That's what my code does. On Tue, Jun 18, 2019 at 4:27 PM Jeff Newmiller <jdnew...@dcn.davis.ca.us> wrote:
> Assuming Peter's equation applies, I think a direct for loop with > multiplication would be a more efficient way to obtain this answer than > repeated use of a power operator. > > On June 18, 2019 8:01:09 AM CDT, Martin Maechler < > maech...@stat.math.ethz.ch> wrote: > >>>>>> peter dalgaard > >>>>>> on Tue, 18 Jun 2019 11:45:39 +0200 writes: > > > > > Sounds like this is isomorphic to reachability in graph > > > theory. I wonder if > > > > > (sum_1^n M^i) > 0 > > > > > would suffice? > > > >neat! (and I guess correct) > > > > > -pd > > > >Which reminds me that in the relatively distant past as > >maintainer of the 'expm' package I had introduced "%^%" (to > >compute matrix *integer* powers) with this first part of help() : > > > >-------------------------------------------------------------------------- > >Matrix Power > > > >Description: > > > > Compute the k-th power of a matrix. Whereas ‘x^k’ computes > > _element wise_ powers, ‘x %^% k’ corresponds to k - 1 matrix > > multiplications, ‘x %*% x %*% ... %*% x’. > > > >Usage: > > > > x %^% k > > > >Arguments: > > > > x: a square matrix. > > > > k: an integer, k >= 0. > > > >Details: > > > > Argument k is coerced to integer using as.integer. > > > > The algorithm uses O(log2(k)) matrix multiplications. > > > >Value: > > > > A matrix of the same dimension as ‘x’. > > > >Note: > > > > If you think you need ‘x^k’ for k < 0, then consider instead > > ‘solve(x %^% (-k))’. > > > >........ > >........ > > > >-------------------------------------------------------------------------- > > > >and I had thought / wondered to myself if this should not be > >brought into base R [or then at least 'Matrix' which is > >installed with R (almost surely)] but I think never got around > >to propose that. > > > >Opinions? > > > > > > >> 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. > > > >______________________________________________ > >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. > > -- > Sent from my phone. Please excuse my brevity. > > ______________________________________________ > 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. > [[alternative HTML version deleted]] ______________________________________________ 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.
