PAR TRANS: Tractable Parallel transport

Par trans showcases a few manifolds with closed-form, computationally efficient parallel transport. The theory is developed in [NgSo24]. Please refer to the github repository for installation instruction.

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Numpy Parallel transport

• par_trans.manifolds
  • Stiefel
    • par_bal()
    • solve_w()
    • Stiefel
  • Flag
    • solve_w()
    • Flag
  • \(\mathrm{GL}^+(n)\)
    • GLpBeta
  • \(\mathrm{SO}(n)\)
    • SOAlpha
• par_trans.expv
  • Expv
    • expm_multiply()
  • Utils
    • asym()
    • cz()
    • hcat()
    • lie()
    • sym()
    • vcat()

JAX Parallel transport

• jax_par_trans.manifolds
  • Stiefel
  • Flag
• jax_par_trans.expv
  • Expv
  • Utils

Indices and tables

• Index

• Module Index

• Search Page

Other Resources:

• Wikipedia
• GitHub

References

[NgSo24]

Nguyen, D.; Sommer, S. (2024). Parallel Transport on Matrix Manifolds and Exponential Action arXiv:2408..06054.