Copyright	(c) Claude Heiland-Allen 2012
License	BSD3
Maintainer	claude@mathr.co.uk
Stability	unstable
Portability	MultiParamTypeClasses, FunctionalDependencies
Safe Haskell	Safe
Language	Haskell98

Data.Complex.Generic.Class

Description

Classes for complex number operations.

Synopsis

Documentation

class ComplexRect c r | c -> r where Source #

Rectangular form.

Minimal complete definition

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

Methods

mkRect :: r -> r -> c Source #

Construction.

real :: r -> c Source #

Construction with imagPart 0.

imag :: r -> c Source #

Construction with realPart 0.

rect :: c -> (r, r) Source #

Deconstruction.

realPart :: c -> r Source #

Get the real part.

imagPart :: c -> r Source #

Get the imaginary part.

conjugate :: c -> c Source #

Conjugation.

magnitudeSquared :: c -> r Source #

Squared magnitude.

sqr :: c -> c Source #

Complex square.

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

Real-complex multiplication.

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

Complex-real multiplication.

Instances

ComplexRect (Complex Double) Double Source #
Methods mkRect :: Double -> Double -> Complex Double Source # real :: Double -> Complex Double Source # imag :: Double -> Complex Double Source # rect :: Complex Double -> (Double, Double) Source # realPart :: Complex Double -> Double Source # imagPart :: Complex Double -> Double Source # conjugate :: Complex Double -> Complex Double Source # magnitudeSquared :: Complex Double -> Double Source # sqr :: Complex Double -> Complex Double Source # (.) :: Double -> Complex Double -> Complex Double Source # (.) :: Complex Double -> Double -> Complex Double Source #
ComplexRect (Complex Float) Float Source #
Methods mkRect :: Float -> Float -> Complex Float Source # real :: Float -> Complex Float Source # imag :: Float -> Complex Float Source # rect :: Complex Float -> (Float, Float) Source # realPart :: Complex Float -> Float Source # imagPart :: Complex Float -> Float Source # conjugate :: Complex Float -> Complex Float Source # magnitudeSquared :: Complex Float -> Float Source # sqr :: Complex Float -> Complex Float Source # (.) :: Float -> Complex Float -> Complex Float Source # (.) :: Complex Float -> Float -> Complex Float Source #
ComplexRect (Complex Int) Int Source #
Methods mkRect :: Int -> Int -> Complex Int Source # real :: Int -> Complex Int Source # imag :: Int -> Complex Int Source # rect :: Complex Int -> (Int, Int) Source # realPart :: Complex Int -> Int Source # imagPart :: Complex Int -> Int Source # conjugate :: Complex Int -> Complex Int Source # magnitudeSquared :: Complex Int -> Int Source # sqr :: Complex Int -> Complex Int Source # (.) :: Int -> Complex Int -> Complex Int Source # (.) :: Complex Int -> Int -> Complex Int Source #
ComplexRect (Complex Int8) Int8 Source #
Methods mkRect :: Int8 -> Int8 -> Complex Int8 Source # real :: Int8 -> Complex Int8 Source # imag :: Int8 -> Complex Int8 Source # rect :: Complex Int8 -> (Int8, Int8) Source # realPart :: Complex Int8 -> Int8 Source # imagPart :: Complex Int8 -> Int8 Source # conjugate :: Complex Int8 -> Complex Int8 Source # magnitudeSquared :: Complex Int8 -> Int8 Source # sqr :: Complex Int8 -> Complex Int8 Source # (.) :: Int8 -> Complex Int8 -> Complex Int8 Source # (.) :: Complex Int8 -> Int8 -> Complex Int8 Source #
ComplexRect (Complex Int16) Int16 Source #
Methods mkRect :: Int16 -> Int16 -> Complex Int16 Source # real :: Int16 -> Complex Int16 Source # imag :: Int16 -> Complex Int16 Source # rect :: Complex Int16 -> (Int16, Int16) Source # realPart :: Complex Int16 -> Int16 Source # imagPart :: Complex Int16 -> Int16 Source # conjugate :: Complex Int16 -> Complex Int16 Source # magnitudeSquared :: Complex Int16 -> Int16 Source # sqr :: Complex Int16 -> Complex Int16 Source # (.) :: Int16 -> Complex Int16 -> Complex Int16 Source # (.) :: Complex Int16 -> Int16 -> Complex Int16 Source #
ComplexRect (Complex Int32) Int32 Source #
Methods mkRect :: Int32 -> Int32 -> Complex Int32 Source # real :: Int32 -> Complex Int32 Source # imag :: Int32 -> Complex Int32 Source # rect :: Complex Int32 -> (Int32, Int32) Source # realPart :: Complex Int32 -> Int32 Source # imagPart :: Complex Int32 -> Int32 Source # conjugate :: Complex Int32 -> Complex Int32 Source # magnitudeSquared :: Complex Int32 -> Int32 Source # sqr :: Complex Int32 -> Complex Int32 Source # (.) :: Int32 -> Complex Int32 -> Complex Int32 Source # (.) :: Complex Int32 -> Int32 -> Complex Int32 Source #
ComplexRect (Complex Int64) Int64 Source #
Methods mkRect :: Int64 -> Int64 -> Complex Int64 Source # real :: Int64 -> Complex Int64 Source # imag :: Int64 -> Complex Int64 Source # rect :: Complex Int64 -> (Int64, Int64) Source # realPart :: Complex Int64 -> Int64 Source # imagPart :: Complex Int64 -> Int64 Source # conjugate :: Complex Int64 -> Complex Int64 Source # magnitudeSquared :: Complex Int64 -> Int64 Source # sqr :: Complex Int64 -> Complex Int64 Source # (.) :: Int64 -> Complex Int64 -> Complex Int64 Source # (.) :: Complex Int64 -> Int64 -> Complex Int64 Source #
ComplexRect (Complex Integer) Integer Source #
Methods mkRect :: Integer -> Integer -> Complex Integer Source # real :: Integer -> Complex Integer Source # imag :: Integer -> Complex Integer Source # rect :: Complex Integer -> (Integer, Integer) Source # realPart :: Complex Integer -> Integer Source # imagPart :: Complex Integer -> Integer Source # conjugate :: Complex Integer -> Complex Integer Source # magnitudeSquared :: Complex Integer -> Integer Source # sqr :: Complex Integer -> Complex Integer Source # (.) :: Integer -> Complex Integer -> Complex Integer Source # (.) :: Complex Integer -> Integer -> Complex Integer Source #
