linear-1.20.7: Linear Algebra

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

Linear.V2

Description

2-D Vectors

Synopsis

- data V2 a = V2 !a !a
- class R1 t where
- class R1 t => R2 t where
- _yx :: R2 t => Lens' (t a) (V2 a)
- ex :: R1 t => E t
- ey :: R2 t => E t
- perp :: Num a => V2 a -> V2 a
- angle :: Floating a => a -> V2 a
- crossZ :: Num a => V2 a -> V2 a -> a

# Documentation

data V2 a Source #

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

Constructors

V2 !a !a |

Instances

Monad V2 Source # |
Methods (>>=) :: V2 a -> (a -> V2 b) -> V2 b # (>>) :: V2 a -> V2 b -> V2 b # return :: a -> V2 a # fail :: String -> V2 a #
Functor V2 Source # |
Methods fmap :: (a -> b) -> V2 a -> V2 b # (<$) :: a -> V2 b -> V2 a #
MonadFix V2 Source # |
Methods mfix :: (a -> V2 a) -> V2 a #
Applicative V2 Source # |
Methods pure :: a -> V2 a # (<*>) :: V2 (a -> b) -> V2 a -> V2 b # (*>) :: V2 a -> V2 b -> V2 b # (<*) :: V2 a -> V2 b -> V2 a #
Foldable V2 Source # |

Methods

fold :: Monoid m => V2 m -> 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 Source # |
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) #
Generic1 V2 Source # |
Associated Types type Rep1 (V2 :: * -> *) :: * -> * # Methods from1 :: V2 a -> Rep1 V2 a # to1 :: Rep1 V2 a -> V2 a #
Distributive V2 Source # |
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 Source # |
Associated Types type Rep (V2 :: * -> *) :: * # Methods tabulate :: (Rep V2 -> a) -> V2 a # index :: V2 a -> Rep V2 -> a #
Eq1 V2 Source # |
Methods liftEq :: (a -> b -> Bool) -> V2 a -> V2 b -> Bool #
Ord1 V2 Source # |
Methods liftCompare :: (a -> b -> Ordering) -> V2 a -> V2 b -> Ordering #
Read1 V2 Source # |
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V2 a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V2 a] #
Show1 V2 Source # |
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V2 a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V2 a] -> ShowS #
MonadZip V2 Source # |
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 Source # |
Methods serializeWith :: MonadPut m => (a -> m ()) -> V2 a -> m () # deserializeWith :: MonadGet m => m a -> m (V2 a) #
Traversable1 V2 Source # |
Methods traverse1 :: Apply f => (a -> f b) -> V2 a -> f (V2 b) # sequence1 :: Apply f => V2 (f b) -> f (V2 b) #
Apply V2 Source # |
Methods (<.>) :: V2 (a -> b) -> V2 a -> V2 b # (.>) :: V2 a -> V2 b -> V2 b # (<.) :: V2 a -> V2 b -> V2 a #
Bind V2 Source # |
Methods (>>-) :: V2 a -> (a -> V2 b) -> V2 b # join :: V2 (V2 a) -> V2 a #
Foldable1 V2 Source # |
Methods fold1 :: Semigroup m => V2 m -> m # foldMap1 :: Semigroup m => (a -> m) -> V2 a -> m # toNonEmpty :: V2 a -> NonEmpty a #
Additive V2 Source # |
Methods zero :: Num a => V2 a Source # (^+^) :: Num a => V2 a -> V2 a -> V2 a Source # (^-^) :: Num a => V2 a -> V2 a -> V2 a Source # lerp :: Num a => a -> V2 a -> V2 a -> V2 a Source # liftU2 :: (a -> a -> a) -> V2 a -> V2 a -> V2 a Source # liftI2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c Source #
Metric V2 Source # |
Methods dot :: Num a => V2 a -> V2 a -> a Source # quadrance :: Num a => V2 a -> a Source # qd :: Num a => V2 a -> V2 a -> a Source # distance :: Floating a => V2 a -> V2 a -> a Source # norm :: Floating a => V2 a -> a Source # signorm :: Floating a => V2 a -> V2 a Source #
Finite V2 Source # |
Associated Types type Size (V2 :: * -> *) :: Nat Source # Methods toV :: V2 a -> V Nat (Size V2) a Source # fromV :: V Nat (Size V2) a -> V2 a Source #
R1 V2 Source # |
Methods _x :: Functor f => (a -> f a) -> V2 a -> f (V2 a) Source #
R2 V2 Source # |
Methods _y :: Functor f => (a -> f a) -> V2 a -> f (V2 a) Source # _xy :: Functor f => (V2 a -> f (V2 a)) -> V2 a -> f (V2 a) Source #
Trace V2 Source # |
Methods trace :: Num a => V2 (V2 a) -> a Source # diagonal :: V2 (V2 a) -> V2 a Source #
Affine V2 Source # |
Associated Types type Diff (V2 :: * -> *) :: * -> * Source # Methods (.-.) :: Num a => V2 a -> V2 a -> Diff V2 a Source # (.+^) :: Num a => V2 a -> Diff V2 a -> V2 a Source # (.-^) :: Num a => V2 a -> Diff V2 a -> V2 a Source #
Unbox a => Vector Vector (V2 a) Source # |

