summaryrefslogtreecommitdiff
path: root/lib/Data/Packed/Matrix.hs
blob: de2300a86be6f406b7f111f6a08ca7cc6f3349cb (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
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}

-----------------------------------------------------------------------------
-- |
-- Module      :  Data.Packed.Matrix
-- Copyright   :  (c) Alberto Ruiz 2007-10
-- License     :  GPL-style
--
-- Maintainer  :  Alberto Ruiz <aruiz@um.es>
-- Stability   :  provisional
-- Portability :  portable
--
-- A Matrix representation suitable for numerical computations using LAPACK and GSL.
--
-- This module provides basic functions for manipulation of structure.

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

module Data.Packed.Matrix (
    Matrix,
    Element,
    rows,cols,
    (><),
    trans,
    reshape, flatten,
    fromLists, toLists, buildMatrix,
    (@@>),
    asRow, asColumn,
    fromRows, toRows, fromColumns, toColumns,
    fromBlocks, toBlocks, toBlocksEvery,
    repmat,
    flipud, fliprl,
    subMatrix, takeRows, dropRows, takeColumns, dropColumns,
    extractRows,
    diagRect, takeDiag,
    liftMatrix, liftMatrix2, liftMatrix2Auto,fromArray2D
) where

import Data.Packed.Internal
import qualified Data.Packed.ST as ST
import Data.List(transpose,intersperse)
import Data.Array


import Data.Binary
import Foreign.Storable
import Control.Monad(replicateM)
--import Control.Arrow((***))
--import GHC.Float(double2Float,float2Double)


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

instance (Binary a, Element a, Storable a) => Binary (Matrix a) where
    put m = do
            let r = rows m
            let c = cols m
            put r
            put c
            mapM_ (\i -> mapM_ (\j -> put $ m @@> (i,j)) [0..(c-1)]) [0..(r-1)]
    get = do
          r <- get
          c <- get
          xs <- replicateM r $ replicateM c get
          return $ fromLists xs

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

instance (Show a, Element a) => (Show (Matrix a)) where
    show m = (sizes++) . dsp . map (map show) . toLists $ m
        where sizes = "("++show (rows m)++"><"++show (cols m)++")\n"

dsp as = (++" ]") . (" ["++) . init . drop 2 . unlines . map (" , "++) . 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 ", "

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

instance (Element a, Read a) => Read (Matrix a) where
    readsPrec _ s = [((rs><cs) . read $ listnums, rest)]
        where (thing,rest) = breakAt ']' s
              (dims,listnums) = breakAt ')' thing
              cs = read . init . fst. breakAt ')' . snd . breakAt '<' $ dims
              rs = read . snd . breakAt '(' .init . fst . breakAt '>' $ dims


breakAt c l = (a++[c],tail b) where
    (a,b) = break (==c) l

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

-- | creates a matrix from a vertical list of matrices
joinVert :: Element t => [Matrix t] -> Matrix t
joinVert ms = case common cols ms of
    Nothing -> error "(impossible) joinVert on matrices with different number of columns"
    Just c  -> reshape c $ join (map flatten ms)

-- | creates a matrix from a horizontal list of matrices
joinHoriz :: Element t => [Matrix t] -> Matrix t
joinHoriz ms = trans. joinVert . map trans $ ms

{- | Creates a matrix from blocks given as a list of lists of matrices.

Single row/column components are automatically expanded to match the
corresponding common row and column:

@\> let disp = putStr . dispf 2
\> let vector xs = fromList xs :: Vector Double
\> let diagl = diag . vector
\> let rowm = asRow . vector

\> disp $ fromBlocks [[ident 5, 7, rowm[10,20]], [3, diagl[1,2,3], 0]]

8x10
1  0  0  0  0  7  7  7  10  20
0  1  0  0  0  7  7  7  10  20
0  0  1  0  0  7  7  7  10  20
0  0  0  1  0  7  7  7  10  20
0  0  0  0  1  7  7  7  10  20
3  3  3  3  3  1  0  0   0   0
3  3  3  3  3  0  2  0   0   0
3  3  3  3  3  0  0  3   0   0@
-}
fromBlocks :: Element t => [[Matrix t]] -> Matrix t
fromBlocks = fromBlocksRaw . adaptBlocks

fromBlocksRaw mms = joinVert . map joinHoriz $ mms

adaptBlocks ms = ms' where
    bc = case common length ms of
          Just c -> c
          Nothing -> error "fromBlocks requires rectangular [[Matrix]]"
    rs = map (compatdim . map rows) ms
    cs = map (compatdim . map cols) (transpose ms)
    szs = sequence [rs,cs]
    ms' = splitEvery bc $ zipWith g szs (concat ms)

    g [Just nr,Just nc] m
                | nr == r && nc == c = m
                | r == 1 && c == 1 = reshape nc (constantD x (nr*nc))
                | r == 1 = fromRows (replicate nr (flatten m))
                | otherwise = fromColumns (replicate nc (flatten m))
      where
        r = rows m
        c = cols m
        x = m@@>(0,0)
    g _ _ = error "inconsistent dimensions in fromBlocks"

