Data.Complex.Generic.Class

Classes for complex number operations.

Documentation

class ComplexRect c r | c -> r where

Rectangular form.

Minimal complete definition

mkRect, real, imag, rect, realPart, imagPart, conjugate, magnitudeSquared, sqr, (.*), (*.)

Methods

mkRect :: r -> r -> c

Construction.

real :: r -> c

Construction with imagPart 0.

imag :: r -> c

Construction with realPart 0.

rect :: c -> (r, r)

Deconstruction.

realPart :: c -> r

Get the real part.

imagPart :: c -> r

Get the imaginary part.

conjugate :: c -> c

Conjugation.

magnitudeSquared :: c -> r

Squared magnitude.

sqr :: c -> c

Complex square.

(.*) :: r -> c -> c infixl 7

Real-complex multiplication.

(*.) :: c -> r -> c infixl 7

Complex-real multiplication.

Instances

ComplexRect (Complex Double) Double

Methods

mkRect :: Double -> Double -> Complex Double

real :: Double -> Complex Double

imag :: Double -> Complex Double

rect :: Complex Double -> (Double, Double)

realPart :: Complex Double -> Double

imagPart :: Complex Double -> Double

conjugate :: Complex Double -> Complex Double

magnitudeSquared :: Complex Double -> Double

sqr :: Complex Double -> Complex Double

(.*) :: Double -> Complex Double -> Complex Double

(*.) :: Complex Double -> Double -> Complex Double

ComplexRect (Complex Float) Float

Methods

mkRect :: Float -> Float -> Complex Float

real :: Float -> Complex Float

imag :: Float -> Complex Float

rect :: Complex Float -> (Float, Float)

realPart :: Complex Float -> Float

imagPart :: Complex Float -> Float

conjugate :: Complex Float -> Complex Float

magnitudeSquared :: Complex Float -> Float

sqr :: Complex Float -> Complex Float

(.*) :: Float -> Complex Float -> Complex Float

(*.) :: Complex Float -> Float -> Complex Float

ComplexRect (Complex Int) Int

Methods

mkRect :: Int -> Int -> Complex Int

real :: Int -> Complex Int

imag :: Int -> Complex Int

rect :: Complex Int -> (Int, Int)

realPart :: Complex Int -> Int

imagPart :: Complex Int -> Int

conjugate :: Complex Int -> Complex Int

magnitudeSquared :: Complex Int -> Int

sqr :: Complex Int -> Complex Int

(.*) :: Int -> Complex Int -> Complex Int

(*.) :: Complex Int -> Int -> Complex Int

ComplexRect (Complex Int8) Int8

Methods

mkRect :: Int8 -> Int8 -> Complex Int8

real :: Int8 -> Complex Int8

imag :: Int8 -> Complex Int8

rect :: Complex Int8 -> (Int8, Int8)

realPart :: Complex Int8 -> Int8

imagPart :: Complex Int8 -> Int8

conjugate :: Complex Int8 -> Complex Int8

magnitudeSquared :: Complex Int8 -> Int8

sqr :: Complex Int8 -> Complex Int8

(.*) :: Int8 -> Complex Int8 -> Complex Int8

(*.) :: Complex Int8 -> Int8 -> Complex Int8

ComplexRect (Complex Int16) Int16

Methods

mkRect :: Int16 -> Int16 -> Complex Int16

real :: Int16 -> Complex Int16

imag :: Int16 -> Complex Int16

rect :: Complex Int16 -> (Int16, Int16)

realPart :: Complex Int16 -> Int16

imagPart :: Complex Int16 -> Int16

conjugate :: Complex Int16 -> Complex Int16

magnitudeSquared :: Complex Int16 -> Int16

sqr :: Complex Int16 -> Complex Int16

(.*) :: Int16 -> Complex Int16 -> Complex Int16

(*.) :: Complex Int16 -> Int16 -> Complex Int16

ComplexRect (Complex Int32) Int32

Methods

mkRect :: Int32 -> Int32 -> Complex Int32

real :: Int32 -> Complex Int32

imag :: Int32 -> Complex Int32

rect :: Complex Int32 -> (Int32, Int32)

realPart :: Complex Int32 -> Int32

imagPart :: Complex Int32 -> Int32

conjugate :: Complex Int32 -> Complex Int32

magnitudeSquared :: Complex Int32 -> Int32

sqr :: Complex Int32 -> Complex Int32

(.*) :: Int32 -> Complex Int32 -> Complex Int32

(*.) :: Complex Int32 -> Int32 -> Complex Int32

ComplexRect (Complex Int64) Int64

Methods

mkRect :: Int64 -> Int64 -> Complex Int64

real :: Int64 -> Complex Int64

imag :: Int64 -> Complex Int64

rect :: Complex Int64 -> (Int64, Int64)

