a -> V1 a -> Bool

maximum :: Ord a => V1 a -> a

minimum :: Ord a => V1 a -> a

sum :: Num a => V1 a -> a

product :: Num a => V1 a -> a

Traversable V1

Methods

traverse :: Applicative f => (a -> f b) -> V1 a -> f (V1 b)

sequenceA :: Applicative f => V1 (f a) -> f (V1 a)

mapM :: Monad m => (a -> m b) -> V1 a -> m (V1 b)

sequence :: Monad m => V1 (m a) -> m (V1 a)

Generic1 V1

Associated Types

type Rep1 (V1 :: * -> *) :: * -> *

Methods

from1 :: V1 a -> Rep1 V1 a

to1 :: Rep1 V1 a -> V1 a

Distributive V1

Methods

distribute :: Functor f => f (V1 a) -> V1 (f a)

collect :: Functor f => (a -> V1 b) -> f a -> V1 (f b)

distributeM :: Monad m => m (V1 a) -> V1 (m a)

collectM :: Monad m => (a -> V1 b) -> m a -> V1 (m b)

Representable V1

Associated Types

type Rep (V1 :: * -> *) :: *

Methods

tabulate :: (Rep V1 -> a) -> V1 a

index :: V1 a -> Rep V1 -> a

MonadZip V1

Methods

mzip :: V1 a -> V1 b -> V1 (a, b)

mzipWith :: (a -> b -> c) -> V1 a -> V1 b -> V1 c

munzip :: V1 (a, b) -> (V1 a, V1 b)

Serial1 V1

Methods

serializeWith :: MonadPut m => (a -> m ()) -> V1 a -> m ()

deserializeWith :: MonadGet m => m a -> m (V1 a)

Traversable1 V1

Methods

traverse1 :: Apply f => (a -> f b) -> V1 a -> f (V1 b)

sequence1 :: Apply f => V1 (f b) -> f (V1 b)

Apply V1

Methods

(<.>) :: V1 (a -> b) -> V1 a -> V1 b

(.>) :: V1 a -> V1 b -> V1 b

(<.) :: V1 a -> V1 b -> V1 a

Bind V1

Methods

(>>-) :: V1 a -> (a -> V1 b) -> V1 b

join :: V1 (V1 a) -> V1 a

Foldable1 V1

Methods

fold1 :: Semigroup m => V1 m -> m

foldMap1 :: Semigroup m => (a -> m) -> V1 a -> m

Eq1 V1

Methods

eq1 :: Eq a => V1 a -> V1 a -> Bool

Ord1 V1

Methods

compare1 :: Ord a => V1 a -> V1 a -> Ordering

Read1 V1

Methods

readsPrec1 :: Read a => Int -> ReadS (V1 a)

Show1 V1

Methods

showsPrec1 :: Show a => Int -> V1 a -> ShowS

Additive V1

Methods

zero :: Num a => V1 a

(^+^) :: Num a => V1 a -> V1 a -> V1 a

(^-^) :: Num a => V1 a -> V1 a -> V1 a

lerp :: Num a => a -> V1 a -> V1 a -> V1 a

liftU2 :: (a -> a -> a) -> V1 a -> V1 a -> V1 a

liftI2 :: (a -> b -> c) -> V1 a -> V1 b -> V1 c

Metric V1

Methods

dot :: Num a => V1 a -> V1 a -> a

quadrance :: Num a => V1 a -> a

qd :: Num a => V1 a -> V1 a -> a

distance :: Floating a => V1 a -> V1 a -> a

norm :: Floating a => V1 a -> a

signorm :: Floating a => V1 a -> V1 a

R1 V1

Methods

_x :: Functor f => (a -> f a) -> V1 a -> f (V1 a)

Trace V1

Methods

trace :: Num a => V1 (V1 a) -> a

diagonal :: V1 (V1 a) -> V1 a

Affine V1

Associated Types

type Diff (V1 :: * -> *) :: * -> *

Methods

(.-.) :: Num a => V1 a -> V1 a -> Diff V1 a

(.+^) :: Num a => V1 a -> Diff V1 a -> V1 a

(.-^) :: Num a => V1 a -> Diff V1 a -> V1 a

Unbox a => Vector Vector (V1 a)

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V1 a) -> m (Vector (V1 a))

basicUnsafeThaw :: PrimMonad m => Vector (V1 a) -> m (Mutable Vector (PrimState m) (V1 a))

basicLength :: Vector (V1 a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (V1 a) -> Vector (V1 a)

basicUnsafeIndexM :: Monad m => Vector (V1 a) -> Int -> m (V1 a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V1 a) -> Vector (V1 a) -> m ()

elemseq :: Vector (V1 a) -> V1 a -> b -> b

Unbox a => MVector MVector (V1 a)

