python:实现strassen matrix multiplication施特拉森矩阵乘法算法
from __future__ import annotations
import math
def default_matrix_multiplication(a: list, b: list) -> list:
if len(a) != 2 or len(a[0]) != 2 or len(b) != 2 or len(b[0]) != 2:
raise Exception("Matrices are not 2x2")
new_matrix = [
[a[0][0] * b[0][0] + a[0][1] * b[1][0], a[0][0] * b[0][1] + a[0][1] * b[1][1]],
[a[1][0] * b[0][0] + a[1][1] * b[1][0], a[1][0] * b[0][1] + a[1][1] * b[1][1]],
]
return new_matrix
def matrix_addition(matrix_a: list, matrix_b: list):
return [
[matrix_a[row][col] + matrix_b[row][col] for col in range(len(matrix_a[row]))]
for row in range(len(matrix_a))
]
def matrix_subtraction(matrix_a: list, matrix_b: list):
return [
[matrix_a[row][col] - matrix_b[row][col] for col in range(len(matrix_a[row]))]
for row in range(len(matrix_a))
]
def split_matrix(a: list) -> tuple[list, list, list, list]:
if len(a) % 2 != 0 or len(a[0]) % 2 != 0:
raise Exception("Odd matrices are not supported!")
matrix_length = len(a)
mid = matrix_length // 2
top_right = [[a[i][j] for j in range(mid, matrix_length)] for i in range(mid)]
bot_right = [
[a[i][j] for j in range(mid, matrix_length)] for i in range(mid, matrix_length)
]
top_left = [[a[i][j] for j in range(mid)] for i in range(mid)]
bot_left = [[a[i][j] for j in range(mid)] for i in range(mid, matrix_length)]
return top_left, top_right, bot_left, bot_right
def matrix_dimensions(matrix: list) -> tuple[int, int]:
return len(matrix), len(matrix[0])
def print_matrix(matrix: list) -> None:
for i in range(len(matrix)):
print(matrix[i])
def actual_strassen(matrix_a: list, matrix_b: list) -> list:
if matrix_dimensions(matrix_a) == (2, 2):
return default_matrix_multiplication(matrix_a, matrix_b)
a, b, c, d = split_matrix(matrix_a)
e, f, g, h = split_matrix(matrix_b)
t1 = actual_strassen(a, matrix_subtraction(f, h))
t2 = actual_strassen(matrix_addition(a, b), h)
t3 = actual_strassen(matrix_addition(c, d), e)
t4 = actual_strassen(d, matrix_subtraction(g, e))
t5 = actual_strassen(matrix_addition(a, d), matrix_addition(e, h))
t6 = actual_strassen(matrix_subtraction(b, d), matrix_addition(g, h))
t7 = actual_strassen(matrix_subtraction(a, c), matrix_addition(e, f))
top_left = matrix_addition(matrix_subtraction(matrix_addition(t5, t4), t2), t6)
top_right = matrix_addition(t1, t2)
bot_left = matrix_addition(t3, t4)
bot_right = matrix_subtraction(matrix_subtraction(matrix_addition(t1, t5), t3), t7)
# construct the new matrix from our 4 quadrants
new_matrix = []
for i in range(len(top_right)):
new_matrix.append(top_left[i] + top_right[i])
for i in range(len(bot_right)):
new_matrix.append(bot_left[i] + bot_right[i])
return new_matrix
def strassen(matrix1: list, matrix2: list) -> list:
if matrix_dimensions(matrix1)[1] != matrix_dimensions(matrix2)[0]:
raise Exception(
"Unable to multiply these matrices, please check the dimensions. n"
f"Matrix A:{matrix1} nMatrix B:{matrix2}"
)
dimension1 = matrix_dimensions(matrix1)
dimension2 = matrix_dimensions(matrix2)
if dimension1[0] == dimension1[1] and dimension2[0] == dimension2[1]:
return [matrix1, matrix2]
maximum = max(max(dimension1), max(dimension2))
maxim = int(math.pow(2, math.ceil(math.log2(maximum))))
new_matrix1 = matrix1
new_matrix2 = matrix2
# Adding zeros to the matrices so that the arrays dimensions are the same and also
# power of 2
for i in range(0, maxim):
if i < dimension1[0]:
for j in range(dimension1[1], maxim):
new_matrix1[i].append(0)
else:
new_matrix1.append([0] * maxim)
if i < dimension2[0]:
for j in range(dimension2[1], maxim):
new_matrix2[i].append(0)
else:
new_matrix2.append([0] * maxim)
final_matrix = actual_strassen(new_matrix1, new_matrix2)
# Removing the additional zeros
for i in range(0, maxim):
if i < dimension1[0]:
for j in range(dimension2[1], maxim):
final_matrix[i].pop()
else:
final_matrix.pop()
return final_matrix
if __name__ == "__main__":
matrix1 = [
[2, 3, 4, 5],
[6, 4, 3, 1],
[2, 3, 6, 7],
[3, 1, 2, 4],
[2, 3, 4, 5],
[6, 4, 3, 1],
[2, 3, 6, 7],
[3, 1, 2, 4],
[2, 3, 4, 5],
[6, 2, 3, 1],
]
matrix2 = [[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
print(strassen(matrix1, matrix2))
