Tag: Matrix Computations

Learn SAS | Programming Tips
Rick Wicklin 0
Flip it. Flip it good.

A SAS user needed to convert a program from MATLAB into the SAS/IML matrix language and asked whether there is a SAS/IML equivalent to the fliplr and flipud functions in MATLAB. These functions flip the columns or rows (respectively) of a matrix; "LR" stands for "left-right" and "UD" stands for

Rick Wicklin 0
Rotation matrices and 3-D data

Rotation matrices are used in computer graphics and in statistical analyses. A rotation matrix is especially easy to implement in a matrix language such as the SAS Interactive Matrix Language (SAS/IML). This article shows how to implement three-dimensional rotation matrices and use them to rotate a 3-D point cloud. Define

Rick Wicklin 0
Visualize a weighted regression

What is weighted regression? How does it differ from ordinary (unweighted) regression? This article describes how to compute and score weighted regression models. Visualize a weighted regression Technically, an "unweighted" regression should be called an "equally weighted " regression since each ordinary least squares (OLS) regression weights each observation equally.

Rick Wicklin 0
Absorbing Markov chains in SAS

Last week I showed how to represent a Markov transition matrix in the SAS/IML matrix language. I also showed how to use matrix multiplication to iterate a state vector, thereby producing a discrete-time forecast of the state of the Markov chain system. This article shows that the expected behavior of

Rick Wicklin 0
Markov transition matrices in SAS/IML

Many computations in elementary probability assume that the probability of an event is independent of previous trials. For example, if you toss a coin twice, the probability of observing "heads" on the second toss does not depend on the result of the first toss. However, there are situations in which

Learn SAS
Rick Wicklin 0
Grids and linear subspaces

A grid is a set of evenly spaced points. You can use SAS to create a grid of points on an interval, in a rectangular region in the plane, or even in higher-dimensional regions like the parallelepiped shown at the left, which is generated by three vectors. You can use

Rick Wicklin 0
Compute the square root matrix

Children in primary school learn that every positive number has a real square root. The number x is a square root of s, if x2 = s. Did you know that matrices can also have square roots? For certain matrices S, you can find another matrix X such that X*X

Rick Wicklin 0
Matrix computations at SAS Global Forum 2016

Last week I attended SAS Global Forum 2016 in Las Vegas. I and more than 5,000 other attendees discussed and shared tips about data analysis and statistics. Naturally, I attended many presentations that featured using SAS/IML software to implement advanced analytical algorithms. Several speakers showed impressive mastery of SAS/IML programming

Rick Wicklin 0
Dummy variables in SAS/IML

Last week I showed how to create dummy variables in SAS by using the GLMMOD procedure. The procedure enables you to create design matrices that encode continuous variables, categorical variables, and their interactions. You can use dummy variables to replace categorical variables in procedures that do not support a CLASS

Rick Wicklin 0
Self-similar structures from Kronecker products

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

Rick Wicklin 0
A matrix computation on Pascal's triangle

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

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