Timeline for Danger of complex arithmetic in scientific computing
Current License: CC BY-SA 4.0
21 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Dec 16, 2021 at 23:11 | history | suggested | Tyberius | CC BY-SA 4.0 |
Code formatting, clarified abbreviation, retag
|
| Dec 16, 2021 at 22:31 | review | Suggested edits | |||
| S Dec 16, 2021 at 23:11 | |||||
| Jul 26, 2017 at 14:06 | comment | added | Vladimir F Героям слава | Good luck with quantum mechanics in real numbers (it is possible). | |
| Jul 26, 2017 at 11:25 | answer | added | H. Rittich | timeline score: 3 | |
| Jun 25, 2015 at 13:08 | comment | added | Federico Poloni | @doetoe My point is that $u^T\bar{v}=\bar{v}^Tu$, so the issue is really only with the order of the arguments. | |
| Jun 25, 2015 at 12:55 | comment | added | doetoe | @FedericoPoloni It depends on your field. In mathematics the standard convention is $u^T\overline v$, while in physics it is $\overline u^Tv$. | |
| May 23, 2015 at 15:22 | comment | added | Federico Poloni | I don't think I have ever seen $u^T\bar{v}$ used in the wild. Sure, when you write a scalar product as $\langle x,y \rangle$ you can choose which argument has to be conjugated, but if one needs to use both notations at the same time the most reasonable thing to do seems swapping the order of the arguments so that the transpose and the conjugate come together. So maybe it is just an issue with the "mathematician's notation" $\langle u,v\rangle$. | |
| May 12, 2015 at 2:49 | comment | added | Jeff Hammond | Please do not interpret flaws in the BLAS interface with mathematical problems. | |
| Mar 23, 2015 at 20:57 | comment | added | Hui Zhang | @FedericoPoloni That is a good point. But that complex numbers occur only in the end as results. Also, the results can again be represented by real and imaginary parts for further applications. | |
| Mar 23, 2015 at 16:49 | answer | added | Julian Cienfuegos | timeline score: -1 | |
| Mar 23, 2015 at 11:57 | comment | added | Federico Poloni | Shall we just always avoid using complex numbers? Please, no. I believe every computational scientist needs unsymmetric eigenvalue decompositions, for instance. | |
| Mar 22, 2015 at 23:07 | comment | added | Wolfgang Bangerth | @hardmath: Sure, but the question was specifically about the statement in deal.II. I don't think that deal.II is internally consistent. | |
| Mar 22, 2015 at 23:06 | comment | added | Wolfgang Bangerth | @BillBarth: At the time the statement was written, we simply did not have any kind of support for complex vectors at all. We do now (on a branch) but I think the situation is the same as before: we're not confident that we current catch all of the places where one has to pay attention to one or the other argument having to be conjugated. | |
| Mar 22, 2015 at 22:54 | comment | added | hardmath♦ | @WolfgangBangerth: I was thinking about a user of libraries (developing software using one or more linear algebra packages) who trusts the third-party software but is aware that these are inconsistent in their treatment of complex inner products. In such a case one might make an effort to maintain compatibility by calling various libraries through "wrappers" that would conjugate or swap arguments as necessary. A fairly small set of test routines would then suffice to maintain consistency as the "outer" software evolves. | |
| Mar 22, 2015 at 14:38 | comment | added | Bill Barth | @WolfgangBangerth, maybe you could explain the deal.ii design decision? | |
| Mar 22, 2015 at 10:56 | comment | added | Wolfgang Bangerth | @hardmath: "small set of test examples" -- in most libraries that comprehensively implement linear algebra operations, there would likely be dozens or hundreds of places where inner products are taken. It would take hundreds of tests to verify their correctness, likely taking months to implement correctly. It's not impossible, of course, and some libraries have done that. It's just a lot of work and not all library authors are confident that they got it right :-( | |
| Mar 22, 2015 at 3:51 | history | tweeted | twitter.com/#!/StackSciComp/status/579490443957821441 | ||
| Mar 21, 2015 at 22:00 | comment | added | Hui Zhang | @hardmath Thank you! I added it in the question. | |
| Mar 21, 2015 at 22:00 | history | edited | Hui Zhang | CC BY-SA 3.0 |
more info
|
| Mar 21, 2015 at 21:36 | comment | added | hardmath♦ | Does anybody really know which root of $-1$ is $i$ and which is $-i$? It would seem that a software developer should include a small set of test examples in their regression suite to guard against incorporating inconsistent conjugations in any lengthy chain of complex arithmetic computations. | |
| Mar 21, 2015 at 20:52 | history | asked | Hui Zhang | CC BY-SA 3.0 |