library(tidyverse)
library(gridExtra)

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

res.all = tibble(trial = rep(1:nTrial, n.Rep * 3),
                 rew = c(as.vector(type1$rew),as.vector(type2$rew),as.vector(type3$rew)),
                 opt = c(as.vector(type1$opt),as.vector(type2$opt),as.vector(type3$opt)),
                 condition = c(rep("0.00", nTrial * n.Rep),
                               rep("0.01", nTrial * n.Rep),
                               rep("0.10", nTrial * n.Rep)))

p1 <- ggplot(res.all) +
  geom_smooth(aes(x = trial, y = rew, color = condition)) +
  ylab("Average Reward")
p2 <- ggplot(res.all) +
  geom_smooth(aes(x = trial, y = opt, color = condition)) +
  ylab("Prop. Optimal Action")
grid.arrange(p1, p2, nrow =2)

softmax = function(nTrial, nRep, tau) {
  rew.hist = opt.hist = matrix(0,nrow=nTrial,ncol=nRep)
  for (i_rep in 1:nRep){
    Q.true=rnorm(10); opt.ID=which.max(Q.true)
    Q.est = Q.cum = act.count=rep(0,10);
    for (i_trial in 1:nTrial) {
      p = exp(Q.est/tau)/sum(exp(Q.est)/tau)
      action = sample(1:10, 1, prob = p)
      rew.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]+rew.hist[i_trial,i_rep]
      Q.est[action]=Q.cum[action]/act.count[action]
    }
  }
  return(list(opt = opt.hist, rew = rew.hist))
}

n.Trial = 1000; n.Rep = 1000
eG00=epGreedy(n.Trial, n.Rep, 0.0)
eG01=epGreedy(n.Trial, n.Rep, 0.1)
sm=softmax(n.Trial, n.Rep, 0.1)
res.all = tibble(trial = rep(1:n.Trial, n.Rep * 3),
                 rew = c(as.vector(eG00$rew),as.vector(eG01$rew),as.vector(sm$rew)),
                 opt = c(as.vector(eG00$opt),as.vector(eG01$opt),as.vector(sm$opt)),
                 condition = c(rep("epsilon = 0.0", n.Trial * n.Rep),
                               rep("epsilon = 0.1", n.Trial * n.Rep),
                               rep("softmax", n.Trial * n.Rep)))
p1 <- ggplot(res.all) +
  geom_smooth(aes(x = trial, y = rew, color = condition)) +
  ylab("Average Reward")

p2 <- ggplot(res.all) +
  geom_smooth(aes(x = trial, y = opt, color = condition)) +
  ylab("Prop. Optimal Action")

grid.arrange(p1, p2, nrow =2)


# RL example
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,]]))
  }
}
print(matrix(V,nrow=5)[5:1,])

# jisshu 1
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;

# policy improvement
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)
  }
}

install.packages("tidyverse")
library(tidyverse)

random.number <- rnorm(1000)
mean(random.number)
mean(random.number <- rnorm(1000))

rnorm(1000) %>% mean()

# CLT
NperSample = 10
SampleSize = 300000

# "traditional"
random.number <- runif(NperSample * SampleSize)
dat <- matrix(random.number, nrow=NperSample)
means <- colMeans(dat)
dens <- density(means)
hist(means, breaks = 100, probability = T, main = "Distributionf of Means")
lines(dens, lwd = 3, col = "orange")


runif(NperSample * SampleSize) %>%
  matrix(nrow=NperSample) %>%
  colMeans() -> means
hist(means, breaks=100,probability = T, main = "Distributionf of Means")
means %>% density() %>% lines(,lwd=3,col='orange')


histWdensity <- function(dat, nbreaks=30, main.txt){
  dens <- density(dat)
  hist(dat, breaks = nbreaks, probability = T, main = main.txt)
  lines(dens, lwd = 3, col = "orange")
}

runif(NperSample * SampleSize) %>%
  matrix(nrow=NperSample) %>%
  colMeans() %>% histWdensity(nbreaks = 100, main.txt = "Distributionf of Means")

dat <- read.csv("http://www.matsuka.info/data_folder/sampleData2013.txt")
dt <- as_tibble(dat)
dt.la <- filter(dt, affil == "LA")

