🧮 NumPHP: Numerical Analysis Toolkit

A high-visibility, step-by-step numerical methods engine built entirely in pure PHP.
Designed to make complex mathematical iterations transparent and easy to visualize.

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🚀 The Backstory

Born during a deep dive into Numerical Analysis in my 3rd university semester, NumPHP was an experiment in defying the status quo. While Python and MATLAB are the standards, I wanted to prove that PHP—the language of the web—could handle complex mathematical iterations just as elegantly.

This toolkit doesn't just give you the answer; it shows you the journey of the algorithm, making it an ideal companion for students and educators.

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✨ Features

• 🔍 Granular Iterations: See every step of the calculation, from initial guess to final convergence.
• 🌐 100% Web-Native: No external compilers or Python environments needed. Just a browser and a PHP server.
• 🛠️ Framework-less: Light, fast, and dependency-free.
• 📊 Comprehensive Toolkit: Includes methods for Root Finding, Linear Systems, and Numerical Integration.
• 🎨 Responsive UI: Clean interface built with modern CSS and vanilla JS for real-time interaction.

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🧪 Mathematical Methods

NumPHP covers the "Big Three" areas of numerical analysis:

Category	Method	Description
Root Finding	Bisection	Bracketing method based on the Intermediate Value Theorem.
	Newton-Raphson	High-speed convergence using derivatives.
	Secant	Root finding without requiring derivative functions.
	False Position	Linear interpolation to find roots.
	Fixed-Point	Iterative process finding $x$ where $f(x) = x$.
Linear Systems	Jacobi	Iterative algorithm for determining the solutions of a system of linear equations.
Integration	Trapezoidal	Approximating the definite integral by using trapezoids.
	Simpson's Rule	High-accuracy integration using parabolic arcs.

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🧬 How the Engine Works

graph TD
    A[User Input] --> B(Method Selector)
    B --> C{Calculation Engine}
    C -->|Loop| D[Apply Formula]
    D --> E[Calculate Error]
    E -->|Tolerance Not Met| D
    E -->|Tolerance Met| F[Final Result]
    D --> G[Record Iteration Data]
    G --> H[Render Results Table]
    F --> H
    
    style C fill:#f9f,stroke:#333,stroke-width:2px
    style H fill:#bbf,stroke:#333,stroke-width:2px

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🛠️ Getting Started

Installation

Since NumPHP is built with pure PHP, you only need a local server (like XAMPP or Nginx) to run it.

1. Clone the Repository:

   git clone https://github.com/rezasadid753/numphp.git
   cd numphp

2. Run: Move the folder to your web directory (htdocs or www) and access it via: http://localhost/numphp

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📁 Directory Structure

NumPHP/
├── 📄 index.php                   # Entry point & Method Switcher
├── 📂 methods/                    # Mathematical Logic
│   ├── method-bisection.php
│   ├── method-jacobi.php
│   ├── method-newton-raphson.php
│   └── ... (and others)
├── 🎨 numerical-analysis.css      # Core Styles
└── ⚡ numerical-analysis.js       # UI Interactivity & Validation

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🎯 Ideal Use Cases

• University Students: Check your manual homework calculations against the step-by-step output.
• CS Educators: Use as a visual demo during lectures to show how different methods converge at different rates.
• Curious Devs: Learn how to implement mathematical formulas in a high-level language like PHP.

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🤝 Contributing

Mathematical accuracy is the priority! If you find a bug in a formula or want to add a new method (like Gauss-Seidel or Runge-Kutta), feel free to:

1. Fork the project.
2. Submit a Pull Request.

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📜 License

This project is open-source under the MIT License.

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Built for the love of math and the power of PHP. 📐