1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470
|
{-# 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. If the matrix is ColumnMajor, this operation requires a transpose.
--
-- @\> 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 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
-------------------------------------------------------------------
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 "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
----------------------------------------------------------------------
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
constantR :: Double -> Int -> Vector Double
constantR = constantAux cconstantR
foreign import ccall unsafe "constantR" cconstantR :: Ptr Double -> TV
constantQ :: Complex Float -> Int -> Vector (Complex Float)
constantQ = constantAux cconstantQ
foreign import ccall unsafe "constantQ" cconstantQ :: Ptr (Complex Float) -> TQV
constantC :: Complex Double -> Int -> Vector (Complex Double)
constantC = constantAux cconstantC
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)
--------------------------------------------------------------------------
-- | 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
|