########################################
#   ch5.1 Monte Carlo policy evaluation 
########################################
#
# reference: http://waxworksmath.com
#
########################################
# function to calc. value of cards
card.value<-function(adj.cards) {
 sum.cards=sum(adj.cards)
 if (any(adj.cards==1) & sum.cards<=11) {
   sum.cards=sum.cards+10;
   usableA=1          #true
  } else {usableA=2}  #false
 return(c(sum.cards,usableA))
}

# function to calc. reward
calc.reward<-function(p.val,d.val) {
  if (p.val>21) { reward=-1
  } else {if (d.val>21) { reward=1
    } else {if (p.val==d.val) {reward=0
      } else{ reward=ifelse(p.val>d.val,1,-1)}
}}}

# main function
BJ_MC_fixedPolicy<-function(policy=20,maxIter=1e6){
  rew.sum=array(0,dim=c(10,10,2))
  rew.count=array(0,dim=c(10,10,2))
  for (i_play in 1:maxIter) {
    cards=sample(rep(1:13,4))
    player=cards[1:2];  adj.player=pmin(player,10)
    dealer=cards[3:4];  adj.dealer=pmin(dealer,10)
    cards=cards[-(1:4)]
    d.val=card.value(adj.dealer)
    p.val=card.value(adj.player)
    state.hist=c(adj.dealer[1],p.val[1],p.val[2])
    while (p.val[1] < policy) {
      player=c(player,cards[1]); adj.player=pmin(player,10)
      cards=cards[-1]
      p.val=card.value(adj.player)
      state.hist=rbind(state.hist,c(adj.dealer[1],p.val[1],p.val[2]))
    }
    while (d.val[1] < 17) {
      dealer=c(dealer,cards[1]); adj.dealer=pmin(dealer,10)
      cards=cards[-1]
      d.val=card.value(adj.dealer)
    }
    rew=calc.reward(p.val[1],d.val[1])
    n.state=nrow(state.hist)
    if (is.null(n.state)) {
      n.state=1
      state.hist=t(as.matrix(state.hist))
    }
    for (i_state in 1:n.state) {
      if (state.hist[i_state,2] > 11 & state.hist[i_state,2] < 22) {
        rew.sum[state.hist[i_state,1],(state.hist[i_state,2]-11),state.hist[i_state,3]]
          = rew.sum[state.hist[i_state,1],(state.hist[i_state,2]-11),state.hist[i_state,3]]+rew
        rew.count[state.hist[i_state,1],(state.hist[i_state,2]-11),state.hist[i_state,3]]
          =rew.count[state.hist[i_state,1],(state.hist[i_state,2]-11),state.hist[i_state,3]]+1
      }
    }
  }
  return(rew.sum/rew.count)
}

# function 2 plot results
plot.BJ_MC<-function(V){
 par(mfrow=c(1,2))
 image(V[,,1],main="with usable Ace",xaxt='n',yaxt='n',
   xlab="Dealer showing",ylab="Player sum")
 axis(1,at=seq(0,1,length.out=10),label=c("A",paste(2:10)))
 axis(2,at=seq(0,1,length.out=10),label=12:21)
 image(V[,,2],main="without usable Ace",xaxt='n',yaxt='n',
   xlab="Dealer showing",ylab="Player sum")
 axis(1,at=seq(0,1,length.out=10),label=c("A",paste(2:10)))
 axis(2,at=seq(0,1,length.out=10),label=12:21)
}

> V=BJ_MC(17)
> plot.BJ_MC(V)

########################################
#   ch5.3 Monte Carlo exploring starts
########################################
# function to calc. value of cards
card.value<-function(adj.cards) {
 sum.cards=sum(adj.cards)
 if (any(adj.cards==1) & sum.cards<=11) {
   sum.cards=sum.cards+10;
   usableA=1             #true
  } else {usableA=2}     #false
 return(c(sum.cards,usableA))
}

# function to calc. reward
calc.reward<-function(p.val,d.val) {
  if (p.val>21) { reward=-1
  } else {if (d.val>21) { reward=1
    } else {if (p.val==d.val) {reward=0
      } else{ reward=ifelse(p.val>d.val,1,-1)}
}}}

