linear-1.20.9: Linear Algebra

Copyright | (C) 2012-2015 Edward Kmett
License | BSD-style (see the file LICENSE)
Maintainer | Edward Kmett <ekmett@gmail.com>
Stability | experimental
Portability | non-portable
Safe Haskell | Trustworthy
Language | Haskell98

Linear.V3

Description

3-D Vectors

Synopsis

- data V3 a = V3 !a !a !a
- cross :: Num a => V3 a -> V3 a -> V3 a
- triple :: Num a => V3 a -> V3 a -> V3 a -> a
- class R1 t where
  - _x :: Lens' (t a) a
- class R1 t => R2 t where
  - _y :: Lens' (t a) a
  - _xy :: Lens' (t a) (V2 a)
- _yx :: R2 t => Lens' (t a) (V2 a)
- class R2 t => R3 t where
  - _z :: Lens' (t a) a
  - _xyz :: Lens' (t a) (V3 a)
- _xz :: R3 t => Lens' (t a) (V2 a)
- _yz :: R3 t => Lens' (t a) (V2 a)
- _zx :: R3 t => Lens' (t a) (V2 a)
- _zy :: R3 t => Lens' (t a) (V2 a)
- _xzy :: R3 t => Lens' (t a) (V3 a)
- _yxz :: R3 t => Lens' (t a) (V3 a)
- _yzx :: R3 t => Lens' (t a) (V3 a)
- _zxy :: R3 t => Lens' (t a) (V3 a)
- _zyx :: R3 t => Lens' (t a) (V3 a)
- ex :: R1 t => E t
- ey :: R2 t => E t
- ez :: R3 t => E t

# Documentation

data V3 a Source #

A 3-dimensional vector

Constructors

V3 !a !a !a |

Instances

Monad V3 Source # |
Instance details Defined in Linear.V3 Methods (>>=) :: V3 a -> (a -> V3 b) -> V3 b Source # (>>) :: V3 a -> V3 b -> V3 b Source # return :: a -> V3 a Source # fail :: String -> V3 a Source #
Functor V3 Source # |
Instance details Defined in Linear.V3 Methods fmap :: (a -> b) -> V3 a -> V3 b Source # (<$) :: a -> V3 b -> V3 a Source #
MonadFix V3 Source # |
Instance details Defined in Linear.V3 Methods mfix :: (a -> V3 a) -> V3 a Source #
Applicative V3 Source # |
Instance details Defined in Linear.V3 Methods pure :: a -> V3 a Source # (<*>) :: V3 (a -> b) -> V3 a -> V3 b Source # liftA2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c Source # (*>) :: V3 a -> V3 b -> V3 b Source # (<*) :: V3 a -> V3 b -> V3 a Source #
Foldable V3 Source # |

