linear-1.20.3: Linear Algebra

Copyright(C) 2012-2015 Edward Kmett
LicenseBSD-style (see the file LICENSE)
MaintainerEdward Kmett <ekmett@gmail.com>
Stabilityexperimental
Portabilitynon-portable
Safe HaskellTrustworthy
LanguageHaskell98

Linear.Quaternion

Description

Quaternions

Synopsis

Documentation

data Quaternion a Source

Quaternions

Constructors

Quaternion !a !(V3 a) 

Instances

Monad Quaternion Source 

Methods

(>>=) :: Quaternion a -> (a -> Quaternion b) -> Quaternion b

(>>) :: Quaternion a -> Quaternion b -> Quaternion b

return :: a -> Quaternion a

fail :: String -> Quaternion a

Functor Quaternion Source 

Methods

fmap :: (a -> b) -> Quaternion a -> Quaternion b

(<$) :: a -> Quaternion b -> Quaternion a

MonadFix Quaternion Source 

Methods

mfix :: (a -> Quaternion a) -> Quaternion a

Applicative Quaternion Source 

Methods

pure :: a -> Quaternion a

(<*>) :: Quaternion (a -> b) -> Quaternion a -> Quaternion b

(*>) :: Quaternion a -> Quaternion b -> Quaternion b

(<*) :: Quaternion a -> Quaternion b -> Quaternion a

Foldable Quaternion Source 

Methods

fold :: Monoid m => Quaternion m -> m

foldMap :: Monoid m => (a -> m) -> Quaternion a -> m

foldr :: (a -> b -> b) -> b -> Quaternion a -> b

foldr' :: (a -> b -> b) -> b -> Quaternion a -> b

foldl :: (b -> a -> b) -> b -> Quaternion a -> b

foldl' :: (b -> a -> b) -> b -> Quaternion a -> b

foldr1 :: (a -> a -> a) -> Quaternion a -> a

foldl1 :: (a -> a -> a) -> Quaternion a -> a

toList :: Quaternion a -> [a]

null :: Quaternion a -> Bool

length :: Quaternion a -> Int

elem :: Eq a => a -> Quaternion a -> Bool

maximum :: Ord a => Quaternion a -> a

minimum :: Ord a => Quaternion a -> a

sum :: Num a => Quaternion a -> a

product :: Num a => Quaternion a -> a

Traversable Quaternion Source 

Methods

traverse :: Applicative f => (a -> f b) -> Quaternion a -> f (Quaternion b)

sequenceA :: Applicative f => Quaternion (f a) -> f (Quaternion a)

mapM :: Monad m => (a -> m b) -> Quaternion a -> m (Quaternion b)

sequence :: Monad m => Quaternion (m a) -> m (Quaternion a)

Generic1 Quaternion Source 

Associated Types

type Rep1 (Quaternion :: * -> *) :: * -> *

Distributive Quaternion Source 

Methods

distribute :: Functor f => f (Quaternion a) -> Quaternion (f a)

collect :: Functor f => (a -> Quaternion b) -> f a -> Quaternion (f b)

distributeM :: Monad m => m (Quaternion a) -> Quaternion (m a)

collectM :: Monad m => (a -> Quaternion b) -> m a -> Quaternion (m b)

Representable Quaternion Source 

Associated Types

type Rep (Quaternion :: * -> *) :: *

Methods

tabulate :: (Rep Quaternion -> a) -> Quaternion a

index :: Quaternion a -> Rep Quaternion -> a

MonadZip Quaternion Source 

Methods

mzip :: Quaternion a -> Quaternion b -> Quaternion (a, b)

mzipWith :: (a -> b -> c) -> Quaternion a -> Quaternion b -> Quaternion c

munzip :: Quaternion (a, b) -> (Quaternion a, Quaternion b)

Serial1 Quaternion Source 

Methods

serializeWith :: MonadPut m => (a -> m ()) -> Quaternion a -> m ()

deserializeWith :: MonadGet m => m a -> m (Quaternion a)

