# STAT_540_Lec_R_05.R

# The while loop!!

# we can always write a while loop instead of a for loop.

# here we don't really NEED a while loop, but just 
# to demonstrate, let's compute the sum with a while loop

x <- c(3,7,8,5,1,4,6,7)

# for loop:

n <- length(x)
val <- 0
for(i in 1:n){
  
  val <- val + x[i]
  
}

val

# let's do the same loop but as a while loop:
i <- 1
val <- 0
while(i <= n){ # this will not run once i = n + 1
  
  val <- val + x[i]
  i <- i + 1 # increment the index
  
}
val

# division: A / B.  
# Here we need a while loop because we don't know how many iterations it will have to run.
 
div <- function(A,B){
  
  Q <- 0
  while(A >= B){
    
    A <- A - B
    Q <- Q + 1
    
  }
  
  output <- list(quotient = Q,
                 remainder = A)
  
  return(output)
  
}

div(76,3)


# while loop for paying off a debt:

B <- 10000 # borrow 10k $$$$$$ for something
r <- 0.05 # annual interest rate (compounded monthly)
p <- 200 # amount you pay every month

m <- 0
while(B >= 0){
  
  B <- B*(1 + r/12) - p
  m <- m + 1
  
}
m # number of months to pay off the loan
m/12 # number of years


# Newton's method for finding a root
# (value of r for which f(r) = 0)


f <- function(r,P,p,n){

  (P / p) * (1 + r)^n * r - (1 + r)^n + 1
  
}

df <- function(r,P,p,n){
  
  (P / p) * (n *(1 + r)^(n-1) * r + (1 + r)^n) - n*(1+r)^(n-1)
  
}

P <- 10000 # 10 k $$
p <- 200 # monthly payment
n <- 60 # number of months to pay off

x <- 0.05/12 # initial guess of monthly interest rate
conv <- FALSE
tol <- 1e-7 # 10^{-7}
while(!conv){ # while not converged....
  
  x0 <- x # save the value before we update
  x <- x - f(x,P,p,n) / df(x,P,p,n) # make the update
  
  conv <- abs(x - x0) < tol # absolute value of change
  
}
x  

# check and see if you found the root of the function:
f(x,P,p,n)