# main function
BJ_MC<-function(maxIter=1e6){
  rew.sum=array(0,dim=c(10,10,2,2))
  rew.count=array(1,dim=c(10,10,2,2))
  Q=array(0,dim=c(10,10,2))
  V=array(0,dim=c(10,10,2))
  policy=array(sample(0:1,10*10*2,replace=T),dim=c(10,10,2))
  # policy: 1 = hit, 0 = stay
  for (i_play in 1:maxIter) {
    # initial draw
    cards=sample(c(rep(1:10,4),rep(10,12)))
    player=cards[1:2]
    dealer=cards[3:4]
    cards=cards[-(1:4)]
    d.val=card.value(dealer)
    p.val=card.value(player)
     
    while( p.val[1] < 12 ) {
      player=c(player,cards[1])
      cards=cards[-1]
      p.val=card.value(player)
    }
    action=sample(0:1,1)
    state.hist=c(dealer[1],p.val[1],p.val[2],(action+1))
    
    # player's action
    while (action==1 & p.val[1]<22) {
      player=c(player,cards[1])
      cards=cards[-1]
      p.val=card.value(player)
      state.hist=rbind(state.hist,c(dealer[1],p.val[1],p.val[2],(action+1)))
      if (p.val[1]<22) {
        action=policy[dealer[1],(p.val[1]-11),p.val[2]]
      }
    }
    
    # dealer's action
    while (d.val[1]<17) {
      dealer=c(dealer,cards[1])
      cards=cards[-1]
      d.val=card.value(dealer)
    }
    rew=calc.reward(p.val[1],d.val[1])
    n.state=nrow(state.hist)
    if (is.null(n.state)) {
      n.state=1
      state.hist=t(as.matrix(state.hist))
    }
    for (i_state in 1:n.state) {
      if (state.hist[i_state,2]>11 & state.hist[i_state,2]<22) {
        ind=state.hist[i_state,]-c(0,11,0,0)
        rew.sum[ind[1],ind[2],ind[3],ind[4]]= rew.sum[ind[1],ind[2],ind[3],ind[4]]+rew
        rew.count[ind[1],ind[2],ind[3],ind[4]]=rew.count[ind[1],ind[2],ind[3],ind[4]]+1
        Q=rew.sum/rew.count;
        policy[,,1]=Q[,,1,1] < Q[,,1,2]
        policy[,,2]=Q[,,2,1] < Q[,,2,2]
      }
    }
  }
  V[,,1]=(rew.sum[,,1,1]+rew.sum[,,1,2])/(rew.count[,,1,1]+rew.count[,,1,2])
  V[,,2]=(rew.sum[,,2,1]+rew.sum[,,2,2])/(rew.count[,,2,1]+rew.count[,,2,2])
  return(list(policy,V,Q))
}


# function 2 plot results
plot.BJ_MC2<-function(V){
 par(mfrow=c(2,2))
 image(V[[2]][,,1],main="Utility with usable Ace",xaxt='n',yaxt='n',
  xlab="Dealer showing",ylab="Player sum")
 axis(1,at=seq(0,1,length.out=10),label=c("A",paste(2:10)))
 axis(2,at=seq(0,1,length.out=10),label=12:21)
 image(V[[2]][,,2],main="Utility without usable Ace",xaxt='n',yaxt='n',
  xlab="Dealer showing",ylab="Player sum")
 axis(1,at=seq(0,1,length.out=10),label=c("A",paste(2:10)))
 axis(2,at=seq(0,1,length.out=10),label=12:21)
 image(V[[1]][,,1],main="Policy with usable Ace",xaxt='n',yaxt='n',
  xlab="Dealer showing",ylab="Player sum")
 axis(1,at=seq(0,1,length.out=10),label=c("A",paste(2:10)))
 axis(2,at=seq(0,1,length.out=10),label=12:21)
 image(V[[1]][,,2],main="Policy without usable Ace",xaxt='n',yaxt='n',
  xlab="Dealer showing",ylab="Player sum")
 axis(1,at=seq(0,1,length.out=10),label=c("A",paste(2:10)))
 axis(2,at=seq(0,1,length.out=10),label=12:21)
}

