#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

# 计算矩阵的逆矩阵
def Inverse(A):
    n = len(A)
    # 计算代数余子式矩阵
    B = [[0 for i in range(n)] for j in range(n)]
    for i in range(n):
        for j in range(n):
            minor = [row[:j] + row[j+1:] for row in (A[:i] + A[i+1:])]
            B[j][i] = ((-1) ** (i + j)) * sum(minor[k][l] * (-1) ** (k + l) for k in range(n - 1) for l in range(n - 1))
    det = Det(A)
    print("det(A):",det)
    if det == 0:
        print("矩阵不可逆")
        return None
    A_inv = [[B[i][j] / det for j in range(n)] for i in range(n)]
    return A_inv

def FixInv(A):
    n = len(A)
    B = [[0 for i in range(n)] for j in range(n)]
    for i in range(n):
        for j in range(n):
            t = [row[:j] + row[j+1:] for row in (A[:i] + A[i+1:])]
            B[j][i] = ((-1) ** (i + j)) * Det(t)
    det = Det(A)
    if det == 0:
        print("矩阵不可逆")
        return None
    A_inv = [[B[i][j] / det for j in range(n)] for i in range(n)]
    return A_inv



if __name__ == "__main__":
    ##########################################################################
    # 把矩阵换成题干的矩阵 #########################
    A = [
        [1,2,-2],
        [1,1,1],
        [2,2,1]
    ]

    DL = [[0 for _ in range(len(A))] for __ in range(len(A))]
    U = [[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:
                DL[i][j] = A[i][j]
            else:
                U[i][j] = -A[i][j]
                

    
    print(f"LU分解的D-L矩阵为: {DL}")
    print(f"LU分解的U矩阵的逆矩阵为: {U}")
    ID = FixInv(DL)
    G = Dot(ID, U)
    print(f"LU分解的G矩阵为: {G}")