"""
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: 期望矩阵，而得到整数/列表
"""
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("期望矩阵，而得到整数/列表")
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: 期望矩阵，而得到整数/列表
"""
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("期望矩阵，而得到整数/列表")
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 = (
"无法乘以维度为 "
f"({rows[0]},{cols[0]}) 和 ({rows[1]},{cols[1]}) 的矩阵"
)
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: nxn 矩阵的维度
:type n: int
:return: 形状为 [n, n] 的单位矩阵
>>> 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: 期望矩阵，而得到整数/列表
"""
if _check_not_integer(matrix):
if return_map:
return map(list, zip(*matrix))
else:
return list(map(list, zip(*matrix)))
raise TypeError("期望矩阵，而得到整数/列表")
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 = (
"操作数的形状不匹配，形状为 "
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]]
matrix_d = [[3, 0, 2], [2, 0, -2], [0, 1, 1]]
print(f"加法操作, {add(matrix_a, matrix_b) } \n")
print(f"乘法操作, {multiply(matrix_a, matrix_b) } \n")
print(f"单位矩阵: {identity(5)}\n")
print(f"{matrix_c} 的子矩阵 = {minor(matrix_c, 1, 2)} \n")
print(f"{matrix_b} 的行列式 = {determinant(matrix_b)} \n")
print(f"{matrix_d} 的逆矩阵 = {inverse(matrix_d)}\n")
if __name__ == "__main__":
import doctest
doctest.testmod()
main()
