This homework is due on Tuesday, September 26st at 12:30pm (the start of class). Please turn in all your work. The purpose of this homework is to explore some of the details of R and update Unix skills. This description may change at any time, however notices about substantial changes (requiring more/less work) will be additionally noted on the class web page. Note that there are two prongs to submission, via Canvas and Bitbucket (in asc-repo/hwk/hw2). You don’t need to use Rmarkdown but your work should be just as pretty if you want full marks.

Problem 1: Unix commands (15 pts)

Update your asc-repo/notes/unix.txt file to include the commands we have discussed in class since homework 1, and any others that you’d like to keep a list of. (Note that the answer to this question does not require files in asc-repo/hw2.)

Problem 2: Immutable objects (30 pts)

Consider the following function which swaps elements i and j of a vector v.

swap <- function(v, i, j) 
    tmp <- v[i]
    v[i] <- v[j]
    v[j] <- tmp 

A disadvantage of this implementation is that it copies the entire vector, v, in order to work with just two of its elements. Consider the following example.

v <- 1:1000000000
system.time(swap(v, i=1, j=2))
##    user  system elapsed 
##   0.488   0.320   0.809
  • Nearly a second to “touch” three numbers isn’t super speedy.

Your tasks on this problem are the following.

  1. Report on how much time it takes to swap two elements (i=1; j=2) directly on the command line, i.e., without wrapping in a function.
  2. Write a new version of the swap function, called swap.eval, which uses quote and eval to perform the calculation just like in part a. but within the function environment and without copying v by working on v in the parent.frame. Although this is a toy example, a similar code might be useful if, say, indicies i and j required substantial pre-calculation within the function before the swap occurred. Demonstrate your swap.eval with i=1; j=2 and report on the time.
  3. Write a similar function named which can be called via that similarly accesses v in the parent frame. Add a print statement at the end of to show the first five elements of v after the swap occurs. Demonstrate with i=1; j=2 and report on the time. Are there any disadvantages to compared to swap.eval?

Note: be sure to try your codes/functions several times to see if the behavior changes from one try to the next.

Problem 3: Bisection broadening (30 pts)

Recall the bisection algorithm and S3 object-oriented implementation from class. The bisection method can be generalized to deal with the case \(f(x_l) f(x_r) > 0\), by broadening the bracket. That is,

  • reduce \(x_l\) and/or increase \(x_r\), and try again.
  • A reasonable choice is to double the width of the interval, i.e.,

\[ \begin{aligned} m &\leftarrow (x_l + x_r)/2, & w &\leftarrow x_r - x_l \\ x_l&\leftarrow m - w, & x_r &\leftarrow m + w. \end{aligned} \]

Your tasks are the following.

  1. Incorporate bracketing into the function we coded. Note that broadening is not guaranteed to find \(x_l\) and \(x_r\) such that \(f(x_l) f(x_r) \leq 0\), so you should include a limit on the number of times broadening is successively tried with a sensible default.

  2. Use your modified function to find a root of the (original) function \(f(x)\) we used in class, but with a different starting interval of \(x_l = 2\) and \(x_r = 3]\), i.e., not containing the root we found in class.

  3. Use your modified function find the root of \[ h(x) = (x - 1)^3 - 2x^2 + 10 - \sin(x), \] starting with \(x_l = 1\) and \(x_r = 2\).

For full credit you must keep everything in the S3 environment with appropriate modifications to your generic methods, etc. You will be judged on style here, in terms of code, S3 behavior, and writeup/demonstration. You may have a separate bisection.R file with your S3 library functions, however your writeup must verbally describe how those functions have changed. I will check for bisection.R in your repository against your description.

Problem 4: R scripts from the Unix prompt (25 pts)

R provides two “commands” to execute scripts (e.g., some R code in file like script.R). What are those commands and what are their differences? Please provide a brief high level description and do not plagiarize. Focus on details like:

  • What happens with plots?
  • What happens with text output that would normally be printed to the screen? What about warnings or errors?
  • What happens with the objects in the workspace when the script terminates.

And be sure to contrast default behavior with options for customization.

Write an R script which renders an Rmarkdown document in HTML and furnishes a companion .R file containing an extraction of the raw code. The script must entirely comprise of R commands (no manual steps like clicking buttons in RStudio). If you are composing this solution in Rmarkdown you may use your homework file hw2_sol.Rmd as an example file, generating hw2_sol.html and hw2_sol.R. Otherwise, you will need to create a simple dummy one for the purposes of illustration. Then describe the single Unix command that you would need to call from the command prompt to cause your .html and .R file to be generated from the Rmd file.

Create a shell script, which is a text file, called with the following two lines

insert your unix command for building from hw2_sol.Rmd here

Make the script file executable with the command chmod +x, and now you can run it from the command line with ./build. Make sure it all works, and that it has been added to your repository in hw2/ because it will be tested.

(Note, don’t add the output .html and .R files to your repository. Don’t forget to add the new commands you’ve learned to your unix.txt file.)