Instance details

Defined in Linear.V3

Methods

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

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

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

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

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

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

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

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

toList :: V3 a -> [a] Source #

null :: V3 a -> Bool Source #

length :: V3 a -> Int Source #

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

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

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

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

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

Traversable V3 Source # |
Instance details Defined in Linear.V3 Methods traverse :: Applicative f => (a -> f b) -> V3 a -> f (V3 b) Source # sequenceA :: Applicative f => V3 (f a) -> f (V3 a) Source # mapM :: Monad m => (a -> m b) -> V3 a -> m (V3 b) Source # sequence :: Monad m => V3 (m a) -> m (V3 a) Source #
Distributive V3 Source # |
Instance details Defined in Linear.V3 Methods distribute :: Functor f => f (V3 a) -> V3 (f a) Source # collect :: Functor f => (a -> V3 b) -> f a -> V3 (f b) Source # distributeM :: Monad m => m (V3 a) -> V3 (m a) Source # collectM :: Monad m => (a -> V3 b) -> m a -> V3 (m b) Source #
Representable V3 Source # |
Instance details Defined in Linear.V3 Associated Types type Rep V3 :: Type Source # Methods tabulate :: (Rep V3 -> a) -> V3 a Source # index :: V3 a -> Rep V3 -> a Source #
Eq1 V3 Source # |
Instance details Defined in Linear.V3 Methods liftEq :: (a -> b -> Bool) -> V3 a -> V3 b -> Bool Source #
Ord1 V3 Source # |
Instance details Defined in Linear.V3 Methods liftCompare :: (a -> b -> Ordering) -> V3 a -> V3 b -> Ordering Source #
Read1 V3 Source # |
Instance details Defined in Linear.V3 Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V3 a) Source # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V3 a] Source # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (V3 a) Source # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [V3 a] Source #
Show1 V3 Source # |
Instance details Defined in Linear.V3 Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V3 a -> ShowS Source # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V3 a] -> ShowS Source #
MonadZip V3 Source # |
Instance details Defined in Linear.V3 Methods mzip :: V3 a -> V3 b -> V3 (a, b) Source # mzipWith :: (a -> b -> c) -> V3 a -> V3 b -> V3 c Source # munzip :: V3 (a, b) -> (V3 a, V3 b) Source #
Serial1 V3 Source # |
Instance details Defined in Linear.V3 Methods serializeWith :: MonadPut m => (a -> m ()) -> V3 a -> m () Source # deserializeWith :: MonadGet m => m a -> m (V3 a) Source #
Hashable1 V3 Source # |
Instance details Defined in Linear.V3 Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> V3 a -> Int Source #
Apply V3 Source # |
Instance details Defined in Linear.V3 Methods (<.>) :: V3 (a -> b) -> V3 a -> V3 b Source # (.>) :: V3 a -> V3 b -> V3 b Source # (<.) :: V3 a -> V3 b -> V3 a Source # liftF2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c Source #
Traversable1 V3 Source # |
Instance details Defined in Linear.V3 Methods traverse1 :: Apply f => (a -> f b) -> V3 a -> f (V3 b) Source # sequence1 :: Apply f => V3 (f b) -> f (V3 b) Source #
Foldable1 V3 Source # |
Instance details Defined in Linear.V3 Methods fold1 :: Semigroup m => V3 m -> m Source # foldMap1 :: Semigroup m => (a -> m) -> V3 a -> m Source # toNonEmpty :: V3 a -> NonEmpty a Source #
Bind V3 Source # |
Instance details Defined in Linear.V3 Methods (>>-) :: V3 a -> (a -> V3 b) -> V3 b Source # join :: V3 (V3 a) -> V3 a Source #
Additive V3 Source # |
Instance details Defined in Linear.V3 Methods zero :: Num a => V3 a Source # (^+^) :: Num a => V3 a -> V3 a -> V3 a Source # (^-^) :: Num a => V3 a -> V3 a -> V3 a Source # lerp :: Num a => a -> V3 a -> V3 a -> V3 a Source # liftU2 :: (a -> a -> a) -> V3 a -> V3 a -> V3 a Source # liftI2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c Source #
Metric V3 Source # |
Instance details Defined in Linear.V3 Methods dot :: Num a => V3 a -> V3 a -> a Source # quadrance :: Num a => V3 a -> a Source # qd :: Num a => V3 a -> V3 a -> a Source # distance :: Floating a => V3 a -> V3 a -> a Source # norm :: Floating a => V3 a -> a Source # signorm :: Floating a => V3 a -> V3 a Source #
Finite V3 Source # |
Instance details Defined in Linear.V3 Associated Types type Size V3 :: Nat Source # Methods toV :: V3 a -> V (Size V3) a Source # fromV :: V (Size V3) a -> V3 a Source #
R1 V3 Source # |
Instance details Defined in Linear.V3 Methods _x :: Lens' (V3 a) 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 #
R3 V3 Source # |
Instance details Defined in Linear.V3 Methods _z :: Lens' (V3 a) a Source # _xyz :: Lens' (V3 a) (V3 a) Source #
Trace V3 Source # |
Instance details Defined in Linear.Trace Methods trace :: Num a => V3 (V3 a) -> a Source # diagonal :: V3 (V3 a) -> V3 a Source #
Affine V3 Source # |
Instance details Defined in Linear.Affine Associated Types type Diff V3 :: Type -> Type Source # Methods (.-.) :: Num a => V3 a -> V3 a -> Diff V3 a Source # (.+^) :: Num a => V3 a -> Diff V3 a -> V3 a Source # (.-^) :: Num a => V3 a -> Diff V3 a -> V3 a Source #
Unbox a => Vector Vector (V3 a) Source # |

