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

Linear.V4

Description

4-D Vectors

Synopsis

data V4 a = V4 !a !a !a !a
vector :: Num a => V3 a -> V4 a
point :: Num a => V3 a -> V4 a
normalizePoint :: Fractional a => V4 a -> V3 a
class R1 (t :: Type -> Type) where
- _x :: Lens' (t a) a
class R1 t => R2 (t :: Type -> Type) where
- _y :: Lens' (t a) a
- _xy :: Lens' (t a) (V2 a)
_yx :: forall (t :: Type -> Type) a. R2 t => Lens' (t a) (V2 a)
class R2 t => R3 (t :: Type -> Type) where
- _z :: Lens' (t a) a
- _xyz :: Lens' (t a) (V3 a)
_xz :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V2 a)
_yz :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V2 a)
_zx :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V2 a)
_zy :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V2 a)
_xzy :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V3 a)
_yxz :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V3 a)
_yzx :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V3 a)
_zxy :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V3 a)
_zyx :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V3 a)
class R3 t => R4 (t :: Type -> Type) where
- _w :: Lens' (t a) a
- _xyzw :: Lens' (t a) (V4 a)
_xw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V2 a)
_yw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V2 a)
_zw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V2 a)
_wx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V2 a)
_wy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V2 a)
_wz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V2 a)
_xyw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a)
_xzw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a)
_xwy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a)
_xwz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a)
_yxw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a)
_yzw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a)
_ywx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a)
_ywz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a)
_zxw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a)
_zyw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a)
_zwx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a)
_zwy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a)
_wxy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a)
_wxz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a)
_wyx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a)
_wyz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a)
_wzx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a)
_wzy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a)
_xywz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_xzyw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_xzwy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_xwyz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_xwzy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_yxzw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_yxwz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_yzxw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_yzwx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_ywxz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_ywzx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_zxyw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_zxwy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_zyxw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_zywx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_zwxy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_zwyx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_wxyz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_wxzy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_wyxz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_wyzx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_wzxy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
_wzyx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a)
ex :: forall (t :: Type -> Type). R1 t => E t
ey :: forall (t :: Type -> Type). R2 t => E t
ez :: forall (t :: Type -> Type). R3 t => E t
ew :: forall (t :: Type -> Type). R4 t => E t

Documentation

data V4 a Source #

A 4-dimensional vector.

