{"id":33509,"date":"2023-02-09T09:16:32","date_gmt":"2023-02-09T03:46:32","guid":{"rendered":"https:\/\/jassweb.com\/solved\/solved-write-this-scala-matrix-multiplication-in-haskell-duplicate\/"},"modified":"2023-02-09T09:16:32","modified_gmt":"2023-02-09T03:46:32","slug":"solved-write-this-scala-matrix-multiplication-in-haskell-duplicate","status":"publish","type":"post","link":"https:\/\/jassweb.com\/solved\/solved-write-this-scala-matrix-multiplication-in-haskell-duplicate\/","title":{"rendered":"[Solved] Write this Scala Matrix multiplication in Haskell [duplicate]"},"content":{"rendered":"<p> [ad_1]<br \/>\n<\/p>\n<div id=\"answer-8327717\" class=\"answer js-answer accepted-answer js-accepted-answer\" data-answerid=\"8327717\" data-parentid=\"8327032\" data-score=\"8\" data-position-on-page=\"1\" data-highest-scored=\"1\" data-question-has-accepted-highest-score=\"1\" itemprop=\"acceptedAnswer\" itemscope itemtype=\"https:\/\/schema.org\/Answer\">\n<div class=\"post-layout\">\n<div class=\"votecell post-layout--left\"><\/div>\n<div class=\"answercell post-layout--right\">\n<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>It&#8217;ll be perfectly safe with a smart constructor and stored dimensions. Of course there are no natural implementations for the operations <code>signum<\/code> and <code>fromIntegral<\/code> (or maybe a diagonal matrix would be fine for the latter).<\/p>\n<pre class=\"lang-hs prettyprint-override\"><code>module Matrix (Matrix(),matrix,matrixTranspose) where\n\nimport Data.List (transpose)\n\ndata Matrix a = Matrix {matrixN :: Int, \n                        matrixM :: Int,\n                        matrixElems :: [[a]]}\n                deriving (Show, Eq)\n\nmatrix :: Int -&gt; Int -&gt; [[a]] -&gt; Matrix a\nmatrix n m vals\n  | length vals \/= m            = error \"Wrong number of rows\"\n  | any (\/=n) $ map length vals = error \"Column length mismatch\"\n  | otherwise = Matrix n m vals\n\nmatrixTranspose (Matrix m n vals) = matrix n m (transpose vals)\n\ninstance Num a =&gt; Num (Matrix a) where\n\n  (+) (Matrix m n vals) (Matrix m' n' vals')\n    | m\/=m' = error \"Row number mismatch\"\n    | n\/=n' = error \"Column number mismatch\"\n    | otherwise = Matrix m n (zipWith (zipWith (+)) vals vals')\n\n  abs (Matrix m n vals) = Matrix m n (map (map abs) vals)\n\n  negate (Matrix m n vals) = Matrix m n (map (map negate) vals)\n\n  (*) (Matrix m n vals) (Matrix n' p vals')\n    | n\/=n' = error \"Matrix dimension mismatch in multiplication\"\n    | otherwise = let tvals' = transpose vals'\n                      dot x y = sum $ zipWith (*) x y\n                      result = map (\\col -&gt; map (dot col) tvals') vals\n                  in Matrix m p result\n<\/code><\/pre>\n<p>Test it in ghci:<\/p>\n<pre class=\"lang-hs prettyprint-override\"><code>*Matrix&gt; let a = matrix 3 2 [[1,0,2],[-1,3,1]]\n*Matrix&gt; let b = matrix 2 3 [[3,1],[2,1],[1,0]]\n*Matrix&gt; a*b\nMatrix {matrixN = 3, matrixM = 3, matrixElems = [[5,1],[4,2]]}\n<\/code><\/pre>\n<p>Since my <code>Num<\/code> instance is generic, it even works for complex matrices out of the box:<\/p>\n<pre class=\"lang-hs prettyprint-override\"><code>Prelude Data.Complex Matrix&gt; let c = matrix 2 2 [[0:+1,1:+0],[5:+2,4:+3]]\nPrelude Data.Complex Matrix&gt; let a = matrix 2 2 [[0:+1,1:+0],[5:+2,4:+3]]\nPrelude Data.Complex Matrix&gt; let b = matrix 2 3 [[3:+0,1],[2,1],[1,0]]\nPrelude Data.Complex Matrix&gt; a\nMatrix {matrixN = 2, matrixM = 2, matrixElems = [[0.0 :+ 1.0,1.0 :+ 0.0],[5.0 :+ 2.0,4.0 :+ 3.0]]}\nPrelude Data.Complex Matrix&gt; b\nMatrix {matrixN = 2, matrixM = 3, matrixElems = [[3.0 :+ 0.0,1.0 :+ 0.0],[2.0 :+ 0.0,1.0 :+ 0.0],[1.0 :+ 0.0,0.0 :+ 0.0]]}\nPrelude Data.Complex Matrix&gt; a*b\nMatrix {matrixN = 2, matrixM = 3, matrixElems = [[2.0 :+ 3.0,1.0 :+ 1.0],[23.0 :+ 12.0,9.0 :+ 5.0]]}\n<\/code><\/pre>\n<hr>\n<p><strong>EDIT: new material<\/strong><\/p>\n<p>Oh, you want to just override the <code>(*)<\/code> function without any <code>Num<\/code> stuff. That&#8217;s possible to o but you&#8217;ll have to remember that the Haskell standard library has reserved <code>(*)<\/code> for use in the <code>Num<\/code> class.