Copyright	[2015..2017] Trevor L. McDonell
License	BSD3
Maintainer	Trevor L. McDonell <tmcdonell@cse.unsw.edu.au>
Stability	experimental
Portability	non-portable (GHC extensions)
Safe Haskell	None
Language	Haskell98

Data.Array.Accelerate.Data.Complex

Contents

Rectangular from
Polar form
Conjugate
Orphan instances

Description

Complex numbers

Synopsis

Rectangular from

data Complex a :: * -> * #

Complex numbers are an algebraic type.

For a complex number z, abs z is a number with the magnitude of z, but oriented in the positive real direction, whereas signum z has the phase of z, but unit magnitude.

The Foldable and Traversable instances traverse the real part first.

Constructors

~a :+ ~a infix 6

forms a complex number from its real and imaginary rectangular components.

Instances

Monad Complex
Methods (>>=) :: Complex a -> (a -> Complex b) -> Complex b # (>>) :: Complex a -> Complex b -> Complex b # return :: a -> Complex a # fail :: String -> Complex a #
Functor Complex
Methods fmap :: (a -> b) -> Complex a -> Complex b # (<$) :: a -> Complex b -> Complex a #
Applicative Complex
Methods pure :: a -> Complex a # (<>) :: Complex (a -> b) -> Complex a -> Complex b # (>) :: Complex a -> Complex b -> Complex b # (<*) :: Complex a -> Complex b -> Complex a #
Foldable Complex
Methods fold :: Monoid m => Complex m -> m # foldMap :: Monoid m => (a -> m) -> Complex a -> m # foldr :: (a -> b -> b) -> b -> Complex a -> b # foldr' :: (a -> b -> b) -> b -> Complex a -> b # foldl :: (b -> a -> b) -> b -> Complex a -> b # foldl' :: (b -> a -> b) -> b -> Complex a -> b # foldr1 :: (a -> a -> a) -> Complex a -> a # foldl1 :: (a -> a -> a) -> Complex a -> a # toList :: Complex a -> [a] # null :: Complex a -> Bool # length :: Complex a -> Int # elem :: Eq a => a -> Complex a -> Bool # maximum :: Ord a => Complex a -> a # minimum :: Ord a => Complex a -> a # sum :: Num a => Complex a -> a # product :: Num a => Complex a -> a #
Traversable Complex
Methods traverse :: Applicative f => (a -> f b) -> Complex a -> f (Complex b) # sequenceA :: Applicative f => Complex (f a) -> f (Complex a) # mapM :: Monad m => (a -> m b) -> Complex a -> m (Complex b) # sequence :: Monad m => Complex (m a) -> m (Complex a) #
Generic1 Complex
Associated Types type Rep1 (Complex :: * -> ) :: -> * # Methods from1 :: Complex a -> Rep1 Complex a # to1 :: Rep1 Complex a -> Complex a #
Unbox a => Vector Vector (Complex a)
Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Complex a) -> m (Vector (Complex a)) # basicUnsafeThaw :: PrimMonad m => Vector (Complex a) -> m (Mutable Vector (PrimState m) (Complex a)) # basicLength :: Vector (Complex a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Complex a) -> Vector (Complex a) # basicUnsafeIndexM :: Monad m => Vector (Complex a) -> Int -> m (Complex a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Complex a) -> Vector (Complex a) -> m () # elemseq :: Vector (Complex a) -> Complex a -> b -> b #
Unbox a => MVector MVector (Complex a)
Methods basicLength :: MVector s (Complex a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (Complex a) -> MVector s (Complex a) # basicOverlaps :: MVector s (Complex a) -> MVector s (Complex a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Complex a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (Complex a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Complex a -> m (MVector (PrimState m) (Complex a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Complex a) -> Int -> m (Complex a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Complex a) -> Int -> Complex a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (Complex a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (Complex a) -> Complex a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Complex a) -> MVector (PrimState m) (Complex a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Complex a) -> MVector (PrimState m) (Complex a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Complex a) -> Int -> m (MVector (PrimState m) (Complex a)) #
