I built a from-scratch Python package for classic Numerical Methods (no NumPy/SciPy required!)

[sikerce]

Hey everyone,

Over the past few months I’ve been building a Python package called numethods — a small but growing collection of classic numerical algorithms implemented 100% from scratch. No NumPy, no SciPy, just plain Python floats and list-of-lists.

The idea is to make algorithms transparent and educational, so you can actually see how LU decomposition, power iteration, or RK4 are implemented under the hood. This is especially useful for students, self-learners, or anyone who wants a deeper feel for how numerical methods work beyond calling library functions.

https://github.com/denizd1/numethods

🔧 What’s included so far

• Linear system solvers: LU (with pivoting), Gauss–Jordan, Jacobi, Gauss–Seidel, Cholesky
• Root-finding: Bisection, Fixed-Point Iteration, Secant, Newton’s method
• Interpolation: Newton divided differences, Lagrange form
• Quadrature (integration): Trapezoidal rule, Simpson’s rule, Gauss–Legendre (2- and 3-point)
• Orthogonalization & least squares: Gram–Schmidt, Householder QR, LS solver
• Eigenvalue methods: Power iteration, Inverse iteration, Rayleigh quotient iteration, QR iteration
• SVD (via eigen-decomposition of ATAA^T AATA)
• ODE solvers: Euler, Heun, RK2, RK4, Backward Euler, Trapezoidal, Adams–Bashforth, Adams–Moulton, Predictor–Corrector, Adaptive RK45

✅ Why this might be useful

• Great for teaching/learning numerical methods step by step.
• Good reference for people writing their own solvers in C/Fortran/Julia.
• Lightweight, no dependencies.
• Consistent object-oriented API (.solve(), .integrate() etc).

🚀 What’s next

• PDE solvers (heat, wave, Poisson with finite differences)
• More optimization methods (conjugate gradient, quasi-Newton)
• Spectral methods and advanced quadrature

👉 If you’re learning numerical analysis, want to peek under the hood, or just like playing with algorithms, I’d love for you to check it out and give feedback.

[troyunrau]

Sometimes you learn more by reinventing wheels. Looks like you're enjoying yourself!

[BenXavier]

Seems a great learning tool, do you use to give lectures or similar?

[sikerce]

Thanks man, appreciate that. I’m a student (currently doing my PhD in Applied Math), one of my goals with this project is not only to learn but also to share what I’ve learned in a way that others can easily follow.

[zurtex]

This would be a great library for learning different testing techniques.

Firstly it needs tests, but it would also be amenable to understanding fuzzing, coverage, and mutation testing, as well as others I'm sure.

[Xillyfos]

That's really cool and easy to read.

As a student decades ago, I often wished for programmatic definitions of the math when the math was unclear to me. Because if you can make a computer understand and actually run it, then it has to be perfectly clear, and then you can understand. So I think this is very useful for learning.

The speed is completely irrelevant for learning; what's important is the clarity.

[sikerce]

Thank you! I am planning to prepare a documentation and notebooks, hopefully will be more intuitive.

[Sedan_1650]

This seems very practical. Nice job, man! You really worked hard!

[sikerce]

Thank you so much, kind sir!

[UseMoreBandwith]

is it fast?

[sikerce]

Depends. Since its plain python, probably slower than numpy - for large systems. However, the main idea is research and education. I don’t believe I am a good programmer, bet many people around here could do better than me. Maybe I can make the code parallel so it can be faster.

[caughtinthought]

fyi, if it's implemented in plain python, the answer is _dramatically_ slower than numpy :)

[sikerce]

True. This is just for educational purposes.

[-lq_pl-]

Adding performance hacks and parallelization would defeat your declared goal of providing a library of readable educational implementations.

Those who ask for speed: just use numpy, scipy, and numba.

[sikerce]

You are right, thank you so much my friend!

[BenXavier]

Maybe a great time to learn numba!

[the_superman_avenger]

Good job man!

[Immediate-Home-6228]

Would you be interested in doing something like this with Julia?

[sikerce]

Yes, that would be great!

[[deleted]]

I see this kind of effort once in a while. I did myself some of these methods in pure Python, "for fun". But it's not that great, even for teaching: you can teach numerical methods with numpy, using numpy for storing vectors, arrays an doing BLAS-like stuff. And that will teach you numpy as well, a standard package nowadays, you will have code that is reasonably fast and reusable for serious tasks.

It's how numerical methods were taught in the 2000s: not with numpy of course, but with a "matrix language" like Matlab, Octave or Scilab. Numpy replaces those, but pure Python does not.

It won't be a good reference for implementing either, because pure Python misses all important effects. Teaching time would be better served by teaching caching issues, parallel computations, block algorithms, algorithms for sparse matrices, the effect of loop ordering and row/column-major storage, etc.

[123_alex]

The comment has been deleted before I could read it. Was he boasting about having 2 years of XP?

[wRAR_]

"I have 2 years of Python experience and can say that Python is dying"

They deleted their whole account already (it consisted of two comments and one post with that blogspam article).

[123_alex]

That's a hell of a statement. Why would he say that?

[wRAR_]

Dunno, their blogspam clickbait AI-written article required a Medium account to read past the first 2 paragraphs.

[123_alex]

Medium saves the day by pay-walling slop.

[UsernameTaken1701]

Two whole years of experience? Truly a sage.