{-# language TypeFamilies #-}
{-# language TypeOperators, GADTs #-}
{-# language FlexibleInstances, FlexibleContexts #-}
-----------------------------------------------------------------------------
-- |
-- Copyright : (C) 2016 Marco Zocca
-- License : GPL-3 (see LICENSE)
-- Maintainer : zocca.marco gmail
-- Stability : provisional
-- Portability : portable
--
-----------------------------------------------------------------------------
module Data.Sparse.Common
( module X,
insertRowWith, insertRow, insertColWith, insertCol,
diagonalSM,
outerProdSV, (><), toSV, svToSM,
lookupRowSM,
extractCol, extractRow,
extractVectorDenseWith, extractRowDense, extractColDense,
extractDiagDense,
extractSubRow, extractSubCol,
extractSubRow_RK, extractSubCol_RK,
fromRowsL, fromRowsV, fromColsV, fromColsL, toRowsL, toColsL) where
-- import Control.Exception
-- import Control.Exception.Common
-- import Control.Monad.Catch
import Data.Sparse.Utils as X
import Data.Sparse.PPrint as X
import Data.Sparse.Types as X
import Data.Sparse.Internal.IntMap2 -- as X
import qualified Data.Sparse.Internal.IntM as I
import Data.Sparse.Internal.IntM (IntM(..))
import Data.Sparse.SpMatrix as X
import Data.Sparse.SpVector as X
-- import Data.Sparse.Internal.CSR as X
import Numeric.Eps as X
import Numeric.LinearAlgebra.Class as X
import qualified Data.IntMap.Strict as IM
import GHC.Exts
import Data.Complex
-- import Control.Applicative
-- import Data.Traversable
import Data.Maybe (fromMaybe, maybe)
import qualified Data.Vector as V
-- withBoundsSM m ij e f
-- | isValidIxSM m ij = f m ij
-- | otherwise = error e
-- | Modify the size of a SpVector. Do not use directly
resizeSV :: Int -> SpVector a -> SpVector a
resizeSV d2 (SV _ sv) = SV d2 sv
-- | Remap the keys of a SpVector. Do not use directly
mapKeysSV :: (IM.Key -> IM.Key) -> SpVector a -> SpVector a
mapKeysSV fk (SV d sv) = SV d $ I.mapKeys fk sv
-- * Insert row/column vector in matrix
-- | Insert row , using the provided row index transformation function
insertRowWith :: (IxCol -> IxCol) -> SpMatrix a -> SpVector a -> IM.Key -> SpMatrix a
insertRowWith fj (SM (m,n) im) (SV d sv) i
| not (inBounds0 m i) = error "insertRowSM : index out of bounds"
| n >= d = SM (m,n) $ I.insert i (insertOrUnion i sv' im) im
| otherwise = error $ "insertRowSM : incompatible dimensions " ++ show (n, d)
where sv' = I.mapKeys fj sv
insertOrUnion i' sv' im' = maybe sv' (I.union sv') (I.lookup i' im')
-- | Insert row
insertRow :: SpMatrix a -> SpVector a -> IM.Key -> SpMatrix a
insertRow = insertRowWith id
-- | Insert column, using the provided row index transformation function
insertColWith :: (IxRow -> IxRow) -> SpMatrix a -> SpVector a -> IxCol -> SpMatrix a
insertColWith fi smm sv j
| not (inBounds0 n j) = error "insertColSM : index out of bounds"
| m >= mv = insIM2 smm vl j
| otherwise = error $ "insertColSM : incompatible dimensions " ++ show (m,mv) where
(m, n) = dim smm
mv = dim sv
vl = toListSV sv
insIM2 im2 ((i,x):xs) j' = insIM2 (insertSpMatrix (fi i) j' x im2) xs j'
insIM2 im2 [] _ = im2
-- | Insert column
insertCol :: SpMatrix a -> SpVector a -> IxCol -> SpMatrix a
insertCol = insertColWith id
-- * Outer vector product
