YAPSS: Yet Another Pseudo-Spectral Solver

YAPSS is a Python library for formulating and solving optimal-control problems with pseudospectral methods.

YAPSS provides:

• Legendre-Gauss, Legendre-Gauss-Radau, and Legendre-Gauss-Lobatto collocation methods, using a computational approach based on the GPOPS-II algorithm of Patterson and Rao (2014)
• Multiple differentiation approaches: automatic differentiation via CasADi, user-supplied derivatives, and central-difference numerical differentiation for problems not amenable to automatic differentiation
• Multi-phase problems and segmented meshes
• An interface designed to identify common formulation errors early
• Worked examples as both Python scripts and Jupyter notebooks

Start here

1. Install YAPSS.
2. Work through the tutorial to define and solve a first problem.
3. Browse the examples for complete applications.

Installation

YAPSS requires Python 3.10 or later. Install it into a virtual environment with pip:

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

Alternatively, install it with Conda:

$ conda create -n yapss-env python=3.10
$ conda activate yapss-env
(yapss-env) $ conda install -c conda-forge yapss

Verify the Installation

Run the HS071 example, a small constrained optimization problem:

(yapss-env) $ python -m yapss.examples.hs071

YAPSS is installed correctly if the run finishes, and the output ends with

Objective value
f(x*) = 1.701402e+01

YAPSS solution is correct.

The value of the final digits of the objective may vary between platforms and solver versions.

Where to go next

• New to YAPSS? Start with the tutorial.
• Looking for a pattern to adapt? Browse the notebook examples or script examples.
• Need API details? See the reference documentation in the navigation sidebar.
• Want to contribute? Contributions are welcome! Read Contributing to YAPSS.

Citing YAPSS

If you use YAPSS in published work, please cite it, giving the version you used. Each release is archived on Zenodo; the DOI below always resolves to the latest version, and the record for each version has its own DOI.

Hall, S. R. (2026). YAPSS: Yet Another Pseudo-Spectral Solver (Version 0.2.3) [Computer software]. https://doi.org/10.5281/zenodo.22402223

The repository's CITATION.cff carries the same metadata in machine-readable form; GitHub's "Cite this repository" button renders it as BibTeX or APA. The Legendre-Gauss-Radau transcription follows Patterson and Rao (2014), cited at the top of this page, which you may wish to cite as well; the Legendre-Gauss and Legendre-Gauss-Lobatto transcriptions extend their approach.

License

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

Documentation

The documentation is available on Read the Docs.