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diff --git a/packages/base/src/Data/Packed/Internal/Matrix.hs b/packages/base/src/Data/Packed/Internal/Matrix.hs
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+{-# LANGUAGE ForeignFunctionInterface #-}
+{-# LANGUAGE FlexibleContexts         #-}
+{-# LANGUAGE FlexibleInstances        #-}
+{-# LANGUAGE BangPatterns             #-}
+
+-- |
+-- Module      :  Data.Packed.Internal.Matrix
+-- Copyright   :  (c) Alberto Ruiz 2007
+-- License     :  BSD3
+-- Maintainer  :  Alberto Ruiz
+-- Stability   :  provisional
+--
+-- Internal matrix representation
+--
+
+module Data.Packed.Internal.Matrix(
+    Matrix(..), rows, cols, cdat, fdat,
+    MatrixOrder(..), orderOf,
+    createMatrix, mat,
+    cmat, fmat,
+    toLists, flatten, reshape,
+    Element(..),
+    trans,
+    fromRows, toRows, fromColumns, toColumns,
+    matrixFromVector,
+    subMatrix,
+    liftMatrix, liftMatrix2,
+    (@@>), atM',
+    singleton,
+    emptyM,
+    size, shSize, conformVs, conformMs, conformVTo, conformMTo
+) where
+
+import Data.Packed.Internal.Common
+import Data.Packed.Internal.Signatures
+import Data.Packed.Internal.Vector
+
+import Foreign.Marshal.Alloc(alloca, free)
+import Foreign.Marshal.Array(newArray)
+import Foreign.Ptr(Ptr, castPtr)
+import Foreign.Storable(Storable, peekElemOff, pokeElemOff, poke, sizeOf)
+import Data.Complex(Complex)
+import Foreign.C.Types
+import System.IO.Unsafe(unsafePerformIO)
+import Control.DeepSeq
+
+-----------------------------------------------------------------
+
+{- Design considerations for the Matrix Type
+   -----------------------------------------
+
+- we must easily handle both row major and column major order,
+  for bindings to LAPACK and GSL/C
+
+- we'd like to simplify redundant matrix transposes:
+   - Some of them arise from the order requirements of some functions
+   - some functions (matrix product) admit transposed arguments
+
+- maybe we don't really need this kind of simplification:
+   - more complex code
+   - some computational overhead
+   - only appreciable gain in code with a lot of redundant transpositions
+     and cheap matrix computations
+
+- we could carry both the matrix and its (lazily computed) transpose.
+  This may save some transpositions, but it is necessary to keep track of the
+  data which is actually computed to be used by functions like the matrix product
+  which admit both orders.
+
+- but if we need the transposed data and it is not in the structure, we must make
+  sure that we touch the same foreignptr that is used in the computation.
+
+- a reasonable solution is using two constructors for a matrix. Transposition just
+  "flips" the constructor. Actual data transposition is not done if followed by a
+  matrix product or another transpose.
+
+-}
+
+data MatrixOrder = RowMajor | ColumnMajor deriving (Show,Eq)
+
+transOrder RowMajor = ColumnMajor
+transOrder ColumnMajor = RowMajor
+{- | Matrix representation suitable for GSL and LAPACK computations.
+
+The elements are stored in a continuous memory array.
+
+-}
+
+data Matrix t = Matrix { irows :: {-# UNPACK #-} !Int
+                       , icols :: {-# UNPACK #-} !Int
+                       , xdat :: {-# UNPACK #-} !(Vector t)
+                       , order :: !MatrixOrder }
+-- RowMajor: preferred by C, fdat may require a transposition
+-- ColumnMajor: preferred by LAPACK, cdat may require a transposition
+
+cdat = xdat
+fdat = xdat
+
+rows :: Matrix t -> Int
+rows = irows
+
+cols :: Matrix t -> Int
+cols = icols
+
+orderOf :: Matrix t -> MatrixOrder
+orderOf = order
+
+
+-- | Matrix transpose.
