YAPSS: Yet Another Pseudo-Spectral Solver

YAPSS is a Python package for numerically solving optimal control problems using pseudospectral methods. Features include:

• Computational approach based on the GPOPS-II algorithm of Patterson and Rao (2014)
• Support for multiple differentiation methods: automatic differentiation via the CasADi package, user-defined derivatives, and central difference numerical differentiation for problems not amenable to automatic differentiation.
• Choice of collocation method, including Legendre-Gauss (LG), Legendre-Gauss-Radau (LGR), and Legendre-Gauss-Lobatto (LGL) options.
• Segmented mesh support, enabling mesh refinement in specific regions. (Automatic mesh refinement is not yet available.)
• An API for defining optimal control problems designed to catch common errors and provide helpful messages.
• Documentation covering installation, setup, and example usage.
• Examples available as both Python scripts and Jupyter notebooks.

Quickstart

To get started, install YAPSS and verify the installation using pip:

$ python -m venv yapss-env
$ source yapss-env/bin/activate
(yapss-env) $ pip install yapss
(yapss-env) $ python -m yapss.examples.isoperimetric

If the console output shows a small relative error and a Matplotlib window displays a circle, the installation is successful!

For more detailed installation instructions, see the next section.

Installation

YAPSS supports installation via Conda or pip. It requires Python 3.9 or later..

Option 1: Using Conda

Create and activate a virtual environment, and install YAPSS:

$ conda create -n yapss-env python=3.9
$ conda activate yapss-env
(yapss-env) $ conda install -c conda-forge yapss

If you encounter the following error during installation

PackagesNotFoundError: The following packages are not available from current channels:
  - yapss

then YAPSS is not yet available on conda-forge. In this case, install from source as follows:

(yapss-env) $ conda install -c conda-forge numpy casadi scipy mpmath matplotlib cyipopt -y
(yapss-env) $ pip install git+https://github.com/stevenrhall/[email protected] --no-deps

The --no-deps flag is important — it prevents pip from reinstalling dependencies that Conda has already installed, avoiding conflicts. You can delete the tag @v0.1.0 to install the latest version, or specify a different version tag.

Option 2: Using Pip

Create and activate a virtual environment, then install YAPSS:

$ python -m venv yapss-env
$ source yapss-env/bin/activate
(yapss-env) $ pip install yapss

To install from source:

(yapss-env) $ pip install git+https://github.com/stevenrhall/[email protected]

Verify the Installation

To verify the installation, run the isoperimetric example:

(yapss-env) $ python -m yapss.examples.isoperimetric

The result should be a matplotlib window with a plot of the optimal curve (a circle), and console output that concludes with something similar to

Maximum area = 0.07957747154594766 (Should be 1 / (4 pi) = 0.07957747154594767)
Relative error in solution = 1.743934249004316e-16

If the plot does not display, add %matplotlib inline in a Jupyter notebook or set the backend with matplotlib.use('Agg') for headless environments.

The console output may differ slightly depending on machine precision. Minor deviations in the final digits are normal, and the relative error should be on the order of machine precision. If it is, the installation is correct.

Additional examples are available in

• the examples/notebooks directory
• the src/yapss/examples directory
• the Examples section of the documentation.

License

YAPSS is licensed under the MIT License. See the LICENSE file for more information.

Documentation

The documentation is available on Read the Docs.

Contributing

YAPSS is open source — contributions are not only welcome but encouraged. See CONTRIBUTING.md for details.