Data.Packed -> base (I)

4 files changed, 1123 insertions, 0 deletions

diff --git a/packages/base/src/Data/Packed/Internal/Common.hs b/packages/base/src/Data/Packed/Internal/Common.hs
new file mode 100644
index 0000000..615bbdf
--- /dev/null
+++ b/packages/base/src/Data/Packed/Internal/Common.hs
@@ -0,0 +1,160 @@
+{-# LANGUAGE CPP #-}
+-- |
+-- Module      :  Data.Packed.Internal.Common
+-- Copyright   :  (c) Alberto Ruiz 2007
+-- License     :  BSD3
+-- Maintainer  :  Alberto Ruiz
+-- Stability   :  provisional
+--
+--
+-- Development utilities.
+--
+
+
+module Data.Packed.Internal.Common(
+  Adapt,
+  app1, app2, app3, app4,
+  app5, app6, app7, app8, app9, app10,
+  (//), check, mbCatch,
+  splitEvery, common, compatdim,
+  fi,
+  table,
+  finit
+) where
+
+import Control.Monad(when)
+import Foreign.C.Types
+import Foreign.Storable.Complex()
+import Data.List(transpose,intersperse)
+import Control.Exception as E
+
+-- | @splitEvery 3 [1..9] == [[1,2,3],[4,5,6],[7,8,9]]@
+splitEvery :: Int -> [a] -> [[a]]
+splitEvery _ [] = []
+splitEvery k l = take k l : splitEvery k (drop k l)
+
+-- | obtains the common value of a property of a list
+common :: (Eq a) => (b->a) -> [b] -> Maybe a
+common f = commonval . map f where
+    commonval :: (Eq a) => [a] -> Maybe a
+    commonval [] = Nothing
+    commonval [a] = Just a
+    commonval (a:b:xs) = if a==b then commonval (b:xs) else Nothing
+
+-- | common value with \"adaptable\" 1
+compatdim :: [Int] -> Maybe Int
+compatdim [] = Nothing
+compatdim [a] = Just a
+compatdim (a:b:xs)
+    | a==b = compatdim (b:xs)
+    | a==1 = compatdim (b:xs)
+    | b==1 = compatdim (a:xs)
+    | otherwise = Nothing
+
+-- | Formatting tool
+table :: String -> [[String]] -> String
+table sep as = unlines . map unwords' $ transpose mtp where 
+    mt = transpose as
+    longs = map (maximum . map length) mt
+    mtp = zipWith (\a b -> map (pad a) b) longs mt
+    pad n str = replicate (n - length str) ' ' ++ str
+    unwords' = concat . intersperse sep
+
+-- | postfix function application (@flip ($)@)
+(//) :: x -> (x -> y) -> y
+infixl 0 //
+(//) = flip ($)
+
+-- | specialized fromIntegral
+fi :: Int -> CInt
+fi = fromIntegral
+
+-- hmm..
+ww2 w1 o1 w2 o2 f = w1 o1 $ w2 o2 . f
+ww3 w1 o1 w2 o2 w3 o3 f = w1 o1 $ ww2 w2 o2 w3 o3 . f
+ww4 w1 o1 w2 o2 w3 o3 w4 o4 f = w1 o1 $ ww3 w2 o2 w3 o3 w4 o4 . f
+ww5 w1 o1 w2 o2 w3 o3 w4 o4 w5 o5 f = w1 o1 $ ww4 w2 o2 w3 o3 w4 o4 w5 o5 . f
+ww6 w1 o1 w2 o2 w3 o3 w4 o4 w5 o5 w6 o6 f = w1 o1 $ ww5 w2 o2 w3 o3 w4 o4 w5 o5 w6 o6 . f
+ww7 w1 o1 w2 o2 w3 o3 w4 o4 w5 o5 w6 o6 w7 o7 f = w1 o1 $ ww6 w2 o2 w3 o3 w4 o4 w5 o5 w6 o6 w7 o7 . f