Methods

basicLength :: MVector s (V1 a) -> Int

basicUnsafeSlice :: Int -> Int -> MVector s (V1 a) -> MVector s (V1 a)

basicOverlaps :: MVector s (V1 a) -> MVector s (V1 a) -> Bool

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V1 a))

basicInitialize :: PrimMonad m => MVector (PrimState m) (V1 a) -> m ()

basicUnsafeReplicate :: PrimMonad m => Int -> V1 a -> m (MVector (PrimState m) (V1 a))

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V1 a) -> Int -> m (V1 a)

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V1 a) -> Int -> V1 a -> m ()

basicClear :: PrimMonad m => MVector (PrimState m) (V1 a) -> m ()

basicSet :: PrimMonad m => MVector (PrimState m) (V1 a) -> V1 a -> m ()

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V1 a) -> MVector (PrimState m) (V1 a) -> m ()

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V1 a) -> MVector (PrimState m) (V1 a) -> m ()

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V1 a) -> Int -> m (MVector (PrimState m) (V1 a))

Num r => Coalgebra r (E V1)

Methods

comult :: (E V1 -> r) -> E V1 -> E V1 -> r

counital :: (E V1 -> r) -> r

Num r => Algebra r (E V1)

Methods

mult :: (E V1 -> E V1 -> r) -> E V1 -> r

unital :: r -> E V1 -> r

Bounded a => Bounded (V1 a)

Methods

minBound :: V1 a

maxBound :: V1 a

Eq a => Eq (V1 a)

Methods

(==) :: V1 a -> V1 a -> Bool

(/=) :: V1 a -> V1 a -> Bool

Floating a => Floating (V1 a)

Methods

pi :: V1 a

exp :: V1 a -> V1 a

log :: V1 a -> V1 a

sqrt :: V1 a -> V1 a

(**) :: V1 a -> V1 a -> V1 a

logBase :: V1 a -> V1 a -> V1 a

sin :: V1 a -> V1 a

cos :: V1 a -> V1 a

tan :: V1 a -> V1 a

asin :: V1 a -> V1 a

acos :: V1 a -> V1 a

atan :: V1 a -> V1 a

sinh :: V1 a -> V1 a

cosh :: V1 a -> V1 a

tanh :: V1 a -> V1 a

asinh :: V1 a -> V1 a

acosh :: V1 a -> V1 a

atanh :: V1 a -> V1 a

Fractional a => Fractional (V1 a)

Methods

(/) :: V1 a -> V1 a -> V1 a

recip :: V1 a -> V1 a

fromRational :: Rational -> V1 a

Data a => Data (V1 a)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> V1 a -> c (V1 a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (V1 a)

toConstr :: V1 a -> Constr

dataTypeOf :: V1 a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (V1 a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V1 a))

gmapT :: (forall b. Data b => b -> b) -> V1 a -> V1 a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V1 a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V1 a -> r

gmapQ :: (forall d. Data d => d -> u) -> V1 a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> V1 a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> V1 a -> m (V1 a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> V1 a -> m (V1 a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> V1 a -> m (V1 a)

Num a => Num (V1 a)

Methods

(+) :: V1 a -> V1 a -> V1 a

(-) :: V1 a -> V1 a -> V1 a

(*) :: V1 a -> V1 a -> V1 a

negate :: V1 a -> V1 a

abs :: V1 a -> V1 a

signum :: V1 a -> V1 a

fromInteger :: Integer -> V1 a

Ord a => Ord (V1 a)

Methods

compare :: V1 a -> V1 a -> Ordering

(<) :: V1 a -> V1 a -> Bool

(<=) :: V1 a -> V1 a -> Bool

(>) :: V1 a -> V1 a -> Bool

(>=) :: V1 a -> V1 a -> Bool

max :: V1 a -> V1 a -> V1 a

min :: V1 a -> V1 a -> V1 a

Read a => Read (V1 a)

Methods

readsPrec :: Int -> ReadS (V1 a)

readList :: ReadS [V1 a]

readPrec :: ReadPrec (V1 a)

readListPrec :: ReadPrec [V1 a]

Show a => Show (V1 a)

Methods

showsPrec :: Int -> V1 a -> ShowS

show :: V1 a -> String

showList :: [V1 a] -> ShowS

Ix a => Ix (V1 a)

