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Determinant and permanent: Difference between revisions
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16</pre>
===Calculation of the determinant===
The computation of the determinant and that of the permanent should be separate tasks. Here is code for computing the determinant (inefficiently):
<lang Haskell>
outer :: (a->b->c) -> [a] -> [b] -> [[c]]
outer f [] _ = []
outer f _ [] = []
outer f (h1:t1) x2 = (f h1 <$> x2) : outer f t1 x2
dot [] [] = 0
dot (h1:t1) (h2:t2) = (h1*h2) + (dot t1 t2)
transpose [] = []
transpose ([] : xss) = transpose xss
transpose ((x:xs) : xss) = (x : [h | (h:_) <- xss]) : transpose (xs : [ t | (_:t) <- xss])
mul :: Num a => [[a]] -> [[a]] -> [[a]]
mul a b = outer dot a (transpose b)
delRow :: Int -> [a] -> [a]
delRow i v =
(first ++ rest) where (first, _:rest) = splitAt i v
delCol :: Int -> [[a]] -> [[a]]
delCol j m = (delRow j) <$> m
adj :: Num a => [[a]] -> [[a]]
adj [] = []
adj m =
[
[(-1)^(i+j) * det (delRow i $ delCol j m)
| i <- [0.. -1+length m]
]
| j <- [0.. -1+length m]
]
det :: Num a => [[a]] -> a
det [] = 1
det m = (mul m (adj m)) !! 0 !! 0
</lang>
=={{header|J}}==
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