人類社交模擬（python實現）

• 基本理論
  
  1. 每個個體看作一個點（暫時用二維的點）【多維情況下，每一個維度都可以是對個人某一屬性的描述】
  2. 點的走向作爲個人的發展情況
  3. 社會初期隨機發展，一定時間後個人發展受朋友影響
  4. 前一次的點與後一次的點構成一個線段
  5. 在某一時間內，人A 對應的線段 與人B 對應的線段相交，則認定兩人相識（成爲朋友）
  6. 兩點之間的距離作爲兩個人親密度的度量，前提是成爲朋友
  7. 在達到一定年齡之後 ， 人們會選擇與自己親密度最佳（距離最小）的異性朋友作爲伴侶（成爲戀人），一定時間後產生新的人類
  8. 未完待續
• 算法實現

Code: humans

# -*- coding: utf-8 -*-
"""
Created on Thu Sep 24 10:48:48 2015

# Human

@author: Zhang_Jun
"""
import random
import math


class human(object):
    def __init__(self,ID):
        self.ID = ID  # 編號
        self.sex = random.randint(1,2)  # 隨機產生性別
        self.x_before = 0 ; self.y_before = 0  # 個人狀態描述(前)
        self.x_after = 0  ; self.y_after = 0   # 個人狀態描述(後)
        self.vector = [self.x_after - self.x_before , self.y_after - self.y_before] # 個人生活方向
        self.ability = 1 # 發展潛力，決定了個人發展方向的模長 
        self.age = 0  # 個人的年齡
        self.friend = [(ID,self)]   #  個人的所有好友列表 (編號，包含好友所有信息的對象)
        self.friend_distance_sex = [(ID,0,0)] # 好友的親密度與性別屬性 (編號、親密度、性別同性與否[0:同性，1：異性])
        self.mate = [ID,self,100000]  #  個人的配偶 ,配偶編號 以及 親密度
        self.stage = 1    # 個人的生存狀況 1 爲 生 0 爲 死
        self.time = 0  # 記錄時間流逝，可以構造一個與年齡轉換的函數 （自定義）

    def initiate_grow(self,step):  # 社會剛形成期間，每個人隨機發展，不受他人影響
        for i in range(step):  # step 爲控制發展次數的參數()
            self.time = self.time + 1   # 每step一次，增加一個時間單位
            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):  # 控制個人能力增長的幅度
    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 direction

def 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




#-------------相遇判斷函數-------------------------
# 線段的交點   ->  是否有交點/交點是否在線段上
# -kx+y=b

def 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 (避免分母爲0的情況)
        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 (避免分母爲0的情況)
        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 精確度問題
            return 0
        else: # 求解兩直線交點
            P=[0,0]
            P[0] = (b1 - b2) / (k2 - k1)
            P[1] = (k2 * b1 - k1 * b2) / (k2-k1)
            # 判斷交點是否在線段上
            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 0

Code: simulate （待註釋）

# -*- coding: utf-8 -*-
"""
Created on Thu Sep 24 11:14:11 2015

@author: Zhang_Jun
"""


import human
import math
import pylab as plt
import numpy as np
import pandas as pd
import seaborn
seaborn.set()


# -------------------------generate humans-----------------

humans = []
human_number = 1000 # number of  initiate humans

for i in range(human_number):
    humans.append(human.human(i))

#----------------------------------------------------------


#-------------------- the initiate grows of humans---------

Time = 2

for 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 rule


marrage_age_bottom = 20
marrage_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 （編號和對象）
        table2 = humans[i].friend_distance_sex    # 朋友的屬性（編號、親密度、性別同性與否） 
        ID_OBJ = pd.DataFrame(table1,columns=('ID','OBJ'))   # 轉化爲pandas 格式
        ID_DIS_Sex = pd.DataFrame(table2,columns=('ID','DIS','SEX'))    # 轉化爲pandas 格式
        S_ID_DIS_SEX = ID_DIS_Sex.sort(columns='DIS')     # 按照親密度排列
        S_ID_DIS_HSEX = S_ID_DIS_SEX[S_ID_DIS_SEX.SEX == 1]   #  獲取異性列表
        if len(S_ID_DIS_HSEX)>0:
            mate_DIS = S_ID_DIS_HSEX.DIS.values[0]  # 記錄與配偶的親密度
            mate_ID = S_ID_DIS_HSEX.ID.values[0]   # 記錄配偶ID
            if mate_DIS < humans[mate_ID].mate[2]:   # A的理想配偶已經有配偶的情況判定及處理
                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)  #  擁有配偶的人數

#-----------------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 friends
for 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)

---

運行以上代碼

500人發展一段時間後的情況圖（某一時刻）

運行後查看變量（人）的情況

In [274]: have_mate
Out[274]: 
[1,
 2,
 3,
 6,
 8,
 9,
 10,
 11,
 13,
 16,
 17,
 18,
 19，
 ...}

In [277]: have_friend
Out[277]: 
{0,
 1,
 2,
 3,
 4,
 5,
 6,
 8,
 9,
 10,
 ...}

In [281]: humans[11].mate
Out[281]: [216, <human.human at 0x3c5a79e8>, 0.12324587994054474]

In [282]: humans[216].mate
Out[282]: [11, <human.human at 0x5fa5ee48>, 0.12324587994054474

朋友圖（多階段發展）

一定時期後形成一定的格局

---

人們的發展方向分佈