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. This blog focuses on statistical programming. It discusses statistical and computational algorithms, statistical graphics, simulation, efficiency, and data analysis. Rick is author of the books Statistical Programming with SAS/IML Software and Simulating Data with SAS.
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In my article about finding an initial guess for root-finding algorithms, I stated that Newton's root-finding method "might not converge or might converge to a root that is far away from the root that you wanted to find." A reader wanted more information about that statement. I have previously shown [...]Post a Comment
A SAS programmer asked an interesting question on a SAS Support Community. The programmer had a nonlinear function with 12 parameters. He also had file that contained 4,000 lines, where each line contained values for the 12 parameters. In other words, the file specified 4,000 different functions. The programmer wanted [...]Post a Comment
A common question from statistical programmers is how to compute the rank of a matrix in SAS. Recall that the rank of a matrix is defined as the number of linearly independent columns in the matrix. (Equivalently, the number of linearly independent rows.) This article describes how to compute the [...]Post a Comment
In my previous post, I showed how to approximate a cumulative density function (CDF) by evaluating only the probability density function. The technique uses the trapezoidal rule of integration to approximate the CDF from the PDF. For common probability distributions, you can use the CDF function in Base SAS to [...]Post a Comment
Evaluating a cumulative distribution function (CDF) can be an expensive operation. Each time you evaluate the CDF for a continuous probability distribution, the software has to perform a numerical integration. (Recall that the CDF at a point x is the integral under the probability density function (PDF) where x is [...]Post a Comment
One of the things I enjoy about blogging is that I often learn something new. Last week I wrote about how to optimize a function that is defined in terms of an integral. While developing the program in the article, I made some mistakes that generated SAS/IML error messages. By [...]Post a Comment
The SAS/IML language is used for many kinds of computations, but three important numerical tasks are integration, optimization, and root finding. Recently a SAS customer asked for help with a problem that involved all three tasks. The customer had an objective function that was defined in terms of an integral. [...]Post a Comment
In SAS software, you can use the QUAD subroutine in the SAS/IML language to evaluate definite integrals on an interval [a, b]. The integral is properly defined only for a < b, but mathematicians define the following convention, which enables you to make sense of reversing the limits of integration: [...]Post a Comment
Last week I described the Hilbert matrix of size n, which is a famous square matrix in numerical linear algebra. It is famous partially because its inverse and its determinant have explicit formulas (that is, we know them exactly), but mainly because the matrix is ill-conditioned for moderate values of [...]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