<\/p>\n<pre class=\"lang-hs prettyprint-override\"><code>module Matrix where\n\nimport qualified Prelude as P\nimport Prelude hiding ((*))\nimport Data.List (transpose)\n\nclass Multiply a where\n  (*) :: a -&gt; a -&gt; a\n\ndata Matrix a = Matrix {matrixN :: Int, \n                        matrixM :: Int,\n                        matrixElems :: [[a]]}\n                deriving (Show, Eq)\n\nmatrix :: Int -&gt; Int -&gt; [[a]] -&gt; Matrix a\nmatrix n m vals\n  | length vals \/= m            = error \"Wrong number of rows\"\n  | any (\/=n) $ map length vals = error \"Column length mismatch\"\n  | otherwise = Matrix n m vals\n\nmatrixTranspose (Matrix m n vals) = matrix n m (transpose vals)\n\ninstance P.Num a =&gt; Multiply (Matrix a) where\n  (*) (Matrix m n vals) (Matrix n' p vals')\n    | n\/=n' = error \"Matrix dimension mismatch in multiplication\"\n    | otherwise = let tvals' = transpose vals'\n                      dot x y = sum $ zipWith (P.*) x y\n                      result = map (\\col -&gt; map (dot col) tvals') vals\n                  in Matrix m p result\n\n\na = matrix 3 2 [[1,2,3],[4,5,6]]\nb = a * matrixTranspose\n<\/code><\/pre>\n<p>Testing in ghci:<\/p>\n<pre class=\"lang-hs prettyprint-override\"><code>*Matrix&gt; b\nMatrix {matrixN = 3, matrixM = 3, matrixElems = [[14,32],[32,77]]}\n<\/code><\/pre>\n<p>There. Now if a third module wants to use both the <code>Matrix<\/code> version of <code>(*)<\/code> and the <code>Prelude<\/code> version of <code>(*)<\/code> it&#8217;ll have to of course import one or the other qualified. But that&#8217;s just business as usual.<\/p>\n<p>I could&#8217;ve done all of this without the <code>Multiply<\/code> type class but this implementation leaves our new shiny <code>(*)<\/code> open for extension in other modules.<\/p>\n<\/p><\/div>\n<div class=\"mt24\"><\/div>\n<\/div>\n<p>            <span class=\"d-none\" itemprop=\"commentCount\">8<\/span> <\/p><\/div>\n<\/div>\n<p>[ad_2]<\/p>\n<p>solved Write this Scala Matrix multiplication in Haskell [duplicate] <\/p>\n","protected":false},"excerpt":{"rendered":"<p>[ad_1] It&#8217;ll be perfectly safe with a smart constructor and stored dimensions. Of course there are no natural implementations for the operations signum and fromIntegral (or maybe a diagonal matrix would be fine for the latter). module Matrix (Matrix(),matrix,matrixTranspose) where import Data.List (transpose) data Matrix a = Matrix {matrixN :: Int, matrixM :: Int, matrixElems &#8230; <a title=\"[Solved] Write this Scala Matrix multiplication in Haskell [duplicate]\" class=\"read-more\" href=\"https:\/\/jassweb.com\/solved\/solved-write-this-scala-matrix-multiplication-in-haskell-duplicate\/\" aria-label=\"More on [Solved] Write this Scala Matrix multiplication in Haskell [duplicate]\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[320],"tags":[1150,802],"class_list":["post-33509","post","type-post","status-publish","format-standard","hentry","category-solved","tag-haskell","tag-scala"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>[Solved] Write this Scala Matrix multiplication in Haskell [duplicate] - JassWeb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/jassweb.com\/solved\/solved-write-this-scala-matrix-multiplication-in-haskell-duplicate\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"[Solved] Write this Scala Matrix multiplication in Haskell [duplicate] - JassWeb\" \/>\n<meta property=\"og:description\" content=\"[ad_1] It&#8217;ll be perfectly safe with a smart constructor and stored dimensions. 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