-- Hoogle documentation, generated by Haddock -- See Hoogle, http://www.haskell.org/hoogle/ -- | Sized types in Haskell using the GHC Nat kind. -- @package sized-types @version 0.5.0 -- | Fin types -- -- Copyright: (c) 2013 University of Kansas License: BSD3 -- -- Maintainer: Andy Gill andygill@ku.edu Stability: unstable -- Portability: ghc module Data.Sized.Fin data Fin (n :: Nat) fromNat :: Sing (n :: Nat) -> Integer corners :: Bounded i => (i, i) -- | A list of all possible values of a type. universe :: (Bounded ix, Ix ix) => [ix] size :: (Bounded ix, Ix ix) => ix -> Int -- | (Kind) This is the kind of type-level natural numbers. data Nat :: * instance Typeable Fin instance Eq (Fin n) instance Ord (Fin n) instance SingI a => Integral (Fin a) instance SingI a => Real (Fin a) instance Enum (Fin a) instance SingI a => Bounded (Fin a) instance SingI a => Ix (Fin a) instance SingI a => Num (Fin a) instance SingI a => Read (Fin a) instance Show (Fin a) -- | Sized matrixes. -- -- Copyright: (c) 2013 University of Kansas License: BSD3 -- -- Maintainer: Andy Gill andygill@ku.edu Stability: unstable -- Portability: ghc module Data.Sized.Matrix -- | A Matrix is an array with the size determined uniquely by the -- type of the index type, ix, with every type in -- ix used. newtype Matrix ix a Matrix :: (Array ix a) -> Matrix ix a -- | A Vector is a 1D Matrix, using a TypeNat to define its length. type Vector (ix :: Nat) a = Matrix (Fin ix) a -- | A Vector2 is a 2D Matrix, using a TypeNat's to define its size. type Vector2 (ix :: Nat) (iy :: Nat) a = Matrix (Fin ix, Fin iy) a -- | matrix turns a finite list into a matrix. You often need to -- give the type of the result. matrix :: (Bounded i, Ix i) => [a] -> Matrix i a -- | what is the population of a matrix? population :: (Bounded i, Ix i) => Matrix i a -> Int allIndices :: (Bounded i, Ix i) => Matrix i a -> [i] -- | zeroOf is for use to force typing issues, and is 0. zeroOf :: (Bounded i, Ix i) => Matrix i a -> i -- | coord returns a matrix filled with indexes. coord :: (Bounded i, Ix i) => Matrix i i -- | Same as for lists. zipWith :: (Bounded i, Ix i) => (a -> b -> c) -> Matrix i a -> Matrix i b -> Matrix i c -- | forEach takes a matrix, and calls a function for each element, -- to give a new matrix of the same size. forEach :: (Bounded i, Ix i) => Matrix i a -> (i -> a -> b) -> Matrix i b -- | forAll creates a matrix out of a mapping from the coordinates. forAll :: (Bounded i, Ix i) => (i -> a) -> Matrix i a -- | mm is the 2D matrix multiply. mm :: (Bounded m, Ix m, Bounded n, Ix n, Bounded o, Ix o, Num a) => Matrix (m, n) a -> Matrix (n, o) a -> Matrix (m, o) a -- | transpose a 2D matrix. transpose :: (Bounded x, Ix x, Bounded y, Ix y) => Matrix (x, y) a -> Matrix (y, x) a -- | return the identity for a specific matrix size. identity :: (Bounded x, Ix x, Num a) => Matrix (x, x) a -- | append to 1D vectors append :: (SingI left, SingI right, SingI (left + right)) => Vector left a -> Vector right a -> Vector (left + right) a -- | stack two matrixes above each other. above :: (SingI top, SingI bottom, SingI y, SingI (top + bottom)) => Vector2 top y a -> Vector2 bottom y a -> Vector2 (top + bottom) y a -- | stack two matrixes beside each other. beside :: (SingI left, SingI right, SingI x, SingI (left + right)) => Vector2 x left a -> Vector2 x right a -> Vector2 x (left + right) a -- | look at a matrix through a functor lens, to another matrix. ixfmap :: (Bounded i, Ix i, Bounded j, Ix j, Functor f) => (i -> f