Numerical Software Development

Copyright 2019, Yung-Yu Chen [email protected]. All rights reserved.

Objectives: This course discusses the art to build numerical software, i.e., computer programs applying numerical methods for solving mathematical or physical problems. We will be using the combination of Python and C++ and related tools (e.g., bash, git, make, etc.) to learn the modern development processes. By completing this course, students will acquire the fundamental skills for developing modern numerical software.

Prerequisites: This is a graduate or senior level course open to students who have taken engineering mathematics or equivalence. Working knowledge of Linux and Unix-like is required. Prior knowledge to numerical methods is recommended. The instructor uses English in the lectures and discussions.

How to study

• This is a practical course. No textbook is available for this specific interdisciplinary subject.
• To study the subject, students are required to research with online documents and source code, and write programs to practice.
• In-class instruction and course notes are provided for guidance.
• References:
  • Computer Systems: A Programmer's Perspective, Randal E. Bryant and David R. O'Hallaron: https://csapp.cs.cmu.edu/
  • Python documentation: https://docs.python.org/3/
  • Cppreference: https://en.cppreference.com/
  • Effective Modern C++, Scott Meyer, O'Reilly, 2014
  • Source code: cpython, numpy, xtensor, and pybind11

Course design

• There are 15 or more lectures for the subjects of numerical software developing using Python and C++.
• There is usually homework given after a lecture to exercise the lectured materials, and it usually requires students to write computer programs in Python and/or C++.
• Mid-term examination will be conducted to assess students' understandings to the analytical materials.
• Term project will be used to assess students' overall coding skills. Presentation is required. Failure to present results in 0 point for this part.
• Grading: homework 30%, mid-term exam: 30%, term project: 40%.
• Lectures:
  1. Python and numpy
  2. C++ and computer architecture
  3. Fundamental engineering practices
  4. Memory management
  5. Matrix operations
  6. Cache optimization
  7. SIMD
  8. Modern C++ I: ownership and meta-programming
  9. Modern C++ II: more than templates
  10. xtensor: arrays in C++
  11. pybind11: binding between Python and C++
  12. cpython API: operate Python from C
  13. Profiling
  14. Array-oriented design
  15. Advanced Python
  16. (Optional) useful architectures for hybrid code
  17. (Optional) application embedding Python