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

data Complex a = !a :+ !a
realPart :: Complex a -> a
imagPart :: Complex a -> a
mkPolar :: Floating a => a -> a -> Complex a
cis :: Floating a => a -> Complex a
polar :: RealFloat a => Complex a -> (a, a)
magnitude :: RealFloat a => Complex a -> a
phase :: RealFloat a => Complex a -> a
conjugate :: Num a => Complex a -> Complex a

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.

Constructors

!a :+ !a infix 6

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

Instances

Eq a => Eq (Complex a) Source

Methods

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

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

RealFloat a => Floating (Complex a) Source

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

RealFloat a => Fractional (Complex a) Source

Methods

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

recip :: Complex a -> Complex a Source

fromRational :: Rational -> Complex a Source

Data a => Data (Complex a) Source

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 :: (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) Source

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) Source

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) Source

Methods

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

show :: Complex a -> String Source

showList :: [Complex a] -> ShowS Source

Storable a => Storable (Complex a) Source

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

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.