Eq a => Eq (Complex a)
Methods (==) :: Complex a -> Complex a -> Bool # (/=) :: Complex a -> Complex a -> Bool #
RealFloat a => Floating (Complex a)
Methods pi :: Complex a # exp :: Complex a -> Complex a # log :: Complex a -> Complex a # sqrt :: Complex a -> Complex a # (**) :: Complex a -> Complex a -> Complex a # logBase :: Complex a -> Complex a -> Complex a # sin :: Complex a -> Complex a # cos :: Complex a -> Complex a # tan :: Complex a -> Complex a # asin :: Complex a -> Complex a # acos :: Complex a -> Complex a # atan :: Complex a -> Complex a # sinh :: Complex a -> Complex a # cosh :: Complex a -> Complex a # tanh :: Complex a -> Complex a # asinh :: Complex a -> Complex a # acosh :: Complex a -> Complex a # atanh :: Complex a -> Complex a # log1p :: Complex a -> Complex a # expm1 :: Complex a -> Complex a # log1pexp :: Complex a -> Complex a # log1mexp :: Complex a -> Complex a #
RealFloat a => Fractional (Complex a)
Methods (/) :: Complex a -> Complex a -> Complex a # recip :: Complex a -> Complex a # fromRational :: Rational -> Complex a #
Data a => Data (Complex a)
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Complex a -> c (Complex a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Complex a) # toConstr :: Complex a -> Constr # dataTypeOf :: Complex a -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Complex a)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Complex a)) # gmapT :: (forall b. Data b => b -> b) -> Complex a -> Complex a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Complex a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Complex a -> r # gmapQ :: (forall d. Data d => d -> u) -> Complex a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Complex a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Complex a -> m (Complex a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Complex a -> m (Complex a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Complex a -> m (Complex a) #
RealFloat a => Num (Complex a)
Methods (+) :: Complex a -> Complex a -> Complex a # (-) :: Complex a -> Complex a -> Complex a # (*) :: Complex a -> Complex a -> Complex a # negate :: Complex a -> Complex a # abs :: Complex a -> Complex a # signum :: Complex a -> Complex a # fromInteger :: Integer -> Complex a #
Read a => Read (Complex a)
Methods readsPrec :: Int -> ReadS (Complex a) # readList :: ReadS [Complex a] # readPrec :: ReadPrec (Complex a) # readListPrec :: ReadPrec [Complex a] #
Show a => Show (Complex a)
Methods showsPrec :: Int -> Complex a -> ShowS # show :: Complex a -> String # showList :: [Complex a] -> ShowS #
Generic (Complex a)
Associated Types type Rep (Complex a) :: * -> * # Methods from :: Complex a -> Rep (Complex a) x # to :: Rep (Complex a) x -> Complex a #
Storable a => Storable (Complex a)
Methods sizeOf :: Complex a -> Int # alignment :: Complex a -> Int # peekElemOff :: Ptr (Complex a) -> Int -> IO (Complex a) # pokeElemOff :: Ptr (Complex a) -> Int -> Complex a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Complex a) # pokeByteOff :: Ptr b -> Int -> Complex a -> IO () # peek :: Ptr (Complex a) -> IO (Complex a) # poke :: Ptr (Complex a) -> Complex a -> IO () #
NFData a => NFData (Complex a)
Methods rnf :: Complex a -> () #
Unbox a => Unbox (Complex a)

