free-vector-spaces-0.1.5.1: Instantiate the classes from the vector-space package with types from linear
Copyright(c) Justus Sagemüller 2016
LicenseGPL v3
Maintainer(@) jsag $ hvl.no
Stabilityexperimental
Portabilityportable
Safe HaskellNone
LanguageHaskell2010

Data.VectorSpace.Free

Description

 
Synopsis

Supported types

Fixed low dimension

These come from the linear package.

data V0 a #

A 0-dimensional vector

>>> pure 1 :: V0 Int
V0
>>> V0 + V0
V0

Instances

Instances details
Monad V0 
Instance details

Defined in Linear.V0

Methods

(>>=) :: V0 a -> (a -> V0 b) -> V0 b #

(>>) :: V0 a -> V0 b -> V0 b #

return :: a -> V0 a #

Functor V0 
Instance details

Defined in Linear.V0

Methods

fmap :: (a -> b) -> V0 a -> V0 b #

(<$) :: a -> V0 b -> V0 a #

MonadFix V0 
Instance details

Defined in Linear.V0

Methods

mfix :: (a -> V0 a) -> V0 a #

Applicative V0 
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 
Instance details

Defined in Linear.V0

Methods

fold :: Monoid m => V0 m -> m #

foldMap :: Monoid m => (a -> m) -> V0 a -> 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 
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 
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 
Instance details

Defined in Linear.V0

Associated Types

type Rep V0 #

Methods

tabulate :: (Rep V0 -> a) -> V0 a #

index :: V0 a -> Rep V0 -> a #

Eq1 V0 
Instance details

Defined in Linear.V0

Methods

liftEq :: (a -> b -> Bool) -> V0 a -> V0 b -> Bool #

Ord1 V0 
Instance details

Defined in Linear.V0

Methods

liftCompare :: (a -> b -> Ordering) -> V0 a -> V0 b -> Ordering #

Read1 V0 
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 
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 
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 
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 
Instance details

Defined in Linear.V0

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> V0 a -> Int #

Apply V0 
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 #

Affine V0 
Instance details

Defined in Linear.Affine

Associated Types

type Diff V0 :: Type -> Type #

Methods

(.-.) :: Num a => V0 a -> V0 a -> Diff V0 a #

(.+^) :: Num a => V0 a -> Diff V0 a -> V0 a #

(.-^) :: Num a => V0 a -> Diff V0 a -> V0 a #

Finite V0 
Instance details

Defined in Linear.V0

Associated Types

type Size V0 :: Nat #

Methods

toV :: V0 a -> V (Size V0) a #

fromV :: V (Size V0) a -> V0 a #

Metric V0 
Instance details

Defined in Linear.V0

Methods

dot :: Num a => V0 a -> V0 a -> a #

quadrance :: Num a => V0 a -> a #

qd :: Num a => V0 a -> V0 a -> a #

distance :: Floating a => V0 a -> V0 a -> a #

norm :: Floating a => V0 a -> a #

signorm :: Floating a => V0 a -> V0 a #

Additive V0 
Instance details

Defined in Linear.V0

Methods

zero :: Num a => V0 a #

(^+^) :: Num a => V0 a -> V0 a -> V0 a #

(^-^) :: Num a => V0 a -> V0 a -> V0 a #

lerp :: Num a => a -> V0 a -> V0 a -> V0 a #

liftU2 :: (a -> a -> a) -> V0 a -> V0 a -> V0 a #

liftI2 :: (a -> b -> c) -> V0 a -> V0 b -> V0 c #

Bind V0 
Instance details

Defined in Linear.V0

Methods

(>>-) :: V0 a -> (a -> V0 b) -> V0 b #

join :: V0 (V0 a) -> V0 a #

Lift (V0 a :: Type) 
Instance details

Defined in Linear.V0

Methods

lift :: V0 a -> Q Exp #

liftTyped :: V0 a -> Q (TExp (V0 a)) #

Vector Vector (V0 a) 
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) 
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)) #

Bounded (V0 a) 
Instance details

Defined in Linear.V0

Methods

minBound :: V0 a #

maxBound :: V0 a #

Enum (V0 a) 
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) 
Instance details

Defined in Linear.V0

Methods

(==) :: V0 a -> V0 a -> Bool #

(/=) :: V0 a -> V0 a -> Bool #

Floating (V0 a) 
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) 
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) 
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 :: forall r r'. (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) 
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) 
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) 
Instance details

Defined in Linear.V0

Show (V0 a) 
Instance details

Defined in Linear.V0

Methods

showsPrec :: Int -> V0 a -> ShowS #

show :: V0 a -> String #

showList :: [V0 a] -> ShowS #

Ix (V0 a) 
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) 
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) 
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) 
Instance details

Defined in Linear.V0

Methods

mempty :: V0 a #

mappend :: V0 a -> V0 a -> V0 a #

mconcat :: [V0 a] -> V0 a #

HasTrie (E V0) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

data (:->:) (E V0) :: Type -> Type #

Methods

trie :: (E V0 -> b) -> E V0 :->: b #

untrie :: (E V0 :->: b) -> E V0 -> b #

enumerate :: (E V0 :->: b) -> [(E V0, b)] #

Storable (V0 a) 
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) 
Instance details

Defined in Linear.V0

Methods

put :: V0 a -> Put #

get :: Get (V0 a) #

putList :: [V0 a] -> Put #

Serial (V0 a) 
Instance details

Defined in Linear.V0

Methods

serialize :: MonadPut m => V0 a -> m () #

deserialize :: MonadGet m => m (V0 a) #

Serialize (V0 a) 
Instance details

Defined in Linear.V0

Methods

put :: Putter (V0 a) #

get :: Get (V0 a) #

NFData (V0 a) 
Instance details

Defined in Linear.V0

Methods

rnf :: V0 a -> () #

Hashable (V0 a) 
Instance details

Defined in Linear.V0

Methods

hashWithSalt :: Int -> V0 a -> Int #

hash :: V0 a -> Int #

Unbox (V0 a) 
Instance details

Defined in Linear.V0

Ixed (V0 a) 
Instance details

Defined in Linear.V0

Methods

ix :: Index (V0 a) -> Traversal' (V0 a) (IxValue (V0 a)) #

Epsilon (V0 a) 
Instance details

Defined in Linear.V0

Methods

nearZero :: V0 a -> Bool #

Show (V0 Double) Source # 
Instance details

Defined in Data.VectorSpace.Free

Show (V0 Float) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

showsPrec :: Int -> V0 Float -> ShowS #

show :: V0 Float -> String #

showList :: [V0 Float] -> ShowS #

Show (V0 Int) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

showsPrec :: Int -> V0 Int -> ShowS #

show :: V0 Int -> String #

showList :: [V0 Int] -> ShowS #

Show (V0 Integer) Source # 
Instance details

Defined in Data.VectorSpace.Free

Random (V0 a) 
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] #

Num s => AffineSpace (V0 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Diff (V0 s) #

Methods

(.-.) :: V0 s -> V0 s -> Diff (V0 s) #

(.+^) :: V0 s -> Diff (V0 s) -> V0 s #

(Num s, AdditiveGroup s) => HasBasis (V0 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Basis (V0 s) #

Methods

basisValue :: Basis (V0 s) -> V0 s #

decompose :: V0 s -> [(Basis (V0 s), Scalar (V0 s))] #

decompose' :: V0 s -> Basis (V0 s) -> Scalar (V0 s) #

Num s => VectorSpace (V0 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Scalar (V0 s) #

Methods

(*^) :: Scalar (V0 s) -> V0 s -> V0 s #

(Num s, AdditiveGroup s) => InnerSpace (V0 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

(<.>) :: V0 s -> V0 s -> Scalar (V0 s) #

Num s => AdditiveGroup (V0 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

zeroV :: V0 s #

(^+^) :: V0 s -> V0 s -> V0 s #

negateV :: V0 s -> V0 s #

(^-^) :: V0 s -> V0 s -> V0 s #

Num s => FiniteFreeSpace (V0 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Generic1 V0 
Instance details

Defined in Linear.V0

Associated Types

type Rep1 V0 :: k -> Type #

Methods

from1 :: forall (a :: k). V0 a -> Rep1 V0 a #

to1 :: forall (a :: k). Rep1 V0 a -> V0 a #

FunctorWithIndex (E V0) V0 
Instance details

Defined in Linear.V0

Methods

imap :: (E V0 -> a -> b) -> V0 a -> V0 b #

FoldableWithIndex (E V0) V0 
Instance details

Defined in Linear.V0

Methods

ifoldMap :: Monoid m => (E V0 -> a -> m) -> V0 a -> m #

ifoldMap' :: Monoid m => (E V0 -> a -> m) -> V0 a -> m #

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 
Instance details

Defined in Linear.V0

Methods

itraverse :: Applicative f => (E V0 -> a -> f b) -> V0 a -> f (V0 b) #

Each (V0 a) (V0 b) a b 
Instance details

Defined in Linear.V0

Methods

each :: Traversal (V0 a) (V0 b) a b #

Num s => AffineSpace (Point V0 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Diff (Point V0 s) #

Methods

(.-.) :: Point V0 s -> Point V0 s -> Diff (Point V0 s) #

(.+^) :: Point V0 s -> Diff (Point V0 s) -> Point V0 s #

type Rep V0 
Instance details

Defined in Linear.V0

type Rep V0 = E V0
type Diff V0 
Instance details

Defined in Linear.Affine

type Diff V0 = V0
type Size V0 
Instance details

Defined in Linear.V0

type Size V0 = 0
newtype MVector s (V0 a) 
Instance details

Defined in Linear.V0

newtype MVector s (V0 a) = MV_V0 Int
type Rep (V0 a) 
Instance details

Defined in Linear.V0

type Rep (V0 a) = D1 ('MetaData "V0" "Linear.V0" "linear-1.21.8-EtxeJWQbh7CIGwzUT72syQ" 'False) (C1 ('MetaCons "V0" 'PrefixI 'False) (U1 :: Type -> Type))
newtype (E V0) :->: a Source # 
Instance details

Defined in Data.VectorSpace.Free

newtype (E V0) :->: a = V0T (V0 a)
newtype Vector (V0 a) 
Instance details

Defined in Linear.V0

newtype Vector (V0 a) = V_V0 Int
type Index (V0 a) 
Instance details

Defined in Linear.V0

type Index (V0 a) = E V0
type IxValue (V0 a) 
Instance details

Defined in Linear.V0

type IxValue (V0 a) = a
type Diff (V0 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

type Diff (V0 s) = V0 s
type Basis (V0 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

type Basis (V0 s) = E V0
type Scalar (V0 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

type Scalar (V0 s) = s
type Rep1 V0 
Instance details

Defined in Linear.V0

type Rep1 V0 = D1 ('MetaData "V0" "Linear.V0" "linear-1.21.8-EtxeJWQbh7CIGwzUT72syQ" 'False) (C1 ('MetaCons "V0" 'PrefixI 'False) (U1 :: Type -> Type))
type Diff (Point V0 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

type Diff (Point V0 s) = V0 s

data 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

Instances

Instances details
Monad V1 
Instance details

Defined in Linear.V1

Methods

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

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

return :: a -> V1 a #

Functor V1 
Instance details

Defined in Linear.V1

Methods

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

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

MonadFix V1 
Instance details

Defined in Linear.V1

Methods

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

Applicative V1 
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 
Instance details

Defined in Linear.V1

Methods

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

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

Defined in Linear.V1

Associated Types

type Rep V1 #

Methods

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

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

Eq1 V1 
Instance details

Defined in Linear.V1

Methods

liftEq :: (a -> b -> Bool) -> V1 a -> V1 b -> Bool #

Ord1 V1 
Instance details

Defined in Linear.V1

Methods

liftCompare :: (a -> b -> Ordering) -> V1 a -> V1 b -> Ordering #

Read1 V1 
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 
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 
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 
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 
Instance details

Defined in Linear.V1

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> V1 a -> Int #

Apply V1 
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 
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) #