Methods

range :: (V1 a, V1 a) -> [V1 a]

index :: (V1 a, V1 a) -> V1 a -> Int

unsafeIndex :: (V1 a, V1 a) -> V1 a -> Int

inRange :: (V1 a, V1 a) -> V1 a -> Bool

rangeSize :: (V1 a, V1 a) -> Int

unsafeRangeSize :: (V1 a, V1 a) -> Int

Generic (V1 a)

Associated Types

type Rep (V1 a) :: * -> *

Methods

from :: V1 a -> Rep (V1 a) x

to :: Rep (V1 a) x -> V1 a

Storable a => Storable (V1 a)

Methods

sizeOf :: V1 a -> Int

alignment :: V1 a -> Int

peekElemOff :: Ptr (V1 a) -> Int -> IO (V1 a)

pokeElemOff :: Ptr (V1 a) -> Int -> V1 a -> IO ()

peekByteOff :: Ptr b -> Int -> IO (V1 a)

pokeByteOff :: Ptr b -> Int -> V1 a -> IO ()

peek :: Ptr (V1 a) -> IO (V1 a)

poke :: Ptr (V1 a) -> V1 a -> IO ()

Binary a => Binary (V1 a)

Methods

put :: V1 a -> Put

get :: Get (V1 a)

Serial a => Serial (V1 a)

Methods

serialize :: MonadPut m => V1 a -> m ()

deserialize :: MonadGet m => m (V1 a)

Serialize a => Serialize (V1 a)

Methods

put :: Putter (V1 a)

get :: Get (V1 a)

NFData a => NFData (V1 a)

Methods

rnf :: V1 a -> ()

Hashable a => Hashable (V1 a)

Methods

hashWithSalt :: Int -> V1 a -> Int

hash :: V1 a -> Int

Unbox a => Unbox (V1 a)

Ixed (V1 a)

Methods

ix :: Index (V1 a) -> Traversal' (V1 a) (IxValue (V1 a))

Epsilon a => Epsilon (V1 a)

Methods

nearZero :: V1 a -> Bool

FunctorWithIndex (E V1) V1

Methods

imap :: (E V1 -> a -> b) -> V1 a -> V1 b

imapped :: (Indexable (E V1) p, Settable f) => p a (f b) -> V1 a -> f (V1 b)

FoldableWithIndex (E V1) V1

Methods

ifoldMap :: Monoid m => (E V1 -> a -> m) -> V1 a -> m

ifolded :: (Indexable (E V1) p, Contravariant f, Applicative f) => p a (f a) -> V1 a -> f (V1 a)

ifoldr :: (E V1 -> a -> b -> b) -> b -> V1 a -> b

ifoldl :: (E V1 -> b -> a -> b) -> b -> V1 a -> b

ifoldr' :: (E V1 -> a -> b -> b) -> b -> V1 a -> b

ifoldl' :: (E V1 -> b -> a -> b) -> b -> V1 a -> b

TraversableWithIndex (E V1) V1

Methods

itraverse :: Applicative f => (E V1 -> a -> f b) -> V1 a -> f (V1 b)

itraversed :: (Indexable (E V1) p, Applicative f) => p a (f b) -> V1 a -> f (V1 b)

Each (V1 a) (V1 b) a b

Methods

each :: Traversal (V1 a) (V1 b) a b

type Rep1 V1

type Rep V1 = E V1

type Diff V1 = V1

data MVector s (V1 a) = MV_V1 (MVector s a)

type Rep (V1 a)

data Vector (V1 a) = V_V1 (Vector a)

type Index (V1 a) = E V1

type IxValue (V1 a) = a

class R1 t where

A space that has at least 1 basis vector _x.

Minimal complete definition

Nothing

Methods

_x :: Lens' (t a) a

>>> V1 2 ^._x
2

>>> V1 2 & _x .~ 3
V1 3

Instances

R1 Identity

Methods

_x :: Functor f => (a -> f a) -> Identity a -> f (Identity a)

R1 V1

Methods

_x :: Functor f => (a -> f a) -> V1 a -> f (V1 a)

R1 V2

Methods

_x :: Functor f => (a -> f a) -> V2 a -> f (V2 a)

R1 V3

Methods

_x :: Functor f => (a -> f a) -> V3 a -> f (V3 a)

R1 V4

Methods

_x :: Functor f => (a -> f a) -> V4 a -> f (V4 a)

R1 f => R1 (Point f)

Methods

_x :: Functor b => (a -> b a) -> Point f a -> b (Point f a)

ex :: R1 t => E t