https://github.com/louis-finegan/langrange-interpolation-c-programming-language-gnuplot

Calculate Langrange-Interpolations in the C programming language and visualise them in gnuplot.
https://github.com/louis-finegan/langrange-interpolation-c-programming-language-gnuplot

c-programming-language csv-parser gnu-linux gnuplot lagrange-interpolation lagrange-polynomial-interpolation makefile mathematics numerical-methods shellscript ubuntu

Last synced: about 10 hours ago
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Calculate Langrange-Interpolations in the C programming language and visualise them in gnuplot.

• Host: GitHub
• URL: https://github.com/louis-finegan/langrange-interpolation-c-programming-language-gnuplot
• Owner: Louis-Finegan
• License: mit
• Created: 2024-05-17T18:53:05.000Z (4 months ago)
• Default Branch: main
• Last Pushed: 2024-05-20T19:05:07.000Z (4 months ago)
• Last Synced: 2024-09-24T21:17:35.462Z (about 15 hours ago)
• Topics: c-programming-language, csv-parser, gnu-linux, gnuplot, lagrange-interpolation, lagrange-polynomial-interpolation, makefile, mathematics, numerical-methods, shellscript, ubuntu
• Language: C
• Homepage:
• Size: 18.6 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Lagrange Interpolation

Written in Ubuntu 23.04 LTS. This progam was written for GNU/Linux systems.

## Visualize lagrange polynomials with GNU plot

Implements Langrange-Interpolation in the `C programming language`. Creates complete polynomials from Node Value pairs in csv files, and creates 2 dimensional plots, using `gnuplot`, which are saved as png files.   

## Dependences

1. gcc

2. gnuplot

## Formulation

Lagrange interpolation is a mathematical method that finds new points $(x,y)$ in between known discrete points $(x_k, y_k)$ for $k \in \mathbb{Z}$. These new points are calculated using a polynomial $P_n(x)$ called the *Lagrange Polynomial*. The maximum value for $k$ is $n$, which is the degree of $P_n(x)$. 

The *Lagrange Polynomial* is written in the following form:

$$P_n(x) = y_0L_0(x) + y_1L_1(x) + \dots + y_nL_n(x)$$

Where $L_k(x)$ is called the *Lagrange Basis*, and is written as such

$$L_i(x) = \frac{x - x_0}{x_i - x_0} \dots \frac{x - x_{i-1}}{x_i - x_{i-1}}\frac{x - x_{i+1}}{x_i - x_{i+1}} \dots \frac{x - x_n}{x_i - x_n} $$

For $n$ known points, or node, value pairs, the lagrange basis would be composed of $n$ basis vectors (Lagrange Basis).

## Example

 

This example takes critical points from a **sine wave**. Using Lagrange Interpolation, an approximation of the complete wave can be constucted.

The data in `data/sine.csv` is format as the following





    

        

            Nodes

            Values

        

    

    

        

            0

            0

        

        

            1.5707

            1

        

        

            3.1416

            0

        

        

            4.7124

            -1

        

        

            6.2832

            0

        

    


The program can be executed by the following

```

./run.sh [csv_file]

```

For this example `csv_file` would be `sine.csv`. If the program ran successfully the following message would appear:

```

Data read successfully

Nodes:  Values:

0.00    0.00

1.57    1.00

3.14    0.00

4.71    -1.00

6.28    0.00

Initializing Lagrange Interpolation

Creating plot

Plot saved as 'img/sine.png'

```

And the following image is saved to `img` as a `png` file type.



  



## License

MIT License - see LICENSE for details.