Affine V1 
Instance details

Defined in Linear.Affine

Associated Types

type Diff V1 :: Type -> Type #

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 #

R1 V1 
Instance details

Defined in Linear.V1

Methods

_x :: Lens' (V1 a) a #

Finite V1 
Instance details

Defined in Linear.V1

Associated Types

type Size V1 :: Nat #

Methods

toV :: V1 a -> V (Size V1) a #

fromV :: V (Size V1) a -> V1 a #

Metric V1 
Instance details

Defined in Linear.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 #

Additive V1 
Instance details

Defined in Linear.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 #

Bind V1 
Instance details

Defined in Linear.V1

Methods

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

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

Foldable1 V1 
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 #

Lift a => Lift (V1 a :: Type) 
Instance details

Defined in Linear.V1

Methods

lift :: V1 a -> Q Exp #

liftTyped :: V1 a -> Q (TExp (V1 a)) #

Unbox a => Vector Vector (V1 a) 
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) 
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)) #

Bounded a => Bounded (V1 a) 
Instance details

Defined in Linear.V1

Methods

minBound :: V1 a #

maxBound :: V1 a #

Eq a => Eq (V1 a) 
Instance details

Defined in Linear.V1

Methods

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

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

Floating a => Floating (V1 a) 
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) 
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) 
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 :: forall r r'. (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) 
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) 
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) 
Instance details

Defined in Linear.V1

Show a => Show (V1 a) 
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) 
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) 
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) 
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) 
Instance details

Defined in Linear.V1

Methods

mempty :: V1 a #

mappend :: V1 a -> V1 a -> V1 a #

mconcat :: [V1 a] -> V1 a #

HasTrie (E V1) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

data (:->:) (E V1) :: Type -> Type #

Methods

trie :: (E V1 -> b) -> E V1 :->: b #

untrie :: (E V1 :->: b) -> E V1 -> b #

enumerate :: (E V1 :->: b) -> [(E V1, b)] #

Storable a => Storable (V1 a) 
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) 
Instance details

Defined in Linear.V1

Methods

put :: V1 a -> Put #

get :: Get (V1 a) #

putList :: [V1 a] -> Put #

Serial a => Serial (V1 a) 
Instance details

Defined in Linear.V1

Methods

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

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

Serialize a => Serialize (V1 a) 
Instance details

Defined in Linear.V1

Methods

put :: Putter (V1 a) #

get :: Get (V1 a) #

NFData a => NFData (V1 a) 
Instance details

Defined in Linear.V1

Methods

rnf :: V1 a -> () #

Hashable a => Hashable (V1 a) 
Instance details

Defined in Linear.V1

Methods

hashWithSalt :: Int -> V1 a -> Int #

hash :: V1 a -> Int #

Unbox a => Unbox (V1 a) 
Instance details

Defined in Linear.V1

Ixed (V1 a) 
Instance details

Defined in Linear.V1

Methods

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

Epsilon a => Epsilon (V1 a) 
Instance details

Defined in Linear.V1

Methods

nearZero :: V1 a -> Bool #

Show (V1 Double) Source # 
Instance details

Defined in Data.VectorSpace.Free

Show (V1 Float) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

showsPrec :: Int -> V1 Float -> ShowS #

show :: V1 Float -> String #

showList :: [V1 Float] -> ShowS #

Show (V1 Int) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

showsPrec :: Int -> V1 Int -> ShowS #

show :: V1 Int -> String #

showList :: [V1 Int] -> ShowS #

Show (V1 Integer) Source # 
Instance details

Defined in Data.VectorSpace.Free

Random a => Random (V1 a) 
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] #

Num s => AffineSpace (V1 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Diff (V1 s) #

Methods

(.-.) :: V1 s -> V1 s -> Diff (V1 s) #

(.+^) :: V1 s -> Diff (V1 s) -> V1 s #

(Num s, AdditiveGroup s) => HasBasis (V1 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Basis (V1 s) #

Methods

basisValue :: Basis (V1 s) -> V1 s #

decompose :: V1 s -> [(Basis (V1 s), Scalar (V1 s))] #

decompose' :: V1 s -> Basis (V1 s) -> Scalar (V1 s) #

Num s => VectorSpace (V1 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Scalar (V1 s) #

Methods

(*^) :: Scalar (V1 s) -> V1 s -> V1 s #

(Num s, AdditiveGroup s) => InnerSpace (V1 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

(<.>) :: V1 s -> V1 s -> Scalar (V1 s) #

Num s => AdditiveGroup (V1 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

zeroV :: V1 s #

(^+^) :: V1 s -> V1 s -> V1 s #

negateV :: V1 s -> V1 s #

(^-^) :: V1 s -> V1 s -> V1 s #

Num s => FiniteFreeSpace (V1 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

(Eq r, Fractional r) => OneDimensional (V1 r) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

(^/^) :: V1 r -> V1 r -> Maybe (Scalar (V1 r)) Source #

(^/!) :: V1 r -> V1 r -> Scalar (V1 r) Source #

Generic1 V1 
Instance details

Defined in Linear.V1

Associated Types

type Rep1 V1 :: k -> Type #

Methods

from1 :: forall (a :: k). V1 a -> Rep1 V1 a #

to1 :: forall (a :: k). Rep1 V1 a -> V1 a #

FunctorWithIndex (E V1) V1 
Instance details

Defined in Linear.V1

Methods

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

FoldableWithIndex (E V1) V1 
Instance details

Defined in Linear.V1

Methods

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

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

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 
Instance details

Defined in Linear.V1

Methods

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

Each (V1 a) (V1 b) a b 
Instance details

Defined in Linear.V1

Methods

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

Field1 (V1 a) (V1 b) a b 
Instance details

Defined in Linear.V1

Methods

_1 :: Lens (V1 a) (V1 b) a b #

Num s => AffineSpace (Point V1 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Diff (Point V1 s) #

Methods

(.-.) :: Point V1 s -> Point V1 s -> Diff (Point V1 s) #

(.+^) :: Point V1 s -> Diff (Point V1 s) -> Point V1 s #

type Rep V1 
Instance details

Defined in Linear.V1

type Rep V1 = E V1
type Diff V1 
Instance details

Defined in Linear.Affine

type Diff V1 = V1
type Size V1 
Instance details

Defined in Linear.V1

type Size V1 = 1
newtype MVector s (V1 a) 
Instance details

Defined in Linear.V1

newtype MVector s (V1 a) = MV_V1 (MVector s a)
type Rep (V1 a) 
Instance details

Defined in Linear.V1

type Rep (V1 a) = D1 ('MetaData "V1" "Linear.V1" "linear-1.21.8-EtxeJWQbh7CIGwzUT72syQ" 'True) (C1 ('MetaCons "V1" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
newtype (E V1) :->: a Source # 
Instance details

Defined in Data.VectorSpace.Free

newtype (E V1) :->: a = V1T (V1 a)
newtype Vector (V1 a) 
Instance details

Defined in Linear.V1

newtype Vector (V1 a) = V_V1 (Vector a)
type Index (V1 a) 
Instance details

Defined in Linear.V1

type Index (V1 a) = E V1
type IxValue (V1 a) 
Instance details

Defined in Linear.V1

type IxValue (V1 a) = a
type Diff (V1 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

type Diff (V1 s) = V1 s
type Basis (V1 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

type Basis (V1 s) = E V1
type Scalar (V1 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

type Scalar (V1 s) = s
type Rep1 V1 
Instance details

Defined in Linear.V1

type Rep1 V1 = D1 ('MetaData "V1" "Linear.V1" "linear-1.21.8-EtxeJWQbh7CIGwzUT72syQ" 'True) (C1 ('MetaCons "V1" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type Diff (Point V1 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

type Diff (Point V1 s) = V1 s

data V2 a #

A 2-dimensional vector

>>> pure 1 :: V2 Int
V2 1 1
>>> V2 1 2 + V2 3 4
V2 4 6
>>> V2 1 2 * V2 3 4
V2 3 8
>>> sum (V2 1 2)
3

