> On 19 Oct 2014, at 19:00 , Spencer Graves > <spencer.gra...@structuremonitoring.com> wrote: > > On 10/19/2014 8:42 AM, peter dalgaard wrote: >>> On 19 Oct 2014, at 16:43 , Wagner Bonat <wbo...@gmail.com> wrote: >>> >>> Dear, >>> >>> I have to compute the trace of a product between four matrices. For >>> example, I know the matrices Wi, Wj and C, I need to compute this >>> >>> -trace(Wi%*%C^-1%*%Wj%*%C^-1) >>> >>> >>> I would like to avoid compute the complete matrix and after take the >>> diagonal, something like >>> >>> sum(diag( solve(Wi,C)%*% solve(Wj,C))) >> <this can't be right: it is C that is the invertible matrix> >> >>> Any idea is welcome. >>> >> The usual "trick" is that the trace of a matrix product is the inner product >> in matrix space, which is just the sum of the elementwise products >> >> tr(AB) = tr(BA) = sum_i sum_j a_ij b_ij. >> >> In R, this becomes simply sum(A*B) -- notice that the ordinary product is >> used, not %*%. So presumably, you are looking for >> >> sum(solve(C, Wi) * solve(C, Wj)) > > missing a transpose?
Yep... tr(AB) = tr(BA) = sum_i sum_j a_ij b_ji which is of course sum(A*t(B)) or vice versa. Thanks. -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd....@cbs.dk Priv: pda...@gmail.com ______________________________________________ R-help@r-project.org mailing list 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.
