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
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
Complex numbers are an algebraic type.
For a complex number z
,
is a number with the magnitude of abs
zz
,
but oriented in the positive real direction, whereas
has the phase of signum
zz
, 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
MonadFix Complex Source # | Since: base-4.15.0.0 |
MonadZip Complex Source # | Since: base-4.15.0.0 |
Foldable Complex Source # | Since: base-4.9.0.0 |
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 # | |
Foldable1 Complex Source # | Since: base-4.18.0.0 |
Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Complex m -> m Source # foldMap1 :: Semigroup m => (a -> m) -> Complex a -> m Source # foldMap1' :: Semigroup m => (a -> m) -> Complex a -> m Source # toNonEmpty :: Complex a -> NonEmpty a Source # maximum :: Ord a => Complex a -> a Source # minimum :: Ord a => Complex a -> a Source # head :: Complex a -> a Source # last :: Complex a -> a Source # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Complex a -> b Source # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Complex a -> b Source # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Complex a -> b Source # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Complex a -> b Source # | |
Eq1 Complex Source # |
Since: base-4.16.0.0 |
Read1 Complex Source # |
Since: base-4.16.0.0 |
Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Complex a) Source # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Complex a] Source # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Complex a) Source # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Complex a] Source # | |
Show1 Complex Source # |
Since: base-4.16.0.0 |
Traversable Complex Source # | Since: base-4.9.0.0 |
Defined in Data.Complex | |
Applicative Complex Source # | Since: base-4.9.0.0 |
Functor Complex Source # | Since: base-4.9.0.0 |
Monad Complex Source # | Since: base-4.9.0.0 |
Generic1 Complex Source # | |
Data a => Data (Complex a) Source # | Since: base-2.1 |
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 # | |
Storable a => Storable (Complex a) Source # | Since: base-4.8.0.0 |
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 # | |
RealFloat a => Floating (Complex a) Source # | Since: base-2.1 |
Defined in Data.Complex Methods 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 # | |
Generic (Complex a) Source # | |
RealFloat a => Num (Complex a) Source # | Since: base-2.1 |
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) Source # | Since: base-2.1 |
RealFloat a => Fractional (Complex a) Source # | Since: base-2.1 |
Show a => Show (Complex a) Source # | Since: base-2.1 |
Eq a => Eq (Complex a) Source # | Since: base-2.1 |
type Rep1 Complex Source # | Since: base-4.9.0.0 |
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)) | |
type Rep (Complex a) Source # | Since: base-4.9.0.0 |
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))) |
Polar form
mkPolar :: Floating a => a -> a -> Complex a Source #
Form a complex number from polar components of magnitude and phase.