j) -> Matrix j a -> Matrix i (f a) -- | grab part of a matrix. cropAt :: (Index i ~ Index ix, Bounded -- i, Ix i, Bounded ix, Ix ix) => Matrix ix a -> ix -> Matrix i -- a cropAt m corner = ixmap ( i -> (addIndex corner (toIndex i))) m -- -- slice a 2D matrix into rows. rows :: (Bounded n, Ix n, Bounded m, Ix m) => Matrix (m, n) a -> Matrix m (Matrix n a) -- | slice a 2D matrix into columns. columns :: (Bounded n, Ix n, Bounded m, Ix m) => Matrix (m, n) a -> Matrix n (Matrix m a) -- | join a matrix of matrixes into a single matrix. joinRows :: (Bounded n, Ix n, Bounded m, Ix m) => Matrix m (Matrix n a) -> Matrix (m, n) a -- | join a matrix of matrixes into a single matrix. joinColumns :: (Bounded n, Ix n, Bounded m, Ix m) => Matrix n (Matrix m a) -> Matrix (m, n) a -- | show2D displays a 2D matrix, and is the worker for show. -- -- 
--   GHCi> matrix [1..42] :: Matrix (Fin 7, Fin 6) Int
--   [  1,  2,  3,  4,  5,  6,
--      7,  8,  9, 10, 11, 12,
--     13, 14, 15, 16, 17, 18,
--     19, 20, 21, 22, 23, 24,
--     25, 26, 27, 28, 29, 30,
--     31, 32, 33, 34, 35, 36,
--     37, 38, 39, 40, 41, 42 ]
--
show2D :: (Bounded n, Ix n, Bounded m, Ix m, Show a) => Matrix (m, n) a -> String -- | S is shown as the contents, without the quotes. One use is a -- matrix of S, so that you can do show-style functions using fmap. newtype S S :: String -> S showAsE :: RealFloat a => Int -> a -> S showAsF :: RealFloat a => Int -> a -> S instance Typeable Matrix instance (Eq a, Ix ix) => Eq (Matrix ix a) instance (Ord a, Ix ix) => Ord (Matrix ix a) instance Show S instance (Show a, Show ix, Bounded ix, Ix ix) => Show (Matrix ix a) instance (Bounded ix, Ix ix) => Foldable (Matrix ix) instance (Bounded ix, Ix ix) => Traversable (Matrix ix) instance (Bounded i, Ix i) => Applicative (Matrix i) instance IArray Matrix a instance Ix ix => Functor (Matrix ix) -- | Sparse Matrix. -- -- Copyright: (c) 2009 University of Kansas License: BSD3 -- -- Maintainer: Andy Gill andygill@ku.edu Stability: unstable -- Portability: ghc module Data.Sized.Sparse.Matrix data SpMatrix ix a SpMatrix :: a -> (Map ix a) -> SpMatrix ix a fromAssocList :: (Ord i, Eq a) => a -> [(i, a)] -> SpMatrix i a toAssocList :: (SpMatrix i a) -> (a, [(i, a)]) -- | getElem looks up an element in the sparse matrix. If the -- element is not found in the sparse matrix, getElem returns the -- default value. getElem :: Ord ix => SpMatrix ix a -> ix -> a fill :: (Bounded ix, Ix ix) => SpMatrix ix a -> Matrix ix a prune :: (Bounded ix, Ix ix, Eq a) => a -> SpMatrix ix a -> SpMatrix ix a -- | Make a Matrix sparse, with a default zero value. sparse :: (Bounded ix, Ix ix, Eq a) => a -> Matrix ix a -> SpMatrix ix a mm :: (Bounded m, Ix m, Bounded n, Ix n, Bounded m', Ix m', Bounded n', Ix n', n ~ m', Num a, Eq a) => SpMatrix (m, n) a -> SpMatrix (m', n') a -> SpMatrix (m, n') a rowSets :: (Bounded a, Ix a, Ord b) => Set (a, b) -> Matrix a (Set b) columnSets :: (Bounded b, Ix b, Ord a) => Set (a, b) -> Matrix b (Set a) transpose :: (Bounded x, Ix x, Bounded y, Ix y, Eq a) => SpMatrix (x, y) a -> SpMatrix (y, x) a zipWith :: (Bounded x, Ix x) => (a -> b -> c) -> SpMatrix x a -> SpMatrix x b -> SpMatrix x c instance (Show a, Show ix, Bounded ix, Ix ix) => Show (SpMatrix ix a) instance (Bounded i, Ix i) => Applicative (SpMatrix i) instance Functor (SpMatrix ix) -- | Signed, fixed sized numbers. -- -- Copyright: (c) 2009 University of Kansas License: BSD3 -- -- Maintainer: Andy Gill andygill@ku.edu Stability: unstable -- Portability: