Data.Sized.Matrix

Sized matrixes.

Copyright: (c) 2009 University of Kansas License: BSD3

Maintainer: Andy Gill [e-mail] Stability: unstable Portability: ghc

Documentation

data Matrix ix a

A Matrix is an array with the sized determined uniquely by the type of the index type, ix.

Constructors

Matrix (Array ix a)

NullMatrix

Instances

Size i => Functor (Matrix i)

Methods

fmap :: (a -> b) -> Matrix i a -> Matrix i b

(<$) :: a -> Matrix i b -> Matrix i a

Size i => Applicative (Matrix i)

Methods

pure :: a -> Matrix i a

(<*>) :: Matrix i (a -> b) -> Matrix i a -> Matrix i b

liftA2 :: (a -> b -> c) -> Matrix i a -> Matrix i b -> Matrix i c

(*>) :: Matrix i a -> Matrix i b -> Matrix i b

(<*) :: Matrix i a -> Matrix i b -> Matrix i a

Size ix => Foldable (Matrix ix)

Methods

fold :: Monoid m => Matrix ix m -> m

foldMap :: Monoid m => (a -> m) -> Matrix ix a -> m

foldr :: (a -> b -> b) -> b -> Matrix ix a -> b

foldr' :: (a -> b -> b) -> b -> Matrix ix a -> b

foldl :: (b -> a -> b) -> b -> Matrix ix a -> b

foldl' :: (b -> a -> b) -> b -> Matrix ix a -> b

foldr1 :: (a -> a -> a) -> Matrix ix a -> a

foldl1 :: (a -> a -> a) -> Matrix ix a -> a

toList :: Matrix ix a -> [a]

null :: Matrix ix a -> Bool

length :: Matrix ix a -> Int

elem :: Eq a => a -> Matrix ix a -> Bool

maximum :: Ord a => Matrix ix a -> a

minimum :: Ord a => Matrix ix a -> a

sum :: Num a => Matrix ix a -> a

product :: Num a => Matrix ix a -> a

Size ix => Traversable (Matrix ix)

Methods

traverse :: Applicative f => (a -> f b) -> Matrix ix a -> f (Matrix ix b)

sequenceA :: Applicative f => Matrix ix (f a) -> f (Matrix ix a)

mapM :: Monad m => (a -> m b) -> Matrix ix a -> m (Matrix ix b)

sequence :: Monad m => Matrix ix (m a) -> m (Matrix ix a)

(Eq a, Ix ix) => Eq (Matrix ix a)

Methods

(==) :: Matrix ix a -> Matrix ix a -> Bool

(/=) :: Matrix ix a -> Matrix ix a -> Bool

(Ord a, Ix ix) => Ord (Matrix ix a)

Methods

compare :: Matrix ix a -> Matrix ix a -> Ordering

(<) :: Matrix ix a -> Matrix ix a -> Bool

(<=) :: Matrix ix a -> Matrix ix a -> Bool

(>) :: Matrix ix a -> Matrix ix a -> Bool

(>=) :: Matrix ix a -> Matrix ix a -> Bool

max :: Matrix ix a -> Matrix ix a -> Matrix ix a

min :: Matrix ix a -> Matrix ix a -> Matrix ix a

(Show a, Size ix) => Show (Matrix ix a)

Methods

showsPrec :: Int -> Matrix ix a -> ShowS

show :: Matrix ix a -> String

showList :: [Matrix ix a] -> ShowS

(!) :: Size n => Matrix n a -> n -> a

! looks up an element in the matrix.

toList :: Size i => Matrix i a -> [a]

toList turns a matrix into an always finite list.

fromList :: forall i a. Size i => [a] -> Matrix i a

fromList turns a finite list into a matrix. You often need to give the type of the result.

matrix :: Size i => [a] -> Matrix i a

matrix turns a finite list into a matrix. You often need to give the type of the result.

indices :: Size i => Matrix i a -> [i]

indices is a version of all that takes a type, for forcing the result type using the Matrix type.

length :: Size i => Matrix i a -> Int

what is the length of a matrix?

assocs :: Size i => Matrix i a -> [(i, a)]

assocs extracts the index/value pairs.

