git.iko.soy/Idris-dev
on 0875310 help sign in
Idris-dev/libs/base/Data/Complex.idr
69 lines 1.7 kB history raw
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 show (r:+i) = "("++show r++":+"++show i++")"
29-- when we have a type class 'Fractional' (which contains Float and Double),
30-- we can do:
31{-
32instance Fractional a => Fractional (Complex a) where
33 (/) (a:+b) (c:+d) = let
34 real = (a*c+b*d)/(c*c+d*d)
35 imag = (b*c-a*d)/(c*c+d*d)
36 in
37 (real:+imag)
38-}
42------------------------------ Polarform
44mkPolar : Float -> Float -> Complex Float
45mkPolar radius angle = radius * cos angle :+ radius * sin angle
47cis : Float -> Complex Float
48cis angle = cos angle :+ sin angle
50magnitude : Complex Float -> Float
51magnitude (r:+i) = sqrt (r*r+i*i)
53phase : Complex Float -> Float
54phase (x:+y) = atan2 y x
57------------------------------ Conjugate
59conjugate : Num a => Complex a -> Complex a
60conjugate (r:+i) = (r :+ (0-i))
62-- We can't do "instance Num a => Num (Complex a)" because
63-- we need "abs" which needs "magnitude" which needs "sqrt" which needs Float
64instance Num (Complex Float) where
65 (+) (a:+b) (c:+d) = ((a+b):+(c+d))
66 (-) (a:+b) (c:+d) = ((a-b):+(c-d))
67 (*) (a:+b) (c:+d) = ((a*c-b*d):+(b*c+a*d))
68 fromInteger x = (fromInteger x:+0)
69 abs (a:+b) = (magnitude (a:+b):+0)