massiv-io-0.1.3.0: Import/export of Image files into massiv Arrays

Copyright(c) Alexey Kuleshevich 2016-2018
LicenseBSD3
MaintainerAlexey Kuleshevich <lehins@yandex.ru>
Stabilityexperimental
Portabilitynon-portable
Safe HaskellNone
LanguageHaskell2010

Graphics.ColorSpace.Complex

Contents

Description

 

Synopsis

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.

Constructors

!a :+ !a infix 6

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

Instances

Monad Complex

Since: 4.9.0.0

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

Since: 4.9.0.0

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 

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) #

Unbox a => Vector Vector (Complex a) 
Unbox a => MVector MVector (Complex a) 
Eq a => Eq (Complex a) 

Methods

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

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

RealFloat a => Floating (Complex a)

Since: 2.1

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: 2.1

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)

Since: 2.1

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) 
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)

Since: 4.8.0.0

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) 

Methods

def :: Complex a #

NFData a => NFData (Complex a) 

Methods

rnf :: Complex a -> () #

Unbox a => Unbox (Complex a) 
(Num e, Elevator e, RealFloat e) => Elevator (Complex e) Source #

Discards imaginary part and changes precision of real part.

Generic1 * Complex 

Associated Types

type Rep1 Complex (f :: Complex -> *) :: k -> * #

Methods

from1 :: f a -> Rep1 Complex f a #

to1 :: Rep1 Complex f a -> f a #

data MVector s (Complex a) 
data MVector s (Complex a) = MV_Complex (MVector s (a, a))
type Rep (Complex a) 
data Vector (Complex a) 
data Vector (Complex a) = V_Complex (Vector (a, a))
type Rep1 * Complex 

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

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 Source #

Extracts the real part of a complex pixel.

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

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) Source #

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

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

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) Source #

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 Source #

The nonnegative magnitude of a complex pixel.

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

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) Source #

The conjugate of a complex pixel.