module Data.Matrix.Generic.Base
( rows
, cols
, dim
, (!)
, unsafeIndex
, empty
, matrix
, flatten
, fromVector
, toRows
, toColumns
, fromRows
, fromColumns
, toList
, toLists
, fromLists
, convert
, tr
, takeRow
, takeColumn
, subMatrix
, ident
, diag
, diagRect
, takeDiag
, fromBlocks
, isSymmetric
, force
, Data.Matrix.Generic.Base.foldl
, imap
, Data.Matrix.Generic.Base.map
, Data.Matrix.Generic.Base.mapM
, Data.Matrix.Generic.Base.mapM_
, Data.Matrix.Generic.Base.forM
, Data.Matrix.Generic.Base.forM_
, generate
) where
import Control.Arrow ((***), (&&&))
import Control.Monad
import qualified Data.Foldable as F
import qualified Data.Vector.Generic as G
import qualified Data.Vector.Generic.Mutable as GM
import Data.Matrix.Generic.Types
rows :: G.Vector v a => Matrix v a -> Int
rows (Matrix m _ _ _ _) = m
cols :: G.Vector v a => Matrix v a -> Int
cols (Matrix _ n _ _ _) = n
dim :: G.Vector v a => Matrix v a -> (Int, Int)
dim (Matrix r c _ _ _) = (r,c)
(!) :: G.Vector v a => Matrix v a -> (Int, Int) -> a
(!) (Matrix _ _ tda offset vec) (i, j) = vec G.! idx
where
idx = offset + i * tda + j
unsafeIndex :: G.Vector v a => Matrix v a -> (Int, Int) -> a
unsafeIndex (Matrix _ _ tda offset vec) (i,j) = vec `G.unsafeIndex` idx
where
idx = offset + i * tda + j
empty :: G.Vector v a => Matrix v a
empty = Matrix 0 0 0 0 G.empty
matrix :: G.Vector v a
=> Int
-> [a]
-> Matrix v a
matrix ncol xs | n `mod` ncol /= 0 = error "incorrect length"
| otherwise = fromVector (nrow,ncol) vec
where
vec = G.fromList xs
nrow = n `div` ncol
n = G.length vec
flatten :: G.Vector v a => Matrix v a -> v a
flatten (Matrix m n tda offset vec)
| n == tda = G.slice offset (m * n) vec
| otherwise = G.generate (m * n) f
where
f i = (G.!) vec $ offset + (i `div` n) * tda + i `mod` n
fromVector :: G.Vector v a => (Int, Int) -> v a -> Matrix v a
fromVector (r,c) = Matrix r c c 0
toList :: G.Vector v a => Matrix v a -> [a]
toList = G.toList . flatten
toRows :: G.Vector v a => Matrix v a -> [v a]
toRows (Matrix m n tda offset vec) = loop 0
where
loop !i | i < m = G.slice (f i) n vec : loop (i+1)
| otherwise = []
f i = offset + i * tda
toColumns :: G.Vector v a => Matrix v a -> [v a]
toColumns m = Prelude.map (takeColumn m) [0 .. c1]
where c = cols m
fromRows :: G.Vector v a => [v a] -> Matrix v a
fromRows xs | any (\x -> G.length x /= c) xs = error "inequal length"
| otherwise = fromVector (r,c) . G.concat $ xs
where
r = length xs
c = G.length . head $ xs
fromColumns :: G.Vector v a => [v a] -> Matrix v a
fromColumns = tr . fromRows
toLists :: G.Vector v a => Matrix v a -> [[a]]
toLists = Prelude.map G.toList . toRows
fromLists :: G.Vector v a => [[a]] -> Matrix v a
fromLists xs = fromVector (r,c) . G.fromList . concat $ xs
where
r = length xs
c = length .head $ xs
convert :: (G.Vector v a, G.Vector w a) => Matrix v a -> Matrix w a
convert (Matrix r c tda offset vec) = Matrix r c tda offset . G.convert $ vec
takeRow :: G.Vector v a => Matrix v a -> Int -> v a
takeRow (Matrix _ c tda offset vec) i = G.slice i' c vec
where
i' = offset + i * tda
takeColumn :: G.Vector v a => Matrix v a -> Int -> v a
takeColumn (Matrix r _ tda offset vec) j = G.create $ GM.new r >>= go idx vec r 0
where
go f vec' r' !i v | i >= r' = return v