Constructors

V4 !a !a !a !a

Instances

Instances details

Representable V4 Source #

Instance details

Defined in Linear.V4

Associated Types

type Rep V4
Instance details Defined in Linear.V4 type Rep V4 = E V4

Methods

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

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

Foldable1 V4 Source #

Instance details

Defined in Linear.V4

Methods

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

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

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

toNonEmpty :: V4 a -> NonEmpty a #

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

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

head :: V4 a -> a #

last :: V4 a -> a #

foldrMap1 :: (a -> b) -> (a -> b -> b) -> V4 a -> b #

foldlMap1' :: (a -> b) -> (b -> a -> b) -> V4 a -> b #

foldlMap1 :: (a -> b) -> (b -> a -> b) -> V4 a -> b #

foldrMap1' :: (a -> b) -> (a -> b -> b) -> V4 a -> b #

Eq1 V4 Source #

Instance details

Defined in Linear.V4

Methods

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

Ord1 V4 Source #

Instance details

Defined in Linear.V4

Methods

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

Read1 V4 Source #

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 Source #

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 #

Serial1 V4 Source #

Instance details

Defined in Linear.V4

Methods

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

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

Distributive V4 Source #

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) #

Applicative V4 Source #

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 #

Functor V4 Source #

Instance details

Defined in Linear.V4

Methods

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

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

Monad V4 Source #

Instance details

Defined in Linear.V4

Methods

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

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

return :: a -> V4 a #

MonadFix V4 Source #

Instance details

Defined in Linear.V4

Methods

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

MonadZip V4 Source #

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) #

Foldable V4 Source #

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 Source #

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) #

Hashable1 V4 Source #

Instance details

Defined in Linear.V4

Methods

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

Affine V4 Source #

Instance details

Defined in Linear.Affine

Associated Types

type Diff V4
Instance details Defined in Linear.Affine type Diff V4 = V4

Methods

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

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

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

Metric V4 Source #

Instance details

Defined in Linear.V4

Methods

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

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

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

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

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

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

Trace V4 Source #

Instance details

Defined in Linear.Trace

Methods

trace :: Num a => V4 (V4 a) -> a Source #

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

Finite V4 Source #

Instance details

Defined in Linear.V4

Associated Types

type Size V4
Instance details Defined in Linear.V4 type Size V4 = 4

Methods

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

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

R1 V4 Source #

Instance details

Defined in Linear.V4

Methods

_x :: Lens' (V4 a) a Source #

R2 V4 Source #

Instance details

Defined in Linear.V4

Methods

_y :: Lens' (V4 a) a Source #

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

R3 V4 Source #

Instance details

Defined in Linear.V4

Methods

_z :: Lens' (V4 a) a Source #

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

R4 V4 Source #

Instance details

Defined in Linear.V4

Methods

_w :: Lens' (V4 a) a Source #

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

Additive V4 Source #

Instance details

Defined in Linear.V4

Methods

zero :: Num a => V4 a Source #

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

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

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

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

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

Apply V4 Source #

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 #

Bind V4 Source #

Instance details

Defined in Linear.V4

Methods

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

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

Traversable1 V4 Source #

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) #

Generic1 V4 Source #

Instance details

Defined in Linear.V4

Associated Types

type Rep1 V4

Instance details

Defined in Linear.V4

type Rep1 V4 = D1 ('MetaData "V4" "Linear.V4" "linear-1.23.2-JQyaOkrxFCJEnC5cyK3gr8" '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)))

Methods

from1 :: V4 a -> Rep1 V4 a #

to1 :: Rep1 V4 a -> V4 a #

Lift a => Lift (V4 a :: Type) Source #

Instance details

Defined in Linear.V4

Methods

lift :: Quote m => V4 a -> m Exp #

liftTyped :: forall (m :: Type -> Type). Quote m => V4 a -> Code m (V4 a) #

Num r => Coalgebra r (E V4) Source #

Instance details

Defined in Linear.Algebra

Methods

comult :: (E V4 -> r) -> E V4 -> E V4 -> r Source #

counital :: (E V4 -> r) -> r Source #

Unbox a => Vector Vector (V4 a) Source #

Instance details

Defined in Linear.V4

Methods

basicUnsafeFreeze :: Mutable Vector s (V4 a) -> ST s (Vector (V4 a)) #

basicUnsafeThaw :: Vector (V4 a) -> ST s (Mutable Vector s (V4 a)) #

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

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

basicUnsafeIndexM :: Vector (V4 a) -> Int -> Box (V4 a) #

basicUnsafeCopy :: Mutable Vector s (V4 a) -> Vector (V4 a) -> ST s () #

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

Unbox a => MVector MVector (V4 a) Source #

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

basicInitialize :: MVector s (V4 a) -> ST s () #

basicUnsafeReplicate :: Int -> V4 a -> ST s (MVector s (V4 a)) #

basicUnsafeRead :: MVector s (V4 a) -> Int -> ST s (V4 a) #

basicUnsafeWrite :: MVector s (V4 a) -> Int -> V4 a -> ST s () #

basicClear :: MVector s (V4 a) -> ST s () #

basicSet :: MVector s (V4 a) -> V4 a -> ST s () #

basicUnsafeCopy :: MVector s (V4 a) -> MVector s (V4 a) -> ST s () #

basicUnsafeMove :: MVector s (V4 a) -> MVector s (V4 a) -> ST s () #

basicUnsafeGrow :: MVector s (V4 a) -> Int -> ST s (MVector s (V4 a)) #

Binary a => Binary (V4 a) Source #

Instance details

Defined in Linear.V4

Methods

put :: V4 a -> Put #

get :: Get (V4 a) #

putList :: [V4 a] -> Put #

Serial a => Serial (V4 a) Source #

Instance details

Defined in Linear.V4

Methods

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

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

Serialize a => Serialize (V4 a) Source #

Instance details

Defined in Linear.V4

Methods

put :: Putter (V4 a) #

get :: Get (V4 a) #

NFData a => NFData (V4 a) Source #

Instance details

Defined in Linear.V4

Methods

rnf :: V4 a -> () #

Monoid a => Monoid (V4 a) Source #

Instance details

Defined in Linear.V4

Methods

mempty :: V4 a #

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

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

Semigroup a => Semigroup (V4 a) Source #

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 #

Data a => Data (V4 a) Source #

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) #

Bounded a => Bounded (V4 a) Source #

Instance details

Defined in Linear.V4

Methods

minBound :: V4 a #

maxBound :: V4 a #

Floating a => Floating (V4 a) Source #

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 #

Storable a => Storable (V4 a) Source #

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 () #

Generic (V4 a) Source #

Instance details

Defined in Linear.V4

Associated Types

type Rep (V4 a)

Instance details

Defined in Linear.V4

type Rep (V4 a) = D1 ('MetaData "V4" "Linear.V4" "linear-1.23.2-JQyaOkrxFCJEnC5cyK3gr8" '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))))

