# with THRESHOLD (theta)
AND.gate <- function(x1, x2){
  w1 = 0.5
  w2 = 0.5
  theta = 0.7
  y.temp = w1*x1 + w2*x2
  if (y.temp <= theta){
    y = 0
  } else {
    y = 1
  }
  return(y)
}

AND.gate <- function(x1, x2){
  w1 = 0.5; w2 = 0.5; theta = 0.7
  return(as.numeric(w1*x1 + w2*x2 > theta))
}

NAND.gate <- function(x1, x2){
  w1 = -0.5; w2 = -0.5; theta = -0.7
  return(as.numeric(w1*x1 + w2*x2 > theta))
}

OR.gate <- function(x1, x2){
  w1 = 0.5; w2 = 0.5; theta = 0.3
  return(as.numeric(w1*x1 + w2*x2 > theta))
}

# with BIAS (b)
AND.gate <- function(x1, x2){
  w1 = 0.5
  w2 = 0.5
  b = -0.7
  y.temp = w1*x1 + w2*x2 + b
  if (y.temp <= 0){
    y = 0
  } else {
    y = 1
  }
  return(y)
}

AND.gate <- function(x1, x2){
  w1 = 0.5; w2 = 0.5; b = -0.7
  return(as.numeric(w1*x1 + w2*x2 + b > 0))
}

NAND.gate <- function(x1, x2){
  w1 = -0.5; w2 = -0.5; b = 0.7
  return(as.numeric(w1*x1 + w2*x2 + b > 0))
}

OR.gate <- function(x1, x2){
  w1 = 0.5; w2 = 0.5; b = -0.3
  return(as.numeric(w1*x1 + w2*x2 + b > 0))
}

NOR.gate <- function(x1, x2){
  w1 = -0.5; w2 = -0.5; b = 0.3
  return(as.numeric(w1*x1 + w2*x2 + b > 0))
}

plot.logic <- function(logic.oper){
  x1 = c(0,0,1,1);
  x2 = c(0,1,0,1);
  if (logic.oper == "and") {
    w1 = 0.5; w2 = 0.5; theta = 0.7;
    true.point = AND.gate(x1,x2)
  } else if (logic.oper == "or") {
    w1 = 0.5; w2 = 0.5; theta = 0.3;
    true.point = OR.gate(x1,x2)
  } else if (logic.oper == "nand") {
    w1 = -0.5; w2 = -0.5; theta = -0.7;
    true.point = NAND.gate(x1,x2)
  } else if (logic.oper == "nor"){
    w1 = -0.5; w2 = -0.5; theta = -0.3;
    true.point = NOR.gate(x1,x2)
  } else {warning("incompatible operator");stop() }
  plot(c(0,0,1,1),c(0,1,0,1),xlim = c(-0.5, 1.5), ylim = c(-0.5, 1.5),
       pch = 20, cex= 2, col = true.point+1)
  abline(a = theta/w1, b = -w1/w2, lwd = 3)
}

XOR.gate <- function(x1, x2){
  gate1 <- NAND.gate(x1,x2)
  gate2 <- OR.gate(x1,x2)
  y <- AND.gate(gate1,gate2)
  return(y)
}

plot.XOR <- function(){
  x1 = c(0,0,1,1);
  x2 = c(0,1,0,1);
  w11 = -0.5; w21 = -0.5; theta1 = -0.7
  w12 = 0.5; w22 = 0.5; theta2 = 0.3
  true.point = XOR.gate(x1, x2)
  plot(c(0,0,1,1),c(0,1,0,1),xlim = c(-0.5, 1.5), ylim = c(-0.5, 1.5),
       pch = 20, cex= 2, col = true.point+1)
  abline(a = theta1/w11, b = -w11/w21, lwd = 3)
  abline(a = theta2/w12, b = -w12/w22, lwd = 3)
}


multi.forwd <- function(x,y){
  return(x*y)
}
multi.bckwd <- function(x, y, dout){
  dx = dout * y
  dy = dout * x
  return(list(dx = dx, dy = dy))
}

apple = 100; n.apple = 2; tax = 1.1
apple.pre.tax = multi.forwd(apple, n.apple)
apple.post.tax = multi.forwd(apple.pre.tax, tax)

dprice = 1
d.apple.post.tax = multi.bckwd(apple.pre.tax, tax, dprice)
d.apple = multi.bckwd(apple, n.apple, d.apple.post.tax$dx)$dx
d.n.apple = multi.bckwd(apple, n.apple, d.apple.post.tax$dx)$dy

add.forwd <- function(x,y){
  return(x + y)
}
add.bckwd <- function(x, y, dout){
  dx = dout
  dy = dout
  return(list(dx = dx, dy = dy))
}

