https://github.com/abdelrhman-ellithy/nm-algorithms
https://github.com/abdelrhman-ellithy/nm-algorithms
Last synced: 2 months ago
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- Host: GitHub
- URL: https://github.com/abdelrhman-ellithy/nm-algorithms
- Owner: Abdelrhman-Ellithy
- License: cc0-1.0
- Created: 2025-02-03T17:01:45.000Z (8 months ago)
- Default Branch: main
- Last Pushed: 2025-06-27T21:22:29.000Z (3 months ago)
- Last Synced: 2025-06-27T22:31:21.723Z (3 months ago)
- Language: TeX
- Size: 12.8 MB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Four New Hybrid Root Bracketing Algorithms: Optimization-Based Approaches for Numerical Root Finding 🚀
## Project Overview
This project presents four novel hybrid root bracketing algorithms that combine the reliability of traditional bracketing methods with the speed of optimization-based techniques. The algorithms are implemented in Python, evaluated on a diverse set of test functions, and analyzed for convergence and computational efficiency. The results are compiled and discussed in an academic LaTeX paper.
👨💻 **Authors:** Abdelrahman Ellithy.
---
## 📁 Repository Structure
- **Python Scripts**: Each algorithm is implemented in its own script (e.g., `06-Optimized-Bisection-FalsePosition.py`, `07-Optimized-Bisection-FalsePosition-Modified-Secant.py`, etc.).
- **Results Files**:
- `Results.db`: SQLite database containing raw results from algorithm runs.
- `Results.xlsx`, `CPU_Times_Per_Algorithm.xlsx`, `Results_tableII.csv`: Processed results and summary tables.
- Plots: PNG files visualizing CPU time and performance (e.g., `avg_cpu_time_per_algorithm.png`, `cpu_time_lineplot_per_problem.png`, etc.).
- **Paper**:
- `hybrid_root_bracketing_paper.tex`: Main LaTeX source for the research paper.
- `hybrid_root_bracketing_paper.pdf`: The only PDF tracked in version control (all other LaTeX build files are ignored).
- `Sample Latex Paper Format file.tex`: Example format for reference.
- **Reference Papers**: PDF files in the `Refrence Papers/` directory (ignored in version control).
- **Analysis Script**: `analyze_results.py` for processing results and generating plots.
- **References**: `refrences.txt` contains a comprehensive list of related works.
- **CI/CD**: `.github/workflows/benchmark.yml` automates benchmarking on push to `main`.
---
## 🧮 About the Algorithms
This project introduces and compares four new hybrid root bracketing algorithms:
- **Optimized Bisection-False Position (Optimized_BF):**
- Combines the reliability of bisection with the speed of the false position method.
- Alternates between bisection and false position steps to quickly reduce the interval containing the root.
- **Optimized Bisection-False Position with Modified Secant (Optimized_BFMS):**
- Extends Optimized_BF by adding a modified secant step for even faster convergence.
- Uses a small perturbation to approximate the derivative and refine the root estimate.
- **Optimized Trisection-False Position (Optimized_TF):**
- Uses trisection (splitting the interval into three) instead of bisection for potentially faster convergence.
- Integrates the false position method for acceleration.
- **Optimized Trisection-False Position with Modified Secant (Optimized_TFMS):**
- Combines trisection, false position, and modified secant steps for maximum efficiency.
- Offers the fastest convergence in most test cases.
All algorithms are designed to guarantee convergence (if the initial interval brackets a root) and are implemented using the SymPy library for high-precision computation.
---
## ▶️ How to Run the Algorithms
1. Ensure you have Python 3.11+ and the required packages:
```bash
pip install sympy numpy pandas matplotlib seaborn
```
2. Run each algorithm script (e.g., `python 06-Optimized-Bisection-FalsePosition.py`). Results will be stored in `Results.db`.
3. To run all algorithms and regenerate results, you can use the provided scripts in sequence or adapt the CI workflow steps.
---
## 📊 Analyzing Results and Generating Plots
- Run `python analyze_results.py` to:
- Summarize CPU time and iteration statistics
- Generate plots (saved as PNG files)
- Output summary tables for inclusion in the paper
---
## 📄 Compiling the LaTeX Paper
1. Make sure you have a LaTeX distribution (e.g., TeX Live, MiKTeX).
2. Compile `hybrid_root_bracketing_paper.tex` using your preferred LaTeX editor or:
```bash
pdflatex hybrid_root_bracketing_paper.tex
bibtex hybrid_root_bracketing_paper
pdflatex hybrid_root_bracketing_paper.tex
pdflatex hybrid_root_bracketing_paper.tex
```
3. The resulting PDF will include all tables, plots, and references.
---
## 🔒 Version Control and .gitignore Policy
- All LaTeX build files (including PDFs) are ignored except for `hybrid_root_bracketing_paper.pdf`, which is tracked for reference.
- Reference papers and sample build artifacts are also ignored to keep the repository clean and focused.
---
## 🛡️ License
- See `LICENSE` for details.