Methods

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

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

Ix a => Ix (V4 a) Source #

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 #

Num a => Num (V4 a) Source #

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 #

Read a => Read (V4 a) Source #

Instance details

Defined in Linear.V4

Methods

readsPrec :: Int -> ReadS (V4 a) #

readList :: ReadS [V4 a] #

readPrec :: ReadPrec (V4 a) #

readListPrec :: ReadPrec [V4 a] #

Fractional a => Fractional (V4 a) Source #

Instance details

Defined in Linear.V4

Methods

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

recip :: V4 a -> V4 a #

fromRational :: Rational -> V4 a #

Show a => Show (V4 a) Source #

Instance details

Defined in Linear.V4

Methods

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

show :: V4 a -> String #

showList :: [V4 a] -> ShowS #

Eq a => Eq (V4 a) Source #

Instance details

Defined in Linear.V4

Methods

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

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

Ord a => Ord (V4 a) Source #

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 #

Hashable a => Hashable (V4 a) Source #

Instance details

Defined in Linear.V4

Methods

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

hash :: V4 a -> Int #

Ixed (V4 a) Source #

Instance details

Defined in Linear.V4

Methods

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

Epsilon a => Epsilon (V4 a) Source #

Instance details

Defined in Linear.V4

Methods

nearZero :: V4 a -> Bool Source #

Random a => Random (V4 a) Source #

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] #

Uniform a => Uniform (V4 a) Source #

Instance details

Defined in Linear.V4

Methods

uniformM :: StatefulGen g m => g -> m (V4 a) #

UniformRange a => UniformRange (V4 a) Source #

Instance details

Defined in Linear.V4

Methods

uniformRM :: StatefulGen g m => (V4 a, V4 a) -> g -> m (V4 a) #

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

Unbox a => Unbox (V4 a) Source #

Instance details

Defined in Linear.V4

FoldableWithIndex (E V4) V4 Source #

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 #

FunctorWithIndex (E V4) V4 Source #

Instance details

Defined in Linear.V4

Methods

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

TraversableWithIndex (E V4) V4 Source #

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 Source #

Instance details

Defined in Linear.V4

Methods

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

Field1 (V4 a) (V4 a) a a Source #

Instance details

Defined in Linear.V4

Methods

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

Field2 (V4 a) (V4 a) a a Source #

Instance details

Defined in Linear.V4

Methods

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

Field3 (V4 a) (V4 a) a a Source #

Instance details

Defined in Linear.V4

Methods

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

Field4 (V4 a) (V4 a) a a Source #

Instance details

Defined in Linear.V4

Methods

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

type Rep V4 Source #

Instance details

Defined in Linear.V4

type Rep V4 = E V4

type Diff V4 Source #

Instance details

Defined in Linear.Affine

type Diff V4 = V4

type Size V4 Source #

Instance details

Defined in Linear.V4

type Size V4 = 4

type Rep1 V4 Source #

Instance details

Defined in Linear.V4

type Rep1 V4 = D1 ('MetaData "V4" "Linear.V4" "linear-1.23.2-JQyaOkrxFCJEnC5cyK3gr8" '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)))

data MVector s (V4 a) Source #

Instance details

Defined in Linear.V4

data MVector s (V4 a) = MV_V4 !Int !(MVector s a)

type Rep (V4 a) Source #

Instance details

Defined in Linear.V4

type Rep (V4 a) = D1 ('MetaData "V4" "Linear.V4" "linear-1.23.2-JQyaOkrxFCJEnC5cyK3gr8" '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))))

type Index (V4 a) Source #

Instance details

Defined in Linear.V4

type Index (V4 a) = E V4

type IxValue (V4 a) Source #

Instance details

Defined in Linear.V4

type IxValue (V4 a) = a

data Vector (V4 a) Source #

Instance details

Defined in Linear.V4

data Vector (V4 a) = V_V4 !Int !(Vector a)

vector :: Num a => V3 a -> V4 a Source #

Convert a 3-dimensional affine vector into a 4-dimensional homogeneous vector, i.e. sets the w coordinate to 0.

point :: Num a => V3 a -> V4 a Source #

Convert a 3-dimensional affine point into a 4-dimensional homogeneous vector, i.e. sets the w coordinate to 1.

normalizePoint :: Fractional a => V4 a -> V3 a Source #

Convert 4-dimensional projective coordinates to a 3-dimensional point. This operation may be denoted, euclidean [x:y:z:w] = (x/w, y/w, z/w) where the projective, homogenous, coordinate [x:y:z:w] is one of many associated with a single point (x/w, y/w, z/w).

class R1 (t :: Type -> Type) where Source #

A space that has at least 1 basis vector _x.

Methods

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

>>> V1 2 ^._x
2

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

Instances

Instances details

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

class R1 t => R2 (t :: Type -> Type) where Source #

A space that distinguishes 2 orthogonal basis vectors _x and _y, but may have more.