ComplexRect (Complex Word) Word Source #
Methods mkRect :: Word -> Word -> Complex Word Source # real :: Word -> Complex Word Source # imag :: Word -> Complex Word Source # rect :: Complex Word -> (Word, Word) Source # realPart :: Complex Word -> Word Source # imagPart :: Complex Word -> Word Source # conjugate :: Complex Word -> Complex Word Source # magnitudeSquared :: Complex Word -> Word Source # sqr :: Complex Word -> Complex Word Source # (.) :: Word -> Complex Word -> Complex Word Source # (.) :: Complex Word -> Word -> Complex Word Source #
ComplexRect (Complex Word8) Word8 Source #
Methods mkRect :: Word8 -> Word8 -> Complex Word8 Source # real :: Word8 -> Complex Word8 Source # imag :: Word8 -> Complex Word8 Source # rect :: Complex Word8 -> (Word8, Word8) Source # realPart :: Complex Word8 -> Word8 Source # imagPart :: Complex Word8 -> Word8 Source # conjugate :: Complex Word8 -> Complex Word8 Source # magnitudeSquared :: Complex Word8 -> Word8 Source # sqr :: Complex Word8 -> Complex Word8 Source # (.) :: Word8 -> Complex Word8 -> Complex Word8 Source # (.) :: Complex Word8 -> Word8 -> Complex Word8 Source #
ComplexRect (Complex Word16) Word16 Source #
Methods mkRect :: Word16 -> Word16 -> Complex Word16 Source # real :: Word16 -> Complex Word16 Source # imag :: Word16 -> Complex Word16 Source # rect :: Complex Word16 -> (Word16, Word16) Source # realPart :: Complex Word16 -> Word16 Source # imagPart :: Complex Word16 -> Word16 Source # conjugate :: Complex Word16 -> Complex Word16 Source # magnitudeSquared :: Complex Word16 -> Word16 Source # sqr :: Complex Word16 -> Complex Word16 Source # (.) :: Word16 -> Complex Word16 -> Complex Word16 Source # (.) :: Complex Word16 -> Word16 -> Complex Word16 Source #
ComplexRect (Complex Word32) Word32 Source #
Methods mkRect :: Word32 -> Word32 -> Complex Word32 Source # real :: Word32 -> Complex Word32 Source # imag :: Word32 -> Complex Word32 Source # rect :: Complex Word32 -> (Word32, Word32) Source # realPart :: Complex Word32 -> Word32 Source # imagPart :: Complex Word32 -> Word32 Source # conjugate :: Complex Word32 -> Complex Word32 Source # magnitudeSquared :: Complex Word32 -> Word32 Source # sqr :: Complex Word32 -> Complex Word32 Source # (.) :: Word32 -> Complex Word32 -> Complex Word32 Source # (.) :: Complex Word32 -> Word32 -> Complex Word32 Source #
ComplexRect (Complex Word64) Word64 Source #
Methods mkRect :: Word64 -> Word64 -> Complex Word64 Source # real :: Word64 -> Complex Word64 Source # imag :: Word64 -> Complex Word64 Source # rect :: Complex Word64 -> (Word64, Word64) Source # realPart :: Complex Word64 -> Word64 Source # imagPart :: Complex Word64 -> Word64 Source # conjugate :: Complex Word64 -> Complex Word64 Source # magnitudeSquared :: Complex Word64 -> Word64 Source # sqr :: Complex Word64 -> Complex Word64 Source # (.) :: Word64 -> Complex Word64 -> Complex Word64 Source # (.) :: Complex Word64 -> Word64 -> Complex Word64 Source #
ComplexRect (Complex CFloat) CFloat Source #
Methods mkRect :: CFloat -> CFloat -> Complex CFloat Source # real :: CFloat -> Complex CFloat Source # imag :: CFloat -> Complex CFloat Source # rect :: Complex CFloat -> (CFloat, CFloat) Source # realPart :: Complex CFloat -> CFloat Source # imagPart :: Complex CFloat -> CFloat Source # conjugate :: Complex CFloat -> Complex CFloat Source # magnitudeSquared :: Complex CFloat -> CFloat Source # sqr :: Complex CFloat -> Complex CFloat Source # (.) :: CFloat -> Complex CFloat -> Complex CFloat Source # (.) :: Complex CFloat -> CFloat -> Complex CFloat Source #
ComplexRect (Complex CDouble) CDouble Source #
Methods mkRect :: CDouble -> CDouble -> Complex CDouble Source # real :: CDouble -> Complex CDouble Source # imag :: CDouble -> Complex CDouble Source # rect :: Complex CDouble -> (CDouble, CDouble) Source # realPart :: Complex CDouble -> CDouble Source # imagPart :: Complex CDouble -> CDouble Source # conjugate :: Complex CDouble -> Complex CDouble Source # magnitudeSquared :: Complex CDouble -> CDouble Source # sqr :: Complex CDouble -> Complex CDouble Source # (.) :: CDouble -> Complex CDouble -> Complex CDouble Source # (.) :: Complex CDouble -> CDouble -> Complex CDouble Source #
Integral t => ComplexRect (Complex (Ratio t)) (Ratio t) Source #
Methods mkRect :: Ratio t -> Ratio t -> Complex (Ratio t) Source # real :: Ratio t -> Complex (Ratio t) Source # imag :: Ratio t -> Complex (Ratio t) Source # rect :: Complex (Ratio t) -> (Ratio t, Ratio t) Source # realPart :: Complex (Ratio t) -> Ratio t Source # imagPart :: Complex (Ratio t) -> Ratio t Source # conjugate :: Complex (Ratio t) -> Complex (Ratio t) Source # magnitudeSquared :: Complex (Ratio t) -> Ratio t Source # sqr :: Complex (Ratio t) -> Complex (Ratio t) Source # (.) :: Ratio t -> Complex (Ratio t) -> Complex (Ratio t) Source # (.) :: Complex (Ratio t) -> Ratio t -> Complex (Ratio t) Source #
HasResolution t => ComplexRect (Complex (Fixed t)) (Fixed t) Source #
Methods mkRect :: Fixed t -> Fixed t -> Complex (Fixed t) Source # real :: Fixed t -> Complex (Fixed t) Source # imag :: Fixed t -> Complex (Fixed t) Source # rect :: Complex (Fixed t) -> (Fixed t, Fixed t) Source # realPart :: Complex (Fixed t) -> Fixed t Source # imagPart :: Complex (Fixed t) -> Fixed t Source # conjugate :: Complex (Fixed t) -> Complex (Fixed t) Source # magnitudeSquared :: Complex (Fixed t) -> Fixed t Source # sqr :: Complex (Fixed t) -> Complex (Fixed t) Source # (.) :: Fixed t -> Complex (Fixed t) -> Complex (Fixed t) Source # (.) :: Complex (Fixed t) -> Fixed t -> Complex (Fixed t) Source #

