Would it make sense to implement a "generic pivot" method, which takes as an argument a function that does the pivot selection (that would then be handled separately over RR/CC vs p-adics)?
Kiran On Wednesday, January 31, 2018 at 2:16:42 AM UTC-8, Nils Bruin wrote: > > I found this over CC and RR as well: the generic matrix inversion in sage > (which is probably what is getting invoked) looks like it's based on > straight-up row reduction: No pivoting (which it wouldn't know how to do in > the generic case). For CC and RR there's PLU decomposition in mpmath which > does use partial pivoting. It would be nice to have "natively" in sage and > would be easy to program and would be nice to have for non-square matrices. > The code is easily adapted (see > https://git.sagemath.org/sage.git/commit?id=f2ccf44acc673458aba3cf92d7692c7a92a505b6 > > for a POC). > > Partial pivoting for p-adic PLU decomposition would be straightforward to > implement as well, and very worthwhile to have. It's well-known that matrix > inversion is tricky business numerically, even for well-conditioned > matrices, but with pivoting one should get reasonable results in a lot more > cases. p-adics might be a little better behaved, but fundamentally the same > numerical considerations play a role. > > On Tuesday, January 30, 2018 at 3:50:45 PM UTC, Simon Brandhorst wrote: >> >> The following may be a bug or me not understanding p-adic floating point >> computations: >> >> >> sage: R = Qp(2,type='floating-point',print_mode='terse') >> sage: M = Matrix(R,4,[0, 0, 1, 1, 2^20, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1]) >> sage: M.det() >> 1048575 >> sage: M.inverse() >> >> --------------------------------------------------------------------------- >> ZeroDivisionError Traceback (most recent call >> last) >> .... >> >> ZeroDivisionError: input matrix must be nonsingular >> >> sage: M = Matrix(R,4,[0, 0, 1, 1, 2^19, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1]) >> sage: M.inverse() >> [ 1048575 2 0 1] >> [274878955520 524288 1 1048575] >> [ 524289 524287 1 524287] >> [274877382656 524289 1048575 524289] >> >> Works. >> > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
