npar.equal <- function(filename,ages,birth.year){
  #################################################################################################################
  # Author: Daniela Kuruczova <daniela.kuruczova@mail.muni.cz>                                                    #
  # Purpose: Finding age where male mortality is equivalent to female mortality for                               #
  #          data downloaded from http://www.mortality.org/                                                       #
  # Arguments: filename = path and name of file to use as data source                                             #
  #            ages = sequence of ages that will be used for the cohort                                           #
  #            birth year = birth year of the cohort                                                              #
  # Output: data frame with items:  "age": female age                                                             # 
  #                                 "EQ": male age with mortality equivalent to females with given age            #
  # Example of use: npar.equal("Mx_1x1_Australia.txt",30:60,1954)                                                 #
  #                                                                                                               # 
  # 2018/11/21 Initial version (DK)                                                                               # 
  #################################################################################################################
  
  #Years to extract from data
  years <- birth.year+ages
  
  #Read data file
  dt <- read.table(filename,header=T,skip=2,na.strings='.')
  
  #Replace character + in Age
  dt$Age <- as.integer(gsub("+", "", as.character(dt$Age),fixed=T))
  
  #Get country name from filename
  country.name <- substr(filename, 8, regexpr('.txt', filename)[1] - 1)
  
  #Filter out data for specified cohort
  dt.to.use <- dt[dt$Age %in% ages & dt$Year %in% years & dt$Year-dt$Age==birth.year,]
  
  #Model calculation
  lambda <- 0.7
  #males
  s.M <- smooth.spline(dt.to.use$Age, dt.to.use$Male,spar=lambda)
  #females
  s.F <- smooth.spline(dt.to.use$Age, dt.to.use$Female,spar=lambda)
  
  res.vector <- c()
  for (i in min(ages):max(ages)){
    
    if(predict(s.M,30)$y<=predict(s.F,i)$y){
      temp.f <- function(x){
        out <- predict(s.M,x)$y - predict(s.F,i)$y
        return(out)
      }
      res <- uniroot(temp.f,c(min(ages),max(ages)))
      res.vector <- c(res.vector,res$root)
    }
    else{
      res.vector <- c(res.vector,NA)}
  }
  output <- data.frame(ages=ages,EQ=res.vector)
  return(output)
}