Copyright	(C) 2012-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	experimental
Portability	non-portable
Safe Haskell	Trustworthy
Language	Haskell2010

Linear.V1

Description

1-D Vectors

Synopsis

newtype V1 a = V1 a
class R1 t where
- _x :: Lens' (t a) a
ex :: R1 t => E t

Documentation

newtype V1 a Source #

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 Source #
Instance details Defined in Linear.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 Source #
Instance details Defined in Linear.V1 Methods fmap :: (a -> b) -> V1 a -> V1 b # (<$) :: a -> V1 b -> V1 a #
MonadFix V1 Source #
Instance details Defined in Linear.V1 Methods mfix :: (a -> V1 a) -> V1 a #
Applicative V1 Source #
Instance details Defined in Linear.V1 Methods pure :: a -> V1 a # (<>) :: V1 (a -> b) -> V1 a -> V1 b # liftA2 :: (a -> b -> c) -> V1 a -> V1 b -> V1 c # (>) :: V1 a -> V1 b -> V1 b # (<*) :: V1 a -> V1 b -> V1 a #
Foldable V1 Source #
Instance details Defined in Linear.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 Source #
Instance details Defined in Linear.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) #
Distributive V1 Source #
Instance details Defined in Linear.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 Source #
Instance details Defined in Linear.V1 Associated Types type Rep V1 :: Type # Methods tabulate :: (Rep V1 -> a) -> V1 a # index :: V1 a -> Rep V1 -> a #
Eq1 V1 Source #
Instance details Defined in Linear.V1 Methods liftEq :: (a -> b -> Bool) -> V1 a -> V1 b -> Bool #
Ord1 V1 Source #
Instance details Defined in Linear.V1 Methods liftCompare :: (a -> b -> Ordering) -> V1 a -> V1 b -> Ordering #
Read1 V1 Source #
Instance details Defined in Linear.V1 Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V1 a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V1 a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (V1 a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [V1 a] #
Show1 V1 Source #
Instance details Defined in Linear.V1 Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V1 a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V1 a] -> ShowS #
MonadZip V1 Source #
Instance details Defined in Linear.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 Source #
Instance details Defined in Linear.V1 Methods serializeWith :: MonadPut m => (a -> m ()) -> V1 a -> m () # deserializeWith :: MonadGet m => m a -> m (V1 a) #
Hashable1 V1 Source #
Instance details Defined in Linear.V1 Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> V1 a -> Int #
Apply V1 Source #
Instance details Defined in Linear.V1 Methods (<.>) :: V1 (a -> b) -> V1 a -> V1 b # (.>) :: V1 a -> V1 b -> V1 b # (<.) :: V1 a -> V1 b -> V1 a # liftF2 :: (a -> b -> c) -> V1 a -> V1 b -> V1 c #
Traversable1 V1 Source #
Instance details Defined in Linear.V1 Methods traverse1 :: Apply f => (a -> f b) -> V1 a -> f (V1 b) # sequence1 :: Apply f => V1 (f b) -> f (V1 b) #
Foldable1 V1 Source #
Instance details Defined in Linear.V1 Methods fold1 :: Semigroup m => V1 m -> m # foldMap1 :: Semigroup m => (a -> m) -> V1 a -> m # toNonEmpty :: V1 a -> NonEmpty a #
Bind V1 Source #
Instance details Defined in Linear.V1 Methods (>>-) :: V1 a -> (a -> V1 b) -> V1 b # join :: V1 (V1 a) -> V1 a #
Additive V1 Source #
Instance details Defined in Linear.V1 Methods zero :: Num a => V1 a Source # (^+^) :: Num a => V1 a -> V1 a -> V1 a Source # (^-^) :: Num a => V1 a -> V1 a -> V1 a Source # lerp :: Num a => a -> V1 a -> V1 a -> V1 a Source # liftU2 :: (a -> a -> a) -> V1 a -> V1 a -> V1 a Source # liftI2 :: (a -> b -> c) -> V1 a -> V1 b -> V1 c Source #
Metric V1 Source #
Instance details Defined in Linear.V1 Methods dot :: Num a => V1 a -> V1 a -> a Source # quadrance :: Num a => V1 a -> a Source # qd :: Num a => V1 a -> V1 a -> a Source # distance :: Floating a => V1 a -> V1 a -> a Source # norm :: Floating a => V1 a -> a Source # signorm :: Floating a => V1 a -> V1 a Source #
