Copyright	(c) Justus Sagemüller 2016
License	GPL v3
Maintainer	(@) jsag $ hvl.no
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell2010

Data.VectorSpace.Free

Contents

Supported types
- Fixed low dimension
- Arbitrary dimension
The vector-space type classes
Orphan instances

Description

Synopsis

data V0 a
data V1 a
data V2 a
data V3 a
data V4 a
type Sequence = GSequence Vector
data FinSuppSeq n
class AdditiveGroup (Diff p) => AffineSpace p where
- type Diff p
- (.-.) :: p -> p -> Diff p
- (.+^) :: p -> Diff p -> p
class AdditiveGroup v where
- zeroV :: v
- (^+^) :: v -> v -> v
- negateV :: v -> v
- (^-^) :: v -> v -> v
class AdditiveGroup v => VectorSpace v where
- type Scalar v
- (*^) :: Scalar v -> v -> v
class (VectorSpace v, AdditiveGroup (Scalar v)) => InnerSpace v where
- (<.>) :: v -> v -> Scalar v
class VectorSpace v => HasBasis v where
- type Basis v
- basisValue :: Basis v -> v
- decompose :: v -> [(Basis v, Scalar v)]
- decompose' :: v -> Basis v -> Scalar v
class (VectorSpace v, Fractional (Scalar v)) => OneDimensional v where
- (^/^) :: v -> v -> Maybe (Scalar v)
- (^/!) :: v -> v -> Scalar v
class (VectorSpace v, Num (Scalar v)) => FreeVectorSpace v where
- (^*^) :: v -> v -> v
- vmap :: (Scalar v -> Scalar v) -> v -> v
class (VectorSpace v, Num (Scalar v)) => FiniteFreeSpace v where
- freeDimension :: Functor p => p v -> Int
- toFullUnboxVect :: Unbox (Scalar v) => v -> Vector (Scalar v)
- unsafeFromFullUnboxVect :: Unbox (Scalar v) => Vector (Scalar v) -> v
- fromUnboxVect :: Unbox (Scalar v) => Vector (Scalar v) -> v

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 Methods readsPrec :: Int -> ReadS (V0 a) # readList :: ReadS [V0 a] # readPrec :: ReadPrec (V0 a) # readListPrec :: ReadPrec [V0 a] #
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 Methods showsPrec :: Int -> V0 Double -> ShowS # show :: V0 Double -> String # showList :: [V0 Double] -> ShowS #
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 Methods showsPrec :: Int -> V0 Integer -> ShowS # show :: V0 Integer -> String # showList :: [V0 Integer] -> ShowS #
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 Methods freeDimension :: Functor p => p (V0 s) -> Int Source # toFullUnboxVect :: V0 s -> Vector (Scalar (V0 s)) Source # unsafeFromFullUnboxVect :: Vector (Scalar (V0 s)) -> V0 s Source # fromUnboxVect :: Vector (Scalar (V0 s)) -> V0 s Source #
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-1.21.9-6oNTW01QwujhmpV2bFQ8C" '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-1.21.9-6oNTW01QwujhmpV2bFQ8C" '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 Methods readsPrec :: Int -> ReadS (V1 a) # readList :: ReadS [V1 a] # readPrec :: ReadPrec (V1 a) # readListPrec :: ReadPrec [V1 a] #
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 Methods showsPrec :: Int -> V1 Double -> ShowS # show :: V1 Double -> String # showList :: [V1 Double] -> ShowS #
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 Methods showsPrec :: Int -> V1 Integer -> ShowS # show :: V1 Integer -> String # showList :: [V1 Integer] -> ShowS #
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 Methods freeDimension :: Functor p => p (V1 s) -> Int Source # toFullUnboxVect :: V1 s -> Vector (Scalar (V1 s)) Source # unsafeFromFullUnboxVect :: Vector (Scalar (V1 s)) -> V1 s Source # fromUnboxVect :: Vector (Scalar (V1 s)) -> V1 s Source #
(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-1.21.9-6oNTW01QwujhmpV2bFQ8C" '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-1.21.9-6oNTW01QwujhmpV2bFQ8C" '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 Methods readsPrec :: Int -> ReadS (V2 a) # readList :: ReadS [V2 a] # readPrec :: ReadPrec (V2 a) # readListPrec :: ReadPrec [V2 a] #
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 Methods showsPrec :: Int -> V2 Double -> ShowS # show :: V2 Double -> String # showList :: [V2 Double] -> ShowS #
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 Methods showsPrec :: Int -> V2 Integer -> ShowS # show :: V2 Integer -> String # showList :: [V2 Integer] -> ShowS #
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 Methods freeDimension :: Functor p => p (V2 s) -> Int Source # toFullUnboxVect :: V2 s -> Vector (Scalar (V2 s)) Source # unsafeFromFullUnboxVect :: Vector (Scalar (V2 s)) -> V2 s Source # fromUnboxVect :: Vector (Scalar (V2 s)) -> V2 s Source #
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-1.21.9-6oNTW01QwujhmpV2bFQ8C" '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-1.21.9-6oNTW01QwujhmpV2bFQ8C" '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 Methods readsPrec :: Int -> ReadS (V3 a) # readList :: ReadS [V3 a] # readPrec :: ReadPrec (V3 a) # readListPrec :: ReadPrec [V3 a] #
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 Methods showsPrec :: Int -> V3 Double -> ShowS # show :: V3 Double -> String # showList :: [V3 Double] -> ShowS #
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 Methods showsPrec :: Int -> V3 Integer -> ShowS # show :: V3 Integer -> String # showList :: [V3 Integer] -> ShowS #
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 Methods freeDimension :: Functor p => p (V3 s) -> Int Source # toFullUnboxVect :: V3 s -> Vector (Scalar (V3 s)) Source # unsafeFromFullUnboxVect :: Vector (Scalar (V3 s)) -> V3 s Source # fromUnboxVect :: Vector (Scalar (V3 s)) -> V3 s Source #
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 type Rep (V3 a) = D1 ('MetaData "V3" "Linear.V3" "linear-1.21.9-6oNTW01QwujhmpV2bFQ8C" 'False) (C1 ('MetaCons "V3" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a))))
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 Rep1 V3 = D1 ('MetaData "V3" "Linear.V3" "linear-1.21.9-6oNTW01QwujhmpV2bFQ8C" 'False) (C1 ('MetaCons "V3" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1)))
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 Methods readsPrec :: Int -> ReadS (V4 a) # readList :: ReadS [V4 a] # readPrec :: ReadPrec (V4 a) # readListPrec :: ReadPrec [V4 a] #
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 Methods showsPrec :: Int -> V4 Double -> ShowS # show :: V4 Double -> String # showList :: [V4 Double] -> ShowS #
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 Methods showsPrec :: Int -> V4 Integer -> ShowS # show :: V4 Integer -> String # showList :: [V4 Integer] -> ShowS #
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 Methods freeDimension :: Functor p => p (V4 s) -> Int Source # toFullUnboxVect :: V4 s -> Vector (Scalar (V4 s)) Source # unsafeFromFullUnboxVect :: Vector (Scalar (V4 s)) -> V4 s Source # fromUnboxVect :: Vector (Scalar (V4 s)) -> V4 s Source #
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 type Rep (V4 a) = D1 ('MetaData "V4" "Linear.V4" "linear-1.21.9-6oNTW01QwujhmpV2bFQ8C" 'False) (C1 ('MetaCons "V4" 'PrefixI 'False) ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)) :: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a))))
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 Rep1 V4 = D1 ('MetaData "V4" "Linear.V4" "linear-1.21.9-6oNTW01QwujhmpV2bFQ8C" 'False) (C1 ('MetaCons "V4" 'PrefixI 'False) ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1) :: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1)))
type Diff (Point V4 s) Source #
Instance details Defined in Data.VectorSpace.Free type Diff (Point V4 s) = V4 s

