summaryrefslogtreecommitdiff
path: root/lib/Data/Packed/Internal/Matrix.hs
blob: 68547bd39f1f463648fd5f69f94572c39a75d8ff (plain)
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
{-# OPTIONS_GHC -fglasgow-exts #-}
{-# LANGUAGE CPP, 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 where

import Data.Packed.Internal.Common
import Data.Packed.Internal.Vector

import Foreign hiding (xor)
import Complex
import Foreign.C.Types
import Foreign.C.String

-----------------------------------------------------------------

{- 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)

-- | Matrix representation suitable for GSL and LAPACK computations.
data Matrix t = MC { rows :: {-# UNPACK #-} !Int
                   , cols :: {-# UNPACK #-} !Int
                   , cdat :: {-# UNPACK #-} !(Vector t) }

              | MF { rows :: {-# UNPACK #-} !Int
                   , cols :: {-# UNPACK #-} !Int
                   , fdat :: {-# UNPACK #-} !(Vector t) }

-- MC: preferred by C, fdat may require a transposition
-- MF: preferred by LAPACK, cdat may require a transposition

xdat MC {cdat = d } = d
xdat MF {fdat = d } = d

orderOf :: Matrix t -> MatrixOrder
orderOf MF{} = ColumnMajor
orderOf MC{} = RowMajor

-- | Matrix transpose.
trans :: Matrix t -> Matrix t
trans MC {rows = r, cols = c, cdat = d } = MF {rows = c, cols = r, fdat = d }
trans MF {rows = r, cols = c, fdat = d } = MC {rows = c, cols = r, cdat = d }

cmat :: (Element t) => Matrix t -> Matrix t
cmat m@MC{} = m
cmat MF {rows = r, cols = c, fdat = d } = MC {rows = r, cols = c, cdat = transdata r d c}

fmat :: (Element t) => Matrix t -> Matrix t
fmat m@MF{} = m
fmat MC {rows = r, cols = c, cdat = d } = MF {rows = r, cols = c, fdat = transdata c d r}

-- C-Haskell matrix adapter
mat :: Adapt (CInt -> CInt -> Ptr t -> r) (Matrix t) r
mat = withMatrix

withMatrix a f =
    withForeignPtr (fptr (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 = cdat . 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 = partit (cols m) . toList . flatten $ m

-- | creates a Matrix from a list of vectors
fromRows :: Element t => [Vector t] -> Matrix t
fromRows vs = case common dim vs of
    Nothing -> error "fromRows applied to [] or to vectors with different sizes"
    Just c  -> reshape c (join vs)

-- | 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@M {rows = r, cols = c} @@> (i,j)
--    | i<0 || i>=r || j<0 || j>=c = error "matrix indexing out of range"
--    | otherwise   = cdat m `at` (i*c+j)

MC {rows = r, cols = c, cdat = v} @@> (i,j)
    | safe      = if i<0 || i>=r || j<0 || j>=c
                    then error "matrix indexing out of range"
                    else v `at` (i*c+j)
    | otherwise = v `at` (i*c+j)

MF {rows = r, cols = c, fdat = v} @@> (i,j)
    | safe      = if i<0 || i>=r || j<0 || j>=c
                    then error "matrix indexing out of range"
                    else v `at` (j*r+i)
    | otherwise = v `at` (j*r+i)
{-# INLINE (@@>) #-}

--  Unsafe matrix access without range checking
atM' MC {cols = c, cdat = v} i j = v `at'` (i*c+j)
atM' MF {rows = r, fdat = v} i j = v `at'` (j*r+i)
{-# INLINE atM' #-}

------------------------------------------------------------------

matrixFromVector RowMajor c v = MC { rows = r, cols = c, cdat = v }
    where (d,m) = dim v `divMod` c
          r | m==0 = d
            | otherwise = error "matrixFromVector"

matrixFromVector ColumnMajor c v = MF { rows = r, cols = c, fdat = v }
    where (d,m) = dim v `divMod` c
          r | m==0 = d
            | otherwise = error "matrixFromVector"

