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{-# LANGUAGE RecordWildCards #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FlexibleInstances #-}
module Numeric.Sparse(
GMatrix(..), CSR(..), mkCSR, fromCSR,
mkSparse, mkDiagR, mkDense,
AssocMatrix,
toDense,
gmXv, (!#>)
)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 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 CSR = CSR
{ csrVals :: Vector Double
, csrCols :: Vector CInt
, csrRows :: Vector CInt
, csrNRows :: Int
, csrNCols :: Int
} deriving Show
data CSC = CSC
{ cscVals :: Vector Double
, cscRows :: Vector CInt
, cscCols :: Vector CInt
, cscNRows :: Int
, cscNCols :: Int
} deriving Show
mkCSR :: AssocMatrix -> CSR
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)
csrNRows = dim csrRows - 1
csrNCols = fromIntegral (V.maximum csrCols)
{- | General matrix with specialized internal representations for
dense, sparse, diagonal, banded, and constant elements.
>>> let m = mkSparse [((0,999),1.0),((1,1999),2.0)]
>>> m
SparseR {gmCSR = CSR {csrVals = fromList [1.0,2.0],
csrCols = fromList [1000,2000],
csrRows = fromList [1,2,3],
csrNRows = 2,
csrNCols = 2000},
nRows = 2,
nCols = 2000}
>>> let m = mkDense (mat 2 [1..4])
>>> m
Dense {gmDense = (2><2)
[ 1.0, 2.0
, 3.0, 4.0 ], nRows = 2, nCols = 2}
-}
data GMatrix
= SparseR
{ gmCSR :: CSR
, nRows :: Int
, nCols :: Int
}
| SparseC
{ gmCSC :: CSC
, nRows :: Int
, nCols :: Int
}
| Diag
{ diagVals :: Vector Double
, nRows :: Int
, nCols :: Int
}
| Dense
{ gmDense :: Matrix Double
, nRows :: Int
, nCols :: Int
}
-- | Banded
deriving Show
mkDense :: Matrix Double -> GMatrix
mkDense m = Dense{..}
where
gmDense = m
nRows = rows m
nCols = cols m
mkSparse :: AssocMatrix -> GMatrix
mkSparse = fromCSR . mkCSR
fromCSR :: CSR -> GMatrix
fromCSR csr = SparseR {..}
where
gmCSR @ CSR {..} = csr
nRows = csrNRows
nCols = csrNCols
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
type IV t = CInt -> Ptr CInt -> t
type V t = CInt -> Ptr Double -> t
type SMxV = V (IV (IV (V (V (IO CInt)))))
gmXv :: GMatrix -> Vector Double -> Vector Double
gmXv SparseR { gmCSR = CSR{..}, .. } v = unsafePerformIO $ do
dim v /= nCols ~!~ printf "gmXv (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
gmXv SparseC { gmCSC = CSC{..}, .. } v = unsafePerformIO $ do
dim v /= nCols ~!~ printf "gmXv (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
gmXv Diag{..} v
| dim v == nCols
= vjoin [ subVector 0 (dim diagVals) v `mul` diagVals
, konst 0 (nRows - dim diagVals) ]
| otherwise = error $ printf "gmXv (Diag): incorrect sizes: (%d,%d) [%d] x %d"
nRows nCols (dim diagVals) (dim v)
gmXv Dense{..} v
| dim v == nCols
= mXv gmDense v
| otherwise = error $ printf "gmXv (Dense): incorrect sizes: (%d,%d) x %d"
nRows nCols (dim v)
{- | general matrix - vector product
>>> let m = mkSparse [((0,999),1.0),((1,1999),2.0)]
>>> m !#> vector [1..2000]
fromList [1000.0,4000.0]
-}
infixr 8 !#>
(!#>) :: GMatrix -> Vector Double -> Vector Double
(!#>) = gmXv
--------------------------------------------------------------------------------
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 CSR CSC
where
tr (CSR vs cs rs n m) = CSC vs cs rs m n
instance Transposable CSC CSR
where
tr (CSC vs rs cs n m) = CSR vs rs cs m n
instance Transposable GMatrix GMatrix
where
tr (SparseR s n m) = SparseC (tr s) m n
tr (SparseC s n m) = SparseR (tr s) m n
tr (Diag v n m) = Diag v m n
tr (Dense a n m) = Dense (tr a) m n
|
