A previous article showed how to use SAS to compute finite-difference derivatives of smooth vector-valued multivariate functions. The article uses the NLPFDD subroutine in SAS/IML to compute the finite-difference derivatives. The article states that the third output argument of the NLPFDD subroutine "contains the matrix product J`*J, where J is
I previously showed how to use SAS to compute finite-difference derivatives for smooth scalar-valued functions of several variables. You can use the NLPFDD subroutine in SAS/IML software to approximate the gradient vector (first derivatives) and the Hessian matrix (second derivatives). The computation uses finite-difference derivatives to approximate the derivatives. The
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
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
On this blog, I write about a diverse set of topics that are relevant to statistical programming and data visualization. In a previous article, I presented some of the most popular blog posts from 2021. The most popular articles often deal with elementary or familiar topics that are useful to
Last year, I wrote almost 100 posts for The DO Loop blog. My most popular articles were about data visualization, statistics and data analysis, and simulation and bootstrapping. If you missed any of these gems when they were first published, here are some of the most popular articles from 2021:
