Iterate through a function until exact value or certain range is reached-CodePudding

I have a function that takes gross income as input and gives me the net income as output:

gross_net <- function(gross_income,
                      social_security = 0.2,
                      tax = 0.3){
  net_income <- (gross_income - gross_income * social_security) * (1 - tax)
  net_income
}

gross_net(2000)

> gross_net(2000)
[1] 1120

I am looking for some kind of iteration that - if I only have a net income value - "tries out" several gross income values in the gross_net function until it picks the right gross income value that corresponds to the net income value. (I know it would probably be faster to invert the function.)

I thought of a while loop that has a lower and upper parameter (e.g. the gross income values that are tried out must lie between 1.1 times the net_income and 2 times the net_income). It should check if gross_net(net_income * upper) is higher than my net_income, if it is higher then try gross_net(net_income * lower). If this is lower than my net_income the try a value a little smaller than the original upper parameter and so on until the gross income value that corresponds to the provided net income value is reached (or until the gross income value is in a certain range).

I tried something like

net_gross <- function(income){
  test_net_income  <- income
  upper <- 2
  lower <- 1.1
  while(test_income != gross_net(test_net_income)){
    if(gross_net(test_net_income * upper) > income)
      upper <- lower   (upper - lower) * 0.9
    test_income <- income * lower
    
    if(gross_net(test_net_income * lower) > income)
      lower <- upper - (upper - lower) * 0.9
    test_income <- income * upper
  }}

but obviously that does not work. Is a while loop even the "right" way to do this? (I explicitly need a solution involving iteration - inverting the function is not an option for me.)

CodePudding user response：

Although this can be solved algebraically, as given in another answer, a more general approach is to use uniroot to find where the function minus target value is zero. e.g. if you want to search the range 0 - 1,000,000

net_gross <- function(income) uniroot(function(x){gross_net(x)-income}, c(0, 1e6))
net_gross(1120)
#$root
#[1] 2000  <- The inverse of 1120
#
#$f.root
#[1] 0
#
#$iter
#[1] 1
#
#$init.it
#[1] NA
#
#$estim.prec
#[1] 998000

CodePudding user response：

As you mentioned, invert the funcion is the best way to get the gross_income value.

what you have is the following formula:

net_income <- (gross_income - gross_income * social_security) * (1 - tax)

Which can be rewritten as

  net_income <-  gross_income*(1-social_security)*(1-tax)

So,solving to get 'gross_income' value:

gross_income <- net_income/((1-social_security)*(1-tax))

And then, you can build the following function

gross_income_solve <- function(net_income, social_security = 0.2, tax = 0.3){
    gross_income <-  net_income/((1-social_security)*(1-tax))
    return(gross_income)
  }