Updating a data.table in R - r

Question

(Edited)
I am using the following code to create two columns in a data.table and update them with some numbers:
T <- data.table(Init_1 = rep(0, 100), Init_2 = rep(0, 100))
for (i in 1:100){
T[, Init_1 := i]
T[, Init_2 := 2*i]
}
I expected that this code would add two columns to the data.table T (Init_1 and Init_2) and fill them with numbers : (1:100) and (2,4,...200) respectively.
However, the code returns constant values:
> T
Init_1 Init_2
1: 100 200
2: 100 200
3: 100 200
4: 100 200
5: 100 200
6: 100 200
7: 100 200
8: 100 200
.................
Could you explain why my code is not working as expected and how it could be fixed?
Your advice will be appreciated.
Edit:
In relation to answer 2, eventually I want to use a function inside the for loop. More specifically:
# A FUNCTION THAT RETURNS THE TRANSITION PROBABILITIES AFTER N STEPS IN A MARKOV CHAIN
#-------------------------------------------------------------------------------------
R <- function(P, n){
if (n==1) return(P)
R(P, n-1) %*% P
}
# A ONE-STEP PROBABILITY MATRIX
#---------------------------------------------------------------------------------------
P = matrix(c(0.6, 0.1, 0.3, 0.2, 0.7, 0.1, 0.3, 0.3, 0.4), nrow = 3, byrow = TRUE)
# EXAMINING THE CONVERGENCE PROCESS OF THE PROBABILITIES OVER TIME
#########################################################################
T <- data.table(Init_1 = rep(0, 100), Init_2 = rep(0, 100))
for (i in 1:100){
T[, Init_1 := R(P, i)[1,1]]
T[, Init_2 := R(P, i)[2,1]]
}
or
for (i in 1:100){
T[, ':=' (Init_1 = R(P, i)[1,1],
Init_2 = R(P, i)[2,1]) ]
}

Answer 1

I'm no data.table expert. But I know it throws
helpful error messages. If you e.g. create an empty data.table and
try to use := to add columns, it says
T <- data.table()
T[,a:=1]
# Error in `[.data.table`(T, , `:=`(a, 1)) :
# Cannot use := to add columns to a null data.table (no columns), currently.
# You can use := to add (empty) columns to a 0-row data.table (1 or more empty columns),
# though.
Your problem might be related. Because data.table(numeric()) or rather T <- data.table(numeric(length = 0)) creates a a 0-row data.table. The empty column gets named V1 by default. Here you could use
:= to add empty columns. However, that's not what you want.
Instead you could do
T <- data.table(numeric(0))
for (i in 1:5){
T <- T[, .(
Init_1=if (exists("Init_1")) c(Init_1, i) else i,
Init_2=if (exists("Init_2")) c(Init_2, 2*i) else 2*i )]
}
T
# Init_1 Init_2
# 1: 1 2
# 2: 2 4
# 3: 3 6
# 4: 4 8
# 5: 5 10
Although that's pretty ugly und probably super unefficient.

Answer 2

First, you should not define a function with name as T. T is reserved for TRUE in logic. Also, it is not recommended to use i for iteration since it is also used for complex number, for example
> (2i)^2
[1] -4+0i
Third, iteration is slow in R. We should avoid to use iteration whenever possible.
Here are the simple codes to generate such matrix. Hope this helps.
T.data <- matrix(NA,nrow=100,ncol=2);
T.data[,1] <- 1:100;
T.data[,2] <- 2*T.data[,1]