[spenczar5]

Are these algorithms efficient even given GPUs? I have the vague impression that GPUs are well-tuned for matrix work. Are those advantages lost when using Geometric Algebra formulations, so you actually dont come out ahead?

This is uninformed speculation, go ahead and correct me!

[hamish_todd]

It's an extremely common misconception that because GPUs have matrix matrix and matrix vector products in the standard, that means GPU companies must be accelerating them.

In fact, because it is SIMD across the shader cores already, you can't necessarily do this. Some GPUs do, some don't

[rhelz]

When you are programming, you have to figure out:

1. What quantity you want to calculate, and 2. What the most efficient way to calculate it is.

PGA (once you spend the--alas--not insubstantial overhead to understand it!) is a really good way of doing #1. Its virtually always a good idea to first try out the simplest and easiest to code up implementation anyways.

And what you get from using PGA to do #1 will certainly be good enough for you to prototype out the rest of your program enough to be able to benchmark it and find out where the real bottlenecks are. Happily, in most cases it will also either be the fastest way to calculate it, or close enough to not be the bottleneck.

And if is a bottleneck, it gives you a deep understanding of the problem you are trying to solve--which, IMHO, is a good idea to have before you just start trying to shave off cycles in hopes of getting it fast enough.

[buildartefact]

This is exactly what the article is about. TLDR they can be roughly equivalent