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

-- | Reverse rows 
flipud :: Element t => Matrix t -> Matrix t
flipud m = fromRows . reverse . toRows $ m

-- | Reverse columns
fliprl :: Element t => Matrix t -> Matrix t
fliprl m = fromColumns . reverse . toColumns $ m

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

{- | creates a rectangular diagonal matrix:

@> diagRect 7 (fromList [10,20,30]) 4 5 :: Matrix Double
(4><5)
 [ 10.0,  7.0,  7.0, 7.0, 7.0
 ,  7.0, 20.0,  7.0, 7.0, 7.0
 ,  7.0,  7.0, 30.0, 7.0, 7.0
 ,  7.0,  7.0,  7.0, 7.0, 7.0 ]@
-}
diagRect :: (Storable t) => t -> Vector t -> Int -> Int -> Matrix t
diagRect z v r c = ST.runSTMatrix $ do
        m <- ST.newMatrix z r c
        let d = min r c `min` (dim v)
        mapM_ (\k -> ST.writeMatrix m k k (v@>k)) [0..d-1]
        return m

-- | extracts the diagonal from a rectangular matrix
takeDiag :: (Element t) => Matrix t -> Vector t
takeDiag m = fromList [flatten m `at` (k*cols m+k) | k <- [0 .. min (rows m) (cols m) -1]]

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

{- | An easy way to create a matrix:

@\> (2><3)[1..6]
(2><3)
 [ 1.0, 2.0, 3.0
 , 4.0, 5.0, 6.0 ]@

This is the format produced by the instances of Show (Matrix a), which
can also be used for input.

The input list is explicitly truncated, so that it can
safely be used with lists that are too long (like infinite lists).

Example:

@\> (2>|<3)[1..]
(2><3)
 [ 1.0, 2.0, 3.0
 , 4.0, 5.0, 6.0 ]@

-}
(><) :: (Storable a) => Int -> Int -> [a] -> Matrix a
r >< c = f where
    f l | dim v == r*c = matrixFromVector RowMajor c v
        | otherwise    = error $ "inconsistent list size = "
                                 ++show (dim v) ++" in ("++show r++"><"++show c++")"
        where v = fromList $ take (r*c) l

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

-- | Creates a matrix with the first n rows of another matrix
takeRows :: Element t => Int -> Matrix t -> Matrix t
takeRows n mt = subMatrix (0,0) (n, cols mt) mt
-- | Creates a copy of a matrix without the first n rows
dropRows :: Element t => Int -> Matrix t -> Matrix t
dropRows n mt = subMatrix (n,0) (rows mt - n, cols mt) mt
-- |Creates a matrix with the first n columns of another matrix
takeColumns :: Element t => Int -> Matrix t -> Matrix t
takeColumns n mt = subMatrix (0,0) (rows mt, n) mt
-- | Creates a copy of a matrix without the first n columns
dropColumns :: Element t => Int -> Matrix t -> Matrix t
dropColumns n mt = subMatrix (0,n) (rows mt, cols mt - n) mt

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

{- | Creates a 'Matrix' from a list of lists (considered as rows).

@\> fromLists [[1,2],[3,4],[5,6]]
(3><2)
 [ 1.0, 2.0
 , 3.0, 4.0
 , 5.0, 6.0 ]@
-}
fromLists :: Element t => [[t]] -> Matrix t
fromLists = fromRows . map fromList

-- | creates a 1-row matrix from a vector
asRow :: Storable a => Vector a -> Matrix a
asRow v = reshape (dim v) v

-- | creates a 1-column matrix from a vector
asColumn :: Storable a => Vector a -> Matrix a
asColumn v = reshape 1 v



{- | creates a Matrix of the specified size using the supplied function to
     to map the row\/column position to the value at that row\/column position.