V=BJ_MC(5e6)
plot.BJ_MC2(V)

#######################################
#   ch4.1 policy evaluation 
########################################
# example 4.1 - bug fixed on 2017.03.21
# defining deterministic trans. matrix
north=c(1:3,15,1:10)
east=2:15;east[ c(3,7,11)]=c(3,7,11)
south=c(5:15,12:14)
west=c(15,1:13);west[ c(4,8,12)]=c(4,8,12)
trM=cbind(north,east,south,west)

# defining Reward & trans. prob.
R=-1;P=0.25;

# iterative policy evaluation
delta=1; gamma=1; tol=1e-8; V=rep(0,15);
while (delta>tol) {
 delta=0;
  for (i_state in 1:14) {
    v=V[i_state]
    V[i_state]=sum(P*(R+gamma*V[trM[i_state,]]))
    delta=max(delta,abs(v-V[i_state]));
  }
}

# result
> matrix(c(0,V),nrow=4)
     [,1] [,2] [,3] [,4]
[1,]    0  -14  -20  -22
[2,]  -14  -18  -20  -20
[3,]  -20  -20  -18  -14
[4,]  -22  -20  -14    0

#####################################
#   ch4.3 Policy Improvement
#   easier one 
#####################################
north=c(1:3,15,1:10)
east=2:15;east[ c(3,7,11)]=c(3,7,11)
south=c(5:15,12:14)
west=c(15,1:13);west[ c(4,8,12)]=c(4,8,12)
trM=cbind(north,east,south,west)
R=-1;P=0.25;V=rep(0,15);
delta=1; gamma=1; tol=1e-10; 
bestP=sample(1:4,14,replace=T)
stable=F;counter=0;
while (stable==F){
  counter=counter+1
  # iterative policy evaluation
  while (delta>tol) {
    delta=0;
    for (i_state in 1:14) {
      v=V[i_state]
      V[i_state]=sum(P*(R+gamma*V[trM[i_state,]]))
      delta=max(delta,abs(v-V[i_state]))
    }
  }
  # policy improvement
  stable=F
  for (i_state in 1:14) {
    b=bestP[i_state]
    bestP[i_state]=which.max(V[trM[i_state,]])
    ifelse((bestP[i_state]==b),stable<-T,stable<-F)
  }
}

# with softmax
R=-1;V=rep(0,15);
bestP=sample(1:4,14,replace=T)
stable=F;counter=0
while (stable==F){
  counter=counter+1
  Vmat=matrix(V[trM],ncol=4)
  Ppolicy=t(apply(Vmat,1,function(x) exp(10*x)/sum(exp(10*x))))
# iterative policy evaluation
  while (delta>tol) {
    delta=0;
    for (i_state in 1:14) {
      v=V[i_state]
      V[i_state]=sum(Ppolicy[i_state]*(R+gamma*V[trM[i_state,]]))
      delta=max(delta,abs(v-V[i_state]))
    }
  }
# policy improvement
  stable=F
  for (i_state in 1:14) {
    b=bestP[i_state]
    bestP[i_state]=which.max(V[trM[i_state,]])
    ifelse((bestP[i_state]==b),stable<-T,stable<-F)
  }
}


