# examples of for loops in R

# Example 1, add the numbers from 1 to n

cat(" Example 1, simple loop, simple summation\n\n")  # two carriage returns to leave a blank line

n   = 6      # the number of terms to add up
sum = 0      # this is "initialization", setting values at the start of a loop

for( i in 1:n) {
   sum = sum + i
   cat("sum is ", sum, " and i is ", i, "\n")
 }
cat( "Done with sum loop. ", i, " terms gave sum = ", sum, "\n")


#  Example 2, the construction 1:n in the for loop makes an R list with the integers (1, 2, ..., n)

cat("\n Example 2, simple loop, add elements of a list\n\n")

list = 1:n
cat("list is ", list, "\n")
list = c(3, -2, 5)
cat("now, list is ", list, "\n\n")

sum = 0      # you have to re-initialize, or you start with sum = 36

for( i in list) {
   sum = sum + i
   cat("sum is ", sum, " and i is ", i, "\n")
 }
cat( "Done with sum loop, ", i, " terms gave sum = ", sum, "\n")


#  Example 3, break out of a loop when a condition is satisfied

n      = 10
target = 30
sum    = 0.

cat("\n Example 3, find how many terms it takes to reach sum > ", target, "\n\n")
for( i in 1:n) {
   sum = sum + i
   cat("sum is ", sum, " and i is ", i, "\n")
   if ( sum > target) break
 }
cat( i, " terms gave sum = ", sum, "\n")


#  Example 4, a different test in the loop

target = 30
sum    = 0.

cat("\n Example 4, a different test in the loop ", target, "\n\n")
for( i in 1:n) {
  
   if ( sum > target) {
      cat("above the target. sum is ", sum, " and i is ", i, "\n")
     }
   else{
     sum = sum + i
     cat("below the target, sum is ", sum, " and i is ", i, "\n")
     }
 }
cat( i, " terms gave sum = ", sum, "\n")


#  Example 5, approximate an integral

cat("\n Example 5, approximate an integral\n\n")

#   Estimate the integral of e^x in the range 0 < x < L
#   Use n rectangles of size dx = L/n

n  = 1000    #  Don't "hard wire" variables in a program that you might ...
L  = 3      #  ... want to change later.
dx = L/n    #  The width of a rectangle

          #  Initialization

x         = 0       #  x will be the point at the left end of an interval
TotalArea = 0

              #  the integration loop

for( i in 1:n) {
  
   RectangleArea = dx*exp(x)              #  The area of this little rectanble
   TotalArea = TotalArea + RectangleArea  #  Add in the area of this rectangle
   x   = x + dx                           #  Increment x to be the left end of the next interval
#  cat("i = ", i, ", and x = ", x, "\n")  #  for debugging, comment this out for production runs
 }

cat("Integrate from 0 to ", L, " using ", n, " points.  Get ", TotalArea,"\n")
ans = exp(L)-1
err = TotalArea - ans
cat("The exact answer is ", ans, " and the error is ", err, "\n\n")