linear-1.20.7: Linear Algebra

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 | Haskell98

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 # |
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 # |
Methods fmap :: (a -> b) -> V0 a -> V0 b # (<$) :: a -> V0 b -> V0 a #
MonadFix V0 Source # |
Methods mfix :: (a -> V0 a) -> V0 a #
Applicative V0 Source # |
Methods pure :: a -> V0 a # (<*>) :: V0 (a -> b) -> V0 a -> V0 b # (*>) :: V0 a -> V0 b -> V0 b # (<*) :: V0 a -> V0 b -> V0 a #
Foldable V0 Source # |

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 # |
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) #
Generic1 V0 Source # |
Associated Types type Rep1 (V0 :: * -> *) :: * -> * # Methods from1 :: V0 a -> Rep1 V0 a # to1 :: Rep1 V0 a -> V0 a #
Distributive V0 Source # |
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 # |
Associated Types type Rep (V0 :: * -> *) :: * # Methods tabulate :: (Rep V0 -> a) -> V0 a # index :: V0 a -> Rep V0 -> a #
Eq1 V0 Source # |
Methods liftEq :: (a -> b -> Bool) -> V0 a -> V0 b -> Bool #
Ord1 V0 Source # |
Methods liftCompare :: (a -> b -> Ordering) -> V0 a -> V0 b -> Ordering #
Read1 V0 Source # |
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V0 a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V0 a] #
Show1 V0 Source # |
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V0 a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V0 a] -> ShowS #
MonadZip V0 Source # |
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 # |
Methods serializeWith :: MonadPut m => (a -> m ()) -> V0 a -> m () # deserializeWith :: MonadGet m => m a -> m (V0 a) #
Apply V0 Source # |
Methods (<.>) :: V0 (a -> b) -> V0 a -> V0 b # (.>) :: V0 a -> V0 b -> V0 b # (<.) :: V0 a -> V0 b -> V0 a #
Bind V0 Source # |
Methods (>>-) :: V0 a -> (a -> V0 b) -> V0 b # join :: V0 (V0 a) -> V0 a #
Additive V0 Source # |
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 # |
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 # |
Associated Types type Size (V0 :: * -> *) :: Nat Source # Methods toV :: V0 a -> V Nat (Size V0) a Source # fromV :: V Nat (Size V0) a -> V0 a Source #
Trace V0 Source # |
Methods trace :: Num a => V0 (V0 a) -> a Source # diagonal :: V0 (V0 a) -> V0 a Source #
Affine V0 Source # |
Associated Types type Diff (V0 :: * -> *) :: * -> * 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 # |

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 # |

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 # |
Methods comult :: (E V0 -> r) -> E V0 -> E V0 -> r Source # counital :: (E V0 -> r) -> r Source #
Num r => Algebra r (E V0) Source # |
Methods mult :: (E V0 -> E V0 -> r) -> E V0 -> r Source # unital :: r -> E V0 -> r Source #
Bounded (V0 a) Source # |
Methods minBound :: V0 a # maxBound :: V0 a #
Enum (V0 a) Source # |
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 # |
Methods (==) :: V0 a -> V0 a -> Bool # (/=) :: V0 a -> V0 a -> Bool #
Floating (V0 a) Source # |

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 # |
Methods (/) :: V0 a -> V0 a -> V0 a # recip :: V0 a -> V0 a # fromRational :: Rational -> V0 a #
Data a => Data (V0 a) Source # |

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 # |
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 # |
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 # |
Methods readsPrec :: Int -> ReadS (V0 a) # readList :: ReadS [V0 a] # readPrec :: ReadPrec (V0 a) # readListPrec :: ReadPrec [V0 a] #
Show (V0 a) Source # |
Methods showsPrec :: Int -> V0 a -> ShowS # show :: V0 a -> String # showList :: [V0 a] -> ShowS #
Ix (V0 a) Source # |
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 # |
Associated Types type Rep (V0 a) :: * -> * # Methods from :: V0 a -> Rep (V0 a) x # to :: Rep (V0 a) x -> V0 a #
Storable (V0 a) Source # |
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 # |
Methods put :: V0 a -> Put # get :: Get (V0 a) # putList :: [V0 a] -> Put #
Serial (V0 a) Source # |
Methods serialize :: MonadPut m => V0 a -> m () # deserialize :: MonadGet m => m (V0 a) #
Serialize (V0 a) Source # |
Methods put :: Putter (V0 a) # get :: Get (V0 a) #
NFData (V0 a) Source # |
Methods rnf :: V0 a -> () #
Hashable (V0 a) Source # |
Methods hashWithSalt :: Int -> V0 a -> Int # hash :: V0 a -> Int #
Unbox (V0 a) Source # |
Ixed (V0 a) Source # |
Methods ix :: Index (V0 a) -> Traversal' (V0 a) (IxValue (V0 a)) #
Epsilon (V0 a) Source # |
Methods nearZero :: V0 a -> Bool Source #
FunctorWithIndex (E V0) V0 Source # |
Methods imap :: (E V0 -> a -> b) -> V0 a -> V0 b # imapped :: (Indexable (E V0) p, Settable f) => p a (f b) -> V0 a -> f (V0 b) #
FoldableWithIndex (E V0) V0 Source # |
Methods ifoldMap :: Monoid m => (E V0 -> a -> m) -> V0 a -> m # ifolded :: (Indexable (E V0) p, Contravariant f, Applicative f) => p a (f a) -> V0 a -> f (V0 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 # |
Methods itraverse :: Applicative f => (E V0 -> a -> f b) -> V0 a -> f (V0 b) # itraversed :: (Indexable (E V0) p, Applicative f) => p a (f b) -> V0 a -> f (V0 b) #
Each (V0 a) (V0 b) a b Source # |
Methods each :: Traversal (V0 a) (V0 b) a b #
type Rep1 V0 Source # |
type Rep1 V0 = D1 (MetaData "V0" "Linear.V0" "linear-1.20.7-CvaXC2ebC1zHQ7FJwFrAk8" False) (C1 (MetaCons "V0" PrefixI False) U1)
type Rep V0 Source # |
type Rep V0 = E V0
type Size V0 Source # |
type Size V0 = 0
type Diff V0 Source # |
type Diff V0 = V0
data MVector s (V0 a) Source # |
data MVector s (V0 a) = MV_V0 Int
type Rep (V0 a) Source # |
type Rep (V0 a) = D1 (MetaData "V0" "Linear.V0" "linear-1.20.7-CvaXC2ebC1zHQ7FJwFrAk8" False) (C1 (MetaCons "V0" PrefixI False) U1)
data Vector (V0 a) Source # |
data Vector (V0 a) = V_V0 Int
type Index (V0 a) Source # |
type Index (V0 a) = E V0
type IxValue (V0 a) Source # |
type IxValue (V0 a) = a