Instances

Instances details
Monad V2 
Instance details

Defined in Linear.V2

Methods

(>>=) :: V2 a -> (a -> V2 b) -> V2 b #

(>>) :: V2 a -> V2 b -> V2 b #

return :: a -> V2 a #

Functor V2 
Instance details

Defined in Linear.V2

Methods

fmap :: (a -> b) -> V2 a -> V2 b #

(<$) :: a -> V2 b -> V2 a #

MonadFix V2 
Instance details

Defined in Linear.V2

Methods

mfix :: (a -> V2 a) -> V2 a #

Applicative V2 
Instance details

Defined in Linear.V2

Methods

pure :: a -> V2 a #

(<*>) :: V2 (a -> b) -> V2 a -> V2 b #

liftA2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c #

(*>) :: V2 a -> V2 b -> V2 b #

(<*) :: V2 a -> V2 b -> V2 a #

Foldable V2 
Instance details

Defined in Linear.V2

Methods

fold :: Monoid m => V2 m -> m #

foldMap :: Monoid m => (a -> m) -> V2 a -> m #

foldMap' :: Monoid m => (a -> m) -> V2 a -> m #

foldr :: (a -> b -> b) -> b -> V2 a -> b #

foldr' :: (a -> b -> b) -> b -> V2 a -> b #

foldl :: (b -> a -> b) -> b -> V2 a -> b #

foldl' :: (b -> a -> b) -> b -> V2 a -> b #

foldr1 :: (a -> a -> a) -> V2 a -> a #

foldl1 :: (a -> a -> a) -> V2 a -> a #

toList :: V2 a -> [a] #

null :: V2 a -> Bool #

length :: V2 a -> Int #

elem :: Eq a => a -> V2 a -> Bool #

maximum :: Ord a => V2 a -> a #

minimum :: Ord a => V2 a -> a #

sum :: Num a => V2 a -> a #

product :: Num a => V2 a -> a #

Traversable V2 
Instance details

Defined in Linear.V2

Methods

traverse :: Applicative f => (a -> f b) -> V2 a -> f (V2 b) #

sequenceA :: Applicative f => V2 (f a) -> f (V2 a) #

mapM :: Monad m => (a -> m b) -> V2 a -> m (V2 b) #

sequence :: Monad m => V2 (m a) -> m (V2 a) #

Distributive V2 
Instance details

Defined in Linear.V2

Methods

distribute :: Functor f => f (V2 a) -> V2 (f a) #

collect :: Functor f => (a -> V2 b) -> f a -> V2 (f b) #

distributeM :: Monad m => m (V2 a) -> V2 (m a) #

collectM :: Monad m => (a -> V2 b) -> m a -> V2 (m b) #

Representable V2 
Instance details

Defined in Linear.V2

Associated Types

type Rep V2 #

Methods

tabulate :: (Rep V2 -> a) -> V2 a #

index :: V2 a -> Rep V2 -> a #

Eq1 V2 
Instance details

Defined in Linear.V2

Methods

liftEq :: (a -> b -> Bool) -> V2 a -> V2 b -> Bool #

Ord1 V2 
Instance details

Defined in Linear.V2

Methods

liftCompare :: (a -> b -> Ordering) -> V2 a -> V2 b -> Ordering #

Read1 V2 
Instance details

Defined in Linear.V2

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V2 a) #

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V2 a] #

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (V2 a) #

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [V2 a] #

Show1 V2 
Instance details

Defined in Linear.V2

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V2 a -> ShowS #

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V2 a] -> ShowS #

MonadZip V2 
Instance details

Defined in Linear.V2

Methods

mzip :: V2 a -> V2 b -> V2 (a, b) #

mzipWith :: (a -> b -> c) -> V2 a -> V2 b -> V2 c #

munzip :: V2 (a, b) -> (V2 a, V2 b) #

Serial1 V2 
Instance details

Defined in Linear.V2

Methods

serializeWith :: MonadPut m => (a -> m ()) -> V2 a -> m () #

deserializeWith :: MonadGet m => m a -> m (V2 a) #

Hashable1 V2 
Instance details

Defined in Linear.V2

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> V2 a -> Int #

Apply V2 
Instance details

Defined in Linear.V2

Methods

(<.>) :: V2 (a -> b) -> V2 a -> V2 b #

(.>) :: V2 a -> V2 b -> V2 b #

(<.) :: V2 a -> V2 b -> V2 a #

liftF2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c #

Traversable1 V2 
Instance details

Defined in Linear.V2

Methods

traverse1 :: Apply f => (a -> f b) -> V2 a -> f (V2 b) #

sequence1 :: Apply f => V2 (f b) -> f (V2 b) #

Affine V2 
Instance details

Defined in Linear.Affine

Associated Types

type Diff V2 :: Type -> Type #

Methods

(.-.) :: Num a => V2 a -> V2 a -> Diff V2 a #

(.+^) :: Num a => V2 a -> Diff V2 a -> V2 a #

(.-^) :: Num a => V2 a -> Diff V2 a -> V2 a #

R2 V2 
Instance details

Defined in Linear.V2

Methods

_y :: Lens' (V2 a) a #

_xy :: Lens' (V2 a) (V2 a) #

R1 V2 
Instance details

Defined in Linear.V2

Methods

_x :: Lens' (V2 a) a #

Finite V2 
Instance details

Defined in Linear.V2

Associated Types

type Size V2 :: Nat #

Methods

toV :: V2 a -> V (Size V2) a #

fromV :: V (Size V2) a -> V2 a #

Metric V2 
Instance details

Defined in Linear.V2

Methods

dot :: Num a => V2 a -> V2 a -> a #

quadrance :: Num a => V2 a -> a #

qd :: Num a => V2 a -> V2 a -> a #

distance :: Floating a => V2 a -> V2 a -> a #

norm :: Floating a => V2 a -> a #

signorm :: Floating a => V2 a -> V2 a #

Additive V2 
Instance details

Defined in Linear.V2

Methods

zero :: Num a => V2 a #

(^+^) :: Num a => V2 a -> V2 a -> V2 a #

(^-^) :: Num a => V2 a -> V2 a -> V2 a #

lerp :: Num a => a -> V2 a -> V2 a -> V2 a #

liftU2 :: (a -> a -> a) -> V2 a -> V2 a -> V2 a #

liftI2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c #

Bind V2 
Instance details

Defined in Linear.V2

Methods

(>>-) :: V2 a -> (a -> V2 b) -> V2 b #

join :: V2 (V2 a) -> V2 a #

Foldable1 V2 
Instance details

Defined in Linear.V2

Methods

fold1 :: Semigroup m => V2 m -> m #

foldMap1 :: Semigroup m => (a -> m) -> V2 a -> m #

toNonEmpty :: V2 a -> NonEmpty a #

Lift a => Lift (V2 a :: Type) 
Instance details

Defined in Linear.V2

Methods

lift :: V2 a -> Q Exp #

liftTyped :: V2 a -> Q (TExp (V2 a)) #

Unbox a => Vector Vector (V2 a) 
Instance details

Defined in Linear.V2

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V2 a) -> m (Vector (V2 a)) #

basicUnsafeThaw :: PrimMonad m => Vector (V2 a) -> m (Mutable Vector (PrimState m) (V2 a)) #

basicLength :: Vector (V2 a) -> Int #

basicUnsafeSlice :: Int -> Int -> Vector (V2 a) -> Vector (V2 a) #

basicUnsafeIndexM :: Monad m => Vector (V2 a) -> Int -> m (V2 a) #

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V2 a) -> Vector (V2 a) -> m () #

elemseq :: Vector (V2 a) -> V2 a -> b -> b #

Unbox a => MVector MVector (V2 a) 
Instance details

Defined in Linear.V2

Methods

basicLength :: MVector s (V2 a) -> Int #

basicUnsafeSlice :: Int -> Int -> MVector s (V2 a) -> MVector s (V2 a) #

basicOverlaps :: MVector s (V2 a) -> MVector s (V2 a) -> Bool #

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V2 a)) #

basicInitialize :: PrimMonad m => MVector (PrimState m) (V2 a) -> m () #

basicUnsafeReplicate :: PrimMonad m => Int -> V2 a -> m (MVector (PrimState m) (V2 a)) #

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V2 a) -> Int -> m (V2 a) #

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V2 a) -> Int -> V2 a -> m () #

basicClear :: PrimMonad m => MVector (PrimState m) (V2 a) -> m () #

basicSet :: PrimMonad m => MVector (PrimState m) (V2 a) -> V2 a -> m () #

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V2 a) -> MVector (PrimState m) (V2 a) -> m () #

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V2 a) -> MVector (PrimState m) (V2 a) -> m () #

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V2 a) -> Int -> m (MVector (PrimState m) (V2 a)) #

Bounded a => Bounded (V2 a) 
Instance details

Defined in Linear.V2

Methods

minBound :: V2 a #

maxBound :: V2 a #

Eq a => Eq (V2 a) 
Instance details

Defined in Linear.V2

Methods

(==) :: V2 a -> V2 a -> Bool #

(/=) :: V2 a -> V2 a -> Bool #

Floating a => Floating (V2 a) 
Instance details

Defined in Linear.V2

Methods

pi :: V2 a #

exp :: V2 a -> V2 a #

log :: V2 a -> V2 a #

sqrt :: V2 a -> V2 a #

(**) :: V2 a -> V2 a -> V2 a #

logBase :: V2 a -> V2 a -> V2 a #

sin :: V2 a -> V2 a #

cos :: V2 a -> V2 a #

tan :: V2 a -> V2 a #

asin :: V2 a -> V2 a #

acos :: V2 a -> V2 a #

atan :: V2 a -> V2 a #

sinh :: V2 a -> V2 a #

cosh :: V2 a -> V2 a #

tanh :: V2 a -> V2 a #

asinh :: V2 a -> V2 a #

acosh :: V2 a -> V2 a #

atanh :: V2 a -> V2 a #

log1p :: V2 a -> V2 a #

expm1 :: V2 a -> V2 a #

log1pexp :: V2 a -> V2 a #

log1mexp :: V2 a -> V2 a #

Fractional a => Fractional (V2 a) 
Instance details

Defined in Linear.V2

Methods

(/) :: V2 a -> V2 a -> V2 a #

recip :: V2 a -> V2 a #

fromRational :: Rational -> V2 a #

Data a => Data (V2 a) 
Instance details

Defined in Linear.V2

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> V2 a -> c (V2 a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (V2 a) #

toConstr :: V2 a -> Constr #

dataTypeOf :: V2 a -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (V2 a)) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V2 a)) #

gmapT :: (forall b. Data b => b -> b) -> V2 a -> V2 a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V2 a -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V2 a -> r #

gmapQ :: (forall d. Data d => d -> u) -> V2 a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> V2 a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> V2 a -> m (V2 a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> V2 a -> m (V2 a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> V2 a -> m (V2 a) #

Num a => Num (V2 a) 
Instance details

Defined in Linear.V2

Methods

(+) :: V2 a -> V2 a -> V2 a #

(-) :: V2 a -> V2 a -> V2 a #

(*) :: V2 a -> V2 a -> V2 a #

negate :: V2 a -> V2 a #

abs :: V2 a -> V2 a #

signum :: V2 a -> V2 a #

fromInteger :: Integer -> V2 a #

Ord a => Ord (V2 a) 
Instance details

Defined in Linear.V2

Methods

compare :: V2 a -> V2 a -> Ordering #

(<) :: V2 a -> V2 a -> Bool #

(<=) :: V2 a -> V2 a -> Bool #

(>) :: V2 a -> V2 a -> Bool #

(>=) :: V2 a -> V2 a -> Bool #

max :: V2 a -> V2 a -> V2 a #

min :: V2 a -> V2 a -> V2 a #

Read a => Read (V2 a) 
Instance details

Defined in Linear.V2

Show a => Show (V2 a) 
Instance details

Defined in Linear.V2

Methods

showsPrec :: Int -> V2 a -> ShowS #

show :: V2 a -> String #

showList :: [V2 a] -> ShowS #

Ix a => Ix (V2 a) 
Instance details

Defined in Linear.V2

Methods

range :: (V2 a, V2 a) -> [V2 a] #

index :: (V2 a, V2 a) -> V2 a -> Int #

unsafeIndex :: (V2 a, V2 a) -> V2 a -> Int #

inRange :: (V2 a, V2 a) -> V2 a -> Bool #

rangeSize :: (V2 a, V2 a) -> Int #

unsafeRangeSize :: (V2 a, V2 a) -> Int #

Generic (V2 a) 
Instance details

Defined in Linear.V2

Associated Types

type Rep (V2 a) :: Type -> Type #

Methods

from :: V2 a -> Rep (V2 a) x #

to :: Rep (V2 a) x -> V2 a #

Semigroup a => Semigroup (V2 a) 
Instance details

Defined in Linear.V2

Methods

(<>) :: V2 a -> V2 a -> V2 a #

sconcat :: NonEmpty (V2 a) -> V2 a #

stimes :: Integral b => b -> V2 a -> V2 a #

Monoid a => Monoid (V2 a) 
Instance details

Defined in Linear.V2

Methods

mempty :: V2 a #

mappend :: V2 a -> V2 a -> V2 a #

mconcat :: [V2 a] -> V2 a #

HasTrie (E V2) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

data (:->:) (E V2) :: Type -> Type #

Methods

trie :: (E V2 -> b) -> E V2 :->: b #

untrie :: (E V2 :->: b) -> E V2 -> b #

enumerate :: (E V2 :->: b) -> [(E V2, b)] #

Storable a => Storable (V2 a) 
Instance details

Defined in Linear.V2

Methods

sizeOf :: V2 a -> Int #

alignment :: V2 a -> Int #

peekElemOff :: Ptr (V2 a) -> Int -> IO (V2 a) #

pokeElemOff :: Ptr (V2 a) -> Int -> V2 a -> IO () #

peekByteOff :: Ptr b -> Int -> IO (V2 a) #

pokeByteOff :: Ptr b -> Int -> V2 a -> IO () #

peek :: Ptr (V2 a) -> IO (V2 a) #

poke :: Ptr (V2 a) -> V2 a -> IO () #

Binary a => Binary (V2 a) 
Instance details

Defined in Linear.V2

Methods

put :: V2 a -> Put #

get :: Get (V2 a) #

putList :: [V2 a] -> Put #

Serial a => Serial (V2 a) 
Instance details

Defined in Linear.V2

Methods

serialize :: MonadPut m => V2 a -> m () #

deserialize :: MonadGet m => m (V2 a) #

Serialize a => Serialize (V2 a) 
Instance details

Defined in Linear.V2

Methods

put :: Putter (V2 a) #

get :: Get (V2 a) #

NFData a => NFData (V2 a) 
Instance details

Defined in Linear.V2

Methods

rnf :: V2 a -> () #

Hashable a => Hashable (V2 a) 
Instance details

Defined in Linear.V2

Methods

hashWithSalt :: Int -> V2 a -> Int #

hash :: V2 a -> Int #

Unbox a => Unbox (V2 a) 
Instance details

Defined in Linear.V2

Ixed (V2 a) 
Instance details

Defined in Linear.V2

Methods

ix :: Index (V2 a) -> Traversal' (V2 a) (IxValue (V2 a)) #

Epsilon a => Epsilon (V2 a) 
Instance details

Defined in Linear.V2

Methods

nearZero :: V2 a -> Bool #

Show (V2 Double) Source # 
Instance details

Defined in Data.VectorSpace.Free

Show (V2 Float) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

showsPrec :: Int -> V2 Float -> ShowS #

show :: V2 Float -> String #

showList :: [V2 Float] -> ShowS #

Show (V2 Int) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

showsPrec :: Int -> V2 Int -> ShowS #

show :: V2 Int -> String #

showList :: [V2 Int] -> ShowS #

Show (V2 Integer) Source # 
Instance details

Defined in Data.VectorSpace.Free

Random a => Random (V2 a) 
Instance details

Defined in Linear.V2

Methods

randomR :: RandomGen g => (V2 a, V2 a) -> g -> (V2 a, g) #

random :: RandomGen g => g -> (V2 a, g) #

randomRs :: RandomGen g => (V2 a, V2 a) -> g -> [V2 a] #

randoms :: RandomGen g => g -> [V2 a] #

Num s => HasCross2 (V2 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

cross2 :: V2 s -> V2 s #

Num s => AffineSpace (V2 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Diff (V2 s) #

Methods

(.-.) :: V2 s -> V2 s -> Diff (V2 s) #

(.+^) :: V2 s -> Diff (V2 s) -> V2 s #

(Num s, AdditiveGroup s) => HasBasis (V2 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Basis (V2 s) #

Methods

basisValue :: Basis (V2 s) -> V2 s #

decompose :: V2 s -> [(Basis (V2 s), Scalar (V2 s))] #

decompose' :: V2 s -> Basis (V2 s) -> Scalar (V2 s) #

Num s => VectorSpace (V2 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Scalar (V2 s) #

Methods

(*^) :: Scalar (V2 s) -> V2 s -> V2 s #

(Num s, AdditiveGroup s) => InnerSpace (V2 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

