Python proof of concept for GBD-PCG.

Solves for x in Ax = b, using the Preconditioned Conjugate Gradient algorithm. It requires A to be a positive semi-definite matrix to guarantee good results.

Only python and numpy are required

You can look at test.py for an example:

from PCG import PCG
options = {'preconditioner_type' : 'SS'}
pcg = PCG(A, b, nx, n_blocks, options = options)
x_pcg = pcg.solve()

This provides the following preconditoners

1. Identity: "0"
2. Jacobi (Diagonal): "J"
3. Block Jacobi (Block-diagonal): "BJ"
4. Symmetric Stair: "SS"

While (1) and (2) only require the matrix A, (3) and (4) additional require the block_size (nx) to be passed in.

To cite this work in your research, please use the following bibtex:

@misc{adabag2023mpcgpu,
      title={MPCGPU: Real-Time Nonlinear Model Predictive Control through Preconditioned Conjugate Gradient on the GPU}, 
      author={Emre Adabag and Miloni Atal and William Gerard and Brian Plancher},
      year={2023},
      eprint={2309.08079},
      archivePrefix={arXiv},
      primaryClass={cs.RO}
}