人类社交模拟（python实现）
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- 基本理论
- 每个个体看作一个点（暂时用二维的点）【多维情况下，每一个维度都可以是对个人某一属性的描述】
- 点的走向作为个人的发展情况
- 社会初期随机发展，一定时间后个人发展受朋友影响
- 前一次的点与后一次的点构成一个线段
- 在某一时间内，
人A 对应的线段 与人B 对应的线段相交，则认定两人相识（成为朋友） - 两点之间的距离作为两个人亲密度的度量，前提是成为朋友
- 在达到一定年龄之后 ， 人们会选择与自己亲密度最佳（距离最小）的异性朋友作为伴侣（成为恋人），一定时间后产生新的人类
- 未完待续
- 算法实现
Code: humans
# -*- coding: utf-8 -*-"""Created on Thu Sep 24 10:48:48 2015# Human@author: Zhang_Jun"""import randomimport mathclass human(object): def __init__(self,ID): self.ID = ID # 编号 self.sex = random.randint(1,2) # 随机产生性别 self.x_before = 0 ; self.y_before = 0 # 个人状态描述(前) self.x_after = 0 ; self.y_after = 0 # 个人状态描述(后) self.vector = [self.x_after - self.x_before , self.y_after - self.y_before] # 个人生活方向 self.ability = 1 # 发展潜力，决定了个人发展方向的模长 self.age = 0 # 个人的年龄 self.friend = [(ID,self)] # 个人的所有好友列表 (编号，包含好友所有信息的对象) self.friend_distance_sex = [(ID,0,0)] # 好友的亲密度与性别属性 (编号、亲密度、性别同性与否[0:同性，1：异性]) self.mate = [ID,self,100000] # 个人的配偶 ,配偶编号 以及 亲密度 self.stage = 1 # 个人的生存状况 1 为 生 0 为 死 self.time = 0 # 记录时间流逝，可以构造一个与年龄转换的函数 （自定义） def initiate_grow(self,step): # 社会刚形成期间，每个人随机发展，不受他人影响 for i in range(step): # step 为控制发展次数的参数() self.time = self.time + 1 # 每step一次，增加一个时间单位 self.x_before = self.x_after angle = random.randint(0,360)/180.0 * math.pi self.x_after = self.x_after + self.ability * math.cos(angle) self.y_before = self.y_after self.y_after = self.y_after + self.ability * math.sin(angle) self.vector = [self.x_after - self.x_before , self.y_after - self.y_before] def grow(self,step,coef_friend,coef_random): self.time = self.time = self.time + 1 self.x_before = self.x_after self.y_before = self.y_after friend_effect = [i * coef_friend for i in norm(sum_direction(self.friend))] angle = random.randint(0,360)/180.0 * math.pi random_effect = [i*coef_random for i in norm([math.cos(angle) , math.sin(angle)])] direction =[i * self.ability for i in norm(sum_list(friend_effect,random_effect))] [self.x_after,self.y_after] = sum_list([self.x_before,self.y_before] , direction) self.vector = [self.x_after - self.x_before , self.y_after - self.y_before] self.ability = sigmoid(inverse_sigmoid(self.ability) + coef_random * random.randint(-5,5)+ coef_friend * inverse_sigmoid(friend_ability(self.friend,self.ability)))def sigmoid(x): # 控制个人能力增长的幅度 return 2.0/(math.exp(-0.1*x)+1)def inverse_sigmoid(y): return 10*math.log(y / (2.0-y) )def sum_list(a,b): return [x+y for x,y in zip(a,b)]def sum_direction(friend_List): direction =[0,0] for friend in friend_List: direction = sum_list(direction,friend[1].vector) return directiondef norm(L): ss = 0 # 平方和 for i in L: ss = ss + i*i sss = math.sqrt(ss) return [x/sss for x in L]def friend_ability(friend_List,self_ability): fri_ability = [fri[1].ability for fri in friend_List] return (1.0*sum(fri_ability)/len(fri_ability) - self_ability)*0.5 + 1#-------------相遇判断函数-------------------------# 线段的交点 -> 是否有交点/交点是否在线段上# -kx+y=bdef meet(human1,human2) : delta =1e-10 P1 = [human1.x_before,human1.y_before] P2 = [human1.x_after,human1.y_after] P3 = [human2.x_before,human2.y_before] P4 = [human2.x_after,human2.y_after] if (P2[0]-P1[0])==0: # in case of denominator equals 0 (避免分母为0的情况) if (P3[0]-P4[0])==0: return 0 else: k2 = 1.0*(P4[1]-P3[1])/(P4[0]-P3[0]) b2 = -k2*P3[0]+P3[1] P = [P1[0],k2*P1[0]+b2] if (P[0]-P1[0])*(P[0]-P2[0])<=0 and (P[0]-P3[0])*(P[0]-P4[0])<=0 \ and (P[1]-P1[1])*(P[1]-P2[1])<=0 and (P[1]-P3[1])*(P[1]-P4[1])<=0 : return 1 else: return 0 elif (P4[0]-P3[0])==0: # in case of denominator equals 0 (避免分母为0的情况) if (P2[0]-P1[0])==0: return 0 else: k1 = 1.0*(P2[1]-P1[1])/(P2[0]-P1[0]) b1 = -k1*P1[0]+P1[1] P = [P3[0],k1*P3[0]+b1] if (P[0]-P1[0])*(P[0]-P2[0])<=0 and (P[0]-P3[0])*(P[0]-P4[0])<=0 \ and (P[1]-P1[1])*(P[1]-P2[1])<=0 and (P[1]-P3[1])*(P[1]-P4[1])<=0 : return 1 else: return 0 else: k1 = 1.0 * (P2[1] - P1[1]) / (P2[0] - P1[0]) k2 = 1.0 * (P4[1] - P3[1]) / (P4[0] - P3[0]) b1 = -k1 * P1[0] + P1[1] b2 = -k2 * P3[0] + P3[1] if abs(k1 - k2) < delta: # if use k1=k2 will cause singular matrix 精确度问题 return 0 else: # 求解两直线交点 P=[0,0] P[0] = (b1 - b2) / (k2 - k1) P[1] = (k2 * b1 - k1 * b2) / (k2-k1) # 判断交点是否在线段上 if (P[0]-P1[0])*(P[0]-P2[0])<=0 and (P[0]-P3[0])*(P[0]-P4[0])<=0 \ and (P[1]-P1[1])*(P[1]-P2[1])<=0 and (P[1]-P3[1])*(P[1]-P4[1])<=0 : return 1 else: return 0Code: simulate （待注释）
# -*- coding: utf-8 -*-"""Created on Thu Sep 24 11:14:11 2015@author: Zhang_Jun"""import humanimport mathimport pylab as pltimport numpy as npimport pandas as pdimport seabornseaborn.set()# -------------------------generate humans-----------------humans = []human_number = 1000 # number of initiate humansfor i in range(human_number): humans.append(human.human(i))#----------------------------------------------------------#-------------------- the initiate grows of humans---------Time = 2for people in humans: people.initiate_grow(Time)#-----------------show the vector of humans--------------------V = [people.vector for people in humans ]human_V = np.array(V)#plt.plot(human_V[:,0],human_V[:,1],'.')#plt.figure()#---------------------------------------------def draw_grow(number): Position =[[people.x_before,people.x_after,people.y_before,people.y_after] for people in humans] X_Position = np.array(Position)[:,:2] Y_Position = np.array(Position)[:,2:] for i in range(number): plt.plot(X_Position[i],Y_Position[i])#---------------------------------------------------------for i in range(10): for people in humans: people.initiate_grow(1) draw_grow(human_number)# after initiate grow , the growth of people should folow some rulemarrage_age_bottom = 20marrage_age_top = 40#--------------------------------------meet -------------Meet=np.zeros(human_number*human_number).reshape(human_number,human_number)Meet_people=[]for t in range(10): for people in humans: people.grow(1,0.8,0.2) #draw_grow(human_number) for i in range(human_number): for j in range(human_number): if Meet[i,j]==0 and i != j: Meet[i,j] = human.meet(humans[i],humans[j]) if Meet[i,j] == 1 and (i,j) not in Meet_people: Meet_people.append((i,j)) #print Meet_people #print Meet for fri in Meet_people: # friend in Meet_people if (fri[1],humans[fri[1]]) not in humans[fri[0]].friend: humans[fri[0]].friend.append((fri[1],humans[fri[1]])) distance = math.sqrt( math.pow(humans[fri[1]].x_after \ - humans[fri[0]].x_after , 2) + math.pow(humans[fri[1]].y_after \ - humans[fri[0]].y_after , 2)) sex_compare = 0 if humans[fri[0]].sex == humans[fri[1]].sex else 1 humans[fri[0]].friend_distance_sex.append((fri[1],distance,sex_compare))# -------------------------------------------------------- #draw_grow(human_number) have_friend = set([p[0] for p in Meet_people]) for i in have_friend: table1 = humans[i].friend # 所有的朋友 （编号和对象） table2 = humans[i].friend_distance_sex # 朋友的属性（编号、亲密度、性别同性与否） ID_OBJ = pd.DataFrame(table1,columns=('ID','OBJ')) # 转化为pandas 格式 ID_DIS_Sex = pd.DataFrame(table2,columns=('ID','DIS','SEX')) # 转化为pandas 格式 S_ID_DIS_SEX = ID_DIS_Sex.sort(columns='DIS') # 按照亲密度排列 S_ID_DIS_HSEX = S_ID_DIS_SEX[S_ID_DIS_SEX.SEX == 1] # 获取异性列表 if len(S_ID_DIS_HSEX)>0: mate_DIS = S_ID_DIS_HSEX.DIS.values[0] # 记录与配偶的亲密度 mate_ID = S_ID_DIS_HSEX.ID.values[0] # 记录配偶ID if mate_DIS < humans[mate_ID].mate[2]: # A的理想配偶已经有配偶的情况判定及处理 humans[humans[mate_ID].mate[0]].mate=[humans[mate_ID].mate[0],humans[mate_ID].mate[1],100000] humans[i].mate = [mate_ID,ID_OBJ[ID_OBJ.ID==mate_ID]['OBJ'].values[0],mate_DIS] humans[mate_ID].mate =[i,humans[i],mate_DIS]have_mate = [i for i in have_friend if humans[i].mate[0]!=i]print len(have_mate) # 拥有配偶的人数#-----------------show the vector of humans--------------------plt.figure()V = [people.vector for people in humans ]human_V = np.array(V)plt.plot(human_V[:,0],human_V[:,1],'.')plt.figure()# draw friendsfor me in have_friend: for number in range(len(humans[me].friend)): Position =[humans[me].x_after,humans[me].friend[number][1].x_after,humans[me].y_after,humans[me].friend[number][1].y_after] plt.plot(Position[:2],Position[2:],'g-',linewidth=0.3)运行以上代码
500人发展一段时间后的情况图（某一时刻）
运行后查看变量（人）的情况
In [274]: have_mateOut[274]: [1, 2, 3, 6, 8, 9, 10, 11, 13, 16, 17, 18, 19， ...}In [277]: have_friendOut[277]: {0, 1, 2, 3, 4, 5, 6, 8, 9, 10, ...}In [281]: humans[11].mateOut[281]: [216, <human.human at 0x3c5a79e8>, 0.12324587994054474]In [282]: humans[216].mateOut[282]: [11, <human.human at 0x5fa5ee48>, 0.12324587994054474朋友图（多阶段发展）
一定时期后形成一定的格局
人们的发展方向分布
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