Sequentially multiply matrices from a list by a vector at time t-1 (recursively)

Question

I am trying to multiply a list of matrices, in the order they appear within the list starting with matrix 1, by an initial vector and then recursively; so matrix 2 from the list multiplied by that resulting vector. I have tried various iteration of lapply and map but am unable to project forward and perform this recursively. More explicitly: A[[1]] % * % allYears[,1], then A[[2]] % * % allYears[,2],.....,A[[4]] % * % allYears[,4] which produces the final 5th column in "allYears". Below is the sample code with the known error in the for loop at A[[i]] indexing as i is not explicitly referenced.

A <- lapply(1:4, function(x)  # construct list of matrices
  matrix(c(0, 0, 10, 
           rbeta(1, 5, 4), 0, 0, 
           0, rbeta(1, 10, 2), 0), nrow=3, ncol=3, byrow=TRUE, ))

n <- c(1000, 100, 10)  # initial vector of abundances

nYears <- 4  # define the number of years to project over

allYears <- matrix(0, nrow=3, ncol=nYears+1)  # build a storage array for all abundances

allYears[, 1] <- n  # set the year 0 abundance   

for (t in 1:(nYears + 1)) {   # loop through all years
  allYears[, t] <- A[[i]] %*% allYears[, t - 1]
}

Answer 1

Based on the description, perhaps we need to loop over the sequence - i.e. length of A is 4, whereas the number of columns of 'allYears' is 5. Create an index from 2 to ncol of 'allYears', then loop over the sequence of that index, extract the corresponding element of 'A' based on the sequence whereas we get the allYears previous column

i1 <- 2:(nYears + 1)
 for(t in seq_along(i1)) {
    allYears[,i1[t]] <-  A[[t]] %*% allYears[,i1[t]-1]
 
 }

-output

> allYears
     [,1]      [,2]      [,3]       [,4]      [,5]
[1,] 1000 100.00000 817.24277 2081.08322  333.6702
[2,]  100 261.46150  55.44237  423.22095 1244.6680
[3,]   10  81.72428 208.10832   33.36702  355.5175