Data.Utils.Matrix

This module defines fixed-size matrices and some basic typeclass instances and operations for them.

Documentation

newtype Matrix m n a

Matrix m n a is the type of matrices with m rows, n columns and entries of type a.

Constructors

Matrix (Vector m (Vector n a))

Instances

Functor (Matrix m n)

(KnownNat m, KnownNat n) => Applicative (Matrix m n)

Foldable (Matrix m n)

Traversable (Matrix m n)

Eq a => Eq (Matrix m n a)

Show a => Show (Matrix m n a)

(<%%>) :: Num a => Matrix m n a -> Vector n a -> Vector m a

Multiplication of a matrix by a (column-)vector.

>>> :set -XDataKinds
>>> (pure 1 :: Matrix 1 2 Int) <%%> cons 1 (cons 2 nil)
[3]

row :: Matrix m n a -> Int -> Maybe (Vector n a)

Gives the matrix row with the specified index (starting at zero) if the index is valid, otherwise Nothing.

>>> :set -XDataKinds
>>> row (pure 42 :: Matrix 2 4 Int) 0
Just [42,42,42,42]

>>> row (pure 42 :: Matrix 2 4 Int) 2
Nothing

column :: Matrix m n a -> Int -> Maybe (Vector m a)

Gives the matrix column with the specified index (starting at zero) if the index is valid, otherwise Nothing.

>>> :set -XDataKinds
>>> column (pure 42 :: Matrix 2 4 Int) 3
Just [42,42]

>>> column (pure 42 :: Matrix 2 4 Int) 4
Nothing

mgenerate :: (KnownNat m, KnownNat n) => ((Int, Int) -> a) -> Matrix m n a

Generates a matrix by applying the given function to each index (row, column).

>>> :set -XDataKinds
>>> mgenerate id :: Matrix 3 2 (Int, Int)
Matrix [[(0,0),(0,1)],[(1,0),(1,1)],[(2,0),(2,1)]]

(!!?) :: Matrix m n a -> (Int, Int) -> Maybe a

Gives the matrix element with the specified index (row, column) if the index is valid, otherwise Nothing.

>>> :set -XDataKinds
>>> let m = mgenerate (uncurry (+)) :: Matrix 2 3 Int
>>> m !!? (0,0)
Just 0

>>> m !!? (1, 2)
Just 3

>>> m !!? (5, 7)
Nothing

transpose :: (KnownNat m, KnownNat n) => Matrix m n a -> Matrix n m a

Transposes a matrix.

>>> transpose (Matrix $ cons (cons 'a' nil) (cons (cons 'b' nil) nil))
Matrix ["ab"]