データ解析基礎論B Reivew01

# central limit theorem
n.sample = 1e6
n.data = 10
dat = matrix(runif(n.sample*n.data), nrow = n.data)
means = colMeans(dat)
sds = apply(dat,2,sd)

hist(means,100,probability = T)
x.temp  = seq(0,1, 0.01)
true.sd = sqrt(1/12)
true.dens = dnorm(x.temp,mean=0.5, sd = true.sd/sqrt(n.data))
lines(x.temp, true.dens,col='red',lwd=2)
ci.low = qnorm(0.025,mean=0.5, sd = true.sd/sqrt(n.data))
ci.high = qnorm(0.975,mean=0.5, sd = true.sd/sqrt(n.data))
abline(v=ci.low,col='blue',lwd=2)
abline(v=ci.high,col='blue',lwd=2)

# standardizing data
z = (means-0.5)/(true.sd/sqrt(n.data))
hist(z,100,probability = T)
x.tempZ = seq(-4,4,0.01)
z.dens = dnorm(x.tempZ,mean=0, sd = 1)
lines(x.tempZ, z.dens,col='red',lwd=2)
ci.lowZ = qnorm(0.025,mean=0, sd = 1)
ci.highZ = qnorm(0.975,mean=0, sd = 1)
abline(v=ci.lowZ,col='blue',lwd=2)
abline(v=ci.highZ,col='blue',lwd=2)

# t distribution
t.temp = seq(-4,4,0.01)
t.dens = dt(t.temp, df=(n.data-1))
lines(t.temp, t.dens,col='green',lwd=2)
ci.lowT = qt(0.025,df=(n.data-1))
ci.highT = qt(0.975,df=(n.data-1))
abline(v=ci.lowT,col='cyan',lwd=2)
abline(v=ci.highT,col='cyan',lwd=2)


### cell automata
nCell=201
nGen=100
res=matrix(0,nrow=nGen,ncol=nCell)
res[1,100]=1
for (i_gen in 2:nGen) {
  for (i_cell in 2:(nCell-1)) {
    res[i_gen,i_cell]=sum(res[i_gen-1,(i_cell-1):(i_cell+1)])%%2;
  } 
 # 左端
  res[i_gen,1]=(res[i_gen-1,nCell]+res[i_gen-1,1]+res[i_gen-1,2])%%2 
 # 右端
  res[i_gen,nCell]=(res[i_gen-1,(nCell-1)]+res[i_gen-1,nCell]+res[i_gen-1,1])%%2;
} 
image(res)


# general version
dec2bin<-function(num, digits=8) {
  bin=c()
  if (num==0){
    bin=0
  } else {
    while(num!=0){
      rem=num%%2
     num=num%/%2
      bin=c(rem,bin)
    }
  }
  if (length(bin) < digits){
    res=matrix(0,nrow=1,ncol=digits)
    res[(digits-length(bin)+1):digits]=bin
  } else {res=bin}
  return(res)
}

transFUN<-function(st,ruleID){
  output=dec2bin(ruleID,8);
  a=matrix(c(1,1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,0,1,0,0,0),nrow=8,byrow=T)
  newSt=output[which(apply(a,1,function(x) {all(x==st)}))]
  return(newSt)
}
ECA<-function(nCell, nGen,ruleID){
  res=matrix(0,nrow=nGen,ncol=nCell)
  res[1,ceiling(nCell/2)]=1;
  for (i_gen in 2:nGen) {
    for (i_cell in 2:(nCell-1)) {
      res[i_gen,i_cell]=transFUN(res[i_gen-1,(i_cell-1):(i_cell+1)],ruleID)
     }
   res[i_gen,1]=transFUN(c(res[i_gen-1,nCell],res[i_gen-1,1],res[i_gen-1,2]),ruleID)
   res[i_gen,nCell]=transFUN(c(res[i_gen-1,(nCell-1)],res[i_gen-1,nCell],res[i_gen-1,1]),ruleID)
  }
  return(res)
}
res<-ECA(200,100,99)
image(res)