realPart :: Complex Int64 -> Int64

imagPart :: Complex Int64 -> Int64

conjugate :: Complex Int64 -> Complex Int64

magnitudeSquared :: Complex Int64 -> Int64

sqr :: Complex Int64 -> Complex Int64

(.*) :: Int64 -> Complex Int64 -> Complex Int64

(*.) :: Complex Int64 -> Int64 -> Complex Int64

ComplexRect (Complex Integer) Integer

Methods

mkRect :: Integer -> Integer -> Complex Integer

real :: Integer -> Complex Integer

imag :: Integer -> Complex Integer

rect :: Complex Integer -> (Integer, Integer)

realPart :: Complex Integer -> Integer

imagPart :: Complex Integer -> Integer

conjugate :: Complex Integer -> Complex Integer

magnitudeSquared :: Complex Integer -> Integer

sqr :: Complex Integer -> Complex Integer

(.*) :: Integer -> Complex Integer -> Complex Integer

(*.) :: Complex Integer -> Integer -> Complex Integer

ComplexRect (Complex Word) Word

Methods

mkRect :: Word -> Word -> Complex Word

real :: Word -> Complex Word

imag :: Word -> Complex Word

rect :: Complex Word -> (Word, Word)

realPart :: Complex Word -> Word

imagPart :: Complex Word -> Word

conjugate :: Complex Word -> Complex Word

magnitudeSquared :: Complex Word -> Word

sqr :: Complex Word -> Complex Word

(.*) :: Word -> Complex Word -> Complex Word

(*.) :: Complex Word -> Word -> Complex Word

ComplexRect (Complex Word8) Word8

Methods

mkRect :: Word8 -> Word8 -> Complex Word8

real :: Word8 -> Complex Word8

imag :: Word8 -> Complex Word8

rect :: Complex Word8 -> (Word8, Word8)

realPart :: Complex Word8 -> Word8

imagPart :: Complex Word8 -> Word8

conjugate :: Complex Word8 -> Complex Word8

magnitudeSquared :: Complex Word8 -> Word8

sqr :: Complex Word8 -> Complex Word8

(.*) :: Word8 -> Complex Word8 -> Complex Word8

(*.) :: Complex Word8 -> Word8 -> Complex Word8

ComplexRect (Complex Word16) Word16

Methods

mkRect :: Word16 -> Word16 -> Complex Word16

real :: Word16 -> Complex Word16

imag :: Word16 -> Complex Word16

rect :: Complex Word16 -> (Word16, Word16)

realPart :: Complex Word16 -> Word16

imagPart :: Complex Word16 -> Word16

conjugate :: Complex Word16 -> Complex Word16

magnitudeSquared :: Complex Word16 -> Word16

sqr :: Complex Word16 -> Complex Word16

(.*) :: Word16 -> Complex Word16 -> Complex Word16

(*.) :: Complex Word16 -> Word16 -> Complex Word16

ComplexRect (Complex Word32) Word32

Methods

mkRect :: Word32 -> Word32 -> Complex Word32

real :: Word32 -> Complex Word32

imag :: Word32 -> Complex Word32

rect :: Complex Word32 -> (Word32, Word32)

realPart :: Complex Word32 -> Word32

imagPart :: Complex Word32 -> Word32

conjugate :: Complex Word32 -> Complex Word32

magnitudeSquared :: Complex Word32 -> Word32

sqr :: Complex Word32 -> Complex Word32

(.*) :: Word32 -> Complex Word32 -> Complex Word32

(*.) :: Complex Word32 -> Word32 -> Complex Word32

ComplexRect (Complex Word64) Word64

Methods

mkRect :: Word64 -> Word64 -> Complex Word64

real :: Word64 -> Complex Word64

imag :: Word64 -> Complex Word64

rect :: Complex Word64 -> (Word64, Word64)

realPart :: Complex Word64 -> Word64

imagPart :: Complex Word64 -> Word64

conjugate :: Complex Word64 -> Complex Word64

magnitudeSquared :: Complex Word64 -> Word64

sqr :: Complex Word64 -> Complex Word64

(.*) :: Word64 -> Complex Word64 -> Complex Word64

(*.) :: Complex Word64 -> Word64 -> Complex Word64

ComplexRect (Complex CFloat) CFloat

Methods

mkRect :: CFloat -> CFloat -> Complex CFloat

real :: CFloat -> Complex CFloat

imag :: CFloat -> Complex CFloat

rect :: Complex CFloat -> (CFloat, CFloat)