(<.>) :: V2 s -> V2 s -> Scalar (V2 s) #

Num s => AdditiveGroup (V2 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

zeroV :: V2 s #

(^+^) :: V2 s -> V2 s -> V2 s #

negateV :: V2 s -> V2 s #

(^-^) :: V2 s -> V2 s -> V2 s #

Num s => FiniteFreeSpace (V2 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Generic1 V2 
Instance details

Defined in Linear.V2

Associated Types

type Rep1 V2 :: k -> Type #

Methods

from1 :: forall (a :: k). V2 a -> Rep1 V2 a #

to1 :: forall (a :: k). Rep1 V2 a -> V2 a #

FunctorWithIndex (E V2) V2 
Instance details

Defined in Linear.V2

Methods

imap :: (E V2 -> a -> b) -> V2 a -> V2 b #

FoldableWithIndex (E V2) V2 
Instance details

Defined in Linear.V2

Methods

ifoldMap :: Monoid m => (E V2 -> a -> m) -> V2 a -> m #

ifoldMap' :: Monoid m => (E V2 -> a -> m) -> V2 a -> m #

ifoldr :: (E V2 -> a -> b -> b) -> b -> V2 a -> b #

ifoldl :: (E V2 -> b -> a -> b) -> b -> V2 a -> b #

ifoldr' :: (E V2 -> a -> b -> b) -> b -> V2 a -> b #

ifoldl' :: (E V2 -> b -> a -> b) -> b -> V2 a -> b #

TraversableWithIndex (E V2) V2 
Instance details

Defined in Linear.V2

Methods

itraverse :: Applicative f => (E V2 -> a -> f b) -> V2 a -> f (V2 b) #

Each (V2 a) (V2 b) a b 
Instance details

Defined in Linear.V2

Methods

each :: Traversal (V2 a) (V2 b) a b #

Field1 (V2 a) (V2 a) a a 
Instance details

Defined in Linear.V2

Methods

_1 :: Lens (V2 a) (V2 a) a a #

Field2 (V2 a) (V2 a) a a 
Instance details

Defined in Linear.V2

Methods

_2 :: Lens (V2 a) (V2 a) a a #

Num s => AffineSpace (Point V2 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Diff (Point V2 s) #

Methods

(.-.) :: Point V2 s -> Point V2 s -> Diff (Point V2 s) #

(.+^) :: Point V2 s -> Diff (Point V2 s) -> Point V2 s #

type Rep V2 
Instance details

Defined in Linear.V2

type Rep V2 = E V2
type Diff V2 
Instance details

Defined in Linear.Affine

type Diff V2 = V2
type Size V2 
Instance details

Defined in Linear.V2

type Size V2 = 2
data MVector s (V2 a) 
Instance details

Defined in Linear.V2

data MVector s (V2 a) = MV_V2 !Int !(MVector s a)
type Rep (V2 a) 
Instance details

Defined in Linear.V2

type Rep (V2 a) = D1 ('MetaData "V2" "Linear.V2" "linear-1.21.8-EtxeJWQbh7CIGwzUT72syQ" 'False) (C1 ('MetaCons "V2" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)))
newtype (E V2) :->: a Source # 
Instance details

Defined in Data.VectorSpace.Free

newtype (E V2) :->: a = V2T (V2 a)
data Vector (V2 a) 
Instance details

Defined in Linear.V2

data Vector (V2 a) = V_V2 !Int !(Vector a)
type Index (V2 a) 
Instance details

Defined in Linear.V2

type Index (V2 a) = E V2
type IxValue (V2 a) 
Instance details

Defined in Linear.V2

type IxValue (V2 a) = a
type Diff (V2 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

type Diff (V2 s) = V2 s
type Basis (V2 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

type Basis (V2 s) = E V2
type Scalar (V2 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

type Scalar (V2 s) = s
type Rep1 V2 
Instance details

Defined in Linear.V2

type Rep1 V2 = D1 ('MetaData "V2" "Linear.V2" "linear-1.21.8-EtxeJWQbh7CIGwzUT72syQ" 'False) (C1 ('MetaCons "V2" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1))
type Diff (Point V2 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

type Diff (Point V2 s) = V2 s

data V3 a #

A 3-dimensional vector

Instances

Instances details
Monad V3 
Instance details

Defined in Linear.V3

Methods

(>>=) :: V3 a -> (a -> V3 b) -> V3 b #

(>>) :: V3 a -> V3 b -> V3 b #

return :: a -> V3 a #

Functor V3 
Instance details

Defined in Linear.V3

Methods

fmap :: (a -> b) -> V3 a -> V3 b #

(<$) :: a -> V3 b -> V3 a #

MonadFix V3 
Instance details

Defined in Linear.V3

Methods

mfix :: (a -> V3 a) -> V3 a #

Applicative V3 
Instance details

Defined in Linear.V3

Methods

pure :: a -> V3 a #

(<*>) :: V3 (a -> b) -> V3 a -> V3 b #

liftA2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c #

(*>) :: V3 a -> V3 b -> V3 b #

(<*) :: V3 a -> V3 b -> V3 a #

Foldable V3 
Instance details

Defined in Linear.V3

Methods

fold :: Monoid m => V3 m -> m #

foldMap :: Monoid m => (a -> m) -> V3 a -> m #

foldMap' :: Monoid m => (a -> m) -> V3 a -> m #

foldr :: (a -> b -> b) -> b -> V3 a -> b #

foldr' :: (a -> b -> b) -> b -> V3 a -> b #

foldl :: (b -> a -> b) -> b -> V3 a -> b #

foldl' :: (b -> a -> b) -> b -> V3 a -> b #

foldr1 :: (a -> a -> a) -> V3 a -> a #

foldl1 :: (a -> a -> a) -> V3 a -> a #

toList :: V3 a -> [a] #

null :: V3 a -> Bool #

length :: V3 a -> Int #

elem :: Eq a => a -> V3 a -> Bool #

maximum :: Ord a => V3 a -> a #

minimum :: Ord a => V3 a -> a #

sum :: Num a => V3 a -> a #

product :: Num a => V3 a -> a #

Traversable V3 
Instance details

Defined in Linear.V3

Methods

traverse :: Applicative f => (a -> f b) -> V3 a -> f (V3 b) #

sequenceA :: Applicative f => V3 (f a) -> f (V3 a) #

mapM :: Monad m => (a -> m b) -> V3 a -> m (V3 b) #

sequence :: Monad m => V3 (m a) -> m (V3 a) #

Distributive V3 
Instance details

Defined in Linear.V3

Methods

distribute :: Functor f => f (V3 a) -> V3 (f a) #

collect :: Functor f => (a -> V3 b) -> f a -> V3 (f b) #

distributeM :: Monad m => m (V3 a) -> V3 (m a) #

collectM :: Monad m => (a -> V3 b) -> m a -> V3 (m b) #

Representable V3 
Instance details

Defined in Linear.V3

Associated Types

type Rep V3 #

Methods

tabulate :: (Rep V3 -> a) -> V3 a #

index :: V3 a -> Rep V3 -> a #

Eq1 V3 
Instance details

Defined in Linear.V3

Methods

liftEq :: (a -> b -> Bool) -> V3 a -> V3 b -> Bool #

Ord1 V3 
Instance details

Defined in Linear.V3

Methods

liftCompare :: (a -> b -> Ordering) -> V3 a -> V3 b -> Ordering #

Read1 V3 
Instance details

Defined in Linear.V3

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V3 a) #

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V3 a] #

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (V3 a) #

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [V3 a] #

Show1 V3 
Instance details

Defined in Linear.V3

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V3 a -> ShowS #

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V3 a] -> ShowS #

MonadZip V3 
Instance details

Defined in Linear.V3

Methods

mzip :: V3 a -> V3 b -> V3 (a, b) #

mzipWith :: (a -> b -> c) -> V3 a -> V3 b -> V3 c #

munzip :: V3 (a, b) -> (V3 a, V3 b) #

Serial1 V3 
Instance details

Defined in Linear.V3

Methods

serializeWith :: MonadPut m => (a -> m ()) -> V3 a -> m () #

deserializeWith :: MonadGet m => m a -> m (V3 a) #

Hashable1 V3 
Instance details

Defined in Linear.V3

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> V3 a -> Int #

Apply V3 
Instance details

Defined in Linear.V3

Methods

(<.>) :: V3 (a -> b) -> V3 a -> V3 b #

(.>) :: V3 a -> V3 b -> V3 b #

(<.) :: V3 a -> V3 b -> V3 a #

liftF2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c #

Traversable1 V3 
Instance details

Defined in Linear.V3

Methods

traverse1 :: Apply f => (a -> f b) -> V3 a -> f (V3 b) #

sequence1 :: Apply f => V3 (f b) -> f (V3 b) #

Affine V3 
Instance details

Defined in Linear.Affine

Associated Types

type Diff V3 :: Type -> Type #

Methods

(.-.) :: Num a => V3 a -> V3 a -> Diff V3 a #

(.+^) :: Num a => V3 a -> Diff V3 a -> V3 a #

(.-^) :: Num a => V3 a -> Diff V3 a -> V3 a #

R3 V3 
Instance details

Defined in Linear.V3

Methods

_z :: Lens' (V3 a) a #

_xyz :: Lens' (V3 a) (V3 a) #

R2 V3 
Instance details

Defined in Linear.V3

Methods

_y :: Lens' (V3 a) a #

_xy :: Lens' (V3 a) (V2 a) #

R1 V3 
Instance details

Defined in Linear.V3

Methods

_x :: Lens' (V3 a) a #

Finite V3 
Instance details

Defined in Linear.V3

Associated Types

type Size V3 :: Nat #

Methods

toV :: V3 a -> V (Size V3) a #

fromV :: V (Size V3) a -> V3 a #

Metric V3 
Instance details

Defined in Linear.V3

Methods

dot :: Num a => V3 a -> V3 a -> a #

quadrance :: Num a => V3 a -> a #

qd :: Num a => V3 a -> V3 a -> a #

distance :: Floating a => V3 a -> V3 a -> a #

norm :: Floating a => V3 a -> a #

signorm :: Floating a => V3 a -> V3 a #

Additive V3 
Instance details

Defined in Linear.V3

Methods

zero :: Num a => V3 a #

(^+^) :: Num a => V3 a -> V3 a -> V3 a #

(^-^) :: Num a => V3 a -> V3 a -> V3 a #

lerp :: Num a => a -> V3 a -> V3 a -> V3 a #

liftU2 :: (a -> a -> a) -> V3 a -> V3 a -> V3 a #

liftI2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c #

Bind V3 
Instance details

Defined in Linear.V3

Methods

(>>-) :: V3 a -> (a -> V3 b) -> V3 b #

join :: V3 (V3 a) -> V3 a #

Foldable1 V3 
Instance details

Defined in Linear.V3

Methods

fold1 :: Semigroup m => V3 m -> m #

foldMap1 :: Semigroup m => (a -> m) -> V3 a -> m #

toNonEmpty :: V3 a -> NonEmpty a #

Lift a => Lift (V3 a :: Type) 
Instance details

Defined in Linear.V3

Methods

lift :: V3 a -> Q Exp #

liftTyped :: V3 a -> Q (TExp (V3 a)) #

Unbox a => Vector Vector (V3 a) 
Instance details

Defined in Linear.V3

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V3 a) -> m (Vector (V3 a)) #

basicUnsafeThaw :: PrimMonad m => Vector (V3 a) -> m (Mutable Vector (PrimState m) (V3 a)) #

basicLength :: Vector (V3 a) -> Int #

basicUnsafeSlice :: Int -> Int -> Vector (V3 a) -> Vector (V3 a) #

basicUnsafeIndexM :: Monad m => Vector (V3 a) -> Int -> m (V3 a) #

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V3 a) -> Vector (V3 a) -> m () #

elemseq :: Vector (V3 a) -> V3 a -> b -> b #

Unbox a => MVector MVector (V3 a) 
Instance details

Defined in Linear.V3

Methods

basicLength :: MVector s (V3 a) -> Int #

basicUnsafeSlice :: Int -> Int -> MVector s (V3 a) -> MVector s (V3 a) #

basicOverlaps :: MVector s (V3 a) -> MVector s (V3 a) -> Bool #

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V3 a)) #

basicInitialize :: PrimMonad m => MVector (PrimState m) (V3 a) -> m () #

basicUnsafeReplicate :: PrimMonad m => Int -> V3 a -> m (MVector (PrimState m) (V3 a)) #

