Matrix algebra ‘from scratch’ with type annotations

Matrix algebra ‘from scratch’ with type annotations

This is the continuation of yesterday’s practice, but now with Matrix operations.

from typing import List, Tuple, Callable

Vector = List[float]
Matrix = List[List[float]]

A = [[1, 2, 3],
     [4, 5, 6]]

B = [[1, 2],
     [3, 4],
     [5, 6]]

Shape

def shape(A: Matrix) -> Tuple[int, int]:
    number_of_rows = len(A)
    number_of_columns = len(A[0]) if A else 0
    return number_of_rows, number_of_columns

assert shape([[1, 2, 3],[4, 5, 6]]) == (2, 3)

Get rows and columns

def get_row(A: Matrix, i: int) -> Vector:
    return A[i]

def get_columns(A: Matrix, i: int) -> Vector:
    return [row[i] for row in A] 

assert get_columns([[1, 2, 3],[4, 5, 6]], 1) == [2, 5]

Create a new matrix from a function of \((i, j)\)

def make_matrix(
    number_of_rows: int,
    number_of_columns: int,
    entry_function: Callable[[int, int], float]
) -> Matrix:
    return [
        [entry_function(i, j) for j in range(number_of_columns)]
        for i in range(number_of_rows)
    ]

assert make_matrix(3, 2, lambda i, j: i + j) == [[0, 1], [1, 2], [2, 3]]

def identity_matrix(n: int) -> Matrix:
    return make_matrix(n, n, lambda i, j: 1 if i == j else 0)

assert identity_matrix(3) == [[1, 0, 0], [0, 1, 0], [0, 0, 1]]

identity_matrix(5)

[[1, 0, 0, 0, 0],
 [0, 1, 0, 0, 0],
 [0, 0, 1, 0, 0],
 [0, 0, 0, 1, 0],
 [0, 0, 0, 0, 1]]