Former college mathematics professor for 19 years where I also taught a variety of programming languages, including Fortran, Modula-2, C, and C++. Former technical writer for 15 years at a large software firm headquartered in Redmond, WA. Current associate faculty at a nearby community college, teaching classes in C++ and computer architecture/assembly language.
I enjoy traipsing around off-trail in Olympic National Park and the North Cascades and elsewhere, as well as riding and tinkering with my four motorcycles.
This article is the second of a two-part series that presents two distinctly different approaches to parallel programming. In the two articles, I use different approaches to solve the same problem: finding the best-fitting line (or regression line) for a set of points. The two different approaches to parallel programming presented in this and the…
This article is the first of a two-part series that presents two distinctly different approaches to parallel programming. In the two articles, I use different approaches to solve the same problem: finding the best-fitting line (or regression line) for a set of points. The two different approaches to parallel programming presented in this and the…
Two of my favorite areas of study are linear algebra and computer programming. In this article I combine these areas by using Python to confirm that a given matrix satisfies the Cayley-Hamilton theorem. The theorem due to Arthur Cayley and William Hamilton states that if ##f(\lambda) = \lambda^n + c_{n-1}\lambda^{n-1} + \dots + c_1\lambda +…
In this Insights article I’ll present an example that shows how Intel® AVX-512 instructions can be used to read a whole row of data in a single operation, and then generate subtotals for some or all of the columns of that table. To motivate the example, I’ll use a table of household expenses in several…
In the first part of this article (AVX-512 Assembly Programing – Opmask Registers for Conditional Arithmetic), we looked at how opmask registers can be used to perform conditional arithmetic. That article ended with two 512-bit ZMM registers that each contained 16 integer values. One of the registers contained 16 partial sums of the positive numbers…
This is the second installment in a continuing series of articles on Intel AVX-512 assembly programming. The first installment is An Intro to AVX-512 Assembly Programming. Problem If you have an array (Array), that contains ArrLen signed integers, how would you find the sums of the positive and negative numbers in the array? A Solution…
History In 1998, the Intel Corporation released processors that supported SIMD (single instruction, multiple data) instructions, enabling processors to carry out multiple arithmetic operations using one instruction. This technology was a first step toward parallelization at the instruction level. The technology, SSE (Streaming SIMD Extensions), made it possible to perform arithmetic operations on four pairs…
The first computer I owned was an Apple IIe computer, with a CPU that ran at slightly over 1 Megahertz (MHz), and with 64 Kilobytes (KB) of RAM, together with two 5 1/4″ floppy drives that could each store 140 Kilobytes (KB) of data. My current computer (which costs about the same as the Apple computer) is…
Two important concepts in Linear Algebra are eigenvectors and eigenvalues for a linear transformation that is represented by a square matrix. Besides being useful in mathematics for solving systems of linear differential equations, diagonalizing matrices, and other applications, eigenvectors and eigenvalues are used in quantum mechanics and molecular physics, chemistry, geology, and many other scientific disciplines. Some definitions: An eigenvector for…
Partial fractions decomposition is an algebraic technique that can be used to decompose (break down) a product of rational expressions into a sum of simpler rational expressions. A rational expression is one in which both the numerator and denominator are polynomials. A proper rational expression is one in which the degree of the numerator is strictly less than the degree…
My previous Insights article, Solving Homogeneous Linear ODEs using Annihilators, discussed several examples of homogeneous differential equations, equations of the form F(y, y’, y”, …) = 0. In this Insights article we will look at equations of the form F(y, y’, y”, …) = g(t), for certain functions g. Ex. 1: y” – 4y’ + 3y…
In this Insights article we’ll look at a limited class of ordinary differential equations — homogeneous linear ODES with constant coefficients. Although there are many differential equations that are outside the scope of this article, there are many applications in mechanics and electronics of the types of differential equations we’ll be looking at. Homogeneous Equations A…
This Insight article is the continuation of the first article, Simple Python Debugging with Pdb: Part 1. In this article, let’s look at another important capability of debuggers: breakpoints. When you set a breakpoint in a program, the debugger executes all of the code up to the breakpoint, and then halts. This allows you to inspect variables…
I’m pretty new to Python, so I was looking around for some debugging tools. At first, I dismissed Pdb (Python debugger) as being too primitive, but after seeing a blog post about using Pdb, I decided that I should give it a try. To get started with Pdb import the pdb module insert a call…