+trans :: Matrix t -> Matrix t
+trans Matrix {irows = r, icols = c, xdat = d, order = o } = Matrix { irows = c, icols = r, xdat = d, order = transOrder o}
+
+cmat :: (Element t) => Matrix t -> Matrix t
+cmat m@Matrix{order = RowMajor} = m
+cmat Matrix {irows = r, icols = c, xdat = d, order = ColumnMajor } = Matrix { irows = r, icols = c, xdat = transdata r d c, order = RowMajor}
+
+fmat :: (Element t) => Matrix t -> Matrix t
+fmat m@Matrix{order = ColumnMajor} = m
+fmat Matrix {irows = r, icols = c, xdat = d, order = RowMajor } = Matrix { irows = r, icols = c, xdat = transdata c d r, order = ColumnMajor}
+
+-- C-Haskell matrix adapter
+-- mat :: Adapt (CInt -> CInt -> Ptr t -> r) (Matrix t) r
+
+mat :: (Storable t) => Matrix t -> (((CInt -> CInt -> Ptr t -> t1) -> t1) -> IO b) -> IO b
+mat a f =
+    unsafeWith (xdat a) $ \p -> do
+        let m g = do
+            g (fi (rows a)) (fi (cols a)) p
+        f m
+
+{- | Creates a vector by concatenation of rows. If the matrix is ColumnMajor, this operation requires a transpose.
+
+>>> flatten (ident 3)
+fromList [1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0]
+
+-}
+flatten :: Element t => Matrix t -> Vector t
+flatten = xdat . cmat
+
+{-
+type Mt t s = Int -> Int -> Ptr t -> s
+
+infixr 6 ::>
+type t ::> s = Mt t s
+-}
+
+-- | the inverse of 'Data.Packed.Matrix.fromLists'
+toLists :: (Element t) => Matrix t -> [[t]]
+toLists m = splitEvery (cols m) . toList . flatten $ m
+
+-- | Create a matrix from a list of vectors.
+-- All vectors must have the same dimension,
+-- or dimension 1, which is are automatically expanded.
+fromRows :: Element t => [Vector t] -> Matrix t
+fromRows [] = emptyM 0 0
+fromRows vs = case compatdim (map dim vs) of
+    Nothing -> error $ "fromRows expects vectors with equal sizes (or singletons), given: " ++ show (map dim vs)
+    Just 0  -> emptyM r 0
+    Just c  -> matrixFromVector RowMajor r c . vjoin . map (adapt c) $ vs
+  where
+    r = length vs
+    adapt c v
+        | c == 0 = fromList[]
+        | dim v == c = v
+        | otherwise = constantD (v@>0) c
+
+-- | extracts the rows of a matrix as a list of vectors
+toRows :: Element t => Matrix t -> [Vector t]
+toRows m
+    | c == 0    = replicate r (fromList[])
+    | otherwise = toRows' 0
+  where
+    v = flatten m
+    r = rows m
+    c = cols m
+    toRows' k | k == r*c  = []
+              | otherwise = subVector k c v : toRows' (k+c)
+
+-- | Creates a matrix from a list of vectors, as columns
+fromColumns :: Element t => [Vector t] -> Matrix t
+fromColumns m = trans . fromRows $ m
+
+-- | Creates a list of vectors from the columns of a matrix
+toColumns :: Element t => Matrix t -> [Vector t]
+toColumns m = toRows . trans $ m
+
+-- | Reads a matrix position.
+(@@>) :: Storable t => Matrix t -> (Int,Int) -> t
+infixl 9 @@>
+m@Matrix {irows = r, icols = c} @@> (i,j)
+    | safe      = if i<0 || i>=r || j<0 || j>=c
+                    then error "matrix indexing out of range"
+                    else atM' m i j
+    | otherwise = atM' m i j
+{-# INLINE (@@>) #-}
+
+--  Unsafe matrix access without range checking
+atM' Matrix {icols = c, xdat = v, order = RowMajor} i j = v `at'` (i*c+j)
+atM' Matrix {irows = r, xdat = v, order = ColumnMajor} i j = v `at'` (j*r+i)
+{-# INLINE atM' #-}
+
+------------------------------------------------------------------
+
+matrixFromVector o r c v
+    | r * c == dim v = m
+    | otherwise = error $ "can't reshape vector dim = "++ show (dim v)++" to matrix " ++ shSize m
+  where
+    m = Matrix { irows = r, icols = c, xdat = v, order = o }
+
+-- allocates memory for a new matrix
+createMatrix :: (Storable a) => MatrixOrder -> Int -> Int -> IO (Matrix a)
+createMatrix ord r c = do
+    p <- createVector (r*c)
+    return (matrixFromVector ord r c p)
+
+{- | Creates a matrix from a vector by grouping the elements in rows with the desired number of columns. (GNU-Octave groups by columns. To do it you can define @reshapeF r = trans . reshape r@
+where r is the desired number of rows.)
