import itertools
def min_path_sets(init_matrix,index_start,index_end):
    import re
    num_point = init_matrix.shape[0]
    min_path_list = []
    for i in range(num_point-1):
        temp = init_matrix**(i+1)
        item = expand(temp[index_start-1,index_end-1])
        list_given = re.sub('[ *123456789]',"",str(item)).split("+")
        
        #删除指定阶数下，路径长度不等于阶数的路
        index_to_delete = []
        for j in range(len(list_given)):
            if len(list_given[j])!=(i+1) or list_given[j]=='0':
                index_to_delete.append(j)
        for counter, index in enumerate(index_to_delete):
            index = index - counter
            list_given.pop(index)
        
        min_path_list.extend(list_given)
    return min_path_list

def str_de_duplication(pstr):
    a = ''
    for i in range(len(pstr)):
        if pstr[i] not in a:
            a+=pstr[i]
    return a

def product_symbol(pstr,my_dict):
    import numpy as np
    value_list = []
    for i in pstr:
        value_list.append(my_dict[i])
    return np.prod(value_list)

def generate_label(path_sets,my_dict):
    import numpy as np
    all_result = []
    for exp_num in range(len(path_sets)):
        item_Combination = list(itertools.combinations(path_sets, exp_num+1))
        item_list = list(map(lambda x: str_de_duplication("".join(x)),item_Combination))
        value_list = list(map(lambda x: product_symbol(x,my_dict),item_list))
        all_result.append(np.sum(value_list)*(-1)**(exp_num))
    return np.sum(all_result)

def Matrix_label(init_matrix,my_dict,index_start,index_end):
    path_sets = min_path_sets(init_matrix,index_start,index_end)
    pro_value = generate_label(path_sets,my_dict)
    return pro_value

from sympy import *
from sympy.abc import A,B,C,D,E,F
index_start = 2
index_end = 1
data = Matrix([[0,A,B],
               [A,0,C],
               [B,C,0]])
my_dict = {'A':0.8,
           'B':0.9,
           'C':0.9}

Matrix_label(data,my_dict,index_start,index_end)