+ww8 w1 o1 w2 o2 w3 o3 w4 o4 w5 o5 w6 o6 w7 o7 w8 o8 f = w1 o1 $ ww7 w2 o2 w3 o3 w4 o4 w5 o5 w6 o6 w7 o7 w8 o8 . f
+ww9 w1 o1 w2 o2 w3 o3 w4 o4 w5 o5 w6 o6 w7 o7 w8 o8 w9 o9 f = w1 o1 $ ww8 w2 o2 w3 o3 w4 o4 w5 o5 w6 o6 w7 o7 w8 o8 w9 o9 . f
+ww10 w1 o1 w2 o2 w3 o3 w4 o4 w5 o5 w6 o6 w7 o7 w8 o8 w9 o9 w10 o10 f = w1 o1 $ ww9 w2 o2 w3 o3 w4 o4 w5 o5 w6 o6 w7 o7 w8 o8 w9 o9 w10 o10 . f
+
+type Adapt f t r = t -> ((f -> r) -> IO()) -> IO()
+
+type Adapt1 f t1 = Adapt f t1 (IO CInt) -> t1 -> String -> IO()
+type Adapt2 f t1 r1 t2 = Adapt f t1 r1 -> t1 -> Adapt1 r1 t2
+type Adapt3 f t1 r1 t2 r2 t3 = Adapt f t1 r1 -> t1 -> Adapt2 r1 t2 r2 t3
+type Adapt4 f t1 r1 t2 r2 t3 r3 t4 = Adapt f t1 r1 -> t1 -> Adapt3 r1 t2 r2 t3 r3 t4
+type Adapt5 f t1 r1 t2 r2 t3 r3 t4 r4 t5 = Adapt f t1 r1 -> t1 -> Adapt4 r1 t2 r2 t3 r3 t4 r4 t5
+type Adapt6 f t1 r1 t2 r2 t3 r3 t4 r4 t5 r5 t6 = Adapt f t1 r1 -> t1 -> Adapt5 r1 t2 r2 t3 r3 t4 r4 t5 r5 t6
+type Adapt7 f t1 r1 t2 r2 t3 r3 t4 r4 t5 r5 t6 r6 t7 = Adapt f t1 r1 -> t1 -> Adapt6 r1 t2 r2 t3 r3 t4 r4 t5 r5 t6 r6 t7
+type Adapt8 f t1 r1 t2 r2 t3 r3 t4 r4 t5 r5 t6 r6 t7 r7 t8 = Adapt f t1 r1 -> t1 -> Adapt7 r1 t2 r2 t3 r3 t4 r4 t5 r5 t6 r6 t7 r7 t8
+type Adapt9 f t1 r1 t2 r2 t3 r3 t4 r4 t5 r5 t6 r6 t7 r7 t8 r8 t9 = Adapt f t1 r1 -> t1 -> Adapt8 r1 t2 r2 t3 r3 t4 r4 t5 r5 t6 r6 t7 r7 t8 r8 t9
+type Adapt10 f t1 r1 t2 r2 t3 r3 t4 r4 t5 r5 t6 r6 t7 r7 t8 r8 t9 r9 t10 = Adapt f t1 r1 -> t1 -> Adapt9 r1 t2 r2 t3 r3 t4 r4 t5 r5 t6 r6 t7 r7 t8 r8 t9 r9 t10
+
+app1 :: f -> Adapt1 f t1
+app2 :: f -> Adapt2 f t1 r1 t2
+app3 :: f -> Adapt3 f t1 r1 t2 r2 t3
+app4 :: f -> Adapt4 f t1 r1 t2 r2 t3 r3 t4
+app5 :: f -> Adapt5 f t1 r1 t2 r2 t3 r3 t4 r4 t5
+app6 :: f -> Adapt6 f t1 r1 t2 r2 t3 r3 t4 r4 t5 r5 t6
+app7 :: f -> Adapt7 f t1 r1 t2 r2 t3 r3 t4 r4 t5 r5 t6 r6 t7
+app8 :: f -> Adapt8 f t1 r1 t2 r2 t3 r3 t4 r4 t5 r5 t6 r6 t7 r7 t8
+app9 :: f -> Adapt9 f t1 r1 t2 r2 t3 r3 t4 r4 t5 r5 t6 r6 t7 r7 t8 r8 t9
+app10 :: f -> Adapt10 f t1 r1 t2 r2 t3 r3 t4 r4 t5 r5 t6 r6 t7 r7 t8 r8 t9 r9 t10
+
+app1 f w1 o1 s = w1 o1 $ \a1 -> f // a1 // check s
+app2 f w1 o1 w2 o2 s = ww2 w1 o1 w2 o2 $ \a1 a2 -> f // a1 // a2 // check s
+app3 f w1 o1 w2 o2 w3 o3 s = ww3 w1 o1 w2 o2 w3 o3 $
+     \a1 a2 a3 -> f // a1 // a2 // a3 // check s
+app4 f w1 o1 w2 o2 w3 o3 w4 o4 s = ww4 w1 o1 w2 o2 w3 o3 w4 o4 $
+     \a1 a2 a3 a4 -> f // a1 // a2 // a3 // a4 // check s
+app5 f w1 o1 w2 o2 w3 o3 w4 o4 w5 o5 s = ww5 w1 o1 w2 o2 w3 o3 w4 o4 w5 o5 $
+     \a1 a2 a3 a4 a5 -> f // a1 // a2 // a3 // a4 // a5 // check s
+app6 f w1 o1 w2 o2 w3 o3 w4 o4 w5 o5 w6 o6 s = ww6 w1 o1 w2 o2 w3 o3 w4 o4 w5 o5 w6 o6 $
+     \a1 a2 a3 a4 a5 a6 -> f // a1 // a2 // a3 // a4 // a5 // a6 // check s
