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.
Magic squares are cool. Algorithms that create magic squares are even cooler. You probably remember magic squares from your childhood: they are n x n matrices that contain the numbers 1,2,...,n2 and for which the row sum, column sum, and the sum of both diagonals are the same value. There are many
When I studied math in school, I learned that the expression a (mod n) is always an integer between 0 and q – 1 for integer values of a and q. It's a nice convention, but SAS and many other computer languages allow the result to be negative if a (or q) is
The other day I was using PROC SGPLOT to create a box plot and I ran a program that was similar to the following: proc sgplot data=sashelp.cars; title "Box Plot: Category = Origin"; vbox Horsepower / category=origin; run; An hour or so later I had a need for another box
The SAS/IML language supports user-defined functions (also called modules). Many SAS/IML programmers know that you can use the RETURN function to return a value from a user-defined function. For example, the following function returns the sum of each column of matrix: proc iml; start ColSum(M); return( M[+, ] ); /*
It is common to want to extract the lower or upper triangular elements of a matrix. For example, if you have a correlation matrix, the lower triangular elements are the nontrivial correlations between variables in your data. As I've written before, you can use the VECH function to extract the
Sometimes a small option can make a big difference. Last week I thought to myself, "I wish there were an option that prevents variable labels from appearing in a table or graph." Well, it turns out that there is! I was using PROC MEANS to display some summary statistics, and
I've seen analyses of Fisher's iris data so often that sometimes I feel like I can smell the flowers' scent. However, yesterday I stumbled upon an analysis that I hadn't seen before. The typical analysis is shown in the documentation for the CANDISC procedure in the SAS/STAT documentation. A (canonical)
A comment to last week's article on "How to get data values out of ODS graphics" indicated that the technique would be useful for changing the title on an ODS graph "without messing around with GTL." You can certainly use the technique for that purpose, but if you want to
Many SAS procedures can produce ODS statistical graphics as naturally as they produce tables. Did you know that it is possible to obtain the numbers underlying an ODS statistical graph? This post shows how. Suppose that a SAS procedure creates a graph that displays a curve and that you want
I received the following question: In the DATA step I always use the ** operator to raise a values to a power, like this: x**2. But on your blog I you use the ## operator to raise values to a power in SAS/IML programs. Does SAS/IML not support the **
Last week I wrote an article in which I pointed out that many SAS programmers write a simulation in SAS by writing a macro loop. This approach is extremely inefficient, so I presented a more efficient technique. Not only is the macro loop approach slow, but there are other undesirable
Over the past few years, and especially since I posted my article on eight tips to make your simulation run faster, I have received many emails (often with attached SAS programs) from SAS users who ask for advice about how to speed up their simulation code. For this reason, I
I have blogged about three different SAS/IML techniques that iterate over categories and process the observations in each category. The three techniques are as follows: Use a WHERE clause on the READ statement to read only the observations in the ith category. This is described in the article "BY-group processing
When you are working with probability distributions (normal, Poisson, exponential, and so forth), there are four essential functions that a statistical programmer needs. As I've written before, for common univariate distributions, SAS provides the following functions: the PDF function, which returns the probability density at a given point the CDF
Suppose that you have two data vectors, x and y, with the same number of elements. How can you rearrange the values of y so that they have the same relative order as the values of x? In other words, find a permutation, π, of the elements of y so
I've been working on a new book about Simulating Data with SAS. In researching the chapter on simulation of multivariate data, I've noticed that the probability density function (PDF) of multivariate distributions is often specified in a matrix form. Consequently, the multivariate density can usually be computed by using the
When I need to graph a function of two variables, I often choose to use a contour plot. A surface plot is probably easier for many people to understand, but it has several disadvantages when compared to a contour plot. For example, the following statements in SAS/IML Studio displays a
I received the following query regarding the RAND function in Base SAS: In SAS, is specifying 0 as a random number seed the same as not specifying a seed at all? The question concerns initializing the SAS random number stream by using the internal system clock. You can do this
I often use the SAS/IML language for simulating data with certain known properties. In fact, I'm writing a book called Simulating Data with SAS. When I simulate repeated measurements (sometimes called replicated data), I often want to generate an ID variable that identifies which measurement is associated with which subject
No matter what statistical programming language you use, be careful of testing for an exact value of a floating-point number. This is known in the world of numerical analysis as "10.0 times 0.1 is hardly ever 1.0" (Kernighan and Plauger, 1974, The Elements of Programming Style). There are many examples
A reader wrote for help with a computational problem. He has a vector of length N and the vector contains integer values in the range [1, 120], which represent months for which events occurred over a 10-year period. The question is: what is the 24-month period for which the most
This is a third post on newspaper stories that I recently read. Today's post deals with science, politics, and rising sea levels. Incidentally, the title is a blatant reference to John Allen Paulos's brilliant book, A Mathematician Reads the Newspaper. Senate approves law that challenges sea-level science The NC legislature
This is my second post on some newspaper articles that I recently read. Today's post deals with academic fraud. Questions linger in academic fraud case Over the past year, the News and Observer has occasionally reported on a scandal at the University of North Carolina at Chapel Hill in which
This past weekend was Father's Day, so I took some time to relax and read the newspaper. I found several stories that suggested interesting statistical questions. Unfortunately, the data are not available for analysis. Nevertheless, the stories are worth sharing. Over the next few days, I'll post my thoughts on
To celebrate special occasions like Father's Day, I like to relax with a cup of coffee and read the newspaper. When I looked at the weather page, I was astonished by the seeming uniformity of temperatures across the contiguous US. The weather map in my newspaper was almost entirely yellow
A collegue who works with time series sent me the following code snippet. He said that the calculation was overflowing and wanted to know if this was a bug in SAS: data A(drop=m); call streaminit(12345); m = 2; x = 0; do i = 1 to 5000; x = m*x
"Help! My simulation is taking too long to run! How can I make it go faster?" I frequently talk with statistical programmers who claim that their "simulations are too slow" (by which they mean, "they take too long"). They suspect that their program is inefficient, but they aren't sure why.
I recently read a blog post in which a SAS user had to rename a bunch of variables named A1, A2,..., A10, such as are contained in the following data set: /* generate data with variables A1-A10 */ data A; array A[10] A1-A10 (1); do i = 1 to 10;
In the SAS/IML language, a user-defined function or subroutine is called a module. Modules are used to extend the capability of the SAS/IML language. In my blog posts, I usually define a module in a PROC IML session and then immediately use it. However, sometimes it is useful to store
In the SAS/IML language, a user-defined function or subroutine is called a module. Modules are used to extend the capability of the SAS/IML language. Usually you need to explicitly load modules before you use them, but there are two cases where PROC IML loads a module automatically. Modules in IMLMLIB
