An empty matrix is a matrix that has zero rows and zero columns. At first "empty matrix" sounds like an oxymoron, but when programming in a matrix language such as SAS/IML, empty matrices arise surprisingly often. Sometimes empty matrices occur because of a typographical error in your program. If you

## Tag: **12.1**

As you develop a program in the SAS/IML language, it is often useful to create graphs to visualize intermediate results. The language supports basic statistical graphics such as bar charts, histograms, scatter plots, and so on. However, you can create more advanced graphics without leaving PROC IML by using the

SAS programmers are probably familiar with how SAS stores a character variable in a data set, but how is a character vector stored in the SAS/IML language? Recall that a character variable is stored by using a fixed-width storage structure. In the SAS DATA step, the maximum number of characters

I enjoy blogging about new functionality in the SAS/IML language because I can go into more depth and provide more complicated examples than the SAS/IML documentation. Today's article is a summary of all of my posts about features that were added to SAS/IML 12.1, which shipped in August 2012 as

Did you know that SAS/IML 12.1 provides built-in functions that compute the norm of a vector or matrix? A vector norm enables you to compute the length of a vector or the distance between two vectors in SAS. Matrix norms are used in numerical linear algebra to estimate the condition

While at SAS Global Forum 2014 I attended a talk by Jorge G. Morel on the analysis of data with overdispersion. (His slides are available, along with a video of his presentation.) The Wikipedia defines overdispersion as "greater variability than expected from a simple model." For count data, the "simple

Last month I blogged about defining SAS/IML functions that have default parameter values. This language feature, which was introduced in SAS/IML 12.1, enables you to skip arguments when you call a user-defined function. The same technique enables you to define optional parameters. Inside the function, you can determine whether the

My previous post described how to use the "missing response trick" to score a regression model. As I said in that article, there are other ways to score a regression model. This article describes using the SCORE procedure, a SCORE statement, the relatively new PLM procedure, and the CODE statement.

One of my favorite new features of SAS/IML 12.1 enables you to define functions that contain default values for parameters. This is extremely useful when you want to write a function that has optional arguments. Example: Centering a data vector It is simple to specify a SAS/IML module with a

Finding the root (or zero) of a function is an important computational task because it enables you to solve nonlinear equations. I have previously blogged about using Newton's method to find a root for a function of several variables. I have also blogged about how to use the bisection method

Last week I showed three ways to sample with replacement in SAS. You can use the SAMPLE function in SAS/IML 12.1 to sample from a finite set or you can use the DATA step or PROC SURVEYSELECT to extract a random sample from a SAS data set. Sampling without replacement

With each release of SAS/IML software, the language provides simple ways to carry out tasks that previously required more effort. In 2010 I blogged about a SAS/IML module that appeared in my book Statistical Programming with SAS/IML Software, which was written by using the SAS/IML 9.2. The blog post showed

The mosaic plot is a graphical visualization of a frequency table. In a previous post, I showed how to use the FREQ procedure to create a mosaic plot. This article shows how to create a mosaic plot by using the MOSAICPARM statement in the graph template language (GTL). (The MOSAICPARM

Mosaic plots (Hartigan and Kleiner, 1981; Friendly, 1994, JASA) are used for exploratory data analysis of categorical data. Mosaic plots have been available for decades in SAS products such as JMP, SAS/INSIGHT, and SAS/IML Studio. However, not all SAS customers have access to these specialized products, so I am pleased

This is the last post in my recent series of articles on computing contours in SAS. Last month a SAS customer asked how to compute the contours of the bivariate normal cumulative distribution function (CDF). Answering that question in a single blog post would have resulted in a long article,

I've written several articles that show how to generate permutations in SAS. In the SAS DATA step, you can use the ALLPEM subroutine to generate all permutations of a DATA step array that contain a small number (18 or fewer) elements. In addition, the PLAN procedure enables you to generate

SAS 9 has supported calling R from the SAS/IML language since 2009. The interface to R is part of the SAS/IML language. However, there have been so many versions of SAS and R since 2009, that it is hard to remember which SAS release supports which versions of R. The

Sometimes it is useful in the SAS/IML language to convert a character string into a vector of one-character values. For example, you might want to count the frequency distribution of characters, which is easy when each character is an element of a vector. The question of how to convert a

How old is your version of SAS software? The graph on the left shows the release dates for various releases of SAS software, beginning with SAS 8.0. The graph is based on a graph on Jiangtang Hu's blog that shows the major SAS releases. As this graph demonstrates, SAS software

One of my favorite features of SAS/IML 12.1 (released with 9.3m2) is that the USE and CLOSE statements support reading data set names that are specified in a SAS/IML matrix. The IMLPlus language in SAS/IML Studio has supported this syntax since the early 2000s, so I am pleased that this

Has anyone noticed that the REG procedure in SAS/STAT 12.1 produces heat maps instead of scatter plots for fit plots and residual plots when the regression involves more than 5,000 observations? I wasn't aware of the change until a colleague informed me, although the change is discussed in the "Details"

PROC UNIVARIATE has provided confidence intervals for standard percentiles (quartiles) for eons. However, in SAS 9.3M2 (featuring the 12.1 analytical procedures) you can use a new feature in PROC UNIVARIATE to compute confidence intervals for a specified list of percentiles. To be clear, percentiles and quantiles are essentially the same

In statistics, distances between observations are used to form clusters, to identify outliers, and to estimate distributions. Distances are used in spatial statistics and in other application areas. There are many ways to define the distance between observations. I have previously written an article that explains Mahalanobis distance, which is

A while ago I saw a blog post on how to simulate Bernoulli outcomes when the probability of generating a 1 (success) varies from observation to observation. I've done this often in SAS, both in the DATA step and in the SAS/IML language. For example, when simulating data that satisfied

A year ago I set out to periodically blog from my perspective of leading R&D for our advanced analytics software. I invited SAS colleagues who also work in various areas of advanced analytics to blog on their own interesting conversations with each other and with customers about the intersection of

Suppose that you want to create a matrix in SAS/IML software that has a special structure, such as a tridiagonal matrix. How do you do it? Or suppose that you want to find elements of a matrix A such that A[i,j] satisfies a certain condition. How do you get the