Question about the difference between the function named '_compute_phi' and '_compute_psi'

Question

Question about the difference between the function named '_compute_phi' and '_compute_psi'

AlbertJNU opened this issue a year ago · comments

Take the _edmd.py in pykoopman.regression as an example. In this file, phi is computed as self._ur.conj().T @ x_col, while psi is computed as self._tmp_compute_psi @ x_col. I can't figure out the true meaning behind the phi and psi, not to mention their difference. Could you please explain it in more detail by Mathematical formula? It would be more appreciated if there are corresponding articles to provide.

Shaowu Pan · Answer 1 · Wed Jul 12 2023 23:58:08 GMT+0800 (China Standard Time)

Take a look at the figure 1 in the paper https://arxiv.org/pdf/2306.12962.pdf You will see psi and phi are different. psi is for Koopman eigenfunctions, and phi are just for observables.

Albert-zhang · Answer 2 · Thu Jul 13 2023 08:47:25 GMT+0800 (China Standard Time)

Thank you for your reply. I have understood!