Instance details

Defined in Linear.V3

Methods

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

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

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

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

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

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

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

Unbox a => MVector MVector (V3 a) Source # |

Instance details

Defined in Linear.V3

Methods

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

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

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

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

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

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

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

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

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

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

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

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

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

Num r => Coalgebra r (E V3) Source # |
Instance details Defined in Linear.Algebra Methods comult :: (E V3 -> r) -> E V3 -> E V3 -> r Source # counital :: (E V3 -> r) -> r Source #
Bounded a => Bounded (V3 a) Source # |
Instance details Defined in Linear.V3 Methods minBound :: V3 a Source # maxBound :: V3 a Source #
Eq a => Eq (V3 a) Source # |
Instance details Defined in Linear.V3 Methods (==) :: V3 a -> V3 a -> Bool Source # (/=) :: V3 a -> V3 a -> Bool Source #
Floating a => Floating (V3 a) Source # |

Instance details

Defined in Linear.V3

Methods

pi :: V3 a Source #

exp :: V3 a -> V3 a Source #

log :: V3 a -> V3 a Source #

sqrt :: V3 a -> V3 a Source #

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

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

sin :: V3 a -> V3 a Source #

cos :: V3 a -> V3 a Source #

tan :: V3 a -> V3 a Source #

asin :: V3 a -> V3 a Source #

acos :: V3 a -> V3 a Source #

atan :: V3 a -> V3 a Source #

sinh :: V3 a -> V3 a Source #

cosh :: V3 a -> V3 a Source #

tanh :: V3 a -> V3 a Source #

asinh :: V3 a -> V3 a Source #

acosh :: V3 a -> V3 a Source #

atanh :: V3 a -> V3 a Source #

log1p :: V3 a -> V3 a Source #

expm1 :: V3 a -> V3 a Source #

log1pexp :: V3 a -> V3 a Source #

log1mexp :: V3 a -> V3 a Source #

Fractional a => Fractional (V3 a) Source # |
Instance details Defined in Linear.V3 Methods (/) :: V3 a -> V3 a -> V3 a Source # recip :: V3 a -> V3 a Source # fromRational :: Rational -> V3 a Source #
Data a => Data (V3 a) Source # |

