Initial commit

LICENSE

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+MIT License
+
+Copyright (c) 2021 Jonas Nicodemus
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

README.md

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+<!-- PROJECT SHIELDS -->
+<!-- [![arXiv][arxiv-shield]][arxiv-url] -->
+<!-- [![DOI][doi-shield]][doi-url] -->
+<!-- [![MIT License][license-shield]][license-url] -->
+<!-- [![LinkedIn][linkedin-shield]][linkedin-url] -->
+
+# Port-Hamiltonian Dynamic Mode Decomposition
+
+We present a novel physics-informed system identification method to construct a passive linear time-invariant system. In more detail, for a given quadratic energy functional, measurements of the input, state, and output of a system in the time domain, we find a realization that approximates the data well while guaranteeing that the energy functional satisfies a dissipation inequality. To this end, we use the framework of port-Hamiltonian (pH) systems and modify the dynamic mode decomposition to be feasible for continuous-time pH systems. We propose an iterative numerical method to solve the corresponding least-squares minimization problem. We construct an effective initialization of the algorithm by studying the least-squares problem in a weighted norm, for which we present the analytical minimum-norm solution. The efficiency of the proposed method is demonstrated with several numerical examples.
+
+<!-- TABLE OF CONTENTS -->
+<details open="open">
+  <summary><h2 style="display: inline-block">Table of Contents</h2></summary>
+  <ol>
+    <li>
+      <a href="#citing">Citing</a>
+    </li>
+    <li>
+      <a href="#installation">Installation</a>
+    </li>
+    <li><a href="#usage">Usage</a></li>
+    <li><a href="#license">License</a></li>
+    <li><a href="#contact">Contact</a></li>
+  </ol>
+</details>
+
+<!-- ## Citing
+If you use this project for academic work, please consider citing our
+[publication][arxiv-url]:
+
+    R. Morandin, J. Nicodemus, and B. Unger
+    Port-Hamiltonian Dynamic Mode Decomposition
+    ArXiv e-print TODO, 2022. -->
+
+## Installation
+A python environment is required with at least **Python 3.10**.
+
+Install dependencies via `pip`:
+   ```sh
+   pip install -r requirements.txt
+   ```
+
+<!-- USAGE EXAMPLES -->
+## Usage
+
+The executable script `main.py` executes the `pHDMD` algorithm for the current configuration, defined in `config.py`. Both files are located in `src`.
+
+<!-- USAGE EXAMPLES -->
+## Documentation
+
+Documentation is available [online][docs-url]
+or you can build it yourself from inside the `docs` directory
+by executing:
+
+    make html
+
+This will generate HTML documentation in `docs/build/html`.
+It is required to have the `sphinx` dependencies installed. This can be done by
+
+    pip install -r requirements.txt
+
+within the `docs` directory.
+
+
+<!-- LICENSE -->
+## License
+
+Distributed under the MIT License. See `LICENSE` for more information.
+
+<!-- CONTACT -->
+## Contact
+Jonas Nicodemus - [email protected]
+
+Benjamin Unger - [email protected]\
+Riccardo Morandin - [email protected] 
+
+Project Link: [https://github.com/Jonas-Nicodemus/phdmd][project-url]
+
+[license-shield]: https://img.shields.io/github/license/Jonas-Nicodemus/phdmd.svg?style=for-the-badge
+[license-url]: https://github.com/Jonas-Nicodemus/phdmd/blob/main/LICENSE
+[linkedin-shield]: https://img.shields.io/badge/-LinkedIn-black.svg?style=for-the-badge&logo=linkedin&colorB=555
+[linkedin-url]: https://linkedin.com/in/jonas-nicodemus-a34931209/
+[doi-shield]: https://img.shields.io/badge/DOI-10.5281%20%2F%20zenodo.5520662-blue.svg?style=for-the-badge
+[doi-url]: https://zenodo.org/badge/latestdoi/409099116
+[arxiv-shield]: https://img.shields.io/badge/arXiv-2109.10793-b31b1b.svg?style=for-the-badge
+[arxiv-url]: https://arxiv.org/abs/2109.10793
+[project-url]:https://github.com/Jonas-Nicodemus/phdmd
+[docs-url]:https://jonas-nicodemus.github.io/phdmd/