Finite V1 Source #
Instance details Defined in Linear.V1 Associated Types type Size V1 :: Nat Source # Methods toV :: V1 a -> V (Size V1) a Source # fromV :: V (Size V1) a -> V1 a Source #
R1 V1 Source #
Instance details Defined in Linear.V1 Methods _x :: Lens' (V1 a) a Source #
Trace V1 Source #
Instance details Defined in Linear.Trace Methods trace :: Num a => V1 (V1 a) -> a Source # diagonal :: V1 (V1 a) -> V1 a Source #
Affine V1 Source #
Instance details Defined in Linear.Affine Associated Types type Diff V1 :: Type -> Type Source # Methods (.-.) :: Num a => V1 a -> V1 a -> Diff V1 a Source # (.+^) :: Num a => V1 a -> Diff V1 a -> V1 a Source # (.-^) :: Num a => V1 a -> Diff V1 a -> V1 a Source #
Unbox a => Vector Vector (V1 a) Source #
Instance details Defined in Linear.V1 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) Source #
Instance details Defined in Linear.V1 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) Source #
Instance details Defined in Linear.Algebra Methods comult :: (E V1 -> r) -> E V1 -> E V1 -> r Source # counital :: (E V1 -> r) -> r Source #
Num r => Algebra r (E V1) Source #
Instance details Defined in Linear.Algebra Methods mult :: (E V1 -> E V1 -> r) -> E V1 -> r Source # unital :: r -> E V1 -> r Source #
Bounded a => Bounded (V1 a) Source #
Instance details Defined in Linear.V1 Methods minBound :: V1 a # maxBound :: V1 a #
Eq a => Eq (V1 a) Source #
Instance details Defined in Linear.V1 Methods (==) :: V1 a -> V1 a -> Bool # (/=) :: V1 a -> V1 a -> Bool #
Floating a => Floating (V1 a) Source #
Instance details Defined in Linear.V1 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 # log1p :: V1 a -> V1 a # expm1 :: V1 a -> V1 a # log1pexp :: V1 a -> V1 a # log1mexp :: V1 a -> V1 a #
Fractional a => Fractional (V1 a) Source #
Instance details Defined in Linear.V1 Methods (/) :: V1 a -> V1 a -> V1 a # recip :: V1 a -> V1 a # fromRational :: Rational -> V1 a #
Data a => Data (V1 a) Source #
Instance details Defined in Linear.V1 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) Source #
Instance details Defined in Linear.V1 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) Source #
Instance details Defined in Linear.V1 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) Source #
Instance details Defined in Linear.V1 Methods readsPrec :: Int -> ReadS (V1 a) # readList :: ReadS [V1 a] # readPrec :: ReadPrec (V1 a) # readListPrec :: ReadPrec [V1 a] #
Show a => Show (V1 a) Source #
Instance details Defined in Linear.V1 Methods showsPrec :: Int -> V1 a -> ShowS # show :: V1 a -> String # showList :: [V1 a] -> ShowS #
Ix a => Ix (V1 a) Source #
Instance details Defined in Linear.V1 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) Source #
Instance details Defined in Linear.V1 Associated Types type Rep (V1 a) :: Type -> Type # Methods from :: V1 a -> Rep (V1 a) x # to :: Rep (V1 a) x -> V1 a #
Semigroup a => Semigroup (V1 a) Source #
Instance details Defined in Linear.V1 Methods (<>) :: V1 a -> V1 a -> V1 a # sconcat :: NonEmpty (V1 a) -> V1 a # stimes :: Integral b => b -> V1 a -> V1 a #
Monoid a => Monoid (V1 a) Source #
Instance details Defined in Linear.V1 Methods mempty :: V1 a # mappend :: V1 a -> V1 a -> V1 a # mconcat :: [V1 a] -> V1 a #
Lift a => Lift (V1 a) Source #
Instance details Defined in Linear.V1 Methods lift :: V1 a -> Q Exp #
Storable a => Storable (V1 a) Source #
Instance details Defined in Linear.V1 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) Source #
Instance details Defined in Linear.V1 Methods put :: V1 a -> Put # get :: Get (V1 a) # putList :: [V1 a] -> Put #
Serial a => Serial (V1 a) Source #
Instance details Defined in Linear.V1 Methods serialize :: MonadPut m => V1 a -> m () # deserialize :: MonadGet m => m (V1 a) #
Serialize a => Serialize (V1 a) Source #
