Loop for dynamic rows in R - r

Question

I don't know If my question is well thought out. I'll try to explain as best as I can. I'm trying to create this model originaly made in Excel into R. The function basically is a sum of products between these four matrices. The left matrices are interaction matrices, so the variables are in the rows as well in the columns. The other two matrices describe the behaviour as times passes, taking data from the previous time step. In excel this is roughly the way it's built:
The cell where the function is applied is the one with the red arrow. I made the following code, starting by making the main function, then making the four matrices and then the loop for applying the fucntion to the matrices.
### MAIN FUNCTION ### This is the main sum product function
func_dxit <- function(xit, ksim, alfa, beta, dkism_evaluar, dt) {
xit_log <- log(xit)
prod_xit <- (-xit * xit_log)
suma_alfa <- crossprod(alfa, ksim_evaluar)
suma_beta <- crossprod(beta, dkism_evaluar)
suma_alfabeta <- (suma_alfa + suma_beta)
dxit <- (prod_xit * suma_alfabeta) * dt
return(dxit)
}
Where "xit" is the value of the element in the first row and first column of the 3rd matrix. "alfa" is the row of left most matrix, "beta" is the row of second one, and "ksim_evaluar" and "dksim_evaluar" are rows of the 3rd and 4th matrices respectively.
### INITIAL DATA ###
ini <- c(0.5,0.05,0.25,0.5,0.3,0.05,0.5,0.5,0.3,0.25,0.2,0.1) # initial values, these are initial values of ksim at time 0, or row 1.
dt <- 0.1 # constant
### ALFA AND BETA MATRICES ###
input_alfa <- matrix(c(
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0), nrow = 12, ncol = 12, byrow = TRUE)
colnames(input_alfa) <- c("unidades de recursos", "volumen de corta",
"acuerdos de venta", "ingresos", "ganancias",
"sanciones", "trabajo comunitario",
"eficiencia de aprovechamiento",
"regeneracion artificial", "esfuerzo de reforestacion",
"regeneracion natural", "productividad")
rownames(input_alfa) <- c("unidades de recursos", "volumen de corta",
"acuerdos de venta", "ingresos", "ganancias",
"sanciones", "trabajo comunitario",
"eficiencia de aprovechamiento",
"regeneracion artificial", "esfuerzo de reforestacion",
"regeneracion natural", "productividad")
input_beta <- matrix(c(
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), nrow = 12, ncol = 12, byrow = TRUE)
colnames(input_beta) <- c("unidades de recursos", "volumen de corta",
"acuerdos de venta", "ingresos", "ganancias",
"sanciones", "trabajo comunitario",
"eficiencia de aprovechamiento",
"regeneracion artificial", "esfuerzo de reforestacion",
"regeneracion natural", "productividad")
rownames(input_beta) <- c("unidades de recursos", "volumen de corta",
"acuerdos de venta", "ingresos", "ganancias",
"sanciones", "trabajo comunitario",
"eficiencia de aprovechamiento",
"regeneracion artificial", "esfuerzo de reforestacion",
"regeneracion natural", "productividad")
Next I made the empty KSIM and DKSIM matrices, except for KSIM which first row is "ini" the initial values.
### KSIM AND DKSIM MATRICES ###
ksim <- matrix(c(
ini,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
), nrow = 26, ncol = 12, byrow = TRUE)
colnames(ksim) <- c("unidades de recursos", "volumen de corta",
"acuerdos de venta", "ingresos", "ganancias",
"sanciones", "trabajo comunitario",
"eficiencia de aprovechamiento",
"regeneracion artificial", "esfuerzo de reforestacion",
"regeneracion natural", "productividad")
rownames(ksim) <- c("0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10",
"11", "12", "13", "14", "15", "16", "17", "18", "19",
"20", "21", "22", "23", "24", "25")
dksim <- matrix(c(
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
), nrow = 26, ncol = 12, byrow = TRUE)
colnames(dksim) <- c("unidades de recursos", "volumen de corta",
"acuerdos de venta", "ingresos", "ganancias",
"sanciones", "trabajo comunitario",
"eficiencia de aprovechamiento", "regeneracion artificial",
"esfuerzo de reforestacion", "regeneracion natural", "productividad")
rownames(dksim) <- c("0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10",
"11", "12", "13", "14", "15", "16", "17", "18", "19",
"20", "21", "22", "23", "24", "25")
Next is to fill up the matrices using a loop that iterates the main function
for (i in 1:26){
xit <- as.vector(ksim[i,])
alfa <- as.vector(input_alfa[1,])
beta <- as.vector(input_beta[1,])
ksim_evaluar <- as.vector(ksim[1,])
dksim_evaluar <- as.vector(dksim[1,])
dksim[i,] <- func_dxit(xit, ksim, alfa, beta, dkism_evaluar,dt)
return (dksim)
}
This does iterate the function over the whole row in dksim. The problem is that for every iteration in the same row, it has to take the "alfa" and "beta" values of the next variable, something that my loop doesn't achieve. That is, it's correctly evaluating the same row for "ksim_evaluar" and "dksim_evaluar" (same time step) but it has to take the next row for "alfa" and "beta" (next variable) as you can see in the green arrow compared with the first image.
For the next iteration it must evaluate the 3rd row, for the next one the 4th and so on. Should this be a nested loop? I hope I explained this correctly, thanks a lot in advance.