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{-# LANGUAGE RecordWildCards #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FlexibleInstances #-}
module Numeric.Sparse(
SMatrix(..),
mkCSR, mkDiag,
AssocMatrix,
toDense,
smXv
)where
import Data.Packed.Numeric
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.Util.CG(CGMat,cgSolve)
import Numeric.LinearAlgebra.Algorithms(linearSolveLS, relativeError, NormType(..))
import Data.Packed.Development
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 CGMat SMatrix
instance CGMat (Matrix Double)
--------------------------------------------------------------------------------
instance Testable SMatrix
where
checkT _ = (ok,info)
where
sma = convo2 20 3
x1 = vect [1..20]
x2 = vect [1..40]
sm = mkCSR sma
dm = toDense sma
s1 = sm ◇ x1
d1 = dm ◇ x1
s2 = tr sm ◇ x2
d2 = tr dm ◇ 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
v = testb 40
s5 = cgSolve False sm v
d5 = denseSolve dm v
info = do
print sm
disp (toDense sma)
print s1; print d1
print s2; print d2
print s3; print d3
print s4; print d4
print s5; print d5
print $ relativeError Infinity s5 d5
ok = s1==d1
&& s2==d2
&& s3==d3
&& s4==d4
&& relativeError Infinity s5 d5 < 1E-10
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
testb n = vect $ take n $ cycle ([0..10]++[9,8..1])
denseSolve a = flatten . linearSolveLS a . asColumn
|