+app7 f w1 o1 w2 o2 w3 o3 w4 o4 w5 o5 w6 o6 w7 o7 s = ww7 w1 o1 w2 o2 w3 o3 w4 o4 w5 o5 w6 o6 w7 o7 $
+     \a1 a2 a3 a4 a5 a6 a7 -> f // a1 // a2 // a3 // a4 // a5 // a6 // a7 // check s
+app8 f w1 o1 w2 o2 w3 o3 w4 o4 w5 o5 w6 o6 w7 o7 w8 o8 s = ww8 w1 o1 w2 o2 w3 o3 w4 o4 w5 o5 w6 o6 w7 o7 w8 o8 $
+     \a1 a2 a3 a4 a5 a6 a7 a8 -> f // a1 // a2 // a3 // a4 // a5 // a6 // a7 // a8 // check s
+app9 f w1 o1 w2 o2 w3 o3 w4 o4 w5 o5 w6 o6 w7 o7 w8 o8 w9 o9 s = ww9 w1 o1 w2 o2 w3 o3 w4 o4 w5 o5 w6 o6 w7 o7 w8 o8 w9 o9 $
+     \a1 a2 a3 a4 a5 a6 a7 a8 a9 -> f // a1 // a2 // a3 // a4 // a5 // a6 // a7 // a8 // a9 // check s
+app10 f w1 o1 w2 o2 w3 o3 w4 o4 w5 o5 w6 o6 w7 o7 w8 o8 w9 o9 w10 o10 s = ww10 w1 o1 w2 o2 w3 o3 w4 o4 w5 o5 w6 o6 w7 o7 w8 o8 w9 o9 w10 o10 $
+     \a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 -> f // a1 // a2 // a3 // a4 // a5 // a6 // a7 // a8 // a9 // a10 // check s
+
+
+
+-- GSL error codes are <= 1024
+-- | error codes for the auxiliary functions required by the wrappers
+errorCode :: CInt -> String
+errorCode 2000 = "bad size"
+errorCode 2001 = "bad function code"
+errorCode 2002 = "memory problem"
+errorCode 2003 = "bad file"
+errorCode 2004 = "singular"
+errorCode 2005 = "didn't converge"
+errorCode 2006 = "the input matrix is not positive definite"
+errorCode 2007 = "not yet supported in this OS"
+errorCode n    = "code "++show n
+
+
+-- | clear the fpu
+foreign import ccall unsafe "asm_finit" finit :: IO ()
+
+-- | check the error code
+check :: String -> IO CInt -> IO ()
+check msg f = do
+#if FINIT
+    finit
+#endif
+    err <- f
+    when (err/=0) $ error (msg++": "++errorCode err)
+    return ()
+
+-- | Error capture and conversion to Maybe
+mbCatch :: IO x -> IO (Maybe x)
+mbCatch act = E.catch (Just `fmap` act) f
+    where f :: SomeException -> IO (Maybe x)
+          f _ = return Nothing
+
diff --git a/packages/base/src/Data/Packed/Internal/Matrix.hs b/packages/base/src/Data/Packed/Internal/Matrix.hs
new file mode 100644
index 0000000..9b831cc
--- /dev/null
+++ b/packages/base/src/Data/Packed/Internal/Matrix.hs
@@ -0,0 +1,422 @@
+{-# 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
+
diff --git a/packages/base/src/Data/Packed/Internal/Signatures.hs b/packages/base/src/Data/Packed/Internal/Signatures.hs
new file mode 100644
index 0000000..acc3070
--- /dev/null
+++ b/packages/base/src/Data/Packed/Internal/Signatures.hs
@@ -0,0 +1,70 @@
+-- |
+-- Module      :  Data.Packed.Internal.Signatures
+-- Copyright   :  (c) Alberto Ruiz 2009
+-- License     :  BSD3
+-- Maintainer  :  Alberto Ruiz
+-- Stability   :  provisional
+--
+-- Signatures of the C functions.
