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  1. type Number = Rational
  2. type Vector = [Number]
  3. type Row    = [Number]
  4. type Matrix = [Row]
  5.  
  6. gauss :: Matrix -> Vector -> Vector
  7. gauss a b = resubstitute $ triangular $ zipWith (++) a $ map (\y -> [y]) b
  8.  
  9. triangular :: Matrix -> Matrix
  10. triangular [] = []
  11. triangular m  = row:(triangular $ map f rows)
  12.     where
  13.     (row:rows) = rotatePivot m
  14.     rotatePivot (row:rows)
  15.     	| (head row) /= 0 = (row:rows)
  16.     	| otherwise       = rotatePivot (rows ++ [row])
  17.     f bs
  18.         | (head bs) == 0 = drop 1 bs
  19.         | otherwise      = drop 1 $ zipWith (-) (map (*c) bs) row
  20.         where 
  21.         c = (head row)/(head bs)  
  22.  
  23. resubstitute :: Matrix -> Vector
  24. resubstitute = reverse . resubstitute' . reverse . map reverse
  25. 	where
  26. 	resubstitute' [] = []
  27. 	resubstitute' (row:rows) = x:(resubstitute' $ map substituteUnknown rows) 
  28. 		where 
  29. 		x = (head row)/(last row)
  30. 		substituteUnknown (a1:(a2:as')) = ((a1-x*a2):as')
  31.  
  32.  
  33. m1 = [[1,1,0], [0,1,1], [1,0,1]] :: Matrix
  34. v1 = [2,3,4] :: Vector
  35. main = print $ gauss m1 v1
Success #stdin #stdout 0s 4716KB
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Standard input is empty
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[3 % 2,1 % 2,5 % 2]
https://ideone.com/Bihfof
language:
Haskell (ghc 8.4.4)
created:
9 years ago
visibility:
public

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