Curve Fitting and Least Squares Approximation

Overview

This project implements various mathematical functions to approximate given data points using the Least Squares Method. The program determines the best-fitting function based on the deviation measure and root mean square deviation.

Features

• Supports multiple function types:
  • Linear function: ( \varphi(x) = ax + b )
  • Quadratic function: ( \varphi(x) = ax^2 + bx + c )
  • Cubic function: ( \varphi(x) = ax^3 + bx^2 + cx + d )
  • Exponential function: ( \varphi(x) = a \cdot b^x )
  • Logarithmic function: ( \varphi(x) = a \cdot \log_b(x) )
  • Power function: ( \varphi(x) = a \cdot x^b )
• Uses the Least Squares Method to determine the optimal coefficients.
• Calculates total deviation and root mean square deviation.
• Reads data from a text file and determines the best-fitting function.
• Plots the original data points and the fitted function graphically.

Installation

Prerequisites

Make sure you have Python 3.x installed along with the required dependencies:

pip install numpy matplotlib

Usage

1. Prepare a data file (data.txt) with values in the format:

   x1,y1
   x2,y2
   ...
   

2. Run the script:

   python main.py

3. The program will output:
   • The best-fitting function.
   • Its coefficients.
   • Deviation measures.
   • A graphical representation of the best function.

Example Output

Наиболее точная функция: Полиномиальная 2-й степени: ϕ(x) = ax² + bx + c
Коэффициенты: [2.5, -1.2, 0.8]
Мера отклонения (S): 0.034

Результаты для всех функций:
...

Graphical Representation

The program generates a plot where:

• Blue dots represent the original data points.
• Red line represents the best-fitting function.

License

This project is open-source and licensed under the MIT License.

Author

Developed by [KatyaZubareva] 🚀