+--
+
+
+module Data.Packed.Internal.Signatures where
+
+import Foreign.Ptr(Ptr)
+import Data.Complex(Complex)
+import Foreign.C.Types(CInt)
+
+type PF = Ptr Float                             --
+type PD = Ptr Double                            --
+type PQ = Ptr (Complex Float)                   --
+type PC = Ptr (Complex Double)                  --
+type TF = CInt -> PF -> IO CInt                 --
+type TFF = CInt -> PF -> TF                     --
+type TFV = CInt -> PF -> TV                     --
+type TVF = CInt -> PD -> TF                     --
+type TFFF = CInt -> PF -> TFF                   --
+type TV = CInt -> PD -> IO CInt                 --
+type TVV = CInt -> PD -> TV                     --
+type TVVV = CInt -> PD -> TVV                   --
+type TFM = CInt -> CInt -> PF -> IO CInt        --
+type TFMFM =  CInt -> CInt -> PF -> TFM         --
+type TFMFMFM =  CInt -> CInt -> PF -> TFMFM     --
+type TM = CInt -> CInt -> PD -> IO CInt         --
+type TMM =  CInt -> CInt -> PD -> TM            --
+type TVMM = CInt -> PD -> TMM                   --
+type TMVMM = CInt -> CInt -> PD -> TVMM         --
+type TMMM =  CInt -> CInt -> PD -> TMM          --
+type TVM = CInt -> PD -> TM                     --
+type TVVM = CInt -> PD -> TVM                   --
+type TMV = CInt -> CInt -> PD -> TV             --
+type TMMV = CInt -> CInt -> PD -> TMV           --
+type TMVM = CInt -> CInt -> PD -> TVM           --
+type TMMVM = CInt -> CInt -> PD -> TMVM         --
+type TCM = CInt -> CInt -> PC -> IO CInt        --
+type TCVCM = CInt -> PC -> TCM                  --
+type TCMCVCM = CInt -> CInt -> PC -> TCVCM      --
+type TMCMCVCM = CInt -> CInt -> PD -> TCMCVCM   --
+type TCMCMCVCM = CInt -> CInt -> PC -> TCMCVCM  --
+type TCMCM = CInt -> CInt -> PC -> TCM          --
+type TVCM = CInt -> PD -> TCM                   --
+type TCMVCM = CInt -> CInt -> PC -> TVCM        --
+type TCMCMVCM = CInt -> CInt -> PC -> TCMVCM    --
+type TCMCMCM = CInt -> CInt -> PC -> TCMCM      --
+type TCV = CInt -> PC -> IO CInt                --
+type TCVCV = CInt -> PC -> TCV                  --
+type TCVCVCV = CInt -> PC -> TCVCV              --
+type TCVV = CInt -> PC -> TV                    --
+type TQV = CInt -> PQ -> IO CInt                --
+type TQVQV = CInt -> PQ -> TQV                  --
+type TQVQVQV = CInt -> PQ -> TQVQV              --
+type TQVF = CInt -> PQ -> TF                    --
+type TQM = CInt -> CInt -> PQ -> IO CInt        --
+type TQMQM = CInt -> CInt -> PQ -> TQM          --
+type TQMQMQM = CInt -> CInt -> PQ -> TQMQM      --
+type TCMCV = CInt -> CInt -> PC -> TCV          --
+type TVCV = CInt -> PD -> TCV                   --
+type TCVM = CInt -> PC -> TM                    --
+type TMCVM = CInt -> CInt -> PD -> TCVM         --
+type TMMCVM = CInt -> CInt -> PD -> TMCVM       --
+
diff --git a/packages/base/src/Data/Packed/Internal/Vector.hs b/packages/base/src/Data/Packed/Internal/Vector.hs
new file mode 100644
index 0000000..d0bc143
--- /dev/null
+++ b/packages/base/src/Data/Packed/Internal/Vector.hs
@@ -0,0 +1,471 @@
+{-# LANGUAGE MagicHash, CPP, UnboxedTuples, BangPatterns, FlexibleContexts #-}
+-- |
+-- Module      :  Data.Packed.Internal.Vector
+-- Copyright   :  (c) Alberto Ruiz 2007
+-- License     :  BSD3
+-- Maintainer  :  Alberto Ruiz
+-- Stability   :  provisional
+--
+-- Vector implementation
+--
+--------------------------------------------------------------------------------
+
+module Data.Packed.Internal.Vector (
+    Vector, dim,
+    fromList, toList, (|>),
