BNFC-2.8.1: A compiler front-end generator.

Safe HaskellNone
LanguageHaskell98

Data.Matrix.Quad

Synopsis

Documentation

data Shape Source

Constructors

Bin Shape Shape 
Leaf 

data Shape' :: Shape -> * where Source

Constructors

Bin' :: !Int -> Shape' s -> Shape' s' -> Shape' (Bin s s') 
Leaf' :: Shape' Leaf 

data SomeShape where Source

Constructors

S :: Shape' s -> SomeShape 

data Mat :: Shape -> Shape -> * -> * where Source

Constructors

Quad :: !(Mat x1 y1 a) -> !(Mat x2 y1 a) -> !(Mat x1 y2 a) -> !(Mat x2 y2 a) -> Mat (Bin x1 x2) (Bin y1 y2) a 
Zero :: Mat x y a 
One :: !a -> Mat Leaf Leaf a 
Row :: Mat x1 Leaf a -> Mat x2 Leaf a -> Mat (Bin x1 x2) Leaf a 
Col :: Mat Leaf y1 a -> Mat Leaf y2 a -> Mat Leaf (Bin y1 y2) a 

Instances

data Vec :: Shape -> * -> * where Source

Constructors

Z :: Vec s a 
O :: a -> Vec Leaf a 
(:!) :: Vec s a -> Vec s' a -> Vec (Bin s s') a 

Instances

row :: Mat x1 Leaf a -> Mat x2 Leaf a -> Mat (Bin x1 x2) Leaf a Source

col :: Mat Leaf y1 a -> Mat Leaf y2 a -> Mat Leaf (Bin y1 y2) a Source

quad :: Mat x1 y1 a -> Mat x2 y1 a -> Mat x1 y2 a -> Mat x2 y2 a -> Mat (Bin x1 x2) (Bin y1 y2) a Source

(.+.) :: AbelianGroupZ a => Mat x y a -> Mat x y a -> Mat x y a Source

mult :: RingP a => Bool -> Mat x y a -> Mat z x a -> Mat z y (Pair a) Source

trav :: AbelianGroupZ a => Mat y x (Pair a) -> Pair (Mat y x a) Source

q0 :: Mat (Bin x x') (Bin y y') a Source

closeDisjointP :: RingP a => Bool -> Mat x x a -> Mat y x (Pair a) -> Mat y y a -> Pair (Mat y x a) Source

showR :: Mat x y a -> String Source

bin' :: Shape' s -> Shape' s' -> Shape' (Bin s s') Source

mkSing :: AbelianGroupZ a => Shape' x -> Shape' y -> a -> Mat x y a Source

data SomeTri a where Source

Constructors

T :: Shape' s -> Pair (Mat s s a) -> SomeTri a 

type Q a = SomeTri a Source

mkUpDiag :: AbelianGroupZ a => [a] -> Shape' s -> Mat s s a Source

close :: RingP a => Bool -> Mat s s (Pair a) -> Pair (Mat s s a) Source

mkTree :: RingP a => [Pair a] -> SomeTri a Source

quad' :: Applicative f => f (Mat x1 y1 a) -> f (Mat x2 y1 a) -> f (Mat x1 y2 a) -> f (Mat x2 y2 a) -> f (Mat (Bin x1 x2) (Bin y1 y2) a) Source

mergein :: RingP a => Bool -> SomeTri a -> Pair a -> SomeTri a -> SomeTri a Source

zw :: (AbelianGroup a, AbelianGroup b) => (a -> b -> c) -> Vec y a -> Vec y b -> Vec y c Source

A variant of zipWith on vectors

lk :: AbelianGroup a => Int -> Shape' x -> Vec x a -> a Source

Lookup in a vector

lin' :: AbelianGroup a => Mat x y a -> Vec y (Vec x a) Source

Linearize a matrix

contents :: Shape' x -> Vec x a -> [(Int, a)] Source

Contents of a vector

first :: (t -> t1) -> (t, t2) -> (t1, t2) Source

second :: (t -> t2) -> (t1, t) -> (t1, t2) Source

data Path :: Shape -> * where Source

Constructors

Here :: Path Leaf 
Low :: Path s -> Path (Bin s s') 
High :: Path s -> Path (Bin s' s) 

(<||>) :: Maybe (a, Path x) -> Maybe (a, Path x') -> Maybe (a, Path (Bin x x')) Source

rightmostOnLine :: Path y -> Mat x y a -> Maybe (a, Path x) Source

What is, and where is the rightmost non-zero element on a given line of the matrix?

isRightmost :: Path x -> Bool Source

Is this the rightmost path?

results' :: AbelianGroup a => Mat y y a -> Path y -> [(Path y, a, Path y)] Source

results :: AbelianGroupZ a => SomeTri a -> [(Int, a, Int)] Source

root' :: AbelianGroup a => Mat x y a -> a Source

square3 :: RingP a => Bool -> Pair a -> Pair a -> SomeTri a Source

(|+|) :: [[a]] -> [[a]] -> [[a]] Source

(-+-) :: [a] -> [a] -> [a] Source

lin :: AbelianGroup a => Shape' x -> Shape' y -> Mat x y a -> [[a]] Source

sparse :: AbelianGroup a => Shape' x -> Shape' y -> Mat x y a -> [(Int, Int, a)] Source

shiftX :: Shape' s -> [(Int, t, t1)] -> [(Int, t, t1)] Source

shiftY :: Shape' s -> [(t, Int, t1)] -> [(t, Int, t1)] Source