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Idris-dev/libs/base/Data/Complex.idr
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1{-
2 (c) 2012 Copyright Mekeor Melire
3-}
6module Data.Complex
8import Data.Floats
10------------------------------ Rectangular form
12infix 6 :+
13data Complex a = (:+) a a
15realPart : Complex a -> a
16realPart (r:+i) = r
18imagPart : Complex a -> a
19imagPart (r:+i) = i
21instance Eq a => Eq (Complex a) where
22 (==) a b = realPart a == realPart b && imagPart a == imagPart b
24instance Show a => Show (Complex a) where
25 showPrec d (r :+ i) = showParens (d >= plus_i) $ showPrec plus_i r ++ " :+ " ++ showPrec plus_i i
26 where plus_i : Prec
27 plus_i = User 6
30-- when we have a type class 'Fractional' (which contains Float and Double),
31-- we can do:
32{-
33instance Fractional a => Fractional (Complex a) where
34 (/) (a:+b) (c:+d) = let
35 real = (a*c+b*d)/(c*c+d*d)
36 imag = (b*c-a*d)/(c*c+d*d)
37 in
38 (real:+imag)
39-}
43------------------------------ Polarform
45mkPolar : Float -> Float -> Complex Float
46mkPolar radius angle = radius * cos angle :+ radius * sin angle
48cis : Float -> Complex Float
49cis angle = cos angle :+ sin angle
51magnitude : Complex Float -> Float
52magnitude (r:+i) = sqrt (r*r+i*i)
54phase : Complex Float -> Float
55phase (x:+y) = atan2 y x
58------------------------------ Conjugate
60conjugate : Num a => Complex a -> Complex a
61conjugate (r:+i) = (r :+ (0-i))
63instance Functor Complex where
64 map f (r :+ i) = f r :+ f i
66instance Neg a => Neg (Complex a) where
67 negate = map negate
69-- We can't do "instance Num a => Num (Complex a)" because
70-- we need "abs" which needs "magnitude" which needs "sqrt" which needs Float
71instance Num (Complex Float) where
72 (+) (a:+b) (c:+d) = ((a+c):+(b+d))
73 (-) (a:+b) (c:+d) = ((a-c):+(b-d))
74 (*) (a:+b) (c:+d) = ((a*c-b*d):+(b*c+a*d))
75 fromInteger x = (fromInteger x:+0)
76 abs (a:+b) = (magnitude (a:+b):+0)