pydmd 0.1.0

Python Dynamic Mode Decomposition.

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**PyDMD**: Python Dynamic Mode Decomposition

## Table of contents
* [Description](#description)
* [Dependencies and installation](#dependencies-and-installation)
* [Installing via PIP](#installing-via-pip)
* [Installing from source](#installing-from-source)
* [Documentation](#documentation)
* [Testing](#testing)
* [Examples](#examples)
* [How to cite](#how-to-cite)
* [References](#references)
* [Recent works with PyDMD](#recent-works-with-pydmd)
* [Authors and contributors](#authors-and-contributors)
* [How to contribute](#how-to-contribute)
* [Submitting a patch](#submitting-a-patch)
* [License](#license)

## Description
**PyDMD** is a Python package that uses **Dynamic Mode Decomposition** for a data-driven model simplification based on spatiotemporal coherent structures.

See the [**Examples**](#examples) section below and the [**Tutorials**](tutorials/README.md) to have an idea of the potential of this package.


## Dependencies and installation
**PyDMD** requires requires `numpy`, `scipy`, `matplotlib`, `sphinx` (for the documentation). The code is compatible with Python 2.7 and Python 3.6. It can be installed using `pip` or directly from the source code.

### Installing via PIP
Mac and Linux users can install pre-built binary packages using pip.
To install the package just type:
```bash
> pip install pydmd
```
To uninstall the package:
```bash
> pip uninstall pydmd
```

### Installing from source
The official distribution is on GitHub, and you can clone the repository using
```bash
> git clone https://github.com/mathLab/PyDMD
```

To install the package just type:
```bash
> python setup.py install
```

To uninstall the package you have to rerun the installation and record the installed files in order to remove them:

```bash
> python setup.py install --record installed_files.txt
> cat installed_files.txt | xargs rm -rf
```

## Documentation
**PyDMD** uses [Sphinx](http://www.sphinx-doc.org/en/stable/) for code documentation. You can view the documentation online [here](http://mathlab.github.io/PyDMD/). To build the html version of the docs locally simply:

```bash
> cd docs
> make html
```

The generated html can be found in `docs/build/html`. Open up the `index.html` you find there to browse.


## Testing

We are using Travis CI for continuous intergration testing. You can check out the current status [here](https://travis-ci.org/mathLab/PyDMD).

To run tests locally:

```bash
> python test.py
```

## Examples
You can find useful tutorials on how to use the package in the [tutorials](tutorials/README.md) folder.

Here we show a simple application (taken from [tutorial 2](tutorials/tutorial-2-adv-dmd.ipynb)): we collect few snapshots from a toy system with some noise and reconstruct the entire system evolution.
<p align="center">
<img src="readme/dmd-example.png" alt>
<em>The original snapshots used as input for the dynamic mode decomposition</em>
</p>

<p align="center">
<img src="readme/dmd-example.gif" alt></br>
<em>The system evolution reconstructed with dynamic mode decomposition</em>
</p>


## How to cite
If you use this package in your publications please cite the package as follows:

```tex
\bibitem{pydmd}
{PyDMD: Python Dynamic Mode Decomposition. Available at}: \href{https://github.com/mathLab/PyDMD}{https://github.com/mathLab/PyDMD}.
```

### References
To implement the various versions of the DMD algorithm we follow these works:

* Kutz, Brunton, Brunton, Proctor. *Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems*. SIAM Other Titles in Applied Mathematics, 2016. [[DOI](https://doi.org/10.1137/1.9781611974508)].
* Gavish, Donoho. *The optimal hard threshold for singular values is 4/sqrt(3)*. IEEE Transactions on Information Theory, 2014. [[DOI](https://doi.org/10.1109/TIT.2014.2323359)].
* Matsumoto, Indinger. *On-the-fly algorithm for Dynamic Mode Decomposition using Incremental Singular Value Decomposition and Total Least Squares*. 2017. [[arXiv](https://arxiv.org/abs/1703.11004)].
* Hemati, Rowley, Deem, Cattafesta. *De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets*. Theoretical and Computational Fluid Dynamics, 2017. [[DOI](https://doi.org/10.1007/s00162-017-0432-2)].
* Dawson, Hemati, Williams, Rowley. *Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition*. Experiments in Fluids, 2016. [[DOI](https://doi.org/10.1007/s00348-016-2127-7)].
* Kutz, Fu, Brunton. *Multiresolution Dynamic Mode Decomposition*. SIAM Journal on Applied Dynamical Systems, 2016. [[DOI](https://doi.org/10.1137/15M1023543)].
* Erichson, Brunton, Kutz. *Compressed dynamic mode decomposition for background modeling*. Journal of Real-Time Image Processing, 2016. [[DOI](https://doi.org/10.1007/s11554-016-0655-2)].
* Le Clainche, Vega. *Higher Order Dynamic Mode Decomposition*. Journal on Applied Dynamical Systems, 2017. [[DOI](https://doi.org/10.1137/15M1054924)].

### Recent works with PyDMD
Here there is a list of the scientific works involving **PyDMD** you can consult and/or cite. If you want to add one, please open a PR.



## Authors and contributors
**PyDMD** is currently developed and mantained at [SISSA mathLab](http://mathlab.sissa.it/) by
* [Nicola Demo](mailto:[e-mail])
* [Marco Tezzele](mailto:[e-mail])

under the supervision of [Prof. Gianluigi Rozza](mailto:[e-mail]).

Contact us by email for further information or questions about **PyDMD**, or suggest pull requests. Contributions improving either the code or the documentation are welcome!


## How to contribute
We'd love to accept your patches and contributions to this project. There are just a few small guidelines you need to follow.

### Submitting a patch

1. It's generally best to start by opening a new issue describing the bug or
feature you're intending to fix. Even if you think it's relatively minor,
it's helpful to know what people are working on. Mention in the initial
issue that you are planning to work on that bug or feature so that it can
be assigned to you.

2. Follow the normal process of [forking][] the project, and setup a new
branch to work in. It's important that each group of changes be done in
separate branches in order to ensure that a pull request only includes the
commits related to that bug or feature.

3. To ensure properly formatted code, please make sure to use 4
spaces to indent the code. The easy way is to run on your bash the provided
script: ./code_formatter.sh. You should also run [pylint][] over your code.
It's not strictly necessary that your code be completely "lint-free",
but this will help you find common style issues.

4. Any significant changes should almost always be accompanied by tests. The
project already has good test coverage, so look at some of the existing
tests if you're unsure how to go about it. We're using [coveralls][] that
is an invaluable tools for seeing which parts of your code aren't being
exercised by your tests.

5. Do your best to have [well-formed commit messages][] for each change.
This provides consistency throughout the project, and ensures that commit
messages are able to be formatted properly by various git tools.

6. Finally, push the commits to your fork and submit a [pull request][]. Please,
remember to rebase properly in order to maintain a clean, linear git history.

[forking]: https://help.github.com/articles/fork-a-repo
[pylint]: https://www.pylint.org/
[coveralls]: https://coveralls.io
[well-formed commit messages]: http://tbaggery.com/2008/04/19/a-note-about-git-commit-messages.html
[pull request]: https://help.github.com/articles/creating-a-pull-request


## License

See the [LICENSE](LICENSE) file for license rights and limitations (MIT).