Having trouble understanding the upper bound and lower bound in the following R code

Question

I have pasted the code i am having an issue with at the end. It contains R command lines to display the observed proportions of correct response over the ability score levels for group 1. The lower bound of ability for group 1 is specified with t1l that implies theta- 1-lower; the upper bound of ability for group 1 is specified with t1u that implies theta-1-upper: Before this code there was another code which defined theta as following:

theta <- seq(-3, 3, .1875)
f <- rep(21, length(theta))

Then this code was mentioned. What i understand is that this code is finding some values between 2 bounds. However feel that if i want to find something in between 1 and 3 then i should make a code which says i want to find values less than 3 and more than 1. However this code does this for the lower bound

theta[g] <= t2l) { lowerg1 <- lowerg1 + 1 }

This means it finds values less than 1? Values less than 1 would be something like 0 , -1 -2 etc and we want to find values in BETWEEN 1 and 3. I feel we should instead say theta[g] >= t2l) so that i can find values larger than 1 so i can find values like 2 which is between 3 and 1 It does the same thing for upper bound. but this will find ALL values below 3 not just between 3 and 1

theta[g] <= t2u) 

This is how i am visualizing things to be going on https://i.stack.imgur.com/uPiiS.png And this is how i feel things should be https://i.stack.imgur.com/Jyly1.png

t2l <- 1
t2u <- 3
lowerg1 <- 0
for (g in 1:length(theta)) {
if (theta[g] <= t2l) { lowerg1 <- lowerg1 + 1 }
}
upperg1 <- 0
for (g in 1:length(theta)) {
if (theta[g] <= t2u) { upperg1 <- upperg1 + 1 }
}
theta2 <- theta[lowerg1:upperg1]
p2 <- p[lowerg1:upperg1]
if (mdl == 1) { maintext <- paste("Group 2", "\n") }
if (mdl == 2) { maintext <- paste("Group 2", "\n") }
if (mdl == 3) { maintext <- paste("Group 2", "\n") }
plot(theta2, p2, xlim=c(-3,3), ylim=c(0,1),
xlab="Ability", ylab="Probability of Correct Response",
main=maintext)

Answer 1

Your code below does exactly what it is supposed to do

t2l <- 1
t2u <- 3
lowerg1 <- 0
for (g in 1:length(theta)) {
  if (theta[g] <= t2l) { lowerg1 <- lowerg1 + 1 }
}
upperg1 <- 0
for (g in 1:length(theta)) {
  if (theta[g] <= t2u) { upperg1 <- upperg1 + 1 }
}
theta2 <- theta[lowerg1:upperg1]

The last time theta[g] <= t2l was when theta was 0.9375 and lowerg1 is 22.

A simpler way to define theta2 is shown below

theta2 <- theta %>% subset(theta>=t2l & theta<=t2u)