Arbitrary dimension

type Sequence = GSequence Vector Source #

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) # Methods fromList :: [Item (FinSuppSeq n)] -> FinSuppSeq n # fromListN :: Int -> [Item (FinSuppSeq n)] -> FinSuppSeq n # toList :: FinSuppSeq n -> [Item (FinSuppSeq n)] #
(Unbox n, Show n) => Show (FinSuppSeq n) Source #
Instance details Defined in Data.VectorSpace.Free.FiniteSupportedSequence Methods showsPrec :: Int -> FinSuppSeq n -> ShowS # show :: FinSuppSeq n -> String # showList :: [FinSuppSeq n] -> ShowS #
(Num n, Unbox n) => AffineSpace (FinSuppSeq n) Source #
Instance details Defined in Data.VectorSpace.Free.FiniteSupportedSequence Associated Types type Diff (FinSuppSeq n) # Methods (.-.) :: FinSuppSeq n -> FinSuppSeq n -> Diff (FinSuppSeq n) # (.+^) :: FinSuppSeq n -> Diff (FinSuppSeq n) -> FinSuppSeq n #
(Num n, Unbox n) => HasBasis (FinSuppSeq n) Source #
Instance details Defined in Data.VectorSpace.Free.FiniteSupportedSequence Associated Types type Basis (FinSuppSeq n) # Methods basisValue :: Basis (FinSuppSeq n) -> FinSuppSeq n # decompose :: FinSuppSeq n -> [(Basis (FinSuppSeq n), Scalar (FinSuppSeq n))] # decompose' :: FinSuppSeq n -> Basis (FinSuppSeq n) -> Scalar (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 Methods zeroV :: FinSuppSeq n # (^+^) :: FinSuppSeq n -> FinSuppSeq n -> FinSuppSeq n # negateV :: FinSuppSeq n -> FinSuppSeq n # (^-^) :: FinSuppSeq n -> FinSuppSeq n -> FinSuppSeq n #
(Num n, AdditiveGroup n, Unbox n) => FreeVectorSpace (FinSuppSeq n) Source #
Instance details Defined in Data.VectorSpace.Free.FiniteSupportedSequence Methods (^*^) :: FinSuppSeq n -> FinSuppSeq n -> FinSuppSeq n Source # vmap :: (Scalar (FinSuppSeq n) -> Scalar (FinSuppSeq n)) -> FinSuppSeq n -> FinSuppSeq n Source #
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 Diff (FinSuppSeq n) = FinSuppSeq n
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 # Methods (.-.) :: Double -> Double -> Diff Double # (.+^) :: Double -> Diff Double -> 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 # Methods (.-.) :: Integer -> Integer -> Diff Integer # (.+^) :: Integer -> Diff Integer -> Integer #
AffineSpace CSChar
Instance details Defined in Data.AffineSpace Associated Types type Diff CSChar # Methods (.-.) :: CSChar -> CSChar -> Diff CSChar # (.+^) :: CSChar -> Diff CSChar -> CSChar #
AffineSpace CShort
Instance details Defined in Data.AffineSpace Associated Types type Diff CShort # Methods (.-.) :: CShort -> CShort -> Diff CShort # (.+^) :: CShort -> Diff CShort -> 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 # Methods (.-.) :: CLLong -> CLLong -> Diff CLLong # (.+^) :: CLLong -> Diff CLLong -> CLLong #
AffineSpace CFloat
Instance details Defined in Data.AffineSpace Associated Types type Diff CFloat # Methods (.-.) :: CFloat -> CFloat -> Diff CFloat # (.+^) :: CFloat -> Diff CFloat -> CFloat #
AffineSpace CDouble
Instance details Defined in Data.AffineSpace Associated Types type Diff CDouble # Methods (.-.) :: CDouble -> CDouble -> Diff CDouble # (.+^) :: CDouble -> Diff CDouble -> CDouble #
AffineSpace CIntMax
Instance details Defined in Data.AffineSpace Associated Types type Diff CIntMax # Methods (.-.) :: CIntMax -> CIntMax -> Diff CIntMax # (.+^) :: CIntMax -> Diff CIntMax -> 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) # Methods (.-.) :: SemisparseSuppSeq n -> SemisparseSuppSeq n -> Diff (SemisparseSuppSeq n) # (.+^) :: SemisparseSuppSeq n -> Diff (SemisparseSuppSeq n) -> SemisparseSuppSeq n #
(Num n, Unbox n) => AffineSpace (SparseSuppSeq n) Source #
Instance details Defined in Data.VectorSpace.Free.FiniteSupportedSequence Associated Types type Diff (SparseSuppSeq n) # Methods (.-.) :: SparseSuppSeq n -> SparseSuppSeq n -> Diff (SparseSuppSeq n) # (.+^) :: SparseSuppSeq n -> Diff (SparseSuppSeq n) -> SparseSuppSeq n #
(Num n, Unbox n) => AffineSpace (FinSuppSeq n) Source #
Instance details Defined in Data.VectorSpace.Free.FiniteSupportedSequence Associated Types type Diff (FinSuppSeq n) # Methods (.-.) :: FinSuppSeq n -> FinSuppSeq n -> Diff (FinSuppSeq n) # (.+^) :: FinSuppSeq n -> Diff (FinSuppSeq n) -> 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 Methods zeroV :: Double # (^+^) :: Double -> Double -> Double # negateV :: Double -> Double # (^-^) :: Double -> Double -> Double #
AdditiveGroup Float
Instance details Defined in Data.AdditiveGroup Methods zeroV :: Float # (^+^) :: Float -> Float -> Float # negateV :: Float -> Float # (^-^) :: Float -> Float -> Float #
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 Methods zeroV :: Integer # (^+^) :: Integer -> Integer -> Integer # negateV :: Integer -> Integer # (^-^) :: Integer -> Integer -> Integer #
AdditiveGroup ()
Instance details Defined in Data.AdditiveGroup Methods zeroV :: () # (^+^) :: () -> () -> () # negateV :: () -> () # (^-^) :: () -> () -> () #
AdditiveGroup CSChar
Instance details Defined in Data.AdditiveGroup Methods zeroV :: CSChar # (^+^) :: CSChar -> CSChar -> CSChar # negateV :: CSChar -> CSChar # (^-^) :: CSChar -> CSChar -> CSChar #
AdditiveGroup CShort
Instance details Defined in Data.AdditiveGroup Methods zeroV :: CShort # (^+^) :: CShort -> CShort -> CShort # negateV :: CShort -> CShort # (^-^) :: CShort -> CShort -> CShort #
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 Methods zeroV :: CLong # (^+^) :: CLong -> CLong -> CLong # negateV :: CLong -> CLong # (^-^) :: CLong -> CLong -> CLong #
AdditiveGroup CLLong
Instance details Defined in Data.AdditiveGroup Methods zeroV :: CLLong # (^+^) :: CLLong -> CLLong -> CLLong # negateV :: CLLong -> CLLong # (^-^) :: CLLong -> CLLong -> CLLong #
AdditiveGroup CFloat
Instance details Defined in Data.AdditiveGroup Methods zeroV :: CFloat # (^+^) :: CFloat -> CFloat -> CFloat # negateV :: CFloat -> CFloat # (^-^) :: CFloat -> CFloat -> CFloat #
