beluga

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PyPI

Examples

Features

• High quality resolution of singular arcs.
• Phaseless construction.
• Discontinuous function modeling.
• Hamiltonian “indirect” methods and definition of co-states.
• Automated Noether’s theorem and symplectic reduction.
• Hermite-Simpson Collocation and Multiple Shooting methods.
• Automated scaling.
• Lots of examples and open-source.

Installation

Installation using pip

If you already have Python 3+ installed along with pip, then do:

$ pip install beluga

This installs the latest version-controlled distribution of beluga from PyPI. Examples in this GitHub repo are updated frequently to reflect changes in beluga and as such may not be compatible with the versions on PyPI. Source code is included with each release, so check under releases on GitHub for examples compatible with older versions of beluga. Old examples are also included in the tarballs on PyPI and GitHub under releases, but are not included in the wheels.

Installation using binaries

Binary files are located on PyPI and GitHub under releases.

GitHub Version

See contributing for more information on installing the latest version from GitHub, reporting issues, and other information on development.

Running a test problem

Open a terminal window and navigate to the folder where you installed beluga. Type the following commands to run the Brachistochrone problem:

$ cd examples/Classic/Brachistochrone
$ python Brachistochrone.py

The solver will proceed to solve the Brachistochrone problem.

Contents

• Optimal Control
  • Setting up a Problem
• beluga Examples
  • Base Class Reference
• Coding new features
• Running unit tests
• beluga Base Reference
  • Introduction
  • Base Class Reference
• BVP Solver Module
  • Introduction
  • Shooting Methods
  • Collocation Methods
  • Base Class Reference
• Codegen Module
  • Introduction
  • Base Class Reference
• Continuation Module
  • Introduction
  • Base Class Reference
• IVP Solver Module
  • Introduction
  • Integration Programs
  • Base Class Reference
• Indirect Optimization Library Module
  • Introduction
  • Indirect and Diffy G
  • Direct
  • Base Class Reference

Indices and tables

• Index
• Module Index
• Search Page

License

Copyright 2020 National Technology & Engineering Solutions of Sandia, LLC (NTESS). Under the terms of Contract DE-NA0003525 with NTESS, the U.S. Government retains certain rights in this software.

MIT License

Copyright (c) 2015-2020 Rapid Design of Systems Laboratory

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.