# network
step.func <- function(x){
  return(as.numeric(x > 0))
}
x = seq(-5, 5, 0.1)
y = step.func(x)
plot(x,y, ylab = 'y', xlab = 'a', type ="l", lwd =2)

sigmoid.func <- function(x){
  return(1/(1+exp(-x)))
}

y = sigmoid.func(x)
plot(x,y, ylab = 'y', xlab = 'a', type ="l", lwd =2)

y.step = step.func(x)
y.sigm = sigmoid.func(x)
plot(x,y.step, ylab = 'y', xlab = 'a', type ="l", lwd =2)
lines(x,y.sigm, lwd =2, lty = 2)

relu.func <- function(x){
  return(pmax(0,x))
}

y.relu = relu.func(x)
plot(x,y.relu, ylab = 'y', xlab = 'a', type ="l", lwd =2)

A = matrix(1:4, nrow = 2, byrow = T)
B = matrix(5:8, nrow = 2, byrow = T)

A = matrix(1:6, nrow = 3, byrow = T)
B = matrix(7:8, nrow = 2, byrow = T)

x = c(1,0.5)
W1 = matrix((1:6)*0.1, nrow = 2)
B1 = (1:3)*0.1
A1 = x%*%W1 + B1
Z1 = sigmoid.func(A1)

W2 = matrix((1:6)*0.1, nrow = 3)
B2 = c(0.1, 0.2)
A2 = Z1%*%W2 + B2
Z2 = sigmoid.func(A2)

W3 = matrix((1:4)*0.1, nrow = 2)
B3 = c(0.1, 0.2)
A3 = Z2%*%W3+ B3
Z3 = A3

# function to initialize 3L network
init.3L.network <- function(){
  W1 = matrix((1:6)*0.1, nrow = 2)
  B1 = (1:3)*0.1
  W2 = matrix((1:6)*0.1, nrow = 3)
  B2 = c(0.1, 0.2)
  W3 = matrix((1:4)*0.1, nrow = 2)
  B3 = c(0.1, 0.2)
  return(list(W1 = W1, B1 = B1, W2 = W2, B2 = B2, W3 = W3, B3 = B3))
}
# feedforward process
forward.3L <- function(network, x){
  A1 = x%*%network$W1 + network$B1
  Z1 = sigmoid.func(A1)
  A2 = Z1%*%network$W2 + network$B2
  Z2 = sigmoid.func(A2)
  A3 = Z2%*%network$W3 + network$B3
  Z3 = sigmoid.func(A3)
  A3 = Z3
  return(A3)
}

network<-init.3L.network()
y = forward.3L(network, c(1, 0.5))

a = c(1010,1000,990)
exp(a)/sum(exp(a))

softmax.func <- function(x){
  max.x = max(x)
  return(exp(x-max.x)/sum(exp(x-max.x)))
}

train <- read.csv('http://www.Matsuka.info/univ/course_folder/MNSTtrain.csv',
                  header=TRUE)
train <- data.matrix(train)
train.x <- train[,-1]
train.y <- train[,1]
train.x <- t(train.x/255)
download.file("http://www.matsuka.info/univ/course_folder/trNetwork.Rdata",
              "trNetwork.Rdata")
load("trNetwork.Rdata")
network=trNetwork


n.train = ncol(train.x)
correct.cl = 0
conf.matrix = matrix(0,10,10)
for (i.loop in 1:n.train){
  y = forward.3L(network,train.x[,i.loop])
  max.y = max.col(y)
  conf.matrix[max.y, (train.y[i.loop]+1)] =
    conf.matrix[max.y, (train.y[i.loop]+1)] + 1
}
accuracy = sum(diag(conf.matrix))/n.train


