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

db_games <- readRDS("db_data.Rda")

# Season 2018/2019
s201819_start <- as.Date("2018-08-24")
s201819_end <- as.Date("2019-05-18")

db_201819 <- subset(db_games, Date >= s201819_start & Date <= s201819_end & League == "Bundesliga")

#B <- generateB(db_201819)
S <- generateA(db_201819, type = 1)
teams <- as.character(unique(db_201819$HomeTeam))
B <- diag(1,length(teams),l ength(teams))*+colSums(S^2)-S*t(S)
all((2*abs(diag(B))) >= rowSums(abs(B),2))
#l <- max(rowSums(abs(B))) # unstable
#l <- minL(B)
l <- abs(min(((2*abs(diag(B))) - rowSums(abs(B),2))))
Bddom <- B + l*diag(nrow(B))
all((2*abs(diag(Bddom))) >= rowSums(abs(Bddom),2))
Binv <- solve(Bddom)
r <- powerMethod(Binv, treshold = 10^(-10))
printStandings(r)
v <- log(r)
printStandings(v)

B%*%r/r # test for EV
sum(r^2) # test NB