module Data.Sparse.Utils where
-- import Control.Arrow (first, second)
import Data.Ord
import qualified Data.Vector as V
-- * Misc. utilities
-- | Intersection and union of sparse lists having indices in _ascending_ order
intersectWith :: Ord i => (a -> a -> b) -> [(i, a)] -> [(i, a)] -> [b]
intersectWith f = intersectWith0 (comparing fst) (lift2snd f)
unionWith :: Ord i =>
(a -> a -> a) -> a -> [(i, a)] -> [(i, a)] -> [(i, a)]
unionWith = unionWith0 compare
-- | Intersection of sparse lists having indices in _descending_ order
intersectWithD :: Ord i => (a -> a -> b) -> [(i, a)] -> [(i, a)] -> [b]
intersectWithD f = intersectWith0 (comparing (Down . fst)) (lift2snd f)
-- | Union of sparse lists having indices in _descending_ order
unionWithD :: Ord i =>
(a -> a -> a) -> a -> [(i, a)] -> [(i, a)] -> [(i, a)]
unionWithD = unionWith0 (comparing Down)
--
intersectWith0 :: (a -> b -> Ordering) -> (a -> b -> c) -> [a] -> [b] -> [c]
intersectWith0 q f = go [] where
go acc ls@(x : xs) rs@(y : ys) =
case q x y of EQ -> go (f x y : acc) xs ys
LT -> go acc xs rs
_ -> go acc ls ys
go acc [] _ = acc
go acc _ [] = acc
unionWith0 :: (i -> i -> Ordering) -> (a -> a -> a) -> a -> [(i, a)] -> [(i, a)] -> [(i, a)]
unionWith0 q f z = go [] where
go acc ls@((ix, x) : xs) rs@((iy, y) : ys) =
case q ix iy of EQ -> go ((ix, f x y) : acc) xs ys
LT -> go ((ix, f x z) : acc) xs rs
_ -> go ((iy, f z y) : acc) ls ys
go acc [] r = acc ++ r
go acc l [] = acc ++ l
-- | Lift a binary function onto the second entry of a tuple
lift2snd :: (t -> t1 -> t2) -> (a, t) -> (a1, t1) -> t2
lift2snd f a b = f (snd a) (snd b)
-- | Wrap a function with a null check, returning in Maybe
safe :: (t -> Bool) -> (t -> a) -> t -> Maybe a
safe q f v | q v = Nothing
| otherwise = Just $ f v
-- | Componentwise tuple operations
-- TODO : use semilattice properties instead
maxTup, minTup :: Ord t => (t, t) -> (t, t) -> (t, t)
maxTup (x1,y1) (x2,y2) = (max x1 x2, max y1 y2)
minTup (x1,y1) (x2,y2) = (min x1 x2, min y1 y2)
-- | integer-indexed ziplist
indexed :: [b] -> [(Int, b)]
indexed xs = indexed' (length xs) xs
indexed' :: Int -> [a] -> [(Int, a)]
indexed' n xs = zip [0 .. n-1] xs
-- | ", 2d arrays
indexed2 :: Int -> [c] -> [(Int, Int, c)]
indexed2 m xs = zip3 (concat $ replicate n ii_) jj_ xs where
ii_ = [0 .. m-1]
jj_ = concatMap (replicate m) [0 .. n-1]
ln = length xs
n = ln `div` m
-- folds
-- | foldr over the results of a fmap
foldrMap :: (Foldable t, Functor t) => (a -> b) -> (b -> c -> c) -> c -> t a -> c
foldrMap ff gg x0 = foldr gg x0 . fmap ff
-- | strict left fold
foldlStrict :: (a -> b -> a) -> a -> [b] -> a
foldlStrict f = go
where
go z [] = z
go z (x:xs) = let z' = f z x in z' `seq` go z' xs
-- | indexed right fold
ifoldr :: Num i =>
(a -> b -> b) -> b -> (i -> c -> d -> a) -> c -> [d] -> b
ifoldr mjoin mneutral f = go 0 where
go i z (x:xs) = mjoin (f i z x) (go (i+1) z xs)
go _ _ [] = mneutral
-- ** Bounds checking
type LB = Int
type UB = Int
inBounds :: LB -> UB -> Int -> Bool
inBounds ibl ibu i = i>= ibl && i<ibu
inBounds2 :: (LB, UB) -> (Int, Int) -> Bool
inBounds2 (ibl,ibu) (ix,iy) = inBounds ibl ibu ix && inBounds ibl ibu iy
-- ", lower bound = 0
inBounds0 :: UB -> Int -> Bool
inBounds0 = inBounds 0
inBounds02 :: (UB, UB) -> (Int, Int) -> Bool
inBounds02 (bx,by) (i,j) = inBounds0 bx i && inBounds0 by j
-- ** Safe indexing
head' :: V.Vector a -> Maybe a
head' = safe V.null V.head
tail' :: V.Vector a -> Maybe (V.Vector a)
tail' = safe V.null V.tail
-- unionWith0 :: (a -> a -> Ordering) -> (a -> a -> a) -> a -> [a] -> [a] -> [a]
-- unionWith0 q f z = go [] where
-- go acc ls@(x : xs) rs@(y : ys) =
-- case q x y of EQ -> go (f x y : acc) xs ys
-- LT -> go (f x z : acc) xs rs
-- _ -> go (f z y : acc) ls ys
-- go acc [] r = acc ++ r
-- go acc l [] = acc ++ l
-- union :: Ord a => [a] -> [a] -> [a]
-- union u_ v_ = go u_ v_ where
-- go [] x = x
-- go y [] = y
-- go uu@(u:us) vv@(v:vs)
-- | u == v = u : go us vs
-- | u < v = u : go us vv
-- | otherwise = v : go uu vs