I previously wrote an article about the Lambert W function. The Lambert W function is the inverse of the function g(x) = x exp(x). This means that you can use it to find the value of x such that g(x)=c for any value of c in the range of g, which
A SAS programmer had many polynomials for which he wanted to compute the real roots. By the Fundamental Theorem of Algebra, every polynomial of degree d has d complex roots. You can find these complex roots by using the POLYROOT function in SAS IML. The programmer only wanted to output
Here's a SAS tip for you. Most SAS programmers know that SAS provides syntax that makes it easy to specify a list of variables. For example, you can use the hyphen and colon operators to specify lists of variables on many SAS statements: You can use the hyphen operator (-)
A colleague asked me an interesting question: Suppose you have a structured correlation matrix, such as a matrix that has a compound symmetric, banded, or an AR1(ρ) structure. If you generate a random correlation matrix that has the same eigenvalues as the structured matrix, does the random matrix have the
In a previous article, I presented some of the most popular blog posts from The DO Loop in 2024. In general, popular articles deal with elementary topics that have broad appeal. However, I also write technical articles about advanced topics, which typically do not make it onto a Top 10
A previous article discusses covariance matrices that have the same set of eigenvalues. The set of eigenvalues is called the spectrum of the matrix. For symmetric matrices, the spectrum contains real numbers. For covariance matrices, which are positive semidefinite, the eigenvalues are nonnegative. It turns out that two symmetric matrices
In 2024, I wrote about 80 articles for The DO Loop blog. My most popular articles were about SAS programming, data visualization, and statistics. If you missed any of these articles, here is the "Reader's Choice Awards" for some of the most popular articles from 2024! SAS Programming The following
A previous article discusses how to generate a random covariance matrix with a specified set of (positive) eigenvalues. A SAS programmer asked whether it is possible to produce a correlation matrix that has a specified set of eigenvalues. After discussing the problem with a friend, I am happy to report
O Christmas tree, O Christmas tree, How lovely are your branches! SAS programmers have a long history of creating yuletide-themed graphics. Christmas trees are a popular image because of their simplicity. I admit that I have indulged more than once in this holiday tradition: An old-school ASCII art image A
While researching the topic of Latin hypercube sampling (LHS), I read an article by Emily Gao (2019) that shows how to use PROC IML in SAS to perform the algorithm. It is possible to simplify Gao's implementation of Latin hypercube sampling in SAS while also making the computation more efficient.
