In today’s Programming Praxis exercise our task is to implement four common matrix operations. The provided Scheme solution has 44 lines. Let’s see what we can do to reduce that a bit.
There are many ways to represent matrices. The most common one in Haskell (if not the most efficient if you need random access) is to use a list of lists, which is what we’ll be using here.
For addition, all we need to do is add the corresponding numbers in the two matrices together.
add :: Num a => [[a]] -> [[a]] -> [[a]] add = zipWith $ zipWith (+)
Scaling (multiplying by a constant) is even simpler: just apply the multiplication to every element.
scale :: Num a => a -> [[a]] -> [[a]] scale = map . map . (*)
For transposition I could’ve just used the definition from Data.List, but that would be cheating. Instead, I figured I would just use a right fold.
transpose :: [[a]] -> [[a]] transpose [] = [] transpose xs = foldr (zipWith (:)) (repeat []) xs
Multiplying two matrices requires multiplying rows and columns. Since nested lists don’t have easy access to columns, we can use the transpose function we just defined to fix that.
mult :: Num a => [[a]] -> [[a]] -> [[a]] mult a b = [map (sum . zipWith (*) r) $ transpose b | r <- a]
And of course we need to test if everything works correctly.
main :: IO () main = do let m = [[1..3],[4..6]] let n = [[1..4], [2..5], [3..6]] print $ add m [[2..4],[3..5]] == [[3,5,7], [7,9,11]] print $ scale 2 m == [[2,4,6], [8,10,12]] print $ mult m n == [[14,20..32], [32,47..77]] print $ transpose m == [[1,4], [2,5], [3,6]]
Yep. And with a 89% reduction in line count, that’s good enough for me.
Tags: bonsai, code, Haskell, kata, matrices, matrix, praxis, programming