AdditiveGroup CDouble
Instance details Defined in Data.AdditiveGroup Methods zeroV :: CDouble # (^+^) :: CDouble -> CDouble -> CDouble # negateV :: CDouble -> CDouble # (^-^) :: CDouble -> CDouble -> CDouble #
AdditiveGroup CIntMax
Instance details Defined in Data.AdditiveGroup Methods zeroV :: CIntMax # (^+^) :: CIntMax -> CIntMax -> CIntMax # negateV :: CIntMax -> CIntMax # (^-^) :: CIntMax -> CIntMax -> CIntMax #
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 # negateV :: V0 s -> V0 s # (^-^) :: V0 s -> V0 s -> V0 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 => 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 => 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 => 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 #
AdditiveGroup a => AdditiveGroup (Sum a)
Instance details Defined in Data.AdditiveGroup Methods zeroV :: Sum a # (^+^) :: Sum a -> Sum a -> Sum a # negateV :: Sum a -> Sum a # (^-^) :: Sum a -> Sum a -> Sum a #
AdditiveGroup (Diff (VRep p)) => AdditiveGroup (GenericDiff p)
Instance details Defined in Data.AffineSpace Methods zeroV :: GenericDiff p # (^+^) :: GenericDiff p -> GenericDiff p -> GenericDiff p # negateV :: GenericDiff p -> GenericDiff p # (^-^) :: GenericDiff p -> GenericDiff p -> GenericDiff p #
(Num n, Unbox n) => AdditiveGroup (SemisparseSuppSeq n) Source #
Instance details Defined in Data.VectorSpace.Free.FiniteSupportedSequence Methods zeroV :: SemisparseSuppSeq n # (^+^) :: SemisparseSuppSeq n -> SemisparseSuppSeq n -> SemisparseSuppSeq n # negateV :: SemisparseSuppSeq n -> SemisparseSuppSeq n # (^-^) :: SemisparseSuppSeq n -> SemisparseSuppSeq n -> SemisparseSuppSeq n #
(Num n, Unbox n) => AdditiveGroup (SparseSuppSeq n) Source #
Instance details Defined in Data.VectorSpace.Free.FiniteSupportedSequence Methods zeroV :: SparseSuppSeq n # (^+^) :: SparseSuppSeq n -> SparseSuppSeq n -> SparseSuppSeq n # negateV :: SparseSuppSeq n -> SparseSuppSeq n # (^-^) :: SparseSuppSeq n -> SparseSuppSeq n -> SparseSuppSeq n #
(Num n, Unbox n) => AdditiveGroup (FinSuppSeq n) Source #
Instance details Defined in Data.VectorSpace.Free.FiniteSupportedSequence Methods zeroV :: FinSuppSeq n # (^+^) :: FinSuppSeq n -> FinSuppSeq n -> FinSuppSeq n # negateV :: FinSuppSeq n -> FinSuppSeq n # (^-^) :: FinSuppSeq n -> FinSuppSeq n -> FinSuppSeq n #
(Num n, Unbox n) => AdditiveGroup (Sequence n) Source #
Instance details Defined in Data.VectorSpace.Free.Sequence Methods zeroV :: Sequence n # (^+^) :: Sequence n -> Sequence n -> Sequence n # negateV :: Sequence n -> Sequence n # (^-^) :: Sequence n -> Sequence n -> Sequence n #
AdditiveGroup v => AdditiveGroup (a -> v)
Instance details Defined in Data.AdditiveGroup Methods zeroV :: a -> v # (^+^) :: (a -> v) -> (a -> v) -> a -> v # negateV :: (a -> v) -> a -> v # (^-^) :: (a -> v) -> (a -> v) -> a -> v #
(AdditiveGroup u, AdditiveGroup v) => AdditiveGroup (u, v)
Instance details Defined in Data.AdditiveGroup Methods zeroV :: (u, v) # (^+^) :: (u, v) -> (u, v) -> (u, v) # negateV :: (u, v) -> (u, v) # (^-^) :: (u, v) -> (u, v) -> (u, v) #
(HasTrie u, AdditiveGroup v) => AdditiveGroup (u :->: v)
Instance details Defined in Data.AdditiveGroup Methods zeroV :: u :->: v # (^+^) :: (u :->: v) -> (u :->: v) -> u :->: v # negateV :: (u :->: v) -> u :->: v # (^-^) :: (u :->: v) -> (u :->: v) -> u :->: v #
(HasBasis a, HasTrie (Basis a), AdditiveGroup u) => AdditiveGroup (a :> u)
Instance details Defined in Data.Maclaurin Methods zeroV :: a :> u # (^+^) :: (a :> u) -> (a :> u) -> a :> u # negateV :: (a :> u) -> a :> u # (^-^) :: (a :> u) -> (a :> u) -> a :> u #
(HasTrie (Basis u), AdditiveGroup v) => AdditiveGroup (u :-* v)
Instance details Defined in Data.LinearMap Methods zeroV :: u :-* v # (^+^) :: (u :-* v) -> (u :-* v) -> u :-* v # negateV :: (u :-* v) -> u :-* v # (^-^) :: (u :-* v) -> (u :-* v) -> u :-* v #
AdditiveGroup a => AdditiveGroup (Rec0 a s)
Instance details Defined in Data.AdditiveGroup Methods zeroV :: Rec0 a s # (^+^) :: Rec0 a s -> Rec0 a s -> Rec0 a s # negateV :: Rec0 a s -> Rec0 a s # (^-^) :: Rec0 a s -> Rec0 a s -> Rec0 a s #
(AdditiveGroup u, AdditiveGroup v, AdditiveGroup w) => AdditiveGroup (u, v, w)
Instance details Defined in Data.AdditiveGroup Methods zeroV :: (u, v, w) # (^+^) :: (u, v, w) -> (u, v, w) -> (u, v, w) # negateV :: (u, v, w) -> (u, v, w) # (^-^) :: (u, v, w) -> (u, v, w) -> (u, v, w) #
(AffineSpace (f p), AffineSpace (g p)) => AdditiveGroup (AffineDiffProductSpace f g p)
Instance details Defined in Data.AffineSpace Methods zeroV :: AffineDiffProductSpace f g p # (^+^) :: AffineDiffProductSpace f g p -> AffineDiffProductSpace f g p -> AffineDiffProductSpace f g p # negateV :: AffineDiffProductSpace f g p -> AffineDiffProductSpace f g p # (^-^) :: AffineDiffProductSpace f g p -> AffineDiffProductSpace f g p -> AffineDiffProductSpace f g p #
(AdditiveGroup (f p), AdditiveGroup (g p)) => AdditiveGroup ((f :*: g) p)
Instance details Defined in Data.AdditiveGroup Methods zeroV :: (f :: g) p # (^+^) :: (f :: g) p -> (f :: g) p -> (f :: g) p # negateV :: (f :: g) p -> (f :: g) p # (^-^) :: (f :: g) p -> (f :: g) p -> (f :*: g) p #
(AdditiveGroup u, AdditiveGroup v, AdditiveGroup w, AdditiveGroup x) => AdditiveGroup (u, v, w, x)
Instance details Defined in Data.AdditiveGroup Methods zeroV :: (u, v, w, x) # (^+^) :: (u, v, w, x) -> (u, v, w, x) -> (u, v, w, x) # negateV :: (u, v, w, x) -> (u, v, w, x) # (^-^) :: (u, v, w, x) -> (u, v, w, x) -> (u, v, w, x) #
AdditiveGroup (f p) => AdditiveGroup (M1 i c f p)
Instance details Defined in Data.AdditiveGroup Methods zeroV :: M1 i c f p # (^+^) :: M1 i c f p -> M1 i c f p -> M1 i c f p # negateV :: M1 i c f p -> M1 i c f p # (^-^) :: M1 i c f p -> M1 i c f p -> M1 i c f p #

