module Data.Matrix.Generic.Base
( rows
, cols
, (!)
, matrix
, flatten
, fromVector
, toRows
, toList
, toLists
, tr
, subMatrix
, ident
, diag
, diagRect
, fromBlocks
, isSymmetric
) 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
(!) :: 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
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 :: 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
toLists :: G.Vector v a => Matrix v a -> [[a]]
toLists = map G.toList . toRows
subMatrix :: G.Vector v a => (Int, Int) -> (Int, Int) -> Matrix v a -> Matrix v a
subMatrix (ri, rj) (ci, cj) (Matrix _ n tda offset vec) =
Matrix m' n' tda offset' vec
where
m' = rj ri + 1
n' = cj ci + 1
offset' = offset + ri * n + ci
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
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 . map ((maximum *** sum) . unzip . 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)