QR and Kaczmarz Algorithm Visualization

This project provides a Python-based graphical user interface (GUI) to visualize and compare numerical methods for solving systems of equations and matrix decompositions. The focus is on:

• QR Algorithm Visualization

• Least Squares Problem Solution

• Comparison of the Kaczmarz Algorithm with QR and Least Squares

The application is built using PyQt5, along with NumPy, joblib, matplotlib and timeit for backend computations.

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Features

1. QR Algorithm Visualizer

• Watch the QR decomposition process step by step.
• Input a matrix and observe the progression of the algorithm.

2. Kaczmarz vs Other Algorithms

• Compare the efficiency and performance of the Kaczmarz Algorithm with:
  • QR decomposition
  • Least squares solutions

3. Least Squares Solution

• Input a matrix to compute and view the least squares solution directly.
• Visual and numerical output to better understand the results.

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Installation and Setup

To run this project, ensure you have the following modules installed:

• PyQt5: For building the graphical user interface.
• NumPy: For numerical computations.
• Joblib: For efficient saving and loading of data.
• timeit: For performance benchmarking.
• Matplotlib: For creating visual representations of algorithm performance

Steps to Set Up

1. Clone this repository to your local machine:

   git clone git@github.com:a-bratosin/Least-squares-tool.git   # Via ssh
   cd Least-squares-tool

2. Create a virtual environment (optional but recommended)

   python -m venv env
   source env/bin/activate  # On Windows: env\Scripts\activate

3. Install dependencies

   pip install PyQt5 numpy joblib timeit matplotlib

4. Run the program

   python menu.py

Usage

Main Menu

The main program is menu.py, which launches the GUI. The interface provides three main functionalities accessible via buttons:

1. QR Algorithm Visualizer

   • Input a matrix and visualize the step-by-step QR decomposition process.

2. Kaczmarz vs Other Algorithms

   • Compare the efficiency of the Kaczmarz Algorithm against QR decomposition and Least Squares solutions.

3. Least Squares Solution

   • Enter a matrix to compute and view the least squares solution.

Input

• Matrices are entered through the graphical user interface (GUI).
• Ensure the input follows the correct format (e.g., numeric matrices).

Each feature provides an intuitive interface to help users understand and compare the algorithms effectively.