Data.Sized.Matrix

Sized matrixes.

Copyright: (c) 2013 University of Kansas License: BSD3

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

Documentation

newtype Matrix ix a

A Matrix is an array with the size determined uniquely by the type of the index type, ix, with every type in ix used.

Constructors

Matrix (Array ix a)

Instances

IArray Matrix a

Ix ix => Functor (Matrix ix)

(Bounded i, Ix i) => Applicative (Matrix i)

(Bounded ix, Ix ix) => Foldable (Matrix ix)

(Bounded ix, Ix ix) => Traversable (Matrix ix)

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

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

(Show a, Show ix, Bounded ix, Ix ix) => Show (Matrix ix a)

Typeable (* -> * -> *) Matrix

type Vector ix a = Matrix (Fin ix) a

A Vector is a 1D Matrix, using a TypeNat to define its length.

type Vector2 ix iy a = Matrix (Fin ix, Fin iy) a

A Vector2 is a 2D Matrix, using a TypeNat's to define its size.

matrix :: forall i a. (Bounded i, Ix i) => [a] -> Matrix i a

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

population :: forall i a. (Bounded i, Ix i) => Matrix i a -> Int

what is the population of a matrix?

allIndices :: (Bounded i, Ix i) => Matrix i a -> [i]

zeroOf :: (Bounded i, Ix i) => Matrix i a -> i

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

coord :: (Bounded i, Ix i) => Matrix i i

coord returns a matrix filled with indexes.

zipWith :: (Bounded i, Ix i) => (a -> b -> c) -> Matrix i a -> Matrix i b -> Matrix i c

Same as for lists.

forEach :: (Bounded i, Ix 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 :: (Bounded i, Ix i) => (i -> a) -> Matrix i a

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

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

mm is the 2D matrix multiply.

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

transpose a 2D matrix.

identity :: (Bounded x, Ix x, Num a) => Matrix (x, x) a

return the identity for a specific matrix size.

append :: (SingI left, SingI right, SingI (left + right)) => Vector left a -> Vector right a -> Vector (left + right) a

append to 1D vectors

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 above 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

stack two matrixes beside each other.

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

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

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

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

slice a 2D matrix into columns.

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

join a matrix of matrixes into a single matrix.

show2D :: (Bounded n, Ix n, Bounded m, Ix m, Show a) => Matrix (m, n) a -> String

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 ]

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

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

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