#模 范数
def Norm(x,v):    
    if len(x[0]) == 1:
        if v == 1:
            return sum([abs(i[0]) for i in x])
        elif v == 2:
            return (sum([i[0]**2 for i in x]))**0.5
        elif v == float("inf"):
            return max([abs(i[0]) for i in x])
    else:
        if v == 1:
            return max([sum([abs(x[i][j]) for i in range(len(x))]) for j in range(len(x[0]))])
        elif v == float("inf"):
            return max([sum([abs(i) for i in x[j]]) for j in range(len(x))])
    return None

# 计算矩阵的点积
def Dot(A,B):
    if len(A[0]) != len(B):
        return None
    return [[sum([A[i][j] * B[j][k] for j in range(len(A[0]))]) for k in range(len(B[0]))] for i in range(len(A))]

# 计算矩阵的行列式
def Det(A):
    if len(A) == 2:
        return A[0][0] * A[1][1] - A[0][1] * A[1][0]
    det = 0
    for c in range(len(A)):
        sub_matrix = [row[:c] + row[c+1:] for row in A[1:]]
        det += ((-1) ** c) * A[0][c] * Det(sub_matrix)
    return det


if __name__ == "__main__":
    ##########################################################################
    # 把矩阵换成题干的矩阵 #########################
    A = [
        [1,2,-2],
        [1,1,1],
        [2,2,1]
    ]
    # 把范数的种类数换成题干的要求，inf是无穷范数 #########################
    LU = A.copy()
    ID = [[0 for _ in range(len(A))] for __ in range(len(A))]
    for i in range(len(A)):
        for j in range(len(A[0])):
            if i == j:
                ID[i][j] = 1/A[i][j]
                LU[i][j] = 0
            else:
                LU[i][j] = -LU[i][j]
    print(f"LU分解的LU矩阵为: {LU}")
    print(f"LU分解的D矩阵的逆矩阵为: {ID}")
    J = Dot(ID, LU)
    print(f"LU分解的J矩阵为: {J}")