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) Source #

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

toConstr :: V3 a -> Constr Source #

dataTypeOf :: V3 a -> DataType Source #

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

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

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

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

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

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

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

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

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

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

Num a => Num (V3 a) Source # |
Instance details Defined in Linear.V3 Methods (+) :: V3 a -> V3 a -> V3 a Source # (-) :: V3 a -> V3 a -> V3 a Source # (*) :: V3 a -> V3 a -> V3 a Source # negate :: V3 a -> V3 a Source # abs :: V3 a -> V3 a Source # signum :: V3 a -> V3 a Source # fromInteger :: Integer -> V3 a Source #
Ord a => Ord (V3 a) Source # |
Instance details Defined in Linear.V3 Methods compare :: V3 a -> V3 a -> Ordering Source # (<) :: V3 a -> V3 a -> Bool Source # (<=) :: V3 a -> V3 a -> Bool Source # (>) :: V3 a -> V3 a -> Bool Source # (>=) :: V3 a -> V3 a -> Bool Source # max :: V3 a -> V3 a -> V3 a Source # min :: V3 a -> V3 a -> V3 a Source #
Read a => Read (V3 a) Source # |
Instance details Defined in Linear.V3 Methods readsPrec :: Int -> ReadS (V3 a) Source # readList :: ReadS [V3 a] Source # readPrec :: ReadPrec (V3 a) Source # readListPrec :: ReadPrec [V3 a] Source #
Show a => Show (V3 a) Source # |
Instance details Defined in Linear.V3 Methods showsPrec :: Int -> V3 a -> ShowS Source # show :: V3 a -> String Source # showList :: [V3 a] -> ShowS Source #
Ix a => Ix (V3 a) Source # |
Instance details Defined in Linear.V3 Methods range :: (V3 a, V3 a) -> [V3 a] Source # index :: (V3 a, V3 a) -> V3 a -> Int Source # unsafeIndex :: (V3 a, V3 a) -> V3 a -> Int inRange :: (V3 a, V3 a) -> V3 a -> Bool Source # rangeSize :: (V3 a, V3 a) -> Int Source # unsafeRangeSize :: (V3 a, V3 a) -> Int
Generic (V3 a) Source # |
Instance details Defined in Linear.V3 Associated Types type Rep (V3 a) :: Type -> Type Source # Methods from :: V3 a -> Rep (V3 a) x Source # to :: Rep (V3 a) x -> V3 a Source #
Lift a => Lift (V3 a) Source # |
Instance details Defined in Linear.V3 Methods lift :: V3 a -> Q Exp Source #
Storable a => Storable (V3 a) Source # |

Instance details

Defined in Linear.V3

Methods

sizeOf :: V3 a -> Int Source #

alignment :: V3 a -> Int Source #

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

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

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

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

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

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

Binary a => Binary (V3 a) Source # |
Instance details Defined in Linear.V3 Methods put :: V3 a -> Put Source # get :: Get (V3 a) Source # putList :: [V3 a] -> Put Source #
Serial a => Serial (V3 a) Source # |
Instance details Defined in Linear.V3 Methods serialize :: MonadPut m => V3 a -> m () Source # deserialize :: MonadGet m => m (V3 a) Source #
Serialize a => Serialize (V3 a) Source # |
Instance details Defined in Linear.V3 Methods put :: Putter (V3 a) Source # get :: Get (V3 a) Source #
NFData a => NFData (V3 a) Source # |
Instance details Defined in Linear.V3 Methods rnf :: V3 a -> () Source #
Hashable a => Hashable (V3 a) Source # |
Instance details Defined in Linear.V3 Methods hashWithSalt :: Int -> V3 a -> Int Source # hash :: V3 a -> Int Source #
Unbox a => Unbox (V3 a) Source # |
Instance details Defined in Linear.V3
Ixed (V3 a) Source # |
Instance details Defined in Linear.V3 Methods ix :: Index (V3 a) -> Traversal' (V3 a) (IxValue (V3 a)) Source #
Epsilon a => Epsilon (V3 a) Source # |
Instance details Defined in Linear.V3 Methods nearZero :: V3 a -> Bool Source #
Generic1 V3 Source # |
Instance details Defined in Linear.V3 Associated Types type Rep1 V3 :: k -> Type Source # Methods from1 :: V3 a -> Rep1 V3 a Source # to1 :: Rep1 V3 a -> V3 a Source #
FunctorWithIndex (E V3) V3 Source # |
Instance details Defined in Linear.V3 Methods imap :: (E V3 -> a -> b) -> V3 a -> V3 b Source # imapped :: IndexedSetter (E V3) (V3 a) (V3 b) a b Source #
FoldableWithIndex (E V3) V3 Source # |
Instance details Defined in Linear.V3 Methods ifoldMap :: Monoid m => (E V3 -> a -> m) -> V3 a -> m Source # ifolded :: IndexedFold (E V3) (V3 a) a Source # ifoldr :: (E V3 -> a -> b -> b) -> b -> V3 a -> b Source # ifoldl :: (E V3 -> b -> a -> b) -> b -> V3 a -> b Source # ifoldr' :: (E V3 -> a -> b -> b) -> b -> V3 a -> b Source # ifoldl' :: (E V3 -> b -> a -> b) -> b -> V3 a -> b Source #
TraversableWithIndex (E V3) V3 Source # |
Instance details Defined in Linear.V3 Methods itraverse :: Applicative f => (E V3 -> a -> f b) -> V3 a -> f (V3 b) Source # itraversed :: IndexedTraversal (E V3) (V3 a) (V3 b) a b Source #
Each (V3 a) (V3 b) a b Source # |
Instance details Defined in Linear.V3 Methods each :: Traversal (V3 a) (V3 b) a b Source #
Field1 (V3 a) (V3 a) a a Source # |
Instance details Defined in Linear.V3 Methods _1 :: Lens (V3 a) (V3 a) a a Source #
Field2 (V3 a) (V3 a) a a Source # |
Instance details Defined in Linear.V3 Methods _2 :: Lens (V3 a) (V3 a) a a Source #
Field3 (V3 a) (V3 a) a a Source # |
Instance details Defined in Linear.V3 Methods _3 :: Lens (V3 a) (V3 a) a a Source #
type Rep V3 Source # |
Instance details Defined in Linear.V3 type Rep V3 = E V3
type Size V3 Source # |
Instance details Defined in Linear.V3 type Size V3 = 3
type Diff V3 Source # |
Instance details Defined in Linear.Affine type Diff V3 = V3
data MVector s (V3 a) Source # |
Instance details Defined in Linear.V3 data MVector s (V3 a) = MV_V3 !Int !(MVector s a)
type Rep (V3 a) Source # |

