Yesterday I blogged about the Hilbert matrix. The (i,j)th element of the Hilbert matrix has the value 1 / (i+j-1), which is the reciprocal of an integer. However, the printed Hilbert matrix did not look exactly like the formula because the elements print as finite-precision decimals. For example, the last
The Hilbert matrix is the most famous ill-conditioned matrix in numerical linear algebra. It is often used in matrix computations to illustrate problems that arise when you compute with ill-conditioned matrices. The Hilbert matrix is symmetric and positive definite, properties that are often associated with "nice" and "tame" matrices. The
I enjoy reading the Graphically Speaking blog because it teaches me a lot about ODS statistical graphics, especially features of the SGPLOT procedure and the Graph Template Language (GTL). Yesterday Sanjay blogged about how to construct a stacked bar chart of percentages so that each bar represents 100%. His chart
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
When spontaneous applause broke out during Dr. Jim Goodnight's presentation at the opening session of SAS Global Forum 2014, I was one of the people cheering the loudest. The SAS CEO had just announced free software for students and professors at universities around the world. The SAS University Edition will
When I visualize three-dimensional data, I prefer to use interactive graphics. For example, I often use the rotating plot in SAS/IML Studio (shown at the left) to create a three-dimensional scatter plot. The interactive plot enables me to rotate the cloud of points and to use a pointer to select
SAS/IML 13.1 shipped a few months ago. I was asked to produce a video that highlights some of the new features in SAS/IML 13.1. In this video I describe several changes to the language before introducing the new built-in subroutines that create ODS statistical graphs. If your browser does not
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
Once again I'll be at SAS Global Forum this year. The 2014 location is Washington, D. C., so I am looking forward to greeting many friends in the government and consulting sectors. I always enjoy talking with SAS customers about statistics, simulations, matrix computations, and the SAS/IML product, so here's
