https://github.com/wondermongering/nonlineardatagen
A flexible Python framework for generating, fitting, and visualizing noisy nonlinear data. Perfect for educational purposes, algorithm testing, and demonstrating statistical concepts. Includes tools for various noise models, custom function fitting, robust error metrics, and publication-quality visualizations
https://github.com/wondermongering/nonlineardatagen
curve-fitting data-simulation data-visualization education educational-tool interpolation mathematical-modelling matplotlib noise-modeling numpy regression-analysis scientific-computing scipy signal-processing statistics teaching-resource time-series-analysis
Last synced: 2 months ago
JSON representation
A flexible Python framework for generating, fitting, and visualizing noisy nonlinear data. Perfect for educational purposes, algorithm testing, and demonstrating statistical concepts. Includes tools for various noise models, custom function fitting, robust error metrics, and publication-quality visualizations
- Host: GitHub
- URL: https://github.com/wondermongering/nonlineardatagen
- Owner: Wondermongering
- License: mit
- Created: 2025-02-02T22:06:17.000Z (3 months ago)
- Default Branch: main
- Last Pushed: 2025-03-02T02:55:36.000Z (2 months ago)
- Last Synced: 2025-03-03T03:30:20.627Z (2 months ago)
- Topics: curve-fitting, data-simulation, data-visualization, education, educational-tool, interpolation, mathematical-modelling, matplotlib, noise-modeling, numpy, regression-analysis, scientific-computing, scipy, signal-processing, statistics, teaching-resource, time-series-analysis
- Language: Python
- Homepage:
- Size: 20.5 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE.txt
Awesome Lists containing this project
README
# NonlinearDataGenerator
A flexible Python framework for generating, fitting, and visualizing synthetic nonlinear data with customizable noise profiles.
## 🚀 Overview
The **NonlinearDataGenerator** is an advanced framework for simulating, manipulating, and analyzing nonlinear data patterns. It provides researchers, data scientists, and educators with a comprehensive toolkit for generating synthetic datasets, adding realistic noise profiles, fitting mathematical models, and evaluating results with robust error metrics.
## ✨ Key Features
- **Customizable Function Library**: Generate data from built-in functions (polynomial, exponential, sigmoid, sine) or define your own custom functions.
- **Diverse Noise Models**: Add various types of noise (Gaussian, uniform, proportional, outliers) to simulate real-world data imperfections.
- **Flexible Fitting Options**: Fit data using polynomial regression or custom functions with support for robust fitting methods to handle outliers.
- **Comprehensive Error Metrics**: Evaluate model performance using multiple metrics (MSE, RMSE, MAE, R²) and parameter uncertainty estimates.
- **Publication-Quality Visualization**: Generate professional plots with optional confidence intervals for clear result interpretation.
- **Extensive Documentation**: Detailed docstrings and examples to guide users through all functionality.
## 📊 Example Usage
```python
# Basic usage with default quadratic function
data_gen = NonlinearDataGenerator()
data_gen.add_noise(noise_level=0.2)
data_gen.fit_data()
data_gen.interpolate_results()
data_gen.plot_results()
# Using a custom sine function with outliers
sine_params = {'amplitude': 2, 'frequency': 0.5, 'phase': 1, 'offset': 3}
sine_gen = NonlinearDataGenerator(
true_function=NonlinearDataGenerator.sine_function,
function_params=sine_params
)
sine_gen.add_noise(noise_level=0.3, noise_type='outliers')
sine_gen.fit_data(fit_function=NonlinearDataGenerator.sine_function, robust=True)
sine_gen.interpolate_results()
sine_gen.plot_results(include_confidence=True)
```
## 📋 Applications
- **Research**: Test and benchmark curve-fitting algorithms and noise-reduction techniques
- **Education**: Demonstrate statistical concepts, regression analysis, and uncertainty quantification
- **Data Science**: Generate synthetic datasets for machine learning model validation
- **Signal Processing**: Simulate signal recovery from noisy measurements
- **Time Series Analysis**: Model and forecast data with nonlinear trends
## 📝 Class Structure
```
NonlinearDataGenerator
├── __init__(true_function, function_params, polynomial_order, x_range, num_points)
├── Built-in Functions
│ ├── _default_quadratic(x, a, b, c)
│ ├── exponential_function(x, a, b, c)
│ ├── sigmoid_function(x, a, b, c, d)
│ └── sine_function(x, amplitude, frequency, phase, offset)
├── Data Operations
│ ├── add_noise(noise_level, noise_type, seed)
│ ├── fit_data(fit_function, p0, method, bounds, robust)
│ └── interpolate_results(x_new, num_points)
└── Analysis and Visualization
├── calculate_error()
└── plot_results(include_confidence, confidence_level, figure_size)
```
## 🛠️ Installation
```bash
# Clone the repository
git clone https://github.com/yourusername/NonlinearDataGenerator.git
# Install dependencies
pip install numpy scipy matplotlib
```
## 🧪 Use Cases
1. **Algorithm Development**: Test and optimize curve-fitting algorithms with controlled noise levels
2. **Educational Demonstrations**: Show how different noise patterns affect model fitting
3. **Benchmark Testing**: Compare performance of different fitting methods or libraries
4. **Data Augmentation**: Generate additional training data for machine learning models
5. **Sensitivity Analysis**: Assess how parameter changes affect output with varying noise conditions
## 📚 Contributing
Contributions are welcome! Please feel free to submit a Pull Request.
## 📜 License
This project is licensed under the MIT License - see the LICENSE file for details.