# learning
apple = 100; n.apple = 2; tax = 1.1
orange = 150; n.orange = 3;

apple.price = multi.forwd(apple, n.apple)
orange.price = multi.forwd(orange, n.orange)
all.price = add.forwd(apple.price, orange.price)
price = multi.forwd(all.price, tax)

dprice = 1
d.all.price = multi.bckwd(all.price, tax, dprice)
d.apple.price = add.bckwd(apple.price, orange.price, d.all.price$dx)$dx
d.orange.price = add.bckwd(orange, n.orange.price, d.all.price$dx)$dy
d.apple = multi.bckwd(apple, n.apple, d.apple.price)$dx
d.n.apple = multi.bckwd(apple, n.apple, d.apple.price)$dy
d.orange = multi.bckwd(orange, n.orange, d.orange.price)$dx
d.n.orange = multi.bckwd(orange, n.orange, d.orange.price)$dy

relu.forwd <- function(x){
  return(pmax(x,0))
}

relu.bckwd <- function(x, dout){
  dout[which(x <= 0)] = 0
  return(dout)
}

sigmoid.forwd <- function(x){
  return(1/(1+exp(-x)))
}

sigmoid.bckwd <- function(x, dout){
  y = sigmoid.forwd(x)
  return(dout*(1-y)*y)
}

affine.forwd <- function(x, W, b){
  return(x%*%W + matrix(1, nrow = nrow(x), ncol = 1)%*%b)
}

affine.bckwd <- function(x, W, b, dout){
  dx = dout%*%t(W)
  dW = t(x)%*%dout
  db = colSums(dout)
  return(list(dx = dx, dW = dW, db = db))
}

softmax.forwd <- function(x, target){
  max.x = apply(x,1,max)
  C = ncol(x)
  x = x - max.x%*%matrix(1,nrow=1,ncol=C)
  y = exp(x)/rowSums(exp(x))
  delta = 1e-7;
  R = nrow(as.matrix(y))
  return(-sum(target*log(y + delta))/R)
}

softmax.bckwd <- function(x, target,  dout = 1){
  max.x = apply(x, 1, max)
  R = nrow(x)
  C = ncol(x)
  x = x - max.x%*%matrix(1,nrow=1,ncol=C)
  y = exp(x)/rowSums(exp(x))
  return((y-target)/R)
}

init.network <- function(n.neurons){
  n.layer = length(n.neurons)
  W = list(); b = list()
  for (i.layer in 1:(n.layer-1)){
    W[[i.layer]] = matrix(rnorm(n.neurons[i.layer]*n.neurons[(i.layer+1)],sd = 0.1),
                          nrow=n.neurons[i.layer])
    b[[i.layer]] =  matrix(rnorm(n.neurons[(i.layer+1)],sd = 0.1), nrow = 1)
  }
  return(list(W = W,b = b))
}

sigmoid.func <- function(x){
  return(1/(1+exp(-x)))
}

relu.func <- function(x){
  y = apply(x,2,function(x) pmax(x,0))
  return(y)
}

activation <- function(A, actFun){
  if (actFun == "sigmoid"){
    return(sigmoid.func(A))
  }
  if (actFun == "relu"){
    return(relu.func(A))
  }
  if (actFun == "softmax"){
    return(softmax(A))
  }
}

feedforward <- function(network, x, actFun) {
  n.layer <- length(network$W)
  batch.size = nrow(x)
  for (i.layer in 1:n.layer){
    A = x%*%network$W[[i.layer]]
    + matrix(1,nrow=batch.size,ncol = 1)%*%network$b[[i.layer]]
    x = activation(A, actFun[i.layer])
  }
  return(x)
}

cross.entropy = function(y, target){
  delta = 1e-7;
  R = nrow(as.matrix(y))
  return(-sum(target*log(y + delta))/R)
}

loss.network = function(params, x, t, actFun){
  y = feedforward(params,x,actFun)
  return(cross.entropy(y, t))
}

softmax <- function(x, target){
  max.x = apply(x,1,max)
  C = ncol(x)
  x = x - max.x%*%matrix(1,nrow=1,ncol=C)
  y = exp(x)/rowSums(exp(x))
  return(y)
}

train.x = as.matrix(iris[,1:4])
train.y.temp = as.numeric(iris[,5])
train.y = matrix(0,nrow = nrow(train.x), ncol =3)
train.y[which(train.y.temp==1), 1]=1
train.y[which(train.y.temp==2), 2]=1
train.y[which(train.y.temp==3), 3]=1

