Dynamic Mode Decomposition (DMD) Algorithm

A repository containing the implementation of the Dynamic Mode Decomposition (DMD) algorithm in Python.

📁 File Structure

.
├── Giftoframes.py
│   ├── Run this file first to seperate each frame of the gif file
├── DMD - gray.ipynb
│   ├── Performing Dynamic mode decomposition
├── Vortexanimation.gif
│   ├── sample video
└── README.md

Table of Contents

Introduction
Requirements
Usage
Parameters
Output
Examples
Conclusion

Introduction

Dynamic Mode Decomposition (DMD) is a data-driven technique that separates a complex system's dynamic behavior into a set of modes, each of which corresponds to a different underlying physical process. It is a mathematical method that can be applied to a wide range of fields such as fluid dynamics, structural mechanics, and electro-magnetics. Requirements

The following packages must be installed prior to running the code:

OpenCV (for creating the dataset)
Numpy
Matplotlib (for visualization purposes)
Scipy

Usage

To use the DMD algorithm, simply import the DMD function and pass in your data matrix X, time-shifted data matrix Xprime, and the number of modes r as input parameters.

python

from dmd import DMD Phi, Lambda, b = DMD(X, Xprime, r)

Parameters

X: A 2D Numpy array representing the data matrix
Xprime: A 2D Numpy array representing the time-shifted data matrix
r: An integer representing the number of modes desired for the output

Output

The function returns three outputs:

Phi: A 2D Numpy array representing the DMD modes
Lambda: A 2D Numpy array representing the eigenvalues of the system
b: A 1D Numpy array representing the coefficients of the DMD modes

*** Important: Make sure that your data is 2-D

Conclusion

This repository provides a simple and easy-to-use implementation of the Dynamic Mode Decomposition (DMD) algorithm in Python. It is intended for researchers, engineers, and students who are interested in exploring the capabilities of this powerful technique for data analysis and system identification. Dynamic mode decomposition (DMD) is a powerful technique for analyzing and modeling the dynamics of complex systems.