矩阵相乘的strausen算法用python代码实现

矩阵相乘的Strassen算法是一种并行化的快速矩阵乘法算法，它将大矩阵分解成更小的部分，通过7次基本的矩阵运算代替传统的8次。虽然对于现代计算机来说，常规的矩阵乘法通常已经足够快，但在某些特定场景，如计算密集型任务或教学演示，Strassen算法可以展示其优势。

以下是使用Python实现Strassen算法的一个简单版本。注意这个版本并未处理边界情况，仅适用于正方形矩阵，并未优化性能：

def add_subtract(a, b, c):
    return [[a[i][j] + b[i][j] - c[i][j] for j in range(n)] for i in range(n)]

def matrix_multiply_strassen(a, b):
    n = len(a)
    if n <= 1:
        return a * b

    # Split matrices into quarters
    a11, a12, a21, a22 = split_matrix(a)
    b11, b12, b21, b22 = split_matrix(b)

    # Perform 7 operations (strassen steps)
    p1 = matrix_multiply_strassen(add_subtract(a11, a22, b22), add_subtract(b11, b22, a21))
    p2 = matrix_multiply_strassen(add_subtract(a21, a22, b11), a11)
    p3 = matrix_multiply_strassen(a22, add_subtract(b21, b11, a11))
    p4 = matrix_multiply_strassen(a11, b12)
    p5 = matrix_multiply_strassen(add_subtract(a21, a11, b11), b22)
    p6 = matrix_multiply_strassen(add_subtract(a12, a22, b21), a21)
    p7 = matrix_multiply_strassen(a12, add_subtract(b11, b12, a22))

    # Assemble the result
    c11 = add_subtract(p1 + p4, p5, p6)
    c12 = add_subtract(p3, p5)
    c21 = add_subtract(p2, p4)
    c22 = p1 + p3 + p2 + p6

    # Merge the parts back together
    return merge_matrices(c11, c12, c21, c22)

# Helper functions to split and merge matrices
def split_matrix(matrix):
    n = len(matrix)
    return [matrix[:n//2][:n//2], matrix[:n//2][n//2:], matrix[n//2:][:n//2], matrix[n//2:][n//2:]]

def merge_matrices(*matrices):
    # ... implementation to combine the split matrices back into one big matrix
    pass