class AdditiveGroup v => VectorSpace v where #

Vector space v.

Minimal complete definition

Nothing

Associated Types

type Scalar v #

type Scalar v = Scalar (VRep v)

Methods

(*^) :: Scalar v -> v -> v infixr 7 #

Scale a vector

Instances

Instances details

VectorSpace Double
Instance details Defined in Data.VectorSpace Associated Types type Scalar Double # Methods (*^) :: Scalar Double -> Double -> Double #
VectorSpace Float
Instance details Defined in Data.VectorSpace Associated Types type Scalar Float # Methods (*^) :: Scalar Float -> Float -> Float #
VectorSpace Int
Instance details Defined in Data.VectorSpace Associated Types type Scalar Int # Methods (*^) :: Scalar Int -> Int -> Int #
VectorSpace Integer
Instance details Defined in Data.VectorSpace Associated Types type Scalar Integer # Methods (*^) :: Scalar Integer -> Integer -> Integer #
VectorSpace CSChar
Instance details Defined in Data.VectorSpace Associated Types type Scalar CSChar # Methods (*^) :: Scalar CSChar -> CSChar -> CSChar #
VectorSpace CShort
Instance details Defined in Data.VectorSpace Associated Types type Scalar CShort # Methods (*^) :: Scalar CShort -> CShort -> CShort #
VectorSpace CInt
Instance details Defined in Data.VectorSpace Associated Types type Scalar CInt # Methods (*^) :: Scalar CInt -> CInt -> CInt #
VectorSpace CLong
Instance details Defined in Data.VectorSpace Associated Types type Scalar CLong # Methods (*^) :: Scalar CLong -> CLong -> CLong #
VectorSpace CLLong
Instance details Defined in Data.VectorSpace Associated Types type Scalar CLLong # Methods (*^) :: Scalar CLLong -> CLLong -> CLLong #
VectorSpace CFloat
Instance details Defined in Data.VectorSpace Associated Types type Scalar CFloat # Methods (*^) :: Scalar CFloat -> CFloat -> CFloat #
VectorSpace CDouble
Instance details Defined in Data.VectorSpace Associated Types type Scalar CDouble # Methods (*^) :: Scalar CDouble -> CDouble -> CDouble #
VectorSpace CIntMax
Instance details Defined in Data.VectorSpace Associated Types type Scalar CIntMax # Methods (*^) :: Scalar CIntMax -> CIntMax -> CIntMax #
VectorSpace v => VectorSpace (Maybe v)
Instance details Defined in Data.VectorSpace Associated Types type Scalar (Maybe v) # Methods (*^) :: Scalar (Maybe v) -> Maybe v -> Maybe v #
Integral a => VectorSpace (Ratio a)
Instance details Defined in Data.VectorSpace Associated Types type Scalar (Ratio a) # Methods (*^) :: Scalar (Ratio a) -> Ratio a -> Ratio a #
(RealFloat v, VectorSpace v) => VectorSpace (Complex v)
Instance details Defined in Data.VectorSpace Associated Types type Scalar (Complex v) # Methods (*^) :: Scalar (Complex v) -> Complex v -> Complex v #
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 => 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 => 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 => 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 => 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 #
VectorSpace (Diff (VRep p)) => VectorSpace (GenericDiff p)
Instance details Defined in Data.AffineSpace Associated Types type Scalar (GenericDiff p) # Methods (*^) :: Scalar (GenericDiff p) -> GenericDiff p -> GenericDiff p #
(Num n, Unbox n) => VectorSpace (SemisparseSuppSeq n) Source #
Instance details Defined in Data.VectorSpace.Free.FiniteSupportedSequence Associated Types type Scalar (SemisparseSuppSeq n) # Methods (*^) :: Scalar (SemisparseSuppSeq n) -> SemisparseSuppSeq n -> SemisparseSuppSeq n #
(Num n, Unbox n) => VectorSpace (SparseSuppSeq n) Source #
Instance details Defined in Data.VectorSpace.Free.FiniteSupportedSequence Associated Types type Scalar (SparseSuppSeq n) # Methods (*^) :: Scalar (SparseSuppSeq n) -> SparseSuppSeq n -> SparseSuppSeq 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, Unbox n) => VectorSpace (Sequence n) Source #
Instance details Defined in Data.VectorSpace.Free.Sequence Associated Types type Scalar (Sequence n) # Methods (*^) :: Scalar (Sequence n) -> Sequence n -> Sequence n #
VectorSpace v => VectorSpace (a -> v)
Instance details Defined in Data.VectorSpace Associated Types type Scalar (a -> v) # Methods (*^) :: Scalar (a -> v) -> (a -> v) -> a -> v #
(VectorSpace u, s ~ Scalar u, VectorSpace v, s ~ Scalar v) => VectorSpace (u, v)
Instance details Defined in Data.VectorSpace Associated Types type Scalar (u, v) # Methods (*^) :: Scalar (u, v) -> (u, v) -> (u, v) #
(HasTrie a, VectorSpace v) => VectorSpace (a :->: v)
Instance details Defined in Data.VectorSpace Associated Types type Scalar (a :->: v) # Methods (*^) :: Scalar (a :->: v) -> (a :->: v) -> a :->: v #
(HasBasis a, HasTrie (Basis a), VectorSpace u) => VectorSpace (a :> u)
Instance details Defined in Data.Maclaurin Associated Types type Scalar (a :> u) # Methods (*^) :: Scalar (a :> u) -> (a :> u) -> a :> u #
(HasTrie (Basis u), VectorSpace v) => VectorSpace (u :-* v)
Instance details Defined in Data.LinearMap Associated Types type Scalar (u :-* v) # Methods (^) :: Scalar (u :- v) -> (u :-* v) -> u :-* v #
VectorSpace a => VectorSpace (Rec0 a s)
Instance details Defined in Data.VectorSpace Associated Types type Scalar (Rec0 a s) # Methods (*^) :: Scalar (Rec0 a s) -> Rec0 a s -> Rec0 a s #
(VectorSpace u, s ~ Scalar u, VectorSpace v, s ~ Scalar v, VectorSpace w, s ~ Scalar w) => VectorSpace (u, v, w)
Instance details Defined in Data.VectorSpace Associated Types type Scalar (u, v, w) # Methods (*^) :: Scalar (u, v, w) -> (u, v, w) -> (u, v, w) #
(AffineSpace (f p), AffineSpace (g p), VectorSpace (Diff (f p)), VectorSpace (Diff (g p)), Scalar (Diff (f p)) ~ Scalar (Diff (g p))) => VectorSpace (AffineDiffProductSpace f g p)
Instance details Defined in Data.AffineSpace Associated Types type Scalar (AffineDiffProductSpace f g p) # Methods (*^) :: Scalar (AffineDiffProductSpace f g p) -> AffineDiffProductSpace f g p -> AffineDiffProductSpace f g p #
(VectorSpace (f p), VectorSpace (g p), Scalar (f p) ~ Scalar (g p)) => VectorSpace ((f :*: g) p)
Instance details Defined in Data.VectorSpace Associated Types type Scalar ((f :: g) p) # Methods (^) :: Scalar ((f :: g) p) -> (f :: g) p -> (f :*: g) p #
(VectorSpace u, s ~ Scalar u, VectorSpace v, s ~ Scalar v, VectorSpace w, s ~ Scalar w, VectorSpace x, s ~ Scalar x) => VectorSpace (u, v, w, x)
Instance details Defined in Data.VectorSpace Associated Types type Scalar (u, v, w, x) # Methods (*^) :: Scalar (u, v, w, x) -> (u, v, w, x) -> (u, v, w, x) #
VectorSpace (f p) => VectorSpace (M1 i c f p)
Instance details Defined in Data.VectorSpace Associated Types type Scalar (M1 i c f p) # Methods (*^) :: Scalar (M1 i c f p) -> M1 i c f p -> M1 i c f p #

class (VectorSpace v, AdditiveGroup (Scalar v)) => InnerSpace v where #

Adds inner (dot) products.

Minimal complete definition

Nothing

Methods

(<.>) :: v -> v -> Scalar v infixr 7 #

Inner/dot product

Instances

Instances details

InnerSpace Double
Instance details Defined in Data.VectorSpace Methods (<.>) :: Double -> Double -> Scalar Double #
InnerSpace Float
Instance details Defined in Data.VectorSpace Methods (<.>) :: Float -> Float -> Scalar Float #
InnerSpace Int
Instance details Defined in Data.VectorSpace Methods (<.>) :: Int -> Int -> Scalar Int #
InnerSpace Integer
Instance details Defined in Data.VectorSpace Methods (<.>) :: Integer -> Integer -> Scalar Integer #
InnerSpace CSChar
Instance details Defined in Data.VectorSpace Methods (<.>) :: CSChar -> CSChar -> Scalar CSChar #
InnerSpace CShort
Instance details Defined in Data.VectorSpace Methods (<.>) :: CShort -> CShort -> Scalar CShort #
InnerSpace CInt
Instance details Defined in Data.VectorSpace Methods (<.>) :: CInt -> CInt -> Scalar CInt #
InnerSpace CLong
Instance details Defined in Data.VectorSpace Methods (<.>) :: CLong -> CLong -> Scalar CLong #
InnerSpace CLLong
Instance details Defined in Data.VectorSpace Methods (<.>) :: CLLong -> CLLong -> Scalar CLLong #
InnerSpace CFloat
Instance details Defined in Data.VectorSpace Methods (<.>) :: CFloat -> CFloat -> Scalar CFloat #
InnerSpace CDouble
Instance details Defined in Data.VectorSpace Methods (<.>) :: CDouble -> CDouble -> Scalar CDouble #
InnerSpace CIntMax
Instance details Defined in Data.VectorSpace Methods (<.>) :: CIntMax -> CIntMax -> Scalar CIntMax #
InnerSpace a => InnerSpace (Maybe a)
Instance details Defined in Data.VectorSpace Methods (<.>) :: Maybe a -> Maybe a -> Scalar (Maybe a) #
Integral a => InnerSpace (Ratio a)
Instance details Defined in Data.VectorSpace Methods (<.>) :: Ratio a -> Ratio a -> Scalar (Ratio a) #
(RealFloat v, InnerSpace v) => InnerSpace (Complex v)
Instance details Defined in Data.VectorSpace Methods (<.>) :: Complex v -> Complex v -> Scalar (Complex v) #
(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 s) => InnerSpace (V4 s) Source #
Instance details Defined in Data.VectorSpace.Free Methods (<.>) :: V4 s -> V4 s -> Scalar (V4 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 s) => InnerSpace (V2 s) Source #
Instance details Defined in Data.VectorSpace.Free Methods (<.>) :: V2 s -> V2 s -> Scalar (V2 s) #
(Num s, AdditiveGroup s) => InnerSpace (V1 s) Source #
Instance details Defined in Data.VectorSpace.Free Methods (<.>) :: V1 s -> V1 s -> Scalar (V1 s) #
InnerSpace (Diff (VRep p)) => InnerSpace (GenericDiff p)
Instance details Defined in Data.AffineSpace Methods (<.>) :: GenericDiff p -> GenericDiff p -> Scalar (GenericDiff p) #
(Num n, AdditiveGroup n, Unbox n) => InnerSpace (SemisparseSuppSeq n) Source #
Instance details Defined in Data.VectorSpace.Free.FiniteSupportedSequence Methods (<.>) :: SemisparseSuppSeq n -> SemisparseSuppSeq n -> Scalar (SemisparseSuppSeq n) #
(Num n, AdditiveGroup n, Unbox n) => InnerSpace (SparseSuppSeq n) Source #
Instance details Defined in Data.VectorSpace.Free.FiniteSupportedSequence Methods (<.>) :: SparseSuppSeq n -> SparseSuppSeq n -> Scalar (SparseSuppSeq 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) #
InnerSpace v => InnerSpace (a -> v)
Instance details Defined in Data.VectorSpace Methods (<.>) :: (a -> v) -> (a -> v) -> Scalar (a -> v) #
(InnerSpace u, s ~ Scalar u, InnerSpace v, s ~ Scalar v) => InnerSpace (u, v)
Instance details Defined in Data.VectorSpace Methods (<.>) :: (u, v) -> (u, v) -> Scalar (u, v) #
(InnerSpace u, s ~ Scalar u, AdditiveGroup s, HasBasis a, HasTrie (Basis a)) => InnerSpace (a :> u)
Instance details Defined in Data.Maclaurin Methods (<.>) :: (a :> u) -> (a :> u) -> Scalar (a :> u) #
InnerSpace a => InnerSpace (Rec0 a s)
Instance details Defined in Data.VectorSpace Methods (<.>) :: Rec0 a s -> Rec0 a s -> Scalar (Rec0 a s) #
(InnerSpace u, s ~ Scalar u, InnerSpace v, s ~ Scalar v, InnerSpace w, s ~ Scalar w) => InnerSpace (u, v, w)
Instance details Defined in Data.VectorSpace Methods (<.>) :: (u, v, w) -> (u, v, w) -> Scalar (u, v, w) #
(AffineSpace (f p), AffineSpace (g p), InnerSpace (Diff (f p)), InnerSpace (Diff (g p)), Scalar (Diff (f p)) ~ Scalar (Diff (g p)), Num (Scalar (Diff (f p)))) => InnerSpace (AffineDiffProductSpace f g p)
Instance details Defined in Data.AffineSpace Methods (<.>) :: AffineDiffProductSpace f g p -> AffineDiffProductSpace f g p -> Scalar (AffineDiffProductSpace f g p) #
(InnerSpace (f p), InnerSpace (g p), Scalar (f p) ~ Scalar (g p), Num (Scalar (f p))) => InnerSpace ((f :*: g) p)
Instance details Defined in Data.VectorSpace Methods (<.>) :: (f :: g) p -> (f :: g) p -> Scalar ((f :*: g) p) #
(InnerSpace u, s ~ Scalar u, InnerSpace v, s ~ Scalar v, InnerSpace w, s ~ Scalar w, InnerSpace x, s ~ Scalar x) => InnerSpace (u, v, w, x)
Instance details Defined in Data.VectorSpace Methods (<.>) :: (u, v, w, x) -> (u, v, w, x) -> Scalar (u, v, w, x) #
InnerSpace (f p) => InnerSpace (M1 i c f p)
Instance details Defined in Data.VectorSpace Methods (<.>) :: M1 i c f p -> M1 i c f p -> Scalar (M1 i c f p) #