realPart :: Complex CFloat -> CFloat

imagPart :: Complex CFloat -> CFloat

conjugate :: Complex CFloat -> Complex CFloat

magnitudeSquared :: Complex CFloat -> CFloat

sqr :: Complex CFloat -> Complex CFloat

(.*) :: CFloat -> Complex CFloat -> Complex CFloat

(*.) :: Complex CFloat -> CFloat -> Complex CFloat

ComplexRect (Complex CDouble) CDouble

Methods

mkRect :: CDouble -> CDouble -> Complex CDouble

real :: CDouble -> Complex CDouble

imag :: CDouble -> Complex CDouble

rect :: Complex CDouble -> (CDouble, CDouble)

realPart :: Complex CDouble -> CDouble

imagPart :: Complex CDouble -> CDouble

conjugate :: Complex CDouble -> Complex CDouble

magnitudeSquared :: Complex CDouble -> CDouble

sqr :: Complex CDouble -> Complex CDouble

(.*) :: CDouble -> Complex CDouble -> Complex CDouble

(*.) :: Complex CDouble -> CDouble -> Complex CDouble

Integral t => ComplexRect (Complex (Ratio t)) (Ratio t)

Methods

mkRect :: Ratio t -> Ratio t -> Complex (Ratio t)

real :: Ratio t -> Complex (Ratio t)

imag :: Ratio t -> Complex (Ratio t)

rect :: Complex (Ratio t) -> (Ratio t, Ratio t)

realPart :: Complex (Ratio t) -> Ratio t

imagPart :: Complex (Ratio t) -> Ratio t

conjugate :: Complex (Ratio t) -> Complex (Ratio t)

magnitudeSquared :: Complex (Ratio t) -> Ratio t

sqr :: Complex (Ratio t) -> Complex (Ratio t)

(.*) :: Ratio t -> Complex (Ratio t) -> Complex (Ratio t)

(*.) :: Complex (Ratio t) -> Ratio t -> Complex (Ratio t)

HasResolution t => ComplexRect (Complex (Fixed t)) (Fixed t)

Methods

mkRect :: Fixed t -> Fixed t -> Complex (Fixed t)

real :: Fixed t -> Complex (Fixed t)

imag :: Fixed t -> Complex (Fixed t)

rect :: Complex (Fixed t) -> (Fixed t, Fixed t)

realPart :: Complex (Fixed t) -> Fixed t

imagPart :: Complex (Fixed t) -> Fixed t

conjugate :: Complex (Fixed t) -> Complex (Fixed t)

magnitudeSquared :: Complex (Fixed t) -> Fixed t

sqr :: Complex (Fixed t) -> Complex (Fixed t)

(.*) :: Fixed t -> Complex (Fixed t) -> Complex (Fixed t)

(*.) :: Complex (Fixed t) -> Fixed t -> Complex (Fixed t)

(/.) :: (Fractional r, ComplexRect c r) => c -> r -> c infixl 6

Complex-real division.

(.+) :: ComplexRect c r => r -> r -> c infix 6

A synonym for mkRect.

class ComplexPolar c r | c -> r where

Polar form.

Minimal complete definition

mkPolar, cis, polar, magnitude, phase

Methods

mkPolar :: r -> r -> c

cis :: r -> c

polar :: c -> (r, r)

magnitude :: c -> r

Magnitude.

phase :: c -> r

Phase in (-pi, pi].

Instances

ComplexPolar (Complex Double) Double

Methods

mkPolar :: Double -> Double -> Complex Double

cis :: Double -> Complex Double

polar :: Complex Double -> (Double, Double)

magnitude :: Complex Double -> Double

phase :: Complex Double -> Double

ComplexPolar (Complex Float) Float

Methods

mkPolar :: Float -> Float -> Complex Float

cis :: Float -> Complex Float

polar :: Complex Float -> (Float, Float)

magnitude :: Complex Float -> Float

phase :: Complex Float -> Float

ComplexPolar (Complex CFloat) CFloat

Methods

mkPolar :: CFloat -> CFloat -> Complex CFloat

cis :: CFloat -> Complex CFloat

polar :: Complex CFloat -> (CFloat, CFloat)

magnitude :: Complex CFloat -> CFloat

phase :: Complex CFloat -> CFloat

ComplexPolar (Complex CDouble) CDouble

Methods

mkPolar :: CDouble -> CDouble -> Complex CDouble

cis :: CDouble -> Complex CDouble

polar :: Complex CDouble -> (CDouble, CDouble)

magnitude :: Complex CDouble -> CDouble

phase :: Complex CDouble -> CDouble