Fixed singular matrix #6
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… or when the problem is not well posed
duembgen
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duembgen
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Thank you for the edits! I just have one question regarding the rank check.
| Hs = [cones.unvec_symm(h, self.n_vars) for h in hs] | ||
| #check compilation warnings | ||
| for i, H in enumerate(Hs): | ||
| H_rank = np.linalg.matrix_rank(Hs, tol=1e-10) |
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I would replace matrix_rank and eigvalsh with one single call to eigvalsh and then checking the number of eigenvalues <= 1e-10. Just to be sure -- is it really necessary to do this check every time? Would it be possible to do it only if necessary (as in the cases below, in a caught exception?)
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Sorry for the late reply, I’ll address each point.
I agree with your suggested modification of using eigvalsh instead of matrix_rank.
As shown in Lemma 5 of the paper, corank(H) = 1 is a sufficient condition for SOSC, which is one of the key assumptions of the main theorem. My intention was to check whether this condition fails before hitting the assertion errors, mainly for diagnostic purposes. If preferred, this check can be moved behind assertion errors or removed entirely.
Regarding all the edits in sdprlayer.py file: they are not required to solve the singular Jacobian issue itself. However, during some runs I sporadically encountered assertion errors, so I added a try–except block to help identify their causes. I’m happy to remove all these changes if you think they’re unnecessary.
- created a function to make them publicly available
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missing flag in calling the SDPRLayer with the list of redundant constraints