-- | Outer product
outerProdSV, (><) :: Num a => SpVector a -> SpVector a -> SpMatrix a
outerProdSV v1 v2 = fromListSM (m, n) ixy where
m = dim v1
n = dim v2
ixy = [(i,j, x * y) | (i,x) <- toListSV v1 , (j, y) <- toListSV v2]
(><) = outerProdSV
-- * Diagonal matrix
-- | Fill the diagonal of a SpMatrix with the components of a SpVector
diagonalSM :: SpVector a -> SpMatrix a
diagonalSM sv = ifoldSV iins (zeroSM n n) sv where
n = dim sv
iins i = insertSpMatrix i i
-- * Matrix-vector conversions
-- | promote a SV to SM
svToSM :: SpVector a -> SpMatrix a
svToSM (SV n d) = SM (n, 1) $ I.singleton 0 d
-- |Demote (n x 1) or (1 x n) SpMatrix to SpVector
toSV :: SpMatrix a -> SpVector a
toSV (SM (m, n) im) = SV d im' where
im' | m < n = snd . head . toList $ im
| otherwise = fmap g im
g = snd . head . toList
d | m==1 && n==1 = 1
| m==1 && n>1 = n
| n==1 && m>1 = m
| otherwise = error $ "toSV : incompatible matrix dimension " ++ show (m,n)
-- | Lookup a row in a SpMatrix; returns an SpVector with the row, if this is non-empty
lookupRowSM :: SpMatrix a -> IxRow -> Maybe (SpVector a)
lookupRowSM sm i = SV (ncols sm) <$> I.lookup i (dat sm)
-- * Extract a SpVector from an SpMatrix
-- ** Sparse extract
-- |Extract ith row
extractRow :: SpMatrix a -> IxRow -> SpVector a
extractRow m i
| inBounds0 (nrows m) i = fromMaybe (zeroSV (ncols m)) (lookupRowSM m i)
| otherwise = error $ unwords ["extractRow : index",show i,"out of bounds"]
-- |Extract jth column
extractCol :: SpMatrix a -> IxCol -> SpVector a
extractCol m j = toSV $ extractColSM m j
-- ** Dense extract (default == 0)
-- | Generic extraction function
extractVectorDenseWith ::
Num a => (Int -> (IxRow, IxCol)) -> SpMatrix a -> SpVector a
extractVectorDenseWith f mm = fromListDenseSV n $ foldr ins [] ll where
ll = [0 .. n - 1]
(_, n) = dim mm
ins i acc = mm @@ f i : acc
-- | Extract ith row (dense)
extractRowDense :: Num a => SpMatrix a -> IxRow -> SpVector a
extractRowDense mm iref = extractVectorDenseWith (\j -> (iref, j)) mm
-- | Extract jth column
extractColDense :: Num a => SpMatrix a -> IxCol -> SpVector a
extractColDense mm jref = extractVectorDenseWith (\i -> (i, jref)) mm
-- | Extract the diagonal
extractDiagDense :: Num a => SpMatrix a -> SpVector a
extractDiagDense = extractVectorDenseWith (\i -> (i, i))
-- | extract row interval (all entries between columns j1 and j2, INCLUDED, are returned)
-- extractSubRow :: SpMatrix a -> IxRow -> (IxCol, IxCol) -> SpVector a
-- extractSubRow m i (j1, j2) = case lookupRowSM m i of
-- Nothing -> zeroSV (ncols m)
-- Just rv -> ifilterSV (\j _ -> j >= j1 && j <= j2) rv
-- |", returning in Maybe
-- extractSubRow :: SpMatrix a -> IxRow -> (Int, Int) -> Maybe (SpVector a)
-- extractSubRow m i (j1, j2) =
-- resizeSV (j2 - j1) . ifilterSV (\j _ -> j >= j1 && j <= j2) <$> lookupRowSM m i
-- | Extract an interval of SpVector components, changing accordingly the resulting SpVector size. Keys are _not_ rebalanced, i.e. components are still labeled according with respect to the source matrix.
extractSubRow :: SpMatrix a -> IxRow -> (Int, Int) -> SpVector a
extractSubRow m i (j1, j2) = fromMaybe (zeroSV deltaj) vfilt where
deltaj = j2 - j1 + 1
vfilt = resizeSV deltaj .
