字典我要纠错

Data.Complex

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

Rectangular form
Polar form
Conjugate

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.

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 :: * -> ) :: -> * 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 (* -> ) 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)
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
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)
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.

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.0.1/docs/html/libraries/base-4.9.0.0/Data-Complex.html

Data.Complex

Data.Complex

Contents

Description

Rectangular form

Constructors

Instances

Methods

Methods

Methods

Methods

Methods

Associated Types

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Associated Types

Methods

Methods

Polar form

Conjugate