class VectorSpace v => HasBasis v where #

Minimal complete definition

Nothing

Associated Types

type Basis v #

Representation of the canonical basis for v

type Basis v = Basis (VRep v)

Methods

basisValue :: Basis v -> v #

Interpret basis rep as a vector

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

Extract coordinates

decompose' :: v -> Basis v -> Scalar v #

Experimental version. More elegant definitions, and friendly to infinite-dimensional vector spaces.

Instances

Instances details

HasBasis Double
Instance details Defined in Data.Basis Associated Types type Basis Double # Methods basisValue :: Basis Double -> Double # decompose :: Double -> [(Basis Double, Scalar Double)] # decompose' :: Double -> Basis Double -> Scalar Double #
HasBasis Float
Instance details Defined in Data.Basis Associated Types type Basis Float # Methods basisValue :: Basis Float -> Float # decompose :: Float -> [(Basis Float, Scalar Float)] # decompose' :: Float -> Basis Float -> Scalar Float #
HasBasis CFloat
Instance details Defined in Data.Basis Associated Types type Basis CFloat # Methods basisValue :: Basis CFloat -> CFloat # decompose :: CFloat -> [(Basis CFloat, Scalar CFloat)] # decompose' :: CFloat -> Basis CFloat -> Scalar CFloat #
HasBasis CDouble
Instance details Defined in Data.Basis Associated Types type Basis CDouble # Methods basisValue :: Basis CDouble -> CDouble # decompose :: CDouble -> [(Basis CDouble, Scalar CDouble)] # decompose' :: CDouble -> Basis CDouble -> Scalar CDouble #
Integral a => HasBasis (Ratio a)
Instance details Defined in Data.Basis Associated Types type Basis (Ratio a) # Methods basisValue :: Basis (Ratio a) -> Ratio a # decompose :: Ratio a -> [(Basis (Ratio a), Scalar (Ratio a))] # decompose' :: Ratio a -> Basis (Ratio a) -> Scalar (Ratio a) #
(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, 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, 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, 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, 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) #
HasBasis (Diff (VRep p)) => HasBasis (GenericDiff p)
Instance details Defined in Data.AffineSpace Associated Types type Basis (GenericDiff p) # Methods basisValue :: Basis (GenericDiff p) -> GenericDiff p # decompose :: GenericDiff p -> [(Basis (GenericDiff p), Scalar (GenericDiff p))] # decompose' :: GenericDiff p -> Basis (GenericDiff p) -> Scalar (GenericDiff p) #
(Num n, Unbox n) => HasBasis (SemisparseSuppSeq n) Source #
Instance details Defined in Data.VectorSpace.Free.FiniteSupportedSequence Associated Types type Basis (SemisparseSuppSeq n) # Methods basisValue :: Basis (SemisparseSuppSeq n) -> SemisparseSuppSeq n # decompose :: SemisparseSuppSeq n -> [(Basis (SemisparseSuppSeq n), Scalar (SemisparseSuppSeq n))] # decompose' :: SemisparseSuppSeq n -> Basis (SemisparseSuppSeq n) -> Scalar (SemisparseSuppSeq n) #
(Num n, Unbox n) => HasBasis (SparseSuppSeq n) Source #
Instance details Defined in Data.VectorSpace.Free.FiniteSupportedSequence Associated Types type Basis (SparseSuppSeq n) # Methods basisValue :: Basis (SparseSuppSeq n) -> SparseSuppSeq n # decompose :: SparseSuppSeq n -> [(Basis (SparseSuppSeq n), Scalar (SparseSuppSeq n))] # decompose' :: SparseSuppSeq n -> Basis (SparseSuppSeq n) -> Scalar (SparseSuppSeq n) #
(Num n, Unbox n) => HasBasis (FinSuppSeq n) Source #
Instance details Defined in Data.VectorSpace.Free.FiniteSupportedSequence Associated Types type Basis (FinSuppSeq n) # Methods basisValue :: Basis (FinSuppSeq n) -> FinSuppSeq n # decompose :: FinSuppSeq n -> [(Basis (FinSuppSeq n), Scalar (FinSuppSeq n))] # decompose' :: FinSuppSeq n -> Basis (FinSuppSeq n) -> Scalar (FinSuppSeq n) #
(Num n, Unbox n) => HasBasis (Sequence n) Source #
Instance details Defined in Data.VectorSpace.Free.Sequence Associated Types type Basis (Sequence n) # Methods basisValue :: Basis (Sequence n) -> Sequence n # decompose :: Sequence n -> [(Basis (Sequence n), Scalar (Sequence n))] # decompose' :: Sequence n -> Basis (Sequence n) -> Scalar (Sequence n) #
(HasBasis u, s ~ Scalar u, HasBasis v, s ~ Scalar v) => HasBasis (u, v)
Instance details Defined in Data.Basis Associated Types type Basis (u, v) # Methods basisValue :: Basis (u, v) -> (u, v) # decompose :: (u, v) -> [(Basis (u, v), Scalar (u, v))] # decompose' :: (u, v) -> Basis (u, v) -> Scalar (u, v) #
HasBasis a => HasBasis (Rec0 a s)
Instance details Defined in Data.Basis Associated Types type Basis (Rec0 a s) # Methods basisValue :: Basis (Rec0 a s) -> Rec0 a s # decompose :: Rec0 a s -> [(Basis (Rec0 a s), Scalar (Rec0 a s))] # decompose' :: Rec0 a s -> Basis (Rec0 a s) -> Scalar (Rec0 a s) #
(HasBasis u, s ~ Scalar u, HasBasis v, s ~ Scalar v, HasBasis w, s ~ Scalar w) => HasBasis (u, v, w)
Instance details Defined in Data.Basis Associated Types type Basis (u, v, w) # Methods basisValue :: Basis (u, v, w) -> (u, v, w) # decompose :: (u, v, w) -> [(Basis (u, v, w), Scalar (u, v, w))] # decompose' :: (u, v, w) -> Basis (u, v, w) -> Scalar (u, v, w) #
(AffineSpace (f p), AffineSpace (g p), HasBasis (Diff (f p)), HasBasis (Diff (g p)), Scalar (Diff (f p)) ~ Scalar (Diff (g p))) => HasBasis (AffineDiffProductSpace f g p)
Instance details Defined in Data.AffineSpace Associated Types type Basis (AffineDiffProductSpace f g p) # Methods basisValue :: Basis (AffineDiffProductSpace f g p) -> AffineDiffProductSpace f g p # decompose :: AffineDiffProductSpace f g p -> [(Basis (AffineDiffProductSpace f g p), Scalar (AffineDiffProductSpace f g p))] # decompose' :: AffineDiffProductSpace f g p -> Basis (AffineDiffProductSpace f g p) -> Scalar (AffineDiffProductSpace f g p) #
(HasBasis (f p), HasBasis (g p), Scalar (f p) ~ Scalar (g p)) => HasBasis ((f :*: g) p)
Instance details Defined in Data.Basis Associated Types type Basis ((f :: g) p) # Methods basisValue :: Basis ((f :: g) p) -> (f :: g) p # decompose :: (f :: g) p -> [(Basis ((f :: g) p), Scalar ((f :: g) p))] # decompose' :: (f :: g) p -> Basis ((f :: g) p) -> Scalar ((f :*: g) p) #
HasBasis (f p) => HasBasis (M1 i c f p)
Instance details Defined in Data.Basis Associated Types type Basis (M1 i c f p) # Methods basisValue :: Basis (M1 i c f p) -> M1 i c f p # decompose :: M1 i c f p -> [(Basis (M1 i c f p), Scalar (M1 i c f p))] # decompose' :: M1 i c f p -> Basis (M1 i c f p) -> Scalar (M1 i c f p) #

