I thought I was doing ok with haskell until I tried to program in
it. :/ I figured the first thing to tackle was something easy
so I hacked up newton's method. Worked great for Double's. Then
I figured I would extend it to work with different types of
Fractionals. What a pain. I finally got that working for Floats
and Rationals but I'm drawing a blank on Complex.
I've got:
import Data.Complex
import Data.Ratio
import Debug.Trace
main = putStrLn $ "answer = " ++ show (newton myd $ -5)
newton :: (Fractional a, Ord a) => (a -> a) -> a -> a
newton f x = newton_h f x 1.0e-6
newton_h, next_x_h, dy_h :: (Fractional a, Ord a) => (a -> a) ->
a -> a -> a
newton_h f x h = until ((<= h) . abs . f) (next_x_h f h) x
next_x_h f h x = trace ("next_x = " ++ show foo) foo
where foo = x - (f x) / (dy_h f x h)
dy_h f x h = ( (f $ x + h) - f x ) / h
-- roundTo :: Fractional a => a -> a -> a
-- roundTo x eps = ((fromRational . toRational) (round $ x /
eps)) * eps
myd :: Double -> Double
myd x = ((x/100 + 1) * x + 1) * x - 10
myf :: Float -> Float
myf x = ((x/100 + 1) * x + 1) * x - 10
myr :: Rational -> Rational
myr x = approxRational myr' 1e-6
where myr' = ((x/100 + 1) * x + 1) * x - 10
myc :: RealFloat a => Complex a -> Complex a
myc x = x * x + 1
When I try
newton myc 5
in ghci I get a warning about newton wanting Ords. Complex
aren't ordered. I figure I need to specify a newton_h that can
handle complex
newton_h f (Complex x) h =
until ((<= h) . realPart . abs . f) (next_x_h f h) x
laughs at me. So does
newton_h f (:+ r im) h =
until ((<= h) .realPart . abs . f) (next_x_h f h) (:+ r im)
although I sure thought I had read that constructors could be
used in pattern matching. I've been working on this for too long
and getting frustrated. Can someone clue me in?
Thanks,
-ljr
--
Lanny Ripple
CC Tools / Cisco Systems, Inc.
