{-# LANGUAGE CPP #-} {-# LANGUAGE FlexibleContexts #-} #ifndef MIN_VERSION_base #define MIN_VERSION_base(x,y,z) 1 #endif ----------------------------------------------------------------------------- -- | -- Module : Data.Complex.Lens -- Copyright : (C) 2012-14 Edward Kmett -- License : BSD-style (see the file LICENSE) -- Maintainer : Edward Kmett <ekmett@gmail.com> -- Stability : experimental -- Portability : non-portable -- -- Lenses and traversals for complex numbers -- ---------------------------------------------------------------------------- module Data.Complex.Lens ( _realPart , _imagPart , _polar , _magnitude , _phase , _conjugate ) where import Control.Applicative import Control.Lens import Data.Complex -- $setup -- >>> import Debug.SimpleReflect -- >>> let { a ≈ b = abs (a - b) < 1e-6; infix 4 ≈ } -- | Access the 'realPart' of a 'Complex' number. -- -- >>> (a :+ b)^._realPart -- a -- -- >>> a :+ b & _realPart *~ 2 -- a * 2 :+ b -- -- @'_realPart' :: 'Functor' f => (a -> f a) -> 'Complex' a -> f ('Complex' a)@ #if MIN_VERSION_base(4,4,0) _realPart :: Lens' (Complex a) a #else _realPart :: RealFloat a => Lens' (Complex a) a #endif _realPart f (a :+ b) = (:+ b) <$> f a {-# INLINE _realPart #-} -- | Access the 'imagPart' of a 'Complex' number. -- -- >>> (a :+ b)^._imagPart -- b -- -- >>> a :+ b & _imagPart *~ 2 -- a :+ b * 2 -- -- @'_imagPart' :: 'Functor' f => (a -> f a) -> 'Complex' a -> f ('Complex' a)@ #if MIN_VERSION_base(4,4,0) _imagPart :: Lens' (Complex a) a #else _imagPart :: RealFloat a => Lens' (Complex a) a #endif _imagPart f (a :+ b) = (a :+) <$> f b {-# INLINE _imagPart #-} -- | This isn't /quite/ a legal 'Lens'. Notably the -- -- @'view' l ('set' l b a) = b@ -- -- law is violated when you set a 'polar' value with 0 'magnitude' and non-zero -- 'phase' as the 'phase' information is lost, or with a negative 'magnitude' -- which flips the 'phase' and retains a positive 'magnitude'. So don't do -- that! -- -- Otherwise, this is a perfectly cromulent 'Lens'. _polar :: RealFloat a => Iso' (Complex a) (a,a) _polar = iso polar (uncurry mkPolar) {-# INLINE _polar #-} -- | Access the 'magnitude' of a 'Complex' number. -- -- >>> (10.0 :+ 20.0) & _magnitude *~ 2 -- 20.0 :+ 40.0 -- -- This isn't /quite/ a legal 'Lens'. Notably the -- -- @'view' l ('set' l b a) = b@ -- -- law is violated when you set a negative 'magnitude'. This flips the 'phase' -- and retains a positive 'magnitude'. So don't do that! -- -- Otherwise, this is a perfectly cromulent 'Lens'. -- -- Setting the 'magnitude' of a zero 'Complex' number assumes the 'phase' is 0. _magnitude :: RealFloat a => Lens' (Complex a) a _magnitude f c = setMag <$> f r where setMag r' | r /= 0 = c * (r' / r :+ 0) | otherwise = r' :+ 0 r = magnitude c {-# INLINE _magnitude #-} -- | Access the 'phase' of a 'Complex' number. -- -- >>> (mkPolar 10 (2-pi) & _phase +~ pi & view _phase) ≈ 2 -- True -- -- This isn't /quite/ a legal 'Lens'. Notably the -- -- @'view' l ('set' l b a) = b@ -- -- law is violated when you set a 'phase' outside the range @(-'pi', 'pi']@. -- The phase is always in that range when queried. So don't do that! -- -- Otherwise, this is a perfectly cromulent 'Lens'. _phase :: RealFloat a => Lens' (Complex a) a _phase f c = setPhase <$> f theta where setPhase theta' = c * cis (theta' - theta) theta = phase c {-# INLINE _phase #-} -- | Access the 'conjugate' of a 'Complex' number. -- -- >>> (2.0 :+ 3.0) & _conjugate . _imagPart -~ 1 -- 2.0 :+ 4.0 -- -- >>> (mkPolar 10.0 2.0 ^. _conjugate . _phase) ≈ (-2.0) -- True _conjugate :: RealFloat a => Iso' (Complex a) (Complex a) _conjugate = involuted conjugate {-# INLINE _conjugate #-}