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> m (V3 a) #

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> V3 a -> m () #

basicClear :: PrimMonad m => MVector (PrimState m) (V3 a) -> m () #

basicSet :: PrimMonad m => MVector (PrimState m) (V3 a) -> V3 a -> m () #

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V3 a) -> MVector (PrimState m) (V3 a) -> m () #

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V3 a) -> MVector (PrimState m) (V3 a) -> m () #

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> m (MVector (PrimState m) (V3 a)) #

Bounded a => Bounded (V3 a) 
Instance details

Defined in Linear.V3

Methods

minBound :: V3 a #

maxBound :: V3 a #

Eq a => Eq (V3 a) 
Instance details

Defined in Linear.V3

Methods

(==) :: V3 a -> V3 a -> Bool #

(/=) :: V3 a -> V3 a -> Bool #

Floating a => Floating (V3 a) 
Instance details

Defined in Linear.V3

Methods

pi :: V3 a #

exp :: V3 a -> V3 a #

log :: V3 a -> V3 a #

sqrt :: V3 a -> V3 a #

(**) :: V3 a -> V3 a -> V3 a #

logBase :: V3 a -> V3 a -> V3 a #

sin :: V3 a -> V3 a #

cos :: V3 a -> V3 a #

tan :: V3 a -> V3 a #

asin :: V3 a -> V3 a #

acos :: V3 a -> V3 a #

atan :: V3 a -> V3 a #

sinh :: V3 a -> V3 a #

cosh :: V3 a -> V3 a #

tanh :: V3 a -> V3 a #

asinh :: V3 a -> V3 a #

acosh :: V3 a -> V3 a #

atanh :: V3 a -> V3 a #

log1p :: V3 a -> V3 a #

expm1 :: V3 a -> V3 a #

log1pexp :: V3 a -> V3 a #

log1mexp :: V3 a -> V3 a #

Fractional a => Fractional (V3 a) 
Instance details

Defined in Linear.V3

Methods

(/) :: V3 a -> V3 a -> V3 a #

recip :: V3 a -> V3 a #

fromRational :: Rational -> V3 a #

Data a => Data (V3 a) 
Instance details

Defined in Linear.V3

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> V3 a -> c (V3 a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (V3 a) #

toConstr :: V3 a -> Constr #

dataTypeOf :: V3 a -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (V3 a)) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V3 a)) #

gmapT :: (forall b. Data b => b -> b) -> V3 a -> V3 a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r #

gmapQ :: (forall d. Data d => d -> u) -> V3 a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> V3 a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a) #

Num a => Num (V3 a) 
Instance details

Defined in Linear.V3

Methods

(+) :: V3 a -> V3 a -> V3 a #

(-) :: V3 a -> V3 a -> V3 a #

(*) :: V3 a -> V3 a -> V3 a #

negate :: V3 a -> V3 a #

abs :: V3 a -> V3 a #

signum :: V3 a -> V3 a #

fromInteger :: Integer -> V3 a #

Ord a => Ord (V3 a) 
Instance details

Defined in Linear.V3

Methods

compare :: V3 a -> V3 a -> Ordering #

(<) :: V3 a -> V3 a -> Bool #

(<=) :: V3 a -> V3 a -> Bool #

(>) :: V3 a -> V3 a -> Bool #

(>=) :: V3 a -> V3 a -> Bool #

max :: V3 a -> V3 a -> V3 a #

min :: V3 a -> V3 a -> V3 a #

Read a => Read (V3 a) 
Instance details

Defined in Linear.V3

Show a => Show (V3 a) 
Instance details

Defined in Linear.V3

Methods

showsPrec :: Int -> V3 a -> ShowS #

show :: V3 a -> String #

showList :: [V3 a] -> ShowS #

Ix a => Ix (V3 a) 
Instance details

Defined in Linear.V3

Methods

range :: (V3 a, V3 a) -> [V3 a] #

index :: (V3 a, V3 a) -> V3 a -> Int #

unsafeIndex :: (V3 a, V3 a) -> V3 a -> Int #

inRange :: (V3 a, V3 a) -> V3 a -> Bool #

rangeSize :: (V3 a, V3 a) -> Int #

unsafeRangeSize :: (V3 a, V3 a) -> Int #

Generic (V3 a) 
Instance details

Defined in Linear.V3

Associated Types

type Rep (V3 a) :: Type -> Type #

Methods

from :: V3 a -> Rep (V3 a) x #

to :: Rep (V3 a) x -> V3 a #

Semigroup a => Semigroup (V3 a) 
Instance details

Defined in Linear.V3

Methods

(<>) :: V3 a -> V3 a -> V3 a #

sconcat :: NonEmpty (V3 a) -> V3 a #

stimes :: Integral b => b -> V3 a -> V3 a #

Monoid a => Monoid (V3 a) 
Instance details

Defined in Linear.V3

Methods

mempty :: V3 a #

mappend :: V3 a -> V3 a -> V3 a #

mconcat :: [V3 a] -> V3 a #

HasTrie (E V3) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

data (:->:) (E V3) :: Type -> Type #

Methods

trie :: (E V3 -> b) -> E V3 :->: b #

untrie :: (E V3 :->: b) -> E V3 -> b #

enumerate :: (E V3 :->: b) -> [(E V3, b)] #

Storable a => Storable (V3 a) 
Instance details

Defined in Linear.V3

Methods

sizeOf :: V3 a -> Int #

alignment :: V3 a -> Int #

peekElemOff :: Ptr (V3 a) -> Int -> IO (V3 a) #

pokeElemOff :: Ptr (V3 a) -> Int -> V3 a -> IO () #

peekByteOff :: Ptr b -> Int -> IO (V3 a) #

pokeByteOff :: Ptr b -> Int -> V3 a -> IO () #

peek :: Ptr (V3 a) -> IO (V3 a) #

poke :: Ptr (V3 a) -> V3 a -> IO () #

Binary a => Binary (V3 a) 
Instance details

Defined in Linear.V3

Methods

put :: V3 a -> Put #

get :: Get (V3 a) #

putList :: [V3 a] -> Put #

Serial a => Serial (V3 a) 
Instance details

Defined in Linear.V3

Methods

serialize :: MonadPut m => V3 a -> m () #

deserialize :: MonadGet m => m (V3 a) #

Serialize a => Serialize (V3 a) 
Instance details

Defined in Linear.V3

Methods

put :: Putter (V3 a) #

get :: Get (V3 a) #

NFData a => NFData (V3 a) 
Instance details

Defined in Linear.V3

Methods

rnf :: V3 a -> () #

Hashable a => Hashable (V3 a) 
Instance details

Defined in Linear.V3

Methods

hashWithSalt :: Int -> V3 a -> Int #

hash :: V3 a -> Int #

Unbox a => Unbox (V3 a) 
Instance details

Defined in Linear.V3

Ixed (V3 a) 
Instance details

Defined in Linear.V3

Methods

ix :: Index (V3 a) -> Traversal' (V3 a) (IxValue (V3 a)) #

Epsilon a => Epsilon (V3 a) 
Instance details

Defined in Linear.V3

Methods

nearZero :: V3 a -> Bool #

Show (V3 Double) Source # 
Instance details

Defined in Data.VectorSpace.Free

Show (V3 Float) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

showsPrec :: Int -> V3 Float -> ShowS #

show :: V3 Float -> String #

showList :: [V3 Float] -> ShowS #

Show (V3 Int) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

showsPrec :: Int -> V3 Int -> ShowS #

show :: V3 Int -> String #

showList :: [V3 Int] -> ShowS #

Show (V3 Integer) Source # 
Instance details

Defined in Data.VectorSpace.Free

Random a => Random (V3 a) 
Instance details

Defined in Linear.V3

Methods

randomR :: RandomGen g => (V3 a, V3 a) -> g -> (V3 a, g) #

random :: RandomGen g => g -> (V3 a, g) #

randomRs :: RandomGen g => (V3 a, V3 a) -> g -> [V3 a] #

randoms :: RandomGen g => g -> [V3 a] #

Num s => HasCross3 (V3 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

cross3 :: V3 s -> V3 s -> V3 s #

Num s => AffineSpace (V3 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Diff (V3 s) #

Methods

(.-.) :: V3 s -> V3 s -> Diff (V3 s) #

(.+^) :: V3 s -> Diff (V3 s) -> V3 s #

(Num s, AdditiveGroup s) => HasBasis (V3 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Basis (V3 s) #

Methods

basisValue :: Basis (V3 s) -> V3 s #

decompose :: V3 s -> [(Basis (V3 s), Scalar (V3 s))] #

decompose' :: V3 s -> Basis (V3 s) -> Scalar (V3 s) #

Num s => VectorSpace (V3 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Scalar (V3 s) #

Methods

(*^) :: Scalar (V3 s) -> V3 s -> V3 s #

(Num s, AdditiveGroup s) => InnerSpace (V3 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

(<.>) :: V3 s -> V3 s -> Scalar (V3 s) #

Num s => AdditiveGroup (V3 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

zeroV :: V3 s #

(^+^) :: V3 s -> V3 s -> V3 s #

negateV :: V3 s -> V3 s #

(^-^) :: V3 s -> V3 s -> V3 s #

Num s => FiniteFreeSpace (V3 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Generic1 V3 
Instance details

Defined in Linear.V3

Associated Types

type Rep1 V3 :: k -> Type #

Methods

from1 :: forall (a :: k). V3 a -> Rep1 V3 a #

to1 :: forall (a :: k). Rep1 V3 a -> V3 a #

FunctorWithIndex (E V3) V3 
Instance details

Defined in Linear.V3

Methods

imap :: (E V3 -> a -> b) -> V3 a -> V3 b #

FoldableWithIndex (E V3) V3 
Instance details

Defined in Linear.V3

Methods

ifoldMap :: Monoid m => (E V3 -> a -> m) -> V3 a -> m #

ifoldMap' :: Monoid m => (E V3 -> a -> m) -> V3 a -> m #

ifoldr :: (E V3 -> a -> b -> b) -> b -> V3 a -> b #

ifoldl :: (E V3 -> b -> a -> b) -> b -> V3 a -> b #

ifoldr' :: (E V3 -> a -> b -> b) -> b -> V3 a -> b #

ifoldl' :: (E V3 -> b -> a -> b) -> b -> V3 a -> b #

TraversableWithIndex (E V3) V3 
Instance details

Defined in Linear.V3

Methods

itraverse :: Applicative f => (E V3 -> a -> f b) -> V3 a -> f (V3 b) #

Each (V3 a) (V3 b) a b 
Instance details

Defined in Linear.V3

Methods

each :: Traversal (V3 a) (V3 b) a b #

Field1 (V3 a) (V3 a) a a 
Instance details

Defined in Linear.V3

Methods

_1 :: Lens (V3 a) (V3 a) a a #

Field2 (V3 a) (V3 a) a a 
Instance details

Defined in Linear.V3

Methods

_2 :: Lens (V3 a) (V3 a) a a #

Field3 (V3 a) (V3 a) a a 
Instance details

Defined in Linear.V3

Methods

_3 :: Lens (V3 a) (V3 a) a a #

Num s => AffineSpace (Point V3 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Diff (Point V3 s) #

Methods

(.-.) :: Point V3 s -> Point V3 s -> Diff (Point V3 s) #

(.+^) :: Point V3 s -> Diff (Point V3 s) -> Point V3 s #

type Rep V3 
Instance details

Defined in Linear.V3

type Rep V3 = E V3
type Diff V3 
Instance details

Defined in Linear.Affine

type Diff V3 = V3
type Size V3 
Instance details

Defined in Linear.V3

type Size V3 = 3
data MVector s (V3 a) 
Instance details

Defined in Linear.V3

data MVector s (V3 a) = MV_V3 !Int !(MVector s a)
type Rep (V3 a) 
Instance details

Defined in Linear.V3

newtype (E V3) :->: a Source # 
Instance details

Defined in Data.VectorSpace.Free

newtype (E V3) :->: a = V3T (V3 a)
data Vector (V3 a) 
Instance details

Defined in Linear.V3

data Vector (V3 a) = V_V3 !Int !(Vector a)
type Index (V3 a) 
Instance details

Defined in Linear.V3

type Index (V3 a) = E V3
type IxValue (V3 a) 
Instance details

Defined in Linear.V3

type IxValue (V3 a) = a
type Diff (V3 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

type Diff (V3 s) = V3 s
type Basis (V3 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

type Basis (V3 s) = E V3
type Scalar (V3 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

type Scalar (V3 s) = s
type Rep1 V3 
Instance details

Defined in Linear.V3

type Diff (Point V3 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

type Diff (Point V3 s) = V3 s

data V4 a #

A 4-dimensional vector.

