Lie algebra example

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+-- The magic of Lie Algebra
+
+import Numeric.LinearAlgebra
+import Text.Printf(printf)
+
+disp = putStrLn . format "  " (printf "%.5f")
+
+rot1 :: Double -> Matrix Double
+rot1 a = (3><3)
+ [ 1, 0, 0
+ , 0, c, s
+ , 0,-s, c ]
+    where c = cos a
+          s = sin a
+
+g1,g2,g3 :: Matrix Double
+
+g1 = (3><3) [0, 0,0
+            ,0, 0,1
+            ,0,-1,0]
+
+rot2 :: Double -> Matrix Double
+rot2 a = (3><3)
+ [ c, 0, s
+ , 0, 1, 0
+ ,-s, 0, c ]
+    where c = cos a
+          s = sin a
+
+g2 = (3><3) [ 0,0,1
+            , 0,0,0
+            ,-1,0,0]
+
+rot3 :: Double -> Matrix Double
+rot3 a = (3><3)
+ [ c, s, 0
+ ,-s, c, 0
+ , 0, 0, 1 ]
+    where c = cos a
+          s = sin a
+
+g3 = (3><3) [ 0,1,0
+            ,-1,0,0
+            , 0,0,0]
+
+deg=pi/180
+
+-- commutator
+infix 8 &
+a & b = a <> b - b <> a
+
+infixl 6 |+|
+a |+| b = a + b + a & b */2  + (a-b) & (a & b) */12
+
+main = do
+   let a =  45*deg
+       b =  50*deg
+       c = -30*deg
+       exact = rot3 a <> rot1 b <> rot2 c
+       lie = a.*g3 |+| b.*g1 |+| c.*g2
+   putStrLn "position in the tangent space:"
+   disp lie
+   putStrLn "exponential map back to the group (2 terms):"
+   disp (expm lie)
+   putStrLn "exact position:"
+   disp exact