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.V0

Description

0-D Vectors

Synopsis

data V0 a = V0

Documentation

data V0 a Source #

A 0-dimensional vector

>>> pure 1 :: V0 Int
V0

>>> V0 + V0
V0

Constructors

V0

Instances

Monad V0 Source #
Instance details Defined in Linear.V0 Methods (>>=) :: V0 a -> (a -> V0 b) -> V0 b # (>>) :: V0 a -> V0 b -> V0 b # return :: a -> V0 a # fail :: String -> V0 a #
Functor V0 Source #
Instance details Defined in Linear.V0 Methods fmap :: (a -> b) -> V0 a -> V0 b # (<$) :: a -> V0 b -> V0 a #
MonadFix V0 Source #
Instance details Defined in Linear.V0 Methods mfix :: (a -> V0 a) -> V0 a #
Applicative V0 Source #
Instance details Defined in Linear.V0 Methods pure :: a -> V0 a # (<>) :: V0 (a -> b) -> V0 a -> V0 b # liftA2 :: (a -> b -> c) -> V0 a -> V0 b -> V0 c # (>) :: V0 a -> V0 b -> V0 b # (<*) :: V0 a -> V0 b -> V0 a #
Foldable V0 Source #
Instance details Defined in Linear.V0 Methods fold :: Monoid m => V0 m -> m # foldMap :: Monoid m => (a -> m) -> V0 a -> m # foldr :: (a -> b -> b) -> b -> V0 a -> b # foldr' :: (a -> b -> b) -> b -> V0 a -> b # foldl :: (b -> a -> b) -> b -> V0 a -> b # foldl' :: (b -> a -> b) -> b -> V0 a -> b # foldr1 :: (a -> a -> a) -> V0 a -> a # foldl1 :: (a -> a -> a) -> V0 a -> a # toList :: V0 a -> [a] # null :: V0 a -> Bool # length :: V0 a -> Int # elem :: Eq a => a -> V0 a -> Bool # maximum :: Ord a => V0 a -> a # minimum :: Ord a => V0 a -> a # sum :: Num a => V0 a -> a # product :: Num a => V0 a -> a #
Traversable V0 Source #
Instance details Defined in Linear.V0 Methods traverse :: Applicative f => (a -> f b) -> V0 a -> f (V0 b) # sequenceA :: Applicative f => V0 (f a) -> f (V0 a) # mapM :: Monad m => (a -> m b) -> V0 a -> m (V0 b) # sequence :: Monad m => V0 (m a) -> m (V0 a) #
Distributive V0 Source #
Instance details Defined in Linear.V0 Methods distribute :: Functor f => f (V0 a) -> V0 (f a) # collect :: Functor f => (a -> V0 b) -> f a -> V0 (f b) # distributeM :: Monad m => m (V0 a) -> V0 (m a) # collectM :: Monad m => (a -> V0 b) -> m a -> V0 (m b) #
Representable V0 Source #
Instance details Defined in Linear.V0 Associated Types type Rep V0 :: Type # Methods tabulate :: (Rep V0 -> a) -> V0 a # index :: V0 a -> Rep V0 -> a #
Eq1 V0 Source #
Instance details Defined in Linear.V0 Methods liftEq :: (a -> b -> Bool) -> V0 a -> V0 b -> Bool #
Ord1 V0 Source #
Instance details Defined in Linear.V0 Methods liftCompare :: (a -> b -> Ordering) -> V0 a -> V0 b -> Ordering #
Read1 V0 Source #
Instance details Defined in Linear.V0 Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V0 a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V0 a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (V0 a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [V0 a] #
Show1 V0 Source #
Instance details Defined in Linear.V0 Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V0 a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V0 a] -> ShowS #
MonadZip V0 Source #
Instance details Defined in Linear.V0 Methods mzip :: V0 a -> V0 b -> V0 (a, b) # mzipWith :: (a -> b -> c) -> V0 a -> V0 b -> V0 c # munzip :: V0 (a, b) -> (V0 a, V0 b) #
Serial1 V0 Source #
Instance details Defined in Linear.V0 Methods serializeWith :: MonadPut m => (a -> m ()) -> V0 a -> m () # deserializeWith :: MonadGet m => m a -> m (V0 a) #
Hashable1 V0 Source #
Instance details Defined in Linear.V0 Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> V0 a -> Int #
Apply V0 Source #
Instance details Defined in Linear.V0 Methods (<.>) :: V0 (a -> b) -> V0 a -> V0 b # (.>) :: V0 a -> V0 b -> V0 b # (<.) :: V0 a -> V0 b -> V0 a # liftF2 :: (a -> b -> c) -> V0 a -> V0 b -> V0 c #
