For loop inside a function to create m number of functions - r

Question

Suppose I have the following function and output:
library('pracma')
xlag= c(1,3,5,8,12,16,19,20,22,24)
f1 <- function(beta){
xlag[1]*exp(beta[1] * 1)/(exp(beta[1] * 1)+exp(beta[1] * 2)+exp(beta[1] * 3)) +
xlag[2]*exp(beta[1] * 2)/(exp(beta[1] * 1)+exp(beta[1] * 2)+exp(beta[1] * 3)) +
xlag[3]*exp(beta[1] * 3)/(exp(beta[1] * 1)+exp(beta[1] * 2)+exp(beta[1] * 3))
}
pracma::jacobian(f1,c(1))
[,1]
[1,] 0.8488091
I wrote a few for loops in the function so I can extend the model for any value s.
h <-function(beta){
s = 1:3
xlag= 1:9
n <-c()
for (i in s) {
n[i] <- exp(beta[1] * s[i])
}
sal <-sum(n)
z <-c()
for (i in s) {
z[i] <- xlag[i]*exp(beta[1] * s[i])/sal
}
sum(z)
}
pracma::jacobian(h,c(1))
[,1]
[1,] 0.8488091
Now I would like to write f for xlag[1:3], xlag[4:6] xlag[7:9].
Such that the Jacobian becomes a matrix with 1 column and 3 rows. Where the first entry is the one specified above. And the second entry is:
f2 <- function(beta){
xlag[4]*exp(beta[4] * 1)/(exp(beta[1] * 1)+exp(beta[1] * 2)+exp(beta[1] * 3)) +
xlag[5]*exp(beta[5] * 2)/(exp(beta[1] * 1)+exp(beta[1] * 2)+exp(beta[1] * 3)) +
xlag[6]*exp(beta[6] * 3)/(exp(beta[1] * 1)+exp(beta[1] * 2)+exp(beta[1] * 3))
}
pracma::jacobian(f2,c(1))
[,1]
[1,] 1.697618
The third entry:
f3 <- function(beta){
xlag[7]*exp(beta[4] * 1)/(exp(beta[1] * 1)+exp(beta[1] * 2)+exp(beta[1] * 3)) +
xlag[8]*exp(beta[5] * 2)/(exp(beta[1] * 1)+exp(beta[1] * 2)+exp(beta[1] * 3)) +
xlag[9]*exp(beta[6] * 3)/(exp(beta[1] * 1)+exp(beta[1] * 2)+exp(beta[1] * 3))
}
pracma::jacobian(f3,c(1))
[,1]
[1,] 0.706992
So I would like h to output:
[,1]
[1,] 0.8488091
[2,] 1.697618
[3,] 0.706992
The jacobian function is structured as follow
library('pracma')
jacobian(f, x0, heps = .Machine$double.eps^(1/3), ...)
f: m functions of n variables.
x0: Numeric vector of length n.
heps: This is h in the derivative formula.
jacobian(): Computes the derivative of each function f_j by variable x_i separately, taking the discrete step h.
So I need 3 functions f1,f2,f3 of one variable. Yielding a matrix of 1 column and 3 rows.
Could anyone help me rewrite h such that I get the desired output?

Answer 1

I have found the solution.
h <-function(beta){
s = 1:3
xlag #total set of xlag variables
u =1:(length(xlag)-length(s)) #basis for loop
n <-c()
for (i in s) {
n[i] <- exp(beta[1] * s[i]) #nominator expo almon
}
sal <-sum(n) #denominator expo almon
z <-c()
for (i in s) {
z[i] <- exp(beta[1] * s[i])/sal #expoalmon
}
final <-c()
for (i in u) {
final[i] <- sum(xlag[(i):(i+2)]*z[1:3])
}
final
}
pracma::jacobian(h,c(1))