Sounds like this is isomorphic to reachability in graph theory. I wonder if
(sum_1^n M^i) > 0 would suffice? -pd > On 18 Jun 2019, at 02:08 , Duncan Murdoch <murdoch.dun...@gmail.com> wrote: > > On 17/06/2019 7:34 p.m., Bert Gunter wrote: >> Depends on what you mean by "simple" of course, but suppose that: >> M[i,j] & M[j,k] & M[k,n] are TRUE and M[i,k] and M[i,n] are FALSE. >> Then the procedure would see that M[i,k] needs to change to TRUE, but not >> that M[i,n] needs to also become TRUE *after* M[i,k] changes. This seems to >> imply that an iterative solution is necessary. > > Right, that's a good point. > > Duncan Murdoch > >> One such procedure, via repeated matrix multiplication to check for and >> impose transitivity, appears to be suggested by this discussion: >> https://math.stackexchange.com/questions/228898/how-to-check-whether-a-relation-is-transitive-from-the-matrix-representation >> Cheers, >> Bert >> On Mon, Jun 17, 2019 at 10:29 AM Duncan Murdoch <murdoch.dun...@gmail.com >> <mailto:murdoch.dun...@gmail.com>> wrote: >> On 17/06/2019 1:19 p.m., Duncan Murdoch wrote: >> > Suppose I have a square logical matrix M which I'm thinking of as a >> > relation between the row/column numbers. >> > >> > I can make it into a symmetric relation (i.e. M[i,j] being TRUE >> implies >> > M[j,i] is TRUE) by the calculation >> > >> > M <- M | t(M) >> > >> > Is there a simple way to ensure transitivity, i.e. M[i,j] & >> M[j,k] both >> > being TRUE implies M[i,k] is TRUE? >> > >> > The operation should only change FALSE or NA values to TRUE >> values; TRUE >> > values should never be changed. >> I also want the changes to be minimal; changing everything to TRUE >> would >> satisfy transitivity, but isn't useful to me. >> Duncan Murdoch >> ______________________________________________ >> R-help@r-project.org <mailto:R-help@r-project.org> mailing list -- >> To UNSUBSCRIBE and more, see >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide >> http://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. >> > > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Office: A 4.23 Email: pd....@cbs.dk Priv: pda...@gmail.com ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