Instances

Instances details
Monad V4 
Instance details

Defined in Linear.V4

Methods

(>>=) :: V4 a -> (a -> V4 b) -> V4 b #

(>>) :: V4 a -> V4 b -> V4 b #

return :: a -> V4 a #

Functor V4 
Instance details

Defined in Linear.V4

Methods

fmap :: (a -> b) -> V4 a -> V4 b #

(<$) :: a -> V4 b -> V4 a #

MonadFix V4 
Instance details

Defined in Linear.V4

Methods

mfix :: (a -> V4 a) -> V4 a #

Applicative V4 
Instance details

Defined in Linear.V4

Methods

pure :: a -> V4 a #

(<*>) :: V4 (a -> b) -> V4 a -> V4 b #

liftA2 :: (a -> b -> c) -> V4 a -> V4 b -> V4 c #

(*>) :: V4 a -> V4 b -> V4 b #

(<*) :: V4 a -> V4 b -> V4 a #

Foldable V4 
Instance details

Defined in Linear.V4

Methods

fold :: Monoid m => V4 m -> m #

foldMap :: Monoid m => (a -> m) -> V4 a -> m #

foldMap' :: Monoid m => (a -> m) -> V4 a -> m #

foldr :: (a -> b -> b) -> b -> V4 a -> b #

foldr' :: (a -> b -> b) -> b -> V4 a -> b #

foldl :: (b -> a -> b) -> b -> V4 a -> b #

foldl' :: (b -> a -> b) -> b -> V4 a -> b #

foldr1 :: (a -> a -> a) -> V4 a -> a #

foldl1 :: (a -> a -> a) -> V4 a -> a #

toList :: V4 a -> [a] #

null :: V4 a -> Bool #

length :: V4 a -> Int #

elem :: Eq a => a -> V4 a -> Bool #

maximum :: Ord a => V4 a -> a #

minimum :: Ord a => V4 a -> a #

sum :: Num a => V4 a -> a #

product :: Num a => V4 a -> a #

Traversable V4 
Instance details

Defined in Linear.V4

Methods

traverse :: Applicative f => (a -> f b) -> V4 a -> f (V4 b) #

sequenceA :: Applicative f => V4 (f a) -> f (V4 a) #

mapM :: Monad m => (a -> m b) -> V4 a -> m (V4 b) #

sequence :: Monad m => V4 (m a) -> m (V4 a) #

Distributive V4 
Instance details

Defined in Linear.V4

Methods

distribute :: Functor f => f (V4 a) -> V4 (f a) #

collect :: Functor f => (a -> V4 b) -> f a -> V4 (f b) #

distributeM :: Monad m => m (V4 a) -> V4 (m a) #

collectM :: Monad m => (a -> V4 b) -> m a -> V4 (m b) #

Representable V4 
Instance details

Defined in Linear.V4

Associated Types

type Rep V4 #

Methods

tabulate :: (Rep V4 -> a) -> V4 a #

index :: V4 a -> Rep V4 -> a #

Eq1 V4 
Instance details

Defined in Linear.V4

Methods

liftEq :: (a -> b -> Bool) -> V4 a -> V4 b -> Bool #

Ord1 V4 
Instance details

Defined in Linear.V4

Methods

liftCompare :: (a -> b -> Ordering) -> V4 a -> V4 b -> Ordering #

Read1 V4 
Instance details

Defined in Linear.V4

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V4 a) #

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V4 a] #

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (V4 a) #

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [V4 a] #

Show1 V4 
Instance details

Defined in Linear.V4

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V4 a -> ShowS #

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V4 a] -> ShowS #

MonadZip V4 
Instance details

Defined in Linear.V4

Methods

mzip :: V4 a -> V4 b -> V4 (a, b) #

mzipWith :: (a -> b -> c) -> V4 a -> V4 b -> V4 c #

munzip :: V4 (a, b) -> (V4 a, V4 b) #

Serial1 V4 
Instance details

Defined in Linear.V4

Methods

serializeWith :: MonadPut m => (a -> m ()) -> V4 a -> m () #

deserializeWith :: MonadGet m => m a -> m (V4 a) #

Hashable1 V4 
Instance details

Defined in Linear.V4

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> V4 a -> Int #

Apply V4 
Instance details

Defined in Linear.V4

Methods

(<.>) :: V4 (a -> b) -> V4 a -> V4 b #

(.>) :: V4 a -> V4 b -> V4 b #

(<.) :: V4 a -> V4 b -> V4 a #

liftF2 :: (a -> b -> c) -> V4 a -> V4 b -> V4 c #

Traversable1 V4 
Instance details

Defined in Linear.V4

Methods

traverse1 :: Apply f => (a -> f b) -> V4 a -> f (V4 b) #

sequence1 :: Apply f => V4 (f b) -> f (V4 b) #

Affine V4 
Instance details

Defined in Linear.Affine

Associated Types

type Diff V4 :: Type -> Type #

Methods

(.-.) :: Num a => V4 a -> V4 a -> Diff V4 a #

(.+^) :: Num a => V4 a -> Diff V4 a -> V4 a #

(.-^) :: Num a => V4 a -> Diff V4 a -> V4 a #

R4 V4 
Instance details

Defined in Linear.V4

Methods

_w :: Lens' (V4 a) a #

_xyzw :: Lens' (V4 a) (V4 a) #

R3 V4 
Instance details

Defined in Linear.V4

Methods

_z :: Lens' (V4 a) a #

_xyz :: Lens' (V4 a) (V3 a) #

R2 V4 
Instance details

Defined in Linear.V4

Methods

_y :: Lens' (V4 a) a #

_xy :: Lens' (V4 a) (V2 a) #

R1 V4 
Instance details

Defined in Linear.V4

Methods

_x :: Lens' (V4 a) a #

Finite V4 
Instance details

Defined in Linear.V4

Associated Types

type Size V4 :: Nat #

Methods

toV :: V4 a -> V (Size V4) a #

fromV :: V (Size V4) a -> V4 a #

Metric V4 
Instance details

Defined in Linear.V4

Methods

dot :: Num a => V4 a -> V4 a -> a #

quadrance :: Num a => V4 a -> a #

qd :: Num a => V4 a -> V4 a -> a #

distance :: Floating a => V4 a -> V4 a -> a #

norm :: Floating a => V4 a -> a #

signorm :: Floating a => V4 a -> V4 a #

Additive V4 
Instance details

Defined in Linear.V4

Methods

zero :: Num a => V4 a #

(^+^) :: Num a => V4 a -> V4 a -> V4 a #

(^-^) :: Num a => V4 a -> V4 a -> V4 a #

lerp :: Num a => a -> V4 a -> V4 a -> V4 a #

liftU2 :: (a -> a -> a) -> V4 a -> V4 a -> V4 a #

liftI2 :: (a -> b -> c) -> V4 a -> V4 b -> V4 c #

Bind V4 
Instance details

Defined in Linear.V4

Methods

(>>-) :: V4 a -> (a -> V4 b) -> V4 b #

join :: V4 (V4 a) -> V4 a #

Foldable1 V4 
Instance details

Defined in Linear.V4

Methods

fold1 :: Semigroup m => V4 m -> m #

foldMap1 :: Semigroup m => (a -> m) -> V4 a -> m #

toNonEmpty :: V4 a -> NonEmpty a #

Lift a => Lift (V4 a :: Type) 
Instance details

Defined in Linear.V4

Methods

lift :: V4 a -> Q Exp #

liftTyped :: V4 a -> Q (TExp (V4 a)) #

Unbox a => Vector Vector (V4 a) 
Instance details

Defined in Linear.V4

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V4 a) -> m (Vector (V4 a)) #

basicUnsafeThaw :: PrimMonad m => Vector (V4 a) -> m (Mutable Vector (PrimState m) (V4 a)) #

basicLength :: Vector (V4 a) -> Int #

basicUnsafeSlice :: Int -> Int -> Vector (V4 a) -> Vector (V4 a) #

basicUnsafeIndexM :: Monad m => Vector (V4 a) -> Int -> m (V4 a) #

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V4 a) -> Vector (V4 a) -> m () #

elemseq :: Vector (V4 a) -> V4 a -> b -> b #

Unbox a => MVector MVector (V4 a) 
Instance details

Defined in Linear.V4

Methods

basicLength :: MVector s (V4 a) -> Int #

basicUnsafeSlice :: Int -> Int -> MVector s (V4 a) -> MVector s (V4 a) #

basicOverlaps :: MVector s (V4 a) -> MVector s (V4 a) -> Bool #

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V4 a)) #

basicInitialize :: PrimMonad m => MVector (PrimState m) (V4 a) -> m () #

basicUnsafeReplicate :: PrimMonad m => Int -> V4 a -> m (MVector (PrimState m) (V4 a)) #

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V4 a) -> Int -> m (V4 a) #

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V4 a) -> Int -> V4 a -> m () #

basicClear :: PrimMonad m => MVector (PrimState m) (V4 a) -> m () #

basicSet :: PrimMonad m => MVector (PrimState m) (V4 a) -> V4 a -> m () #

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V4 a) -> MVector (PrimState m) (V4 a) -> m () #

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V4 a) -> MVector (PrimState m) (V4 a) -> m () #

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V4 a) -> Int -> m (MVector (PrimState m) (V4 a)) #

Bounded a => Bounded (V4 a) 
Instance details

Defined in Linear.V4

Methods

minBound :: V4 a #

maxBound :: V4 a #

Eq a => Eq (V4 a) 
Instance details

Defined in Linear.V4

Methods

(==) :: V4 a -> V4 a -> Bool #

(/=) :: V4 a -> V4 a -> Bool #

Floating a => Floating (V4 a) 
Instance details

Defined in Linear.V4

Methods

pi :: V4 a #

exp :: V4 a -> V4 a #

log :: V4 a -> V4 a #

sqrt :: V4 a -> V4 a #

(**) :: V4 a -> V4 a -> V4 a #

logBase :: V4 a -> V4 a -> V4 a #

sin :: V4 a -> V4 a #

cos :: V4 a -> V4 a #

tan :: V4 a -> V4 a #

asin :: V4 a -> V4 a #

acos :: V4 a -> V4 a #

atan :: V4 a -> V4 a #

sinh :: V4 a -> V4 a #

cosh :: V4 a -> V4 a #

tanh :: V4 a -> V4 a #

asinh :: V4 a -> V4 a #

acosh :: V4 a -> V4 a #

atanh :: V4 a -> V4 a #

log1p :: V4 a -> V4 a #

expm1 :: V4 a -> V4 a #

log1pexp :: V4 a -> V4 a #

log1mexp :: V4 a -> V4 a #

Fractional a => Fractional (V4 a) 
Instance details

Defined in Linear.V4

Methods

(/) :: V4 a -> V4 a -> V4 a #

recip :: V4 a -> V4 a #

fromRational :: Rational -> V4 a #

Data a => Data (V4 a) 
Instance details

Defined in Linear.V4

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> V4 a -> c (V4 a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (V4 a) #

toConstr :: V4 a -> Constr #

dataTypeOf :: V4 a -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (V4 a)) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V4 a)) #

gmapT :: (forall b. Data b => b -> b) -> V4 a -> V4 a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V4 a -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V4 a -> r #

gmapQ :: (forall d. Data d => d -> u) -> V4 a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> V4 a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> V4 a -> m (V4 a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> V4 a -> m (V4 a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> V4 a -> m (V4 a) #

