add examples

1 files changed, 56 insertions, 0 deletions

diff --git a/examples/kalman.hs b/examples/kalman.hs
new file mode 100644
index 0000000..ccb8083
--- /dev/null
+++ b/examples/kalman.hs
@@ -0,0 +1,56 @@
+import LinearAlgebra
+import Graphics.Plot
+import LinearAlgebra.Instances
+
+--import GSLHaskell
+
+vector l = fromList l :: Vector Double
+matrix ls = fromLists ls :: Matrix Double
+diagl = diag . vector
+
+f = matrix [[1,0,0,0],
+            [1,1,0,0],
+            [0,0,1,0],
+            [0,0,0,1]]
+
+h = matrix [[0,-1,1,0],
+            [0,-1,0,1]]
+
+q = diagl [1,1,0,0]
+
+r = diagl [2,2]
+
+s0 = State (vector [0, 0, 10, -10]) (diagl [10,0, 100, 100])
+
+data System = System {kF, kH, kQ, kR :: Matrix Double}
+data State = State {sX :: Vector Double , sP :: Matrix Double}
+type Measurement = Vector Double
+
+kalman :: System -> State -> Measurement -> State
+kalman (System f h q r) (State x p) z = State x' p' where
+    px = f <> x                            -- prediction
+    pq = f <> p <> trans f                 -- its covariance
+    y  = z - h <> px                       -- residue
+    cy = h <> pq <> trans h + r            -- its covariance
+    k  = pq <> trans h <> inv cy           -- kalman gain
+    x' = px + k <> y                       -- new state
+    p' = (ident (dim x) - k <> h) <> pq   -- its covariance
+
+sys = System f h q r
+
+zs = [vector [15-k,-20-k] | k <- [0..]]
+
+xs = s0 : zipWith (kalman sys) xs zs
+
+des = map (sqrt.takeDiag.sP) xs
+
+evolution n (xs,des) =
+    vector [1.. fromIntegral n]:(toColumns $ fromRows $ take n (zipWith (-) (map sX xs) des)) ++
+    (toColumns $ fromRows $ take n (zipWith (+) (map sX xs) des))
+
+main = do
+    print $ fromRows $ take 10 (map sX xs)
+    mapM_ (print . sP) $ take 10 xs
+    mplot (evolution 20 (xs,des))
+
+--(<>) = multiply
\ No newline at end of file