| otherwise = do GM.unsafeWrite v i $ vec' G.! f i
go f vec' r' (i+1) v
idx i = offset + i * tda + j
subMatrix :: G.Vector v a
=> (Int, Int)
-> (Int, Int)
-> Matrix v a -> Matrix v a
subMatrix (i,j) (i',j') (Matrix _ n tda offset vec)
| m' <= 0 || n' <= 0 = empty
| otherwise = Matrix m' n' tda offset' vec
where
m' = i' i + 1
n' = j' j + 1
offset' = offset + i * n + j
tr :: G.Vector v a => Matrix v a -> Matrix v a
tr (Matrix r c tda offset vec) = fromVector (c,r) $ G.generate (r*c) f
where
f i = vec G.! (offset + i `mod` r * tda + i `div` r)
ident :: (Num a, G.Vector v a) => Int -> Matrix v a
ident n = diagRect 0 (n,n) $ replicate n 1
diag :: (Num a, G.Vector v a, F.Foldable t)
=> t a
-> Matrix v a
diag d = diagRect 0 (n,n) d
where n = length . F.toList $ d
diagRect :: (G.Vector v a, F.Foldable t)
=> a
-> (Int, Int)
-> t a
-> Matrix v a
diagRect z0 (r,c) d = fromVector (r,c) $ G.create $ GM.replicate n z0 >>= go d c
where
go xs c' v = F.foldlM f 0 xs >> return v
where
f !i x = GM.unsafeWrite v (i*(c'+1)) x >> return (i+1)
n = r * c
takeDiag :: G.Vector v a => Matrix v a -> v a
takeDiag mat@(Matrix r c _ _ _) = G.generate n $ \i -> unsafeIndex mat (i,i)
where
n = min r c
fromBlocks :: G.Vector v a
=> a
-> [[Matrix v a]]
-> Matrix v a
fromBlocks d ms = fromVector (m,n) $ G.create $ GM.replicate (m*n) d >>= go n ms
where
go n' xss v = foldM_ f 0 xss >> return v
where
f !cr xs = do (r', _) <- foldM g (0, 0) xs
return $ cr + r'
where
g (!maxR, !cc) x = do
let c = cols x
r = rows x
vec = flatten x
step i u = do
GM.unsafeWrite v ((cr + i `div` c) * n' + i `mod` c + cc) u
return (i+1)
G.foldM'_ step (0::Int) vec
return (max maxR r, cc + c)
(m, n) = (sum *** maximum) . unzip . Prelude.map ((maximum *** sum) .
unzip . Prelude.map (rows &&& cols)) $ ms
isSymmetric :: (Eq a, G.Vector v a) => Matrix v a -> Bool
isSymmetric m@(Matrix r c _ _ _) | r /= c = False
| otherwise = all f [0 .. r1]
where
f i = all g [i + 1 .. c1]
where g j = m ! (i,j) == m ! (j,i)
force :: G.Vector v a => Matrix v a -> Matrix v a
force m@(Matrix r c _ _ _) = fromVector (r,c) . G.force . flatten $ m
imap :: (G.Vector v a, G.Vector v b) => ((Int, Int) -> a -> b) -> Matrix v a -> Matrix v b
imap f m@(Matrix r c _ _ _) = fromVector (r,c) $ G.imap f' . flatten $ m
where
f' i = f (i `div` c, i `mod` c)
map :: (G.Vector v a, G.Vector v b) => (a -> b) -> Matrix v a -> Matrix v b
map f m@(Matrix r c _ _ _) = fromVector (r,c) $ G.map f . flatten $ m
foldl :: G.Vector v b => (a -> b -> a) -> a -> Matrix v b -> a
foldl f acc m = G.foldl f acc . flatten $ m
mapM :: (G.Vector v a, G.Vector v b, Monad m) => (a -> m b) -> Matrix v a -> m (Matrix v b)
mapM f m@(Matrix r c _ _ _) = liftM (fromVector (r,c)) . G.mapM f . flatten $ m
mapM_ :: (G.Vector v a, Monad m) => (a -> m b) -> Matrix v a -> m ()
mapM_ f = G.mapM_ f . flatten
forM :: (G.Vector v a, G.Vector v b, Monad m) => Matrix v a -> (a -> m b) -> m (Matrix v b)
forM = flip Data.Matrix.Generic.Base.mapM
forM_ :: (G.Vector v a, Monad m) => Matrix v a -> (a -> m b) -> m ()
forM_ = flip Data.Matrix.Generic.Base.mapM_
generate :: G.Vector v a => (Int, Int) -> ((Int, Int) -> a) -> Matrix v a
generate (r,c) f = fromVector (r,c) . G.generate (r*c) $ \i -> f (i `div` c, i `mod` c)