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
|
{-# LANGUAGE RecordWildCards #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FlexibleInstances #-}
module Data.Packed.Internal.Sparse(
SMatrix(..),
mkCSR, mkDiag,
AssocMatrix,
toDense,
smXv
)where
import Numeric.Container
import qualified Data.Vector.Storable as V
import Data.Function(on)
import Control.Arrow((***))
import Control.Monad(when)
import Data.List(groupBy, sort)
import Foreign.C.Types(CInt(..))
import Numeric.LinearAlgebra.Devel
import System.IO.Unsafe(unsafePerformIO)
import Foreign(Ptr)
import Text.Printf(printf)
infixl 0 ~!~
c ~!~ msg = when c (error msg)
type AssocMatrix = [((Int,Int),Double)]
data SMatrix
= CSR
{ csrVals :: Vector Double
, csrCols :: Vector CInt
, csrRows :: Vector CInt
, nRows :: Int
, nCols :: Int
}
| CSC
{ cscVals :: Vector Double
, cscRows :: Vector CInt
, cscCols :: Vector CInt
, nRows :: Int
, nCols :: Int
}
| Diag
{ diagVals :: Vector Double
, nRows :: Int
, nCols :: Int
}
-- | Banded
deriving Show
mkCSR :: AssocMatrix -> SMatrix
mkCSR sm' = CSR{..}
where
sm = sort sm'
rws = map ((fromList *** fromList)
. unzip
. map ((succ.fi.snd) *** id)
)
. groupBy ((==) `on` (fst.fst))
$ sm
rszs = map (fi . dim . fst) rws
csrRows = fromList (scanl (+) 1 rszs)
csrVals = vjoin (map snd rws)
csrCols = vjoin (map fst rws)
nRows = dim csrRows - 1
nCols = fromIntegral (V.maximum csrCols)
mkDiagR r c v
| dim v <= min r c = Diag{..}
| otherwise = error $ printf "mkDiagR: incorrect sizes (%d,%d) [%d]" r c (dim v)
where
nRows = r
nCols = c
diagVals = v
mkDiag v = mkDiagR (dim v) (dim v) v
type IV t = CInt -> Ptr CInt -> t
type V t = CInt -> Ptr Double -> t
type SMxV = V (IV (IV (V (V (IO CInt)))))
smXv :: SMatrix -> Vector Double -> Vector Double
smXv CSR{..} v = unsafePerformIO $ do
dim v /= nCols ~!~ printf "smXv (CSR): incorrect sizes: (%d,%d) x %d" nRows nCols (dim v)
r <- createVector nRows
app5 c_smXv vec csrVals vec csrCols vec csrRows vec v vec r "CSRXv"
return r
smXv CSC{..} v = unsafePerformIO $ do
dim v /= nCols ~!~ printf "smXv (CSC): incorrect sizes: (%d,%d) x %d" nRows nCols (dim v)
r <- createVector nRows
app5 c_smTXv vec cscVals vec cscRows vec cscCols vec v vec r "CSCXv"
return r
smXv Diag{..} v
| dim v == nCols
= vjoin [ subVector 0 (dim diagVals) v `mul` diagVals
, konst 0 (nRows - dim diagVals) ]
| otherwise = error $ printf "smXv (Diag): incorrect sizes: (%d,%d) [%d] x %d"
nRows nCols (dim diagVals) (dim v)
instance Contraction SMatrix (Vector Double) (Vector Double)
where
contraction = smXv
--------------------------------------------------------------------------------
foreign import ccall unsafe "smXv"
c_smXv :: SMxV
foreign import ccall unsafe "smTXv"
c_smTXv :: SMxV
--------------------------------------------------------------------------------
toDense :: AssocMatrix -> Matrix Double
toDense asm = assoc (r+1,c+1) 0 asm
where
(r,c) = (maximum *** maximum) . unzip . map fst $ asm
instance Transposable (SMatrix)
where
tr (CSR vs cs rs n m) = CSC vs cs rs m n
tr (CSC vs rs cs n m) = CSR vs rs cs m n
tr (Diag v n m) = Diag v m n
instance Transposable (Matrix Double)
where
tr = trans
--------------------------------------------------------------------------------
instance Testable SMatrix
where
checkT _ = (ok,info)
where
sma = convo2 20 3
x1 = vect [1..20]
x2 = vect [1..40]
sm = mkCSR sma
s1 = sm ◇ x1
d1 = toDense sma ◇ x1
s2 = tr sm ◇ x2
d2 = tr (toDense sma) ◇ x2
sdia = mkDiagR 40 20 (vect [1..10])
s3 = sdia ◇ x1
s4 = tr sdia ◇ x2
ddia = diagRect 0 (vect [1..10]) 40 20
d3 = ddia ◇ x1
d4 = tr ddia ◇ x2
info = do
print sm
disp (toDense sma)
print s1; print d1
print s2; print d2
print s3; print d3
print s4; print d4
ok = s1==d1
&& s2==d2
&& s3==d3
&& s4==d4
disp = putStr . dispf 2
vect = fromList :: [Double] -> Vector Double
convomat :: Int -> Int -> AssocMatrix
convomat n k = [ ((i,j `mod` n),1) | i<-[0..n-1], j <- [i..i+k-1]]
convo2 :: Int -> Int -> AssocMatrix
convo2 n k = m1 ++ m2
where
m1 = convomat n k
m2 = map (((+n) *** id) *** id) m1
|