Small

class (VectorSpace v, Fractional (Scalar v)) => OneDimensional v where Source #

Minimal complete definition

Nothing

Methods

(^/^) :: v -> v -> Maybe (Scalar v) infixr 7 Source #

Compare the (directed) length of two vectors.

default (^/^) :: (Generic v, OneDimensional (VRep v), Scalar (VRep v) ~ Scalar v) => v -> v -> Maybe (Scalar v) Source #

(^/!) :: v -> v -> Scalar v infixr 7 Source #

Unsafe version of ^/^.

Instances

Instances details

OneDimensional Double Source #
Instance details Defined in Data.VectorSpace.Free Methods (^/^) :: Double -> Double -> Maybe (Scalar Double) Source # (^/!) :: Double -> Double -> Scalar Double Source #
OneDimensional Float Source #
Instance details Defined in Data.VectorSpace.Free Methods (^/^) :: Float -> Float -> Maybe (Scalar Float) Source # (^/!) :: Float -> Float -> Scalar Float Source #
OneDimensional CFloat Source #
Instance details Defined in Data.VectorSpace.Free Methods (^/^) :: CFloat -> CFloat -> Maybe (Scalar CFloat) Source # (^/!) :: CFloat -> CFloat -> Scalar CFloat Source #
OneDimensional CDouble Source #
Instance details Defined in Data.VectorSpace.Free Methods (^/^) :: CDouble -> CDouble -> Maybe (Scalar CDouble) Source # (^/!) :: CDouble -> CDouble -> Scalar CDouble Source #
Integral i => OneDimensional (Ratio i) Source #
Instance details Defined in Data.VectorSpace.Free Methods (^/^) :: Ratio i -> Ratio i -> Maybe (Scalar (Ratio i)) Source # (^/!) :: Ratio i -> Ratio i -> Scalar (Ratio i) Source #
(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 #
OneDimensional a => OneDimensional (Rec0 a s) Source #
Instance details Defined in Data.VectorSpace.Free Methods (^/^) :: Rec0 a s -> Rec0 a s -> Maybe (Scalar (Rec0 a s)) Source # (^/!) :: Rec0 a s -> Rec0 a s -> Scalar (Rec0 a s) Source #
OneDimensional (f p) => OneDimensional (M1 i c f p) Source #
Instance details Defined in Data.VectorSpace.Free Methods (^/^) :: M1 i c f p -> M1 i c f p -> Maybe (Scalar (M1 i c f p)) Source # (^/!) :: M1 i c f p -> M1 i c f p -> Scalar (M1 i c f p) Source #

Free

class (VectorSpace v, Num (Scalar v)) => FreeVectorSpace v where Source #

Vector spaces that are spanned by a specific, canonical set of basis vectors.

Methods

(^*^) :: v -> v -> v Source #

Element-wise multiplication, equivalent to Matlab's .* operator or liftI2 (*).

vmap :: (Scalar v -> Scalar v) -> v -> v Source #

Like a monomorphic fmap. Only guaranteed to act on the nonzero entries; whether the function is also applied on zeroes is instance-specific.

Instances

Instances details

FreeVectorSpace Double Source #
Instance details Defined in Data.VectorSpace.Free.Class Methods (^*^) :: Double -> Double -> Double Source # vmap :: (Scalar Double -> Scalar Double) -> Double -> Double Source #
FreeVectorSpace Float Source #
Instance details Defined in Data.VectorSpace.Free.Class Methods (^*^) :: Float -> Float -> Float Source # vmap :: (Scalar Float -> Scalar Float) -> Float -> Float Source #
FreeVectorSpace Int Source #
Instance details Defined in Data.VectorSpace.Free.Class Methods (^*^) :: Int -> Int -> Int Source # vmap :: (Scalar Int -> Scalar Int) -> Int -> Int Source #
FreeVectorSpace Integer Source #
Instance details Defined in Data.VectorSpace.Free.Class Methods (^*^) :: Integer -> Integer -> Integer Source # vmap :: (Scalar Integer -> Scalar Integer) -> Integer -> Integer Source #
FreeVectorSpace CSChar Source #
Instance details Defined in Data.VectorSpace.Free.Class Methods (^*^) :: CSChar -> CSChar -> CSChar Source # vmap :: (Scalar CSChar -> Scalar CSChar) -> CSChar -> CSChar Source #
FreeVectorSpace CShort Source #
Instance details Defined in Data.VectorSpace.Free.Class Methods (^*^) :: CShort -> CShort -> CShort Source # vmap :: (Scalar CShort -> Scalar CShort) -> CShort -> CShort Source #
FreeVectorSpace CInt Source #
Instance details Defined in Data.VectorSpace.Free.Class Methods (^*^) :: CInt -> CInt -> CInt Source # vmap :: (Scalar CInt -> Scalar CInt) -> CInt -> CInt Source #
FreeVectorSpace CLong Source #
Instance details Defined in Data.VectorSpace.Free.Class Methods (^*^) :: CLong -> CLong -> CLong Source # vmap :: (Scalar CLong -> Scalar CLong) -> CLong -> CLong Source #
FreeVectorSpace CLLong Source #
Instance details Defined in Data.VectorSpace.Free.Class Methods (^*^) :: CLLong -> CLLong -> CLLong Source # vmap :: (Scalar CLLong -> Scalar CLLong) -> CLLong -> CLLong Source #
FreeVectorSpace CFloat Source #
Instance details Defined in Data.VectorSpace.Free.Class Methods (^*^) :: CFloat -> CFloat -> CFloat Source # vmap :: (Scalar CFloat -> Scalar CFloat) -> CFloat -> CFloat Source #
FreeVectorSpace CDouble Source #
Instance details Defined in Data.VectorSpace.Free.Class Methods (^*^) :: CDouble -> CDouble -> CDouble Source # vmap :: (Scalar CDouble -> Scalar CDouble) -> CDouble -> CDouble Source #
FreeVectorSpace CIntMax Source #
Instance details Defined in Data.VectorSpace.Free.Class Methods (^*^) :: CIntMax -> CIntMax -> CIntMax Source # vmap :: (Scalar CIntMax -> Scalar CIntMax) -> CIntMax -> CIntMax Source #
Integral a => FreeVectorSpace (Ratio a) Source #
Instance details Defined in Data.VectorSpace.Free.Class Methods (^*^) :: Ratio a -> Ratio a -> Ratio a Source # vmap :: (Scalar (Ratio a) -> Scalar (Ratio a)) -> Ratio a -> Ratio a Source #
(Num n, Unbox n) => FreeVectorSpace (SemisparseSuppSeq n) Source #
Instance details Defined in Data.VectorSpace.Free.FiniteSupportedSequence Methods (^*^) :: SemisparseSuppSeq n -> SemisparseSuppSeq n -> SemisparseSuppSeq n Source # vmap :: (Scalar (SemisparseSuppSeq n) -> Scalar (SemisparseSuppSeq n)) -> SemisparseSuppSeq n -> SemisparseSuppSeq n Source #
(Num n, Unbox n) => FreeVectorSpace (SparseSuppSeq n) Source #
Instance details Defined in Data.VectorSpace.Free.FiniteSupportedSequence Methods (^*^) :: SparseSuppSeq n -> SparseSuppSeq n -> SparseSuppSeq n Source # vmap :: (Scalar (SparseSuppSeq n) -> Scalar (SparseSuppSeq n)) -> SparseSuppSeq n -> SparseSuppSeq n Source #
(Num n, AdditiveGroup n, Unbox n) => FreeVectorSpace (FinSuppSeq n) Source #
Instance details Defined in Data.VectorSpace.Free.FiniteSupportedSequence Methods (^*^) :: FinSuppSeq n -> FinSuppSeq n -> FinSuppSeq n Source # vmap :: (Scalar (FinSuppSeq n) -> Scalar (FinSuppSeq n)) -> FinSuppSeq n -> FinSuppSeq n Source #
(FreeVectorSpace v, FreeVectorSpace w, Scalar v ~ Scalar w) => FreeVectorSpace (v, w) Source #
Instance details Defined in Data.VectorSpace.Free.Class Methods (^*^) :: (v, w) -> (v, w) -> (v, w) Source # vmap :: (Scalar (v, w) -> Scalar (v, w)) -> (v, w) -> (v, w) Source #
(FreeVectorSpace u, FreeVectorSpace v, FreeVectorSpace w, Scalar v ~ Scalar u, Scalar v ~ Scalar w) => FreeVectorSpace (u, v, w) Source #
Instance details Defined in Data.VectorSpace.Free.Class Methods (^*^) :: (u, v, w) -> (u, v, w) -> (u, v, w) Source # vmap :: (Scalar (u, v, w) -> Scalar (u, v, w)) -> (u, v, w) -> (u, v, w) Source #
(FreeVectorSpace u, FreeVectorSpace v, FreeVectorSpace w, FreeVectorSpace x, Scalar x ~ Scalar v, Scalar v ~ Scalar u, Scalar v ~ Scalar w) => FreeVectorSpace (u, v, w, x) Source #
Instance details Defined in Data.VectorSpace.Free.Class Methods (^*^) :: (u, v, w, x) -> (u, v, w, x) -> (u, v, w, x) Source # vmap :: (Scalar (u, v, w, x) -> Scalar (u, v, w, x)) -> (u, v, w, x) -> (u, v, w, x) Source #

