empty hmatrix-base

1 files changed, 50 insertions, 0 deletions

diff --git a/packages/hmatrix/examples/ode.hs b/packages/hmatrix/examples/ode.hs
new file mode 100644
index 0000000..dc6e0ec
--- /dev/null
+++ b/packages/hmatrix/examples/ode.hs
@@ -0,0 +1,50 @@
+{-# 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
+
+