# "Power-Method"
powerMethod <- function(A, r0 = rep(1, nrow(A)), treshold = 10^(-10))
{
  r_alt <- r0
  matExp <- A
  for (i in 2:10000) # large enough (or while(true))
  {
    matExp <- matExp%*%A
    r <- matExp%*%r0/norm(matExp%*%r0,'F')
    #print(r)
    if (norm(r-r_alt,'F') < treshold)
    {
      print(paste0("Found solution after ", i, " iterations."))
      break
    }
    r_alt <- r
  }
  return(r)
}

# Type 0: A with a_ij equals 1 for win, 0.5 for draw and 0 for loss
# Type 1: S_ij: team i scored s_ij points versus team j
# Type 2: A with a_ij = (S_ij+1)/(S_ij+S_ji+2)
generateA <- function(dataSet, type = 0)
{
  teams <- as.character(unique(dataSet$HomeTeam))
  A <- matrix(0, nrow=length(teams), ncol=length(teams)) # named matrix
  rownames(A) <- teams
  colnames(A) <- teams
  for (i in 1:nrow(dataSet))
  {
    homeTeam <- as.character(dataSet$HomeTeam[i])
    awayTeam <- as.character(dataSet$AwayTeam[i])
    if (type == 0)
    {
      gd <- dataSet$FTHG[i] - dataSet$FTAG[i]
      if (gd > 0)
      {
        A[homeTeam,awayTeam] <- A[homeTeam,awayTeam] + 1
      }
      else if (gd < 0)
      {
        A[awayTeam,homeTeam] <- A[awayTeam,homeTeam] + 1
      }
      else
      {
        A[homeTeam,awayTeam] <- A[homeTeam,awayTeam] + 0.5
        A[awayTeam,homeTeam] <- A[awayTeam,homeTeam] + 0.5
      }   
    }
    else if (type == 1)
    {
      A[homeTeam,awayTeam] <- A[homeTeam,awayTeam] + dataSet$FTHG[i]
      A[awayTeam,homeTeam] <- A[awayTeam,homeTeam] + dataSet$FTAG[i]
    }
    else if (type == 2)
    {
      A[homeTeam,awayTeam] <- A[homeTeam,awayTeam] + (dataSet$FTHG[i]+1)/(dataSet$FTHG[i]+dataSet$FTAG[i]+2)
      A[awayTeam,homeTeam] <- A[awayTeam,homeTeam] + (dataSet$FTAG[i]+1)/(dataSet$FTHG[i]+dataSet$FTAG[i]+2)
    }
  }
  return(A)
}