-- allocates memory for a new matrix
createMatrix :: (Storable a) => MatrixOrder -> Int -> Int -> IO (Matrix a)
createMatrix order r c = do
    p <- createVector (r*c)
    return (matrixFromVector order 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 :: Element 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 :: (Element a, Element b) => (Vector a -> Vector b) -> Matrix a -> Matrix b
liftMatrix f MC { cols = c, cdat = d } = matrixFromVector RowMajor    c (f d)
liftMatrix f MF { cols = c, fdat = d } = matrixFromVector ColumnMajor 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 m1 of
        MC {} -> matrixFromVector RowMajor    (cols m1) (f (cdat m1) (flatten m2))
        MF {} -> matrixFromVector ColumnMajor (cols m1) (f (fdat m1) ((fdat.fmat) m2))


compat :: Matrix a -> Matrix b -> Bool
compat m1 m2 = rows m1 == rows m2 && cols m1 == cols m2

------------------------------------------------------------------

-- | Auxiliary class.
class (Storable a, Floating a) => Element a where
    subMatrixD :: (Int,Int) -- ^ (r0,c0) starting position 
               -> (Int,Int) -- ^ (rt,ct) dimensions of submatrix
               -> Matrix a -> Matrix a
    transdata :: Int -> Vector a -> Int -> Vector a
    constantD  :: a -> Int -> Vector a

instance Element Double where
    subMatrixD = subMatrix'
    transdata  = transdataAux ctransR     -- transdata'
    constantD  = constantAux cconstantR   -- constant'

instance Element (Complex Double) where
    subMatrixD = subMatrix'
    transdata  = transdataAux ctransC     -- transdata'
    constantD  = constantAux cconstantC   -- constant'

-------------------------------------------------------------------

transdata' :: Storable a => Int -> Vector a -> Int -> Vector a
transdata' c1 v c2 =
    if noneed
        then v
        else unsafePerformIO $ do
                w <- createVector (r2*c2)
                withForeignPtr (fptr v) $ \p ->
                    withForeignPtr (fptr 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)
            withForeignPtr (fptr d) $ \pd ->
                withForeignPtr (fptr 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

foreign import ccall "transR" ctransR :: TMM
foreign import ccall "transC" ctransC :: TCMCM
----------------------------------------------------------------------

constant' v n = unsafePerformIO $ do
    w <- createVector n
    withForeignPtr (fptr 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

constantR :: Double -> Int -> Vector Double
constantR = constantAux cconstantR
foreign import ccall "constantR" cconstantR :: Ptr Double -> TV

constantC :: Complex Double -> Int -> Vector (Complex Double)
constantC = constantAux cconstantC
foreign import ccall "constantC" cconstantC :: Ptr (Complex Double) -> TCV
----------------------------------------------------------------------

-- | 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)
    withForeignPtr (fptr v) $ \p ->
        withForeignPtr (fptr 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) (MC _r c v) = MC rt ct $ subMatrix'' (r0,c0) (rt,ct) c v
subMatrix' (r0,c0) (rt,ct) m = trans $ subMatrix' (c0,r0) (ct,rt) (trans m)

--------------------------------------------------------------------------

-- | obtains the complex conjugate of a complex vector
conj :: Vector (Complex Double) -> Vector (Complex Double)
conj = mapVector conjugate

-- | creates a complex vector from vectors with real and imaginary parts
toComplex :: (Vector Double, Vector Double) ->  Vector (Complex Double)
toComplex (r,i) = asComplex $ flatten $ fromColumns [r,i]

-- | the inverse of 'toComplex'
fromComplex :: Vector (Complex Double) -> (Vector Double, Vector Double)
fromComplex z = (r,i) where
    [r,i] = toColumns $ reshape 2 $ asReal z

--------------------------------------------------------------------------

-- | 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 "matrix_fprintf" matrix_fprintf :: Ptr CChar -> Ptr CChar -> CInt -> TM