About this blog
Rick Wicklin, PhD, is a distinguished researcher in computational statistics at SAS and is a principal developer of PROC IML and SAS/IML Studio. His areas of expertise include computational statistics, statistical graphics, statistical simulation, and modern methods in statistical data analysis. Rick is author of the books Statistical Programming with SAS/IML Software and Simulating Data with SAS.
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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 […]Post a Comment
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 […]Post a Comment
In a previous post, I stated that you should avoid matrix multiplication that involves a huge diagonal matrix because that operation can be carried out more efficiently. Here's another tip that sometimes improves the efficiency of matrix multiplication: use parentheses to prevent the creation of large matrices. Matrix multiplication is […]Post a Comment
I love working with SAS Technical Support because I get to see real problems that SAS customers face as they use SAS/IML software. The other day I advised a customer how to improve the efficiency of a computation that involved multiplying large matrices. In this article I describe an important […]Post a Comment
Dear Rick, I am trying to create a numerical matrix with 100,000 rows and columns in PROC IML. I get the following error: (execution) Unable to allocate sufficient memory. Can IML allocate a matrix of this size? What is wrong? Several times a month I see a variation of this […]Post a Comment
Just one last short article about properties of the Hilbert matrix. I've already blogged about how to construct a Hilbert matrix in the SAS/IML language and how to compute a formula for the determinant. One reason that the Hilbert matrix is a famous (some would say infamous!) example in numerical […]Post a Comment
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 […]Post a Comment
Recently a SAS/IML programmer asked a question regarding how to perform matrix arithmetic when some of the data are in vectors and other are in matrices. The programmer wanted to add the following matrices: The problem was that the numbers in the first two matrices were stored in vectors. The […]Post a Comment
For programmers who are learning the SAS/IML language, it is sometimes confusing that there are two kinds of multiplication operators, whereas in the SAS DATA step there is only scalar multiplication. This article describes the multiplication operators in the SAS/IML language and how to use them to perform common tasks […]Post a Comment
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 […]Post a Comment