docs/Makefile

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+# Minimal makefile for Sphinx documentation
+#
+
+# You can set these variables from the command line, and also
+# from the environment for the first two.
+SPHINXOPTS    ?=
+SPHINXBUILD   ?= sphinx-build
+SOURCEDIR     = source
+BUILDDIR      = build
+
+# Put it first so that "make" without argument is like "make help".
+help:
+	@$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
+
+.PHONY: help Makefile
+
+# Catch-all target: route all unknown targets to Sphinx using the new
+# "make mode" option.  $(O) is meant as a shortcut for $(SPHINXOPTS).
+%: Makefile
+	@$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)

docs/make.bat

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+@ECHO OFF
+
+pushd %~dp0
+
+REM Command file for Sphinx documentation
+
+if "%SPHINXBUILD%" == "" (
+	set SPHINXBUILD=sphinx-build
+)
+set SOURCEDIR=source
+set BUILDDIR=build
+
+%SPHINXBUILD% >NUL 2>NUL
+if errorlevel 9009 (
+	echo.
+	echo.The 'sphinx-build' command was not found. Make sure you have Sphinx
+	echo.installed, then set the SPHINXBUILD environment variable to point
+	echo.to the full path of the 'sphinx-build' executable. Alternatively you
+	echo.may add the Sphinx directory to PATH.
+	echo.
+	echo.If you don't have Sphinx installed, grab it from
+	echo.https://www.sphinx-doc.org/
+	exit /b 1
+)
+
+if "%1" == "" goto help
+
+%SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O%
+goto end
+
+:help
+%SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O%
+
+:end
+popd

docs/requirements.txt

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+Sphinx>=4.5.0
+sphinx-rtd-theme>=1.0.0
+sphinxcontrib-bibtex>=2.4.2
+sphinxcontrib-katex>=0.8.6

docs/source/algorithm.rst

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+algorithm package
+=================
+
+Submodules
+----------
+
+algorithm.phdmd module
+----------------------
+
+.. automodule:: algorithm.phdmd
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+algorithm.skew\_procrustes module
+---------------------------------
+
+.. automodule:: algorithm.skew_procrustes
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+algorithm.spsd\_procrustes module
+---------------------------------
+
+.. automodule:: algorithm.spsd_procrustes
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+Module contents
+---------------
+
+.. automodule:: algorithm
+   :members:
+   :undoc-members:
+   :show-inheritance:

docs/source/bibliography.rst

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+************
+Bibliography
+************
+
+..
+   see https://sphinxcontrib-bibtex.readthedocs.io/en/latest/usage.html for options
+
+.. bibliography::