Apply Quaternion Source 
Bind Quaternion Source 

Methods

(>>-) :: Quaternion a -> (a -> Quaternion b) -> Quaternion b

join :: Quaternion (Quaternion a) -> Quaternion a

Eq1 Quaternion Source 

Methods

eq1 :: Eq a => Quaternion a -> Quaternion a -> Bool

Ord1 Quaternion Source 

Methods

compare1 :: Ord a => Quaternion a -> Quaternion a -> Ordering

Read1 Quaternion Source 

Methods

readsPrec1 :: Read a => Int -> ReadS (Quaternion a)

Show1 Quaternion Source 

Methods

showsPrec1 :: Show a => Int -> Quaternion a -> ShowS

Additive Quaternion Source 

Methods

zero :: Num a => Quaternion a Source

(^+^) :: Num a => Quaternion a -> Quaternion a -> Quaternion a Source

(^-^) :: Num a => Quaternion a -> Quaternion a -> Quaternion a Source

lerp :: Num a => a -> Quaternion a -> Quaternion a -> Quaternion a Source

liftU2 :: (a -> a -> a) -> Quaternion a -> Quaternion a -> Quaternion a Source

liftI2 :: (a -> b -> c) -> Quaternion a -> Quaternion b -> Quaternion c Source

Metric Quaternion Source 
Hamiltonian Quaternion Source 

Methods

_j :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a) Source

_k :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a) Source

_ijk :: Functor f => (V3 a -> f (V3 a)) -> Quaternion a -> f (Quaternion a) Source

Complicated Quaternion Source 

Methods

_e :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a) Source

_i :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a) Source

Trace Quaternion Source 
Affine Quaternion Source 

Associated Types

type Diff (Quaternion :: * -> *) :: * -> * Source

Unbox a => Vector Vector (Quaternion a) Source 
Unbox a => MVector MVector (Quaternion a) Source 
(Num r, TrivialConjugate r) => Coalgebra r (E Quaternion) Source 

Methods

comult :: (E Quaternion -> r) -> E Quaternion -> E Quaternion -> r Source

counital :: (E Quaternion -> r) -> r Source

(Num r, TrivialConjugate r) => Algebra r (E Quaternion) Source 

Methods

mult :: (E Quaternion -> E Quaternion -> r) -> E Quaternion -> r Source

unital :: r -> E Quaternion -> r Source

Eq a => Eq (Quaternion a) Source 

Methods

(==) :: Quaternion a -> Quaternion a -> Bool

(/=) :: Quaternion a -> Quaternion a -> Bool

RealFloat a => Floating (Quaternion a) Source 
RealFloat a => Fractional (Quaternion a) Source 
Data a => Data (Quaternion a) Source 

Methods

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

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

toConstr :: Quaternion a -> Constr

dataTypeOf :: Quaternion a -> DataType

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

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

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

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

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

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

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

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

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

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

RealFloat a => Num (Quaternion a) Source 
Ord a => Ord (Quaternion a) Source 
Read a => Read (Quaternion a) Source 
Show a => Show (Quaternion a) Source 
Ix a => Ix (Quaternion a) Source 
Generic (Quaternion a) Source 

Associated Types

type Rep (Quaternion a) :: * -> *

Methods

from :: Quaternion a -> Rep (Quaternion a) x

to :: Rep (Quaternion a) x -> Quaternion a

Storable a => Storable (Quaternion a) Source 

Methods

sizeOf :: Quaternion a -> Int

alignment :: Quaternion a -> Int

peekElemOff :: Ptr (Quaternion a) -> Int -> IO (Quaternion a)

pokeElemOff :: Ptr (Quaternion a) -> Int -> Quaternion a -> IO ()

peekByteOff :: Ptr b -> Int -> IO (Quaternion a)

pokeByteOff :: Ptr b -> Int -> Quaternion a -> IO ()

peek :: Ptr (Quaternion a) -> IO (Quaternion a)

poke :: Ptr (Quaternion a) -> Quaternion a -> IO ()

Binary a => Binary (Quaternion a) Source 

Methods

put :: Quaternion a -> Put

get :: Get (Quaternion a)

Serial a => Serial (Quaternion a) Source 

Methods

serialize :: MonadPut m => Quaternion a -> m ()

deserialize :: MonadGet m => m (Quaternion a)

Serialize a => Serialize (Quaternion a) Source 

Methods

put :: Putter (Quaternion a)

get :: Get (Quaternion a)

