Graphics.ColorSpace.Complex

Rectangular form

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

Monad Complex

Since: base-4.9.0.0

Defined in Data.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

Since: base-4.9.0.0

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

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

Defined in Data.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

Since: base-4.9.0.0

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)

Hashable1 Complex

Defined in Data.Hashable.Class

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> Complex a -> Int

Unbox a => Vector Vector (Complex a)

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)

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))

Eq a => Eq (Complex a)

Since: base-2.1

Defined in Data.Complex

Methods

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

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

RealFloat a => Floating (Complex a)

Since: base-2.1

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 => Fractional (Complex a)

Since: base-2.1

Defined in Data.Complex

Methods

(/) :: Complex a -> Complex a -> Complex a

recip :: Complex a -> Complex a

fromRational :: Rational -> Complex a

Data a => Data (Complex a)

Since: base-2.1

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 :: (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

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

Read a => Read (Complex a)

Since: base-2.1

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

Defined in Data.Complex

Methods

showsPrec :: Int -> Complex a -> ShowS

show :: Complex a -> String

showList :: [Complex a] -> ShowS

Generic (Complex a)

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

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 ()

(Default a, RealFloat a) => Default (Complex a)

Defined in Data.Default.Class

Methods

def :: Complex a

NFData a => NFData (Complex a)

Defined in Control.DeepSeq

Methods

rnf :: Complex a -> ()

Hashable a => Hashable (Complex a)

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Complex a -> Int

hash :: Complex a -> Int

Unbox a => Unbox (Complex a)

Defined in Data.Vector.Unboxed.Base

(Num e, Elevator e, RealFloat e) => Elevator (Complex e)

Discards imaginary part and changes precision of real part.

Defined in Graphics.ColorSpace.Elevator

Methods

eToWord8 :: Complex e -> Word8

eToWord16 :: Complex e -> Word16

eToWord32 :: Complex e -> Word32

eToWord64 :: Complex e -> Word64

eToFloat :: Complex e -> Float

eToDouble :: Complex e -> Double

eFromDouble :: Double -> Complex e

Generic1 Complex

Defined in Data.Complex

Associated Types

type Rep1 Complex :: k -> Type

Methods

from1 :: Complex a -> Rep1 Complex a

to1 :: Rep1 Complex a -> Complex a

newtype MVector s (Complex a)

Defined in Data.Vector.Unboxed.Base

newtype MVector s (Complex a) = MV_Complex (MVector s (a, a))

type Rep (Complex a)

Since: base-4.9.0.0

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)

Defined in Data.Vector.Unboxed.Base

newtype Vector (Complex a) = V_Complex (Vector (a, a))

type Rep1 Complex

Since: base-4.9.0.0

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))

(+:) :: ColorSpace cs e => Pixel cs e -> Pixel cs e -> Pixel cs (Complex e) infix 6

Constrcut a complex pixel from two pixels representing real and imaginary parts.

 PixelRGB 4 8 6 +: PixelRGB 7 1 1 == PixelRGB (4 :+ 7) (8 :+ 1) (6 :+ 1)

realPart :: (ColorSpace cs e, RealFloat e) => Pixel cs (Complex e) -> Pixel cs e

Extracts the real part of a complex pixel.

imagPart :: (ColorSpace cs e, RealFloat e) => Pixel cs (Complex e) -> Pixel cs e

Extracts the imaginary part of a complex pixel.

Polar form

mkPolar :: (ColorSpace cs e, RealFloat e) => Pixel cs e -> Pixel cs e -> Pixel cs (Complex e)

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

cis :: (ColorSpace cs e, RealFloat e) => Pixel cs e -> Pixel cs (Complex e)

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

polar :: (ColorSpace cs e, RealFloat e) => Pixel cs (Complex e) -> (Pixel cs e, Pixel cs e)

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

magnitude :: (ColorSpace cs e, RealFloat e) => Pixel cs (Complex e) -> Pixel cs e

The nonnegative magnitude of a complex pixel.

phase :: (ColorSpace cs e, RealFloat e) => Pixel cs (Complex e) -> Pixel cs e

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

Conjugate

conjugate :: (ColorSpace cs e, RealFloat e) => Pixel cs (Complex e) -> Pixel cs (Complex e)

The conjugate of a complex pixel.