#####################################
#   ch4.4 Value Iteration 
#####################################
# example 4.3
V=c(rep(0,100),1);V.hist=c()
p=c(0.4,0.6);
gamma=1;delta=1; tol=1e-20
max.a=rep(0,101)
while (delta>tol) {
  delta=0;
  for (i_state in 1:99) {
    v=V[i_state+1]
    temp=matrix(0,nrow=1,ncol=i_state)
    for (i_action in 1:i_state) {
       temp[i_action]=sum(p*(gamma*c(V[(min(i_state+i_action,100)+1)],
         V[(max(i_state-i_action,0)+1)])))
     }
    V[i_state+1]=max(temp)
    max.a[i_state+1]=which.max(round(temp,8))
    delta=max(delta,abs(v-V[i_state+1]))
  }
  V.hist=rbind(V.hist,V)
}
# plotting results
par(mfrow=c(1,2))
plot(V.hist[1,],type='l',lwd=2,xlab="Capital",ylab="Value Estimates",col='red')
lines(V.hist[2,],lwd=2,col='blue')
lines(V.hist[3,],lwd=2,col='green')
lines(V.hist[32,],lwd=2,col='black')
legend("topleft",c("sweep 1","sweep 2","sweep 3", "sweep 32"),
 col=c("red","blue","green","black"),lwd=2)
barplot(max.a,xlab="Capital",ylab="Final Policy",col="white")

chapter 3 - example 3.8 & 3.12
bug fixed on 2015.12.18
#####################################
#     Ch3.7 Value function
#####################################
# example 3.8: Gridworld
# initializing value vector
V=rep(0,25);                

# defining probability matrix
P=matrix(1/4,nrow=25,ncol=4) # 

# defining deterministic transition matrix
north=c(2:25,25)
north[ c(5,10,15,20,25)]=c(5,10,15,20,25)
east=c(6:25,21:25)
west=c(1:5,1:20)
south=c(1,1:24)
south[ c(1,6,11,16,21)]=c(1,6,11,16,21)
trM=cbind(north,east,south,west)
trM[10,]=6
trM[20,]=18

# defining reward matrix
R=matrix(0,nrow=25,ncol=4)
R[which(trM==1:25)]=-1
R[10,]=10
R[20,]=5

# calculating state-values iteratively
# fixed number of iterations 
nRep=1000; gamma=0.9;
for (i_rep in 1:nRep) {
  V.old=V
  for (i_state in 1:25) {
    V[i_state]=sum(P[i_state,]*(R[i_state,]+gamma*V.old[trM[i_state,]]))
  }
}

# result
> matrix(V,nrow=5)[5:1,]
            [,1]       [,2]       [,3]       [,4]       [,5]
[1,]  3.30899634  8.7892919  4.4276192  5.3223676  1.4921788
[2,]  1.52158807  2.9923179  2.2501400  1.9075717  0.5474027
[3,]  0.05082249  0.7381706  0.6731133  0.3581862 -0.4031411
[4,] -0.97359230 -0.4354954 -0.3548823 -0.5856051 -1.1830751
[5,] -1.85770055 -1.3452313 -1.2292673 -1.4229181 -1.9751790

#####################################
#  ch3.8 optimal value function
#####################################
# example 3.12
V.star=V; # V calculated as in exp3.8
iter=0;maxItr=1000;delta=1;tol=1e-5;
while(iter < maxItr & delta > tol) {
  delta=0;iter=iter+1
  V.star.old=V.star
  for (i_state in 1:25) {
    v=V.star[i_state]
    V.star[i_state]=max(R[i_state,]+gamma*V.star.old[trM[i_state,]])
    delta=max(delta,abs(v-V.star[i_state]))
  }
}
# result - ex3.12
> matrix(V.star,nrow=5)[5:1,]
         [,1]     [,2]     [,3]     [,4]     [,5]
[1,] 21.97746 24.41940 21.97746 19.41941 17.47747
[2,] 19.77971 21.97746 19.77971 17.80174 16.02157
[3,] 17.80173 19.77971 17.80174 16.02157 14.41941
[4,] 16.02156 17.80173 16.02156 14.41940 12.97746
[5,] 14.41940 16.02156 14.41940 12.97746 11.67972

