https://github.com/leonburghardtdev/gaussianeliminationalgorithm

This program implements the Gaussian Elimination algorithm, a fundamental method in linear algebra for solving systems of linear equations, determining matrix inverses, and calculating determinants.
https://github.com/leonburghardtdev/gaussianeliminationalgorithm

csharp gauss-elimination linear-algebra tu-dortmund wpf

Last synced: 22 days ago
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This program implements the Gaussian Elimination algorithm, a fundamental method in linear algebra for solving systems of linear equations, determining matrix inverses, and calculating determinants.

• Host: GitHub
• URL: https://github.com/leonburghardtdev/gaussianeliminationalgorithm
• Owner: LeonBurghardtDev
• License: apache-2.0
• Created: 2024-12-19T01:59:13.000Z (28 days ago)
• Default Branch: master
• Last Pushed: 2024-12-19T17:15:59.000Z (27 days ago)
• Last Synced: 2024-12-22T08:15:48.348Z (25 days ago)
• Topics: csharp, gauss-elimination, linear-algebra, tu-dortmund, wpf
• Language: C#
• Homepage: https://leon-burghardt.dev
• Size: 43.9 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • Funding: .github/FUNDING.yml
  • License: LICENSE.txt

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README

        
# Gaussian Elimination Algorithm

## Overview

This program implements the **Gaussian Elimination** algorithm, a fundamental method in linear algebra for solving systems of linear equations, determining matrix inverses, and calculating determinants.

The project is inspired by the teachings of **Stefan Harmeling** in the Linear Algebra lecture at TU Dortmund. It translates mathematical concepts into a practical and interactive tool with a graphical user interface (GUI) built in WPF (Windows Presentation Foundation).

## Features

- **Matrix Input:** Allows users to input a matrix and a right-hand side vector via a GUI.

- **Gaussian Elimination:** Automatically performs forward elimination and backward substitution to solve the system of equations.

- **Detailed Logs:** Displays step-by-step logs of the calculations, highlighting pivot operations, row eliminations, and the final solution.

- **Results Display:** Clearly shows the original matrix, the transformed matrix, the right-hand side vector, and the solution in a structured format inspired by LaTeX-style formatting.

- **Error Handling:** Validates user input and provides feedback if the system is unsolvable or invalid data is provided.

## How It Works (Mathematical Explanation)

The program implements the Gaussian Elimination algorithm in two main phases:

### 1. Forward Elimination

- **Goal:** Transform the input matrix into an upper triangular matrix.

- For each pivot column:

  1. Ensure the pivot element is non-zero (row swaps if necessary).

  2. Eliminate all entries below the pivot by subtracting suitable multiples of the pivot row.

### 2. Backward Substitution

- **Goal:** Solve for the unknowns starting from the last row.

- Starting from the last equation, substitute the known values into the equations above to solve for all variables.

**Example:** For the system Ax = b, where:

A = [[2, 1],

     [1, 3]],

b = [8, 13]

The program performs elimination to solve for x.

## How to Use

1. **Input Matrix and Vector:**

   - Enter the matrix and right-hand side vector in the input fields provided in the GUI.

   - Alternatively, use the "Fill with Random Values" button to generate a random solvable system.

2. **Start the Calculation:**

   - Click the "Solve" button to begin the Gaussian Elimination process.

   - The program will validate your input, perform the calculations, and display the results.

3. **Review the Results:**

   - The original matrix, the transformed matrix, the solution vector, and detailed logs are displayed in the result window.

4. **Close the Result Window:**

   - Use the "OK" button to close the result window.

## Known Issues

While the program has been extensively tested, there may still be edge cases or unexpected errors. For example:

- Extremely large matrices or floating-point precision issues might lead to inaccuracies.

- Non-invertible matrices (singular matrices) will cause the program to throw exceptions.

If you encounter any bugs or errors, I would greatly appreciate it if you could report them.

## How to Report Issues

Feel free to reach out to me via my website: [Leon Burghardt](https://leon-burghardt.dev). Your feedback will help improve the tool for everyone!

## License

This program was developed by **Leon Burghardt** in 2024. All rights reserved.

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Thank you for using this program! I hope it serves as a helpful tool for understanding and applying Gaussian Elimination in your studies or work.