Instance details Defined in Linear.V1 Methods put :: Putter (V1 a) # get :: Get (V1 a) #
NFData a => NFData (V1 a) Source #
Instance details Defined in Linear.V1 Methods rnf :: V1 a -> () #
Hashable a => Hashable (V1 a) Source #
Instance details Defined in Linear.V1 Methods hashWithSalt :: Int -> V1 a -> Int # hash :: V1 a -> Int #
Unbox a => Unbox (V1 a) Source #
Instance details Defined in Linear.V1
Ixed (V1 a) Source #
Instance details Defined in Linear.V1 Methods ix :: Index (V1 a) -> Traversal' (V1 a) (IxValue (V1 a)) #
Random a => Random (V1 a) Source #
Instance details Defined in Linear.V1 Methods randomR :: RandomGen g => (V1 a, V1 a) -> g -> (V1 a, g) # random :: RandomGen g => g -> (V1 a, g) # randomRs :: RandomGen g => (V1 a, V1 a) -> g -> [V1 a] # randoms :: RandomGen g => g -> [V1 a] #
Epsilon a => Epsilon (V1 a) Source #
Instance details Defined in Linear.V1 Methods nearZero :: V1 a -> Bool Source #
Generic1 V1 Source #
Instance details Defined in Linear.V1 Associated Types type Rep1 V1 :: k -> Type # Methods from1 :: V1 a -> Rep1 V1 a # to1 :: Rep1 V1 a -> V1 a #
FunctorWithIndex (E V1) V1 Source #
Instance details Defined in Linear.V1 Methods imap :: (E V1 -> a -> b) -> V1 a -> V1 b # imapped :: IndexedSetter (E V1) (V1 a) (V1 b) a b #
FoldableWithIndex (E V1) V1 Source #
Instance details Defined in Linear.V1 Methods ifoldMap :: Monoid m => (E V1 -> a -> m) -> V1 a -> m # ifolded :: IndexedFold (E V1) (V1 a) 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 Source #
Instance details Defined in Linear.V1 Methods itraverse :: Applicative f => (E V1 -> a -> f b) -> V1 a -> f (V1 b) # itraversed :: IndexedTraversal (E V1) (V1 a) (V1 b) a b #
Each (V1 a) (V1 b) a b Source #
Instance details Defined in Linear.V1 Methods each :: Traversal (V1 a) (V1 b) a b #
Field1 (V1 a) (V1 b) a b Source #
Instance details Defined in Linear.V1 Methods _1 :: Lens (V1 a) (V1 b) a b #
type Rep V1 Source #
Instance details Defined in Linear.V1 type Rep V1 = E V1
type Size V1 Source #
Instance details Defined in Linear.V1 type Size V1 = 1
type Diff V1 Source #
Instance details Defined in Linear.Affine type Diff V1 = V1
newtype MVector s (V1 a) Source #
Instance details Defined in Linear.V1 newtype MVector s (V1 a) = MV_V1 (MVector s a)
type Rep (V1 a) Source #
Instance details Defined in Linear.V1 type Rep (V1 a) = D1 (MetaData "V1" "Linear.V1" "linear-1.21.3-4VKk0ANeJOgJLRUVoSPnwE" True) (C1 (MetaCons "V1" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
newtype Vector (V1 a) Source #
Instance details Defined in Linear.V1 newtype Vector (V1 a) = V_V1 (Vector a)
type Index (V1 a) Source #
Instance details Defined in Linear.V1 type Index (V1 a) = E V1
type IxValue (V1 a) Source #
Instance details Defined in Linear.V1 type IxValue (V1 a) = a
type Rep1 V1 Source #
Instance details Defined in Linear.V1 type Rep1 V1 = D1 (MetaData "V1" "Linear.V1" "linear-1.21.3-4VKk0ANeJOgJLRUVoSPnwE" True) (C1 (MetaCons "V1" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

class R1 t where Source #

A space that has at least 1 basis vector _x.

Methods

_x :: Lens' (t a) a Source #

>>> V1 2 ^._x
2

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

Instances

R1 Identity Source #
Instance details Defined in Linear.V1 Methods _x :: Lens' (Identity a) a Source #
R1 V1 Source #
Instance details Defined in Linear.V1 Methods _x :: Lens' (V1 a) a Source #
R1 V2 Source #
Instance details Defined in Linear.V2 Methods _x :: Lens' (V2 a) a Source #
R1 V3 Source #
Instance details Defined in Linear.V3 Methods _x :: Lens' (V3 a) a Source #
R1 V4 Source #
Instance details Defined in Linear.V4 Methods _x :: Lens' (V4 a) a Source #
R1 Quaternion Source #
Instance details Defined in Linear.Quaternion Methods _x :: Lens' (Quaternion a) a Source #
R1 f => R1 (Point f) Source #
Instance details Defined in Linear.Affine Methods _x :: Lens' (Point f a) a Source #

ex :: R1 t => E t Source #