Bind V0 Source #
Instance details Defined in Linear.V0 Methods (>>-) :: V0 a -> (a -> V0 b) -> V0 b # join :: V0 (V0 a) -> V0 a #
Additive V0 Source #
Instance details Defined in Linear.V0 Methods zero :: Num a => V0 a Source # (^+^) :: Num a => V0 a -> V0 a -> V0 a Source # (^-^) :: Num a => V0 a -> V0 a -> V0 a Source # lerp :: Num a => a -> V0 a -> V0 a -> V0 a Source # liftU2 :: (a -> a -> a) -> V0 a -> V0 a -> V0 a Source # liftI2 :: (a -> b -> c) -> V0 a -> V0 b -> V0 c Source #
Metric V0 Source #
Instance details Defined in Linear.V0 Methods dot :: Num a => V0 a -> V0 a -> a Source # quadrance :: Num a => V0 a -> a Source # qd :: Num a => V0 a -> V0 a -> a Source # distance :: Floating a => V0 a -> V0 a -> a Source # norm :: Floating a => V0 a -> a Source # signorm :: Floating a => V0 a -> V0 a Source #
Finite V0 Source #
Instance details Defined in Linear.V0 Associated Types type Size V0 :: Nat Source # Methods toV :: V0 a -> V (Size V0) a Source # fromV :: V (Size V0) a -> V0 a Source #
Trace V0 Source #
Instance details Defined in Linear.Trace Methods trace :: Num a => V0 (V0 a) -> a Source # diagonal :: V0 (V0 a) -> V0 a Source #
Affine V0 Source #
Instance details Defined in Linear.Affine Associated Types type Diff V0 :: Type -> Type Source # Methods (.-.) :: Num a => V0 a -> V0 a -> Diff V0 a Source # (.+^) :: Num a => V0 a -> Diff V0 a -> V0 a Source # (.-^) :: Num a => V0 a -> Diff V0 a -> V0 a Source #
Vector Vector (V0 a) Source #
Instance details Defined in Linear.V0 Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V0 a) -> m (Vector (V0 a)) # basicUnsafeThaw :: PrimMonad m => Vector (V0 a) -> m (Mutable Vector (PrimState m) (V0 a)) # basicLength :: Vector (V0 a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (V0 a) -> Vector (V0 a) # basicUnsafeIndexM :: Monad m => Vector (V0 a) -> Int -> m (V0 a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V0 a) -> Vector (V0 a) -> m () # elemseq :: Vector (V0 a) -> V0 a -> b -> b #
MVector MVector (V0 a) Source #
Instance details Defined in Linear.V0 Methods basicLength :: MVector s (V0 a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (V0 a) -> MVector s (V0 a) # basicOverlaps :: MVector s (V0 a) -> MVector s (V0 a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V0 a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (V0 a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> V0 a -> m (MVector (PrimState m) (V0 a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V0 a) -> Int -> m (V0 a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V0 a) -> Int -> V0 a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (V0 a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (V0 a) -> V0 a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V0 a) -> MVector (PrimState m) (V0 a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V0 a) -> MVector (PrimState m) (V0 a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V0 a) -> Int -> m (MVector (PrimState m) (V0 a)) #
Num r => Coalgebra r (E V0) Source #
Instance details Defined in Linear.Algebra Methods comult :: (E V0 -> r) -> E V0 -> E V0 -> r Source # counital :: (E V0 -> r) -> r Source #
Num r => Algebra r (E V0) Source #
Instance details Defined in Linear.Algebra Methods mult :: (E V0 -> E V0 -> r) -> E V0 -> r Source # unital :: r -> E V0 -> r Source #
Bounded (V0 a) Source #
Instance details Defined in Linear.V0 Methods minBound :: V0 a # maxBound :: V0 a #
Enum (V0 a) Source #
Instance details Defined in Linear.V0 Methods succ :: V0 a -> V0 a # pred :: V0 a -> V0 a # toEnum :: Int -> V0 a # fromEnum :: V0 a -> Int # enumFrom :: V0 a -> [V0 a] # enumFromThen :: V0 a -> V0 a -> [V0 a] # enumFromTo :: V0 a -> V0 a -> [V0 a] # enumFromThenTo :: V0 a -> V0 a -> V0 a -> [V0 a] #