NFData a => NFData (Quaternion a) Source 

Methods

rnf :: Quaternion a -> ()

Hashable a => Hashable (Quaternion a) Source 

Methods

hashWithSalt :: Int -> Quaternion a -> Int

hash :: Quaternion a -> Int

Unbox a => Unbox (Quaternion a) Source 
Ixed (Quaternion a) Source 
(RealFloat a, Epsilon a) => Epsilon (Quaternion a) Source 
(Conjugate a, RealFloat a) => Conjugate (Quaternion a) Source 
FunctorWithIndex (E Quaternion) Quaternion Source 

Methods

imap :: (E Quaternion -> a -> b) -> Quaternion a -> Quaternion b

imapped :: (Indexable (E Quaternion) p, Settable f) => p a (f b) -> Quaternion a -> f (Quaternion b)

FoldableWithIndex (E Quaternion) Quaternion Source 

Methods

ifoldMap :: Monoid m => (E Quaternion -> a -> m) -> Quaternion a -> m

ifolded :: (Indexable (E Quaternion) p, Contravariant f, Applicative f) => p a (f a) -> Quaternion a -> f (Quaternion a)

ifoldr :: (E Quaternion -> a -> b -> b) -> b -> Quaternion a -> b

ifoldl :: (E Quaternion -> b -> a -> b) -> b -> Quaternion a -> b

ifoldr' :: (E Quaternion -> a -> b -> b) -> b -> Quaternion a -> b

ifoldl' :: (E Quaternion -> b -> a -> b) -> b -> Quaternion a -> b

TraversableWithIndex (E Quaternion) Quaternion Source 

Methods

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

itraversed :: (Indexable (E Quaternion) p, Applicative f) => p a (f b) -> Quaternion a -> f (Quaternion b)

Each (Quaternion a) (Quaternion b) a b Source 

Methods

each :: Traversal (Quaternion a) (Quaternion b) a b

type Rep1 Quaternion Source 
type Rep Quaternion = E Quaternion Source 
type Diff Quaternion = Quaternion Source 
data MVector s (Quaternion a) = MV_Quaternion !Int (MVector s a) Source 
type Rep (Quaternion a) Source 
data Vector (Quaternion a) = V_Quaternion !Int (Vector a) Source 
type Index (Quaternion a) = E Quaternion Source 
type IxValue (Quaternion a) = a Source 

class Complicated t where Source

A vector space that includes the basis elements _e and _i

Minimal complete definition

Nothing

Methods

_e, _i :: Lens' (t a) a Source

Instances

Complicated Complex Source 

Methods

_e :: Functor f => (a -> f a) -> Complex a -> f (Complex a) Source

_i :: Functor f => (a -> f a) -> Complex a -> f (Complex a) Source

Complicated Quaternion Source 

Methods

_e :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a) Source

_i :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a) Source

class Complicated t => Hamiltonian t where Source

A vector space that includes the basis elements _e, _i, _j and _k

Minimal complete definition

Nothing

Methods

_j, _k :: Lens' (t a) a Source

_ijk :: Lens' (t a) (V3 a) Source

Instances

Hamiltonian Quaternion Source 

Methods

_j :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a) Source

_k :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a) Source

_ijk :: Functor f => (V3 a -> f (V3 a)) -> Quaternion a -> f (Quaternion a) Source

slerp :: RealFloat a => Quaternion a -> Quaternion a -> a -> Quaternion a Source

Spherical linear interpolation between two quaternions.

asinq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a Source

asin with a specified branch cut.

acosq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a Source

acos with a specified branch cut.

atanq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a Source

atan with a specified branch cut.

asinhq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a Source

asinh with a specified branch cut.

acoshq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a Source

acosh with a specified branch cut.

atanhq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a Source

atanh with a specified branch cut.

absi :: Floating a => Quaternion a -> a Source

norm of the imaginary component

pow :: RealFloat a => Quaternion a -> a -> Quaternion a Source

raise a Quaternion to a scalar power

rotate :: (Conjugate a, RealFloat a) => Quaternion a -> V3 a -> V3 a Source

Apply a rotation to a vector.

axisAngle :: (Epsilon a, Floating a) => V3 a -> a -> Quaternion a Source

axisAngle axis theta builds a Quaternion representing a rotation of theta radians about axis.