+    vjoin, (@>), safe, at, at', subVector, takesV,
+    mapVector, mapVectorWithIndex, zipVectorWith, unzipVectorWith,
+    mapVectorM, mapVectorM_, mapVectorWithIndexM, mapVectorWithIndexM_,
+    foldVector, foldVectorG, foldLoop, foldVectorWithIndex,
+    createVector, vec,
+    asComplex, asReal, float2DoubleV, double2FloatV,
+    stepF, stepD, condF, condD,
+    conjugateQ, conjugateC,
+    cloneVector,
+    unsafeToForeignPtr,
+    unsafeFromForeignPtr,
+    unsafeWith
+) where
+
+import Data.Packed.Internal.Common
+import Data.Packed.Internal.Signatures
+import Foreign.Marshal.Array(peekArray, copyArray, advancePtr)
+import Foreign.ForeignPtr(ForeignPtr, castForeignPtr)
+import Foreign.Ptr(Ptr)
+import Foreign.Storable(Storable, peekElemOff, pokeElemOff, sizeOf)
+import Foreign.C.Types
+import Data.Complex
+import Control.Monad(when)
+import System.IO.Unsafe(unsafePerformIO)
+
+#if __GLASGOW_HASKELL__ >= 605
+import GHC.ForeignPtr           (mallocPlainForeignPtrBytes)
+#else
+import Foreign.ForeignPtr       (mallocForeignPtrBytes)
+#endif
+
+import GHC.Base
+#if __GLASGOW_HASKELL__ < 612
+import GHC.IOBase hiding (liftIO)
+#endif
+
+import qualified Data.Vector.Storable as Vector
+import Data.Vector.Storable(Vector,
+                            fromList,
+                            unsafeToForeignPtr,
+                            unsafeFromForeignPtr,
+                            unsafeWith)
+
+
+-- | Number of elements
+dim :: (Storable t) => Vector t -> Int
+dim = Vector.length
+
+
+-- C-Haskell vector adapter
+-- vec :: Adapt (CInt -> Ptr t -> r) (Vector t) r
+vec :: (Storable t) => Vector t -> (((CInt -> Ptr t -> t1) -> t1) -> IO b) -> IO b
+vec x f = unsafeWith x $ \p -> do
+    let v g = do
+        g (fi $ dim x) p
+    f v
+{-# INLINE vec #-}
+
+
+-- allocates memory for a new vector
+createVector :: Storable a => Int -> IO (Vector a)
+createVector n = do
+    when (n < 0) $ error ("trying to createVector of negative dim: "++show n)
+    fp <- doMalloc undefined
+    return $ unsafeFromForeignPtr fp 0 n
+  where
+    --
+    -- Use the much cheaper Haskell heap allocated storage
+    -- for foreign pointer space we control
+    --
+    doMalloc :: Storable b => b -> IO (ForeignPtr b)
+    doMalloc dummy = do
+#if __GLASGOW_HASKELL__ >= 605
+        mallocPlainForeignPtrBytes (n * sizeOf dummy)
+#else
+        mallocForeignPtrBytes      (n * sizeOf dummy)
+#endif
+
+{- | creates a Vector from a list:
+
+@> fromList [2,3,5,7]
+4 |> [2.0,3.0,5.0,7.0]@
+
+-}
+
+safeRead v = inlinePerformIO . unsafeWith v
+{-# INLINE safeRead #-}
+
+inlinePerformIO :: IO a -> a
+inlinePerformIO (IO m) = case m realWorld# of (# _, r #) -> r
+{-# INLINE inlinePerformIO #-}
+
+{- | extracts the Vector elements to a list
+
+>>> toList (linspace 5 (1,10))
+[1.0,3.25,5.5,7.75,10.0]
+
+-}
+toList :: Storable a => Vector a -> [a]
+toList v = safeRead v $ peekArray (dim v)
+
+{- | Create a vector from a list of elements and explicit dimension. The input
+     list is explicitly truncated if it is too long, so it may safely
+     be used, for instance, with infinite lists.
+
+>>> 5 |> [1..]
+fromList [1.0,2.0,3.0,4.0,5.0]
+
+-}
+(|>) :: (Storable a) => Int -> [a] -> Vector a
+infixl 9 |>
+n |> l = if length l' == n
+            then fromList l'
+            else error "list too short for |>"
+  where l' = take n l
+
+
+-- | access to Vector elements without range checking
+at' :: Storable a => Vector a -> Int -> a
+at' v n = safeRead v $ flip peekElemOff n
+{-# INLINE at' #-}
+
+--
+-- turn off bounds checking with -funsafe at configure time.
