Copyright	[2015..2020] The Accelerate Team
License	BSD3
Maintainer	Trevor L. McDonell <trevor.mcdonell@gmail.com>
Stability	experimental
Portability	non-portable (GHC extensions)
Safe Haskell	None
Language	Haskell2010

Data.Array.Accelerate.Data.Complex

Contents

Rectangular from
Polar form
Conjugate
Orphan instances

Description

Complex numbers, stored in the usual C-style array-of-struct representation, for easy interoperability.

Synopsis

data Complex a = !a :+ !a
pattern (::+) :: Elt a => Exp a -> Exp a -> Exp (Complex a)
real :: Elt a => Exp (Complex a) -> Exp a
imag :: Elt a => Exp (Complex a) -> Exp a
mkPolar :: forall a. Floating a => Exp a -> Exp a -> Exp (Complex a)
cis :: forall a. Floating a => Exp a -> Exp (Complex a)
polar :: RealFloat a => Exp (Complex a) -> Exp (a, a)
magnitude :: RealFloat a => Exp (Complex a) -> Exp a
magnitude' :: RealFloat a => Exp (Complex a) -> Exp a
phase :: RealFloat a => Exp (Complex a) -> Exp a
conjugate :: Num a => Exp (Complex a) -> Exp (Complex a)

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.

Note that Complex's instances inherit the deficiencies from the type parameter's. For example, Complex Float's Ord instance has similar problems to Float's.

Constructors

!a :+ !a infix 6

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

Instances

Instances details

Monad Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods (>>=) :: Complex a -> (a -> Complex b) -> Complex b # (>>) :: Complex a -> Complex b -> Complex b # return :: a -> Complex a #
Functor Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods fmap :: (a -> b) -> Complex a -> Complex b # (<$) :: a -> Complex b -> Complex a #
Applicative Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods pure :: a -> Complex a # (<>) :: Complex (a -> b) -> Complex a -> Complex b # liftA2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c # (>) :: Complex a -> Complex b -> Complex b # (<*) :: Complex a -> Complex b -> Complex a #
Foldable Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods fold :: Monoid m => Complex m -> m # foldMap :: Monoid m => (a -> m) -> Complex a -> 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	Since: base-4.9.0.0
Instance details Defined in Data.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) #
Representable Complex
Instance details Defined in Data.Functor.Rep Associated Types type Rep Complex # Methods tabulate :: (Rep Complex -> a) -> Complex a # index :: Complex a -> Rep Complex -> a #
Hashable1 Complex
Instance details Defined in Data.Hashable.Class Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> Complex a -> Int #
Traversable1 Complex
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Complex a -> f (Complex b) # sequence1 :: Apply f => Complex (f b) -> f (Complex b) #
Functor Complex Source #	Since: 1.2.0.0
Instance details Defined in Data.Array.Accelerate.Data.Complex Methods fmap :: (Elt a, Elt b, Elt (Complex a), Elt (Complex b)) => (Exp a -> Exp b) -> Exp (Complex a) -> Exp (Complex b) Source # (<$) :: (Elt a, Elt b, Elt (Complex a), Elt (Complex b)) => Exp a -> Exp (Complex b) -> Exp (Complex a) Source #
Unbox a => Vector Vector (Complex a)
Instance details Defined in Data.Vector.Unboxed.Base 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)
Instance details Defined in Data.Vector.Unboxed.Base 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)) #
Elt a => Unlift Exp (Complex (Exp a)) Source #
Instance details Defined in Data.Array.Accelerate.Data.Complex Methods unlift :: Exp (Plain (Complex (Exp a))) -> Complex (Exp a) Source #
(Lift Exp a, Elt (Plain a)) => Lift Exp (Complex a) Source #
Instance details Defined in Data.Array.Accelerate.Data.Complex Associated Types type Plain (Complex a) Source # Methods lift :: Complex a -> Exp (Plain (Complex a)) Source #
(FromIntegral a b, Num b, Elt (Complex b)) => FromIntegral a (Complex b) Source #
Instance details Defined in Data.Array.Accelerate.Data.Complex Methods fromIntegral :: Exp a -> Exp (Complex b) Source #
Eq a => Eq (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods (==) :: Complex a -> Complex a -> Bool # (/=) :: Complex a -> Complex a -> Bool #
RealFloat a => Floating (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex 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 => Floating (Exp (Complex a)) Source #
Instance details Defined in Data.Array.Accelerate.Data.Complex 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 (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods (/) :: Complex a -> Complex a -> Complex a # recip :: Complex a -> Complex a # fromRational :: Rational -> Complex a #
RealFloat a => Fractional (Exp (Complex a)) Source #
Instance details Defined in Data.Array.Accelerate.Data.Complex Methods (/) :: Exp (Complex a) -> Exp (Complex a) -> Exp (Complex a) # recip :: Exp (Complex a) -> Exp (Complex a) # fromRational :: Rational -> Exp (Complex a) #
Data a => Data (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex 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 :: forall r r'. (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)	Since: base-2.1
Instance details Defined in Data.Complex 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 #
RealFloat a => Num (Exp (Complex a)) Source #
Instance details Defined in Data.Array.Accelerate.Data.Complex 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) #
Read a => Read (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods readsPrec :: Int -> ReadS (Complex a) # readList :: ReadS [Complex a] # readPrec :: ReadPrec (Complex a) # readListPrec :: ReadPrec [Complex a] #
Show a => Show (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods showsPrec :: Int -> Complex a -> ShowS # show :: Complex a -> String # showList :: [Complex a] -> ShowS #
Generic (Complex a)	Since: base-4.9.0.0
Instance details Defined in Data.Complex Associated Types type Rep (Complex a) :: Type -> Type # Methods from :: Complex a -> Rep (Complex a) x # to :: Rep (Complex a) x -> Complex a #
Storable a => Storable (Complex a)	Since: base-4.8.0.0
Instance details Defined in Data.Complex 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)
Instance details Defined in Control.DeepSeq Methods rnf :: Complex a -> () #
Hashable a => Hashable (Complex a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Complex a -> Int # hash :: Complex a -> Int #
Unbox a => Unbox (Complex a)
Instance details Defined in Data.Vector.Unboxed.Base
Elt a => Elt (Complex a) Source #
Instance details Defined in Data.Array.Accelerate.Data.Complex Associated Types type EltR (Complex a) Methods eltR :: TypeR (EltR (Complex a)) tagsR :: [TagR (EltR (Complex a))] fromElt :: Complex a -> EltR (Complex a) toElt :: EltR (Complex a) -> Complex a
Eq a => Eq (Complex a) Source #
Instance details Defined in Data.Array.Accelerate.Data.Complex Methods (==) :: Exp (Complex a) -> Exp (Complex a) -> Exp Bool Source # (/=) :: Exp (Complex a) -> Exp (Complex a) -> Exp Bool Source #
Generic1 Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Associated Types type Rep1 Complex :: k -> Type # Methods from1 :: forall (a :: k). Complex a -> Rep1 Complex a # to1 :: forall (a :: k). Rep1 Complex a -> Complex a #
Each (Complex a) (Complex b) a b	`each` :: (`RealFloat` a, `RealFloat` b) => `Traversal` (`Complex` a) (`Complex` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Complex a) (Complex b) a b #
type Rep Complex
Instance details Defined in Data.Functor.Rep type Rep Complex = Bool
newtype MVector s (Complex a)
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s (Complex a) = MV_Complex (MVector s (a, a))
type Rep (Complex a)
Instance details Defined in Data.Complex type Rep (Complex a) = D1 ('MetaData "Complex" "Data.Complex" "base" 'False) (C1 ('MetaCons ":+" ('InfixI 'NotAssociative 6) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)))
newtype Vector (Complex a)
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector (Complex a) = V_Complex (Vector (a, a))
type Index (Complex a)
Instance details Defined in Control.Lens.At type Index (Complex a) = Int
type Plain (Complex a) Source #
Instance details Defined in Data.Array.Accelerate.Data.Complex type Plain (Complex a) = Complex (Plain a)
type Rep1 Complex
Instance details Defined in Data.Complex type Rep1 Complex = D1 ('MetaData "Complex" "Data.Complex" "base" 'False) (C1 ('MetaCons ":+" ('InfixI 'NotAssociative 6) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1))