Num a => Num (V4 a) 
Instance details

Defined in Linear.V4

Methods

(+) :: V4 a -> V4 a -> V4 a #

(-) :: V4 a -> V4 a -> V4 a #

(*) :: V4 a -> V4 a -> V4 a #

negate :: V4 a -> V4 a #

abs :: V4 a -> V4 a #

signum :: V4 a -> V4 a #

fromInteger :: Integer -> V4 a #

Ord a => Ord (V4 a) 
Instance details

Defined in Linear.V4

Methods

compare :: V4 a -> V4 a -> Ordering #

(<) :: V4 a -> V4 a -> Bool #

(<=) :: V4 a -> V4 a -> Bool #

(>) :: V4 a -> V4 a -> Bool #

(>=) :: V4 a -> V4 a -> Bool #

max :: V4 a -> V4 a -> V4 a #

min :: V4 a -> V4 a -> V4 a #

Read a => Read (V4 a) 
Instance details

Defined in Linear.V4

Show a => Show (V4 a) 
Instance details

Defined in Linear.V4

Methods

showsPrec :: Int -> V4 a -> ShowS #

show :: V4 a -> String #

showList :: [V4 a] -> ShowS #

Ix a => Ix (V4 a) 
Instance details

Defined in Linear.V4

Methods

range :: (V4 a, V4 a) -> [V4 a] #

index :: (V4 a, V4 a) -> V4 a -> Int #

unsafeIndex :: (V4 a, V4 a) -> V4 a -> Int #

inRange :: (V4 a, V4 a) -> V4 a -> Bool #

rangeSize :: (V4 a, V4 a) -> Int #

unsafeRangeSize :: (V4 a, V4 a) -> Int #

Generic (V4 a) 
Instance details

Defined in Linear.V4

Associated Types

type Rep (V4 a) :: Type -> Type #

Methods

from :: V4 a -> Rep (V4 a) x #

to :: Rep (V4 a) x -> V4 a #

Semigroup a => Semigroup (V4 a) 
Instance details

Defined in Linear.V4

Methods

(<>) :: V4 a -> V4 a -> V4 a #

sconcat :: NonEmpty (V4 a) -> V4 a #

stimes :: Integral b => b -> V4 a -> V4 a #

Monoid a => Monoid (V4 a) 
Instance details

Defined in Linear.V4

Methods

mempty :: V4 a #

mappend :: V4 a -> V4 a -> V4 a #

mconcat :: [V4 a] -> V4 a #

HasTrie (E V4) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

data (:->:) (E V4) :: Type -> Type #

Methods

trie :: (E V4 -> b) -> E V4 :->: b #

untrie :: (E V4 :->: b) -> E V4 -> b #

enumerate :: (E V4 :->: b) -> [(E V4, b)] #

Storable a => Storable (V4 a) 
Instance details

Defined in Linear.V4

Methods

sizeOf :: V4 a -> Int #

alignment :: V4 a -> Int #

peekElemOff :: Ptr (V4 a) -> Int -> IO (V4 a) #

pokeElemOff :: Ptr (V4 a) -> Int -> V4 a -> IO () #

peekByteOff :: Ptr b -> Int -> IO (V4 a) #

pokeByteOff :: Ptr b -> Int -> V4 a -> IO () #

peek :: Ptr (V4 a) -> IO (V4 a) #

poke :: Ptr (V4 a) -> V4 a -> IO () #

Binary a => Binary (V4 a) 
Instance details

Defined in Linear.V4

Methods

put :: V4 a -> Put #

get :: Get (V4 a) #

putList :: [V4 a] -> Put #

Serial a => Serial (V4 a) 
Instance details

Defined in Linear.V4

Methods

serialize :: MonadPut m => V4 a -> m () #

deserialize :: MonadGet m => m (V4 a) #

Serialize a => Serialize (V4 a) 
Instance details

Defined in Linear.V4

Methods

put :: Putter (V4 a) #

get :: Get (V4 a) #

NFData a => NFData (V4 a) 
Instance details

Defined in Linear.V4

Methods

rnf :: V4 a -> () #

Hashable a => Hashable (V4 a) 
Instance details

Defined in Linear.V4

Methods

hashWithSalt :: Int -> V4 a -> Int #

hash :: V4 a -> Int #

Unbox a => Unbox (V4 a) 
Instance details

Defined in Linear.V4

Ixed (V4 a) 
Instance details

Defined in Linear.V4

Methods

ix :: Index (V4 a) -> Traversal' (V4 a) (IxValue (V4 a)) #

Epsilon a => Epsilon (V4 a) 
Instance details

Defined in Linear.V4

Methods

nearZero :: V4 a -> Bool #

Show (V4 Double) Source # 
Instance details

Defined in Data.VectorSpace.Free

Show (V4 Float) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

showsPrec :: Int -> V4 Float -> ShowS #

show :: V4 Float -> String #

showList :: [V4 Float] -> ShowS #

Show (V4 Int) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

showsPrec :: Int -> V4 Int -> ShowS #

show :: V4 Int -> String #

showList :: [V4 Int] -> ShowS #

Show (V4 Integer) Source # 
Instance details

Defined in Data.VectorSpace.Free

Random a => Random (V4 a) 
Instance details

Defined in Linear.V4

Methods

randomR :: RandomGen g => (V4 a, V4 a) -> g -> (V4 a, g) #

random :: RandomGen g => g -> (V4 a, g) #

randomRs :: RandomGen g => (V4 a, V4 a) -> g -> [V4 a] #

randoms :: RandomGen g => g -> [V4 a] #

Num s => AffineSpace (V4 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Diff (V4 s) #

Methods

(.-.) :: V4 s -> V4 s -> Diff (V4 s) #

(.+^) :: V4 s -> Diff (V4 s) -> V4 s #

(Num s, AdditiveGroup s) => HasBasis (V4 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Basis (V4 s) #

Methods

basisValue :: Basis (V4 s) -> V4 s #

decompose :: V4 s -> [(Basis (V4 s), Scalar (V4 s))] #

decompose' :: V4 s -> Basis (V4 s) -> Scalar (V4 s) #

Num s => VectorSpace (V4 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Scalar (V4 s) #

Methods

(*^) :: Scalar (V4 s) -> V4 s -> V4 s #

(Num s, AdditiveGroup s) => InnerSpace (V4 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

(<.>) :: V4 s -> V4 s -> Scalar (V4 s) #

Num s => AdditiveGroup (V4 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

zeroV :: V4 s #

(^+^) :: V4 s -> V4 s -> V4 s #

negateV :: V4 s -> V4 s #

(^-^) :: V4 s -> V4 s -> V4 s #

Num s => FiniteFreeSpace (V4 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Generic1 V4 
Instance details

Defined in Linear.V4

Associated Types

type Rep1 V4 :: k -> Type #

Methods

from1 :: forall (a :: k). V4 a -> Rep1 V4 a #

to1 :: forall (a :: k). Rep1 V4 a -> V4 a #

FunctorWithIndex (E V4) V4 
Instance details

Defined in Linear.V4

Methods

imap :: (E V4 -> a -> b) -> V4 a -> V4 b #

FoldableWithIndex (E V4) V4 
Instance details

Defined in Linear.V4

Methods

ifoldMap :: Monoid m => (E V4 -> a -> m) -> V4 a -> m #

ifoldMap' :: Monoid m => (E V4 -> a -> m) -> V4 a -> m #

ifoldr :: (E V4 -> a -> b -> b) -> b -> V4 a -> b #

ifoldl :: (E V4 -> b -> a -> b) -> b -> V4 a -> b #

ifoldr' :: (E V4 -> a -> b -> b) -> b -> V4 a -> b #

ifoldl' :: (E V4 -> b -> a -> b) -> b -> V4 a -> b #

TraversableWithIndex (E V4) V4 
Instance details

Defined in Linear.V4

Methods

itraverse :: Applicative f => (E V4 -> a -> f b) -> V4 a -> f (V4 b) #

Each (V4 a) (V4 b) a b 
Instance details

Defined in Linear.V4

Methods

each :: Traversal (V4 a) (V4 b) a b #

Field1 (V4 a) (V4 a) a a 
Instance details

Defined in Linear.V4

Methods

_1 :: Lens (V4 a) (V4 a) a a #

Field2 (V4 a) (V4 a) a a 
Instance details

Defined in Linear.V4

Methods

_2 :: Lens (V4 a) (V4 a) a a #

Field3 (V4 a) (V4 a) a a 
Instance details

Defined in Linear.V4

Methods

_3 :: Lens (V4 a) (V4 a) a a #

Field4 (V4 a) (V4 a) a a 
Instance details

Defined in Linear.V4

Methods

_4 :: Lens (V4 a) (V4 a) a a #

Num s => AffineSpace (Point V4 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Diff (Point V4 s) #

Methods

(.-.) :: Point V4 s -> Point V4 s -> Diff (Point V4 s) #

(.+^) :: Point V4 s -> Diff (Point V4 s) -> Point V4 s #

type Rep V4 
Instance details

Defined in Linear.V4

type Rep V4 = E V4
type Diff V4 
Instance details

Defined in Linear.Affine

type Diff V4 = V4
type Size V4 
Instance details

Defined in Linear.V4

type Size V4 = 4
data MVector s (V4 a) 
Instance details

Defined in Linear.V4

data MVector s (V4 a) = MV_V4 !Int !(MVector s a)
type Rep (V4 a) 
Instance details

Defined in Linear.V4

newtype (E V4) :->: a Source # 
Instance details

Defined in Data.VectorSpace.Free

newtype (E V4) :->: a = V4T (V4 a)
data Vector (V4 a) 
Instance details

Defined in Linear.V4

data Vector (V4 a) = V_V4 !Int !(Vector a)
type Index (V4 a) 
Instance details

Defined in Linear.V4

type Index (V4 a) = E V4
type IxValue (V4 a) 
Instance details

Defined in Linear.V4

type IxValue (V4 a) = a
type Diff (V4 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

type Diff (V4 s) = V4 s
type Basis (V4 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

type Basis (V4 s) = E V4
type Scalar (V4 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

type Scalar (V4 s) = s
type Rep1 V4 
Instance details

Defined in Linear.V4

type Diff (Point V4 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

type Diff (Point V4 s) = V4 s

Arbitrary dimension

data FinSuppSeq n Source #

The space of finitely-supported sequences is an infinite-dimensional space. An vector of length l is here understood as an infinite sequence that begins with l nonzero values, and continues with infinite zeroes.

You may also consider this as the type that languages like Octave/Matlab (as well as Haskell's hmatrix library) approximate with their “vectors”, with one important difference: there is no such thing as a dimensional-mismatch error, since we consider all these vectors as elements of the same infinite-dimensional space. Adding two different-size vectors will simply zero-pad the shorter, and unlike in Matlab this behaviour extends consequently to matrix multiplication etc. (defined in linearmap-category)

Of course it can make sense to constrain the dimension, but for this the type system should be used, not runtime checks.

(This is the same behaviour that the linear library gives to the standard list and vector types, but the problem there is that it can't use unboxed arrays as these are not functors, but unboxing is crucial for performance.)

Instances

Instances details
Unbox n => IsList (FinSuppSeq n) Source # 
Instance details

Defined in Data.VectorSpace.Free.FiniteSupportedSequence

Associated Types

type Item (FinSuppSeq n) #

(Unbox n, Show n) => Show (FinSuppSeq n) Source # 
Instance details

Defined in Data.VectorSpace.Free.FiniteSupportedSequence

(Num n, Unbox n) => AffineSpace (FinSuppSeq n) Source # 
Instance details

Defined in Data.VectorSpace.Free.FiniteSupportedSequence

Associated Types

type Diff (FinSuppSeq n) #

(Num n, Unbox n) => HasBasis (FinSuppSeq n) Source # 
Instance details

Defined in Data.VectorSpace.Free.FiniteSupportedSequence

Associated Types

type Basis (FinSuppSeq n) #

(Num n, Unbox n) => VectorSpace (FinSuppSeq n) Source # 
Instance details

Defined in Data.VectorSpace.Free.FiniteSupportedSequence

Associated Types

type Scalar (FinSuppSeq n) #

Methods

(*^) :: Scalar (FinSuppSeq n) -> FinSuppSeq n -> FinSuppSeq n #

(Num n, AdditiveGroup n, Unbox n) => InnerSpace (FinSuppSeq n) Source # 
Instance details

Defined in Data.VectorSpace.Free.FiniteSupportedSequence

Methods

(<.>) :: FinSuppSeq n -> FinSuppSeq n -> Scalar (FinSuppSeq n) #

(Num n, Unbox n) => AdditiveGroup (FinSuppSeq n) Source # 
Instance details

Defined in Data.VectorSpace.Free.FiniteSupportedSequence

(Num n, AdditiveGroup n, Unbox n) => FreeVectorSpace (FinSuppSeq n) Source # 
Instance details