ifilterSV (\j _ -> j >= j1 && j <= j2) <$> lookupRowSM m i
-- | extract row interval, rebalance keys by subtracting lowest one
extractSubRow_RK :: SpMatrix a -> IxRow -> (IxCol, IxCol) -> SpVector a
extractSubRow_RK m i (j1, j2) = mapKeysSV (subtract j1) $ extractSubRow m i (j1, j2)
-- toSV $ extractSubRowSM_RK m i (j1, j2)
-- | extract column interval
extractSubCol :: SpMatrix a -> IxCol -> (IxRow, IxRow) -> SpVector a
extractSubCol m j (i1, i2) = toSV $ extractSubColSM m j (i1, i2)
-- | extract column interval, rebalance keys by subtracting lowest one
extractSubCol_RK :: SpMatrix a -> IxCol -> (IxRow, IxRow) -> SpVector a
extractSubCol_RK m j (i1, i2) = toSV $ extractSubColSM_RK m j (i1, i2)
-- ** Matrix action on a vector
{-
FIXME : matVec is more general than SpVector's :
\m v -> fmap (`dot` v) m
:: (Normed f1, Num b, Functor f) => f (f1 b) -> f1 b -> f b
-}
instance (InnerSpace t, Scalar t ~ t) => LinearVectorSpace (SpVector t) where
type MatrixType (SpVector t) = SpMatrix t
(#>) = matVecSD
(<#) = vecMatSD
matVecSD :: (InnerSpace t, Scalar t ~ t) => SpMatrix t -> SpVector t -> SpVector t
matVecSD (SM (nr, nc) mdata) (SV n sv)
| nc == n = SV nr $ fmap (`dot` sv) mdata
| otherwise = error $ "matVec : mismatched dimensions " ++ show (nc, n)
-- |Vector-on-matrix (FIXME : transposes matrix: more costly than `matVec`, I think)
vecMatSD :: (InnerSpace t, Scalar t ~ t) => SpVector t -> SpMatrix t -> SpVector t
vecMatSD (SV n sv) (SM (nr, nc) mdata)
| n == nr = SV nc $ fmap (`dot` sv) (transposeIM2 mdata)
| otherwise = error $ "vecMat : mismatching dimensions " ++ show (n, nr)
-- -- generalized matVec : we require a function `rowsf` that produces a functor of elements of a Hilbert space (the rows of `m`)
-- matVecG :: (Hilbert v, Functor f, f (Scalar v) ~ v) => (m -> f v) -> m -> v -> v
-- matVecG rowsf m v = fmap (`dot` v) (rowsf m)
-- matVecGA
-- :: (Hilbert v, Traversable t, t (Scalar v) ~ v) =>
-- (m -> t v) -> m -> v -> v
-- matVecGA rowsf m v = traverse (<.> v) (rowsf m)
-- -- -- Really, a matrix is just notation for a linear map between two finite-dimensional Hilbert spaces, i.e.
-- matVec :: (Hilbert u, Hilbert v) => (u -> v) -> u -> v
-- which is a specialization of a function application operator like ($) :: (a -> b) -> a -> b
-- -- -- from `vector-space`
-- data a -* b where
-- Dot :: VectorSpace b => b -> (b -* Scalar b)
-- (:&&) :: (a -* c) -> (a -* d) -> (a -* (c, d)) -- a,c,d should be constrained
-- apply :: Hilbert a => (a -* b) -> (a -> b)
-- apply (Dot b) = dot b
-- apply (f :&& g) = apply f &&& apply g
-- where (u &&& v) a = (u a, v a) -- (&&&) from Control.Arrow
-- -- type a :~ b = Scalar a ~ Scalar b
-- | Pack a list of SpVectors as rows of an SpMatrix
fromRowsL :: [SpVector a] -> SpMatrix a
fromRowsL = fromRowsV . V.fromList
-- | Pack a list of SpVectors as columns an SpMatrix
fromColsL :: [SpVector a] -> SpMatrix a
fromColsL = fromColsV . V.fromList
-- | Unpack the rows of an SpMatrix into a list of SpVectors
toRowsL :: SpMatrix a -> [SpVector a]
