Linear System Solver

A Python desktop application to solve systems of linear equations using various numerical methods.

Features

• Solve using Gaussian Elimination, Matrix Inversion, Jacobi, and Gauss-Seidel methods.
• Visualize intermediate steps and error convergence with Matplotlib.
• Validate solutions automatically.
• Export results and error plots to CSV or PDF.
• Supports matrix sizes from 2x2 up to 5x5.
• User-friendly Tkinter GUI.
• Step-by-step visualization and error tracking for iterative methods.
• Modular design for easy extension.

Installation

1. Clone or download this repository.
2. Install dependencies:

   pip install -r requirements.txt

Usage

Run the application:

python main.py

How to Use

1. Select Matrix Size: Choose the size (2x2 to 5x5) from the dropdown.
2. Enter Coefficients: Fill in the matrix A and vector b in the input fields.
3. Choose Method: Select a solution method from the dropdown.
4. Solve: Click Solve to compute the solution.
5. Visualize: Click Visualize Steps to see the step-by-step process and error convergence (for iterative methods).
6. Export: Use the export feature to save results as CSV or PDF.
7. Reset: Click Reset to clear all fields and outputs.

Example

Input:

• Matrix Size: 4

• A: [ 10.0, -1.0, 2.0, 0.0], [ -1.0, 11.0, -1.0, 3.0], [ 2.0, -1.0, 10.0, -1.0], [ 0.0, 3.0, -1.0, 8.0]

• b: [6.0, 25.0, -11.0, 15.0]

Output:

Solution x = [ 1.  2. -1.  1.]
Validation: True

Extending

Add new methods under the methods/ folder following the existing interface:

def solve(A, b, **kwargs):
    # Your implementation
    return x, steps  # or x, steps, errors for iterative methods

Dependencies

• numpy
• matplotlib
• fpdf
• imageio
• tkinter (built-in)

Troubleshooting

• If you encounter issues with the GUI, ensure you are running Python 3.x and all dependencies are installed.
• For PDF export, make sure the fpdf package is installed.

License

This project is for educational and research purposes.