Many applications in mathematics and statistics require the numerical computation of the derivatives of smooth multivariate functions. For simple algebraic and trigonometric functions, you often can write down expressions for the first and second partial derivatives. However, for complicated functions, the formulas can get unwieldy (and some applications do not
An experienced SAS programmer recently switched to SAS Viya and asked how to discover what products are available on his version of Viya. We discussed a few older SAS 9 procedures, and I showed him a new Viya-specific way to get information about his version of SAS and his licensed
It is important to be able to detect whether a numerical matrix is symmetric. Some operations in linear algebra require symmetric matrices. Sometimes, you can use special algorithms to factor a symmetric matrix. In both cases, you need to test a matrix for symmetry. A symmetric matrix must be square.
A SAS programmer asked an interesting question: If data in a time series has missing values, can you plot a dashed line to indicate that the response is missing at some times? A simple way to achieve this is by overlaying two lines. The first line (the "bottom" line in
This article implements Passing-Bablok regression in SAS. Passing-Bablok regression is a one-variable regression technique that is used to compare measurements from different instruments or medical devices. The measurements of the two variables (X and Y) are both measured with errors. Consequently, you cannot use ordinary linear regression, which assumes that
For some reason, SAS programmers like to express their love by writing SAS programs. Since Valentine's Day is next week, I thought I would add another SAS graphic to the collection of ways to use SAS to express your love. Last week, I showed how to use vector operation and
I recently showed how to find the intersection between a line and a circle. While working on the problem, I was reminded of a fun mathematical game. Suppose you make a billiard table in the shape of a circle or an ellipse. What is the path for a ball at
Recently, I needed to implement a line search algorithm in SAS. The line search is illustrated by the figure at the right. You start with a point, p, in d-dimensional space and a direction vector, v. (In the figure, d=2, but in general d > 1.) The goal is to
Recently, a SAS programmer commented about one of my blog posts. He said that he had found an alternative answer on another website. Whereas my answer was formulated in terms of the normal cumulative distribution function (CDF), the other answer used the ERF function. This article shows the relationship between
Sometimes it is useful to know the extreme values in data. You might need to know the Top 5 or the Top 10 smallest data values. Or, the Top 5 or Top 10 largest data values. There are many ways to do this in SAS, but this article shows examples