params = init.network(c(4,15,3))
batch_size = 10; n.iter =5000; lambda =0.05
n.train = nrow(train.x)
params = init.network(c(4,30,3))
batch_size = 10; n.iter =5000; lambda =0.01
n.train = nrow(train.x)
loss = rep(0,n.iter)
for (i.iter in 1:n.iter){
  batch_mask = sample(1:n.train, batch_size)
  x.batch = train.x[batch_mask,]
  t.batch = train.y[batch_mask,]
  a1 = affine.forwd(x.batch,params$W[[1]],params$b[[1]])
  z1 = sigmoid.forwd(a1)
  a2 = affine.forwd(z1,params$W[[2]],params$b[[2]])
  z2 = softmax.forwd(a2,t.batch)
  dwSM = softmax.bckwd(a2, t.batch, 1)
  dwA2 = affine.bckwd(a1,params$W[[2]],params$b[[2]],dwSM)
  dwSG = sigmoid.bckwd(a1,dwA2$dx)
  dwA1 = affine.bckwd(x.batch,params$W[[1]],params$b[[1]],dwSG)
  params$W[[2]] = params$W[[2]] - lambda*dwA2$dW
  params$b[[2]] = params$b[[2]] - lambda*dwA2$db
  params$W[[1]] = params$W[[1]] - lambda*dwA1$dW
  params$b[[1]] = params$b[[1]] - lambda*dwA1$db
  loss[i.iter] = loss.network(params,x.batch,t.batch,c("sigmoid","softmax"))
}
plot(loss,type='l', xlab = "trial")

mk_MC_seq <- function(){
  # defining transitino matrix & probs.
  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)
  P=rep(0.25,4)
  # creating sequence
  state = sample(1:14,1)
  state.seq = state
  while(state!=15){
    action = sample(1:4,1,prob = P)
    state.seq = c(state.seq,trM[state,action])
    state = trM[state,action]  
  }
  return(state.seq = state.seq)
}

# update Vs

cal.cumV.MC <- function(cumV, state.seq,state.count){
  r = -1
  uniq.seq = unique(state.seq)
  for (i.uniq in 1:(length(uniq.seq)-1)){
    first.visit = which(state.seq == uniq.seq[i.uniq])[1]
    cumV[uniq.seq[i.uniq]] = cumV[uniq.seq[i.uniq]] + r*(length(state.seq)-first.visit)
  }
  state.count[uniq.seq] = state.count[uniq.seq] + 1
  return(list(cumV = cumV, state.count = state.count))
}


# main script
max.iter = 10000;
state.count=rep(0,15); cumV = rep(0,14)
for (i.iter in 1:max.iter){
  state.seq = mk_MC_seq()
  updates = cal.cumV.MC(cumV, state.seq, state.count)
  state.count = updates$state.count
  cumV = updates$cumV
}
V = matrix(c(0,cumV/state.count[1:14],0),nrow=4)


# function to calc. card values
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)
      }
    }
  }
}

# playing a single game
play.BJ <- function(policy){
  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)
  }
  return(list(p.val = p.val, d.val = d.val, state.hist = state.hist))
}

# 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) {
    result <- play.BJ(policy)
    p.val = result$p.val
    d.val = result$d.val
    state.hist = result$state.hist
    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)
}

play.BJ2 <- function(policy){
  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)
  }
  # initial random action
  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)
  }
  return(list(p.val = p.val, d.val = d.val, state.hist = state.hist))
}
  

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) {
    result = play.BJ2(policy)
    p.val = result$p.val
    d.val = result$d.val
    state.hist = result$state.hist
    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))
}

# TD random walk
TD0.ex1<-function(maxItr,alpha,gamma) {
  V=c(0,rep(0.5,5),0)
  V.hist=matrix(0,nrow=maxItr+1,ncol=5)
  V.hist[1,]=V[2:6]
  P.act=matrix(0.5,ncol=7,nrow=2)
  for (i_rep in 1:maxItr) {
    state=5
    while (state!=1 & state!=7) {
      action=sample(c(-1,1),1,prob=P.act[,state])
      state.old=state
      state=state+action
      r=ifelse(state==7,1,0)
      V[state.old]=V[state.old]+alpha*(r+gamma*V[state]-V[state.old])
    }
    V.hist[(i_rep+1),]=V[2:6]
  }
  return(V.hist)  
}

