Copyright	(c) The University of Glasgow 2001
License	BSD-style (see the file libraries/base/LICENSE)
Maintainer	libraries@haskell.org
Stability	provisional
Portability	portable
Safe Haskell	Trustworthy
Language	Haskell2010

Data.Complex

Contents

Rectangular form
Polar form
Conjugate

Description

Complex numbers.

Synopsis

Rectangular form

data Complex a Source

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

realPart :: Complex a -> a Source

Extracts the real part of a complex number.

imagPart :: Complex a -> a Source

Extracts the imaginary part of a complex number.

Polar form

mkPolar :: Floating a => a -> a -> Complex a Source

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

cis :: Floating a => a -> Complex a Source

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

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

The function polar takes a complex number and returns a (magnitude, phase) pair 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 :: RealFloat a => Complex a -> a Source

The nonnegative magnitude of a complex number.

phase :: RealFloat a => Complex a -> 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 => Complex a -> Complex a Source

The conjugate of a complex number.