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

Complex-real division.

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

A synonym for mkRect.

class ComplexPolar c r | c -> r where Source #

Polar form.

Minimal complete definition

mkPolar, cis, polar, magnitude, phase

Methods

mkPolar :: r -> r -> c Source #

cis :: r -> c Source #

polar :: c -> (r, r) Source #

magnitude :: c -> r Source #

Magnitude.

phase :: c -> r Source #

Phase in (-pi, pi].

Instances

ComplexPolar (Complex Double) Double Source #
Methods mkPolar :: Double -> Double -> Complex Double Source # cis :: Double -> Complex Double Source # polar :: Complex Double -> (Double, Double) Source # magnitude :: Complex Double -> Double Source # phase :: Complex Double -> Double Source #
ComplexPolar (Complex Float) Float Source #
Methods mkPolar :: Float -> Float -> Complex Float Source # cis :: Float -> Complex Float Source # polar :: Complex Float -> (Float, Float) Source # magnitude :: Complex Float -> Float Source # phase :: Complex Float -> Float Source #
ComplexPolar (Complex CFloat) CFloat Source #
Methods mkPolar :: CFloat -> CFloat -> Complex CFloat Source # cis :: CFloat -> Complex CFloat Source # polar :: Complex CFloat -> (CFloat, CFloat) Source # magnitude :: Complex CFloat -> CFloat Source # phase :: Complex CFloat -> CFloat Source #
ComplexPolar (Complex CDouble) CDouble Source #
Methods mkPolar :: CDouble -> CDouble -> Complex CDouble Source # cis :: CDouble -> Complex CDouble Source # polar :: Complex CDouble -> (CDouble, CDouble) Source # magnitude :: Complex CDouble -> CDouble Source # phase :: Complex CDouble -> CDouble Source #