class (VectorSpace v, Num (Scalar v)) => FiniteFreeSpace v where Source #

Minimal complete definition

Nothing

Methods

freeDimension :: Functor p => p v -> Int Source #

default freeDimension :: (Generic v, FiniteFreeSpace (VRep v)) => p v -> Int Source #

toFullUnboxVect :: Unbox (Scalar v) => v -> Vector (Scalar v) Source #

default toFullUnboxVect :: (Generic v, FiniteFreeSpace (VRep v), Unbox (Scalar v), Scalar (VRep v) ~ Scalar v) => v -> Vector (Scalar v) Source #

unsafeFromFullUnboxVect :: Unbox (Scalar v) => Vector (Scalar v) -> v Source #

default unsafeFromFullUnboxVect :: (Generic v, FiniteFreeSpace (VRep v), Unbox (Scalar v), Scalar (VRep v) ~ Scalar v) => Vector (Scalar v) -> v Source #

fromUnboxVect :: Unbox (Scalar v) => Vector (Scalar v) -> v Source #

Instances

Instances details

FiniteFreeSpace Double Source #
Instance details Defined in Data.VectorSpace.Free Methods freeDimension :: Functor p => p Double -> Int Source # toFullUnboxVect :: Double -> Vector (Scalar Double) Source # unsafeFromFullUnboxVect :: Vector (Scalar Double) -> Double Source # fromUnboxVect :: Vector (Scalar Double) -> Double Source #
FiniteFreeSpace Float Source #
Instance details Defined in Data.VectorSpace.Free Methods freeDimension :: Functor p => p Float -> Int Source # toFullUnboxVect :: Float -> Vector (Scalar Float) Source # unsafeFromFullUnboxVect :: Vector (Scalar Float) -> Float Source # fromUnboxVect :: Vector (Scalar Float) -> Float Source #
FiniteFreeSpace Int Source #
Instance details Defined in Data.VectorSpace.Free Methods freeDimension :: Functor p => p Int -> Int Source # toFullUnboxVect :: Int -> Vector (Scalar Int) Source # unsafeFromFullUnboxVect :: Vector (Scalar Int) -> Int Source # fromUnboxVect :: Vector (Scalar Int) -> Int Source #
Num s => FiniteFreeSpace (V0 s) Source #
Instance details Defined in Data.VectorSpace.Free Methods freeDimension :: Functor p => p (V0 s) -> Int Source # toFullUnboxVect :: V0 s -> Vector (Scalar (V0 s)) Source # unsafeFromFullUnboxVect :: Vector (Scalar (V0 s)) -> V0 s Source # fromUnboxVect :: Vector (Scalar (V0 s)) -> V0 s Source #
Num s => FiniteFreeSpace (V4 s) Source #
Instance details Defined in Data.VectorSpace.Free Methods freeDimension :: Functor p => p (V4 s) -> Int Source # toFullUnboxVect :: V4 s -> Vector (Scalar (V4 s)) Source # unsafeFromFullUnboxVect :: Vector (Scalar (V4 s)) -> V4 s Source # fromUnboxVect :: Vector (Scalar (V4 s)) -> V4 s Source #
Num s => FiniteFreeSpace (V3 s) Source #
Instance details Defined in Data.VectorSpace.Free Methods freeDimension :: Functor p => p (V3 s) -> Int Source # toFullUnboxVect :: V3 s -> Vector (Scalar (V3 s)) Source # unsafeFromFullUnboxVect :: Vector (Scalar (V3 s)) -> V3 s Source # fromUnboxVect :: Vector (Scalar (V3 s)) -> V3 s Source #
Num s => FiniteFreeSpace (V2 s) Source #
Instance details Defined in Data.VectorSpace.Free Methods freeDimension :: Functor p => p (V2 s) -> Int Source # toFullUnboxVect :: V2 s -> Vector (Scalar (V2 s)) Source # unsafeFromFullUnboxVect :: Vector (Scalar (V2 s)) -> V2 s Source # fromUnboxVect :: Vector (Scalar (V2 s)) -> V2 s Source #
Num s => FiniteFreeSpace (V1 s) Source #
Instance details Defined in Data.VectorSpace.Free Methods freeDimension :: Functor p => p (V1 s) -> Int Source # toFullUnboxVect :: V1 s -> Vector (Scalar (V1 s)) Source # unsafeFromFullUnboxVect :: Vector (Scalar (V1 s)) -> V1 s Source # fromUnboxVect :: Vector (Scalar (V1 s)) -> V1 s Source #
(FiniteFreeSpace u, FiniteFreeSpace v, Scalar u ~ Scalar v) => FiniteFreeSpace (u, v) Source #
Instance details Defined in Data.VectorSpace.Free Methods freeDimension :: Functor p => p (u, v) -> Int Source # toFullUnboxVect :: (u, v) -> Vector (Scalar (u, v)) Source # unsafeFromFullUnboxVect :: Vector (Scalar (u, v)) -> (u, v) Source # fromUnboxVect :: Vector (Scalar (u, v)) -> (u, v) Source #
FiniteFreeSpace a => FiniteFreeSpace (Rec0 a s) Source #
Instance details Defined in Data.VectorSpace.Free Methods freeDimension :: Functor p => p (Rec0 a s) -> Int Source # toFullUnboxVect :: Rec0 a s -> Vector (Scalar (Rec0 a s)) Source # unsafeFromFullUnboxVect :: Vector (Scalar (Rec0 a s)) -> Rec0 a s Source # fromUnboxVect :: Vector (Scalar (Rec0 a s)) -> Rec0 a s Source #
(FiniteFreeSpace (f p), FiniteFreeSpace (g p), Scalar (f p) ~ Scalar (g p)) => FiniteFreeSpace ((f :*: g) p) Source #
Instance details Defined in Data.VectorSpace.Free Methods freeDimension :: Functor p0 => p0 ((f :: g) p) -> Int Source # toFullUnboxVect :: (f :: g) p -> Vector (Scalar ((f :: g) p)) Source # unsafeFromFullUnboxVect :: Vector (Scalar ((f :: g) p)) -> (f :: g) p Source # fromUnboxVect :: Vector (Scalar ((f :: g) p)) -> (f :*: g) p Source #
FiniteFreeSpace (f p) => FiniteFreeSpace (M1 i c f p) Source #
Instance details Defined in Data.VectorSpace.Free Methods freeDimension :: Functor p0 => p0 (M1 i c f p) -> Int Source # toFullUnboxVect :: M1 i c f p -> Vector (Scalar (M1 i c f p)) Source # unsafeFromFullUnboxVect :: Vector (Scalar (M1 i c f p)) -> M1 i c f p Source # fromUnboxVect :: Vector (Scalar (M1 i c f p)) -> M1 i c f p Source #