epGreedy = function(nTrial,nRep,epsilon) {
ret.hist=matrix(0,nrow=nTrial,ncol=nRep)
opt.hist=ret.hist
for (i_rep in 1:nRep){
  Q.true=rnorm(10);Q.est=rep(0,10);
  Q.cum=rep(0,10);act.count=rep(0,10);
  opt.ID=which.max(Q.true)
  for (i_trial in 1:nTrial) {
    if (runif(1) < epsilon) {
      action=sample(1:10,1)
    } else {
      action=which.max(Q.est)
    }
    ret.hist[i_trial,i_rep]=rnorm(1)+Q.true[action]
    opt.hist[i_trial,i_rep]=action==opt.ID
    act.count[action]=act.count[action]+1
    Q.cum[action]=Q.cum[action]+ret.hist[i_trial,i_rep]
    Q.est[action]=Q.cum[action]/act.count[action]
  }
}
return(data.frame(opt=rowMeans(opt.hist),ret=rowMeans(ret.hist)))
}
type1=epGreedy(1000,2000,0.0)
type2=epGreedy(1000,2000,0.01)
type3=epGreedy(1000,2000,0.1)

par(mfrow=c(2,1))
plot(type3$ret,type='l',xlab="Play",ylab="average reward")
lines(type2$ret,type='l',col='red')
lines(type1$ret,type='l',col='green')
legend("bottomright",c("epsilon=0.00","epsilon=0.01","epsilon=0.10"),
  col=c("black","red","green"),lty=c(1,1,1))
plot(type3$opt,type='l',xlab="Play",ylab="% optimal action")
lines(type2$opt,type='l',col='red')
lines(type1$opt,type='l',col='green')
legend("bottomright",c("epsilon=0.00","epsilon=0.01","epsilon=0.10"),
  col=c("black","red","green"),lty=c(1,1,1))

#####################################
#  Generalised Version - ch2.5 & 2.7
#####################################
epGreedyG = function(nTrial,nRep,epsilon,LR,constantLR="F",initialQ) {
# generalized version of epsilon-greedy 
ret.hist=matrix(0,nrow=nTrial,ncol=nRep)
opt.hist=ret.hist
for (i_rep in 1:nRep){
  Q.true=rnorm(10);Q.est=rep(initialQ,10);act.count=rep(0,10);
  opt.ID=which.max(Q.true)
  for (i_trial in 1:nTrial) {
    if (runif(1) < epsilon) {
      action=sample(1:10,1)
    } else {
      action=which.max(Q.est)
    }
    ret.hist[i_trial,i_rep]=rnorm(1)+Q.true[action]
    opt.hist[i_trial,i_rep]=action==opt.ID
    act.count[action]=act.count[action]+1
    if (constantLR=="F"){LR=1/act.count[action]}
    Q.est[action]=Q.est[action]+LR*(ret.hist[i_trial,i_rep]-Q.est[action])
  }
}
return(data.frame(opt=rowMeans(opt.hist),ret=rowMeans(ret.hist)))
}

#################################
#  ch2.4 softmax
#################################
RLsoftmax = function(nTrial,nRep,temp) {
ret.hist=matrix(0,nrow=nTrial,ncol=nRep)
opt.hist=ret.hist
for (i_rep in 1:nRep){
  Q.true=rnorm(10);Q.est=rep(0,10);
  Q.cum=rep(0,10);act.count=rep(0,10);
  opt.ID=which.max(Q.true)
  t=temp
  for (i_trial in 1:nTrial) {
    action=sample(1:10,1,prob=exp(Q.est/t)/sum(exp(Q.est/t)))
    ret.hist[i_trial,i_rep]=rnorm(1)+Q.true[action]
    opt.hist[i_trial,i_rep]=action==opt.ID
    act.count[action]=act.count[action]+1
    Q.cum[action]=Q.cum[action]+ret.hist[i_trial,i_rep]
    Q.est[action]=Q.cum[action]/act.count[action]
    t=max(0.001,0.995*t)
  }
}
return(data.frame(opt=rowMeans(opt.hist),ret=rowMeans(ret.hist)))
}

