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{-# LANGUAGE ViewPatterns #-}
import Numeric.GSL.ODE
import Numeric.LinearAlgebra
import Graphics.Plot
import Debug.Trace(trace)
debug x = trace (show x) x
vanderpol mu = do
let xdot mu t [x,v] = [v, -x + mu * v * (1-x^2)]
ts = linspace 1000 (0,50)
sol = toColumns $ odeSolve (xdot mu) [1,0] ts
mplot (ts : sol)
mplot sol
harmonic w d = do
let xdot w d t [x,v] = [v, a*x + b*v] where a = -w^2; b = -2*d*w
ts = linspace 100 (0,20)
sol = odeSolve (xdot w d) [1,0] ts
mplot (ts : toColumns sol)
kepler v a = mplot (take 2 $ toColumns sol) where
xdot t [x,y,vx,vy] = [vx,vy,x*k,y*k]
where g=1
k=(-g)*(x*x+y*y)**(-1.5)
ts = linspace 100 (0,30)
sol = odeSolve xdot [4, 0, v * cos (a*degree), v * sin (a*degree)] ts
degree = pi/180
main = do
vanderpol 2
harmonic 1 0
harmonic 1 0.1
kepler 0.3 60
kepler 0.4 70
vanderpol' 2
-- example of odeSolveV with jacobian
vanderpol' mu = do
let xdot mu t (toList->[x,v]) = fromList [v, -x + mu * v * (1-x^2)]
jac t (toList->[x,v]) = (2><2) [ 0 , 1
, -1-2*x*v*mu, mu*(1-x**2) ]
ts = linspace 1000 (0,50)
hi = (ts!1 - ts!0)/100
sol = toColumns $ odeSolveV (MSBDF jac) hi 1E-8 1E-8 (xdot mu) (fromList [1,0]) ts
mplot sol
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