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) Source # |

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)) #

Num r => Coalgebra r (E V2) Source # |
Methods comult :: (E V2 -> r) -> E V2 -> E V2 -> r Source # counital :: (E V2 -> r) -> r Source #
Bounded a => Bounded (V2 a) Source # |
Methods minBound :: V2 a # maxBound :: V2 a #
Eq a => Eq (V2 a) Source # |
Methods (==) :: V2 a -> V2 a -> Bool # (/=) :: V2 a -> V2 a -> Bool #
Floating a => Floating (V2 a) Source # |

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) Source # |
Methods (/) :: V2 a -> V2 a -> V2 a # recip :: V2 a -> V2 a # fromRational :: Rational -> V2 a #
Data a => Data (V2 a) Source # |

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 :: (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) Source # |
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) Source # |
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) Source # |
Methods readsPrec :: Int -> ReadS (V2 a) # readList :: ReadS [V2 a] # readPrec :: ReadPrec (V2 a) # readListPrec :: ReadPrec [V2 a] #
Show a => Show (V2 a) Source # |
Methods showsPrec :: Int -> V2 a -> ShowS # show :: V2 a -> String # showList :: [V2 a] -> ShowS #
Ix a => Ix (V2 a) Source # |
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) Source # |
Associated Types type Rep (V2 a) :: * -> * # Methods from :: V2 a -> Rep (V2 a) x # to :: Rep (V2 a) x -> V2 a #
Storable a => Storable (V2 a) Source # |
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) Source # |
Methods put :: V2 a -> Put # get :: Get (V2 a) # putList :: [V2 a] -> Put #
Serial a => Serial (V2 a) Source # |
Methods serialize :: MonadPut m => V2 a -> m () # deserialize :: MonadGet m => m (V2 a) #
Serialize a => Serialize (V2 a) Source # |
Methods put :: Putter (V2 a) # get :: Get (V2 a) #
NFData a => NFData (V2 a) Source # |
Methods rnf :: V2 a -> () #
Hashable a => Hashable (V2 a) Source # |
Methods hashWithSalt :: Int -> V2 a -> Int # hash :: V2 a -> Int #
Unbox a => Unbox (V2 a) Source # |
Ixed (V2 a) Source # |
Methods ix :: Index (V2 a) -> Traversal' (V2 a) (IxValue (V2 a)) #
Epsilon a => Epsilon (V2 a) Source # |
Methods nearZero :: V2 a -> Bool Source #
FunctorWithIndex (E V2) V2 Source # |
Methods imap :: (E V2 -> a -> b) -> V2 a -> V2 b # imapped :: (Indexable (E V2) p, Settable f) => p a (f b) -> V2 a -> f (V2 b) #
FoldableWithIndex (E V2) V2 Source # |
Methods ifoldMap :: Monoid m => (E V2 -> a -> m) -> V2 a -> m # ifolded :: (Indexable (E V2) p, Contravariant f, Applicative f) => p a (f a) -> V2 a -> f (V2 a) # 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 Source # |
Methods itraverse :: Applicative f => (E V2 -> a -> f b) -> V2 a -> f (V2 b) # itraversed :: (Indexable (E V2) p, Applicative f) => p a (f b) -> V2 a -> f (V2 b) #
Each (V2 a) (V2 b) a b Source # |
Methods each :: Traversal (V2 a) (V2 b) a b #
type Rep1 V2 Source # |
type Rep1 V2 = D1 (MetaData "V2" "Linear.V2" "linear-1.20.7-CvaXC2ebC1zHQ7FJwFrAk8" False) (C1 (MetaCons "V2" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1)))
type Rep V2 Source # |
type Rep V2 = E V2
type Size V2 Source # |
type Size V2 = 2
type Diff V2 Source # |
type Diff V2 = V2
data MVector s (V2 a) Source # |
data MVector s (V2 a) = MV_V2 !Int !(MVector s a)
type Rep (V2 a) Source # |
type Rep (V2 a) = D1 (MetaData "V2" "Linear.V2" "linear-1.20.7-CvaXC2ebC1zHQ7FJwFrAk8" False) (C1 (MetaCons "V2" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a))))
data Vector (V2 a) Source # |
data Vector (V2 a) = V_V2 !Int !(Vector a)
type Index (V2 a) Source # |
type Index (V2 a) = E V2
type IxValue (V2 a) Source # |
type IxValue (V2 a) = a