ghc module Data.Sized.Signed data Signed (ix :: Nat) toVector :: SingI ix => Signed ix -> Vector ix Bool fromVector :: SingI ix => Vector ix Bool -> Signed ix type S2 = Signed 2 type S3 = Signed 3 type S4 = Signed 4 type S5 = Signed 5 type S6 = Signed 6 type S7 = Signed 7 type S8 = Signed 8 type S9 = Signed 9 type S10 = Signed 10 type S11 = Signed 11 type S12 = Signed 12 type S13 = Signed 13 type S14 = Signed 14 type S15 = Signed 15 type S16 = Signed 16 type S17 = Signed 17 type S18 = Signed 18 type S19 = Signed 19 type S20 = Signed 20 type S21 = Signed 21 type S22 = Signed 22 type S23 = Signed 23 type S24 = Signed 24 type S25 = Signed 25 type S26 = Signed 26 type S27 = Signed 27 type S28 = Signed 28 type S29 = Signed 29 type S30 = Signed 30 type S31 = Signed 31 type S32 = Signed 32 instance Typeable Signed instance Eq (Signed ix) instance Ord (Signed ix) instance SingI ix => Bounded (Signed ix) instance SingI ix => FiniteBits (Signed ix) instance SingI ix => Bits (Signed ix) instance SingI ix => Enum (Signed ix) instance SingI ix => Real (Signed ix) instance SingI ix => Num (Signed ix) instance SingI ix => Integral (Signed ix) instance SingI ix => Read (Signed ix) instance SingI ix => Show (Signed ix) -- | Unsigned, fixed sized numbers. -- -- Copyright: (c) 2009 University of Kansas License: BSD3 -- -- Maintainer: Andy Gill andygill@ku.edu Stability: unstable -- Portability: ghc module Data.Sized.Unsigned data Unsigned (ix :: Nat) toVector :: SingI ix => Unsigned ix -> Vector ix Bool fromVector :: SingI ix => Vector ix Bool -> Unsigned ix showBits :: SingI ix => Unsigned ix -> String -- | common; numerically boolean. type U1 = Unsigned 1 type U2 = Unsigned 2 type U3 = Unsigned 3 type U4 = Unsigned 4 type U5 = Unsigned 5 type U6 = Unsigned 6 type U7 = Unsigned 7 type U8 = Unsigned 8 type U9 = Unsigned 9 type U10 = Unsigned 10 type U11 = Unsigned 11 type U12 = Unsigned 12 type U13 = Unsigned 13 type U14 = Unsigned 14 type U15 = Unsigned 15 type U16 = Unsigned 16 type U17 = Unsigned 17 type U18 = Unsigned 18 type U19 = Unsigned 19 type U20 = Unsigned 20 type U21 = Unsigned 21 type U22 = Unsigned 22 type U23 = Unsigned 23 type U24 = Unsigned 24 type U25 = Unsigned 25 type U26 = Unsigned 26 type U27 = Unsigned 27 type U28 = Unsigned 28 type U29 = Unsigned 29 type U30 = Unsigned 30 type U31 = Unsigned 31 type U32 = Unsigned 32 instance Typeable Unsigned instance Eq (Unsigned ix) instance Ord (Unsigned ix) instance SingI ix => Ix (Unsigned ix) instance SingI ix => Bounded (Unsigned ix) instance SingI ix => FiniteBits (Unsigned ix) instance SingI ix => Bits (Unsigned ix) instance SingI ix => Enum (Unsigned ix) instance SingI ix => Real (Unsigned ix) instance SingI ix => Num (Unsigned ix) instance SingI ix => Integral (Unsigned ix) instance SingI ix => Read (Unsigned ix) instance Show (Unsigned ix) module Data.Sized.Sampled data Sampled (m :: Nat) (n :: Nat) Sampled :: (Signed n) -> Rational -> Sampled toVector :: (SingI m, SingI n) => Sampled m n -> Vector n Bool fromVector :: (SingI n, SingI m) => Vector n Bool -> Sampled m n mkSampled :: (SingI n, SingI m) => Rational -> Sampled m n instance (SingI ix, SingI m) => Enum (Sampled m ix) instance (SingI ix, SingI m) => Fractional (Sampled m ix) instance (SingI ix, SingI m) => Real (Sampled m ix) instance (SingI ix, SingI m) => Num (Sampled m ix) instance (SingI ix, SingI m) => Read (Sampled m ix) instance SingI ix => Show (Sampled m ix) instance SingI ix => Ord (Sampled m ix) instance SingI ix => Eq (Sampled m ix)