+-- ghc will optimise away the salways true case at compile time.
+--
+#if defined(UNSAFE)
+safe :: Bool
+safe = False
+#else
+safe = True
+#endif
+
+-- | access to Vector elements with range checking.
+at :: Storable a => Vector a -> Int -> a
+at v n
+    | safe      = if n >= 0 && n < dim v
+                    then at' v n
+                    else error "vector index out of range"
+    | otherwise = at' v n
+{-# INLINE at #-}
+
+{- | takes a number of consecutive elements from a Vector
+
+>>> subVector 2 3 (fromList [1..10])
+fromList [3.0,4.0,5.0]
+
+-}
+subVector :: Storable t => Int       -- ^ index of the starting element
+                        -> Int       -- ^ number of elements to extract
+                        -> Vector t  -- ^ source
+                        -> Vector t  -- ^ result
+subVector = Vector.slice
+
+
+{- | Reads a vector position:
+
+>>> fromList [0..9] @> 7
+7.0
+
+-}
+(@>) :: Storable t => Vector t -> Int -> t
+infixl 9 @>
+(@>) = at
+
+
+{- | concatenate a list of vectors
+
+>>> vjoin [fromList [1..5::Double], konst 1 3]
+fromList [1.0,2.0,3.0,4.0,5.0,1.0,1.0,1.0]
+
+-}
+vjoin :: Storable t => [Vector t] -> Vector t
+vjoin [] = fromList []
+vjoin [v] = v
+vjoin as = unsafePerformIO $ do
+    let tot = sum (map dim as)
+    r <- createVector tot
+    unsafeWith r $ \ptr ->
+        joiner as tot ptr
+    return r
+  where joiner [] _ _ = return ()
+        joiner (v:cs) _ p = do
+            let n = dim v
+            unsafeWith v $ \pb -> copyArray p pb n
+            joiner cs 0 (advancePtr p n)
+
+
+{- | Extract consecutive subvectors of the given sizes.
+
+>>> takesV [3,4] (linspace 10 (1,10::Double))
+[fromList [1.0,2.0,3.0],fromList [4.0,5.0,6.0,7.0]]
+
+-}
+takesV :: Storable t => [Int] -> Vector t -> [Vector t]
+takesV ms w | sum ms > dim w = error $ "takesV " ++ show ms ++ " on dim = " ++ (show $ dim w)
+            | otherwise = go ms w
+    where go [] _ = []
+          go (n:ns) v = subVector 0 n v
+                      : go ns (subVector n (dim v - n) v)
+
+---------------------------------------------------------------
+
+-- | transforms a complex vector into a real vector with alternating real and imaginary parts 
+asReal :: (RealFloat a, Storable a) => Vector (Complex a) -> Vector a
+asReal v = unsafeFromForeignPtr (castForeignPtr fp) (2*i) (2*n)
+    where (fp,i,n) = unsafeToForeignPtr v
+
+-- | transforms a real vector into a complex vector with alternating real and imaginary parts
+asComplex :: (RealFloat a, Storable a) => Vector a -> Vector (Complex a)
+asComplex v = unsafeFromForeignPtr (castForeignPtr fp) (i `div` 2) (n `div` 2)
+    where (fp,i,n) = unsafeToForeignPtr v
+
+---------------------------------------------------------------
+
+float2DoubleV :: Vector Float -> Vector Double
+float2DoubleV v = unsafePerformIO $ do
+    r <- createVector (dim v)
+    app2 c_float2double vec v vec r "float2double"
+    return r
+
+double2FloatV :: Vector Double -> Vector Float
+double2FloatV v = unsafePerformIO $ do
+    r <- createVector (dim v)
+    app2 c_double2float vec v vec r "double2float2"
+    return r
+
+
+foreign import ccall unsafe "float2double" c_float2double:: TFV
+foreign import ccall unsafe "double2float" c_double2float:: TVF
+
+---------------------------------------------------------------
+
+stepF :: Vector Float -> Vector Float
+stepF v = unsafePerformIO $ do
+    r <- createVector (dim v)
+    app2 c_stepF vec v vec r "stepF"
+    return r
+
+stepD :: Vector Double -> Vector Double
+stepD v = unsafePerformIO $ do
+    r <- createVector (dim v)
+    app2 c_stepD vec v vec r "stepD"
+    return r
+
+foreign import ccall unsafe "stepF" c_stepF :: TFF
+foreign import ccall unsafe "stepD" c_stepD :: TVV
+
+---------------------------------------------------------------
+
+condF :: Vector Float -> Vector Float -> Vector Float -> Vector Float -> Vector Float -> Vector Float
+condF x y l e g = unsafePerformIO $ do
+    r <- createVector (dim x)
+    app6 c_condF vec x vec y vec l vec e vec g vec r "condF"
+    return r
+
+condD :: Vector Double -> Vector Double -> Vector Double -> Vector Double -> Vector Double -> Vector Double