#################################
# ch2.8 reinforcement comparison
################################# 
reinfComp = function(nTrial,nRep,alpha,beta) {
ret.hist=matrix(0,nrow=nTrial,ncol=nRep)
opt.hist=ret.hist
for (i_rep in 1:nRep){
  Q.true=rnorm(10);p=rep(0,10);r.ave=0;
  opt.ID=which.max(Q.true)
  for (i_trial in 1:nTrial) {
    action=sample(1:10,1,prob=exp(p)/sum(exp(p)))
    ret.hist[i_trial,i_rep]=rnorm(1)+Q.true[action]
    opt.hist[i_trial,i_rep]=action==opt.ID
    p[action]=p[action]+beta*(ret.hist[i_trial,i_rep]-r.ave)
    r.ave=r.ave+alpha*(ret.hist[i_trial,i_rep]-r.ave)
  }
}
return(data.frame(opt=rowMeans(opt.hist),ret=rowMeans(ret.hist)))
}

#################################
# ch2.9 pursuit method
#################################
pursuit= function(nTrial,nRep,beta) {
ret.hist=matrix(0,nrow=nTrial,ncol=nRep)
opt.hist=ret.hist
for (i_rep in 1:nRep){
  Q.true=rnorm(10);p=rep(1/10,10);act.count=rep(0,10);Q.est=rep(0,10)
  opt.ID=which.max(Q.true)
  for (i_trial in 1:nTrial) {
    actTemp=which.max(Q.est)
    p[actTemp]=p[actTemp]+beta*(1-p[actTemp])
    nonA=(1:10)[-actTemp]
    p[nonA]=p[nonA]+beta*(-p[nonA])
    action=sample(1:10,1,prob=p)
    ret.hist[i_trial,i_rep]=rnorm(1)+Q.true[action]
    opt.hist[i_trial,i_rep]=action==opt.ID
    act.count[action]=act.count[action]+1
    Q.est[action]=Q.est[action]+1/act.count[action]*(ret.hist[i_trial,i_rep]-Q.est[action])
  }
}
return(data.frame(opt=rowMeans(opt.hist),ret=rowMeans(ret.hist)))
}

社会を＜モデル＞でみる：数理社会学への招待
29章：なぜ差別しなくても外国人居住区ができるのか
○と♯の２つのグループが存在し、以下の条件で他の場所へ移動する。
○: 近隣に２人以下○の場合、
♯: 近隣の1/3以上が♯でない場合、

# 1 epochの内、数回移動する可能性のある場合
FUNmigration<-function(field_size=6, Nsharp=10, Ncircle=10) {
  
Nempty=(field_size^2-Nsharp-Ncircle)
society<-matrix(sample(c(rep(0,Nempty),rep(1,Ncircle),rep(2,Nsharp))),ncol=field_size)
# plotting initial config.
par(mfrow=c(1,2))
idx1<-which(society==1,arr.ind=T);idx2<-which(society==2,arr.ind=T)
plot(idx1[,1],idx1[,2],type="n",xlim=c(0.5,field_size+0.5),
  ylim=c(0.5,field_size+0.5),main="Initial Arrangement",
  xlab="location @ x", ylab="location @ y")
text(idx1[,1],idx1[,2],"o",cex=4,col="red");text(idx2[,1],idx2[,2],"#",cex=4,col="blue")

# main 
moved=1;counter=0
while (moved>0&counter<1000) {
  counter=counter+1;moved=0
  for (i_row in 1:field_size) {
    for (i_col in 1:field_size) {
      # checking sharps
      if (society[i_row,i_col]==2) {
        neR_IDX=max((i_row-1),1):min((i_row+1),field_size);
        neC_IDX=max((i_col-1),1):min((i_col+1),field_size);
        n_sharp=sum(society[neR_IDX,neC_IDX]==2)-1;
        n_circle=sum(society[neR_IDX,neC_IDX]==1);
        if (n_sharp+n_circle==0 | n_sharp/(n_sharp+n_circle) < (1/3)) {
          moved=moved+1;
          loc_mov=sample(which(society==0),1)
          society[i_row,i_col]=0
          society[loc_mov]=2
        }
      }
      # checking circles
     if (society[i_row,i_col]==1) {
       neR_IDX=max((i_row-1),1):min((i_row+1),field_size);
       neC_IDX=max((i_col-1),1):min((i_col+1),field_size);
       n_circle=sum(society[neR_IDX,neC_IDX]==1)-1;
       if (n_circle < 3) {
         moved=moved+1;
         loc_mov=sample(which(society==0),1)
         society[i_row,i_col]=0
         society[loc_mov]=1
        }
      }
    }
  }
}
# plotting final config.
idx1<-which(society==1,arr.ind=T)
idx2<-which(society==2,arr.ind=T)
plot(idx1[,1],idx1[,2],type="n",xlim=c(0.5,field_size+0.5),ylim=c(0.5,field_size+0.5),
  main="Arragement After Migration",,xlab="location @ x", ylab="location @ y")
text(idx1[,1],idx1[,2],"o",cex=4,col="red")
text(idx2[,1],idx2[,2],"#",cex=4,col="blue")
}