dt.la2 <- filter(dt, affil == "LA" & grade == "SP")
dt.laNot2 <- filter(dt, affil == "LA" & grade != "SP")

dt.GB <- select(dt, grade, nbooks)
dtWOgender <- select(dt, -gender)

dt.arranged <- arrange(dt, affil, grade)

dt.weekly <- mutate(dt,nbooksWeek = nbooks / 52)

dt.atLeastOneBook <- mutate(dt, atleastOneBook = (nbooks/52) >= 1)
dt.atLeastOneBook <- mutate(dt, atleastOneBook = (nbooks/12) >= 1)

dt.BWindex = mutate(dt, nbooksWeek = nbooks / 52, idx = nbooksWeek / (12*7-Hworked))

dt.byGrade <- group_by(dt, grade)
summarize(dt.byGrade, ave.books = mean(nbooks,na.rm = TRUE), ave.Hworked = mean(Hworked, na.rm = TRUE))

dt.byGrAf <- group_by(dt, grade, affil)
dt.summ <- summarize(dt.byGrAf, ave.books = mean(nbooks,na.rm = TRUE), ave.Hworked = mean(Hworked, na.rm = TRUE), N = n())

dt.summ2 <- dt %>%
  group_by(grade, affil) %>%
  summarize(ave.books = mean(nbooks,na.rm = TRUE), ave.Hworked = mean(Hworked, na.rm = TRUE), N = n()) %>% filter(N > 2) %>% arrange(desc(ave.books))

plot(x = dt.summ2$ave.books, y = dt.summ2$ave.Hworked, pch=20, cex = 3,xlab = "Ave. # books read",ylab = "Ave hours worked")

dt <- read_csv("http://www.matsuka.info/data_folder/sampleData2013.txt",col_names = TRUE)

dt.summ3 <- dt %>%
  group_by(grade, gender) %>%
  summarize(ave.books = mean(nbooks,na.rm = TRUE), ave.Hworked = mean(Hworked, na.rm = TRUE))

dt.summ3G <- dt.summ3 %>% gather('ave.books', 'ave.Hworked', key = 'ave.values', value = "BorW")

dt.summ3SformG <- spread(dt.summ3G, key = ave.values, value =BorW)

dt.sumLA <- dt %>% filter(affil=="LA") %>% group_by(grade) %>% summarize(ave.books = mean(nbooks))

toeic <- tibble(
  grade = factor(c("SP", "JR")),
  score = c(800,830),
)

new.dt1 <- dt.sumLA %>% inner_join(toeic, by = "grade")

dt.sumLA <- add_row(dt.sumLA, grade = c("MS"), ave.books = (13))
toeic2 <- tibble(
  grade = factor(c("SP", "JR","DR")),
  score = c(800,830,900),
)
new.dt3 <- full_join(dt.sumLA, toeic2)

new.dt4 <- left_join(dt.sumLA, toeic2)
new.dt5 <- right_join(dt.sumLA, toeic2)

# CLT
NperSample = 10
SampleSize = 300000

runif(NperSample * SampleSize) %>%
  matrix(nrow=NperSample) %>%
  colMeans() %>% tibble(sample.mean = .) -> means

ggplot(means,aes(x = sample.mean, y = ..density..)) +
  geom_histogram(bins=200) +
  geom_density(colour = "orange",size=2)

ggplot(means,aes(x = sample.mean, y = ..density..)) +
  geom_histogram(bins=200) +
  geom_line(stat = "density", colour = "orange",size=2)

runif(NperSample * SampleSize) %>%
  matrix(nrow=NperSample) %>%
  colMeans() %>% tibble(sample.mean = .) %>%
  ggplot(., aes(x = sample.mean, y = ..density..)) +
  geom_histogram(bins=100,colour = "grey20") +
  geom_line(stat = "density", colour = "skyblue",size=2)


dat <- read.csv("http://www.matsuka.info/data_folder/sampleData2013.txt")
dt <- as_tibble(dat)




ggplot(dt, aes(x = Hworked, y = nbooks)) +
  geom_point(size = 3)

ggplot(dt) +
  geom_point(aes(x = Hworked, y = nbooks, color = grade),size = 3)

ggplot(dt) +
  geom_point(aes(x = Hworked, y = nbooks, shape = grade),size = 5)

