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Data.Complex

Copyright (c) The University of Glasgow 2001
License BSD-style (see the file libraries/base/LICENSE)
Maintainer [email protected]
Stability provisional
Portability portable
Safe Haskell Trustworthy
Language Haskell2010

Description

Complex numbers.

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.

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 Source

(>>) :: Complex a -> Complex b -> Complex b Source

return :: a -> Complex a Source

Functor Complex

Since: base-4.9.0.0
Instance details

Defined in Data.Complex

Methods

fmap :: (a -> b) -> Complex a -> Complex b Source

(<$) :: a -> Complex b -> Complex a Source

Applicative Complex

Since: base-4.9.0.0
Instance details

Defined in Data.Complex

Methods

pure :: a -> Complex a Source

(<*>) :: Complex (a -> b) -> Complex a -> Complex b Source

liftA2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c Source

(*>) :: Complex a -> Complex b -> Complex b Source

(<*) :: Complex a -> Complex b -> Complex a Source

Foldable Complex

Since: base-4.9.0.0
Instance details

Defined in Data.Complex

Methods

fold :: Monoid m => Complex m -> m Source

foldMap :: Monoid m => (a -> m) -> Complex a -> 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

Since: base-4.9.0.0
Instance details

Defined in Data.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

Eq a => Eq (Complex a)

Since: base-2.1
Instance details

Defined in Data.Complex

Methods

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

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

RealFloat a => Floating (Complex a)

Since: base-2.1
Instance details

Defined in Data.Complex

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)

Since: base-2.1
Instance details

Defined in Data.Complex

Methods

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

recip :: Complex a -> Complex a Source

fromRational :: Rational -> Complex a Source

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) 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 t => (forall d. Data d => c (t d)) -> Maybe (c (Complex a)) Source

dataCast2 :: Typeable 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 :: forall r r'. (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)

Since: base-2.1
Instance details

Defined in Data.Complex

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)

Since: base-2.1
Instance details

Defined in Data.Complex

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)

Since: base-2.1
Instance details

Defined in Data.Complex

Methods

showsPrec :: Int -> Complex a -> ShowS Source

show :: Complex a -> String Source

showList :: [Complex a] -> ShowS Source

Generic (Complex a)

Since: base-4.9.0.0
Instance details

Defined in Data.Complex

Associated Types

type Rep (Complex a) :: Type -> Type Source

Methods

from :: Complex a -> Rep (Complex a) x Source

to :: Rep (Complex a) x -> Complex a Source

Storable a => Storable (Complex a)

Since: base-4.8.0.0
Instance details

Defined in Data.Complex

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

Generic1 Complex

Since: base-4.9.0.0
Instance details

Defined in Data.Complex

Associated Types

type Rep1 Complex :: k -> Type Source

Methods

from1 :: forall (a :: k). Complex a -> Rep1 Complex a Source

to1 :: forall (a :: k). Rep1 Complex a -> Complex a Source

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)))
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))

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.

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.8.3/docs/html/libraries/base-4.13.0.0/Data-Complex.html