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{-# OPTIONS_GHC -Wall #-}
import Numeric.Sundials.Arkode.ODE
import Numeric.LinearAlgebra
import Plots as P
import qualified Diagrams.Prelude as D
import Diagrams.Backend.Rasterific
import Control.Lens
brusselator :: a -> [Double] -> [Double]
brusselator _t x = [ a - (w + 1) * u + v * u^(2::Int)
, w * u - v * u^(2::Int)
, (b - w) / eps - w * u
]
where
a = 1.0
b = 3.5
eps = 5.0e-6
u = x !! 0
v = x !! 1
w = x !! 2
stiffish :: Double -> [Double] -> [Double]
stiffish t v = [ lamda * u + 1.0 / (1.0 + t * t) - lamda * atan t ]
where
lamda = -100.0
u = v !! 0
lSaxis :: [[Double]] -> P.Axis B D.V2 Double
lSaxis xs = P.r2Axis &~ do
let ts = xs!!0
us = xs!!1
vs = xs!!2
ws = xs!!3
P.linePlot' $ zip ts us
P.linePlot' $ zip ts vs
P.linePlot' $ zip ts ws
kSaxis :: [(Double, Double)] -> P.Axis B D.V2 Double
kSaxis xs = P.r2Axis &~ do
P.linePlot' xs
main :: IO ()
main = do
do let res = odeSolve brusselator [1.2, 3.1, 3.0] (fromList [0.0, 0.1 .. 10.0])
putStrLn $ show res
renderRasterific "diagrams/brusselator.png"
(D.dims2D 500.0 500.0)
(renderAxis $ lSaxis $ [0.0, 0.1 .. 10.0]:(toLists $ tr res))
do let res = odeSolve stiffish [0.0] (fromList [0.0, 0.1 .. 10.0])
putStrLn $ show res
renderRasterific "diagrams/stiffish.png"
(D.dims2D 500.0 500.0)
(renderAxis $ kSaxis $ zip [0.0, 0.1 .. 10.0] (concat $ toLists res))
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