ggplot(dt) +
  geom_point(aes(x = Hworked, y = nbooks),size = 5) +
  facet_wrap(~ grade, nrow = 1)

ggplot(dt) +
  geom_smooth(aes(x = Hworked, y = nbooks))

ggplot(dt) +
  geom_smooth(aes(x = Hworked, y = nbooks, linetype = grade))

ggplot(dt) +
  geom_smooth(aes(x = Hworked, y = nbooks)) +
  facet_wrap(~ grade, nrow = 4)

ggplot(dt) +
  geom_smooth(aes(x = Hworked, y = nbooks)) +
  geom_point(aes(x = Hworked, y = nbooks), size = 4)

ggplot(dt) +
  geom_smooth(aes(x = Hworked, y = nbooks), colour = "black", se = FALSE) +
  geom_point(aes(x = Hworked, y = nbooks, color = grade), size = 4)

ggplot(dt) +
  geom_smooth(aes(x = Hworked, y = nbooks, color = grade), se = FALSE) +
  geom_point(aes(x = Hworked, y = nbooks, color = grade), size = 4)


plot1 <- ggplot(dt) +
  geom_smooth(aes(x = Hworked, y = nbooks, color = grade), se = FALSE) +
  geom_point(aes(x = Hworked, y = nbooks, color = grade), size = 4)
plot1 + xlab("Hours worked") + ylab("Number of books read")

plot1 + xlab("Hours worked") +  ylab("Number of books read") +
  theme(axis.title.x = element_text(face = "italic",size = 14, colour = "navy"),
        axis.title.y = element_text(face = "bold",size = 10, colour = "darkgreen"))

ggplot(filter(dt, affil == "LA")) +
  geom_point(aes(x = Hworked, y = nbooks, color = grade), size = 4)


dt$grade <- fct_relevel(dt$grade, "FR","SP","JR","SR")
group_by(dt, grade) %>% summarize(ave.books = mean(nbooks, na.rm = T)) %>%
  ggplot() + geom_bar(aes(x = grade, y = ave.books), stat = "identity")


ggplot(dt) + geom_bar(aes(x = grade))
dt %>% count(grade)

group_by(dt, grade) %>% summarize(ave.books = mean(nbooks, na.rm = T),
                                  se = sd(nbooks, na.rm =T)/sqrt(n())) %>%
  ggplot(aes(x = grade, y = ave.books)) +
  geom_bar(stat = "identity", fill = "grey70") +
  geom_errorbar(aes(ymin = ave.books - se, ymax = ave.books +se), width = 0.2) +
  ylab("Average # books read")

ggplot(dt) +
  geom_boxplot(aes(x = grade, y = nbooks))
ggplot(dt) +
  geom_boxplot(aes(x = grade, y = nbooks)) +
  coord_flip()


ggplot(dt,aes(x = Hworked, y = nbooks)) +
  stat_density2d(aes(colour =..level..)) +
  geom_point()

ggplot(dt,aes(x = Hworked, y = nbooks)) +
  stat_density2d(aes(alpha =..density..), geom="tile",contour=F) +
  geom_point(alpha =0.4)



ggplot(dt) +
  stat_summary(aes(x = grade, y = nbooks),
               fun.y = mean,
               fun.ymin = function(x) mean(x) - sd(x),
               fun.ymax = function(x) mean(x) + sd(x))


dat <- read.csv("http://www.matsuka.info/data_folder/datWA01.txt")
dt <- as_tibble(dat)
dt.lm <- lm(h~shoesize, dt)
cfs <- coef(dt.lm)
ggplot(dt, aes(x = shoesize, y = h)) +
  geom_point() +
  geom_abline(intercept = cfs[1], slope = cfs[2], col = "red") +
  geom_text( x= 22, y =175, aes(label = paste("r^2  =", round(summary(dt.lm)$r.squared,3))))

10.11ABの講義は家族が急病の為、休講とさせてください。直前の連絡で申し訳ありません。
次回の講義・実習は10.25日です。
補講日は次回、皆さんの都合で調整しましょう。
補講日の候補は11.01、12.27、 および、東大が指定している補講日である、12.25（午後）、01.17（午前）、01.20、01.21です。