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"""

Functions for 2D matrix operations

"""

from __future__ import annotations

from typing import Any

def add(*matrix_s: list[list[int]]) -> list[list[int]]:

"""

>>> add([[1,2],[3,4]],[[2,3],[4,5]])

[[3, 5], [7, 9]]

>>> add([[1.2,2.4],[3,4]],[[2,3],[4,5]])

[[3.2, 5.4], [7, 9]]

>>> add([[1, 2], [4, 5]], [[3, 7], [3, 4]], [[3, 5], [5, 7]])

[[7, 14], [12, 16]]

>>> add([3], [4, 5])

Traceback (most recent call last):

...

TypeError: Expected a matrix, got int/list instead

"""

if all(_check_not_integer(m) for m in matrix_s):

for i in matrix_s[1:]:

_verify_matrix_sizes(matrix_s[0], i)

return [[sum(t) for t in zip(*m)] for m in zip(*matrix_s)]

raise TypeError("Expected a matrix, got int/list instead")

def subtract(matrix_a: list[list[int]], matrix_b: list[list[int]]) -> list[list[int]]:

"""

>>> subtract([[1,2],[3,4]],[[2,3],[4,5]])

[[-1, -1], [-1, -1]]

>>> subtract([[1,2.5],[3,4]],[[2,3],[4,5.5]])

[[-1, -0.5], [-1, -1.5]]

>>> subtract([3], [4, 5])

Traceback (most recent call last):

...

TypeError: Expected a matrix, got int/list instead

"""

if (

_check_not_integer(matrix_a)

and _check_not_integer(matrix_b)

and _verify_matrix_sizes(matrix_a, matrix_b)

return [[i - j for i, j in zip(*m)] for m in zip(matrix_a, matrix_b)]

raise TypeError("Expected a matrix, got int/list instead")

def scalar_multiply(matrix: list[list[int]], n: float) -> list[list[float]]:

"""

>>> scalar_multiply([[1,2],[3,4]],5)

[[5, 10], [15, 20]]

>>> scalar_multiply([[1.4,2.3],[3,4]],5)

[[7.0, 11.5], [15, 20]]

"""

return [[x * n for x in row] for row in matrix]

def multiply(matrix_a: list[list[int]], matrix_b: list[list[int]]) -> list[list[int]]:

"""

>>> multiply([[1,2],[3,4]],[[5,5],[7,5]])

[[19, 15], [43, 35]]

>>> multiply([[1,2.5],[3,4.5]],[[5,5],[7,5]])

[[22.5, 17.5], [46.5, 37.5]]

>>> multiply([[1, 2, 3]], [[2], [3], [4]])

[[20]]

"""

if _check_not_integer(matrix_a) and _check_not_integer(matrix_b):

rows, cols = _verify_matrix_sizes(matrix_a, matrix_b)

if cols[0] != rows[1]:

msg = (

"Cannot multiply matrix of dimensions "

f"({rows[0]},{cols[0]}) and ({rows[1]},{cols[1]})"

)

raise ValueError(msg)

return [

[sum(m * n for m, n in zip(i, j)) for j in zip(*matrix_b)] for i in matrix_a

]

def identity(n: int) -> list[list[int]]:

"""

:param n: dimension for nxn matrix

:type n: int

:return: Identity matrix of shape [n, n]

>>> identity(3)

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

"""

n = int(n)

return [[int(row == column) for column in range(n)] for row in range(n)]

def transpose(

matrix: list[list[int]], return_map: bool = True

) -> list[list[int]] | map[list[int]]:

"""

>>> transpose([[1,2],[3,4]]) # doctest: +ELLIPSIS

<map object at ...

>>> transpose([[1,2],[3,4]], return_map=False)

[[1, 3], [2, 4]]

>>> transpose([1, [2, 3]])

Traceback (most recent call last):

...

TypeError: Expected a matrix, got int/list instead

"""

if _check_not_integer(matrix):

if return_map:

return map(list, zip(*matrix))

else:

return list(map(list, zip(*matrix)))

raise TypeError("Expected a matrix, got int/list instead")

def minor(matrix: list[list[int]], row: int, column: int) -> list[list[int]]:

"""

>>> minor([[1, 2], [3, 4]], 1, 1)

[[1]]

"""

minor = matrix[:row] + matrix[row + 1 :]

return [row[:column] + row[column + 1 :] for row in minor]

def determinant(matrix: list[list[int]]) -> Any:

"""

>>> determinant([[1, 2], [3, 4]])

-2

>>> determinant([[1.5, 2.5], [3, 4]])

-1.5

"""

if len(matrix) == 1:

return matrix[0][0]

return sum(

x * determinant(minor(matrix, 0, i)) * (-1) ** i

for i, x in enumerate(matrix[0])

)

def inverse(matrix: list[list[int]]) -> list[list[float]] | None:

"""

>>> inverse([[1, 2], [3, 4]])

[[-2.0, 1.0], [1.5, -0.5]]

>>> inverse([[1, 1], [1, 1]])

"""

# https://stackoverflow.com/questions/20047519/python-doctests-test-for-none

det = determinant(matrix)

if det == 0:

return None

matrix_minor = [

[determinant(minor(matrix, i, j)) for j in range(len(matrix))]

for i in range(len(matrix))

]

cofactors = [

[x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row])]

for row in range(len(matrix))

]

adjugate = list(transpose(cofactors))

return scalar_multiply(adjugate, 1 / det)

def _check_not_integer(matrix: list[list[int]]) -> bool:

return not isinstance(matrix, int) and not isinstance(matrix[0], int)

def _shape(matrix: list[list[int]]) -> tuple[int, int]:

return len(matrix), len(matrix[0])

def _verify_matrix_sizes(

matrix_a: list[list[int]], matrix_b: list[list[int]]

) -> tuple[tuple[int, int], tuple[int, int]]:

shape = _shape(matrix_a) + _shape(matrix_b)

if shape[0] != shape[3] or shape[1] != shape[2]:

msg = (

"operands could not be broadcast together with shape "

f"({shape[0], shape[1]}), ({shape[2], shape[3]})"

)

raise ValueError(msg)

return (shape[0], shape[2]), (shape[1], shape[3])

def main() -> None:

matrix_a = [[12, 10], [3, 9]]

matrix_b = [[3, 4], [7, 4]]

matrix_c = [[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]

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