+
+>>> reshape 4 (fromList [1..12])
+(3><4)
+ [ 1.0,  2.0,  3.0,  4.0
+ , 5.0,  6.0,  7.0,  8.0
+ , 9.0, 10.0, 11.0, 12.0 ]
+
+-}
+reshape :: Storable t => Int -> Vector t -> Matrix t
+reshape 0 v = matrixFromVector RowMajor 0 0 v
+reshape c v = matrixFromVector RowMajor (dim v `div` c) c v
+
+singleton x = reshape 1 (fromList [x])
+
+-- | application of a vector function on the flattened matrix elements
+liftMatrix :: (Storable a, Storable b) => (Vector a -> Vector b) -> Matrix a -> Matrix b
+liftMatrix f Matrix { irows = r, icols = c, xdat = d, order = o } = matrixFromVector o r c (f d)
+
+-- | application of a vector function on the flattened matrices elements
+liftMatrix2 :: (Element t, Element a, Element b) => (Vector a -> Vector b -> Vector t) -> Matrix a -> Matrix b -> Matrix t
+liftMatrix2 f m1 m2
+    | not (compat m1 m2) = error "nonconformant matrices in liftMatrix2"
+    | otherwise = case orderOf m1 of
+        RowMajor    -> matrixFromVector RowMajor    (rows m1) (cols m1) (f (xdat m1) (flatten m2))
+        ColumnMajor -> matrixFromVector ColumnMajor (rows m1) (cols m1) (f (xdat m1) ((xdat.fmat) m2))
+
+
+compat :: Matrix a -> Matrix b -> Bool
+compat m1 m2 = rows m1 == rows m2 && cols m1 == cols m2
+
+------------------------------------------------------------------
+
+{- | Supported matrix elements.
+
+    This class provides optimized internal
+    operations for selected element types.
+    It provides unoptimised defaults for any 'Storable' type,
+    so you can create instances simply as:
+    @instance Element Foo@.
+-}
+class (Storable a) => Element a where
+    subMatrixD :: (Int,Int) -- ^ (r0,c0) starting position 
+               -> (Int,Int) -- ^ (rt,ct) dimensions of submatrix
+               -> Matrix a -> Matrix a
+    subMatrixD = subMatrix'
+    transdata :: Int -> Vector a -> Int -> Vector a
+    transdata = transdataP -- transdata'
+    constantD  :: a -> Int -> Vector a
+    constantD = constantP -- constant'
+
+
+instance Element Float where
+    transdata  = transdataAux ctransF
+    constantD  = constantAux cconstantF
+
+instance Element Double where
+    transdata  = transdataAux ctransR
+    constantD  = constantAux cconstantR
+
+instance Element (Complex Float) where
+    transdata  = transdataAux ctransQ
+    constantD  = constantAux cconstantQ
+
+instance Element (Complex Double) where
+    transdata  = transdataAux ctransC
+    constantD  = constantAux cconstantC
+
+-------------------------------------------------------------------
+
+transdataAux fun c1 d c2 =
+    if noneed
+        then d
+        else unsafePerformIO $ do
+            v <- createVector (dim d)
+            unsafeWith d $ \pd ->
+                unsafeWith v $ \pv ->
+                    fun (fi r1) (fi c1) pd (fi r2) (fi c2) pv // check "transdataAux"
+            return v
+  where r1 = dim d `div` c1
+        r2 = dim d `div` c2
+        noneed = dim d == 0 || r1 == 1 || c1 == 1
+
+transdataP :: Storable a => Int -> Vector a -> Int -> Vector a
+transdataP c1 d c2 =
+    if noneed
+       then d
+       else unsafePerformIO $ do
+          v <- createVector (dim d)
+          unsafeWith d $ \pd ->
+              unsafeWith v $ \pv ->
+                  ctransP (fi r1) (fi c1) (castPtr pd) (fi sz) (fi r2) (fi c2) (castPtr pv) (fi sz) // check "transdataP"
+          return v
+   where r1 = dim d `div` c1
+         r2 = dim d `div` c2
+         sz = sizeOf (d @> 0)
+         noneed = dim d == 0 || r1 == 1 || c1 == 1
+
+foreign import ccall unsafe "transF" ctransF :: TFMFM
+foreign import ccall unsafe "transR" ctransR :: TMM
+foreign import ccall unsafe "transQ" ctransQ :: TQMQM
+foreign import ccall unsafe "transC" ctransC :: TCMCM
+foreign import ccall unsafe "transP" ctransP :: CInt -> CInt -> Ptr () -> CInt -> CInt -> CInt -> Ptr () -> CInt -> IO CInt
+
+----------------------------------------------------------------------
+
+constantAux fun x n = unsafePerformIO $ do
+    v <- createVector n
+    px <- newArray [x]
+    app1 (fun px) vec v "constantAux"
+    free px
+    return v
+
+foreign import ccall unsafe "constantF" cconstantF :: Ptr Float -> TF
+
+foreign import ccall unsafe "constantR" cconstantR :: Ptr Double -> TV
+
+foreign import ccall unsafe "constantQ" cconstantQ :: Ptr (Complex Float) -> TQV
+
+foreign import ccall unsafe "constantC" cconstantC :: Ptr (Complex Double) -> TCV
+
+constantP :: Storable a => a -> Int -> Vector a
+constantP a n = unsafePerformIO $ do
+    let sz = sizeOf a
+    v <- createVector n
+    unsafeWith v $ \p -> do
+       alloca $ \k -> do
+                      poke k a
+                      cconstantP (castPtr k) (fi n) (castPtr p) (fi sz) // check "constantP"
+    return v
+foreign import ccall unsafe "constantP" cconstantP :: Ptr () -> CInt -> Ptr () -> CInt -> IO CInt
+
+----------------------------------------------------------------------
+
+-- | Extracts a submatrix from a matrix.