# constant step-size Monte Carlo
constMC.ex1<-function(maxItr,alpha) {
  V=c(0,rep(0.5,5),0)
  V.hist=matrix(0,nrow=maxItr+1,5)
  V.hist[1,]=V[2:6]
  P.act=matrix(0.5,ncol=7,nrow=2)
  for (i_rep in 1:maxItr) {
    state=5;
    state.hist=state
    while (state!=1 & state!=7) {
      action=sample(c(-1,1),1,prob=P.act[,state])
      state=state+action
      state.hist=cbind(state.hist,state)
    }
    R=ifelse(state==7,1,0)
    n.state=length(state.hist)
    for (i_state in 1:(n.state-1)) {
      V[state.hist[i_state]]=V[state.hist[i_state]]+
        alpha*(R-V[state.hist[i_state]])
    }
    V.hist[(i_rep+1),]=V[2:6]
  }
  return(V.hist)  
}

# (re)creating Fig 6.7
alphaTD=c(0.05,0.075,0.1,0.15)
alphaMC=c(0.01,0.02,0.03,0.04)
n.alphas=length(alphaTD)
pchs=0:(0+n.alphas)
true.V=1:5*(1/6)
n_rep=100
sqs=seq(1,101,2)
plot(0,0,type='n',xlim=c(0,100),ylim=c(0,0.25))
for (i_alpha in 1:n.alphas) {
  rmsTD=matrix(0,101,n_rep)
  rmsMC=matrix(0,101,n_rep)
  for (i_rep in 1:n_rep) {
    resTD=TD0.ex1(100,alphaTD[i_alpha],1)
    resMC=constMC.ex1(100,alphaTD[i_alpha])
    for (i_gen in 1:101) {
      rmsTD[i_gen,i_rep]=sqrt(mean((resTD[i_gen,]-true.V)^2))
      rmsMC[i_gen,i_rep]=sqrt(mean((resMC[i_gen,]-true.V)^2))
    }
  }
  mTD=rowMeans(rmsTD)
  mMC=rowMeans(rmsMC)
  lines(mTD,col='red')
  lines(mMC,col='blue')
  lines(sqs,mTD[sqs],col='red',pch=pchs[i_alpha],type='p')
  lines(sqs,mMC[sqs],col='blue',pch=pchs[i_alpha],type='p')
}
labs=c("MC, alpha=0.01",
       "MC, alpha=0.02", 
       "MC, alpha=0.03",
       "MC, alpha=0.04",
       "TD, alpha=0.05",
       "TD, alpha=0.075",
       "TD, alpha=0.10",
       "TD, alpha=0.15")  
legend('topright',labs,col=c(rep('blue',4),rep('red',4)),pch=rep(0:3,2),lwd=1.5)


sarsa.ex6.5<-function(maxItr,alpha,gamma,epsilon) {
  # field size: 7row x 10column
  # horizontal move ->  COLUMN 
  # vertical move     ->  ROW 
  # effect of wind     ->  ROW
  # actions: 1-up, 2-right, 3-down, 4-left 
  act.V=matrix(c(1,0,0,1,-1,0,0,-1),nrow=4,byrow=T)
  wind=matrix(c(0,0,0,0,0,0,1,0,1,0,1,0,2,0,2,0,1,0,0,0),byrow=T,nrow=10)
  goal=c(4,8)
  Qs=array(0,dim=c(7,10,4))
  for (i_rep in 1:maxItr) {
    state=c(4,1) # start
    if (runif(1) > epsilon) {
      move=which.max(Qs[state[1],state[2],])
    } else { move=sample(1:4,1)}
    while (!all(state==goal)) {
      st.old=state
      mv.old=move
      state=state+act.V[move,]+wind[state[2],]
      if (state[1]<1) {state[1]=1}
      if (state[1]>7) {state[1]=7}
      if (state[2]<1) {state[2]=1}
      if (state[2]>10) {state[2]=10}
      if (runif(1) > epsilon) {
        move=which.max(Qs[state[1],state[2],])
      } else { move=sample(1:4,1)}
      rew=ifelse(all(state==goal),0,-1)
      Qs[st.old[1],st.old[2],mv.old]=Qs[st.old[1],st.old[2],mv.old]
      +alpha*(rew+gamma* Qs[state[1],state[2],move]
              -Qs[st.old[1],st.old[2],mv.old])
    }
  }
  return(Qs)
}    