# 1 epochの内、１度のみ移動する場合
FUNmigration <- function(soc.size = 6, n.circle = 10, n.sharp = 10) {
  r.sample = sample(soc.size ^ 2)
  society = matrix(0, soc.size, soc.size)
  society[r.sample[1:n.circle]] = 1
  society[r.sample[(n.circle + 1):(n.circle + n.sharp)]] = 2
  
  # plotting initial config.
  par(mfrow = c(1, 2))
  idx1 <- which(society == 1, arr.ind = T)
  idx2 <- which(society == 2, arr.ind = T)
  plot(idx1[, 1], idx1[, 2], type = "n", xlim = c(0.5, soc.size + 0.5),
    ylim = c(0.5, soc.size + 0.5), main = "Initial Arrangement",
    xlab = "location @ x", ylab = "location @ y")
  text(idx1[, 1], idx1[, 2], "o", cex = 3, col = "red")
  text(idx2[, 1], idx2[, 2], "#", cex = 3, col = "blue")
  move = 1
  while (move != 0 ) {
    # circles
    move = 0
    c.pos = which(society == 1, arr.ind = T)
    for (i.c in 1:n.circle) {
      r.idx = c(max(1, c.pos[i.c, 1] - 1), min(soc.size, c.pos[i.c, 1] + 1))
      c.idx = c(max(1, c.pos[i.c, 2] - 1), min(soc.size, c.pos[i.c, 2] + 1))
      neighber  = society[r.idx[1]:r.idx[2], c.idx[1]:c.idx[2]]
      neighber.c = sum(neighber == 1) - 1
      if (neighber.c < 3) {
        move = 1
        move.idx = which(society == 0)
        society[sample(move.idx, 1)] = 1
        society[c.pos[i.c, 1], c.pos[i.c, 2]] = 0
      }
    }
    # sharps
    s.pos = which(society == 2, arr.ind = T)
    for (i.s in 1:n.sharp) {
      r.idx = c(max(1, s.pos[i.s, 1] - 1), min(soc.size, s.pos[i.s, 1] + 1))
      c.idx = c(max(1, s.pos[i.s, 2] - 1), min(soc.size, s.pos[i.s, 2] + 1))
      neighbor  = society[r.idx[1]:r.idx[2], c.idx[1]:c.idx[2]]
      neighbor.s = sum(neighbor == 2) - 1
      neighbor.all = sum(neighbor != 0) - 1
      prop.s = max(0, neighbor.s / neighbor.all, na.rm = T)
      if (prop.s < 1 / 3) {
        move = 1
        move.idx = which(society == 0)
        society[sample(move.idx, 1)] = 2
        society[s.pos[i.s, 1], s.pos[i.s, 2]] = 0
      }
    }
  }
  idx1 <- which(society == 1, arr.ind = T)
  idx2 <- which(society == 2, arr.ind = T)
  plot(idx1[, 1], idx1[, 2], type = "n",
    xlim = c(0.5, soc.size + 0.5), ylim = c(0.5, soc.size + 0.5),
    main = "Arragement After Migration", xlab = "location @ x", ylab = "location @ y")
  text(idx1[, 1], idx1[, 2], "o", cex = 3, col = "red")
  text(idx2[, 1], idx2[, 2], "#", cex = 3, col = "blue")
}