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module Main where
import System.Random.Mersenne as M
import Data.Vector.Unboxed.Mutable as U
import Control.Monad.State as S
import Control.Monad.Primitive
import Control.Applicative
import Control.Concurrent
import Graphics.UI.SDL as SDL
newtype Grid = Grid { unG :: (Int, MVector (PrimState IO) Int) }
newtype Ising = Ising { unI :: (M.MTGen, Grid) }
type Pos = (Int, Int)
(|>) :: Grid -> Pos -> IO Int
(Grid (n,g)) |> (x,y) | x == n = U.unsafeRead g (y*n)
| x == -1 = U.unsafeRead g (y*n + n - 1)
| y == n = U.unsafeRead g x
| y == -1 = U.unsafeRead g ((n - 1)*n + x)
| otherwise = U.unsafeRead g (y*n + x)
(<==) :: Pos -> Int -> (Pos, Int)
pos <== val = (pos,val)
(<|) :: Grid -> (Pos, Int) -> IO ()
Grid (n,g) <| ((x,y), val) = U.unsafeWrite g (y*n + x) val
infixr 1 <==
infixr 0 <|
-- Just a shortcut
l = lift
-- Initialize a ising system
initIsing :: M.MTGen -> Int -> IO Ising
initIsing rg n = do
g <- U.new $ n*n
grid <- return $ Grid (n, g)
let spin x = x + (x - 1)
sequence_ [ do rnumber <- random rg
grid <| (i,j) <== spin (rnumber `mod` 2) |
i <- [0..n - 1], j <- [0..n - 1] ]
return $ Ising (rg, grid)
-- Update the grid of Ising Model 'ns' steps in temperatur 't'
updateIsing :: Int -> Double -> StateT Ising IO ()
updateIsing ns t = up 0 ns
where
up i ns | i == ns = return ()
| otherwise = do
Ising (rg, grid@(Grid (n,_))) <- S.get
x <- l $ (`mod` n) <$> random rg
y <- l $ (`mod` n) <$> random rg
(e,s) <- l $ calc_energy grid (x,y)
if e < 0
then do l $ grid <| (x,y) <== negate s
else do p <- l $ (random rg :: IO Double)
when (p < exp (-2*(fromIntegral e)/t)) $
l $ grid <| (x,y) <== negate s
up (i + 1) ns
calc_energy g (x,y) = do
s <- g |> (x,y)
e <- (s*).(sum) <$> (mapM (g |>) [ (x, y - 1)
, (x, y + 1)
, (x - 1, y)
, (x + 1, y) ])
return (e, s)
-- Draw ising
drawIsing screen (Ising (_, grid@(Grid (n,_)))) = do
sequence [ drawSquare screen i j | i <- [0..n - 1], j <- [0..n - 1] ]
SDL.flip screen
where drawSquare s i j = do
s <- grid |> (i,j)
let color 1 = 0xFF0000
color _ = 0x00FF00
sSize = screen_size `div` n
rect i j = Just $ Rect (i*sSize) (j*sSize) sSize sSize
SDL.fillRect screen (rect i j) (SDL.Pixel $ color s)
return ()
-- Update ising and draw
sdlUpIsing i t c s
| t < 0 = return ()
| otherwise = do
evalStateT (updateIsing 1000 t) i
drawIsing s i
threadDelay 1
sdlUpIsing i (t - 0.001) (c + 1) s
screen_size = 400
main = do
SDL.init [InitEverything]
setVideoMode screen_size screen_size 32 []
screen <- SDL.getVideoSurface
rg <- M.newMTGen Nothing
i <- initIsing rg 200
forkIO . forever $ waitEvent >>= \e -> when (e == Quit) quit
sdlUpIsing i 3 0 screen