toRowsL aa = map (extractRow aa) [0 .. m-1] where
(m,n) = dim aa
-- | Unpack the columns of an SpMatrix into a list of SpVectors
toColsL :: SpMatrix a -> [SpVector a]
toColsL aa = map (extractCol aa) [0 .. n-1] where
(m,n) = dim aa
-- | Pack a V.Vector of SpVectors as columns of an SpMatrix
fromColsV :: V.Vector (SpVector a) -> SpMatrix a
fromColsV qv = V.ifoldl' ins (zeroSM m n) qv where
n = V.length qv
m = dim $ V.head qv
ins mm i c = insertCol mm c i
-- | Pack a V.Vector of SpVectors as rows of an SpMatrix
fromRowsV :: V.Vector (SpVector a) -> SpMatrix a
fromRowsV qv = V.ifoldl' ins (zeroSM m n) qv where
n = V.length qv
m = svDim $ V.head qv
ins mm i c = insertRow mm c i
-- * Pretty printing
showNz :: (Epsilon a, Show a) => a -> String
showNz x | nearZero x = " _ "
| otherwise = show x
toDenseRow :: Num a => SpMatrix a -> IM.Key -> [a]
toDenseRow sm irow =
fmap (\icol -> sm @@ (irow,icol)) [0..ncols sm-1]
prdR, prdC :: PPrintOptions
prdR = PPOpts 4 2 7 -- reals
prdC = PPOpts 4 2 16 -- complex values
-- -- printDenseSM :: (Show t, Num t) => SpMatrix t -> IO ()
-- printDenseSM :: (ScIx c ~ (Int, Int), FDSize c ~ (Int, Int), SpContainer c a, Show a, Epsilon a) => c a -> IO ()
printDenseSM sm = do
newline
putStrLn $ sizeStrSM sm
newline
prd0 sm
printDenseSM0
:: (SpMatrix a -> IxRow -> Int -> String) -> SpMatrix a -> IO ()
printDenseSM0 f sm = do
printDenseSM' sm 5 5
newline
where
printDenseSM' sm' nromax ncomax = mapM_ putStrLn rr_' where
(nr, _) = (nrows sm, ncols sm)
rr_ = map (\i -> f sm' i ncomax) [0..nr-1]
rr_' | nr > nromax = take (nromax - 2) rr_ ++ [" ... "] ++[last rr_]
| otherwise = rr_
printDenseSM0r :: SpMatrix Double -> IO ()
printDenseSM0r sm = printDenseSM0 g sm
where
g sm' irow ncolmax = printDN (ncols sm') ncolmax prdR $ toDenseRow sm' irow
printDenseSM0c :: SpMatrix (Complex Double) -> IO ()
printDenseSM0c sm = printDenseSM0 g sm
where
g sm' irow ncolmax = printCN (ncols sm') ncolmax prdC $ toDenseRow sm' irow
-- printDenseSV :: (Show t, Epsilon t) => SpVector t -> IO ()
printDenseSV :: PrintDense (SpVector a) => SpVector a -> IO ()
printDenseSV sv = do
newline
putStrLn $ sizeStrSV sv
newline
prd0 sv
printDenseSV0r :: SpVector Double -> IO ()
printDenseSV0r = printDenseSV0 g where
g l n = printDN l n prdR
printDenseSV0c :: SpVector (Complex Double) -> IO ()
printDenseSV0c = printDenseSV0 g where
g l n = printCN l n prdC
printDenseSV0 :: Num a =>
(Int -> Int -> [a] -> String) -> SpVector a -> IO ()
printDenseSV0 f sv = do
printDenseSV' (svDim sv) 5
newline where
printDenseSV' l n = putStrLn (f l n vd)
vd = toDenseListSV sv
-- ** Pretty printer typeclass
instance PrintDense (SpVector Double) where
prd = printDenseSV
prd0 = printDenseSV0r
instance PrintDense (SpVector (Complex Double)) where
prd = printDenseSV
prd0 = printDenseSV0c
instance PrintDense (SpMatrix Double) where
prd = printDenseSM
prd0 = printDenseSM0r
instance PrintDense (SpMatrix (Complex Double)) where
prd = printDenseSM
prd0 = printDenseSM0c
-- instance (Elt a, Show a) => PrintDense (CsrMatrix a) where
-- prd = printDenseSM