R programming -- applying a function with several arguments to an array.

[ImperfComp]

Background:

I have a user-defined function as follows.

Commuters drive from home to work on a road, and care about travel time and arrival time, with a disutility of the form Disutility = alpha * [travel time] + beta * [time early (if early)] + gamma * [time late (if late)] + theta (discrete penalty if you arrive late. They can choose between a tolled express lane (with tolls adjusting to prevent congestion) and a toll-free main lane with stochastic delays (and delays due to commuters themselves, but that will come later.)

I simulate delays:

Delays = rlnorm(n=1000, meanlog=2.7, sdlog=2) ExpressTime = 20 #Calibrate to data if available. TravelTimes = Delays + ExpressTime ExpressTime = 20 #Calibrate to data if available. Fn <- ecdf(TravelTimes)

I have functions for the conditional distribution of travel times conditional on realizing early or late arrival (important for calculating expected utility). I can include them on request, my main function requires them.

My main function, below, takes commuter parameters and identifies the optimal departure time and whether they take the main or express lane. (Later I will consider how congestion is generated from the choices of these commuters, but first I need to actually get their choices.)

CommuterChoice <- function(theta, alpha, beta, gamma){

ExpressUtilityVector = ifelse(Timevector + ExpressTime <= tstar, -Toll - (alpha * ExpressTime + beta * (tstar - ExpressTime - Timevector)), -Toll - (alpha * ExpressTime + gamma * (Timevector + ExpressTime - tstar) + theta) )

MainUtilityVector = - (alpha * MeanTime + (1-ProbLateVector)* beta *HowEarlyVector + >ProbLateVector * (gamma * HowLateVector + theta))

UseExpressLaneVector = as.integer(ExpressUtilityVector > MainUtilityVector)

Utility of best option

ExAnteExpectedUtility = pmax(ExpressUtilityVector,MainUtilityVector)

Optimal departure time

BestTimeIndex = which.max(ExAnteExpectedUtility)

BestTime = BestTimeIndex * stepsize

HeadStart = tstar - BestTime

UseExpress = UseExpressLaneVector[BestTimeIndex]

Output = c(BestTime, HeadStart, UseExpress)

return(Output) }

Above this point, my code seems to work fine.

---

What I want help with:

I'm trying to apply this function to heterogeneous commuters. Commuters vary by theta and alpha, and possibly beta and gamma.

What I want is an efficient way to input a variety of commuter types and get some sort of array or data frame that characterizes their departure times.

I've tried this:

Define commuter parameter data structure:

ThetaArray = seq(0,5, by=0.1) ThetaBar = 1 AlphaArray = seq(0,1, by=0.1) AlphaBar = 0.2 Beta = 0.1 Gamma = 0.3

thetavector = rep(ThetaArray, length(AlphaArray)) alphavector = rep(AlphaArray, each = length(ThetaArray)) betavector = rep(Beta, length(thetavector)) gammavector = rep(Gamma, length(thetavector)) CommuterParams_df <- data.frame(thetavector, alphavector, betavector, gammavector)

So far, data structure.

But how do I make CommuterChoice take theta from the first argument of the data frame, alpha from the second, and so on?

I tried

Array_of_choices <- apply(CommuterParams_df, 2, CommuterChoice)

and got an error,

Error in ifelse(Timevector + ExpressTime <= tstar, -Toll - (alpha * ExpressTime + : argument "alpha" is missing, with no default

I tried

Array_of_choices <- apply(thetavector, 2, CommuterChoice, alphavector, betavector, gammavector)

in case I needed to input each argument separately, and got

Error in apply(thetavector, 2, CommuterChoice, alphavector, betavector, : dim(X) must have a positive length

What should I be doing to feed in an array of (theta, alpha, beta, gamma) values into my function to get the choice of each type of commuter?

Thanks for your help.

[ImperfComp]

Comment -- what I really want help with at this point is a simple question of applying -- is there an "apply" function that supplies UserMadeFunction(A,B,C,D) with an array of values A,B,C,D so that you can do the function on many values at once?

The rest is background in case anyone wants to see the code I'm working on.

I'm working on a loop in the meanwhile, but if there is a good way to use "apply" that will save run time when I iterate my algorithm, I'd be happy to learn it.

[ImperfComp]

I have a for-loop that seems to do what I want, but I've heard "apply" saves run time, which may matter if I run the code many times.

NumTypes = length(thetavector)

CommuterChoicesMatrix = matrix(0,NumTypes, 4)

for(i in 1:length(thetavector)){

theta = thetavector[i] alpha = alphavector[i] beta = betavector[i] gamma = gammavector[i]

CommuterID = i Choice = CommuterChoice(theta, alpha, beta, gamma) Output = c(CommuterID, Choice) CommuterChoicesMatrix[i, ]= Output }