Integrata

A growing Fortran project demonstrating numerical integration using Simpson’s Rule, with plans to expand into a full suite of numerical methods and scientific computing tools.

Manual build and run instructions included for quick start.

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📂 Project Structure

Integrata/
├── src/
│   ├── simpson.f90         # Simpson’s Rule integration module
│   ├── trapezoidal.f90     # Trapezoidal Rule integration module
│   ├── input_utils.f90     # Input and error handling utilities
│   ├── menu.f90            # Menu and selection utilities
│   └── integrata.f90       # Unified interface module
├── app/
│   └── main.f90            # Main program using the modules
├── test/
│   ├── test_simpson.f90    # Legacy test for Simpson's Rule
│   └── test_integration.f90 # Comprehensive tests for Simpson's & Trapezoidal rules
├── Makefile                # Build and run automation
└── README.md               # This file

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🛠️ Building and Running

Prerequisites

• Fortran compiler: gfortran or any Fortran 2008+ compliant compiler.

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Build and run the main program

make        # builds the main program (main.exe)
make run    # builds and runs the main program

Build and run tests

make test   # builds and runs all tests (Simpson's & Trapezoidal)
make test_simpson      # legacy test for Simpson's Rule only
make test_integration  # comprehensive tests for both rules

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Features

• Modular Fortran codebase: each integration method and utility in its own file
• Supports Simpson’s Rule and Trapezoidal Rule
• Choose between sin(x) and cos(x) as test functions
• Robust, user-friendly input validation (including support for 'pi')
• Easy build and run with Makefile

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🧮 About Simpson’s and Trapezoidal Rule Integration

Simpson’s Rule and the Trapezoidal Rule are classic methods for approximating definite integrals. This project demonstrates both, with a modular, extensible Fortran codebase.

Simpson’s Rule:

∫ₐᵇ f(x) dx ≈ (h/3) [f(a) + 4 Σ_odd f(xᵢ) + 2 Σ_even f(xᵢ) + f(b)] where h = (b - a) / n, n even.

Trapezoidal Rule:

∫ₐᵇ f(x) dx ≈ h/2 [f(a) + 2 Σ f(xᵢ) + f(b)] where h = (b - a) / n, n ≥ 1.

Visualization of intervals:

a  x1  x2  x3  x4  ...  xn-1  b
|---|---|---|---|-------|---|
	 ^   ^   ^           ^   
 odd even odd         odd

⚠️ Notes

• The number of subintervals n must be even for Simpson’s Rule.
• The program will stop with a clear error if invalid input is provided.

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🧩 Future plans for Integrata

Feature	Status	Notes
Add other numerical methods	In progress	Trapezoidal, Romberg, etc.
Support adaptive integration	Planned	Dynamic subinterval sizing
GUI frontend	Idea	Simple Qt or web UI
FPM package support	In progress	For easy building & testing

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📖 Documentation

Code Structure

• src/simpson.f90: Simpson’s Rule implementation (module)
• src/trapezoidal.f90: Trapezoidal Rule implementation (module)
• src/input_utils.f90: Input parsing, validation, and error handling utilities
• src/menu.f90: Menu and selection utilities for user interaction
• src/integrata.f90: Unified interface module, re-exports all integration methods
• app/main.f90: Main program, orchestrates user input, method selection, and output
• test/test_simpson.f90: Legacy test for Simpson’s Rule
• test/test_integration.f90: Comprehensive tests for Simpson’s & Trapezoidal rules

Usage

Run make to build, make run to build and run, and make test to run tests. The program will prompt for:

• Lower and upper bounds (accepts numbers or 'pi')
• Number of intervals (n)
• Function to integrate (sin(x) or cos(x))
• Integration method (Simpson’s or Trapezoidal)

Extending Integrata

• To add a new integration method, create a new module in src/ and add it to integrata.f90.
• To add more test functions, define them in main.f90 and update the menu logic.
• For more advanced input or CLI features, extend input_utils.f90 and menu.f90.

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🤝 Contributing

Contributions welcome! Feel free to open issues or pull requests.

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