High Performance Python

Chapter 6. Matrix and Vector Computation

Questions You’ll Be Able to Answer After This Chapter

• What are the bottlenecks in vector calculations?
• What tools can I use to see how efficiently the CPU is doing my calculations?
• Why is numpy better at numerical calculations than pure Python?
• What are cache-misses and page-faults?
• How can I track the memory allocations in my code?

Regardless of what problem you are trying to solve on a computer, you will encounter vector computation at some point. Vector calculations are integral to how a computer works and how it tries to speed up runtimes of programs down at the silicon level—the only thing the computer knows how to do is operate on numbers, and knowing how to do several of those calculations at once will speed up your program.

In this chapter, we try to unwrap some of the complexities of this problem by focusing on a relatively simple mathematical problem, solving the diffusion equation, and understanding what is happening at the CPU level. By understanding how different Python code affects the CPU and how to effectively probe these things, we can learn how to understand other problems as well.

We will start by introducing the problem and coming up with a quick solution using pure Python. After identifying some memory issues and trying to fix them using pure Python, we will introduce numpy and identify how and why it speeds up our code. Then we will start doing some algorithmic changes and specialize our code to solve the problem at ...