Representation of a matrix. You can create matrices of any type but arithmetic operations in Matrix.Operations requires the matrices to have numeric types.

Create an empty matrix.

size empty == (0, 0)

Create a matrix with a given size, filled with a default value.

repeat 2 3 0 ~= [ [ 0, 0, 0 ], [ 0, 0, 0 ] ]

Createsa matrix with a given size, with the elements at index (i, j) initialized to the result of f (i, j).

initialize 3 3 (\(i,j) -> if i == j then 1 else 0) == identity 3

Create the identity matrix of dimension n.

Create a matrix from a list given the desired size. If the list has a length inferior to n * m, returns Nothing.

fromList 2 2 [1,1,1,1,1] == Just <| repeat 2 2 1
fromList 3 3 [0,1,2] == Nothing

Create a matrix from a list of lists. If any inner list is shorter than the first, returns Nothing. Otherwise, the length of the first list determines the width of the matrix.

fromLists [] == Just empty
fromLists [[]] == Just empty
fromLists [ [1,2,3], [1,2] ] == Nothing
fromLists [ [1,0], [0, 1] ] == Just <| identity 2

Return the number of rows in a given matrix.

Return the number of columns in a given matrix.

Return the dimensions of a given matrix in the form (rows, columns).

Return Just the element at the index or Nothing if the index is out of bounds.

Apply a function on every element of a matrix

Apply a function between pairwise elements of two matrices. If the matrices are of differents sizes, returns Nothing.

Return the transpose of a matrix.

Perform the standard matrix multiplication. If the dimensions of the matrices are incompatible, returns Nothing.

Convert the matrix to a flat list.

toList (identity 3) == [1,0,0,0,1,0,0,0,1]

Convert the matrix to a list of lists.

toLists (identity 3) = [ [1,0,0], [0,1,0], [0,0,1] ]

Convert a matrix to a formatted string.

pretty (identity 3) = """
    [ [ 1, 0, 0 ]
    , [ 0, 1, 0 ]
    , [ 0, 0, 1 ] ]
"""