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POTroubles with matrix division
primarykey
Id
11193110
data
AcceptedAnswerId
11193351
AnswerCount
2
ClosedDate
CommentCount
2
CommunityOwnedDate
CreationDate
2012-06-25T16:14:54.050
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2012-06-25T18:19:07.243
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2012-06-25T18:18:50.693
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Score
-1
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text
Body
I had the idea to write a matrix division in Haskell as <code>Muliply A* Inverse B</code>. I wrote some code to do that, but the compiler had the idea to stop me. It shows the following error: <pre><code>Invalid type signature :MatrixDivision :: Matrix-> Matrix-> Matrix at line 86:1 Should be of (variable)::(Type) </code></pre> What do I wrong? This is the code: <pre><code>import List type Vector = [Int] type Matrix = [Vector] --basic constructions for vectors zeroVector :: Int -> Vector zeroVector n = replicate n 0 --basic operations for vectors dotProduct :: Vector -> Vector -> Int dotProduct v w = sum ( zipWith (*) v w ) vectorSum :: Vector -> Vector -> Vector vectorSum = zipWith (+) vectorScalarProduct :: Int -> Vector -> Vector vectorScalarProduct n vec = [ n * x | x <- vec ] --basic constructions for matrices -- elemMatrix n i j v is the n-by-n elementary matrix with -- entry v in the (i,j) place elemMatrix :: Int -> Int -> Int -> Int -> Matrix elemMatrix n i j v = [ [ entry row column | column <- [1..n] ] | row <- [1..n] ] where entry x y | x == y = 1 | x == i && y == j = v | otherwise = 0 idMatrix :: Int -> Matrix idMatrix n = elemMatrix n 1 1 1 zeroMatrix :: Int -> Int -> Matrix zeroMatrix i j = replicate i (zeroVector j) --basic operations for matrices matrixSum :: Matrix -> Matrix -> Matrix matrixSum = zipWith vectorSum matrixScalarProduct :: Int -> Matrix -> Matrix matrixScalarProduct n m = [ vectorScalarProduct n row | row <- m ] matrixProduct :: Matrix -> Matrix -> Matrix matrixProduct m n = [ map (dotProduct r) (transpose n) | r <- m ] {- The determinant and inverse functions given here are only for examples of Haskell syntax. Efficient versions using row operations are implemented in RowOperations.hs .-} --determinant using cofactors remove :: Matrix -> Int -> Int -> Matrix remove m i j | m == [] || i < 1 || i > numRows m || j < 1 || j > numColumns m = error "(i,j) out of range" | otherwise = transpose ( cut (transpose ( cut m i ) ) j ) determinant :: Matrix -> Int determinant [] = error "determinant: 0-by-0 matrix" determinant [[n]] = n determinant m = sum [ (-1)^(j+1) * (head m)!!(j-1) * determinant (remove m 1 j) | j <- [1..(numColumns m) ] ] --inverse cofactor :: Matrix -> Int -> Int -> Int cofactor m i j = (-1)^(i+j) * determinant (remove m i j) cofactorMatrix :: Matrix -> Matrix cofactorMatrix m = [ [ (cofactor m i j) | j <- [1..n] ] | i <- [1..n] ] where n = length m inverse :: Matrix -> Matrix inverse m = transpose [ [ quot x ( determinant m) | x <- row ] | row <- (cofactorMatrix m) ] --Matrix Division MatrixDivision :: Matrix -> Matrix -> Matrix MatrixDivision m n = matrixProduct m inverse(n) </code></pre> I wrote the full code to give more information.
Tags
<haskell>
Title
Troubles with matrix division
singulars
PostAcceptedAnswerId
1. PO
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1. This table or related slice is empty.
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1. PTQuestion
UserLastEditorUserId
1. USkiritsuku
UserOwnerUserId
1. USAbdalla Adam
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1. PL
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1. This table or related slice is empty.
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1. This table or related slice is empty.
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1. PO
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 PTAnswer
2. PO
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1. VO
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CommentsPostId
1. COpossible duplicate of [Why does Haskell force data constructor's first letter to be upper case?](http://stackoverflow.com/questions/6237775/why-does-haskell-force-data-constructors-first-letter-to-be-upper-case)
 singulars
 PostPostId
 POTroubles with matrix division
 UserUserId
 USLambdageek
2. CO..and you need to indent the guards `|` by one after `entry x y` in the `where` clause of `elemMatrix`.
 singulars
 PostPostId
 POTroubles with matrix division
 UserUserId
 USAndrewC

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