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|
{-# LANGUAGE ForeignFunctionInterface #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE BangPatterns #-}
-----------------------------------------------------------------------------
-- |
-- Module : Data.Packed.Internal.Matrix
-- Copyright : (c) Alberto Ruiz 2007
-- License : GPL-style
--
-- Maintainer : Alberto Ruiz <aruiz@um.es>
-- Stability : provisional
-- Portability : portable (uses FFI)
--
-- Internal matrix representation
--
-----------------------------------------------------------------------------
-- #hide
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',
saveMatrix,
singleton,
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 Foreign.C.String(newCString)
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
@\> flatten ('ident' 3)
9 |> [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
-- not yet admitted by my haddock version
-- 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 vs = case compatdim (map dim vs) of
Nothing -> error "fromRows applied to [] or to vectors with different sizes"
Just c -> reshape c . join . map (adapt c) $ vs
where
adapt c v | 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 = 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 c v = Matrix { irows = r, icols = c, xdat = v, order = o }
where (d,m) = dim v `quotRem` c
r | m==0 = d
| otherwise = error "matrixFromVector"
-- 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 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 c v = matrixFromVector RowMajor 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 { icols = c, xdat = d, order = o } = matrixFromVector o 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 (cols m1) (f (xdat m1) (flatten m2))
ColumnMajor -> matrixFromVector ColumnMajor (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 CFloat where
transdata = transdataAux ctransCF
constantD = constantAux cconstantCF
instance Element Double where
transdata = transdataAux ctransR
constantD = constantAux cconstantR
instance Element CDouble where
transdata = transdataAux ctransCR
constantD = constantAux cconstantCR
instance Element (Complex Float) where
transdata = transdataAux ctransQ
constantD = constantAux cconstantQ
instance Element (Complex CFloat) where
transdata = transdataAux ctransCQ
constantD = constantAux cconstantCQ
instance Element (Complex Double) where
transdata = transdataAux ctransC
constantD = constantAux cconstantC
instance Element (Complex CDouble) where
transdata = transdataAux ctransCC
constantD = constantAux cconstantCC
-------------------------------------------------------------------
transdata' :: Storable a => Int -> Vector a -> Int -> Vector a
transdata' c1 v c2 =
if noneed
then v
else unsafePerformIO $ do
w <- createVector (r2*c2)
unsafeWith v $ \p ->
unsafeWith w $ \q -> do
let go (-1) _ = return ()
go !i (-1) = go (i-1) (c1-1)
go !i !j = do x <- peekElemOff p (i*c1+j)
pokeElemOff q (j*c2+i) x
go i (j-1)
go (r1-1) (c1-1)
return w
where r1 = dim v `div` c1
r2 = dim v `div` c2
noneed = r1 == 1 || c1 == 1
-- {-# SPECIALIZE transdata' :: Int -> Vector Double -> Int -> Vector Double #-}
-- {-# SPECIALIZE transdata' :: Int -> Vector (Complex Double) -> Int -> Vector (Complex Double) #-}
-- I don't know how to specialize...
-- The above pragmas only seem to work on top level defs
-- Fortunately everything seems to work using the above class
-- C versions, still a little faster:
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 = 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 = r1 == 1 || c1 == 1
foreign import ccall unsafe "transF" ctransF :: TFMFM
foreign import ccall unsafe "transF" ctransCF :: CInt -> CInt -> Ptr CFloat -> CInt -> CInt -> Ptr CFloat -> IO CInt
foreign import ccall unsafe "transR" ctransR :: TMM
foreign import ccall unsafe "transR" ctransCR :: CInt -> CInt -> Ptr CDouble -> CInt -> CInt -> Ptr CDouble -> IO CInt
foreign import ccall unsafe "transQ" ctransQ :: TQMQM
foreign import ccall unsafe "transQ" ctransCQ :: CInt -> CInt -> Ptr (Complex CFloat) -> CInt -> CInt -> Ptr (Complex CFloat) -> IO CInt
foreign import ccall unsafe "transC" ctransC :: TCMCM
foreign import ccall unsafe "transC" ctransCC :: CInt -> CInt -> Ptr (Complex CDouble) -> CInt -> CInt -> Ptr (Complex CDouble) -> IO CInt
foreign import ccall unsafe "transP" ctransP :: CInt -> CInt -> Ptr () -> CInt -> CInt -> CInt -> Ptr () -> CInt -> IO CInt
----------------------------------------------------------------------
constant' v n = unsafePerformIO $ do
w <- createVector n
unsafeWith w $ \p -> do
let go (-1) = return ()
go !k = pokeElemOff p k v >> go (k-1)
go (n-1)
return w
-- C versions
constantAux fun x n = unsafePerformIO $ do
v <- createVector n
px <- newArray [x]
app1 (fun px) vec v "constantAux"
free px
return v
constantF :: Float -> Int -> Vector Float
constantF = constantAux cconstantF
foreign import ccall unsafe "constantF" cconstantF :: Ptr Float -> TF
foreign import ccall unsafe "constantF" cconstantCF :: Ptr CFloat -> CInt -> Ptr CFloat -> IO CInt
constantR :: Double -> Int -> Vector Double
constantR = constantAux cconstantR
foreign import ccall unsafe "constantR" cconstantR :: Ptr Double -> TV
foreign import ccall unsafe "constantR" cconstantCR :: Ptr CDouble -> CInt -> Ptr CDouble -> IO CInt
constantQ :: Complex Float -> Int -> Vector (Complex Float)
constantQ = constantAux cconstantQ
foreign import ccall unsafe "constantQ" cconstantQ :: Ptr (Complex Float) -> TQV
foreign import ccall unsafe "constantQ" cconstantCQ :: Ptr (Complex CFloat) -> CInt -> Ptr (Complex CFloat) -> IO CInt
constantC :: Complex Double -> Int -> Vector (Complex Double)
constantC = constantAux cconstantC
foreign import ccall unsafe "constantC" cconstantC :: Ptr (Complex Double) -> TCV
foreign import ccall unsafe "constantC" cconstantCC :: Ptr (Complex CDouble) -> CInt -> Ptr (Complex CDouble) -> IO CInt
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)
--------------------------------------------------------------------------
-- | Saves a matrix as 2D ASCII table.
saveMatrix :: FilePath
-> String -- ^ format (%f, %g, %e)
-> Matrix Double
-> IO ()
saveMatrix filename fmt m = do
charname <- newCString filename
charfmt <- newCString fmt
let o = if orderOf m == RowMajor then 1 else 0
app1 (matrix_fprintf charname charfmt o) mat m "matrix_fprintf"
free charname
free charfmt
foreign import ccall unsafe "matrix_fprintf" matrix_fprintf :: Ptr CChar -> Ptr CChar -> CInt -> TM
----------------------------------------------------------------------
conformMs ms = map (conformMTo (r,c)) ms
where
r = maximum (map rows ms)
c = maximum (map cols ms)
conformVs vs = map (conformVTo n) vs
where
n = maximum (map dim vs)
conformMTo (r,c) m
| size m == (r,c) = m
| size m == (1,1) = reshape 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)++")"
----------------------------------------------------------------------
instance (Storable t, NFData t) => NFData (Matrix t)
where
rnf m | d > 0 = rnf (v @> 0)
| otherwise = ()
where
d = dim v
v = xdat m
|