Minimal complete definition

_xy

Methods

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

>>> V2 1 2 ^._y
2

>>> V2 1 2 & _y .~ 3
V2 1 3

_xy :: Lens' (t a) (V2 a) Source #

Instances

Instances details

R2 Quaternion Source #
Instance details Defined in Linear.Quaternion Methods _y :: Lens' (Quaternion a) a Source # _xy :: Lens' (Quaternion a) (V2 a) Source #
R2 V2 Source #
Instance details Defined in Linear.V2 Methods _y :: Lens' (V2 a) a Source # _xy :: Lens' (V2 a) (V2 a) Source #
R2 V3 Source #
Instance details Defined in Linear.V3 Methods _y :: Lens' (V3 a) a Source # _xy :: Lens' (V3 a) (V2 a) Source #
R2 V4 Source #
Instance details Defined in Linear.V4 Methods _y :: Lens' (V4 a) a Source # _xy :: Lens' (V4 a) (V2 a) Source #
R2 f => R2 (Point f) Source #
Instance details Defined in Linear.Affine Methods _y :: Lens' (Point f a) a Source # _xy :: Lens' (Point f a) (V2 a) Source #

_yx :: forall (t :: Type -> Type) a. R2 t => Lens' (t a) (V2 a) Source #

>>> V2 1 2 ^. _yx
V2 2 1

class R2 t => R3 (t :: Type -> Type) where Source #

A space that distinguishes 3 orthogonal basis vectors: _x, _y, and _z. (It may have more)

Methods

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

>>> V3 1 2 3 ^. _z
3

_xyz :: Lens' (t a) (V3 a) Source #

Instances

Instances details

R3 Quaternion Source #
Instance details Defined in Linear.Quaternion Methods _z :: Lens' (Quaternion a) a Source # _xyz :: Lens' (Quaternion a) (V3 a) Source #
R3 V3 Source #
Instance details Defined in Linear.V3 Methods _z :: Lens' (V3 a) a Source # _xyz :: Lens' (V3 a) (V3 a) Source #
R3 V4 Source #
Instance details Defined in Linear.V4 Methods _z :: Lens' (V4 a) a Source # _xyz :: Lens' (V4 a) (V3 a) Source #
R3 f => R3 (Point f) Source #
Instance details Defined in Linear.Affine Methods _z :: Lens' (Point f a) a Source # _xyz :: Lens' (Point f a) (V3 a) Source #

_xz :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V2 a) Source #

_yz :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V2 a) Source #

_zx :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V2 a) Source #

_zy :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V2 a) Source #

_xzy :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V3 a) Source #

_yxz :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V3 a) Source #

_yzx :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V3 a) Source #

_zxy :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V3 a) Source #

_zyx :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V3 a) Source #

class R3 t => R4 (t :: Type -> Type) where Source #

A space that distinguishes orthogonal basis vectors _x, _y, _z, _w. (It may have more.)

Methods

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

>>> V4 1 2 3 4 ^._w
4

_xyzw :: Lens' (t a) (V4 a) Source #

Instances

Instances details

R4 Quaternion Source #
Instance details Defined in Linear.Quaternion Methods _w :: Lens' (Quaternion a) a Source # _xyzw :: Lens' (Quaternion a) (V4 a) Source #
R4 V4 Source #
Instance details Defined in Linear.V4 Methods _w :: Lens' (V4 a) a Source # _xyzw :: Lens' (V4 a) (V4 a) Source #
R4 f => R4 (Point f) Source #
Instance details Defined in Linear.Affine Methods _w :: Lens' (Point f a) a Source # _xyzw :: Lens' (Point f a) (V4 a) Source #

_xw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V2 a) Source #

_yw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V2 a) Source #

_zw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V2 a) Source #

_wx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V2 a) Source #

_wy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V2 a) Source #

_wz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V2 a) Source #

_xyw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a) Source #

_xzw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a) Source #

_xwy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a) Source #

_xwz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a) Source #

_yxw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a) Source #

_yzw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a) Source #

_ywx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a) Source #

_ywz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a) Source #

_zxw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a) Source #

_zyw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a) Source #

_zwx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a) Source #

_zwy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a) Source #

_wxy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a) Source #

_wxz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a) Source #

_wyx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a) Source #

_wyz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a) Source #

_wzx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a) Source #

_wzy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V3 a) Source #

_xywz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_xzyw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_xzwy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_xwyz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_xwzy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_yxzw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_yxwz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_yzxw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_yzwx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_ywxz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_ywzx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_zxyw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_zxwy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_zyxw :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_zywx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_zwxy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_zwyx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_wxyz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_wxzy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_wyxz :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_wyzx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_wzxy :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

_wzyx :: forall (t :: Type -> Type) a. R4 t => Lens' (t a) (V4 a) Source #

ex :: forall (t :: Type -> Type). R1 t => E t Source #

ey :: forall (t :: Type -> Type). R2 t => E t Source #

ez :: forall (t :: Type -> Type). R3 t => E t Source #

ew :: forall (t :: Type -> Type). R4 t => E t Source #