Defined in Data.VectorSpace.Free.FiniteSupportedSequence

type Item (FinSuppSeq n) Source # 
Instance details

Defined in Data.VectorSpace.Free.FiniteSupportedSequence

type Item (FinSuppSeq n) = n
type Diff (FinSuppSeq n) Source # 
Instance details

Defined in Data.VectorSpace.Free.FiniteSupportedSequence

type Basis (FinSuppSeq n) Source # 
Instance details

Defined in Data.VectorSpace.Free.FiniteSupportedSequence

type Basis (FinSuppSeq n) = Int
type Scalar (FinSuppSeq n) Source # 
Instance details

Defined in Data.VectorSpace.Free.FiniteSupportedSequence

type Scalar (FinSuppSeq n) = n

The vector-space type classes

General

These come from the vector-space package.

class AdditiveGroup (Diff p) => AffineSpace p where #

Minimal complete definition

Nothing

Associated Types

type Diff p #

Associated vector space

type Diff p = GenericDiff p

Methods

(.-.) :: p -> p -> Diff p infix 6 #

Subtract points

(.+^) :: p -> Diff p -> p infixl 6 #

Point plus vector

Instances

Instances details
AffineSpace Double 
Instance details

Defined in Data.AffineSpace

Associated Types

type Diff Double #

AffineSpace Float 
Instance details

Defined in Data.AffineSpace

Associated Types

type Diff Float #

Methods

(.-.) :: Float -> Float -> Diff Float #

(.+^) :: Float -> Diff Float -> Float #

AffineSpace Int 
Instance details

Defined in Data.AffineSpace

Associated Types

type Diff Int #

Methods

(.-.) :: Int -> Int -> Diff Int #

(.+^) :: Int -> Diff Int -> Int #

AffineSpace Integer 
Instance details

Defined in Data.AffineSpace

Associated Types

type Diff Integer #

AffineSpace CSChar 
Instance details

Defined in Data.AffineSpace

Associated Types

type Diff CSChar #

AffineSpace CShort 
Instance details

Defined in Data.AffineSpace

Associated Types

type Diff CShort #

AffineSpace CInt 
Instance details

Defined in Data.AffineSpace

Associated Types

type Diff CInt #

Methods

(.-.) :: CInt -> CInt -> Diff CInt #

(.+^) :: CInt -> Diff CInt -> CInt #

AffineSpace CLong 
Instance details

Defined in Data.AffineSpace

Associated Types

type Diff CLong #

Methods

(.-.) :: CLong -> CLong -> Diff CLong #

(.+^) :: CLong -> Diff CLong -> CLong #

AffineSpace CLLong 
Instance details

Defined in Data.AffineSpace

Associated Types

type Diff CLLong #

AffineSpace CFloat 
Instance details

Defined in Data.AffineSpace

Associated Types

type Diff CFloat #

AffineSpace CDouble 
Instance details

Defined in Data.AffineSpace

Associated Types

type Diff CDouble #

AffineSpace CIntMax 
Instance details

Defined in Data.AffineSpace

Associated Types

type Diff CIntMax #

Integral a => AffineSpace (Ratio a) 
Instance details

Defined in Data.AffineSpace

Associated Types

type Diff (Ratio a) #

Methods

(.-.) :: Ratio a -> Ratio a -> Diff (Ratio a) #

(.+^) :: Ratio a -> Diff (Ratio a) -> Ratio a #

Num s => AffineSpace (V0 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Diff (V0 s) #

Methods

(.-.) :: V0 s -> V0 s -> Diff (V0 s) #

(.+^) :: V0 s -> Diff (V0 s) -> V0 s #

Num s => AffineSpace (V4 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Diff (V4 s) #

Methods

(.-.) :: V4 s -> V4 s -> Diff (V4 s) #

(.+^) :: V4 s -> Diff (V4 s) -> V4 s #

Num s => AffineSpace (V3 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Diff (V3 s) #

Methods

(.-.) :: V3 s -> V3 s -> Diff (V3 s) #

(.+^) :: V3 s -> Diff (V3 s) -> V3 s #

Num s => AffineSpace (V2 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Diff (V2 s) #

Methods

(.-.) :: V2 s -> V2 s -> Diff (V2 s) #

(.+^) :: V2 s -> Diff (V2 s) -> V2 s #

Num s => AffineSpace (V1 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Diff (V1 s) #

Methods

(.-.) :: V1 s -> V1 s -> Diff (V1 s) #

(.+^) :: V1 s -> Diff (V1 s) -> V1 s #

(Num n, Unbox n) => AffineSpace (SemisparseSuppSeq n) Source # 
Instance details

Defined in Data.VectorSpace.Free.FiniteSupportedSequence

Associated Types

type Diff (SemisparseSuppSeq n) #

(Num n, Unbox n) => AffineSpace (SparseSuppSeq n) Source # 
Instance details

Defined in Data.VectorSpace.Free.FiniteSupportedSequence

Associated Types

type Diff (SparseSuppSeq n) #

(Num n, Unbox n) => AffineSpace (FinSuppSeq n) Source # 
Instance details

Defined in Data.VectorSpace.Free.FiniteSupportedSequence

Associated Types

type Diff (FinSuppSeq n) #

(Num n, Unbox n) => AffineSpace (Sequence n) Source # 
Instance details

Defined in Data.VectorSpace.Free.Sequence

Associated Types

type Diff (Sequence n) #

Methods

(.-.) :: Sequence n -> Sequence n -> Diff (Sequence n) #

(.+^) :: Sequence n -> Diff (Sequence n) -> Sequence n #

AffineSpace p => AffineSpace (a -> p) 
Instance details

Defined in Data.AffineSpace

Associated Types

type Diff (a -> p) #

Methods

(.-.) :: (a -> p) -> (a -> p) -> Diff (a -> p) #

(.+^) :: (a -> p) -> Diff (a -> p) -> a -> p #

(AffineSpace p, AffineSpace q) => AffineSpace (p, q) 
Instance details

Defined in Data.AffineSpace

Associated Types

type Diff (p, q) #

Methods

(.-.) :: (p, q) -> (p, q) -> Diff (p, q) #

(.+^) :: (p, q) -> Diff (p, q) -> (p, q) #

Num s => AffineSpace (Point V0 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Diff (Point V0 s) #

Methods

(.-.) :: Point V0 s -> Point V0 s -> Diff (Point V0 s) #

(.+^) :: Point V0 s -> Diff (Point V0 s) -> Point V0 s #

Num s => AffineSpace (Point V4 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Diff (Point V4 s) #

Methods

(.-.) :: Point V4 s -> Point V4 s -> Diff (Point V4 s) #

(.+^) :: Point V4 s -> Diff (Point V4 s) -> Point V4 s #

Num s => AffineSpace (Point V3 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Diff (Point V3 s) #

Methods

(.-.) :: Point V3 s -> Point V3 s -> Diff (Point V3 s) #

(.+^) :: Point V3 s -> Diff (Point V3 s) -> Point V3 s #

Num s => AffineSpace (Point V2 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Diff (Point V2 s) #

Methods

(.-.) :: Point V2 s -> Point V2 s -> Diff (Point V2 s) #

(.+^) :: Point V2 s -> Diff (Point V2 s) -> Point V2 s #

Num s => AffineSpace (Point V1 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Associated Types

type Diff (Point V1 s) #

Methods

(.-.) :: Point V1 s -> Point V1 s -> Diff (Point V1 s) #

(.+^) :: Point V1 s -> Diff (Point V1 s) -> Point V1 s #

AffineSpace a => AffineSpace (Rec0 a s) 
Instance details

Defined in Data.AffineSpace

Associated Types

type Diff (Rec0 a s) #

Methods

(.-.) :: Rec0 a s -> Rec0 a s -> Diff (Rec0 a s) #

(.+^) :: Rec0 a s -> Diff (Rec0 a s) -> Rec0 a s #

(AffineSpace p, AffineSpace q, AffineSpace r) => AffineSpace (p, q, r) 
Instance details

Defined in Data.AffineSpace

Associated Types

type Diff (p, q, r) #

Methods

(.-.) :: (p, q, r) -> (p, q, r) -> Diff (p, q, r) #

(.+^) :: (p, q, r) -> Diff (p, q, r) -> (p, q, r) #

(AffineSpace (f p), AffineSpace (g p)) => AffineSpace (AffineDiffProductSpace f g p) 
Instance details

Defined in Data.AffineSpace

Associated Types

type Diff (AffineDiffProductSpace f g p) #

Methods

(.-.) :: AffineDiffProductSpace f g p -> AffineDiffProductSpace f g p -> Diff (AffineDiffProductSpace f g p) #

(.+^) :: AffineDiffProductSpace f g p -> Diff (AffineDiffProductSpace f g p) -> AffineDiffProductSpace f g p #

(AffineSpace (f p), AffineSpace (g p)) => AffineSpace ((f :*: g) p) 
Instance details

Defined in Data.AffineSpace

Associated Types

type Diff ((f :*: g) p) #

Methods

(.-.) :: (f :*: g) p -> (f :*: g) p -> Diff ((f :*: g) p) #

(.+^) :: (f :*: g) p -> Diff ((f :*: g) p) -> (f :*: g) p #

AffineSpace (f p) => AffineSpace (M1 i c f p) 
Instance details

Defined in Data.AffineSpace

Associated Types

type Diff (M1 i c f p) #

Methods

(.-.) :: M1 i c f p -> M1 i c f p -> Diff (M1 i c f p) #

(.+^) :: M1 i c f p -> Diff (M1 i c f p) -> M1 i c f p #

class AdditiveGroup v where #

Additive group v.

Minimal complete definition

Nothing

Methods

zeroV :: v #

The zero element: identity for (^+^)

(^+^) :: v -> v -> v infixl 6 #

Add vectors

negateV :: v -> v #

Additive inverse

(^-^) :: v -> v -> v infixl 6 #

Group subtraction

Instances

Instances details
AdditiveGroup Double 
Instance details

Defined in Data.AdditiveGroup

AdditiveGroup Float 
Instance details

Defined in Data.AdditiveGroup

AdditiveGroup Int 
Instance details

Defined in Data.AdditiveGroup

Methods

zeroV :: Int #

(^+^) :: Int -> Int -> Int #

negateV :: Int -> Int #

(^-^) :: Int -> Int -> Int #

AdditiveGroup Integer 
Instance details

Defined in Data.AdditiveGroup

AdditiveGroup () 
Instance details

Defined in Data.AdditiveGroup

Methods

zeroV :: () #

(^+^) :: () -> () -> () #

negateV :: () -> () #

(^-^) :: () -> () -> () #

AdditiveGroup CSChar 
Instance details

Defined in Data.AdditiveGroup

AdditiveGroup CShort 
Instance details

Defined in Data.AdditiveGroup

AdditiveGroup CInt 
Instance details

Defined in Data.AdditiveGroup

Methods

zeroV :: CInt #

(^+^) :: CInt -> CInt -> CInt #

negateV :: CInt -> CInt #

(^-^) :: CInt -> CInt -> CInt #

AdditiveGroup CLong 
Instance details

Defined in Data.AdditiveGroup

AdditiveGroup CLLong 
Instance details

Defined in Data.AdditiveGroup

AdditiveGroup CFloat 
Instance details

Defined in Data.AdditiveGroup

AdditiveGroup CDouble 
Instance details

Defined in Data.AdditiveGroup

AdditiveGroup CIntMax 
Instance details

Defined in Data.AdditiveGroup

AdditiveGroup a => AdditiveGroup (Maybe a) 
Instance details

Defined in Data.AdditiveGroup

Methods

zeroV :: Maybe a #

(^+^) :: Maybe a -> Maybe a -> Maybe a #

negateV :: Maybe a -> Maybe a #

(^-^) :: Maybe a -> Maybe a -> Maybe a #

Integral a => AdditiveGroup (Ratio a) 
Instance details

Defined in Data.AdditiveGroup

Methods

zeroV :: Ratio a #

(^+^) :: Ratio a -> Ratio a -> Ratio a #

negateV :: Ratio a -> Ratio a #

(^-^) :: Ratio a -> Ratio a -> Ratio a #

(RealFloat v, AdditiveGroup v) => AdditiveGroup (Complex v) 
Instance details

Defined in Data.AdditiveGroup

Methods

zeroV :: Complex v #

(^+^) :: Complex v -> Complex v -> Complex v #

negateV :: Complex v -> Complex v #

(^-^) :: Complex v -> Complex v -> Complex v #

Num s => AdditiveGroup (V0 s) Source # 
Instance details

Defined in Data.VectorSpace.Free

Methods

zeroV :: V0 s #

(^+^) :: V0 s -> V0 s -> V0 s #