+subMatrix :: Element a
+          => (Int,Int) -- ^ (r0,c0) starting position 
+          -> (Int,Int) -- ^ (rt,ct) dimensions of submatrix
+          -> Matrix a -- ^ input matrix
+          -> Matrix a -- ^ result
+subMatrix (r0,c0) (rt,ct) m
+    | 0 <= r0 && 0 <= rt && r0+rt <= (rows m) &&
+      0 <= c0 && 0 <= ct && c0+ct <= (cols m) = subMatrixD (r0,c0) (rt,ct) m
+    | otherwise = error $ "wrong subMatrix "++
+                          show ((r0,c0),(rt,ct))++" of "++show(rows m)++"x"++ show (cols m)
+
+subMatrix'' (r0,c0) (rt,ct) c v = unsafePerformIO $ do
+    w <- createVector (rt*ct)
+    unsafeWith v $ \p ->
+        unsafeWith w $ \q -> do
+            let go (-1) _ = return ()
+                go !i (-1) = go (i-1) (ct-1)
+                go !i !j = do x <- peekElemOff p ((i+r0)*c+j+c0)
+                              pokeElemOff      q (i*ct+j) x
+                              go i (j-1)
+            go (rt-1) (ct-1)
+    return w
+
+subMatrix' (r0,c0) (rt,ct) (Matrix { icols = c, xdat = v, order = RowMajor}) = Matrix rt ct (subMatrix'' (r0,c0) (rt,ct) c v) RowMajor
+subMatrix' (r0,c0) (rt,ct) m = trans $ subMatrix' (c0,r0) (ct,rt) (trans m)
+
+--------------------------------------------------------------------------
+
+maxZ xs = if minimum xs == 0 then 0 else maximum xs
+
+conformMs ms = map (conformMTo (r,c)) ms
+  where
+    r = maxZ (map rows ms)
+    c = maxZ (map cols ms)
+    
+
+conformVs vs = map (conformVTo n) vs
+  where
+    n = maxZ (map dim vs)
+
+conformMTo (r,c) m
+    | size m == (r,c) = m
+    | size m == (1,1) = matrixFromVector RowMajor r c (constantD (m@@>(0,0)) (r*c))
+    | size m == (r,1) = repCols c m
+    | size m == (1,c) = repRows r m
+    | otherwise = error $ "matrix " ++ shSize m ++ " cannot be expanded to (" ++ show r ++ "><"++ show c ++")"
+
+conformVTo n v
+    | dim v == n = v
+    | dim v == 1 = constantD (v@>0) n
+    | otherwise = error $ "vector of dim=" ++ show (dim v) ++ " cannot be expanded to dim=" ++ show n
+
+repRows n x = fromRows (replicate n (flatten x))
+repCols n x = fromColumns (replicate n (flatten x))
+
+size m = (rows m, cols m)
+
+shSize m = "(" ++ show (rows m) ++"><"++ show (cols m)++")"
+
+emptyM r c = matrixFromVector RowMajor r c (fromList[])
+
+----------------------------------------------------------------------
+
+instance (Storable t, NFData t) => NFData (Matrix t)
+  where
+    rnf m | d > 0     = rnf (v @> 0)
+          | otherwise = ()
+      where
+        d = dim v
+        v = xdat m
+