Rules
See the Section about Rules for Quizzes and Homeworks on the General Info page.
Your work handed into Moodle should be a plain text file with R commands and comments that can be run to produce what you did. We do not take your word for what the output is. We run it ourselves.
Note: Plain text
specifically excludes
Microsoft Word native format (extension .docx). If you have to
Word as your text editor, then save as and choose the format to be
Text (.txt) or something like that. Then upload the
saved plain text file.
If you have questions about the quiz, ask them in the Moodle forum for this quiz. Here is the link for that https://ay16.moodle.umn.edu/mod/forum/view.php?id=1241814.
On future assignments you can use knitr or rmarkdown
after we have talked about it. But avoid that on this assignment.
Quizzes must uploaded by the end of class (1:10). Moodle actually allows a few minutes after that. Here is the link for uploading the quiz https://ay16.moodle.umn.edu/mod/assign/view.php?id=1241821.
Homeworks must uploaded before midnight the day they are due. Here is the link for uploading the homework. https://ay16.moodle.umn.edu/mod/assign/view.php?id=1241828.
Quiz 2
Problem 1
Write an R function that, given a numeric matrix A and a numeric vector x, calculates xT A− 1 x. Note that this only makes sense when A is a square matrix and the dimension of x is the same as the dimensions of the row and column dimensions of A.
Follow GIEMO (garbage in, error messages out). Make sure your function
gives an error when the dimensions are wrong or when either argument is not
numeric. When either argument contains
NA, NaN, Inf, -Inf, your
function can give an error, give a warning, or produce one of these results
(your choice).
We deduct points for actually inverting the matrix A. Think of this in terms of solving linear equations, instead.
We deduct points for using a loop or loops.
Not only write a function, but also show it working on the data obtained by the R command
load(url("http://www.stat.umn.edu/geyer/s17/3701/data/q2p1.rda"))
ls()
(This loads two R objects: a matrix a and a vector x.)
Problem 2
Rewrite your function for the preceding problem so it is a binary operator rather than an apparent function call, that is, if your function from the preceding problem was invoked
alice(a, x)rewrite it so it is invoked
a %alice% x(of course, you can change
alice to any other valid R name.
Problem 3
Write a function that takes a numeric matrix and standardizes
its
columns (we will explain what this means). For any vector x
its standardization
is computed as follows.
(x - mean(x)) / sd(x)
Note that in the special case that the matrix has only one row, it cannot
be standardized (because in that case the standard deviation of the columns
is zero
and the algorithm wants to divide by zero. You can either produce an error,
a warning, or all components of the result NA, NaN,
Inf, or -Inf, your choice.
There is no deduction of points for using a loop or loops in this problem.
Not only write a function, but also show it working on the data obtained by the R command
load(url("http://www.stat.umn.edu/geyer/s17/3701/data/q2p3.rda"))
ls()
(This loads one R object: a matrix a.)
But it might be better to add the error check
stopifnot(nrow(a) > 1)
to the definition of standardize.