+condD x y l e g = unsafePerformIO $ do
+    r <- createVector (dim x)
+    app6 c_condD vec x vec y vec l vec e vec g vec r "condD"
+    return r
+
+foreign import ccall unsafe "condF" c_condF :: CInt -> PF -> CInt -> PF -> CInt -> PF -> TFFF
+foreign import ccall unsafe "condD" c_condD :: CInt -> PD -> CInt -> PD -> CInt -> PD -> TVVV
+
+--------------------------------------------------------------------------------
+
+conjugateAux fun x = unsafePerformIO $ do
+    v <- createVector (dim x)
+    app2 fun vec x vec v "conjugateAux"
+    return v
+
+conjugateQ :: Vector (Complex Float) -> Vector (Complex Float)
+conjugateQ = conjugateAux c_conjugateQ
+foreign import ccall unsafe "conjugateQ" c_conjugateQ :: TQVQV
+
+conjugateC :: Vector (Complex Double) -> Vector (Complex Double)
+conjugateC = conjugateAux c_conjugateC
+foreign import ccall unsafe "conjugateC" c_conjugateC :: TCVCV
+
+--------------------------------------------------------------------------------
+
+cloneVector :: Storable t => Vector t -> IO (Vector t)
+cloneVector v = do
+        let n = dim v
+        r <- createVector n
+        let f _ s _ d =  copyArray d s n >> return 0
+        app2 f vec v vec r "cloneVector"
+        return r
+
+------------------------------------------------------------------
+
+-- | map on Vectors
+mapVector :: (Storable a, Storable b) => (a-> b) -> Vector a -> Vector b
+mapVector f v = unsafePerformIO $ do
+    w <- createVector (dim v)
+    unsafeWith v $ \p ->
+        unsafeWith w $ \q -> do
+            let go (-1) = return ()
+                go !k = do x <- peekElemOff p k
+                           pokeElemOff      q k (f x)
+                           go (k-1)
+            go (dim v -1)
+    return w
+{-# INLINE mapVector #-}
+
+-- | zipWith for Vectors
+zipVectorWith :: (Storable a, Storable b, Storable c) => (a-> b -> c) -> Vector a -> Vector b -> Vector c
+zipVectorWith f u v = unsafePerformIO $ do
+    let n = min (dim u) (dim v)
+    w <- createVector n
+    unsafeWith u $ \pu ->
+        unsafeWith v $ \pv ->
+            unsafeWith w $ \pw -> do
+                let go (-1) = return ()
+                    go !k = do x <- peekElemOff pu k
+                               y <- peekElemOff pv k
+                               pokeElemOff      pw k (f x y)
+                               go (k-1)
+                go (n -1)
+    return w
+{-# INLINE zipVectorWith #-}
+
+-- | unzipWith for Vectors
+unzipVectorWith :: (Storable (a,b), Storable c, Storable d) 
+                   => ((a,b) -> (c,d)) -> Vector (a,b) -> (Vector c,Vector d)
+unzipVectorWith f u = unsafePerformIO $ do
+      let n = dim u
+      v <- createVector n
+      w <- createVector n
+      unsafeWith u $ \pu ->
+          unsafeWith v $ \pv ->
+              unsafeWith w $ \pw -> do
+                  let go (-1) = return ()
+                      go !k   = do z <- peekElemOff pu k
+                                   let (x,y) = f z 
+                                   pokeElemOff      pv k x
+                                   pokeElemOff      pw k y
+                                   go (k-1)
+                  go (n-1)
+      return (v,w)
+{-# INLINE unzipVectorWith #-}
+
+foldVector :: Storable a => (a -> b -> b) -> b -> Vector a -> b
+foldVector f x v = unsafePerformIO $
+    unsafeWith v $ \p -> do
+        let go (-1) s = return s
+            go !k !s = do y <- peekElemOff p k
+                          go (k-1::Int) (f y s)
+        go (dim v -1) x
+{-# INLINE foldVector #-}
+
+-- the zero-indexed index is passed to the folding function
+foldVectorWithIndex :: Storable a => (Int -> a -> b -> b) -> b -> Vector a -> b
+foldVectorWithIndex f x v = unsafePerformIO $
+    unsafeWith v $ \p -> do
+        let go (-1) s = return s
+            go !k !s = do y <- peekElemOff p k
+                          go (k-1::Int) (f k y s)
+        go (dim v -1) x
+{-# INLINE foldVectorWithIndex #-}
+
+foldLoop f s0 d = go (d - 1) s0
+     where
+       go 0 s = f (0::Int) s
+       go !j !s = go (j - 1) (f j s)
+
+foldVectorG f s0 v = foldLoop g s0 (dim v)
+    where g !k !s = f k (at' v) s
+          {-# INLINE g #-} -- Thanks to Ryan Ingram (http://permalink.gmane.org/gmane.comp.lang.haskell.cafe/46479)
