source("eigenvalueRanking.R")
source("formattedOutput.R")

db_games <- readRDS("db_data.Rda")

# Seasons
s201516_start <- as.Date("2015-08-24")
s201516_end <- as.Date("2016-05-14")
s201617_start <- as.Date("2016-08-26")
s201617_end <- as.Date("2017-05-20")
s201718_start <- as.Date("2017-08-18")
s201718_end <- as.Date("2018-05-12")
s201819_start <- as.Date("2018-08-24")
s201829_1half <- as.Date("2018-12-23")
s201819_end <- as.Date("2019-05-18")
s201920_start <- as.Date("2019-08-16")
s201920_1half <- as.Date("2019-12-22")

db_201516 <- subset(db_games, Date >= s201516_start & Date <= s201516_end & League == "Bundesliga")
db_201617 <- subset(db_games, Date >= s201617_start & Date <= s201617_end & League == "Bundesliga")
db_201718 <- subset(db_games, Date >= s201718_start & Date <= s201718_end & League == "Bundesliga")
db_201819 <- subset(db_games, Date >= s201819_start & Date <= s201819_end & League == "Bundesliga")
db_201819_1half <- subset(db_games, Date >= s201819_start & Date <= s201829_1half & League == "Bundesliga")
db_201920_1half <- subset(db_games, Date >= s201920_start & Date <= s201920_1half & League == "Bundesliga")

games <- db_201819
games <- na.omit(games)
games <- games[order(games$Date),]
teams <- as.character(unique(games$HomeTeam))
n <- length(teams)

r_init <- 0.1

# BTL Maximum-Likelihood
Aml <- generateA(games, 3)
ak <- rowSums(Aml) # row sum for a_k
r <- rep(r_init, n) # result vector
names(r) <- colnames(Aml)

# settings
h <- 0.001
treshold <- 10^(-10)
maxIter <- 20000

dr <- function(r)
{
  ddr <- ak/r
  for(k in 1:n)
  {
    ddr[k] <- ddr[k] - sum((Aml[,k]+Aml[k,])/(r+r[k]))
  }
  return(ddr)
}

i <- 0
repeat # euler Verfahren
{
  i <- i + 1
  r_old <- r
  r <- r_old + h * dr(r_old)
  print(paste0("Iterations: ", i, " Error: ", norm(t(r-r_old),'F')))
  if (norm(t(r-r_old),'F') < treshold) # Abbruchbedingung! Konvergenz!
  {
    print(paste0("Found solution after ", i, " iterations."))
    break
  }
  if (i > maxIter)
  {
    print(paste0("Can't find solution within maxIter = ", maxIter, " iterations."))
    break
  }
}
printStandings(r)
print(sum(r^2))