type Rep1 Complex
type Rep1 Complex = D1 (MetaData "Complex" "Data.Complex" "base" False) (C1 (MetaCons ":+" (InfixI NotAssociative 6) False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1)))
data MVector s (Complex a)
data MVector s (Complex a) = MV_Complex (MVector s (a, a))
type Rep (Complex a)
type Rep (Complex a) = D1 (MetaData "Complex" "Data.Complex" "base" False) (C1 (MetaCons ":+" (InfixI NotAssociative 6) False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a))))
data Vector (Complex a)
data Vector (Complex a) = V_Complex (Vector (a, a))
type Plain (Complex a) Source #
type Plain (Complex a) = Complex (Plain a)

real :: Elt a => Exp (Complex a) -> Exp a Source #

Return the real part of a complex number

imag :: Elt a => Exp (Complex a) -> Exp a Source #

Return the imaginary part of a complex number

Polar form

mkPolar :: forall a. Floating a => Exp a -> Exp a -> Exp (Complex a) Source #

Form a complex number from polar components of magnitude and phase.

cis :: forall a. Floating a => Exp a -> Exp (Complex a) Source #

cis t is a complex value with magnitude 1 and phase t (modulo 2*pi).

polar :: RealFloat a => Exp (Complex a) -> Exp (a, a) Source #

The function polar takes a complex number and returns a (magnitude, phase) pair in canonical form: the magnitude is non-negative, and the phase in the range (-pi, pi]; if the magnitude is zero, then so is the phase.

magnitude :: RealFloat a => Exp (Complex a) -> Exp a Source #

The non-negative magnitude of a complex number

phase :: RealFloat a => Exp (Complex a) -> Exp a Source #

The phase of a complex number, in the range (-pi, pi]. If the magnitude is zero, then so is the phase.

Conjugate

conjugate :: Num a => Exp (Complex a) -> Exp (Complex a) Source #

Return the complex conjugate of a complex number, defined as

conjugate(Z) = X - iY

Orphan instances

(FromIntegral a b, Num b) => FromIntegral a (Complex b) Source #
Methods fromIntegral :: Exp a -> Exp (Complex b) Source #
Elt a => Unlift Exp (Complex (Exp a)) Source #
Methods unlift :: Exp (Plain (Complex (Exp a))) -> Complex (Exp a) Source #
(Lift Exp a, Elt (Plain a)) => Lift Exp (Complex a) Source #
Associated Types type Plain (Complex a) :: * Source # Methods lift :: Complex a -> Exp (Plain (Complex a)) Source #
RealFloat a => Floating (Exp (Complex a)) Source #
Methods pi :: Exp (Complex a) # exp :: Exp (Complex a) -> Exp (Complex a) # log :: Exp (Complex a) -> Exp (Complex a) # sqrt :: Exp (Complex a) -> Exp (Complex a) # (**) :: Exp (Complex a) -> Exp (Complex a) -> Exp (Complex a) # logBase :: Exp (Complex a) -> Exp (Complex a) -> Exp (Complex a) # sin :: Exp (Complex a) -> Exp (Complex a) # cos :: Exp (Complex a) -> Exp (Complex a) # tan :: Exp (Complex a) -> Exp (Complex a) # asin :: Exp (Complex a) -> Exp (Complex a) # acos :: Exp (Complex a) -> Exp (Complex a) # atan :: Exp (Complex a) -> Exp (Complex a) # sinh :: Exp (Complex a) -> Exp (Complex a) # cosh :: Exp (Complex a) -> Exp (Complex a) # tanh :: Exp (Complex a) -> Exp (Complex a) # asinh :: Exp (Complex a) -> Exp (Complex a) # acosh :: Exp (Complex a) -> Exp (Complex a) # atanh :: Exp (Complex a) -> Exp (Complex a) # log1p :: Exp (Complex a) -> Exp (Complex a) # expm1 :: Exp (Complex a) -> Exp (Complex a) # log1pexp :: Exp (Complex a) -> Exp (Complex a) # log1mexp :: Exp (Complex a) -> Exp (Complex a) #
RealFloat a => Fractional (Exp (Complex a)) Source #
Methods (/) :: Exp (Complex a) -> Exp (Complex a) -> Exp (Complex a) # recip :: Exp (Complex a) -> Exp (Complex a) # fromRational :: Rational -> Exp (Complex a) #
RealFloat a => Num (Exp (Complex a)) Source #
Methods (+) :: Exp (Complex a) -> Exp (Complex a) -> Exp (Complex a) # (-) :: Exp (Complex a) -> Exp (Complex a) -> Exp (Complex a) # (*) :: Exp (Complex a) -> Exp (Complex a) -> Exp (Complex a) # negate :: Exp (Complex a) -> Exp (Complex a) # abs :: Exp (Complex a) -> Exp (Complex a) # signum :: Exp (Complex a) -> Exp (Complex a) # fromInteger :: Integer -> Exp (Complex a) #
Elt a => Elt (Complex a) Source #
Methods eltType :: Complex a -> TupleType (EltRepr (Complex a)) fromElt :: Complex a -> EltRepr (Complex a) toElt :: EltRepr (Complex a) -> Complex a
Eq a => Eq (Complex a) Source #
Methods (==) :: Exp (Complex a) -> Exp (Complex a) -> Exp Bool Source # (/=) :: Exp (Complex a) -> Exp (Complex a) -> Exp Bool Source #