+{-# INLINE foldVectorG #-}
+
+-------------------------------------------------------------------
+
+-- | monadic map over Vectors
+--    the monad @m@ must be strict
+mapVectorM :: (Storable a, Storable b, Monad m) => (a -> m b) -> Vector a -> m (Vector b)
+mapVectorM f v = do
+    w <- return $! unsafePerformIO $! createVector (dim v)
+    mapVectorM' w 0 (dim v -1)
+    return w
+    where mapVectorM' w' !k !t
+              | k == t               = do
+                                       x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k 
+                                       y <- f x
+                                       return $! inlinePerformIO $! unsafeWith w' $! \q -> pokeElemOff q k y
+              | otherwise            = do
+                                       x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k 
+                                       y <- f x
+                                       _ <- return $! inlinePerformIO $! unsafeWith w' $! \q -> pokeElemOff q k y
+                                       mapVectorM' w' (k+1) t
+{-# INLINE mapVectorM #-}
+
+-- | monadic map over Vectors
+mapVectorM_ :: (Storable a, Monad m) => (a -> m ()) -> Vector a -> m ()
+mapVectorM_ f v = do
+    mapVectorM' 0 (dim v -1)
+    where mapVectorM' !k !t
+              | k == t            = do
+                                    x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k
+                                    f x
+              | otherwise         = do
+                                    x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k 
+                                    _ <- f x
+                                    mapVectorM' (k+1) t
+{-# INLINE mapVectorM_ #-}
+
+-- | monadic map over Vectors with the zero-indexed index passed to the mapping function
+--    the monad @m@ must be strict
+mapVectorWithIndexM :: (Storable a, Storable b, Monad m) => (Int -> a -> m b) -> Vector a -> m (Vector b)
+mapVectorWithIndexM f v = do
+    w <- return $! unsafePerformIO $! createVector (dim v)
+    mapVectorM' w 0 (dim v -1)
+    return w
+    where mapVectorM' w' !k !t
+              | k == t               = do
+                                       x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k 
+                                       y <- f k x
+                                       return $! inlinePerformIO $! unsafeWith w' $! \q -> pokeElemOff q k y
+              | otherwise            = do
+                                       x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k 
+                                       y <- f k x
+                                       _ <- return $! inlinePerformIO $! unsafeWith w' $! \q -> pokeElemOff q k y
+                                       mapVectorM' w' (k+1) t
+{-# INLINE mapVectorWithIndexM #-}
+
+-- | monadic map over Vectors with the zero-indexed index passed to the mapping function
+mapVectorWithIndexM_ :: (Storable a, Monad m) => (Int -> a -> m ()) -> Vector a -> m ()
+mapVectorWithIndexM_ f v = do
+    mapVectorM' 0 (dim v -1)
+    where mapVectorM' !k !t
+              | k == t            = do
+                                    x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k
+                                    f k x
+              | otherwise         = do
+                                    x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k 
+                                    _ <- f k x
+                                    mapVectorM' (k+1) t
+{-# INLINE mapVectorWithIndexM_ #-}
+
+
+mapVectorWithIndex :: (Storable a, Storable b) => (Int -> a -> b) -> Vector a -> Vector b
+--mapVectorWithIndex g = head . mapVectorWithIndexM (\a b -> [g a b])
+mapVectorWithIndex f v = unsafePerformIO $ do
+    w <- createVector (dim v)
+    unsafeWith v $ \p ->
+        unsafeWith w $ \q -> do
+            let go (-1) = return ()
+                go !k = do x <- peekElemOff p k
+                           pokeElemOff      q k (f k x)
+                           go (k-1)
+            go (dim v -1)
+    return w
+{-# INLINE mapVectorWithIndex #-}
+
+