Instance details

Defined in Linear.V3

type Rep (V3 a) = D1 (MetaData "V3" "Linear.V3" "linear-1.20.9-AXvcltmUzhAPqVQGbnzsL" 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))))

data Vector (V3 a) Source # |
Instance details Defined in Linear.V3 data Vector (V3 a) = V_V3 !Int !(Vector a)
type Index (V3 a) Source # |
Instance details Defined in Linear.V3 type Index (V3 a) = E V3
type IxValue (V3 a) Source # |
Instance details Defined in Linear.V3 type IxValue (V3 a) = a
type Rep1 V3 Source # |

Instance details

Defined in Linear.V3

type Rep1 V3 = D1 (MetaData "V3" "Linear.V3" "linear-1.20.9-AXvcltmUzhAPqVQGbnzsL" 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)))

cross :: Num a => V3 a -> V3 a -> V3 a Source #

cross product

triple :: Num a => V3 a -> V3 a -> V3 a -> a Source #

scalar triple product

class R1 t 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

R1 Identity Source # |
Instance details Defined in Linear.V1 Methods _x :: Lens' (Identity 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 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

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 :: R2 t => Lens' (t a) (V2 a) Source #

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

class R2 t => R3 t 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

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 :: R3 t => Lens' (t a) (V2 a) Source #

_yz :: R3 t => Lens' (t a) (V2 a) Source #

_zx :: R3 t => Lens' (t a) (V2 a) Source #

_zy :: R3 t => Lens' (t a) (V2 a) Source #

_xzy :: R3 t => Lens' (t a) (V3 a) Source #

_yxz :: R3 t => Lens' (t a) (V3 a) Source #

_yzx :: R3 t => Lens' (t a) (V3 a) Source #

_zxy :: R3 t => Lens' (t a) (V3 a) Source #

_zyx :: R3 t => Lens' (t a) (V3 a) Source #

ex :: R1 t => E t Source #

ey :: R2 t => E t Source #

ez :: R3 t => E t Source #