(//) :: Size i => Matrix i e -> [(i, e)] -> Matrix i e

accum :: Size i => (e -> a -> e) -> Matrix i e -> [(i, a)] -> Matrix i e

zeroOf :: Size i => Matrix i a -> i

zeroOf is for use to force typing issues, and is 0.

coord :: Size i => Matrix i i

coord returns a matrix filled with indexes.

zipWith :: Size i => (a -> b -> c) -> Matrix i a -> Matrix i b -> Matrix i c

Same as for lists.

forEach :: Size i => Matrix i a -> (i -> a -> b) -> Matrix i b

forEach takes a matrix, and calls a function for each element, to give a new matrix of the same size.

forAll :: Size i => (i -> a) -> Matrix i a

forAll creates a matrix out of a mapping from the coordinates.

mm :: (Size m, Size n, Size m', Size n', n ~ m', Num a) => Matrix (m, n) a -> Matrix (m', n') a -> Matrix (m, n') a

mm is the 2D matrix multiply.

transpose :: (Size x, Size y) => Matrix (x, y) a -> Matrix (y, x) a

transpose a 2D matrix.

identity :: (Size x, Num a) => Matrix (x, x) a

return the identity for a specific matrix size.

above :: (Size m, Size top, Size bottom, Size both, ADD top bottom ~ both, SUB both top ~ bottom, SUB both bottom ~ top) => Matrix (top, m) a -> Matrix (bottom, m) a -> Matrix (both, m) a

stack two matrixes above each other.

beside :: (Size m, Size left, Size right, Size both, ADD left right ~ both, SUB both left ~ right, SUB both right ~ left) => Matrix (m, left) a -> Matrix (m, right) a -> Matrix (m, both) a

stack two matrixes beside each other.

append :: (Size left, Size right, Size both, ADD left right ~ both, SUB both left ~ right, SUB both right ~ left) => Matrix left a -> Matrix right a -> Matrix both a

append two 1-d matrixes

ixmap :: (Size i, Size j) => (i -> j) -> Matrix j a -> Matrix i a

look at a matrix through a lens to another matrix.

ixfmap :: (Size i, Size j, Functor f) => (i -> f j) -> Matrix j a -> Matrix i (f a)

look at a matrix through a functor lens, to another matrix.

cropAt :: (Index i ~ Index ix, Size i, Size ix) => Matrix ix a -> ix -> Matrix i a

grab part of a matrix.

rows :: (Bounded n, Size n, Bounded m, Size m) => Matrix (m, n) a -> Matrix m (Matrix n a)

slice a 2D matrix into rows.

columns :: (Bounded n, Size n, Bounded m, Size m) => Matrix (m, n) a -> Matrix n (Matrix m a)

slice a 2D matrix into columns.

joinRows :: (Bounded n, Size n, Bounded m, Size m) => Matrix m (Matrix n a) -> Matrix (m, n) a

join a matrix of matrixes into a single matrix.

joinColumns :: (Bounded n, Size n, Bounded m, Size m) => Matrix n (Matrix m a) -> Matrix (m, n) a

join a matrix of matrixes into a single matrix.

unitRow :: (Size m, Bounded m) => Matrix m a -> Matrix (X1, m) a

generate a 2D single row from a 1D matrix.

unRow :: (Size m, Bounded m) => Matrix (X1, m) a -> Matrix m a

generate a 1D matrix from a 2D matrix.

unitColumn :: (Size m, Bounded m) => Matrix m a -> Matrix (m, X1) a

generate a 2D single column from a 1D matrix.

unColumn :: (Size m, Bounded m) => Matrix (m, X1) a -> Matrix m a

generate a 1D matrix from a 2D matrix.

squash :: (Size n, Size m) => Matrix m a -> Matrix n a

very general; required that m and n have the same number of elements, rebundle please.

showMatrix :: (Size n, Size m) => Matrix (m, n) String -> String

showMatrix displays a 2D matrix, and is the worker for show.

GHCi> matrix [1..42] :: Matrix (X7,X6) 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 ]

newtype S

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.

Constructors

S String

Instances

Show S

Methods

showsPrec :: Int -> S -> ShowS

show :: S -> String

showList :: [S] -> ShowS

showAsE :: RealFloat a => Int -> a -> S

showAsF :: RealFloat a => Int -> a -> S

scanM :: (Size ix, Bounded ix, Enum ix) => ((left, a, right) -> (right, b, left)) -> (left, Matrix ix a, right) -> (right, Matrix ix b, left)

scanL :: (Size ix, Bounded ix, Enum ix) => ((a, right) -> (right, b)) -> (Matrix ix a, right) -> (right, Matrix ix b)

scanR :: (Size ix, Bounded ix, Enum ix) => ((left, a) -> (b, left)) -> (left, Matrix ix a) -> (Matrix ix b, left)

module Data.Sized.Ix