@> buildMatrix 3 4 (\ (r,c) -> fromIntegral r * fromIntegral c)
(3><4)
 [ 0.0, 0.0, 0.0, 0.0, 0.0
 , 0.0, 1.0, 2.0, 3.0, 4.0
 , 0.0, 2.0, 4.0, 6.0, 8.0]@

Hilbert matrix of order N:

@hilb n = buildMatrix n n (\(i,j)->1/(fromIntegral i + fromIntegral j +1))@

-}
buildMatrix :: Element a => Int -> Int -> ((Int, Int) -> a) -> Matrix a
buildMatrix rc cc f =
    fromLists $ map (map f)
    	$ map (\ ri -> map (\ ci -> (ri, ci)) [0 .. (cc - 1)]) [0 .. (rc - 1)]

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

fromArray2D :: (Storable e) => Array (Int, Int) e -> Matrix e
fromArray2D m = (r><c) (elems m)
    where ((r0,c0),(r1,c1)) = bounds m
          r = r1-r0+1
          c = c1-c0+1


-- | rearranges the rows of a matrix according to the order given in a list of integers. 
extractRows :: Element t => [Int] -> Matrix t -> Matrix t
extractRows l m = fromRows $ extract (toRows m) l
    where extract l' is = [l'!!i |i<-is]

{- | creates matrix by repetition of a matrix a given number of rows and columns

@> repmat (ident 2) 2 3 :: Matrix Double
(4><6)
 [ 1.0, 0.0, 1.0, 0.0, 1.0, 0.0
 , 0.0, 1.0, 0.0, 1.0, 0.0, 1.0
 , 1.0, 0.0, 1.0, 0.0, 1.0, 0.0
 , 0.0, 1.0, 0.0, 1.0, 0.0, 1.0 ]@

-}
repmat :: (Element t) => Matrix t -> Int -> Int -> Matrix t
repmat m r c = fromBlocks $ splitEvery c $ replicate (r*c) m

-- | A version of 'liftMatrix2' which automatically adapt matrices with a single row or column to match the dimensions of the other matrix.
liftMatrix2Auto :: (Element t, Element a, Element b)
             => (Vector a -> Vector b -> Vector t) -> Matrix a -> Matrix b -> Matrix t
liftMatrix2Auto f m1 m2 | compat' m1 m2 = lM f m1 m2
                     | rows m1 == rows m2 && cols m2 == 1 = lM f m1 (repCols (cols m1) m2)
                     | rows m1 == rows m2 && cols m1 == 1 = lM f (repCols (cols m2) m1) m2
                     | cols m1 == cols m2 && rows m2 == 1 = lM f m1 (repRows (rows m1) m2)
                     | cols m1 == cols m2 && cols m1 == 1 = lM f (repRows (rows m2) m1) m2
                     | rows m1 == 1 && cols m2 == 1 = lM f (repRows (rows m2) m1) (repCols (cols m1) m2)
                     | cols m1 == 1 && rows m2 == 1 = lM f (repCols (cols m2) m1) (repRows (rows m1) m2)
                     | otherwise    = error $ "nonconformable matrices in liftMatrix2Auto: " ++ show (size m1) ++ ", " ++ show (size m2)

size m = (rows m, cols m)

lM f m1 m2 = reshape (max (cols m1) (cols m2)) (f (flatten m1) (flatten m2))

repRows n x = fromRows (replicate n (flatten x))
repCols n x = fromColumns (replicate n (flatten x))

compat' :: Matrix a -> Matrix b -> Bool
compat' m1 m2 = rows m1 == 1 && cols m1 == 1
             || rows m2 == 1 && cols m2 == 1
             || rows m1 == rows m2 && cols m1 == cols m2

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

toBlockRows [r] m | r == rows m = [m]
toBlockRows rs m = map (reshape (cols m)) (takesV szs (flatten m))
    where szs = map (* cols m) rs

toBlockCols [c] m | c == cols m = [m]
toBlockCols cs m = map trans . toBlockRows cs . trans $ m

-- | Partition a matrix into blocks with the given numbers of rows and columns.
-- The remaining rows and columns are discarded.
toBlocks :: (Element t) => [Int] -> [Int] -> Matrix t -> [[Matrix t]]
toBlocks rs cs m = map (toBlockCols cs) . toBlockRows rs $ m

-- | Fully partition a matrix into blocks of the same size. If the dimensions are not
-- a multiple of the given size the last blocks will be smaller.
toBlocksEvery :: (Element t) => Int -> Int -> Matrix t -> [[Matrix t]]
toBlocksEvery r c m = toBlocks rs cs m where
    (qr,rr) = rows m `divMod` r
    (qc,rc) = cols m `divMod` c
    rs = replicate qr r ++ if rr > 0 then [rr] else []
    cs = replicate qc c ++ if rc > 0 then [rc] else []

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