A = [
    [0, 3, 4],
    [1, -1, 1],
    [2, 1, 2]
]

b = [1, 2, 3]

# 列主元高斯消元法
def SovleRowMain(A,b):
    ks = 0.00000001
    n = len(A)
    if len(A[0]) != n:
        raise ValueError("A要为方阵")
    if len(b) != n:
        raise ValueError("b与A的行数不匹配")
    p = list(range(n))
    for i in range(n):
        row_max = abs(A[i][i])
        row_max_index = i
        for j in range(i + 1, n):
            if abs(A[j][i]) > row_max:
                row_max = abs(A[j][i])
                row_max_index = j
        A[i], A[row_max_index] = A[row_max_index], A[i]
        b[i], b[row_max_index] = b[row_max_index], b[i]
        p[i], p[row_max_index] = p[row_max_index], p[i]

        if abs(A[i][i]) < ks:
            raise ValueError("A矩阵奇异，无法进行高斯消元")
        for j in range(i + 1, n):
            m = A[j][i] / A[i][i]
            A[j][i] = m
            for k in range(i + 1, n):
                A[j][k] -= m * A[i][k]
            b[j] -= m * b[i]

    if abs(A[n - 1][n - 1]) < ks:
        raise ValueError("A矩阵奇异，无法进行高斯消元")
    
    # 回代求解
    b[n - 1] /= A[n - 1][n - 1]
    for i in range(n - 2, -1, -1):
        for j in range(i + 1, n):
            b[i] -= A[i][j] * b[j]
        b[i] /= A[i][i]

    # 得到L,U和P矩阵
    L = [[0 for i in range(n)] for j in range(n)]
    U = [[0 for i in range(n)] for j in range(n)]
    P = [[0 for i in range(n)] for j in range(n)]
    for i in range(n):
        for j in range(n):
            if i == j:
                L[i][j] = 1
                U[i][j] = A[i][j]
            elif i < j:
                U[i][j] = A[i][j]
            else:
                L[i][j] = A[i][j]

        P[i][p[i]] = 1
    return P,L,U,b

def prettyPrintMatrix(matrix):
    for row in matrix:
        print(row)


if __name__ == "__main__":
    # A = np.array(A, dtype=float)
    # b = np.array(b, dtype=float)
    P,L,U,x = SovleRowMain(A, b)
    print("P:")
    prettyPrintMatrix(P)
    print("L:")
    prettyPrintMatrix(L)
    print("U:")
    prettyPrintMatrix(U)
    print("x:")
    print(x)