pattern (::+) :: Elt a => Exp a -> Exp a -> Exp (Complex a) infix 6 Source #

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

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

As magnitude, but ignore floating point rounding and use the traditional (simpler to evaluate) definition.

Since: 1.3.0.0

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

Functor Complex Source #	Since: 1.2.0.0
Instance details Methods fmap :: (Elt a, Elt b, Elt (Complex a), Elt (Complex b)) => (Exp a -> Exp b) -> Exp (Complex a) -> Exp (Complex b) Source # (<$) :: (Elt a, Elt b, Elt (Complex a), Elt (Complex b)) => Exp a -> Exp (Complex b) -> Exp (Complex a) Source #
Elt a => Unlift Exp (Complex (Exp a)) Source #
Instance details Methods unlift :: Exp (Plain (Complex (Exp a))) -> Complex (Exp a) Source #
(Lift Exp a, Elt (Plain a)) => Lift Exp (Complex a) Source #
Instance details Associated Types type Plain (Complex a) Source # Methods lift :: Complex a -> Exp (Plain (Complex a)) Source #
(FromIntegral a b, Num b, Elt (Complex b)) => FromIntegral a (Complex b) Source #
Instance details Methods fromIntegral :: Exp a -> Exp (Complex b) Source #
RealFloat a => Floating (Exp (Complex a)) Source #
Instance details 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 #
Instance details 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 #
Instance details 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 #
Instance details Associated Types type EltR (Complex a) Methods eltR :: TypeR (EltR (Complex a)) tagsR :: [TagR (EltR (Complex a))] fromElt :: Complex a -> EltR (Complex a) toElt :: EltR (Complex a) -> Complex a
Eq a => Eq (Complex a) Source #
Instance details Methods (==) :: Exp (Complex a) -> Exp (Complex a) -> Exp Bool Source # (/=) :: Exp (Complex a) -> Exp (Complex a) -> Exp Bool Source #