Eq (V0 a) Source #
Instance details Defined in Linear.V0 Methods (==) :: V0 a -> V0 a -> Bool # (/=) :: V0 a -> V0 a -> Bool #
Floating (V0 a) Source #
Instance details Defined in Linear.V0 Methods pi :: V0 a # exp :: V0 a -> V0 a # log :: V0 a -> V0 a # sqrt :: V0 a -> V0 a # (**) :: V0 a -> V0 a -> V0 a # logBase :: V0 a -> V0 a -> V0 a # sin :: V0 a -> V0 a # cos :: V0 a -> V0 a # tan :: V0 a -> V0 a # asin :: V0 a -> V0 a # acos :: V0 a -> V0 a # atan :: V0 a -> V0 a # sinh :: V0 a -> V0 a # cosh :: V0 a -> V0 a # tanh :: V0 a -> V0 a # asinh :: V0 a -> V0 a # acosh :: V0 a -> V0 a # atanh :: V0 a -> V0 a # log1p :: V0 a -> V0 a # expm1 :: V0 a -> V0 a # log1pexp :: V0 a -> V0 a # log1mexp :: V0 a -> V0 a #
Fractional (V0 a) Source #
Instance details Defined in Linear.V0 Methods (/) :: V0 a -> V0 a -> V0 a # recip :: V0 a -> V0 a # fromRational :: Rational -> V0 a #
Data a => Data (V0 a) Source #
Instance details Defined in Linear.V0 Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> V0 a -> c (V0 a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (V0 a) # toConstr :: V0 a -> Constr # dataTypeOf :: V0 a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (V0 a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V0 a)) # gmapT :: (forall b. Data b => b -> b) -> V0 a -> V0 a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V0 a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V0 a -> r # gmapQ :: (forall d. Data d => d -> u) -> V0 a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> V0 a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> V0 a -> m (V0 a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> V0 a -> m (V0 a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> V0 a -> m (V0 a) #
Num (V0 a) Source #
Instance details Defined in Linear.V0 Methods (+) :: V0 a -> V0 a -> V0 a # (-) :: V0 a -> V0 a -> V0 a # (*) :: V0 a -> V0 a -> V0 a # negate :: V0 a -> V0 a # abs :: V0 a -> V0 a # signum :: V0 a -> V0 a # fromInteger :: Integer -> V0 a #
Ord (V0 a) Source #
Instance details Defined in Linear.V0 Methods compare :: V0 a -> V0 a -> Ordering # (<) :: V0 a -> V0 a -> Bool # (<=) :: V0 a -> V0 a -> Bool # (>) :: V0 a -> V0 a -> Bool # (>=) :: V0 a -> V0 a -> Bool # max :: V0 a -> V0 a -> V0 a # min :: V0 a -> V0 a -> V0 a #
Read (V0 a) Source #
Instance details Defined in Linear.V0 Methods readsPrec :: Int -> ReadS (V0 a) # readList :: ReadS [V0 a] # readPrec :: ReadPrec (V0 a) # readListPrec :: ReadPrec [V0 a] #
Show (V0 a) Source #
Instance details Defined in Linear.V0 Methods showsPrec :: Int -> V0 a -> ShowS # show :: V0 a -> String # showList :: [V0 a] -> ShowS #
Ix (V0 a) Source #
Instance details Defined in Linear.V0 Methods range :: (V0 a, V0 a) -> [V0 a] # index :: (V0 a, V0 a) -> V0 a -> Int # unsafeIndex :: (V0 a, V0 a) -> V0 a -> Int inRange :: (V0 a, V0 a) -> V0 a -> Bool # rangeSize :: (V0 a, V0 a) -> Int # unsafeRangeSize :: (V0 a, V0 a) -> Int
Generic (V0 a) Source #
Instance details Defined in Linear.V0 Associated Types type Rep (V0 a) :: Type -> Type # Methods from :: V0 a -> Rep (V0 a) x # to :: Rep (V0 a) x -> V0 a #
Semigroup (V0 a) Source #
Instance details Defined in Linear.V0 Methods (<>) :: V0 a -> V0 a -> V0 a # sconcat :: NonEmpty (V0 a) -> V0 a # stimes :: Integral b => b -> V0 a -> V0 a #
Monoid (V0 a) Source #
Instance details Defined in Linear.V0 Methods mempty :: V0 a # mappend :: V0 a -> V0 a -> V0 a # mconcat :: [V0 a] -> V0 a #
Lift (V0 a) Source #
Instance details Defined in Linear.V0 Methods lift :: V0 a -> Q Exp #