# running example
Qs=sarsa.ex6.5(5e6,0.1,1,0.1)
# sim optimal actions
state=c(4,1);goal=c(4,8);
state.hist=state
while (!all(state==goal)) {
  moveID=which.max(Qs[state[1],state[2],])
  state=state+act.V[moveID,]+wind[state[2],]
  if (state[1]<1) {state[1]=1}
  if (state[1]>7) {state[1]=7}
  if (state[2]<1) {state[2]=1}
  if (state[2]>10) {state[2]=10}
  state.hist=rbind(state.hist,state)
}
# plotting results
plot(0,0,type='n',xlim=c(0,11),ylim=c(0,8),xlab="",ylab="",
     main="Learned policies -- Sarsa")
lines(1,4,type='p',pch=19,col='red',cex=2)
lines(8,4,type='p',pch=19,col='red',cex=2)
dirs=c("up","right","down","left" )
for (i_row in 1:7) {
  for (i_col in 1:10) {
    best.move=dirs[which.max(Qs[i_row,i_col,])]
    text(i_col,i_row,best.move)
  }
}
lines(state.hist[,2],state.hist[,1],col="red",lwd=2)


Qlearn.ex6.5<-function(maxItr,alpha,gamma,epsilon) {
  # field size: 7row x 10column
  # horizontal move ->  COLUMN 
  # vertical move     ->  ROW 
  # effect of wind     ->  ROW
  # actions: 1-up, 2-right, 3-down, 4-left 
  act.V=matrix(c(1,0,0,1,-1,0,0,-1),nrow=4,byrow=T)
  wind=matrix(c(0,0,0,0,0,0,1,0,1,0,1,0,2,0,2,0,1,0,0,0),byrow=T,nrow=10)
  goal=c(4,8)
  Qs=array(0,dim=c(7,10,4))
  for (i_rep in 1:maxItr) {
    state=c(4,1) # start
    while (!all(state==goal)) {
      if (runif(1) > epsilon) {
        move=which.max(Qs[state[1],state[2],])
      } else { move=sample(1:4,1)}
      sIDX=state
      state=state+act.V[move,]+wind[state[2],]
      if (state[1]<1) {state[1]=1}
      if (state[1]>7) {state[1]=7}
      if (state[2]<1) {state[2]=1}
      if (state[2]>10) {state[2]=10}   
      max.Q=max(Qs[state[1],state[2],])
      rew=ifelse(all(state==goal),0,-1)
      Qs[sIDX[1],sIDX[2],move]=Qs[sIDX[1],sIDX[2],move]
      +alpha*(rew+gamma* max.Q-Qs[sIDX[1],sIDX[2],move])
    }
  }
  return(Qs)
}

Qs=Qlearn.ex6.5(1e6,0.05,1,0.1)
# sim optimal actions
state=c(4,1);goal=c(4,8);
state.hist=state
while (!all(state==goal)) {
  moveID=which.max(Qs[state[1],state[2],])
  state=state+act.V[moveID,]+wind[state[2],]
  if (state[1]<1) {state[1]=1}
  if (state[1]>7) {state[1]=7}
  if (state[2]<1) {state[2]=1}
  if (state[2]>10) {state[2]=10}
  state.hist=rbind(state.hist,state)
}
# plotting results
plot(0,0,type='n',xlim=c(0,11),ylim=c(0,8),xlab="",ylab="",
     main="Learned policies -- Q-learning")
lines(1,4,type='p',pch=19,col='red',cex=2)
lines(8,4,type='p',pch=19,col='red',cex=2)
dirs=c("up","right","down","left" )
for (i_row in 1:7) {
  for (i_col in 1:10) {
    best.move=dirs[which.max(Qs[i_row,i_col,])]
    text(i_col,i_row,best.move)
  }
}
lines(state.hist[,2],state.hist[,1],col="red",lwd=2)