Numerical Algorithms Library

Overview

This library provides a comprehensive collection of digital signal processing (DSP), control algorithms, filters, optimizers, and estimators designed for robust and efficient signal analysis, manipulation, and system control. Developed to address complex technical challenges, the library offers a flexible and extensible framework for engineers, researchers, and developers working in signal processing, control systems, and related domains.

Getting Started

Refer to the documentation to quickly integrate and utilize the library's signal processing and control algorithms in your projects.

Documentation

Category	Description
Analysis	FFT, Power Spectral Density, DCT, Window Functions
Control Analysis	Frequency Response, Root Locus
Controllers	PID, LQR, MPC
Dynamics	Euler-Lagrange, Newton-Euler, Recursive Newton-Euler, ABA
Estimators	Linear Regression, Yule-Walker (offline), Recursive Least Squares (online)
Filters	Kalman, Extended Kalman, Unscented Kalman, FIR, IIR
Kinematics	Forward Kinematics
Neural Network	Layers, activations, losses, model
Optimization	Gradient Descent
Regularization	L1 (Lasso), L2 (Ridge)
Solvers	Gaussian Elimination, Levinson-Durbin, Durand-Kerner, Cholesky, DARE
Performance Optimization	Compiler optimizations, SIMD

Each category page lists its algorithms with a brief description and links to the detailed documentation.

Simulator

The simulator/ directory contains interactive Qt-based GUI applications for visualizing and experimenting with the library's algorithms. These are desktop tools intended for development and exploration, separate from the core embedded-targeted library.

Building the Simulator

The simulator requires Qt6 and is disabled by default. Enable it with:

cmake --preset host  # host preset enables it automatically
# or manually:
cmake -DNUMERICAL_TOOLBOX_BUILD_SIMULATOR=ON ...

Prerequisites: qt6-base-dev and libgl1-mesa-dev (Ubuntu/Debian).

How to Run the Simulator

The simulator includes a Qt-based GUI for real-time visualization. Since the development environment runs inside a Dev Container, an X server on the host machine is required to display the GUI.

Host Setup

Windows

1. Install VcXsrv (free) or X410 from the Microsoft Store.
2. Launch VcXsrv with the following settings:
   • Multiple windows
   • Start no client
   • Disable access control (checked)
3. Open the project in VS Code and reopen in the Dev Container.

Linux

1. Allow Docker containers to access your X server:

xhost +local:docker

2. Open the project in VS Code and reopen in the Dev Container.

Note: The Dev Container sets DISPLAY=host.docker.internal:0.0 to forward GUI windows over TCP. On Linux, if you prefer Unix socket forwarding, you can override DISPLAY to :0 inside the container and add a bind mount for /tmp/.X11-unix.

Contributing

Contributions, issues, and feature requests are welcome. Please check the contributing guidelines before submitting pull requests.

License

[Specify your license here - e.g., MIT, Apache 2.0]