-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/
-- | utilities for DP
--
-- Small set of utility functions
@package DPutils
@version 0.0.0.2
-- | Pipes that introduce parallelism on different levels.
module Pipes.Parallel
-- | Evaluates chunks of pipes elements in parallel with a pure function.
pipePar :: (Monad m) => Int -> Strategy b -> (a -> b) -> Pipe a b m ()
-- | Evaluates chunks of pipes elements in parallel with a pure function.
-- Before and after each parallel step, a monadic function is run. This
-- allows generation of certain statistics or information during runs.
pipeParBA :: (Monad m) => Int -> Strategy b -> (a -> b) -> ([a] -> m (x, [a])) -> (x -> [b] -> m [b]) -> Pipe a b m ()
-- | Triangular numbers and various helper functions.
--
-- Main use is for linearization of triangular array indexing.
--
-- Triangular numbers: @ T_n = Σ_{k=1)^n k = 1 + 2 + 3 + ... + n =
--
-- n * (n+1) / 2 = (n+1) choose 2 @
module Math.TriangularNumbers
-- | Triangular numbers.
--
-- https://oeis.org/A000217
triangularNumber :: Int -> Int
-- | Size of an upper triangle starting at i and ending at
-- j. "(0,N)" what be the normal thing to use.
linearizeUppertri :: (Int, Int) -> Int
-- | Subword indexing. Given the longest subword and the current subword,
-- calculate a linear index "[0,..]". "(l,n)" in this case means "l"ower
-- bound, length "n". And "(i,j)" is the normal index.
--
--
-- 0 1 2 3 <- j = ...
--
-- 0 1 2 3 i=0
-- _ 4 5 6 i=1
-- _ _ 7 8 i=2
-- 9 i=3
--
-- i=2, j=3 -> (4+1) * i - tri i + j
--
-- _
-- _ _ the triangular number to subtract.
--
toLinear :: Int -> (Int, Int) -> Int
-- | Linear index to paired.
--
-- We have indices in [0,N], and linear index k.
--
--
-- (N+1)*i - (i*(i+1)/2) + j == K
--
fromLinear :: Int -> Int -> (Int, Int)
module Data.Paired.Common
-- | Shall we combine elements on the main diagonal as well?
--
-- If we choose NoDiag, we deal with upper triangular matrices
-- that are effectively one element smaller.
data OnDiag
OnDiag :: OnDiag
NoDiag :: OnDiag
-- | Select only a subset of the possible enumerations.
data Enumerate
-- | Enumerate all elements
All :: Enumerate
-- | Enumerate from a value and at most N elements
FromN :: Int -> Int -> Enumerate
-- | If the size of the input is known before-hand or not.
data SizeHint
UnknownSize :: SizeHint
KnownSize :: Int -> SizeHint
instance GHC.Classes.Eq Data.Paired.Common.SizeHint
instance GHC.Classes.Eq Data.Paired.Common.Enumerate
instance GHC.Classes.Eq Data.Paired.Common.OnDiag
-- | Efficient enumeration of subsets of triangular elements. Given a list
-- [1..n] we want to enumerate a subset [(i,j)] of
-- ordered pairs in such a way that we only have to hold the elements
-- necessary for this subset in memory.
module Data.Paired.Foldable
-- | Generalized upper triangular elements. Given a list of elements
-- [e_1,...,e_k], we want to return pairs (e_i,e_j)
-- such that we have all ordered pairs with i<j (if
-- NoDiagonal elements), or i<=j (if
-- OnDiagonal elements).
--
-- upperTri will force the spine of t a but is consumed
-- linearly with a strict Data.Foldable.foldl'. Internally we
-- keep a Data.IntMap of the retained elements.
--
-- This is important if the Enumerate type is set to FromN k
-- n. We start at the kth element, and produce n
-- elements.
--
-- TODO compare IntMap and HashMap.
--
-- TODO inRange is broken.
upperTri :: (Foldable t) => SizeHint -> OnDiag -> Enumerate -> t a -> Either String (IntMap a, Int, [((Int, Int), (a, a))])
module Data.Paired.Vector
-- | Upper triangular elements.
upperTriVG :: (Vector v a, Vector w (a, a)) => OnDiag -> v a -> (Int, w (a, a))
-- | Outer pairing of all as with all bs. This one is
-- quasi-trivial, but here for completeness.
rectangularVG :: (Vector va a, Vector vb b, Vector w (a, b)) => va a -> vb b -> (Int, w (a, b))