Storable (V0 a) Source #
Instance details Defined in Linear.V0 Methods sizeOf :: V0 a -> Int # alignment :: V0 a -> Int # peekElemOff :: Ptr (V0 a) -> Int -> IO (V0 a) # pokeElemOff :: Ptr (V0 a) -> Int -> V0 a -> IO () # peekByteOff :: Ptr b -> Int -> IO (V0 a) # pokeByteOff :: Ptr b -> Int -> V0 a -> IO () # peek :: Ptr (V0 a) -> IO (V0 a) # poke :: Ptr (V0 a) -> V0 a -> IO () #
Binary (V0 a) Source #
Instance details Defined in Linear.V0 Methods put :: V0 a -> Put # get :: Get (V0 a) # putList :: [V0 a] -> Put #
Serial (V0 a) Source #
Instance details Defined in Linear.V0 Methods serialize :: MonadPut m => V0 a -> m () # deserialize :: MonadGet m => m (V0 a) #
Serialize (V0 a) Source #
Instance details Defined in Linear.V0 Methods put :: Putter (V0 a) # get :: Get (V0 a) #
NFData (V0 a) Source #
Instance details Defined in Linear.V0 Methods rnf :: V0 a -> () #
Hashable (V0 a) Source #
Instance details Defined in Linear.V0 Methods hashWithSalt :: Int -> V0 a -> Int # hash :: V0 a -> Int #
Unbox (V0 a) Source #
Instance details Defined in Linear.V0
Ixed (V0 a) Source #
Instance details Defined in Linear.V0 Methods ix :: Index (V0 a) -> Traversal' (V0 a) (IxValue (V0 a)) #
Random (V0 a) Source #
Instance details Defined in Linear.V0 Methods randomR :: RandomGen g => (V0 a, V0 a) -> g -> (V0 a, g) # random :: RandomGen g => g -> (V0 a, g) # randomRs :: RandomGen g => (V0 a, V0 a) -> g -> [V0 a] # randoms :: RandomGen g => g -> [V0 a] #
Epsilon (V0 a) Source #
Instance details Defined in Linear.V0 Methods nearZero :: V0 a -> Bool Source #
Generic1 V0 Source #
Instance details Defined in Linear.V0 Associated Types type Rep1 V0 :: k -> Type # Methods from1 :: V0 a -> Rep1 V0 a # to1 :: Rep1 V0 a -> V0 a #
FunctorWithIndex (E V0) V0 Source #
Instance details Defined in Linear.V0 Methods imap :: (E V0 -> a -> b) -> V0 a -> V0 b # imapped :: IndexedSetter (E V0) (V0 a) (V0 b) a b #
FoldableWithIndex (E V0) V0 Source #
Instance details Defined in Linear.V0 Methods ifoldMap :: Monoid m => (E V0 -> a -> m) -> V0 a -> m # ifolded :: IndexedFold (E V0) (V0 a) a # ifoldr :: (E V0 -> a -> b -> b) -> b -> V0 a -> b # ifoldl :: (E V0 -> b -> a -> b) -> b -> V0 a -> b # ifoldr' :: (E V0 -> a -> b -> b) -> b -> V0 a -> b # ifoldl' :: (E V0 -> b -> a -> b) -> b -> V0 a -> b #
TraversableWithIndex (E V0) V0 Source #
Instance details Defined in Linear.V0 Methods itraverse :: Applicative f => (E V0 -> a -> f b) -> V0 a -> f (V0 b) # itraversed :: IndexedTraversal (E V0) (V0 a) (V0 b) a b #
Each (V0 a) (V0 b) a b Source #
Instance details Defined in Linear.V0 Methods each :: Traversal (V0 a) (V0 b) a b #
type Rep V0 Source #
Instance details Defined in Linear.V0 type Rep V0 = E V0
type Size V0 Source #
Instance details Defined in Linear.V0 type Size V0 = 0
type Diff V0 Source #
Instance details Defined in Linear.Affine type Diff V0 = V0
newtype MVector s (V0 a) Source #
Instance details Defined in Linear.V0 newtype MVector s (V0 a) = MV_V0 Int
type Rep (V0 a) Source #
Instance details Defined in Linear.V0 type Rep (V0 a) = D1 (MetaData "V0" "Linear.V0" "linear-1.21.3-4VKk0ANeJOgJLRUVoSPnwE" False) (C1 (MetaCons "V0" PrefixI False) (U1 :: Type -> Type))
newtype Vector (V0 a) Source #
Instance details Defined in Linear.V0 newtype Vector (V0 a) = V_V0 Int
type Index (V0 a) Source #
Instance details Defined in Linear.V0 type Index (V0 a) = E V0
type IxValue (V0 a) Source #
Instance details Defined in Linear.V0 type IxValue (V0 a) = a
type Rep1 V0 Source #
Instance details Defined in Linear.V0 type Rep1 V0 = D1 (MetaData "V0" "Linear.V0" "linear-1.21.3-4VKk0ANeJOgJLRUVoSPnwE" False) (C1 (MetaCons "V0" PrefixI False) (U1 :: Type -> Type))