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 # |
Methods _x :: Functor f => (a -> f a) -> Identity a -> f (Identity a) Source #
R1 V1 Source # |
Methods _x :: Functor f => (a -> f a) -> V1 a -> f (V1 a) Source #
R1 V2 Source # |
Methods _x :: Functor f => (a -> f a) -> V2 a -> f (V2 a) Source #
R1 V3 Source # |
Methods _x :: Functor f => (a -> f a) -> V3 a -> f (V3 a) Source #
R1 V4 Source # |
Methods _x :: Functor f => (a -> f a) -> V4 a -> f (V4 a) Source #
R1 f => R1 (Point f) Source # |
Methods _x :: Functor f => (a -> f a) -> Point f a -> f (Point f a) Source #

class R1 t => R2 t where Source #

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

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 # |
Methods _y :: Functor f => (a -> f a) -> V2 a -> f (V2 a) Source # _xy :: Functor f => (V2 a -> f (V2 a)) -> V2 a -> f (V2 a) Source #
R2 V3 Source # |
Methods _y :: Functor f => (a -> f a) -> V3 a -> f (V3 a) Source # _xy :: Functor f => (V2 a -> f (V2 a)) -> V3 a -> f (V3 a) Source #
R2 V4 Source # |
Methods _y :: Functor f => (a -> f a) -> V4 a -> f (V4 a) Source # _xy :: Functor f => (V2 a -> f (V2 a)) -> V4 a -> f (V4 a) Source #
R2 f => R2 (Point f) Source # |
Methods _y :: Functor f => (a -> f a) -> Point f a -> f (Point f a) Source # _xy :: Functor f => (V2 a -> f (V2 a)) -> Point f a -> f (Point f a) Source #

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

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

ex :: R1 t => E t Source #

ey :: R2 t => E t Source #

perp :: Num a => V2 a -> V2 a Source #

the counter-clockwise perpendicular vector

    >>> perp $ V2 10 20
    V2 (-20) 10

angle :: Floating a => a -> V2 a Source #

crossZ :: Num a => V2 a -> V2 a -> a Source #

The Z-component of the cross product of two vectors in the XY-plane.

    >>> crossZ (V2 1 0) (V2 0 1)
    1