Rick Wicklin, PhD, is a distinguished researcher in computational statistics at SAS and is a principal developer of SAS/IML software. His areas of expertise include computational statistics, simulation, statistical graphics, and modern methods in statistical data analysis. Rick is author of the books Statistical Programming with SAS/IML Software and Simulating Data with SAS.
I began 2015 by compiling a list of popular articles from my blog in 2014. Although this "People's Choice" list contains many interesting articles, some of my favorites did not make the list. Today I present the "Editor's Choice" list of articles that deserve a second look. I've highlighted one
A SAS programmer recently posted a question to the SAS/IML Support Community about how to compute the kth smallest value in a vector of numbers. In the DATA step, you can use the SMALLEST function to find the smallest value in an array, but there is no equivalent built-in function
I published 118 blog posts in 2014. This article presents my most popular posts from 2014 and late 2013. 2014 will always be a special year for me because it was the year that the SAS University Edition was launched. The University Edition means that SAS/IML is available to all
I recently posted an article about self-similar structures that arise in Pascal's triangle. Did you know that the Kronecker product (or direct product) can be used to create matrices that have self-similar structure? The basic idea is to start with a 0/1 matrix and compute a sequence of direct products
Like most programming languages, the SAS/IML language has many functions. However, the SAS/IML language also has quite a few operators. Operators can act on a matrix or on rows or columns of a matrix. They are less intuitive, but can be quite powerful because they enable you perform computations without
O Christmas tree, O Christmas tree, One year a fractal made thee! O Christmas tree, O Christmas tree, A heat map can display thee! From Pascal's matrix we define! Reflect across, divide by nine. O Christmas tree, O Christmas tree, Self-similar and so divine! Eventually I will run out of
There are many ways to multiply scalars, vectors, and matrices, but the Kronecker product (also called the direct product) is multiplication on steroids. The Kronecker product looks scary, but it is actually simple. The Kronecker product is merely a way to pack multiples of a matrix B into a block
A colleague asked me a question regarding my recent post about the Pascal triangle matrix. While responding to his question, I discovered a program that I had written in 1999 that computed with a Pascal triangle matrix. Wow, I've been computing with Pascal's triangle for 15 years! I don't know
Pascal's triangle is the name given to the triangular array of binomial coefficients. The nth row is the set of coefficients in the expansion of the binomial expression (1 + x)n. Complicated stuff, right? Well, yes and no. Pascal's triangle is known to many school children who have never heard of polynomials
A common question on SAS discussion forums is how to compute the minimum and maximum values across several variables. It is easy to compute statistics across rows by using the DATA step. This article shows how to compute the minimum and maximum values for each observation (across variables) and, for
I've written about how to generate a sample from a multivariate normal (MVN) distribution in SAS by using the RANDNORMAL function in SAS/IML software. Last week a SAS/IML programmer showed me a program that simulated MVN data and computed the resulting covariance matrix for each simulated sample. The purpose of
SAS software contains a lot of features, and each release adds more.To make sure that you do not miss new features that appear in the SAS/IML language, the word cloud on the right sidebar of my blog contains numbers that relate to SAS or SAS/IML releases. For example, you can
My colleagues at the SAS & R blog recently posted an example of how to program a permutation test in SAS and R. Their SAS implementation used Base SAS and was "relatively cumbersome" (their words) when compared with the R code. In today's post I implement the permutation test in
I sometimes wonder whether some functions and options in SAS software ever get used. Last week I was reviewing new features that were added to SAS/IML 13.1. One of the new functions is the CV function, which computes the sample coefficient of variation for data. Maybe it is just me,
Have you ever noticed that some SAS/IML programmers use the CALL statement to call a subroutine, whereas others use the RUN statement? Have you ever wondered why the SAS/IML language has two statements that do the same thing? It turns out that the CALL statement and the RUN statement do
When I studied high school geometry, I noticed that many homework problems involved right triangles whose side lengths were integers. The canonical example is the 3-4-5 right triangle, which has legs of length 3 and 4 and a hypotenuse of length 5. The triple (3, 4, 5) is called a
I was recently asked about how to use the SAS/IML language to efficiently add a constant to every element of a matrix diagonal. Mathematically, the task is to form the matrix sum A + kI, where A is an n x n matrix, k is a scalar value, and I is the
My colleague Robert Allison has a knack for finding fascinating data. Last week he did it again by locating data about how blood types and Rh factors vary among countries. He produced a series of eight world maps, each showing the prevalence of a blood type (A+, A-, B+, B-,
In my article about how to create a quantile plot, I chose not to discuss a theoretical issue that occasionally occurs. The issue is that for discrete data (which includes rounded values), it might be impossible to use quantile values to split the data into k groups where each group
It has been three months since the introduction of the SAS/IML File Exchange, so I thought I'd give a short update on recent submissions and activity. (Note: The File Exchange was merged into the SAS Community Library in 2022.) Users have submitted eight new articles. The application areas include experimental
The other day I was doing some computations that caused me to wonder, "What is the smallest power of 2 that is greater than a given number?" The mathematics is straightforward. Given a number n, find the least value of k such that 2k ≥ n or, equivalently, k ≥
Many people enjoy solving word games such as the daily Cryptoquote puzzle, which uses a simple substitution cipher to disguise a witty or wise quote by a famous person. A common way to attack the puzzle is frequency analysis. In frequency analysis you identify letters and pairs of letters (bigrams)
One of my presentations at SAS Global Forum 2014 was about the new heat map functions in SAS/IML 13.1. Over the summer I created a short video of my presentation, which gives an overview of visualizing matrices with heat maps, and describes how to choose colors for heat maps: If
What is kurtosis? What does negative or positive kurtosis mean, and why should you care? How do you compute kurtosis in SAS software? It is not clear from the definition of kurtosis what (if anything) kurtosis tells us about the shape of a distribution, or why kurtosis is relevant to
A few years ago I wrote an article that shows how to compute the log-determinant of a covariance matrix in SAS. This computation is often required to evaluate a log-likelihood function. My algorithm used the ROOT function in SAS/IML to compute a Cholesky decomposition of the covariance matrix. The Cholesky
My previous blog post describes how to implement Conway's Game of Life by using the dynamically linked graphics in SAS/IML Studio. But the Game of Life is not the only kind of cellular automata. This article describes a system of cellular automata that is known as Wolfram's Rule 30. In
A colleague jokingly teases me whenever I write a blog that demonstrates how to write fun and exciting programs by using SAS software. "Why do you get to have all the fun?" he mock-chides. Today I'm ready to face his ribbing, because this article is about Conway's Game of Life
The tail of a probability distribution is an important notion in probability and statistics, but did you know that there is not a rigorous definition for the "tail"? The term is primarily used intuitively to mean the part of a distribution that is far from the distribution's peak or center.
It usually takes more than three weeks to prepare a good impromptu speech. --Mark Twain In the popular Cryptoquote puzzle, you are presented with an enciphered version of a quote by a famous person. One of the appeals of the puzzle for me is reading the deciphered quote, such
SAS/IML 13.1 includes a handy function for programmers who write a lot of modules. The PARENTNAME function obtains the name of the symbol that was passed in as a parameter to a user-defined module. How is this useful? Well, suppose that you want to create a SAS/IML module that prints