docs/source/conf.py

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+# Configuration file for the Sphinx documentation builder.
+#
+# This file only contains a selection of the most common options. For a full
+# list see the documentation:
+# https://www.sphinx-doc.org/en/master/usage/configuration.html
+
+# -- Path setup --------------------------------------------------------------
+
+# If extensions (or modules to document with autodoc) are in another directory,
+# add these directories to sys.path here. If the directory is relative to the
+# documentation root, use os.path.abspath to make it absolute, like shown here.
+#
+import os
+import sys
+sys.path.insert(0, os.path.abspath('../../src'))
+
+
+# -- Project information -----------------------------------------------------
+
+project = 'pHDMD'
+copyright = '2022, Jonas Nicodemus'
+author = 'Jonas Nicodemus'
+
+# The full version, including alpha/beta/rc tags
+release = '1.0.0'
+
+
+# -- General configuration ---------------------------------------------------
+
+# Add any Sphinx extension module names here, as strings. They can be
+# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
+# ones.
+extensions = ['sphinx.ext.autodoc',
+              'sphinx.ext.napoleon',
+              'sphinxcontrib.katex',
+              'sphinxcontrib.bibtex',
+]
+
+import sphinxcontrib.katex as katex
+
+latex_macros = r"""
+    \def \i                {\mathrm{i}}
+    \def \e              #1{\mathrm{e}^{#1}}
+    \def \vec            #1{\mathbf{#1}}
+    \def \x                {\vec{x}}
+    \def \d                {\operatorname{d}\!}
+    \def \dirac          #1{\operatorname{\delta}\left(#1\right)}
+    \def \scalarprod   #1#2{\left\langle#1,#2\right\rangle}
+    \def \timeStep          {\delta_t}
+    \def \nrSnapshots       {M}
+    \def \nrSnapshotsGen    {\tilde{\nrSnapshots}}
+    \def \state             {x}
+    \def \stateVar          {\state}
+    \def \stateDim          {n}
+    \def \stateDimRed       {r}
+    \def \inpVar            {u}
+    \def \inputVar          {\inpVar}
+    \def \inpVarDim         {m}
+    \def \inputDim          {\inpVarDim}
+    \def \outVar            {y}
+    \def \outputVar         {\outVar}
+    \def \dmdV              {X_+}
+    \def \dmdW              {X_{-}}
+    \def \dmdY              {Y}
+    \def \dmdU              {U}
+    \def \dataZ             {\mathcal{Z}}
+    \def \dataT             {\mathcal{T}}
+    \def \dmdJJ             {\widetilde{\mathcal{J}}}
+    \def \dmdRR             {\widetilde{\mathcal{R}}}
+"""
+
+# Translate LaTeX macros to KaTeX and add to options for HTML builder
+katex_macros = katex.latex_defs_to_katex_macros(latex_macros)
+katex_options = 'macros: {' + katex_macros + '}'
+
+# Add LaTeX macros for LATEX builder
+latex_elements = {'preamble': latex_macros}
+
+bibtex_bibfiles = ['refs.bib']
+
+# Add any paths that contain templates here, relative to this directory.
+templates_path = ['_templates']
+
+# List of patterns, relative to source directory, that match files and
+# directories to ignore when looking for source files.
+# This pattern also affects html_static_path and html_extra_path.
+exclude_patterns = []
+
+
+# -- Options for HTML output -------------------------------------------------
+
+# The theme to use for HTML and HTML Help pages.  See the documentation for
+# a list of builtin themes.
+#
+html_theme = 'sphinx_rtd_theme'
+
+# # Material theme options (see theme.conf for more information)
+# html_theme_options = {
+#
+#     # Set the name of the project to appear in the navigation.
+#     'nav_title': 'pHDMD',
+#
+#     # Set you GA account ID to enable tracking
+#     'google_analytics_account': 'UA-XXXXX',
+#
+#     # Specify a base_url used to generate sitemap.xml. If not
+#     # specified, then no sitemap will be built.
+#     'base_url': 'https://project.github.io/project',
+#
+#     # Set the color and the accent color
+#     'color_primary': 'blue',
+#     'color_accent': 'light-blue',
+#
+#     # Set the repo location to get a badge with stats
+#     # TODO: change when release
+#     'repo_url': 'https://github.com/Jonas-Nicodemus/crispy-pancake',
+#     'repo_name': 'crispy-pancake',
+#
+#     # Visible levels of the global TOC; -1 means unlimited
+#     'globaltoc_depth': 3,
+#     # If False, expand all TOC entries
+#     'globaltoc_collapse': False,
+#     # If True, show hidden TOC entries
+#     'globaltoc_includehidden': False,
+# }
+
+# Add any paths that contain custom static files (such as style sheets) here,
+# relative to this directory. They are copied after the builtin static files,
+# so a file named "default.css" will overwrite the builtin "default.css".
+html_static_path = ['_static']

docs/source/contact.rst

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+Contact
+=======
+
+Jonas Nicodemus - [email protected]
+
+Benjamin Unger - [email protected]
+
+Riccardo Morandin - [email protected]
+
+Project link: https://github.com/Jonas-Nicodemus/phdmd