mae <- function(x,y)
{
  mean(abs(x-y))
}

mse <- function(x,y)
{
  mean((x-y)^2)
}

rmse <- function(x,y)
{
  sqrt(mse(x,y))
}

mape <- function(x,y)
{
  100*mean(abs((x-y)/x))
}