Orphan instances

HasTrie (E V0) Source #
Instance details 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)] #
HasTrie (E V4) Source #
Instance details 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)] #
HasTrie (E V3) Source #
Instance details 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)] #
HasTrie (E V2) Source #
Instance details 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)] #
HasTrie (E V1) Source #
Instance details 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)] #
Show (V0 Double) Source #
Instance details Methods showsPrec :: Int -> V0 Double -> ShowS # show :: V0 Double -> String # showList :: [V0 Double] -> ShowS #
Show (V0 Float) Source #
Instance details Methods showsPrec :: Int -> V0 Float -> ShowS # show :: V0 Float -> String # showList :: [V0 Float] -> ShowS #
Show (V0 Int) Source #
Instance details Methods showsPrec :: Int -> V0 Int -> ShowS # show :: V0 Int -> String # showList :: [V0 Int] -> ShowS #
Show (V0 Integer) Source #
Instance details Methods showsPrec :: Int -> V0 Integer -> ShowS # show :: V0 Integer -> String # showList :: [V0 Integer] -> ShowS #
Show (V4 Double) Source #
Instance details Methods showsPrec :: Int -> V4 Double -> ShowS # show :: V4 Double -> String # showList :: [V4 Double] -> ShowS #
Show (V4 Float) Source #
Instance details Methods showsPrec :: Int -> V4 Float -> ShowS # show :: V4 Float -> String # showList :: [V4 Float] -> ShowS #
Show (V4 Int) Source #
Instance details Methods showsPrec :: Int -> V4 Int -> ShowS # show :: V4 Int -> String # showList :: [V4 Int] -> ShowS #
Show (V4 Integer) Source #
Instance details Methods showsPrec :: Int -> V4 Integer -> ShowS # show :: V4 Integer -> String # showList :: [V4 Integer] -> ShowS #
Show (V3 Double) Source #
Instance details Methods showsPrec :: Int -> V3 Double -> ShowS # show :: V3 Double -> String # showList :: [V3 Double] -> ShowS #
Show (V3 Float) Source #
Instance details Methods showsPrec :: Int -> V3 Float -> ShowS # show :: V3 Float -> String # showList :: [V3 Float] -> ShowS #
Show (V3 Int) Source #
Instance details Methods showsPrec :: Int -> V3 Int -> ShowS # show :: V3 Int -> String # showList :: [V3 Int] -> ShowS #
Show (V3 Integer) Source #
Instance details Methods showsPrec :: Int -> V3 Integer -> ShowS # show :: V3 Integer -> String # showList :: [V3 Integer] -> ShowS #
Show (V2 Double) Source #
Instance details Methods showsPrec :: Int -> V2 Double -> ShowS # show :: V2 Double -> String # showList :: [V2 Double] -> ShowS #
Show (V2 Float) Source #
Instance details Methods showsPrec :: Int -> V2 Float -> ShowS # show :: V2 Float -> String # showList :: [V2 Float] -> ShowS #
Show (V2 Int) Source #
Instance details Methods showsPrec :: Int -> V2 Int -> ShowS # show :: V2 Int -> String # showList :: [V2 Int] -> ShowS #
Show (V2 Integer) Source #
Instance details Methods showsPrec :: Int -> V2 Integer -> ShowS # show :: V2 Integer -> String # showList :: [V2 Integer] -> ShowS #
Show (V1 Double) Source #
Instance details Methods showsPrec :: Int -> V1 Double -> ShowS # show :: V1 Double -> String # showList :: [V1 Double] -> ShowS #
Show (V1 Float) Source #
Instance details Methods showsPrec :: Int -> V1 Float -> ShowS # show :: V1 Float -> String # showList :: [V1 Float] -> ShowS #
Show (V1 Int) Source #
Instance details Methods showsPrec :: Int -> V1 Int -> ShowS # show :: V1 Int -> String # showList :: [V1 Int] -> ShowS #
Show (V1 Integer) Source #
Instance details Methods showsPrec :: Int -> V1 Integer -> ShowS # show :: V1 Integer -> String # showList :: [V1 Integer] -> ShowS #
Num s => HasCross2 (V2 s) Source #
Instance details Methods cross2 :: V2 s -> V2 s #
Num s => HasCross3 (V3 s) Source #
Instance details Methods cross3 :: V3 s -> V3 s -> V3 s #
Num s => AffineSpace (V0 s) Source #
Instance details 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 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 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 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 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 (V0 s) Source #
Instance details 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, AdditiveGroup s) => HasBasis (V4 s) Source #
Instance details 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, AdditiveGroup s) => HasBasis (V3 s) Source #
Instance details 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, AdditiveGroup s) => HasBasis (V2 s) Source #
Instance details 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, AdditiveGroup s) => HasBasis (V1 s) Source #
Instance details 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 (V0 s) Source #
Instance details Associated Types type Scalar (V0 s) # Methods (*^) :: Scalar (V0 s) -> V0 s -> V0 s #
Num s => VectorSpace (V4 s) Source #
Instance details Associated Types type Scalar (V4 s) # Methods (*^) :: Scalar (V4 s) -> V4 s -> V4 s #
Num s => VectorSpace (V3 s) Source #
Instance details Associated Types type Scalar (V3 s) # Methods (*^) :: Scalar (V3 s) -> V3 s -> V3 s #
Num s => VectorSpace (V2 s) Source #
Instance details Associated Types type Scalar (V2 s) # Methods (*^) :: Scalar (V2 s) -> V2 s -> V2 s #
Num s => VectorSpace (V1 s) Source #
Instance details Associated Types type Scalar (V1 s) # Methods (*^) :: Scalar (V1 s) -> V1 s -> V1 s #
(Num s, AdditiveGroup s) => InnerSpace (V0 s) Source #
Instance details Methods (<.>) :: V0 s -> V0 s -> Scalar (V0 s) #
(Num s, AdditiveGroup s) => InnerSpace (V4 s) Source #
Instance details Methods (<.>) :: V4 s -> V4 s -> Scalar (V4 s) #
(Num s, AdditiveGroup s) => InnerSpace (V3 s) Source #
Instance details Methods (<.>) :: V3 s -> V3 s -> Scalar (V3 s) #
(Num s, AdditiveGroup s) => InnerSpace (V2 s) Source #
Instance details Methods (<.>) :: V2 s -> V2 s -> Scalar (V2 s) #
(Num s, AdditiveGroup s) => InnerSpace (V1 s) Source #
Instance details Methods (<.>) :: V1 s -> V1 s -> Scalar (V1 s) #
Num s => AdditiveGroup (V0 s) Source #
Instance details Methods zeroV :: V0 s # (^+^) :: V0 s -> V0 s -> V0 s # negateV :: V0 s -> V0 s # (^-^) :: V0 s -> V0 s -> V0 s #
Num s => AdditiveGroup (V4 s) Source #
Instance details Methods zeroV :: V4 s # (^+^) :: V4 s -> V4 s -> V4 s # negateV :: V4 s -> V4 s # (^-^) :: V4 s -> V4 s -> V4 s #
Num s => AdditiveGroup (V3 s) Source #
Instance details Methods zeroV :: V3 s # (^+^) :: V3 s -> V3 s -> V3 s # negateV :: V3 s -> V3 s # (^-^) :: V3 s -> V3 s -> V3 s #
Num s => AdditiveGroup (V2 s) Source #
Instance details Methods zeroV :: V2 s # (^+^) :: V2 s -> V2 s -> V2 s # negateV :: V2 s -> V2 s # (^-^) :: V2 s -> V2 s -> V2 s #
Num s => AdditiveGroup (V1 s) Source #
Instance details Methods zeroV :: V1 s # (^+^) :: V1 s -> V1 s -> V1 s # negateV :: V1 s -> V1 s # (^-^) :: V1 s -> V1 s -> V1 s #
Num s => AffineSpace (Point V0 s) Source #
Instance details 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 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 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 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 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 #