examples/bool.hs

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+-- vectorized boolean operations defined in terms of step or cond
+
+import Numeric.LinearAlgebra
+
+infix  4  .==., ./=., .<., .<=., .>=., .>.
+infixr 3  .&&.
+infixr 2  .||.
+
+a .<.  b = step (b-a)
+a .<=. b = cond a b 1 1 0
+a .==. b = cond a b 0 1 0
+a ./=. b = cond a b 1 0 1
+a .>=. b = cond a b 0 1 1
+a .>.  b = step (a-b)
+
+a .&&. b  = step (a*b)
+a .||. b  = step (a+b)
+no a      = 1-a
+xor a b   = a ./=. b
+equiv a b = a .==. b
+imp a b   = no a .||. b
+
+taut x = minElement x == 1
+
+-- examples
+
+clip a b x = cond y b y y b where y = cond x a a x x
+
+disp = putStr . dispf 3
+
+eye n = ident n :: Matrix Double
+row = asRow . fromList    :: [Double] -> Matrix Double
+col = asColumn . fromList :: [Double] -> Matrix Double
+
+m = (3><4) [1..] :: Matrix Double
+
+p = row [0,0,1,1]
+q = row [0,1,0,1]
+
+main = do
+    print $ find (>6) m
+    disp $ assoc (6,8) 7 $ zip (find (/=0) (eye 5)) [10..]
+    disp $ m .>=. 10  .||.  m .<. 4
+    (disp . fromColumns . map flatten) [p, q, p.&&.q, p .||.q, p `xor` q, p `equiv` q, p `imp` q]
+    print $ taut $ (p `imp` q ) `equiv` (no q `imp` no p)
+    print $ taut $ (xor p q) `equiv` (p .&&. no q .||. no p .&&. q)
+    disp $ clip 3 8 m
+    disp $ col [1..7] .<=. row [1..5]
+    disp $ cond (col [1..3]) (row [1..4]) m 50 (3*m)
+