| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell2010 |
Data.Complex
Description
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, 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) # | |
| RealFloat a => Floating (Complex a) # | |
Defined in Data.Complex Methods exp :: Complex a -> Complex a # log :: Complex a -> Complex a # sqrt :: Complex a -> Complex a # (**) :: Complex a -> Complex a -> Complex a # logBase :: Complex a -> Complex a -> Complex a # sin :: Complex a -> Complex a # cos :: Complex a -> Complex a # tan :: Complex a -> Complex a # asin :: Complex a -> Complex a # acos :: Complex a -> Complex a # atan :: Complex a -> Complex a # sinh :: Complex a -> Complex a # cosh :: Complex a -> Complex a # tanh :: Complex a -> Complex a # asinh :: Complex a -> Complex a # | |
| RealFloat a => Fractional (Complex a) # | |
| RealFloat a => Num (Complex a) # | |
| Read a => Read (Complex a) # | |
| Show a => Show (Complex a) # | |
Polar form
mkPolar :: Floating a => a -> a -> Complex a #
Form a complex number from polar components of magnitude and phase.
cis :: Floating a => a -> Complex a #
cis t is a complex value with magnitude 1 and phase t (modulo 2 * pi).
polar :: RealFloat a => Complex a -> (a, a) #
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.
phase :: RealFloat a => Complex a -> a #
The phase of a complex number, in the range (-pi, pi]. If the magnitude is zero, then so is the phase.