June 2018 Update

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-14.hs

@@ -1 +1,44 @@
-g (n,(a,b)) = (2*n,(2*a*b-a*a,a*a+b*b))     -- iterate g (1,(1,1)) ; a is nth
+import Data.List (transpose)
+
+fib
+  :: (Integral b, Num a)
+  => b -> a
+fib 0 = 0 -- this line is necessary because "something ^ 0" returns "fromInteger 1", which unfortunately
+-- in our case is not our multiplicative identity (the identity matrix) but just a 1x1 matrix of 1
+fib n = (last . head . unMat) (Mat [[1, 1], [1, 0]] ^ n)
+
+-- Code adapted from Matrix exponentiation operator task ---------------------
+(<+>)
+  :: Num c
+  => [c] -> [c] -> [c]
+(<+>) = zipWith (+)
+
+(<*>)
+  :: Num a
+  => [a] -> [a] -> a
+(<*>) = (sum .) . zipWith (*)
+
+newtype Mat a = Mat
+  { unMat :: [[a]]
+  } deriving (Eq)
+
+instance Show a =>
+         Show (Mat a) where
+  show xm = "Mat " ++ show (unMat xm)
+
+instance Num a =>
+         Num (Mat a) where
+  negate xm = Mat $ map (map negate) $ unMat xm
+  xm + ym = Mat $ zipWith (<+>) (unMat xm) (unMat ym)
+  xm * ym =
+    Mat
+      [ [ xs Main.<*> ys -- to distinguish from standard applicative operator
+        | ys <- transpose $ unMat ym ]
+      | xs <- unMat xm ]
+  fromInteger n = Mat [[fromInteger n]]
+  abs = undefined
+  signum = undefined
+
+-- TEST ----------------------------------------------------------------------
+main :: IO ()
+main = (print . take 10 . show . fib) (10 ^ 5)